2.44 ( 1) *diff d fM*

#

*z*

diameter [m]; *ddiff* = diffraction limited minimum object diameter [m];

10.6px/mm, the field-of-view is about 95mm wide by 95mm high.

**2.2.5 Phase-and-precession-direction-resolved PIV** 

= particle image diameter [m] and *dp* = particle diameter [m].

used [m], (532nm for frequency doubled Nd:YAG);

where,

lens aberrations:

is presented in Fig. 4b.

**2.2.5.1 Overall system timing** 

where, *d*

*o o*

*a*

2 2 ( 1) *diff*

*fd M M*

*M* = magnification factor, *zo* = distance between image plane and lens [m]; *Zo* = distance between object plane and lens [m]; *f#* = f-stop; *f* = focal length of lens [m]; *Da* = aperture

To estimate the particle image diameter, the following equation is used neglecting effects of

 <sup>2</sup> <sup>2</sup> *<sup>p</sup> diff d Md d*

The depth-of-field was calculated for each experimental setup, assuming a mean particle diameter of about 1m, *f#* = 5.6, laser wavelength of 532nm, and a nominal image pixel size of 9m. In general, the depth-of-field exceeds 5.75mm for a magnification (px/mm) of 15. Since all the experiments have light sheet thicknesses of less than 3mm and a magnification of not more than 15px/mm, the depth-of-field used is appropriate and all the particles moving into or out of the light sheet were thus in focus. For a typical magnification of

Various methods of triggering a data collection system based on external reference conditions have been used by researchers to study time-dependent flows. As noted above, it is necessary to develop a data-collection system that resolves both precession direction and phase. This is achieved with a triggering system using a pair of hot-wire probes to detect the phase and direction of precession. The components to be synchronised are the PIV lasers, the camera system and the triggering system. A block diagram showing the interaction between each system is presented in Fig. 4a while the timing diagram for the trigger system

An ATMEL microprocessor interfaced the laser and camera system with the external hotwire sensor-trigger system. An important criterion for stable and reliable operation of the

*<sup>Z</sup>* (2-1)

*<sup>f</sup> <sup>f</sup> D* (2-2)

(2-4)

*<sup>z</sup>*= depth-of-field [m].

(2-5)

= wavelength of light

(2-3)

where, *ffl\_nom*=Nominal flashlamp frequency [Hz]; *ffl\_min*=Minimum flashlamp frequency [Hz]; *ffl\_max*=Maximum flashlamp frequency [Hz]; *fl\_nom*=Nominal flashlamp time interval [sec]; *fl\_min*=Minimum flashlamp time interval [sec], and *fl\_max*=Maximum flashlamp time interval [sec].

The next step is to choose an appropriate time window that selects a particular band of precession frequency. In the present case, the precession frequency is nominally 5Hz and a frequency range between 3 and 6Hz was chosen. The 3 and 6Hz cut-off frequency range was chosen to match the –3dB frequency interval for a 5Hz precession frequency.

If the frequency range were to be shifted to a higher precession frequency envelope, i.e., from 3 and 6Hz to 4 and 7Hz, fluid structures having a higher precession frequency will be recorded. Although slightly different sizes of structures may be observed, the overall flow topology of the higher precession frequency flow is not expected to be markedly different from the lower frequency flow topology. Data collection time may be increased for the 4 to

PIV as a Complement to LDA in the Study of an Unsteady Oscillating Turbulent Flow 241

laser trigger and a camera signal are sent simultaneously. If there is no match, the laser trigger will still send a signal to the lasers 100ms after the last known laser trigger, and PIV laser pulses are still produced without the activation of the PIV camera. This was required to

The microcontroller employed for this work was an Atmel A90S2313-10PC integrated circuit with a clock frequency of 10MHz. Thus the time resolution for this system can be as small as 0.1s for each clock cycle. Programming the trigger acceptance window was carried out by transferring the microcontroller to an STK500 programmer's board and downloading the

Adjustable Schmitt triggers were used to convert the hot-wire signals to TTL-compatible phase pulses with minimal phase lag. Also to minimise the phase lag in the triggering time, short wire-runs were made between the trigger system and the microprocessor. The Schmitt trigger is made from a CMOS 4050 buffer (Lancaster, 1997) with two triggering voltage levels, an upper trigger level (UTL) and a lower trigger level (LTL). Whenever a signal voltage level rises above the upper trigger voltage level, the Schmitt trigger immediately outputs a step change to a high voltage value (+V). If the signal voltage level falls over time, but remains above the lower trigger voltage level, the output continues to remain high. However, when the signal level decreases below the lower trigger voltage level, a step change from high to low (~0V) signal is output from the CMOS 4050 buffer. The region between the trigger levels is known as a "dead band" in which the Schmitt trigger ignores

The width of the "dead band" is adjusted with the use of various resistance values (Lancaster, 1997). The use of such a trigger is advantageous to the phase detection of the precessing jet flow because it is possible to trigger the flow on the rising edge of the unfiltered hot-wire signal just before the centre of the jet sweeps past. By using a low-pass filter with a phase lag equal to the time from the trigger to the peak signal region of the jet, it was possible to capture an image of the peak flow coinciding with the physical location of

A limitation in the use of the Schmitt trigger is its inability to adjust to variable signal voltage levels. This introduces a "phase jitter band" which varies with fluctuating signal amplitudes. This is estimated to be about ±7 for a repeatable flow (such as a mechanical precessing jet flow) and ±30 for the present FPJ flow. Furthermore, to obtain a small phase jitter band, the upper trigger level had to be set high, so that only a limited large amplitude flow precession would activate the trigger system. This increases the experimental time considerably by reducing the sampling rate (to approximately 1 image for every 300 flow

A simple check was made to verify the direction selectivity of the sensor system with a mechanically precessing jet (MPJ) (Schneider *et al.*, 1997a and 1997b). For brevity, details of the experiment are not shown here; see Wong (2004) for further details. However, the

maintain stability in the laser system.

instruction set to the microcontroller's non-volatile memory.

**2.2.5.4 Verifying the operation of the direction sensors** 

**2.2.5.2 Atmel microcontroller** 

**2.2.5.3 Trigger system** 

any other voltage signals.

the lag hot-wire probe.

cycles).

7Hz range since the probability of detecting an event decreases as the range is shifted from the –3dB range (located between 3 and 6Hz). This argument similarly applies if the frequency range was shifted to a lower one, such as a range between 2 and 5Hz.

Legend:

UTL: Upper trigger level

LTL: Lower trigger level

Assume *s1* and *s3* are not within the *valid separation time* between Schmitt triggers and *s2* is within the valid separation time between Schmitt triggers

Fig. 4.b. General timing diagram for the phase and precession-direction-resolved PIV experiment.

The main parameters that determined the time window calculations are: linear (or circumferential) separation distance between the two hot-wire probes, radial distance from the hot-wire probe sensing element to the geometric centre of the FPJ, and a frequency bandwidth that characterises the precessing jet (in this case between 3 and 6Hz). The filtering criteria accompanying these parameters are: the jet does not 'flip' across the exit face of the nozzle during one cycle of jet precession, rather the jet takes a circular path about the axis of the chamber, the output from the two-probe arrangement is adjusted to give similar voltage responses to similar velocity fluctuations, and the probes are separated sufficiently to not to interfere with each other.

Following the selection of the frequency bandwidth, a time window for valid inter-trigger times can be set in the microprocessor. The inter-trigger time was the time between triggers that was accepted by the microprocessor as a valid coincidence window for which another comparison can be made with the arrival of a valid laser-trigger. When a valid signal trigger time is sensed after the lag hot-wire probe, an internal comparison is made immediately by the microprocessor to see if a valid laser trigger window has arrived. If there is a match, a laser trigger and a camera signal are sent simultaneously. If there is no match, the laser trigger will still send a signal to the lasers 100ms after the last known laser trigger, and PIV laser pulses are still produced without the activation of the PIV camera. This was required to maintain stability in the laser system.

### **2.2.5.2 Atmel microcontroller**

240 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

7Hz range since the probability of detecting an event decreases as the range is shifted from the –3dB range (located between 3 and 6Hz). This argument similarly applies if the

*s3* are not within the *valid separation time* between Schmitt triggers and

*s2*

*fl-s*

*fl\_nom* *s3*

*fl\_nom*

The main parameters that determined the time window calculations are: linear (or circumferential) separation distance between the two hot-wire probes, radial distance from the hot-wire probe sensing element to the geometric centre of the FPJ, and a frequency bandwidth that characterises the precessing jet (in this case between 3 and 6Hz). The filtering criteria accompanying these parameters are: the jet does not 'flip' across the exit face of the nozzle during one cycle of jet precession, rather the jet takes a circular path about the axis of the chamber, the output from the two-probe arrangement is adjusted to give similar voltage responses to similar velocity fluctuations, and the probes are separated

Following the selection of the frequency bandwidth, a time window for valid inter-trigger times can be set in the microprocessor. The inter-trigger time was the time between triggers that was accepted by the microprocessor as a valid coincidence window for which another comparison can be made with the arrival of a valid laser-trigger. When a valid signal trigger time is sensed after the lag hot-wire probe, an internal comparison is made immediately by the microprocessor to see if a valid laser trigger window has arrived. If there is a match, a

Fig. 4.b. General timing diagram for the phase and precession-direction-resolved PIV

UTL LTL

LTL UTL

*s2* is within the

frequency range was shifted to a lower one, such as a range between 2 and 5Hz.

Legend:

Assume *s1* and 

experiment.

UTL: Upper trigger level LTL: Lower trigger level

Camera output pulse

Lead hot-wire

Lag hot-wire

Lead filtered hot-wire

Lag filtered hot-wire

Lead Schmitt trigger

Lag Schmitt trigger

PIV Laser pulse (to DG-535)

valid separation time between Schmitt triggers

*s1*

> *fl\_nom*

sufficiently to not to interfere with each other.

The microcontroller employed for this work was an Atmel A90S2313-10PC integrated circuit with a clock frequency of 10MHz. Thus the time resolution for this system can be as small as 0.1s for each clock cycle. Programming the trigger acceptance window was carried out by transferring the microcontroller to an STK500 programmer's board and downloading the instruction set to the microcontroller's non-volatile memory.

### **2.2.5.3 Trigger system**

Adjustable Schmitt triggers were used to convert the hot-wire signals to TTL-compatible phase pulses with minimal phase lag. Also to minimise the phase lag in the triggering time, short wire-runs were made between the trigger system and the microprocessor. The Schmitt trigger is made from a CMOS 4050 buffer (Lancaster, 1997) with two triggering voltage levels, an upper trigger level (UTL) and a lower trigger level (LTL). Whenever a signal voltage level rises above the upper trigger voltage level, the Schmitt trigger immediately outputs a step change to a high voltage value (+V). If the signal voltage level falls over time, but remains above the lower trigger voltage level, the output continues to remain high. However, when the signal level decreases below the lower trigger voltage level, a step change from high to low (~0V) signal is output from the CMOS 4050 buffer. The region between the trigger levels is known as a "dead band" in which the Schmitt trigger ignores any other voltage signals.

The width of the "dead band" is adjusted with the use of various resistance values (Lancaster, 1997). The use of such a trigger is advantageous to the phase detection of the precessing jet flow because it is possible to trigger the flow on the rising edge of the unfiltered hot-wire signal just before the centre of the jet sweeps past. By using a low-pass filter with a phase lag equal to the time from the trigger to the peak signal region of the jet, it was possible to capture an image of the peak flow coinciding with the physical location of the lag hot-wire probe.

A limitation in the use of the Schmitt trigger is its inability to adjust to variable signal voltage levels. This introduces a "phase jitter band" which varies with fluctuating signal amplitudes. This is estimated to be about ±7 for a repeatable flow (such as a mechanical precessing jet flow) and ±30 for the present FPJ flow. Furthermore, to obtain a small phase jitter band, the upper trigger level had to be set high, so that only a limited large amplitude flow precession would activate the trigger system. This increases the experimental time considerably by reducing the sampling rate (to approximately 1 image for every 300 flow cycles).

### **2.2.5.4 Verifying the operation of the direction sensors**

A simple check was made to verify the direction selectivity of the sensor system with a mechanically precessing jet (MPJ) (Schneider *et al.*, 1997a and 1997b). For brevity, details of the experiment are not shown here; see Wong (2004) for further details. However, the

PIV as a Complement to LDA in the Study of an Unsteady Oscillating Turbulent Flow 243

shown as contours. The difference between each contour level is 0.2. The location of the light sheet was fixed at *x'/D2*=0.05. For each experiment, the hot-wire parameters were re-

The criterion for the best location was chosen by a combination of visual inspection of each successive image pair to decide on the location that results in the least spatial jitter and also by ensemble-averaging the results. In Fig. 6, the locations for *x'/D2*=0.12, 0.25 and 0.75 appear to produce similar results in the total magnitude of in-plane velocities. Locating the probe at *x'/D2*=0.50 appears to average data over two precession directions, as shown by the larger 'footprint' at the 0.2(*v*2+*w*2)1/2 contour. This location coincides with the zone of flow convergence (location of time-averaged, but not instantaneous, flow convergence downstream from the exit plane). Thus, any probe location which senses the magnitude of fluctuating velocities of the emerging precessing jet, other than at a location near to the zone of flow convergence, is a valid choice for the present experiment. The probes were finally located at *x'/D2*=0.12 and *r/D2*=0.61. This location, which is also approximately 130 to 150 from the peak in-plane velocity magnitude, resulted in the least influence of the probe and probe holder on the overall flow and was not in the plane of the light-sheet. Experiments conducted in the x'-r plane of the local jet centreline show that the instantaneous jet

Nathan & Kelso, 2008). Based on the 0.5(*u*2+*v*2)1/2max contours, the range of emergence angles was estimated to be approximately ±15 about the local jet centreline. This range of angles is two times the value of the minimum phase resolution (±30) in the azimuthal direction

The separation distance between the probes also plays a key role in determining the success of the technique. The lag hot-wire probe was positioned at a radial distance of approximately *r/D2*=0.61 and a downstream location of *x'/D2*=0.12, as determined from Section 2.2.5.5. To solve for an appropriate probe separation distance, *sc*, the following empirical criteria should be satisfied: the highest precession frequency of interest (i.e. 6Hz) should be at least 100 times lower than the smallest clock cycle of the Atmel controller, and the circumferential distance, *sc*, travelled by the precessing flow at a fixed radius, *rs*, from the nozzle axis should not be more than 10% of the circumference (*sf*) described by the radius *rs.*

We can derive the time it takes for the flow to travel between the lead and the lag hot-wire probe (i.e. the separation time, *Tsep*) given the precession frequency of interest (i.e. 3 or 6 Hz),

> 2 *<sup>c</sup> sep*

Where, *sc* = probe separation distance [m], *rs* = radial distance between the lag hot-wire

To calculate the separation time between the lead and lag hot-wire probe for the ATMEL

*<sup>s</sup> <sup>T</sup>* 

probe and the nozzle axis [m], and *fp* = precession frequency of interest [Hz].

controller time, we use the following conversion formula:

*s p*

*r f* (2-6)

=53) is relatively constant within *x'*=40mm (or *x'/D2*=0.625) (Wong,

adjusted to suit the new flow conditions for each hot-wire probe location.

emergence angle (

That is, *sc* < 0.1 *sf*.

from the following equation:

(*y-z* plane) (Wong, Nathan & Kelso, 2008).

**2.2.5.6 Selecting the separation distance of the probes** 

physical rotation of the MPJ nozzle allows confirmation that the lead hot-wire probe is always exposed to the advancing jet before the lag hot-wire probe. This was found to result in a constant stream of camera signals being sent to the PIV system for data collection, as shown in Fig. 5. To confirm the directional selectivity of the system, the rotation direction of the MPJ was then reversed. This resulted in no triggering of the camera, demonstrating that the system is effective at discriminating precession direction. These experiments also showed that the mean phase lag between the lag hot-wire and the core of the jet is approximately 23.8 with an error band (or jitter) of ±7 as shown in Fig. 5. This phase jitter is caused by several factors, namely, the 3Hz frequency window chosen, the varying exit angle of the jet, and the selection of the UTL of the Schmitt trigger (that relates to the selection of higher magnitudes of velocities before the data collection system is allowed to trigger).

Fig. 5. Verifying the selectivity and phase of the direction sensors with a mechanical precessing jet (*de*=3mm) exiting at =45 from the spinning axis rotation in a clockwise fashion at *fp*=9Hz. The nozzle is centred at *y*=0 mm and *z*=0 mm. **a)** Phase-lag () of the jet relative to the lag hot-wire probe, where *jitter* refers to phase-jitter in the measurements; **b)** Pseudo-streamlines are shown with velocity vectors while coloured contours represent inplane velocity magnitudes (*v*2+*w*2)1/2 normalised by (*v*2+*w*2)1/2*max*=18m/s. Measurements are for a light sheet at *x'/de* =11.3 and probe at *x'/de* =6.7 (and *r/de*=11) for an ensemble of 50 image pairs.

#### **2.2.5.5 Optimising the location of the trigger probes in the FPJ flow**

To measure the FPJ flow reliably, a suitable location is needed for the hot-wire probes. Nathan (1988) demonstrated that the introduction of a foreign object (such as a long rod) within the FPJ nozzle cavity will unnecessarily perturb the precessing flow mechanism. In order to avoid this, the probes were positioned outside, but as close as practical to the exit plane of the nozzle to reduce jitter, minimize the interference of the probes and probe holder, and maximize the signal strength of the flow. The lag hot-wire probe was positioned parallel to the nozzle axis with its centre at *r/D2*=0.61 in the *y-z* plane for a total of 4 downstream locations, namely *x'/D2*=0.12, 0.25, 0.50 and 0.75. An ensemble average of 50 image pairs are presented in Fig. 6, in which the phase-averaged velocities (*v*2+*w*2)1/2 are non-dimensionalised by the maximum in-plane velocity for each measurement plane and

physical rotation of the MPJ nozzle allows confirmation that the lead hot-wire probe is always exposed to the advancing jet before the lag hot-wire probe. This was found to result in a constant stream of camera signals being sent to the PIV system for data collection, as shown in Fig. 5. To confirm the directional selectivity of the system, the rotation direction of the MPJ was then reversed. This resulted in no triggering of the camera, demonstrating that the system is effective at discriminating precession direction. These experiments also showed that the mean phase lag between the lag hot-wire and the core of the jet is approximately 23.8 with an error band (or jitter) of ±7 as shown in Fig. 5. This phase jitter is caused by several factors, namely, the 3Hz frequency window chosen, the varying exit angle of the jet, and the selection of the UTL of the Schmitt trigger (that relates to the selection of higher magnitudes of


Fig. 5. Verifying the selectivity and phase of the direction sensors with a mechanical

Pseudo-streamlines are shown with velocity vectors while coloured contours represent inplane velocity magnitudes (*v*2+*w*2)1/2 normalised by (*v*2+*w*2)1/2*max*=18m/s. Measurements are for a light sheet at *x'/de* =11.3 and probe at *x'/de* =6.7 (and *r/de*=11) for an ensemble of 50

To measure the FPJ flow reliably, a suitable location is needed for the hot-wire probes. Nathan (1988) demonstrated that the introduction of a foreign object (such as a long rod) within the FPJ nozzle cavity will unnecessarily perturb the precessing flow mechanism. In order to avoid this, the probes were positioned outside, but as close as practical to the exit plane of the nozzle to reduce jitter, minimize the interference of the probes and probe holder, and maximize the signal strength of the flow. The lag hot-wire probe was positioned parallel to the nozzle axis with its centre at *r/D2*=0.61 in the *y-z* plane for a total of 4 downstream locations, namely *x'/D2*=0.12, 0.25, 0.50 and 0.75. An ensemble average of 50 image pairs are presented in Fig. 6, in which the phase-averaged velocities (*v*2+*w*2)1/2 are non-dimensionalised by the maximum in-plane velocity for each measurement plane and

fashion at *fp*=9Hz. The nozzle is centred at *y*=0 mm and *z*=0 mm. **a)** Phase-lag (


0

10

z (mm) 20

30

b)


*jitter* refers to phase-jitter in the measurements; **b)**

) of the jet

=45 from the spinning axis rotation in a clockwise

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

20 m/s

Norm. Vel

velocities before the data collection system is allowed to trigger).

Axial distance from jet exit: Probe : x'=20mm Lightsheet: x'=34mm

**2.2.5.5 Optimising the location of the trigger probes in the FPJ flow** 

jitter approx 7<sup>o</sup>


0.9

0.5

=23.8o

precessing jet (*de*=3mm) exiting at

relative to the lag hot-wire probe, where

Lag HW


image pairs.


0

10

z (mm) 20

30

a)

Lead HW

shown as contours. The difference between each contour level is 0.2. The location of the light sheet was fixed at *x'/D2*=0.05. For each experiment, the hot-wire parameters were readjusted to suit the new flow conditions for each hot-wire probe location.

The criterion for the best location was chosen by a combination of visual inspection of each successive image pair to decide on the location that results in the least spatial jitter and also by ensemble-averaging the results. In Fig. 6, the locations for *x'/D2*=0.12, 0.25 and 0.75 appear to produce similar results in the total magnitude of in-plane velocities. Locating the probe at *x'/D2*=0.50 appears to average data over two precession directions, as shown by the larger 'footprint' at the 0.2(*v*2+*w*2)1/2 contour. This location coincides with the zone of flow convergence (location of time-averaged, but not instantaneous, flow convergence downstream from the exit plane). Thus, any probe location which senses the magnitude of fluctuating velocities of the emerging precessing jet, other than at a location near to the zone of flow convergence, is a valid choice for the present experiment. The probes were finally located at *x'/D2*=0.12 and *r/D2*=0.61. This location, which is also approximately 130 to 150 from the peak in-plane velocity magnitude, resulted in the least influence of the probe and probe holder on the overall flow and was not in the plane of the light-sheet. Experiments conducted in the x'-r plane of the local jet centreline show that the instantaneous jet emergence angle (=53) is relatively constant within *x'*=40mm (or *x'/D2*=0.625) (Wong, Nathan & Kelso, 2008). Based on the 0.5(*u*2+*v*2)1/2max contours, the range of emergence angles was estimated to be approximately ±15 about the local jet centreline. This range of angles is two times the value of the minimum phase resolution (±30) in the azimuthal direction (*y-z* plane) (Wong, Nathan & Kelso, 2008).

#### **2.2.5.6 Selecting the separation distance of the probes**

The separation distance between the probes also plays a key role in determining the success of the technique. The lag hot-wire probe was positioned at a radial distance of approximately *r/D2*=0.61 and a downstream location of *x'/D2*=0.12, as determined from Section 2.2.5.5. To solve for an appropriate probe separation distance, *sc*, the following empirical criteria should be satisfied: the highest precession frequency of interest (i.e. 6Hz) should be at least 100 times lower than the smallest clock cycle of the Atmel controller, and the circumferential distance, *sc*, travelled by the precessing flow at a fixed radius, *rs*, from the nozzle axis should not be more than 10% of the circumference (*sf*) described by the radius *rs.* That is, *sc* < 0.1 *sf*.

We can derive the time it takes for the flow to travel between the lead and the lag hot-wire probe (i.e. the separation time, *Tsep*) given the precession frequency of interest (i.e. 3 or 6 Hz), from the following equation:

$$T\_{sep} = \frac{s\_c}{2\pi r\_s f\_p} \tag{2-6}$$

Where, *sc* = probe separation distance [m], *rs* = radial distance between the lag hot-wire probe and the nozzle axis [m], and *fp* = precession frequency of interest [Hz].

To calculate the separation time between the lead and lag hot-wire probe for the ATMEL controller time, we use the following conversion formula:

$$T\_{atmle} = \frac{T\_{sep} \times 10 \times 10^6}{1024} \tag{2-7}$$

PIV as a Complement to LDA in the Study of an Unsteady Oscillating Turbulent Flow 245

wires should not exceed 36). Alternative probe separation distances of *sc*=5, 10, 15 and 20mm were also considered. However, for this case, a probe separation of 15mm was chosen

The overall PIV system was combined with the phase-and-precession-direction stationary hot-wire sensors. In addition, a Tektronix TDS 210 Real Time Oscilloscope was used to monitor important signal outputs while a PC30D multi-channel A/D converter was used to collect various voltage signals from the Schmitt trigger inputs/outputs, the camera outputs and the laser outputs. The hot-wires were fully annealed prior to the experiments and the hot-wire system was designed for a short warm-up time and turned on at least 2 hours prior to use. If the hot-wire system was not allowed to stabilize, the data collected would be contaminated by electronic drift and lead to a false activation of the Schmitt triggers, and hence introduce errors in the detection of directional flow changes. Both hot-wire probes were held by probe holders and positioned at *x'/D2*=0.16 and *r/D2*=0.61. They were initially spaced approximately 1mm apart so that they sensed the same magnitude and frequency of flow. Both hot-wire channels (using an overheat ratio of 1.2) were adjusted to respond equally to a 1KHz square wave test. The signals from each hot-wire channel were passed to 4-pole Butterworth (maximally flat) Krohn-Hite filters (Model 3322) and low-pass filtered at the appropriate frequency (30Hz in the present experiments). Both filters were previously adjusted to give the same roll-off and filter frequency response for the same velocity fluctuations. Air was supplied to the FPJ at the experimental condition required and the output of each wire was adjusted to match and to fit within a 0 to +5 volts window. After calibration, the lag hot-wire probe was positioned at a radial distance of approximately *r/D2*=0.61, a downstream location of *x'/D2*=0.12 and a distance of 15mm from the lead hotwire probe. Note that time-averaged PIV experiments employed the same experimental arrangement except with the phase-triggering de-activated and the hot-wire system

Before each experiment, a calibration ruler was positioned within the plane of the laser sheet and its image recorded. This allowed the magnification (in px/mm) of each image to be recorded. An iterative process was then carried out to optimise the experiment so that each run had a velocity data yield of greater than 95%. Firstly, an estimate of the flow velocities was made and a few images taken to assess the relative movement of the correlation peak for a specific interrogation window and a tolerable dynamic velocity range (DVR). The DVR is defined by Adrian (1997) as the ratio of the largest resolvable velocity to the smallest resolvable velocity by the PIV system. An optimum out-of-plane motion of ¼ the lightsheet thickness suggested by Keane and Adrian (1990) was chosen for particles moving perpendicular to the lightsheet. The out-of-plane velocity for the FPJ flow was assumed to be of similar magnitude to the in-plane velocities. The software used for all the image processing, PivView 1.7, was assumed to have a sub-pixel resolution of 0.1 pixel. An acceptable level of cross-correlation signal was achieved by setting the time delay,

(typically 10s), so that an out-of-plane particle motion of ¼ the lightsheet thickness was achieved. Thus, a maximum particle movement of between 3 and 4 pixels was achieved for an interrogation window (IW) of 16x16 pixels with no overlap. A resampling technique after

*t*

as best satisfying the two criteria mentioned earlier.

**2.2.5.7 Final setup of the system** 

removed.

**2.2.6 PIV image pair data processing** 

The smallest clock resolution (i.e. 1 integer clock cycle) of the ATMEL microcontroller was approximately 0.1ms. Based on the criterion mentioned earlier and for accuracy, a minimum clock time of approximately *Tatmel*=10ms (or 97 clock cycles) for *fp*=6Hz was used. Subsequently, *Tatmel*=20ms (or 195 clock cycles) was selected for *fp*=3 Hz. The circumference, *sf*, travelled by the flow around a circular path for *rs*=0.6*D2* is calculated from:

$$\mathbf{s}\_f = \mathbf{2}\pi r\_s \tag{2-8}$$

Fig. 6. In-plane velocity magnitude contours, (*v*2+*w*2)1/2, for 4 spatial positions that were tested for the best placement of probes. Velocities are non-dimensionalised by maximum inplane velocity for respective locations. Precession of the flow from an observer looking upstream is in a clockwise direction. *Red*=59K, *Std*=0.00117.

This gives us a circumference of approximately 245mm. If we allow the flow at that radius (*rs*) to travel at most 10% of that circumference every cycle, then an appropriate separation distance would need to be less than 24.5mm (that is, an angular separation between the wires should not exceed 36). Alternative probe separation distances of *sc*=5, 10, 15 and 20mm were also considered. However, for this case, a probe separation of 15mm was chosen as best satisfying the two criteria mentioned earlier.

#### **2.2.5.7 Final setup of the system**

244 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

*sep*

The smallest clock resolution (i.e. 1 integer clock cycle) of the ATMEL microcontroller was approximately 0.1ms. Based on the criterion mentioned earlier and for accuracy, a minimum clock time of approximately *Tatmel*=10ms (or 97 clock cycles) for *fp*=6Hz was used. Subsequently, *Tatmel*=20ms (or 195 clock cycles) was selected for *fp*=3 Hz. The circumference,


0

z/D2

0.5

b) x'/D2=0.25

Fig. 6. In-plane velocity magnitude contours, (*v*2+*w*2)1/2, for 4 spatial positions that were tested for the best placement of probes. Velocities are non-dimensionalised by maximum inplane velocity for respective locations. Precession of the flow from an observer looking


0

z/D2

0.5

d) x'/D2=0.75

This gives us a circumference of approximately 245mm. If we allow the flow at that radius (*rs*) to travel at most 10% of that circumference every cycle, then an appropriate separation distance would need to be less than 24.5mm (that is, an angular separation between the

upstream is in a clockwise direction. *Red*=59K, *Std*=0.00117.

0

0.2

Lag hot-wire location

Lag hot-wire location


0.


0.2

0.4

0.6

0.8

0.6

4

0.6 0.8

0.2


0

z/D2

0.5


0

z/D2

0.5

a) x'/D2=0.12

c) x'/D2=0.50

*T*

*atmel*

*sf*, travelled by the flow around a circular path for *rs*=0.6*D2* is calculated from:

2 *<sup>f</sup> <sup>s</sup> s r*

<sup>6</sup> 10 10 1024

*<sup>T</sup>* (2-7)

(2-8)

0.2

0.2

Lag hot-wire location

Lag hot-wire location

0.4 0.6 0.8



0.2

0.4

0.6

0.8

The overall PIV system was combined with the phase-and-precession-direction stationary hot-wire sensors. In addition, a Tektronix TDS 210 Real Time Oscilloscope was used to monitor important signal outputs while a PC30D multi-channel A/D converter was used to collect various voltage signals from the Schmitt trigger inputs/outputs, the camera outputs and the laser outputs. The hot-wires were fully annealed prior to the experiments and the hot-wire system was designed for a short warm-up time and turned on at least 2 hours prior to use. If the hot-wire system was not allowed to stabilize, the data collected would be contaminated by electronic drift and lead to a false activation of the Schmitt triggers, and hence introduce errors in the detection of directional flow changes. Both hot-wire probes were held by probe holders and positioned at *x'/D2*=0.16 and *r/D2*=0.61. They were initially spaced approximately 1mm apart so that they sensed the same magnitude and frequency of flow. Both hot-wire channels (using an overheat ratio of 1.2) were adjusted to respond equally to a 1KHz square wave test. The signals from each hot-wire channel were passed to 4-pole Butterworth (maximally flat) Krohn-Hite filters (Model 3322) and low-pass filtered at the appropriate frequency (30Hz in the present experiments). Both filters were previously adjusted to give the same roll-off and filter frequency response for the same velocity fluctuations. Air was supplied to the FPJ at the experimental condition required and the output of each wire was adjusted to match and to fit within a 0 to +5 volts window. After calibration, the lag hot-wire probe was positioned at a radial distance of approximately *r/D2*=0.61, a downstream location of *x'/D2*=0.12 and a distance of 15mm from the lead hotwire probe. Note that time-averaged PIV experiments employed the same experimental arrangement except with the phase-triggering de-activated and the hot-wire system removed.

### **2.2.6 PIV image pair data processing**

Before each experiment, a calibration ruler was positioned within the plane of the laser sheet and its image recorded. This allowed the magnification (in px/mm) of each image to be recorded. An iterative process was then carried out to optimise the experiment so that each run had a velocity data yield of greater than 95%. Firstly, an estimate of the flow velocities was made and a few images taken to assess the relative movement of the correlation peak for a specific interrogation window and a tolerable dynamic velocity range (DVR). The DVR is defined by Adrian (1997) as the ratio of the largest resolvable velocity to the smallest resolvable velocity by the PIV system. An optimum out-of-plane motion of ¼ the lightsheet thickness suggested by Keane and Adrian (1990) was chosen for particles moving perpendicular to the lightsheet. The out-of-plane velocity for the FPJ flow was assumed to be of similar magnitude to the in-plane velocities. The software used for all the image processing, PivView 1.7, was assumed to have a sub-pixel resolution of 0.1 pixel. An acceptable level of cross-correlation signal was achieved by setting the time delay, *t* (typically 10s), so that an out-of-plane particle motion of ¼ the lightsheet thickness was achieved. Thus, a maximum particle movement of between 3 and 4 pixels was achieved for an interrogation window (IW) of 16x16 pixels with no overlap. A resampling technique after

PIV as a Complement to LDA in the Study of an Unsteady Oscillating Turbulent Flow 247

revealed the presence of a number of vortical features near to the FPJ exit plane at *x'/D2*=0.11. (Wong, Nathan & Kelso, 2008). The presence of these structures was further studied by conducting time-averaged surface flow visualisation on the downstream surface of the centrebody using an alcohol-powder mixture. While these experiments are qualitative, they provide important insight into some of the features measured from the PIV

> Primary line of separation

Fig. 7. a) Surface flow visualisation on FPJ nozzle at 10m/s free-stream inlet jet velocity. b) Interpretation of flow topology (Adapted from Wong *et al.* 2008 and reprinted with

permission from Cambridge University Press). Steady deflected flow emerging from the left

A steady (non-precessing) jet that deflects at a large exit angle to the nozzle axis was obtained by removing the chamber-section of the FPJ nozzle (chamber-lip-centrebody arrangement) from the supply pipe and introducing an alternative source air at an eccentric location within the inlet plane. The air was supplied by diverting a portion of the flow from a wind tunnel using a suitable turning vane. The deflected air-stream emerging from the exit lip was checked with a cotton tuft attached to a metal rod. As expected, with this arrangement no precession of the jet was detected, but instead the emerging jet was

Zdravkovich *et al*. (1998) studied coin-like cylinders using a talcum powder-paraffin film mixture; and Potts and Crowther (2000) used kerosene and fluorescent dye powder to study inclined disc-wings. In the present experiments, the use of white talcum powder and

provide a suitable mixture for surface flow visualization on the centrebody surface. The centrebody and nozzle exit were first painted matt black to provide good contrast from the white powder. The mixture was stirred thoroughly before being applied as a thin and uniform film over the region of interest which was initially positioned horizontally. Excess

=5.23×10-7kg/(m.s),

~45o. *Red*~10K, *Std*=0. `F' is focus, `S' is saddle and

=802kg/m3) was found to

Secondary line of separation

S

N

Line of attachment

S

F

deflected steadily at approximately 45o relative to the nozzle axis.

experiments, which do not measure the surface flow field.

(a) (b)

is deflected to the right and emerges at

methylated spirit (96% ethanol @ 20oC:

`N' is node.

Hart (2000) reduced the number of spurious vectors due to no overlap used. A global histogram method was used to interactively select the region of interest and to exclude potential outliers. The software stored the 3 highest correlation peaks per correlation calculation. If the highest peak was an outlier, the next highest peak was selected and so on. When a spurious vector was marked, it was replaced by bi-linear interpolation using information from surrounding vectors. When several immediate neighbours were also outliers, then a Gaussian-weighted interpolation scheme was used. The measurement volume was typically 1.5 x 1.5 x 2mm3 for a scaling of 10.6px/mm, Such small pixel displacements may result in a poor dynamic velocity range in these experiments. Nevertheless, broad features of the flow can still be obtained. A total of 350 image pairs (recorded over 35 seconds) were recorded for the time-average PIV experiments and due to resource limitations 50 image pairs (taking up to 2 hours to collect) were recorded for each phase angle of the phase-average PIV experiment. With only 50 samples collected in the phase-averaged PIV experiment, only the mean data are presented in this chapter.

#### **2.2.7 LDA and PIV experimental uncertainties**

Experimental uncertainty calculations follow the method proposed by Martin, Pugliese and Leishman (2000) and Kline and McClintock (1953). For LDA, the calibration uncertainties associated with measurement of probe length, measurement of beam separation and data acquisition uncertainties are approximately 3.4% of the measured velocity for 95% confidence interval (c.i.). For PIV, the uncertainties associated with camera calibration and jitter in the laser-timing system are approximately 7% of the measured velocity at 95% c.i.. Other sources of PIV errors (or *r.m.s*. uncertainties) as suggested in Raffel et al (1998) attributable to particle image diameter, particle image displacement, ratio of particle image size and pixel size, particle image shift, image quantisation, background noise of the image, displacement gradients and out-of-plane motions are estimated to be 1.3% of the measured velocity.

Another major source of error for both techniques is due to phase uncertainties of the jet motion in the azimuthal and axial planes. These were estimated to be 30 and 15 respectively for the directionally-resolved phase-averaged PIV experiments, and potentially 60 and 15 respectively for the non-directionally resolved phase-averaged LDA experiments. Larger phase uncertainties in both planes contribute to a reduction of the phase-averaged magnitudes compared to velocities obtained during an instantaneous event.

#### **2.2.8 Surface flow visualisation**

The purpose of surface flow visualisation is to make visible the patterns of skin-friction lines (Maltby, 1962) and critical points on the surface of (wind-tunnel) models, so that the flow around the surface can be interpreted and understood (Perry & Chong, 1987). This method relies on the response of the visualisation media to skin friction stresses generated by the airstream flowing over the object's surface, and on the media film being thin enough to be unaffected by pressure gradients (Tobak & Peake, 1979). It should be noted that the response time of this technique is much too long to allow it to represent the instantaneous state of the flow. Instead, the results reflect a pattern caused by the flow's interaction with the surface over a period of time commensurate with the drying time of the media (Hunt et al, 1978). The axial vorticity fields obtained using the phase-precession-direction resolved PIV

Hart (2000) reduced the number of spurious vectors due to no overlap used. A global histogram method was used to interactively select the region of interest and to exclude potential outliers. The software stored the 3 highest correlation peaks per correlation calculation. If the highest peak was an outlier, the next highest peak was selected and so on. When a spurious vector was marked, it was replaced by bi-linear interpolation using information from surrounding vectors. When several immediate neighbours were also outliers, then a Gaussian-weighted interpolation scheme was used. The measurement volume was typically 1.5 x 1.5 x 2mm3 for a scaling of 10.6px/mm, Such small pixel displacements may result in a poor dynamic velocity range in these experiments. Nevertheless, broad features of the flow can still be obtained. A total of 350 image pairs (recorded over 35 seconds) were recorded for the time-average PIV experiments and due to resource limitations 50 image pairs (taking up to 2 hours to collect) were recorded for each phase angle of the phase-average PIV experiment. With only 50 samples collected in the

phase-averaged PIV experiment, only the mean data are presented in this chapter.

Experimental uncertainty calculations follow the method proposed by Martin, Pugliese and Leishman (2000) and Kline and McClintock (1953). For LDA, the calibration uncertainties associated with measurement of probe length, measurement of beam separation and data acquisition uncertainties are approximately 3.4% of the measured velocity for 95% confidence interval (c.i.). For PIV, the uncertainties associated with camera calibration and jitter in the laser-timing system are approximately 7% of the measured velocity at 95% c.i.. Other sources of PIV errors (or *r.m.s*. uncertainties) as suggested in Raffel et al (1998) attributable to particle image diameter, particle image displacement, ratio of particle image size and pixel size, particle image shift, image quantisation, background noise of the image, displacement gradients and out-of-plane motions are estimated to be 1.3% of the measured

Another major source of error for both techniques is due to phase uncertainties of the jet motion in the azimuthal and axial planes. These were estimated to be 30 and 15 respectively for the directionally-resolved phase-averaged PIV experiments, and potentially 60 and 15 respectively for the non-directionally resolved phase-averaged LDA experiments. Larger phase uncertainties in both planes contribute to a reduction of the phase-averaged magnitudes compared to velocities obtained during an instantaneous event.

The purpose of surface flow visualisation is to make visible the patterns of skin-friction lines (Maltby, 1962) and critical points on the surface of (wind-tunnel) models, so that the flow around the surface can be interpreted and understood (Perry & Chong, 1987). This method relies on the response of the visualisation media to skin friction stresses generated by the airstream flowing over the object's surface, and on the media film being thin enough to be unaffected by pressure gradients (Tobak & Peake, 1979). It should be noted that the response time of this technique is much too long to allow it to represent the instantaneous state of the flow. Instead, the results reflect a pattern caused by the flow's interaction with the surface over a period of time commensurate with the drying time of the media (Hunt et al, 1978). The axial vorticity fields obtained using the phase-precession-direction resolved PIV

**2.2.7 LDA and PIV experimental uncertainties** 

velocity.

**2.2.8 Surface flow visualisation** 

revealed the presence of a number of vortical features near to the FPJ exit plane at *x'/D2*=0.11. (Wong, Nathan & Kelso, 2008). The presence of these structures was further studied by conducting time-averaged surface flow visualisation on the downstream surface of the centrebody using an alcohol-powder mixture. While these experiments are qualitative, they provide important insight into some of the features measured from the PIV experiments, which do not measure the surface flow field.

Fig. 7. a) Surface flow visualisation on FPJ nozzle at 10m/s free-stream inlet jet velocity. b) Interpretation of flow topology (Adapted from Wong *et al.* 2008 and reprinted with permission from Cambridge University Press). Steady deflected flow emerging from the left is deflected to the right and emerges at ~45o. *Red*~10K, *Std*=0. `F' is focus, `S' is saddle and `N' is node.

A steady (non-precessing) jet that deflects at a large exit angle to the nozzle axis was obtained by removing the chamber-section of the FPJ nozzle (chamber-lip-centrebody arrangement) from the supply pipe and introducing an alternative source air at an eccentric location within the inlet plane. The air was supplied by diverting a portion of the flow from a wind tunnel using a suitable turning vane. The deflected air-stream emerging from the exit lip was checked with a cotton tuft attached to a metal rod. As expected, with this arrangement no precession of the jet was detected, but instead the emerging jet was deflected steadily at approximately 45o relative to the nozzle axis.

Zdravkovich *et al*. (1998) studied coin-like cylinders using a talcum powder-paraffin film mixture; and Potts and Crowther (2000) used kerosene and fluorescent dye powder to study inclined disc-wings. In the present experiments, the use of white talcum powder and methylated spirit (96% ethanol @ 20oC: =5.23×10-7kg/(m.s), =802kg/m3) was found to provide a suitable mixture for surface flow visualization on the centrebody surface. The centrebody and nozzle exit were first painted matt black to provide good contrast from the white powder. The mixture was stirred thoroughly before being applied as a thin and uniform film over the region of interest which was initially positioned horizontally. Excess

PIV as a Complement to LDA in the Study of an Unsteady Oscillating Turbulent Flow 249

0

0

0.05

0.1

u'/ui

0.15

0.2

b)LDA - RMS



0

0

0

0

0

Fig. 8. Comparison between time-averaged LDA and PIV axial velocities at *x'/D2*=0.16. The origins of the upwards-shifted ordinates are indicated on the right axis for contraction () and orifice () inlets respectively. The left axis refers to the pipe case (). All velocity values are normalised with the respective bulk inlet velocity *ui*, for each inlet case. See Table 1 and

0

0.05

0.1

u'/ui

0.15

0.2

0

0

**3.2 Comparison of conditional-directionally averaged PIV and conditional non-**

LDA results while the open triangles represent the mean PIV results (obtained at

Fig. 9a shows the radial distributions of phase-averaged axial velocity at *x'/D2*=0.16, obtained using both LDA and PIV techniques. These were measured for *Red*=84,500, *Std*=0.0015 and *ui*=78.7m/s for the LDA, and *Red*=59,000, *Std*=0.0017 and *ui*=55m/s for the PIV technique respectively. The closed squares represent the transit-time weighted mean

Upper and lower confidence intervals (C.I.) at 95% confidence for the PIV measurements are

=60o).

Table 2, for LDA and PIV conditions respectively.



c) PIV - Mean d) PIV - RMS

0

0

0.05

0.1

u/ui

0.15

0.2

0.05

0.1

u/ui

0.15

0.2

a) LDA - Mean

represented as dotted lines and solid lines respectively.

**directionally averaged LDA results** 

mixture was drained off by slightly tilting the model until the desired film thickness was achieved. An optimum film is achieved when the mixture just 'wets' the sample's surface. This was an iterative process as it was difficult to quantify the optimum film thickness due to the rapid evaporation of the methylated spirit. The FPJ nozzle was positioned vertically at the working section with the deflector facing upstream, such that the flow emerging from the nozzle exit plane was deflected by about 45o as indicated by a cotton tuft held by a thin rod positioned in the centre of the exit lip, just above the centrebody.

The most obvious flow features, such as the flow reattachment location and the foci, could be seen to form immediately on the matt black surface of the centrebody (Fig. 7a). More features were revealed as the methylated spirit evaporated over time, leaving only the white talcum powder behind. An interpretation of surface flow topology is shown in Fig. 7b. The influence of the centrebody supports were also considered in the experiments, however, it was found that the orientation of the supports does not greatly affect the distinctive flow patterns observed on the upper surface of the centrebody. As such, a study on the centrebody supports is not further discussed here.

### **3. Final discussion of key results and issues**

#### **3.1 Comparison of time-averaged PIV and LDA results**

This section discusses the time-average results for the Chamber-Lip-Centrebody (Ch-L-CB) case for both the 1-D LDA and PIV results. For the LDA experiments, only the jet was seeded and local seeding was applied to seed the ambient fluid during each measurement. This explained the higher validated LDA bursts (nominally 1000) in the locations –0.7<*r/R2*<+0.7 during the experiments compared to between 10 and 1000 bursts/second outside these locations. Since this configuration was found to generate the precessing jet mode most of the time, any attempts to seed the region near to *r/R2*=0 was problematic since the presence of the seeding device may have an unwanted influence over the emerging flow. The poor seeding explains a decrease in the LDA burst rate beyond the region –0.7<*r/R2*<+0.7 in these measurements. However, this did not unduly affect the present results in Fig. 8a and b, (except, for the orifice case) since an acceptable number of validated LDA burst samples (generally greater than 4000) and data rate (at least 10 times higher than the local precession frequency) were achieved. Refer to Wong (2004) for more details. The results of the PIV experiments are also provided in Fig. 8c and Fig. 8d and specific details pertaining to both these experiments are also found in Table 1 and Table 2.

Generally, the axial velocity trends in the PIV and LDA data in the region –0.8<*r/R2*<+0.8 typically vary by *u/ui*=0.02. However, in the regions beyond this, the LDA data are expected to over-estimate the true velocity values due to insufficient global seeding. This means that unseeded ambient fluid entrained into the FPJ nozzle will not be recorded, while seeding from the bulk jet will be sampled most of the time. This introduces a velocity bias towards a higher velocity flow, especially in the region beyond *r/R2*=0.8. Thus, the flow structure beyond the exit lip cannot be elucidated clearly. This is evident in the contrasting results obtained by means of PIV, which employed uniform global seeding instead of localised seeding. The PIV results in Fig. 8c (Mean) and Fig. 8d (RMS) beyond *r/R2*=1.0 reflect a truer velocity profile as opposed to the LDA results in that region. As explained before, this is due to poor localised seeding beyond the exit lip radius, *R2*.

mixture was drained off by slightly tilting the model until the desired film thickness was achieved. An optimum film is achieved when the mixture just 'wets' the sample's surface. This was an iterative process as it was difficult to quantify the optimum film thickness due to the rapid evaporation of the methylated spirit. The FPJ nozzle was positioned vertically at the working section with the deflector facing upstream, such that the flow emerging from the nozzle exit plane was deflected by about 45o as indicated by a cotton tuft held by a thin

The most obvious flow features, such as the flow reattachment location and the foci, could be seen to form immediately on the matt black surface of the centrebody (Fig. 7a). More features were revealed as the methylated spirit evaporated over time, leaving only the white talcum powder behind. An interpretation of surface flow topology is shown in Fig. 7b. The influence of the centrebody supports were also considered in the experiments, however, it was found that the orientation of the supports does not greatly affect the distinctive flow patterns observed on the upper surface of the centrebody. As such, a study on the

This section discusses the time-average results for the Chamber-Lip-Centrebody (Ch-L-CB) case for both the 1-D LDA and PIV results. For the LDA experiments, only the jet was seeded and local seeding was applied to seed the ambient fluid during each measurement. This explained the higher validated LDA bursts (nominally 1000) in the locations –0.7<*r/R2*<+0.7 during the experiments compared to between 10 and 1000 bursts/second outside these locations. Since this configuration was found to generate the precessing jet mode most of the time, any attempts to seed the region near to *r/R2*=0 was problematic since the presence of the seeding device may have an unwanted influence over the emerging flow. The poor seeding explains a decrease in the LDA burst rate beyond the region –0.7<*r/R2*<+0.7 in these measurements. However, this did not unduly affect the present results in Fig. 8a and b, (except, for the orifice case) since an acceptable number of validated LDA burst samples (generally greater than 4000) and data rate (at least 10 times higher than the local precession frequency) were achieved. Refer to Wong (2004) for more details. The results of the PIV experiments are also provided in Fig. 8c and Fig. 8d and specific details pertaining to both

Generally, the axial velocity trends in the PIV and LDA data in the region –0.8<*r/R2*<+0.8 typically vary by *u/ui*=0.02. However, in the regions beyond this, the LDA data are expected to over-estimate the true velocity values due to insufficient global seeding. This means that unseeded ambient fluid entrained into the FPJ nozzle will not be recorded, while seeding from the bulk jet will be sampled most of the time. This introduces a velocity bias towards a higher velocity flow, especially in the region beyond *r/R2*=0.8. Thus, the flow structure beyond the exit lip cannot be elucidated clearly. This is evident in the contrasting results obtained by means of PIV, which employed uniform global seeding instead of localised seeding. The PIV results in Fig. 8c (Mean) and Fig. 8d (RMS) beyond *r/R2*=1.0 reflect a truer velocity profile as opposed to the LDA results in that region. As explained before, this is due

rod positioned in the centre of the exit lip, just above the centrebody.

centrebody supports is not further discussed here.

**3. Final discussion of key results and issues** 

these experiments are also found in Table 1 and Table 2.

to poor localised seeding beyond the exit lip radius, *R2*.

**3.1 Comparison of time-averaged PIV and LDA results** 

Fig. 8. Comparison between time-averaged LDA and PIV axial velocities at *x'/D2*=0.16. The origins of the upwards-shifted ordinates are indicated on the right axis for contraction () and orifice () inlets respectively. The left axis refers to the pipe case (). All velocity values are normalised with the respective bulk inlet velocity *ui*, for each inlet case. See Table 1 and Table 2, for LDA and PIV conditions respectively.

#### **3.2 Comparison of conditional-directionally averaged PIV and conditional nondirectionally averaged LDA results**

Fig. 9a shows the radial distributions of phase-averaged axial velocity at *x'/D2*=0.16, obtained using both LDA and PIV techniques. These were measured for *Red*=84,500, *Std*=0.0015 and *ui*=78.7m/s for the LDA, and *Red*=59,000, *Std*=0.0017 and *ui*=55m/s for the PIV technique respectively. The closed squares represent the transit-time weighted mean LDA results while the open triangles represent the mean PIV results (obtained at =60o). Upper and lower confidence intervals (C.I.) at 95% confidence for the PIV measurements are represented as dotted lines and solid lines respectively.

PIV as a Complement to LDA in the Study of an Unsteady Oscillating Turbulent Flow 251

by *u/ui*=0.02 and 0.035 respectively. The larger magnitudes in the LDA results relative to the PIV measurements on the right-hand side of the jet are attributed to LDA velocity bias towards the higher velocities, as discussed above, noting also that the effectiveness of the external seeding of the measurement region decreases with distance downstream from the FPJ exit plane. Again, these differences may also be attributed to a better phase and

Fig. 9. Comparison between phase-averaged LDA and PIV axial velocities at *x'/D2*=0.16, 0.48 and 0.79. Shown also are lower and upper 95% confidence interval (C.I.) for PIV results. Axial velocities are non-dimensionalised by *ui*=78.7m/s for LDA and *ui*=55.0 m/s for PIV.

0

0.05

u/ui

0.1

0.15


Lead hot wire (HW) Lag HW

d) Coordinate system of HW position

=120o)

> LDA - Mean PIV - Mean PIV - Lower C.I. PIV - Upper C.I.

Centrebody support

Fig. 10 illustrates the development of the 0.50 and 0.9 *(v2+w2)½x',max* contours for various downstream sections from the exit lip taken from phase-averaged PIV measurements in the *y-z* plane. The jet is initially kidney-shaped (Fig. 10a), but as it converges to *x'/D2*=0.58 (Fig.

LDA:*Red*=84,500 and *Std*=0.0015. PIV:*Red*=59,000 and *Std*=0.0017.

LDA - Mean PIV - Mean PIV - Lower C.I. PIV - Upper C.I.

**3.3 Construction of flow topology** 

0

0.05

u/ui

0.1

0.15

0

0.05

u/ui

0.1

0.15

c) LDA & PIV (

a) LDA & PIV (

=135o)



directional accuracy for the PIV measurements than for the LDA measurements.

=60o) b) LDA & PIV (

LDA - Mean PIV - Mean PIV - Lower C.I. PIV - Upper C.I.


Table 1. Summary of experimental conditions used for the FPJ nozzles measured using LDA.


Table 2. Summary of experimental inlet conditions, in the absence of the nozzle chamber, used for the FPJ nozzles measured in time-averaged PIV experiments.

The phase-averaged LDA results broadly agree well, in terms of profile shapes and velocity magnitudes, with the PIV results within the range 2 0.5 / 0.1 *r D* . The LDA velocity measurements are generally larger than the PIV velocity measurements in the ranges –0.48<*r/D2*<–0.5 and *r/D2* > +0.1. This can be explained by the differences in seeding methods. In the LDA experiments, the co-flow was only seeded from one local azimuthal location, i.e. it was seeded asymmetrically, so that the two measurements agree well for the side that was well seeded. However, the LDA will over-estimate the velocity for the region in which the ambient fluid was poorly seeded, so was subject to a velocity bias. In contrast, the seeding in the PIV experiment was uniform in the azimuthal direction.

In general, as shown in Fig. 9a, the axial velocity trend using both techniques rises from *u/ui*=0 near to *r/D2*= - 0.5 and peaks at approximately *u/ui*=0.10, after which it decreases to a minimum near to *r/D2*=+0.1 before rising again to a second maximum of *u/ui*~0.085 at *r/D2*=+0.30 for the PIV measurements and *u/ui*~0.04 at *r/D2*=+0.38 for the LDA measurements. There is an apparent shift of the second peak for the LDA results and also a decrease in the LDA axial velocities between 0.1<*r/D2*<0.4, despite transit-time weighted corrections to account for velocity bias. These differences may be attributed to a better phase and directional accuracy for the PIV measurements than for the LDA measurements.

Fig. 9b and Fig. 9c present the radial distributions of the phase-averaged PIV and LDA results for downstream locations at *x'/D2*=0.48 and 0.79 respectively. Again, both techniques show similar axial velocity trends and have comparable velocity magnitudes, differing only

Contraction 140 150,000 14436 2 Orifice 96 103,000 15465 2

Table 1. Summary of experimental conditions used for the FPJ nozzles measured using

N

Pipe 34.5 37,100 700 3.393.392 1.74 10 9.45 Contraction 29.7 31,900 1049 3.593.592 1.82 12 8.91 Orifice 26.4 28,400 1047 3.683.682 1.9 12 8.69

Table 2. Summary of experimental inlet conditions, in the absence of the nozzle chamber,

The phase-averaged LDA results broadly agree well, in terms of profile shapes and velocity magnitudes, with the PIV results within the range 2 0.5 / 0.1 *r D* . The LDA velocity measurements are generally larger than the PIV velocity measurements in the ranges –0.48<*r/D2*<–0.5 and *r/D2* > +0.1. This can be explained by the differences in seeding methods. In the LDA experiments, the co-flow was only seeded from one local azimuthal location, i.e. it was seeded asymmetrically, so that the two measurements agree well for the side that was well seeded. However, the LDA will over-estimate the velocity for the region in which the ambient fluid was poorly seeded, so was subject to a velocity bias. In contrast,

In general, as shown in Fig. 9a, the axial velocity trend using both techniques rises from *u/ui*=0 near to *r/D2*= - 0.5 and peaks at approximately *u/ui*=0.10, after which it decreases to a minimum near to *r/D2*=+0.1 before rising again to a second maximum of *u/ui*~0.085 at *r/D2*=+0.30 for the PIV measurements and *u/ui*~0.04 at *r/D2*=+0.38 for the LDA measurements. There is an apparent shift of the second peak for the LDA results and also a decrease in the LDA axial velocities between 0.1<*r/D2*<0.4, despite transit-time weighted corrections to account for velocity bias. These differences may be attributed to a better phase

and directional accuracy for the PIV measurements than for the LDA measurements.

Fig. 9b and Fig. 9c present the radial distributions of the phase-averaged PIV and LDA results for downstream locations at *x'/D2*=0.48 and 0.79 respectively. Again, both techniques show similar axial velocity trends and have comparable velocity magnitudes, differing only

used for the FPJ nozzles measured in time-averaged PIV experiments.

the seeding in the PIV experiment was uniform in the azimuthal direction.

Average number of LDA bursts per location

Probe dimensions: axial, radial, tangential (*mm*)

Probe volume: axial, radial, tangential (mm)

0.171.650.17

Step size: axial, radial, mm

Step size (mm)

2

t (s) px/mm

Reynolds Number Based on *ui* measured at *x/d*=1

Pipe 103 111,000 13150

Reynolds Number based on *ui* and *d* measured at *x/d*=1

Type of Inlet Bulk

Type of Inlet Bulk

LDA.

Velocity, *ui* m/s

Velocity, *ui*  m/s

by *u/ui*=0.02 and 0.035 respectively. The larger magnitudes in the LDA results relative to the PIV measurements on the right-hand side of the jet are attributed to LDA velocity bias towards the higher velocities, as discussed above, noting also that the effectiveness of the external seeding of the measurement region decreases with distance downstream from the FPJ exit plane. Again, these differences may also be attributed to a better phase and directional accuracy for the PIV measurements than for the LDA measurements.

Fig. 9. Comparison between phase-averaged LDA and PIV axial velocities at *x'/D2*=0.16, 0.48 and 0.79. Shown also are lower and upper 95% confidence interval (C.I.) for PIV results. Axial velocities are non-dimensionalised by *ui*=78.7m/s for LDA and *ui*=55.0 m/s for PIV. LDA:*Red*=84,500 and *Std*=0.0015. PIV:*Red*=59,000 and *Std*=0.0017.

#### **3.3 Construction of flow topology**

Fig. 10 illustrates the development of the 0.50 and 0.9 *(v2+w2)½x',max* contours for various downstream sections from the exit lip taken from phase-averaged PIV measurements in the *y-z* plane. The jet is initially kidney-shaped (Fig. 10a), but as it converges to *x'/D2*=0.58 (Fig.

PIV as a Complement to LDA in the Study of an Unsteady Oscillating Turbulent Flow 253

The pair of vortices emerging from the middle of the centrebody represents the centrebody (CB) vortex pair which originate from the foci located to either side of the centrebody surface. These vortices move closer to each other with downstream distance and finally annihilate one another by *x'/D2* ~ 0.5. The thin black dashed line represents the vortex that is thought to originate from the edge of the centrebody (that is, the Edge 1 vortex). The 'legs' of this vortex form a pair of longitudinal vortices downstream of the centrebody (the Edge 1 vortex pair). These appear as positive and negative vorticity regions as seen by a downstream observer. This vortex pair departs the centrebody at an inclined angle, cutting the lower measurement planes at a large angle. Thus, the vortex pair appears as two kidneyshaped patterns near to the leading edge of the high velocity jet stream in the vorticity results of the transverse PIV measurements as given in Fig. 11a. Wong, Nathan and Kelso (2008) showed that the negative leg of this Edge 1 vortex follows the trajectory of the jet fairly closely. The positive Edge 1 vortex is initially located in the vicinity of *y/D2*=+0.1 and *z/D2*=+0.4, but at a distance *x'/D2*=0.58 it moves towards *y/D2*=+0.6 and *z/D2*=+0.15 with increasing radius from the nozzle axis while departing in a direction opposite to the jet

The thin blue solid line in Fig. 11c represents the core of a vortex that sits slightly above the surface of the exit lip and then lifts away from the exit at the rear side of the exiting jet (opposite the side from which the jet emerges). The lift-off occurs at an azimuthal angle of 130 to 150 from the center of the emerging jet. The legs of this lifted vortex form the 'Edge 2 vortex pair'. The vorticity associated with this vortex is observed most clearly in the longitudinal phase-averaged PIV experiments provided in Fig. 11b. The emerging jet separates at the exit lip to form a saddle-focus pattern at *r/D2*=0.6 at *x'/D2*=0.05 as illustrated in Fig. 11b. This pattern appears to be generated by the separation of the external flow entrained along the outside surface of the FPJ nozzle, and the separation of the exiting FPJ flow at the edge of the lip. The focus seen in Fig. 11b has a direction of rotation (clockwise) that is consistent with the vorticity that would be shed from the outer

By inspection of Fig. 11a, Fig. 11b and the conjectured topology of Fig. 11c, the Edge 1 vortex and the Edge 2 vortex are of the same sign of circulation. If the emerging jet were to depart along the geometric axis (i.e. without deflection), then the Edge 2 vortex should remain in a closed 'circular' loop (or ring) sitting above the exit lip. However, the asymmetry of the emerging jet causes one end of this vortex loop to be entrained into the emerging jet flow between approximately 130 and 150 ahead of the advancing jet (Wong, Nathan & Kelso, 2008). This range of angles is similar to the separation angles of the surface flows in jets in crossflow (Fric & Roshko, 1994). Thus the edge vortex forms a horseshoe-shaped loop with either side of the loop being entrained into the advancing and receding sides of the jet. The lift-up of the Edge 2 vortex 'pair' from the surface of the exit lip appears initially to influence the trajectory of the Edge 1 vortex. The trajectories of the two 'legs' of the Edge 2 vortex follow the same trend as the Edge 1 vortex, in terms of the *y-z* trajectory with downstream distance, albeit with a slight delay in phase. The presence of the Edge 2 vortex pair below the core of the jet was detected in earlier phase-averaged LDA studies (Wong *et al*., 2003) and in the 0.5(*v*2+*w*2)1/2max velocity contours of the phase-and-precession-direction-resolved

precession.

surface of the FPJ.

PIV studies (see Fig. 10g).

10 f), it becomes an almost round jet. The approximate trajectory of the jet centreline in the transverse cross-section initially deflects to the left of the advancing side of the jet, but this deflection is most noticeable after the convergence location at approximately *x'/D2*= 0.58.

Wong, Nathan and Kelso (2008) summarised the important features identified in the phaseaveraged longitudinal (*x'-r* plane) PIV results. These were, a saddle above a reversed flow region near to the exit plane in the central region of the nozzle, a region of separation on the surface of the exit lip whereby the head of the focus points inwards, the mean extent of the flow convergence region, a region of separation on the surface of the exit lip where the head of the focus points outwards, and a conjectured streamline pattern describing the structure of an Edge 2 and an Edge 3 vortices. Some of these features are shown in Fig. 11a.

Fig. 10. Cross-sectional development of the jet downstream showing 0.5 and 0.9 (*v*2+*w*2)½*x',max* contour levels. Note that by *x'/D2*=0.58, the jet is almost round. *D2*=64mm. *Red*=59K, *Std*=0.0017.

10 f), it becomes an almost round jet. The approximate trajectory of the jet centreline in the transverse cross-section initially deflects to the left of the advancing side of the jet, but this deflection is most noticeable after the convergence location at approximately *x'/D2*= 0.58.

Wong, Nathan and Kelso (2008) summarised the important features identified in the phaseaveraged longitudinal (*x'-r* plane) PIV results. These were, a saddle above a reversed flow region near to the exit plane in the central region of the nozzle, a region of separation on the surface of the exit lip whereby the head of the focus points inwards, the mean extent of the flow convergence region, a region of separation on the surface of the exit lip where the head of the focus points outwards, and a conjectured streamline pattern describing the structure

Fig. 10. Cross-sectional development of the jet downstream showing 0.5 and 0.9 (*v*2+*w*2)½*x',max*

contour levels. Note that by *x'/D2*=0.58, the jet is almost round. *D2*=64mm. *Red*=59K,

*Std*=0.0017.

of an Edge 2 and an Edge 3 vortices. Some of these features are shown in Fig. 11a.

The pair of vortices emerging from the middle of the centrebody represents the centrebody (CB) vortex pair which originate from the foci located to either side of the centrebody surface. These vortices move closer to each other with downstream distance and finally annihilate one another by *x'/D2* ~ 0.5. The thin black dashed line represents the vortex that is thought to originate from the edge of the centrebody (that is, the Edge 1 vortex). The 'legs' of this vortex form a pair of longitudinal vortices downstream of the centrebody (the Edge 1 vortex pair). These appear as positive and negative vorticity regions as seen by a downstream observer. This vortex pair departs the centrebody at an inclined angle, cutting the lower measurement planes at a large angle. Thus, the vortex pair appears as two kidneyshaped patterns near to the leading edge of the high velocity jet stream in the vorticity results of the transverse PIV measurements as given in Fig. 11a. Wong, Nathan and Kelso (2008) showed that the negative leg of this Edge 1 vortex follows the trajectory of the jet fairly closely. The positive Edge 1 vortex is initially located in the vicinity of *y/D2*=+0.1 and *z/D2*=+0.4, but at a distance *x'/D2*=0.58 it moves towards *y/D2*=+0.6 and *z/D2*=+0.15 with increasing radius from the nozzle axis while departing in a direction opposite to the jet precession.

The thin blue solid line in Fig. 11c represents the core of a vortex that sits slightly above the surface of the exit lip and then lifts away from the exit at the rear side of the exiting jet (opposite the side from which the jet emerges). The lift-off occurs at an azimuthal angle of 130 to 150 from the center of the emerging jet. The legs of this lifted vortex form the 'Edge 2 vortex pair'. The vorticity associated with this vortex is observed most clearly in the longitudinal phase-averaged PIV experiments provided in Fig. 11b. The emerging jet separates at the exit lip to form a saddle-focus pattern at *r/D2*=0.6 at *x'/D2*=0.05 as illustrated in Fig. 11b. This pattern appears to be generated by the separation of the external flow entrained along the outside surface of the FPJ nozzle, and the separation of the exiting FPJ flow at the edge of the lip. The focus seen in Fig. 11b has a direction of rotation (clockwise) that is consistent with the vorticity that would be shed from the outer surface of the FPJ.

By inspection of Fig. 11a, Fig. 11b and the conjectured topology of Fig. 11c, the Edge 1 vortex and the Edge 2 vortex are of the same sign of circulation. If the emerging jet were to depart along the geometric axis (i.e. without deflection), then the Edge 2 vortex should remain in a closed 'circular' loop (or ring) sitting above the exit lip. However, the asymmetry of the emerging jet causes one end of this vortex loop to be entrained into the emerging jet flow between approximately 130 and 150 ahead of the advancing jet (Wong, Nathan & Kelso, 2008). This range of angles is similar to the separation angles of the surface flows in jets in crossflow (Fric & Roshko, 1994). Thus the edge vortex forms a horseshoe-shaped loop with either side of the loop being entrained into the advancing and receding sides of the jet. The lift-up of the Edge 2 vortex 'pair' from the surface of the exit lip appears initially to influence the trajectory of the Edge 1 vortex. The trajectories of the two 'legs' of the Edge 2 vortex follow the same trend as the Edge 1 vortex, in terms of the *y-z* trajectory with downstream distance, albeit with a slight delay in phase. The presence of the Edge 2 vortex pair below the core of the jet was detected in earlier phase-averaged LDA studies (Wong *et al*., 2003) and in the 0.5(*v*2+*w*2)1/2max velocity contours of the phase-and-precession-direction-resolved PIV studies (see Fig. 10g).

PIV as a Complement to LDA in the Study of an Unsteady Oscillating Turbulent Flow 255

The study illustrates that a pre-requisite to the detailed application of laser diagnostic tools such as PIV and LDA is an adequate understanding of the qualitative features of the flow of interest. This is necessary for the design and careful application of appropriate triggering conditional statistics. When dealing with turbulent flow coupled with time-variant threedimensional fluidic oscillations, it is important to match the flow conditions with the technical limits of the flow instrumentation. For the investigation of the fluidic precessing jet flow, the Schmitt filter was found to be effective in allowing two carefully-placed hot wire probes to provide a trigger to discriminate for both phase and direction of the oscillation, both of which vary randomly. This trigger allowed resolution of the azimuthal component of the flow velocity in the PIV data, which were smoothed out in the LDA measurements and also triggered on phase only, and not on direction. For the measurement of unconditioned statistics, such as the mean and *r.m.s.* statistical quantities, good agreement was found here between the PIV and LDA techniques for those regions of the flow in which both techniques were well seeded. As expected, some disagreements were found in those regions of the flow in which the seeding of the ambient air was poor, due to the nonuniform seeding technique, where the strong entrainment of unseeded ambient fluid led to

The authors acknowledge the Australian Research Council, Schools of Mechanical and Chemical Engineering (University of Adelaide) and Division of Mechanical Engineering (University of Wales, Cardiff) for various in-kind assistance, equipment and facility support. CYW also acknowledges the International Postgraduate Research Scholarship that enabled this research to be conducted. The authors are also grateful to the various peer-reviewers

Adrian R.J. (1997) Dynamic ranges of velocity and spatial resolution of particle image

Durst F., Melling A. & Whitelaw J.H. (1981) *Principles and practice of laser-Doppler* 

Fernandes E.C. & Heitor M.V. (1998) On the extension of laser-Doppler anemometer to the

Fick W., Griffiths A.J. & O'Doherty T. (1997) Visualisation of the precessing vortex core in an unconfined swirling flow. *Optical Diagnostics in Engineering*, 2(1), pp.19-31. Fric T.F. & Roshko A. (1994) Vortical structure in the wake of a transverse jet. *J. Fluid Mech.*,

Guo B.Y. (2000) *CFD simulation of flow instability in axisymmetric sudden expansions*. PhD

Thesis, Dept. of Chem. Eng., The University of Sydney, Australia.

analysis of oscillating flames. In, *Proc. 9th Int. Sym. On Appl. Laser Techniques to Fluid* 

velocimetry. *Meas. Sci. Technol*., 8, pp.1393-1398.

*Mechanics*, Lisbon, Portugal, 1, pp.3.3.1-3.3.9, 13-16 July.

*anemometry.* Academic press, London.

**4. Conclusion** 

a systematic velocity bias for the LDA case.

who have reviewed this manuscript.

279, pp.1-47.

**5. Acknowledgment** 

**6. References** 

Fig. 11. Typical vorticity fields in the a) *y-z* plane @ x'/D2=0.19 and b) *x'-r* plane @ =60. c) Qualitative interpretation of experimental data. (Adapted from Wong *et al.* 2008 and reprinted with permission from Cambridge University Press).

### **4. Conclusion**

254 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

300 200 100 0 -100 -200 -300 -400 -500

Centrebody vortex pair

> Centrebody vortex


vorticity sign

Core of emerging jet

Edge 1 vortex pair

0.5

0.9


c)


0

0.5

z/D2

1

a)

y

Fig. 11. Typical vorticity fields in the a) *y-z* plane @ x'/D2=0.19 and b) *x'-r* plane @ =60. c) Qualitative interpretation of experimental data. (Adapted from Wong *et al.* 2008 and

Edge 1 vortex pair

0

0.5

Edge 2 vortex

x'/D2

1

Flow convergence

(1/s) (1/s)

Edge 2 vortex pair

Focus & Saddle


Region Saddle

<sup>y</sup> b)

(Edge 3 vortex) Hard to distinguish in axial vorticity plots,

Centrebody therefore not discussed

reprinted with permission from Cambridge University Press).

The study illustrates that a pre-requisite to the detailed application of laser diagnostic tools such as PIV and LDA is an adequate understanding of the qualitative features of the flow of interest. This is necessary for the design and careful application of appropriate triggering conditional statistics. When dealing with turbulent flow coupled with time-variant threedimensional fluidic oscillations, it is important to match the flow conditions with the technical limits of the flow instrumentation. For the investigation of the fluidic precessing jet flow, the Schmitt filter was found to be effective in allowing two carefully-placed hot wire probes to provide a trigger to discriminate for both phase and direction of the oscillation, both of which vary randomly. This trigger allowed resolution of the azimuthal component of the flow velocity in the PIV data, which were smoothed out in the LDA measurements and also triggered on phase only, and not on direction. For the measurement of unconditioned statistics, such as the mean and *r.m.s.* statistical quantities, good agreement was found here between the PIV and LDA techniques for those regions of the flow in which both techniques were well seeded. As expected, some disagreements were found in those regions of the flow in which the seeding of the ambient air was poor, due to the nonuniform seeding technique, where the strong entrainment of unseeded ambient fluid led to a systematic velocity bias for the LDA case.

### **5. Acknowledgment**

The authors acknowledge the Australian Research Council, Schools of Mechanical and Chemical Engineering (University of Adelaide) and Division of Mechanical Engineering (University of Wales, Cardiff) for various in-kind assistance, equipment and facility support. CYW also acknowledges the International Postgraduate Research Scholarship that enabled this research to be conducted. The authors are also grateful to the various peer-reviewers who have reviewed this manuscript.

### **6. References**


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**Micro-PIV Applications** 

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**Micro-PIV Applications** 

258 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

Zdravkovich M.M., Flaherty A.J., Pahle M.G. & Skelhorne I.A. (1998). Some aerodynamic

**10** 

*USA* 

**µ-PIV for the Analysis of Flow Fields near** 

Eiichiro Yamaguchi, Bradford J. Smith and Donald P. Gaver III

Understanding the micro-scale multi-phase fluid dynamics in the respiratory system during the airway re-opening process has been considered as one of the key aspects necessary to

In a healthy lung, the inside surface of respiratory airways is coated with a thin film of lipids and proteins called lung surfactants (LS) which dynamically alter the surface tension and stabilize airways and reduce the work of breathing. Certain clinical events, such as gastric content aspiration, pneumonia, near-drowning, toxic gas inhalation, or chest/lung trauma will trigger lung surfactant "inactivation". This inactivation is caused by the presence of LS inhibitors, including a variety of water-soluble and surface-active serum protein substances, such as albumin, fibrinogen, and IgG that are normally absent from the airway. These can leak through the capillary membrane from the damaged cells, causing LS to lose its ability to lower surface tension necessary for the lung function (Zasadzinski et al. 2010). Mechanical ventilation is inarguably a necessary life-sustaining form of medical intervention at this stage. However, since the leaked proteins inactivate the lung surfactants, the air-liquid interface exerts a wider range of excessive, irregular mechanical stresses and strains on the delicate and highly-sensitive tissues that make up the airways and alveoli of the lung, resulting ventilator-induced lung injury (VILI). This progressive failure will eventually cause more complex pathological conditions such as Acute Lung Injury (ALI) or Acute Respiratory Distress Syndrome (ARDS). Likewise surfactant deficiency, a hallmark of Respiratory Distress Syndrome of premature infants, leads to large interfacial stress that can damage airways and alveoli during an infant's first breaths which clears amniotic fluid from

Multiple protective techniques to minimize airway epithelial damage have been developed including low-volume ventilation, positive-end-expiratory-pressure, and surfactant replacement therapy (Clements and Avery 1998). Although these techniques have contributed greatly to reducing instances of VILI, further improvements still must be made to better treat patients with fewer resulting complications (Gaver III et al. 2006). There are about 200,000 ARDS cases per year in U.S. with mortality rate of 40-46% (Mclntyre et al.

improve the survival rate of clinical treatments for various respiratory diseases.

the airways is it introduces air to the deep lung and alveoli.

2000; Ware and Matthay 2000).

**1. Introduction 1.1 Background** 

**a Propagating Air-Liquid Interface** 

*Department of Biomedical Engineering* 

*Tulane University* 

## **µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface**

Eiichiro Yamaguchi, Bradford J. Smith and Donald P. Gaver III

*Department of Biomedical Engineering Tulane University USA* 

### **1. Introduction**

#### **1.1 Background**

Understanding the micro-scale multi-phase fluid dynamics in the respiratory system during the airway re-opening process has been considered as one of the key aspects necessary to improve the survival rate of clinical treatments for various respiratory diseases.

In a healthy lung, the inside surface of respiratory airways is coated with a thin film of lipids and proteins called lung surfactants (LS) which dynamically alter the surface tension and stabilize airways and reduce the work of breathing. Certain clinical events, such as gastric content aspiration, pneumonia, near-drowning, toxic gas inhalation, or chest/lung trauma will trigger lung surfactant "inactivation". This inactivation is caused by the presence of LS inhibitors, including a variety of water-soluble and surface-active serum protein substances, such as albumin, fibrinogen, and IgG that are normally absent from the airway. These can leak through the capillary membrane from the damaged cells, causing LS to lose its ability to lower surface tension necessary for the lung function (Zasadzinski et al. 2010). Mechanical ventilation is inarguably a necessary life-sustaining form of medical intervention at this stage. However, since the leaked proteins inactivate the lung surfactants, the air-liquid interface exerts a wider range of excessive, irregular mechanical stresses and strains on the delicate and highly-sensitive tissues that make up the airways and alveoli of the lung, resulting ventilator-induced lung injury (VILI). This progressive failure will eventually cause more complex pathological conditions such as Acute Lung Injury (ALI) or Acute Respiratory Distress Syndrome (ARDS). Likewise surfactant deficiency, a hallmark of Respiratory Distress Syndrome of premature infants, leads to large interfacial stress that can damage airways and alveoli during an infant's first breaths which clears amniotic fluid from the airways is it introduces air to the deep lung and alveoli.

Multiple protective techniques to minimize airway epithelial damage have been developed including low-volume ventilation, positive-end-expiratory-pressure, and surfactant replacement therapy (Clements and Avery 1998). Although these techniques have contributed greatly to reducing instances of VILI, further improvements still must be made to better treat patients with fewer resulting complications (Gaver III et al. 2006). There are about 200,000 ARDS cases per year in U.S. with mortality rate of 40-46% (Mclntyre et al. 2000; Ware and Matthay 2000).

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 263

progressing semi-infinite bubble tip is dominated by convective transport driven by hydrodynamics movement of the liquid phase (Fig. 2). The complex convective transport dynamics occurring during pulsatile bubble propagation are further explored using finite time Lyapunov exponents (Smith et al. 2011). During the bubble forward and retrograde bubble propagation, converging and diverging stagnation regions exist on the bubble surface due to the flow circulation in the liquid phase. It causes non-uniform nonequilibrium surfactant concentration distribution along the interface. The experimental data of pulsating bubble surfactometer (Fig. 2-i) indicates that the distribution will cause significant difference of surface tension along the interface resulting non-uniform normal stress and tangential Marangoni stress distributions across the interface. Since the shape of the bubble tip interface and thickness of liquid deposited in the wake of propagating bubble

> /

(i) (ii)

bubble interface shape accordingly.

Fig. 2. (i) Hysteresis loop of dynamic surface tension from the pulsating bubble

indicate that pulsatile bubble motion generates a non-uniform non-equilibrium LS

concentration across the interface, and the resulting Marangoni stress distribution alters the

surfactometer, and graphical schemes of LS layer formation during (a) spreading and (b) collapsing of the surface (Krueger and Gaver III 2000). (ii) Prediction schemes of LS collapse and spread patterns during (a) forward progressing and (b) retracting mean motion of bubble tip. Bright spots on the fluorescent particle images on the right panels show particle flocculation indicating converging/diverging stagnation points in corresponding mean flow motions (Yamaguchi et al. 2009). The experimental observations and computer simulations

fluid, *γ* is the interfacial tension, and *U* is the mean flow velocity (Fairbrother and Stubbs 1935), wide deviation of the interface shapes will be expected from range of surface tension during the pulsatile motions (Fig. 2-ii). The non-equilibrium stresses and interface shapes during the retracting motion will reduce both the pressure drop and deleterious mechanical stresses on the epithelial cells (Ghadialli and Gaver, 2003; Ratulowski and Chang, 1990; Yap and Gaver, 1998). Theoretical studies by Zimmer et al. (2005) suggest that pulsatile motion

, where *μ* is the dynamic viscosity of the

can be defined by capillary number, *Ca U*

Gaver III et al. (1990; 1996) modeled the airway re-opening process by propagating a semiinfinite bubble into a narrow fluid-occluded channel with walls coated by pulmonary epithelial cells. Bilek et al. (2003) and Key et al. (2004) demonstrated using *in vitro* studies that the rate of cell damage increases with decreasing bubble propagation speed. With the aid of computational simulations, further analyses of the experimental results have indicated that the pressure gradient, not shear stress, is primarily responsible for cellular damage. The pressure gradient is the only stress component to increase with decreasing bubble velocity in the target flow conditions, indicating that excessive pressure gradients damage the cellular lining of the airway. That study has confirmed that the widely accepted stress prediction model of the collapsed airway reopening (Fig. 1) can be applied to rigid tube models.

Fig. 1. Schematic of the stress distribution prediction from a model of flexible airway reopening (Gaver III et al. 1996). The cells far downstream are unstressed (1). As the bubble approaches, the cell is pulled up and toward the bubble (2). As the bubble passes, the cell is pushed away from the bubble (3). After the bubble has passed, the cell is pushed outward (4).

Follow-up studies by numerous groups have investigated this system and were found to be consistent with the theoretical predictions (Jacob and Gaver III 2005; Huh et al. 2007; Yalcin et al. 2007). Furthermore, Jacob and Gaver III (2005) included the influence of cell topography into the computational model, and found that the pressure gradient acting on the epithelial cells was even more pronounced than the original computations had demonstrated. These results have led to an interest in more detailed information of local fluid dynamics near the tip of the penetrating semi-infinite bubble. Smith & Gaver (2008) computationally investigated the flow fields surrounding a pulsating finger of air as it propagated along a rigid tube filled with a viscous Newtonian fluid. That study provides highly dynamic and intriguing spatial and temporal characteristics of the flow dynamics surrounding the bubble tip, and further elucidates the established relationship between pressure gradient and bubble velocity.

Since inactivated or insufficient amount of lung surfactants are one of important factors for controlling the cellar damage during the airway reopening, diffusive molecular transport of LS near the air-liquid interface including mechanism of competitive adsorption between lung surfactant and the inhibitors are well-studied areas (Refer to the review article of the surfactant inactivation by Zasadzinski et al. (2010) for detail.). It is predicted that for the airway reopening case, collapsing and re-spreading process of LS layer at the surface of the

Gaver III et al. (1990; 1996) modeled the airway re-opening process by propagating a semiinfinite bubble into a narrow fluid-occluded channel with walls coated by pulmonary epithelial cells. Bilek et al. (2003) and Key et al. (2004) demonstrated using *in vitro* studies that the rate of cell damage increases with decreasing bubble propagation speed. With the aid of computational simulations, further analyses of the experimental results have indicated that the pressure gradient, not shear stress, is primarily responsible for cellular damage. The pressure gradient is the only stress component to increase with decreasing bubble velocity in the target flow conditions, indicating that excessive pressure gradients damage the cellular lining of the airway. That study has confirmed that the widely accepted stress prediction model of the

collapsed airway reopening (Fig. 1) can be applied to rigid tube models.

Fig. 1. Schematic of the stress distribution prediction from a model of flexible airway reopening (Gaver III et al. 1996). The cells far downstream are unstressed (1). As the bubble approaches, the cell is pulled up and toward the bubble (2). As the bubble passes, the cell is pushed away from the bubble (3). After the bubble has passed, the cell is pushed outward (4).

elucidates the established relationship between pressure gradient and bubble velocity.

Since inactivated or insufficient amount of lung surfactants are one of important factors for controlling the cellar damage during the airway reopening, diffusive molecular transport of LS near the air-liquid interface including mechanism of competitive adsorption between lung surfactant and the inhibitors are well-studied areas (Refer to the review article of the surfactant inactivation by Zasadzinski et al. (2010) for detail.). It is predicted that for the airway reopening case, collapsing and re-spreading process of LS layer at the surface of the

Follow-up studies by numerous groups have investigated this system and were found to be consistent with the theoretical predictions (Jacob and Gaver III 2005; Huh et al. 2007; Yalcin et al. 2007). Furthermore, Jacob and Gaver III (2005) included the influence of cell topography into the computational model, and found that the pressure gradient acting on the epithelial cells was even more pronounced than the original computations had demonstrated. These results have led to an interest in more detailed information of local fluid dynamics near the tip of the penetrating semi-infinite bubble. Smith & Gaver (2008) computationally investigated the flow fields surrounding a pulsating finger of air as it propagated along a rigid tube filled with a viscous Newtonian fluid. That study provides highly dynamic and intriguing spatial and temporal characteristics of the flow dynamics surrounding the bubble tip, and further progressing semi-infinite bubble tip is dominated by convective transport driven by hydrodynamics movement of the liquid phase (Fig. 2). The complex convective transport dynamics occurring during pulsatile bubble propagation are further explored using finite time Lyapunov exponents (Smith et al. 2011). During the bubble forward and retrograde bubble propagation, converging and diverging stagnation regions exist on the bubble surface due to the flow circulation in the liquid phase. It causes non-uniform nonequilibrium surfactant concentration distribution along the interface. The experimental data of pulsating bubble surfactometer (Fig. 2-i) indicates that the distribution will cause significant difference of surface tension along the interface resulting non-uniform normal stress and tangential Marangoni stress distributions across the interface. Since the shape of the bubble tip interface and thickness of liquid deposited in the wake of propagating bubble can be defined by capillary number, *Ca U* / , where *μ* is the dynamic viscosity of the fluid, *γ* is the interfacial tension, and *U* is the mean flow velocity (Fairbrother and Stubbs 1935), wide deviation of the interface shapes will be expected from range of surface tension during the pulsatile motions (Fig. 2-ii). The non-equilibrium stresses and interface shapes during the retracting motion will reduce both the pressure drop and deleterious mechanical stresses on the epithelial cells (Ghadialli and Gaver, 2003; Ratulowski and Chang, 1990; Yap and Gaver, 1998). Theoretical studies by Zimmer et al. (2005) suggest that pulsatile motion

Fig. 2. (i) Hysteresis loop of dynamic surface tension from the pulsating bubble surfactometer, and graphical schemes of LS layer formation during (a) spreading and (b) collapsing of the surface (Krueger and Gaver III 2000). (ii) Prediction schemes of LS collapse and spread patterns during (a) forward progressing and (b) retracting mean motion of bubble tip. Bright spots on the fluorescent particle images on the right panels show particle flocculation indicating converging/diverging stagnation points in corresponding mean flow motions (Yamaguchi et al. 2009). The experimental observations and computer simulations indicate that pulsatile bubble motion generates a non-uniform non-equilibrium LS concentration across the interface, and the resulting Marangoni stress distribution alters the bubble interface shape accordingly.

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 265

observation window regardless of the direction of bubble propagation. The combination of linear actuators and the translating stage allowed the tracking of progressing bubble tip over 10-12 cm continuously, and made it possible to obtain the flow fields under realistic airway

Even though it is still possible to statistically estimate the geographical location and shape of the air-liquid interface, the method does not provide sufficient accuracy to examine the bubble tip shapes under a complex flow input where the interface may experience large deformations imposed by a quick alteration of local surface tension resulted from collapsing and re-spreading of the lung surfactant on the interface. Separately obtained ensemble averaged shadowgraph images under the same flow condition could help to improve the estimation of the bubble shape deformations in relatively stable case. Smith, et al. (2011) utilize shadowgraph and µ-PIV data to examine molecular transport phenomena near the interface of the pulsating bubbles by combining the experimental data and the Finite-Time Lyapunov Exponent (FTLE), and the Boundary Element Method (BEM). They used a strobe flash lamp as the backlight illumination source, and repeat the same data acquisition process they did for µ-PIV with the addition of a custom-made microscale position indicator. Since the shadowgraph image does not contain any spatial or dynamic information to connect to corresponding PIV data, the absolute position of the bubble tip was the only information used to estimate the mean velocity input at a given instant. The different refractive index of air and liquid phases imposes a clearly visible interfacial shadow on the image. The instantaneous interfacial shapes were then averaged in discrete intervals determined by the position indicator. The ensemble-averaged bubble shapes were then superimposed on the previously obtained flow fields to give a complete description of the flow field near the interface. Although the separate shadowgraph and PIV acquisition provided satisfactory results for this simple case, the ambiguity on the estimation of mean velocity from the position indicator, difficulty of reproducing multiple identical experiments, and complex post-processing scheme will pose clear limitations for the detailed flow analysis of more

In order to overcome these disadvantages, the simultaneous use of PIV and a pulsed shadowgraph technique to detect the precise position of air-liquid interface in slug flows for relatively large size capillaries (about 2-3 cm of diameter) was performed by Norueria et al. (2003). That group utilized a Nd:YAG laser sheet illumination technique originally used for PIV and a sheet of LED arrays for uniform backlight illumination for the pulsed shadowgraph. A single camera was used to acquire PIV and shadowgraph data simultaneously. The image was then separated during the post-processing to give an accurate instantaneous interface shape for the flow field analysis. Although it has provided sufficient accuracy and great simplicity for the relatively large scale slug flow measurement, the single camera and post–process separation are not suitable for the current microscale multiphase application. The reliability of the post process separation is limited by the low signal-to-noise (S/N) ratio at the center of the tube and near the air-liquid interface. Here, the combination of the volumetric illumination technique (μ-PIV) in conjunction with a nonuniform channel depth provides the greatest amount of noise along with strong random refraction patterns of the fluorescent emission. To compensate for this type of problem, Meinhart et al. (2000) proposed a phase-averaged velocity field algorithm to overcome these low signal-to-noise ratio situations; however, this technique is difficult to implement in a multi-phase flow scenario. Additionally, Mielink and Saetran (2006) proposed a selective

reopening patterns, such as simulated pulsatile ventilation.

unstable and realistic flow conditions.

may concentrate surfactant in high resistance regions near the progressing bubble. The bulk pressure drop measurement of a pulsating progressing bubble with LS in rigid cylindrical capillary (Pillert and Gaver III 2009) and *in-vitro* experiment of cell damage during the simulated airway reopening (Glindmeyer et al. 2011) confirmed this theory, and shown that pulsatile motion significantly reduced cell damage in comparison to linear motion airway reopening.

Due to the technical difficulties associated with whole field fluid dynamics measurements of such an unsteady interface, no experimental data are available to confirm the micro-scale relationship between the convection patterns in the sub-layer and LS distributions with local pressure and shear stress distributions. These factors also limit the investigation of LS inactivation, since identifying the difference between the inactivation and lack of LS in terms of the interface shape and the convection pattern will provide significant insight to understand the competitive adsorption mechanics.

### **1.2 Flow visualization of progressing semi-infinite bubble tip**

Particle image velocimetry (PIV) is a well established and highly versatile technology for investigating the hydrodynamic properties of macro- and micro-scale flows (Adrian 2005). In micro-particle image velocimetry (μ-PIV) experiments, the entire test section volume is illuminated using a cone of light emanating from the recording lens, rather than the light sheet used in conventional PIV. The narrow focal depth of the objective lens results in a pseudo 2-D plane of focused particles for the correlation procedure (Santiago et al. 1998). A proper set of fluorescent seeding particles and an optical high-pass filter are employed to separate the signal from background noise. These innovations reduce the difficulties involved in creating a light sheet at the micron scale and in fabricating a microfluidic apparatus with multi-angled optical access windows that would otherwise be necessary with conventional PIV. As such, this technique is suitable to obtain instantaneous wholefield velocity information on the micro-scale.

Yamaguchi et al. (2009) performed µ-PIV investigations of flow fields surrounding a steadily progressing semi-infinite bubble tip in a smoothed wall straight glass capillary having a diameter of 312 µm. They employed a computer-controlled linear actuator system to control the steady propagation of a long finger of air, and let the bubble tip pass repeatedly under the fixed microscope observation window at controlled timing. The repeated data acquisition was necessary because the contributions of Brownian motion to an instantaneous velocity field are relatively significant and cannot be ignored due to the micron-size of the seeding particles, combined with their small displacements near the capillary tube wall. The location of the air-liquid interface in the fluorescent particle image was statistically estimated from accumulated instantaneous vector fields by identifying the significant rise of velocity fluctuations across the interface. The ensemble averaging method successfully reduced related errors for the steady low-Reynolds number flow measurements. The obtained ensemble averaged flow fields agree very well with the previously obtained computational simulations. Later the group developed a translating microscope stage system (Fig. 3) to vastly improve the capability and efficiency of image acquisition under complex flow patterns (Smith et al. 2010). The translating stage is a computer controlled sliding microscope stage that is programmed to give a counter motion opposite to the mean flow input. Therefore, in theory, the progressing bubble tip stays in the microscope

may concentrate surfactant in high resistance regions near the progressing bubble. The bulk pressure drop measurement of a pulsating progressing bubble with LS in rigid cylindrical capillary (Pillert and Gaver III 2009) and *in-vitro* experiment of cell damage during the simulated airway reopening (Glindmeyer et al. 2011) confirmed this theory, and shown that pulsatile motion significantly reduced cell damage in comparison to linear motion airway

Due to the technical difficulties associated with whole field fluid dynamics measurements of such an unsteady interface, no experimental data are available to confirm the micro-scale relationship between the convection patterns in the sub-layer and LS distributions with local pressure and shear stress distributions. These factors also limit the investigation of LS inactivation, since identifying the difference between the inactivation and lack of LS in terms of the interface shape and the convection pattern will provide significant insight to

Particle image velocimetry (PIV) is a well established and highly versatile technology for investigating the hydrodynamic properties of macro- and micro-scale flows (Adrian 2005). In micro-particle image velocimetry (μ-PIV) experiments, the entire test section volume is illuminated using a cone of light emanating from the recording lens, rather than the light sheet used in conventional PIV. The narrow focal depth of the objective lens results in a pseudo 2-D plane of focused particles for the correlation procedure (Santiago et al. 1998). A proper set of fluorescent seeding particles and an optical high-pass filter are employed to separate the signal from background noise. These innovations reduce the difficulties involved in creating a light sheet at the micron scale and in fabricating a microfluidic apparatus with multi-angled optical access windows that would otherwise be necessary with conventional PIV. As such, this technique is suitable to obtain instantaneous whole-

Yamaguchi et al. (2009) performed µ-PIV investigations of flow fields surrounding a steadily progressing semi-infinite bubble tip in a smoothed wall straight glass capillary having a diameter of 312 µm. They employed a computer-controlled linear actuator system to control the steady propagation of a long finger of air, and let the bubble tip pass repeatedly under the fixed microscope observation window at controlled timing. The repeated data acquisition was necessary because the contributions of Brownian motion to an instantaneous velocity field are relatively significant and cannot be ignored due to the micron-size of the seeding particles, combined with their small displacements near the capillary tube wall. The location of the air-liquid interface in the fluorescent particle image was statistically estimated from accumulated instantaneous vector fields by identifying the significant rise of velocity fluctuations across the interface. The ensemble averaging method successfully reduced related errors for the steady low-Reynolds number flow measurements. The obtained ensemble averaged flow fields agree very well with the previously obtained computational simulations. Later the group developed a translating microscope stage system (Fig. 3) to vastly improve the capability and efficiency of image acquisition under complex flow patterns (Smith et al. 2010). The translating stage is a computer controlled sliding microscope stage that is programmed to give a counter motion opposite to the mean flow input. Therefore, in theory, the progressing bubble tip stays in the microscope

reopening.

understand the competitive adsorption mechanics.

field velocity information on the micro-scale.

**1.2 Flow visualization of progressing semi-infinite bubble tip** 

observation window regardless of the direction of bubble propagation. The combination of linear actuators and the translating stage allowed the tracking of progressing bubble tip over 10-12 cm continuously, and made it possible to obtain the flow fields under realistic airway reopening patterns, such as simulated pulsatile ventilation.

Even though it is still possible to statistically estimate the geographical location and shape of the air-liquid interface, the method does not provide sufficient accuracy to examine the bubble tip shapes under a complex flow input where the interface may experience large deformations imposed by a quick alteration of local surface tension resulted from collapsing and re-spreading of the lung surfactant on the interface. Separately obtained ensemble averaged shadowgraph images under the same flow condition could help to improve the estimation of the bubble shape deformations in relatively stable case. Smith, et al. (2011) utilize shadowgraph and µ-PIV data to examine molecular transport phenomena near the interface of the pulsating bubbles by combining the experimental data and the Finite-Time Lyapunov Exponent (FTLE), and the Boundary Element Method (BEM). They used a strobe flash lamp as the backlight illumination source, and repeat the same data acquisition process they did for µ-PIV with the addition of a custom-made microscale position indicator. Since the shadowgraph image does not contain any spatial or dynamic information to connect to corresponding PIV data, the absolute position of the bubble tip was the only information used to estimate the mean velocity input at a given instant. The different refractive index of air and liquid phases imposes a clearly visible interfacial shadow on the image. The instantaneous interfacial shapes were then averaged in discrete intervals determined by the position indicator. The ensemble-averaged bubble shapes were then superimposed on the previously obtained flow fields to give a complete description of the flow field near the interface. Although the separate shadowgraph and PIV acquisition provided satisfactory results for this simple case, the ambiguity on the estimation of mean velocity from the position indicator, difficulty of reproducing multiple identical experiments, and complex post-processing scheme will pose clear limitations for the detailed flow analysis of more unstable and realistic flow conditions.

In order to overcome these disadvantages, the simultaneous use of PIV and a pulsed shadowgraph technique to detect the precise position of air-liquid interface in slug flows for relatively large size capillaries (about 2-3 cm of diameter) was performed by Norueria et al. (2003). That group utilized a Nd:YAG laser sheet illumination technique originally used for PIV and a sheet of LED arrays for uniform backlight illumination for the pulsed shadowgraph. A single camera was used to acquire PIV and shadowgraph data simultaneously. The image was then separated during the post-processing to give an accurate instantaneous interface shape for the flow field analysis. Although it has provided sufficient accuracy and great simplicity for the relatively large scale slug flow measurement, the single camera and post–process separation are not suitable for the current microscale multiphase application. The reliability of the post process separation is limited by the low signal-to-noise (S/N) ratio at the center of the tube and near the air-liquid interface. Here, the combination of the volumetric illumination technique (μ-PIV) in conjunction with a nonuniform channel depth provides the greatest amount of noise along with strong random refraction patterns of the fluorescent emission. To compensate for this type of problem, Meinhart et al. (2000) proposed a phase-averaged velocity field algorithm to overcome these low signal-to-noise ratio situations; however, this technique is difficult to implement in a multi-phase flow scenario. Additionally, Mielink and Saetran (2006) proposed a selective

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 267

polyimide protective layer (Flexible Fused Silica Capillary Tubing, Polymicro Technologies, AZ) was selected because of good optical transparency and flexibility. The capillary tube was trimmed to approximately 30cm in length and the middle section (about 10 cm) of the external protective layer was carefully removed to increase the optical transparency of the observation region. It should be noted that the removal of the protecting layer will drastically decrease resistance to any kind of stress inputs, and the testing section will become extremely fragile. However, it was necessary to overcome the low transparency of the test liquid (as discussed below in the sample preparation section) in order to maintain the required fluorescent seeding density. Therefore, the removal of the protective coating would not be required for certain low seeding density applications. The capillary generally provides good transparency under Nd:YAG laser with the protective layer (Natrajan et al.

Two identical capillary tubes were closely aligned in parallel, and glued onto a 12.5x5 cm microscope slide at both ends. In order to make the capillary section straight, a custommade holding clamp was used to provide a small amount of tension while adjusting the capillary positions on the slide glass. A custom fabricated water jacket was attached on the top of the glass slide and carefully sealed, allowing temperature control of a water reservoir at 37C during the experiments. The finished apparatus has at least 10cm of continuous observation section for two identical capillary tubes in parallel. The setting of the parallel channels was necessary to capture the bubble tip motion (the upper channel) and the stage movement (the lower quiescent channel) simultaneously (Fig. 3-iii). Even though the motion of the translating stage system is controlled by a precision linear motor, it was impossible to eliminate many sources of mechanical vibrations during the experiment. Therefore the acquisition of precise instantaneous stage movement was necessary to accurately recover actual subtracted mean velocity from the pulsatile bubble motion. To do so, the µ-PIV was used to simultaneously measure the solid body motion of a 'tracking channel' attached to the stage in order to identify the stage velocity. The 3:7 of Glycerol:Water solution with 0.02 vol% of fluorescent particles (see the sample preparation for the seeding particle choice) was mixed to achieve a neutral buoyancy, and the tracking channel was filled with the liquid and sealed on both side to prevent any external input during the experiment. The experimental channel was connected to 1/16" PEEK tubing through sets of micro-tubing attachments (Upchurch, CA) to connect the flow generating unit. Finally, the apparatus was set on the translating stage to perform continuous data acquisition of a progressing bubble

over 10-12 cm of capillary under various temperatures in single experiment.

An electromagnetic precision actuator system (Electromagnetic direct linear motor P01- 23x80/30x90 and E200-AT, LinMot Incorporated, Switzerland) was employed to control the bubble movement. The linear motor system consists of a magnetically driven actuator with a computer-based feedback and control system. The actuator is composed of a fixed stator with a linearly-aligned electromagnet and a position sensor for feedback, paired with a magnet-filled slider. It is driven by a servo controller that is run using supplied programming and monitoring software (LinMot-Talk, LinMot Inc.). The actuator has a speed range of 1 mm/sec to 20 cm/sec with less than 0.1 % position error at a 10 cm stroke. The translating stage and appropriate sizes of micro-syringes were attached directly to the

**2.2 Flow generating system and the pulsatile flow input setting** 

slider to provide a wide range of flexibility and control.

2007).

seeding method to reduce out-of-focus noise. Unfortunately, the 3-D nature of the flows investigated in our study make this technique untenable.

It is, therefore, necessary for the current application to optically separate the simultaneously acquired µ-PIV and shadowgraph images, and then record these images on two separate identical monochrome CCDs. The separation can be done by combining the proper choice of illumination sources, fluorescent materials, and epi-fluorescent filters. The images from two CCDs are then combined in post-processing to give accurate air-liquid interface information for the vector interrogation of the fluorescent images. Even though the implementation of the two cameras increases the complexity of the system development especially for optical adjustments and calibrations, it is expected to; i) be more affordable than using a three-CCD PIV capable camera, ii) have cleaner image separation by the eliminating signal interferences, and iii) have simpler post-processing.

### **2. Experiments**

The development and descriptions of two-camera two-laser -PIV/Shadowgraph simultaneous data acquisition system will be described in this section. The includes the experimental setup and a brief explanation of the previously developed flow controlling system and the translating stage. Since the actual observation of the complex micro-multiphase flows that include measurement of fluid flow fields in the neighborhood of propagating semi-infinite bubble having unsteady motions under influence of the lung surfactant can only be accomplished by combining and controlling the custom-made apparatus, the flow generating system, and the translating stage for continuous data acquisition, it is important to have dedicated subsections for each component.

#### **2.1 Assembly of flow apparatus and the translating stage system**

Continuous data acquisition of the progressing semi-infinite bubble is required for the current applications. It would not be practical to have a combination of a wide view lens with a super hi-resolution CCD in order to maintain enough spatial resolution for such a moving interface. Instead, the implementation of an interface tracking device and a moderate resolution CCD to keep the bubble tip within the fixed microscope observation window is a more practical and versatile solution to the target application. The computercontrolled translating microscope stage has been developed for this purpose. In summary, the translating stage keeps the relative position of the bubble tip within a fixed microscope observation window by mechanically sliding the entire microscope observation stage to cancel the given flow input. (a tread mill would be the closest analogy.) Precision 3-axis adjustable mechanisms for the flow apparatus allow alignment under the microscope for a flexible channel and the objective lens choices. The stage motion is controlled by attaching a computer-programmable linear actuator. A detailed technical description of this device is found in Smith et al. (2010) (Fig. 3-i provides a computer rendering of the translating stage.).

A uniform cylindrical channel with a smooth wall is the appropriate choice for the current experimental setup to the simulate airway reopening process, since most of the previous theoretical/experimental studies were associated with the similar geometrical configuration as discussed in previous section. A capillary tube made of fused silica coated with a

seeding method to reduce out-of-focus noise. Unfortunately, the 3-D nature of the flows

It is, therefore, necessary for the current application to optically separate the simultaneously acquired µ-PIV and shadowgraph images, and then record these images on two separate identical monochrome CCDs. The separation can be done by combining the proper choice of illumination sources, fluorescent materials, and epi-fluorescent filters. The images from two CCDs are then combined in post-processing to give accurate air-liquid interface information for the vector interrogation of the fluorescent images. Even though the implementation of the two cameras increases the complexity of the system development especially for optical adjustments and calibrations, it is expected to; i) be more affordable than using a three-CCD PIV capable camera, ii) have cleaner image separation by the eliminating signal

The development and descriptions of two-camera two-laser -PIV/Shadowgraph simultaneous data acquisition system will be described in this section. The includes the experimental setup and a brief explanation of the previously developed flow controlling system and the translating stage. Since the actual observation of the complex micro-multiphase flows that include measurement of fluid flow fields in the neighborhood of propagating semi-infinite bubble having unsteady motions under influence of the lung surfactant can only be accomplished by combining and controlling the custom-made apparatus, the flow generating system, and the translating stage for continuous data

Continuous data acquisition of the progressing semi-infinite bubble is required for the current applications. It would not be practical to have a combination of a wide view lens with a super hi-resolution CCD in order to maintain enough spatial resolution for such a moving interface. Instead, the implementation of an interface tracking device and a moderate resolution CCD to keep the bubble tip within the fixed microscope observation window is a more practical and versatile solution to the target application. The computercontrolled translating microscope stage has been developed for this purpose. In summary, the translating stage keeps the relative position of the bubble tip within a fixed microscope observation window by mechanically sliding the entire microscope observation stage to cancel the given flow input. (a tread mill would be the closest analogy.) Precision 3-axis adjustable mechanisms for the flow apparatus allow alignment under the microscope for a flexible channel and the objective lens choices. The stage motion is controlled by attaching a computer-programmable linear actuator. A detailed technical description of this device is found in Smith et al. (2010) (Fig. 3-i provides a computer rendering of the translating

A uniform cylindrical channel with a smooth wall is the appropriate choice for the current experimental setup to the simulate airway reopening process, since most of the previous theoretical/experimental studies were associated with the similar geometrical configuration as discussed in previous section. A capillary tube made of fused silica coated with a

acquisition, it is important to have dedicated subsections for each component.

**2.1 Assembly of flow apparatus and the translating stage system** 

investigated in our study make this technique untenable.

interferences, and iii) have simpler post-processing.

**2. Experiments** 

stage.).

polyimide protective layer (Flexible Fused Silica Capillary Tubing, Polymicro Technologies, AZ) was selected because of good optical transparency and flexibility. The capillary tube was trimmed to approximately 30cm in length and the middle section (about 10 cm) of the external protective layer was carefully removed to increase the optical transparency of the observation region. It should be noted that the removal of the protecting layer will drastically decrease resistance to any kind of stress inputs, and the testing section will become extremely fragile. However, it was necessary to overcome the low transparency of the test liquid (as discussed below in the sample preparation section) in order to maintain the required fluorescent seeding density. Therefore, the removal of the protective coating would not be required for certain low seeding density applications. The capillary generally provides good transparency under Nd:YAG laser with the protective layer (Natrajan et al. 2007).

Two identical capillary tubes were closely aligned in parallel, and glued onto a 12.5x5 cm microscope slide at both ends. In order to make the capillary section straight, a custommade holding clamp was used to provide a small amount of tension while adjusting the capillary positions on the slide glass. A custom fabricated water jacket was attached on the top of the glass slide and carefully sealed, allowing temperature control of a water reservoir at 37C during the experiments. The finished apparatus has at least 10cm of continuous observation section for two identical capillary tubes in parallel. The setting of the parallel channels was necessary to capture the bubble tip motion (the upper channel) and the stage movement (the lower quiescent channel) simultaneously (Fig. 3-iii). Even though the motion of the translating stage system is controlled by a precision linear motor, it was impossible to eliminate many sources of mechanical vibrations during the experiment. Therefore the acquisition of precise instantaneous stage movement was necessary to accurately recover actual subtracted mean velocity from the pulsatile bubble motion. To do so, the µ-PIV was used to simultaneously measure the solid body motion of a 'tracking channel' attached to the stage in order to identify the stage velocity. The 3:7 of Glycerol:Water solution with 0.02 vol% of fluorescent particles (see the sample preparation for the seeding particle choice) was mixed to achieve a neutral buoyancy, and the tracking channel was filled with the liquid and sealed on both side to prevent any external input during the experiment. The experimental channel was connected to 1/16" PEEK tubing through sets of micro-tubing attachments (Upchurch, CA) to connect the flow generating unit. Finally, the apparatus was set on the translating stage to perform continuous data acquisition of a progressing bubble over 10-12 cm of capillary under various temperatures in single experiment.

#### **2.2 Flow generating system and the pulsatile flow input setting**

An electromagnetic precision actuator system (Electromagnetic direct linear motor P01- 23x80/30x90 and E200-AT, LinMot Incorporated, Switzerland) was employed to control the bubble movement. The linear motor system consists of a magnetically driven actuator with a computer-based feedback and control system. The actuator is composed of a fixed stator with a linearly-aligned electromagnet and a position sensor for feedback, paired with a magnet-filled slider. It is driven by a servo controller that is run using supplied programming and monitoring software (LinMot-Talk, LinMot Inc.). The actuator has a speed range of 1 mm/sec to 20 cm/sec with less than 0.1 % position error at a 10 cm stroke. The translating stage and appropriate sizes of micro-syringes were attached directly to the slider to provide a wide range of flexibility and control.

For the current experiment, the pulsatile flow input for simulated airway reopening is defined as the linear addition of a constant mean velocity and a sinusoidal oscillation (Fig. 3). The equation is given as

$$\text{Ca}(t) = \text{Ca}\_M + \text{Ca}\_\Omega \sin(\Omega t) \,\text{,}\tag{1}$$

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 269

operational error of less than 0.1 %. The same linear actuator attached was also attached to the translating stage, and was programmed to give *UM-actuator3*=-5.5 mm/sec during the data acquisition. Therefore the fixed microscope window captures the bubble tip throughout the experiment. As mentioned above, a secondary capillary was used as the instantaneous stage velocity indicator, so the recovery of absolute input velocity and cancellation of mechanical

The μ-PIV/Shadowgraph simultaneous data acquisition system developed for the current application is depicted in Fig. 4. An inverted microscope (Nikon Eclipse TE2000-U, Nikon Corporation, Japan) with a 10x objective lens (*NA*=0.30 Plan Flour, Nikon Corporation, Japan) and two identical 2048x2048 pixel CCD cameras (12 bit, 4MP, TSI POWERVIEW Plus, TSI Incorporated, MN) provides the observation area of 1523x1523 µm with a theoretical pixel resolution of 0.744 µm/pixel. Two cameras are attached to the side optical port by

For the µ-PIV, the volumetric illumination was provided by a dual pulse Nd:YAG laser (*λ*=532 nm, Power=15mJ/pulse, Pulse duration=4 ns, New Wave Laser Pulse Solo Mini, New Wave Research, CA). The beam was directed via fiber optics to an optical port on the microscope. It was then refracted by the epi-fluorescent prism/filter cube and guided through the objective lens to volumetrically illuminate the whole test section under the field of view. The sample liquid inside of the capillary tube was seeded with *dp*=1 µm fluorescent particles (refer to sample preparation section for details) that have excitation/emission peaks at 535/575 nm. Therefore only returning emission from the particles passed the dichroic filer (*λ*>550 nm) in the first cube. Finally, it was navigated to CCD Camera A through the second filter set (epi-fluorescent prism/filter cube 2 in Fig. 4.) to provide a pure

For the shadowgraph, an LED pulsed red laser (*λ*=660 nm, Power=2nJ/pulse, Pulse duration=15ns, MPL-III-660, Opto Engine LLC, UT) was selected for source of the backlight illumination. The laser is directed via fiber optics to the top of the flow apparatus where the collimator (*NA*=0.25, *f*=36.01mm, F810FC-780, ThorLabs, NJ) is attached directly above the observation window providing approximately 1.0 cm diameter spot of uniform illumination. The projected shadowgraph image signal shares the same optical path with the µ-PIV signal. It passes the first and second dichroic filters, and was navigated to CCD

The epi-fluorescent prism/filter cube 2 was selected to minimize cross-talk especially on CCD Camera A due to the signal-to-noise ratio sensitivity of vector interrogation process. Since images on CCD Camera B were used only to detect the bubble interface shape, and unmistakable sharp contrast at the air-liquid interface, clarity of the shadowgraph data was often dominated by setting of the illumination strength. A dichroic prism having a combination of a low-pass filter at 625 nm (625DCLP, Chroma Technology Corp, VT) and a cleaning band pass filter of 595nm/±40nm (D595/40x, Chroma Technology Corp, VT)

Timing of the cameras and lasers were controlled by a multi-channel laser pulse synchronizer (Model 610035, TSI Inc.) which also sends a queue signal for the linear actuator

provided excellent separation of the fluorescent particle image for CCD Camera A.

Camera B to record the shadowgraph image of the air-water interface.

noise from the translating stage can easily be obtained from this information.

**2.3 System configuration and optical setup** 

fluorescent particle image of the test section.

using double port adapter (Y-QT, Nikon Corporation, Japan).

where *CaM*, and *Ca* are the mean and oscillatory capillary numbers (dimensionless velocity expression) where *Ca t U t* () () , with *µ* is fluid viscosity, *γ* is the surface tension, *U(t)* is the cross-sectional average bubble velocity, <sup>2</sup> *Ut Qt R* () () , where *Q(t)* is the timedependent flow rate. Therefore integration over the experimental duration gives the instantaneous actuator position for the flow input of the pulsatile motion;

() cos( ) *Zt U t A t total M* , (2)

where *VM* is the mean velocity, and *A* is amplitude of the oscillation.

Fig. 3*.* (i) Scheme of the translating stage system (Smith et al. 2010), (ii) description of the flow generating system input/output, and (iii) sample microscope image of the testing section. The flow generating system is connected to channel 1, while channel 2 in Fig. 3-iii is used as the stage velocity indicator. The translating stage slides the entire microscope stage to cancel the mean bubble motion. The oscillating motion stays in the fixed microscope observation window. It significantly increases data acquisition ability and efficiency of measuring complex time dependent flows.

In order to examine the significant interfacial deformation and alterations in the flow pattern, parameters must be carefully selected to allow bubble tip retraction during the oscillation cycle without applying unrealistic frequencies and amplitudes. For the current experiment, mean bubble velocity *UM*=5.5 mm/sec, amplitude *A*=2.0 mm, and frequency =2 Hz provide a balance of the continuous acquisition efficiency over 10 seconds and the accuracy of the flow driving system. Since the target capillary tube diameter was 552 µm (see sample preparation section), a 25 µl syringe (Gastight Syringe 1707, Hamilton Company, NV) and 1 l syringe (Microliter Syringe 7000.5, Hamilton Company, NV) were chosen to drive the mean and oscillatory component respectively. Therefore the input parameters for actuator operation were determined to be *UM-actuator1*=2.97 mm/sec, *Aactuator2*=26.97 mm, and *actuator2* =2 Hz. The parameters fit within the range of acceptable operational error of less than 0.1 %. The same linear actuator attached was also attached to the translating stage, and was programmed to give *UM-actuator3*=-5.5 mm/sec during the data acquisition. Therefore the fixed microscope window captures the bubble tip throughout the experiment. As mentioned above, a secondary capillary was used as the instantaneous stage velocity indicator, so the recovery of absolute input velocity and cancellation of mechanical noise from the translating stage can easily be obtained from this information.

### **2.3 System configuration and optical setup**

268 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

For the current experiment, the pulsatile flow input for simulated airway reopening is defined as the linear addition of a constant mean velocity and a sinusoidal oscillation

dependent flow rate. Therefore integration over the experimental duration gives the

() cos( ) *Zt U t A t total M* , (2)

Fig. 3*.* (i) Scheme of the translating stage system (Smith et al. 2010), (ii) description of the flow generating system input/output, and (iii) sample microscope image of the testing section. The flow generating system is connected to channel 1, while channel 2 in Fig. 3-iii is used as the stage velocity indicator. The translating stage slides the entire microscope stage to cancel the mean bubble motion. The oscillating motion stays in the fixed microscope observation window. It significantly increases data acquisition ability and efficiency of

In order to examine the significant interfacial deformation and alterations in the flow pattern, parameters must be carefully selected to allow bubble tip retraction during the oscillation cycle without applying unrealistic frequencies and amplitudes. For the current experiment, mean bubble velocity *UM*=5.5 mm/sec, amplitude *A*=2.0 mm, and frequency

 =2 Hz provide a balance of the continuous acquisition efficiency over 10 seconds and the accuracy of the flow driving system. Since the target capillary tube diameter was 552 µm (see sample preparation section), a 25 µl syringe (Gastight Syringe 1707, Hamilton Company, NV) and 1 l syringe (Microliter Syringe 7000.5, Hamilton Company, NV) were chosen to drive the mean and oscillatory component respectively. Therefore the input parameters for actuator operation were determined to be *UM-actuator1*=2.97 mm/sec,

*actuator2* =2 Hz. The parameters fit within the range of acceptable

*Ca t Ca Ca t* ( ) *<sup>M</sup>* sin( ), (1)

, with *µ* is fluid viscosity, *γ* is the surface tension, *U(t)* is

<sup>2</sup> *Ut Qt R* () () , where *Q(t)* is the time-

are the mean and oscillatory capillary numbers (dimensionless velocity

(Fig. 3). The equation is given as

expression) where *Ca t U t* () ()

measuring complex time dependent flows.

*Aactuator2*=26.97 mm, and

the cross-sectional average bubble velocity,

 

instantaneous actuator position for the flow input of the pulsatile motion;

where *VM* is the mean velocity, and *A* is amplitude of the oscillation.

where *CaM*, and *Ca*

The μ-PIV/Shadowgraph simultaneous data acquisition system developed for the current application is depicted in Fig. 4. An inverted microscope (Nikon Eclipse TE2000-U, Nikon Corporation, Japan) with a 10x objective lens (*NA*=0.30 Plan Flour, Nikon Corporation, Japan) and two identical 2048x2048 pixel CCD cameras (12 bit, 4MP, TSI POWERVIEW Plus, TSI Incorporated, MN) provides the observation area of 1523x1523 µm with a theoretical pixel resolution of 0.744 µm/pixel. Two cameras are attached to the side optical port by using double port adapter (Y-QT, Nikon Corporation, Japan).

For the µ-PIV, the volumetric illumination was provided by a dual pulse Nd:YAG laser (*λ*=532 nm, Power=15mJ/pulse, Pulse duration=4 ns, New Wave Laser Pulse Solo Mini, New Wave Research, CA). The beam was directed via fiber optics to an optical port on the microscope. It was then refracted by the epi-fluorescent prism/filter cube and guided through the objective lens to volumetrically illuminate the whole test section under the field of view. The sample liquid inside of the capillary tube was seeded with *dp*=1 µm fluorescent particles (refer to sample preparation section for details) that have excitation/emission peaks at 535/575 nm. Therefore only returning emission from the particles passed the dichroic filer (*λ*>550 nm) in the first cube. Finally, it was navigated to CCD Camera A through the second filter set (epi-fluorescent prism/filter cube 2 in Fig. 4.) to provide a pure fluorescent particle image of the test section.

For the shadowgraph, an LED pulsed red laser (*λ*=660 nm, Power=2nJ/pulse, Pulse duration=15ns, MPL-III-660, Opto Engine LLC, UT) was selected for source of the backlight illumination. The laser is directed via fiber optics to the top of the flow apparatus where the collimator (*NA*=0.25, *f*=36.01mm, F810FC-780, ThorLabs, NJ) is attached directly above the observation window providing approximately 1.0 cm diameter spot of uniform illumination. The projected shadowgraph image signal shares the same optical path with the µ-PIV signal. It passes the first and second dichroic filters, and was navigated to CCD Camera B to record the shadowgraph image of the air-water interface.

The epi-fluorescent prism/filter cube 2 was selected to minimize cross-talk especially on CCD Camera A due to the signal-to-noise ratio sensitivity of vector interrogation process. Since images on CCD Camera B were used only to detect the bubble interface shape, and unmistakable sharp contrast at the air-liquid interface, clarity of the shadowgraph data was often dominated by setting of the illumination strength. A dichroic prism having a combination of a low-pass filter at 625 nm (625DCLP, Chroma Technology Corp, VT) and a cleaning band pass filter of 595nm/±40nm (D595/40x, Chroma Technology Corp, VT) provided excellent separation of the fluorescent particle image for CCD Camera A.

Timing of the cameras and lasers were controlled by a multi-channel laser pulse synchronizer (Model 610035, TSI Inc.) which also sends a queue signal for the linear actuator

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 271

Nile Red was selected as fluorescent material for the current µ-PIV application due to excitation/emission peaks combination at *λ*=535/575 nm, since the emission spectrum was ideal for the combination with the LED red laser (*λ*=675 nm) for the shadowgraph. Then fluorescent particle diameter was determined as *dp*=1 µm (Nile Red FluoSpheres, Invitrogen Corporation, CA) based on previously discussed pixel resolution of the observation

The vector interrogation window size (32x32 pixels with 50 % overlap) was determined by combination of a pixel resolution, and capillary diameter. For the current research objectives, it was preferred to have at least 40 vectors across the diameter of the capillary in order to allow detailed examination near the air-liquid interface. Since the capillary diameter *D*=552 µm has been set by balancing the slowest reliable velocity of the linear motors and the maximum experimental duration of the chosen syringe size, *552/(0.744\*40)=18.55* pixels/vector provide sufficient resolution. Particle seeding density was determined by trial and error using measurement of Poiseulle flow with the same capillary tube and the same pixel resolution after initial estimation of density by using the methodologies described in Olsen and Adrian (2000) and Meinhart et al. (1999). Visibility is lowest at the center of the capillary because the transparency of the liquid is limited by the concentration of lung surfactant and other proteins. Therefore, the optimal seeding concentration was determined by limiting vector loss during the interrogation at the centerline to less than 1.0 % and the axial vector fluctuation of the time ensemble averaged velocity to within 2.0 % in the *r < 0.9R* region, where *r* is radial coordinate and *R* is radius of capillary. The seeding density 0.02 vol% with *dp*=1.0 µm particle for the current setup was

Dulbecco's Phosphate Buffered Saline 1x (DPBS) (Invitrogen, CA) was used as a base buffer solution. This is the buffer solution adjusted to have the same osmolarity and ion concentration as that of human serum. It also contains the necessary ions, such as sodium chloride, sodium phosphate, and potassium phosphate, for the lung surfactant proteins to be functional. Infasurf (calfactant) (35 mg/ml concentration, ONY Inc, NY) was chosen for the current experiment as LS. It is a lavage of natural calf lung surfactant with no tissues which is used clinically for RDS treatment. The mixture of DPBS and 0.02 vol% of the fluorescent particle was set as the standard 'DPBS solution' for the series of experiments. 0.01 mg/ml of Infasurf was added to make 'Infasurf solution' for the current experiments. The concentration 0.01 mg/ml of Infasurf is very low in comparison with previously reported values (Glindmeyer et al. 2011). However it was a sufficient concentration to observe the surface deformation under influence of LS in the current application. It was also convenient to use the lowest concentration for the system evaluation in order to avoid the unwanted external noise factors, such as, colloidal stability and the wall contamination issues. The Infasurf solution had to be kept at 37C before and during the experiment in order for LS to work properly. It was

also necessary to use it within two to three days after opening original Infasurf bottle.

Colloidal stability of the fluorescent particle is critical to ensure the quality of µ-PIV data. For investigations of airway reopening phenomena, it is necessary to use specific electrolytes, organic compounds, and proteins in order to evaluate LS functions during the measurements. The functional properties of the fluorescent particle are highly sensitive to the balance of electrical charge between the particle surface and the buffer solution.

**2.4 Preparation of sample testing liquid and preliminary stability test** 

window.

determined to meet there criteria.

Fig. 4. Schematic of the simultaneous µ-PIV/shadowgraph data acquisition system. The system utilizes two identical monochrome cameras, two lasers having different wave length, and two dichroic beam separation filter sets to simultaneously record µ-PIV and shadowgraph images. Continuous data acquisition of the progressing bubble tip having unsteady motions is achieved by the integrated precision linear motor that generates flow and translates the microscope stage system.

flow generating system and the translating stage. Since the µ-PIV employs cross-correlation analysis, two separate fluorescence images separated by a very short time (*dT*=200-700 ns) were captured at every data acquisition time-point. On the other hand, the shadowgraph requires only one frame and one exposure to obtain the data at the same time-point. The timing and control signals for the cameras and lasers were, therefore, adjusted to capture one shadowgraph image at the timing of the first frame exposure of the µ-PIV. The system management, data acquisition control, and image display are controlled by Insight 3G (TSI Inc., MN).

Fig. 4. Schematic of the simultaneous µ-PIV/shadowgraph data acquisition system. The system utilizes two identical monochrome cameras, two lasers having different wave length,

shadowgraph images. Continuous data acquisition of the progressing bubble tip having unsteady motions is achieved by the integrated precision linear motor that generates flow

flow generating system and the translating stage. Since the µ-PIV employs cross-correlation analysis, two separate fluorescence images separated by a very short time (*dT*=200-700 ns) were captured at every data acquisition time-point. On the other hand, the shadowgraph requires only one frame and one exposure to obtain the data at the same time-point. The timing and control signals for the cameras and lasers were, therefore, adjusted to capture one shadowgraph image at the timing of the first frame exposure of the µ-PIV. The system management, data acquisition control, and image display are controlled by Insight 3G (TSI

and two dichroic beam separation filter sets to simultaneously record µ-PIV and

and translates the microscope stage system.

Inc., MN).

### **2.4 Preparation of sample testing liquid and preliminary stability test**

Nile Red was selected as fluorescent material for the current µ-PIV application due to excitation/emission peaks combination at *λ*=535/575 nm, since the emission spectrum was ideal for the combination with the LED red laser (*λ*=675 nm) for the shadowgraph. Then fluorescent particle diameter was determined as *dp*=1 µm (Nile Red FluoSpheres, Invitrogen Corporation, CA) based on previously discussed pixel resolution of the observation window.

The vector interrogation window size (32x32 pixels with 50 % overlap) was determined by combination of a pixel resolution, and capillary diameter. For the current research objectives, it was preferred to have at least 40 vectors across the diameter of the capillary in order to allow detailed examination near the air-liquid interface. Since the capillary diameter *D*=552 µm has been set by balancing the slowest reliable velocity of the linear motors and the maximum experimental duration of the chosen syringe size, *552/(0.744\*40)=18.55* pixels/vector provide sufficient resolution. Particle seeding density was determined by trial and error using measurement of Poiseulle flow with the same capillary tube and the same pixel resolution after initial estimation of density by using the methodologies described in Olsen and Adrian (2000) and Meinhart et al. (1999). Visibility is lowest at the center of the capillary because the transparency of the liquid is limited by the concentration of lung surfactant and other proteins. Therefore, the optimal seeding concentration was determined by limiting vector loss during the interrogation at the centerline to less than 1.0 % and the axial vector fluctuation of the time ensemble averaged velocity to within 2.0 % in the *r < 0.9R* region, where *r* is radial coordinate and *R* is radius of capillary. The seeding density 0.02 vol% with *dp*=1.0 µm particle for the current setup was determined to meet there criteria.

Dulbecco's Phosphate Buffered Saline 1x (DPBS) (Invitrogen, CA) was used as a base buffer solution. This is the buffer solution adjusted to have the same osmolarity and ion concentration as that of human serum. It also contains the necessary ions, such as sodium chloride, sodium phosphate, and potassium phosphate, for the lung surfactant proteins to be functional. Infasurf (calfactant) (35 mg/ml concentration, ONY Inc, NY) was chosen for the current experiment as LS. It is a lavage of natural calf lung surfactant with no tissues which is used clinically for RDS treatment. The mixture of DPBS and 0.02 vol% of the fluorescent particle was set as the standard 'DPBS solution' for the series of experiments. 0.01 mg/ml of Infasurf was added to make 'Infasurf solution' for the current experiments. The concentration 0.01 mg/ml of Infasurf is very low in comparison with previously reported values (Glindmeyer et al. 2011). However it was a sufficient concentration to observe the surface deformation under influence of LS in the current application. It was also convenient to use the lowest concentration for the system evaluation in order to avoid the unwanted external noise factors, such as, colloidal stability and the wall contamination issues. The Infasurf solution had to be kept at 37C before and during the experiment in order for LS to work properly. It was also necessary to use it within two to three days after opening original Infasurf bottle.

Colloidal stability of the fluorescent particle is critical to ensure the quality of µ-PIV data. For investigations of airway reopening phenomena, it is necessary to use specific electrolytes, organic compounds, and proteins in order to evaluate LS functions during the measurements. The functional properties of the fluorescent particle are highly sensitive to the balance of electrical charge between the particle surface and the buffer solution.

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 273

visual conformation of the image or the quality of vector interrogation near the centerline. It should be noted that the experiment was design to 'boost' particle flocculation effect by adding excess amount of Infasurf and albumin. In fact, the effect of the flocculation could

The data acquisition frame rate was set to 7.5 images/sec (15 pulses/sec for the Nd:YAG laser, since the µ-PIV requires 2 frames to obtains one vector field.), and the duration of a single continuous trial was set to 60 images/run. This requires a minimum of 60/7.5=8 seconds of continuous data acquisition. Since the bubble mean velocity was defined to be 5.5 mm/sec and the translating stage provided about 10-12 cm of continuous observation window, this setting gave enough safety margin for pre- and post- adjustment time for the

The pulsatile frequency was *Ω*=2 Hz, therefore each experimental run could capture 16 cycles with 3.75 images/cycle. Repeating data acquisition and cycle averaging were employed to increase the temporal resolution (the number of image capturing points per cycle) and accuracy of ensemble averages (total number of images at the same instantaneous flow condition) to fully analyze the effect of LS on flow patterns. The stability of the testing solution shown in the previous section ensures repeatability of experimental trials. By initiating each trial with a different cycle phase, the temporal resolution was increased by accumulating the images from each repeating trial. Cycle averaging over the same experimental run was also applicable to the current application to increase the temporal resolution. Pulsating bubble surfactometer experiments have shown that cycle-averaged surface tension and the hysteresis loops of Infasurf solution were saturated after 3-4 cycles and became independent of the number of cycles (Krueger and Gaver III 2000). Therefore, the data acquisition was started after the solution passed at least ten cycles. Since the frame timing returned to the same point in the cycle every 15 image acquisition (every 4 seconds, or 4 cycles) a single continuous acquisition with cycle averaging provided 15 images/cycle with 4 images for each time-point in the cycle. In the current experimental setup, the oscillation amplitude was *A*=2 mm, which is wider than the microscope's field of view. Since at least 550 µm of the liquid phase ahead of the bubble tip was necessary to obtain the instantaneous downstream velocity for each image, in order to compute ensemble average, it was necessary to maintain the bubble at least 1000 µm from end of the image. Therefore at least two acquisitions focusing on different part of the cycle were necessary to capture the

The simultaneous µ-PIV/shadowgraph data acquisitions for the previously described pulsatile flow condition were preformed approximately 20 times (total 1200 images) for the DPBS and the Infasurf solutions. Roughly 30% of the images were selected for analysis because they had a sufficient length of liquid phase to compute the downstream mean velocity. There images were then interrogated and filtered by using the bubble tip and channel wall geometrical information from the corresponding simultaneous shadowgraph images. The interrogation employs a recursive Nyquist grid with a FFT correlation engine and a Gaussian peak algorithm with a 64x64 pixels first interrogation window, and a 32x32 pixel second interrogation window. The resulting vector fields were validated by standard deviation, local magnitude difference, and velocity range filters. Finally, the vector fields

not be identified for the current 0.01 mg/ml Infasurf solution even after 50 hours.

**2.5 Experimental procedure and data processing** 

entire cycle with sufficient liquid phase visible in the field of view.

flow generating system.

Fig. 5. Colloidal stability tests of 1.0 mg/ml Infasurf solution with 5.0 mg/ml albumin. (i) µ-PIV images of fluorescent particle flocculation at1, 3, and 5 hours. (ii) Velocity fluctuations along the channel radial direction over 100 axial positions during steady Poiseuille flow (U=5.5 mm/sec) in the cylindrical channel. After 5 hours, the particle aggregations are visible in the fluorescent images and affect on the vector interrogation result.

Even though it is safe to assume that fluorescent particles in the standard PBS are stable, since the pH of DPBS is 7.1±0.1 and the surface of the particle is cationic (Invitrogen 2004), colloidal stability under influence of Infasurf and additional LS inhibitors, such as albumin, must be carefully evaluated prior to the design of the experimental process. In order to verify the colloidal stability of the particle solution, the accuracy of µ-PIV data with a solution of 1.0 mg/ml of Infasurf with 5.0 mg/ml albumin using steady Poiseuille flow was evaluated. The capillary was filled with the solution and kept at 37C. As soon as the system reached stable temperature, the linear motor system was set to give a constant forward mean velocity at *U*=5.5 mm/sec , and 20 µ-PIV images were recorded. The process was repeated every 30 minutes for 5 hours. The velocity fluctuations of the ensemble axial velocity component over 100 axial positions were computed for the reliability evaluation of the vector interrogation over the progressing particle flocculation (Fig. 5). The result shows that the solution was stable for the µ-PIV data acquisition at least 3 hours after it was mixed. However, after 5 hours particle flocculation was severe and clearly identifiable either by the visual conformation of the image or the quality of vector interrogation near the centerline. It should be noted that the experiment was design to 'boost' particle flocculation effect by adding excess amount of Infasurf and albumin. In fact, the effect of the flocculation could not be identified for the current 0.01 mg/ml Infasurf solution even after 50 hours.

#### **2.5 Experimental procedure and data processing**

272 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

Fig. 5. Colloidal stability tests of 1.0 mg/ml Infasurf solution with 5.0 mg/ml albumin. (i) µ-PIV images of fluorescent particle flocculation at1, 3, and 5 hours. (ii) Velocity fluctuations along the channel radial direction over 100 axial positions during steady Poiseuille flow (U=5.5 mm/sec) in the cylindrical channel. After 5 hours, the particle aggregations are

Even though it is safe to assume that fluorescent particles in the standard PBS are stable, since the pH of DPBS is 7.1±0.1 and the surface of the particle is cationic (Invitrogen 2004), colloidal stability under influence of Infasurf and additional LS inhibitors, such as albumin, must be carefully evaluated prior to the design of the experimental process. In order to verify the colloidal stability of the particle solution, the accuracy of µ-PIV data with a solution of 1.0 mg/ml of Infasurf with 5.0 mg/ml albumin using steady Poiseuille flow was evaluated. The capillary was filled with the solution and kept at 37C. As soon as the system reached stable temperature, the linear motor system was set to give a constant forward mean velocity at *U*=5.5 mm/sec , and 20 µ-PIV images were recorded. The process was repeated every 30 minutes for 5 hours. The velocity fluctuations of the ensemble axial velocity component over 100 axial positions were computed for the reliability evaluation of the vector interrogation over the progressing particle flocculation (Fig. 5). The result shows that the solution was stable for the µ-PIV data acquisition at least 3 hours after it was mixed. However, after 5 hours particle flocculation was severe and clearly identifiable either by the

visible in the fluorescent images and affect on the vector interrogation result.

The data acquisition frame rate was set to 7.5 images/sec (15 pulses/sec for the Nd:YAG laser, since the µ-PIV requires 2 frames to obtains one vector field.), and the duration of a single continuous trial was set to 60 images/run. This requires a minimum of 60/7.5=8 seconds of continuous data acquisition. Since the bubble mean velocity was defined to be 5.5 mm/sec and the translating stage provided about 10-12 cm of continuous observation window, this setting gave enough safety margin for pre- and post- adjustment time for the flow generating system.

The pulsatile frequency was *Ω*=2 Hz, therefore each experimental run could capture 16 cycles with 3.75 images/cycle. Repeating data acquisition and cycle averaging were employed to increase the temporal resolution (the number of image capturing points per cycle) and accuracy of ensemble averages (total number of images at the same instantaneous flow condition) to fully analyze the effect of LS on flow patterns. The stability of the testing solution shown in the previous section ensures repeatability of experimental trials. By initiating each trial with a different cycle phase, the temporal resolution was increased by accumulating the images from each repeating trial. Cycle averaging over the same experimental run was also applicable to the current application to increase the temporal resolution. Pulsating bubble surfactometer experiments have shown that cycle-averaged surface tension and the hysteresis loops of Infasurf solution were saturated after 3-4 cycles and became independent of the number of cycles (Krueger and Gaver III 2000). Therefore, the data acquisition was started after the solution passed at least ten cycles. Since the frame timing returned to the same point in the cycle every 15 image acquisition (every 4 seconds, or 4 cycles) a single continuous acquisition with cycle averaging provided 15 images/cycle with 4 images for each time-point in the cycle. In the current experimental setup, the oscillation amplitude was *A*=2 mm, which is wider than the microscope's field of view. Since at least 550 µm of the liquid phase ahead of the bubble tip was necessary to obtain the instantaneous downstream velocity for each image, in order to compute ensemble average, it was necessary to maintain the bubble at least 1000 µm from end of the image. Therefore at least two acquisitions focusing on different part of the cycle were necessary to capture the entire cycle with sufficient liquid phase visible in the field of view.

The simultaneous µ-PIV/shadowgraph data acquisitions for the previously described pulsatile flow condition were preformed approximately 20 times (total 1200 images) for the DPBS and the Infasurf solutions. Roughly 30% of the images were selected for analysis because they had a sufficient length of liquid phase to compute the downstream mean velocity. There images were then interrogated and filtered by using the bubble tip and channel wall geometrical information from the corresponding simultaneous shadowgraph images. The interrogation employs a recursive Nyquist grid with a FFT correlation engine and a Gaussian peak algorithm with a 64x64 pixels first interrogation window, and a 32x32 pixel second interrogation window. The resulting vector fields were validated by standard deviation, local magnitude difference, and velocity range filters. Finally, the vector fields

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 275

images at an instantaneous downstream velocity *U*=5.5 mm/sec with the bubble progressing from left to right. *U* was calculated by taking the average velocity more than 1.5R downstream from the tip of the bubble. A band of fluorescent particles is visible in the lower part of image, which provides the stage velocity throughout the use of a second channel filled with the quiescent fluid. The figure demonstrates that the image separation through the dichroic filter is very good since there is virtually no cross-talk signal from the shadowgraph illumination in the particle image, and particles at the center of the channel are clearly distinguishable. As mentioned in the previous section the interfacial shape especially near the center of the channel is difficult to obtain from the fluorescent image which necessitates the use of a

Camera B in Fig. 6 presents the corresponding shadowgraph image. In this image, a large amount of random speckle pattern noise caused by coherent laser is visible. However, the degree of noise does not cause difficulty in determining the interfacial shape in the current case. The speckle could be eliminated by using diverse polarizations and wavelengths if necessary in future application. There is slight amount of cross-talk noise from the fluorescent particle emission due to the broad emission spectrum and less strict clean-up

The interface geometry and channel wall information from Camera B were used to generate a grid mask for the vector interrogation of the Camera A image. The mask greatly increases the accuracy of the flow field measurement near the bubble tip especially during the reverse flow phase where significant interface deformations and instabilities exist. Two examples at the instantaneous downstream velocity *U*=-6.5 mm/sec (the bubble is progressing to the left) are shown in Fig.7. In both cases, the bubble shape estimation and the vector interrogation near the interface would be very inaccurate without the geometrical information from the corresponding shadowgraph image. Moreover, statistical analysis of the instability during the reverse flow phase is possible with this technology. This may provide information related to important physical characteristic of dynamic behavior of LS with and without competitive adsorption by using one-by-one corresponding interface

separate simultaneous technique to determine the interface shape.

filter setting. This does not cause problems in the interface detection.

shape information, flow patterns near the bubble tip and downstream velocity.

ensemble-average of over 20 instantaneous images taken at point (b) in Fig. 8-i.

**bubble tip under influence of the pulmonary surfactant** 

**3.2 Data analysis of the bubble shape and the flow field surrounding semi-infinite** 

The cycle averaged downstream velocities and bubble tip curvatures are displayed in Fig. 8. The data in Fig. 8-i clearly demonstrate excellent controllability of the flow generating system and the translating stage. The observed mean forward velocity is 5.5 mm/sec and the peak forward/backward velocities are about 18.5/-12.5 mm/sec. The reverse flow phase exists between 0.58< *t/T* < 0.92, where *T*=0.5 sec is period and *t* is time in the sinusoidal cycle. Both the DPBS and Infasurf solutions follow the input very closely with exception of slight phase delay on the Infasurf solution due to the large interface deformation. The corresponding ensemble-averaged interfacial curvatures of the bubble tip and fluctuations at each phase are shown in Fig. 8-ii. The interfacial curvature (*κ*) was calculated by first applying cubic smoothing splines on the interface and computing the arc length (*s*) around the centerline to obtain the radius of the oscillating interface at the centreline (*Ro*) (Thieman 2011). Details of the interfacial curvature and flow patterns (streamlines) at the reverse flow phase with and without the effect of Infasurf are shown in Fig. 9. These figures represent the

were divided into 16 bins based on the instantaneous downstream velocity to compute the ensemble average of each point in the cycle.

### **3. Results and conclusions**

### **3.1 Image quality and efficiency of the system**

Examples of the simultaneously acquired instantaneous µ-PIV and shadowgraphy images are presented in Fig. 6. In this figure Camera A provides one of the two fluorescent particle

Fig. 6. Sample of simultaneously acquired µ-PIV (Camera A) and shadowgraph (Camera B) images under pulsatile flow input. Testing solution is the DPBS, and instantaneous downstream velocity is U=5.5 mm/sec.

were divided into 16 bins based on the instantaneous downstream velocity to compute the

Examples of the simultaneously acquired instantaneous µ-PIV and shadowgraphy images are presented in Fig. 6. In this figure Camera A provides one of the two fluorescent particle

Fig. 6. Sample of simultaneously acquired µ-PIV (Camera A) and shadowgraph (Camera B)

images under pulsatile flow input. Testing solution is the DPBS, and instantaneous

downstream velocity is U=5.5 mm/sec.

ensemble average of each point in the cycle.

**3.1 Image quality and efficiency of the system** 

**3. Results and conclusions** 

images at an instantaneous downstream velocity *U*=5.5 mm/sec with the bubble progressing from left to right. *U* was calculated by taking the average velocity more than 1.5R downstream from the tip of the bubble. A band of fluorescent particles is visible in the lower part of image, which provides the stage velocity throughout the use of a second channel filled with the quiescent fluid. The figure demonstrates that the image separation through the dichroic filter is very good since there is virtually no cross-talk signal from the shadowgraph illumination in the particle image, and particles at the center of the channel are clearly distinguishable. As mentioned in the previous section the interfacial shape especially near the center of the channel is difficult to obtain from the fluorescent image which necessitates the use of a separate simultaneous technique to determine the interface shape.

Camera B in Fig. 6 presents the corresponding shadowgraph image. In this image, a large amount of random speckle pattern noise caused by coherent laser is visible. However, the degree of noise does not cause difficulty in determining the interfacial shape in the current case. The speckle could be eliminated by using diverse polarizations and wavelengths if necessary in future application. There is slight amount of cross-talk noise from the fluorescent particle emission due to the broad emission spectrum and less strict clean-up filter setting. This does not cause problems in the interface detection.

The interface geometry and channel wall information from Camera B were used to generate a grid mask for the vector interrogation of the Camera A image. The mask greatly increases the accuracy of the flow field measurement near the bubble tip especially during the reverse flow phase where significant interface deformations and instabilities exist. Two examples at the instantaneous downstream velocity *U*=-6.5 mm/sec (the bubble is progressing to the left) are shown in Fig.7. In both cases, the bubble shape estimation and the vector interrogation near the interface would be very inaccurate without the geometrical information from the corresponding shadowgraph image. Moreover, statistical analysis of the instability during the reverse flow phase is possible with this technology. This may provide information related to important physical characteristic of dynamic behavior of LS with and without competitive adsorption by using one-by-one corresponding interface shape information, flow patterns near the bubble tip and downstream velocity.

#### **3.2 Data analysis of the bubble shape and the flow field surrounding semi-infinite bubble tip under influence of the pulmonary surfactant**

The cycle averaged downstream velocities and bubble tip curvatures are displayed in Fig. 8. The data in Fig. 8-i clearly demonstrate excellent controllability of the flow generating system and the translating stage. The observed mean forward velocity is 5.5 mm/sec and the peak forward/backward velocities are about 18.5/-12.5 mm/sec. The reverse flow phase exists between 0.58< *t/T* < 0.92, where *T*=0.5 sec is period and *t* is time in the sinusoidal cycle. Both the DPBS and Infasurf solutions follow the input very closely with exception of slight phase delay on the Infasurf solution due to the large interface deformation. The corresponding ensemble-averaged interfacial curvatures of the bubble tip and fluctuations at each phase are shown in Fig. 8-ii. The interfacial curvature (*κ*) was calculated by first applying cubic smoothing splines on the interface and computing the arc length (*s*) around the centerline to obtain the radius of the oscillating interface at the centreline (*Ro*) (Thieman 2011). Details of the interfacial curvature and flow patterns (streamlines) at the reverse flow phase with and without the effect of Infasurf are shown in Fig. 9. These figures represent the ensemble-average of over 20 instantaneous images taken at point (b) in Fig. 8-i.

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 277

Fig. 8. (i) Measured downstream mean velocity in the cycle, and (ii) corresponding bubble tip curvature. Only the Infasurf solution display significant bubble interface deformation and fluctuation of curvature (see Fig. 7) during the reverse flow phase. The result is explained very well by the LS adsorption/desorption prediction model (Fig. 2), since the DPBS under the same flow condition and the Infasurf without sinusoidal flow input do not

show similar deformations.

Fig. 7*.* Examples of the unsteady air-liquid interface during the reverse flow phase of downstream flow in pulsatile flow. The instantaneous downstream mean velocity was about U=-6.5 mm/sec for the both cases (position (b) in Fig. 8-i).

Significant interfacial deformation is only visible with the Infasurf solution during pulsatile flow. Almost negligible interface deformation is visible for the DPBS solution under the same pulsatile flow condition. The Infasurf solution with steady flow (*U*=5.5 mm/sec, gray straight line with circle in Fig. 8-ii) does not show any deformation. This experimental result is consistent with the hypothesis presented in Fig. 2 that predicts a significant interfacial deformation for the Infasurf solution during pulsatile flow.

During the reverse flow phase, converging stagnation region (ring in 3D) is located near the capillary walls (Fig. 9). Since the multi-layer formation and collapse of Infasurf dramatically lower the local surface tension relative to the expanding (diverging) region at the center (Fig. 2-i), the gradient of surface tension causes strong Marangoni stress tangential to the interface and rigidifies the interface. The very small curvature shift of the DPBS solution suggests insignificance of fluid dynamic effect on the interface shape. The curvature of the Infasurf solution during the forward flow phase is constantly lower than exists with steady flow due to the consistently lower surface tension caused by larger surface accumulation of Infasurf throughout the pulsatile motion. Glindmeyer et al. (2011) recently performed invitro experiments of LS effects on cell-laden rigid tube, and reported reduced cell damage during the reverse flow region. This finding coincides with the change of the interface and flow pattern near the bubble tip, and provides a physicochemical basis for the reduction of cell damage.

Fig. 7*.* Examples of the unsteady air-liquid interface during the reverse flow phase of

U=-6.5 mm/sec for the both cases (position (b) in Fig. 8-i).

deformation for the Infasurf solution during pulsatile flow.

cell damage.

downstream flow in pulsatile flow. The instantaneous downstream mean velocity was about

Significant interfacial deformation is only visible with the Infasurf solution during pulsatile flow. Almost negligible interface deformation is visible for the DPBS solution under the same pulsatile flow condition. The Infasurf solution with steady flow (*U*=5.5 mm/sec, gray straight line with circle in Fig. 8-ii) does not show any deformation. This experimental result is consistent with the hypothesis presented in Fig. 2 that predicts a significant interfacial

During the reverse flow phase, converging stagnation region (ring in 3D) is located near the capillary walls (Fig. 9). Since the multi-layer formation and collapse of Infasurf dramatically lower the local surface tension relative to the expanding (diverging) region at the center (Fig. 2-i), the gradient of surface tension causes strong Marangoni stress tangential to the interface and rigidifies the interface. The very small curvature shift of the DPBS solution suggests insignificance of fluid dynamic effect on the interface shape. The curvature of the Infasurf solution during the forward flow phase is constantly lower than exists with steady flow due to the consistently lower surface tension caused by larger surface accumulation of Infasurf throughout the pulsatile motion. Glindmeyer et al. (2011) recently performed invitro experiments of LS effects on cell-laden rigid tube, and reported reduced cell damage during the reverse flow region. This finding coincides with the change of the interface and flow pattern near the bubble tip, and provides a physicochemical basis for the reduction of

Fig. 8. (i) Measured downstream mean velocity in the cycle, and (ii) corresponding bubble tip curvature. Only the Infasurf solution display significant bubble interface deformation and fluctuation of curvature (see Fig. 7) during the reverse flow phase. The result is explained very well by the LS adsorption/desorption prediction model (Fig. 2), since the DPBS under the same flow condition and the Infasurf without sinusoidal flow input do not show similar deformations.

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 279

An increasing curvature fluctuation (instability) is also noticeable during the reverse flow phase with the pulsatile flow and Infasurf (examples of unsteady interface are shown in Fig. 7). It can be hypothesized that the increasing fluctuation is a result of weakened wetting of the contaminated glass capillary wall since a glass surface is hydrophilic and has almost perfect wettability. Therefore if any kind of protein substances from the Infasurf solution adheres to the surface, it will certainly cause a loss of wettability. Since the trailing edge of tip of the semi-infinite bubble is a thin-film region, surface stability which is sensitive to surface energy balance is very low at the contaminated area causing dewetting regions. This is not a problem for a forwarding bubble, because the thin-film region is behind it. However, for the reverse flow the region is traversed by the returning bubble interface during a stage when it has the lowest local surface tension point very close to the wall. A rewetting of the relatively hydrophobic region certainly causes stiff 'stick-slip' motions of the interface near the wall and results in widely diverged unevenly deformed instantaneous

The simultaneous acquisition allows researchers to examine every single instantaneous velocity profile with a corresponding interfacial shape. Therefore vector fields of obviously skewed bubble tip shapes could be eliminated manually during the process of ensemble averaging, if they want to focus on LS effect and subsurface flow pattern. This will be increasingly important for the analysis of multi-phase fluid dynamics regarding the airway reopening problem, since obvious further investigations of the current application are to examine effects of higher Infasurf concentration to interface shape and interactions between LS inhibitors. It is possible to approach the contamination of the glass tube by developing a surface modification technique for the glass surface. For example, protein contaminations can be reduced by using a surface coating agent such as 2-[methoxy(polyethylenxy-propyl)trimethoxysilane (Tech-90, Gelest Inc., PA). This grafts poly(ethylene glycol) polymer chains on glass surface (Sui et al. 2006) and reduces nonspecific binding of proteins in the Infasurf solution. Using the simultaneous µ-PIV/shadowgraph acquisition system will also be a powerful tool to examine the effectiveness of various surface modification methods by evaluating the fluctuations during

In summary, the simultaneous µ-PIV/shadowgraph acquisition system has been demonstrated as a powerful analysis tool for the complex multi-phase micro-biofluidic investigation, such as investigation of physicochemical interaction of lung surfactant during mechanically ventilated reopening of fluid-occluded respiratory airway. Complex flow controls, continuous data acquisition, and the simultaneous µ-PIV/shadowgraph acquisition with two separate cameras are all required to investigate this system, and the successful combination of the system opens the door to further investigations of this complex system and will allow the investigation of the role of LS inhibitors and the effect of

This material is based upon work supported by the National Science Foundation under grant No. CBET-1033619, and the National Institutes of Health through grant R01-HL81266

interface shapes during the reverse flow phase.

the reverse flow phase.

**4. Acknowledgment** 

surface properties to the flow fields.

Fig. 9. Ensemble averaged streamlines and bubble shapes. Both figures have the same downstream mean velocity U=5.9 mm/sec (position (b) in Fig. 8-i). The bubble shape and flow pattern in (II) are significantly altered by accumulated LS around converging stagnation points (ring in 3D) near the wall. This difference has been observed only during the reverse flow region, and matches very well with reduced cellular damage that exists during reverse flow observed of in-vitro experiments (Glindmeyer et al. 2011).

Fig. 9. Ensemble averaged streamlines and bubble shapes. Both figures have the same downstream mean velocity U=5.9 mm/sec (position (b) in Fig. 8-i). The bubble shape and flow pattern in (II) are significantly altered by accumulated LS around converging

during reverse flow observed of in-vitro experiments (Glindmeyer et al. 2011).

stagnation points (ring in 3D) near the wall. This difference has been observed only during the reverse flow region, and matches very well with reduced cellular damage that exists

An increasing curvature fluctuation (instability) is also noticeable during the reverse flow phase with the pulsatile flow and Infasurf (examples of unsteady interface are shown in Fig. 7). It can be hypothesized that the increasing fluctuation is a result of weakened wetting of the contaminated glass capillary wall since a glass surface is hydrophilic and has almost perfect wettability. Therefore if any kind of protein substances from the Infasurf solution adheres to the surface, it will certainly cause a loss of wettability. Since the trailing edge of tip of the semi-infinite bubble is a thin-film region, surface stability which is sensitive to surface energy balance is very low at the contaminated area causing dewetting regions. This is not a problem for a forwarding bubble, because the thin-film region is behind it. However, for the reverse flow the region is traversed by the returning bubble interface during a stage when it has the lowest local surface tension point very close to the wall. A rewetting of the relatively hydrophobic region certainly causes stiff 'stick-slip' motions of the interface near the wall and results in widely diverged unevenly deformed instantaneous interface shapes during the reverse flow phase.

The simultaneous acquisition allows researchers to examine every single instantaneous velocity profile with a corresponding interfacial shape. Therefore vector fields of obviously skewed bubble tip shapes could be eliminated manually during the process of ensemble averaging, if they want to focus on LS effect and subsurface flow pattern. This will be increasingly important for the analysis of multi-phase fluid dynamics regarding the airway reopening problem, since obvious further investigations of the current application are to examine effects of higher Infasurf concentration to interface shape and interactions between LS inhibitors. It is possible to approach the contamination of the glass tube by developing a surface modification technique for the glass surface. For example, protein contaminations can be reduced by using a surface coating agent such as 2-[methoxy(polyethylenxy-propyl)trimethoxysilane (Tech-90, Gelest Inc., PA). This grafts poly(ethylene glycol) polymer chains on glass surface (Sui et al. 2006) and reduces nonspecific binding of proteins in the Infasurf solution. Using the simultaneous µ-PIV/shadowgraph acquisition system will also be a powerful tool to examine the effectiveness of various surface modification methods by evaluating the fluctuations during the reverse flow phase.

In summary, the simultaneous µ-PIV/shadowgraph acquisition system has been demonstrated as a powerful analysis tool for the complex multi-phase micro-biofluidic investigation, such as investigation of physicochemical interaction of lung surfactant during mechanically ventilated reopening of fluid-occluded respiratory airway. Complex flow controls, continuous data acquisition, and the simultaneous µ-PIV/shadowgraph acquisition with two separate cameras are all required to investigate this system, and the successful combination of the system opens the door to further investigations of this complex system and will allow the investigation of the role of LS inhibitors and the effect of surface properties to the flow fields.

### **4. Acknowledgment**

This material is based upon work supported by the National Science Foundation under grant No. CBET-1033619, and the National Institutes of Health through grant R01-HL81266

µ-PIV for the Analysis of Flow Fields near a Propagating Air-Liquid Interface 281

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**11** 

*Greece* 

*In Vitro* **and** *In Vivo*

*Bioinformatics Lab, School of Health Sciences,* 

*Technological Educational Institute (TEI) of Larissa, Larissa,* 

Aristotle G. Koutsiaris

**Digital Micro PIV (μPIV) and Velocity Profiles** 

The term **Particle Image Velocimetry (PIV)**, in the technical world, is used to describe a powerful, automated flow visualization method which quantifies the instantaneous flow velocity field in 2 dimensions. PIV gives valuable information on how velocity field changes at a specific measurement plane, at regular time intervals, selected by

Correlation techniques were used extensively for the measurement of fluid velocity. In temporal correlation techniques, velocity is inversely proportional to the transit time for flow tracers to cross a fixed distance. In **spatial correlation techniques**, the velocity is directly proportional to the displacement of flow tracers in a fixed time interval. In this sense, many video techniques, high speed cinematography and PIV can be classified as

The term "**Digital**" refers to the fully digital implementation of the method, namely the use of a digital camera connected directly to a digital electronic computer in order to acquire flow images and then to estimate the correlation function. This may seem a common place today, but a lot of early implementations used to have special electrooptical and electromechanical hardware for the estimation of the correlation function (optical correlation) or film cameras with laser scanners (optical – digital correlation). Later, fully electronic PIV implementations appeared using analog together with digital hardware: analog CCD cameras connected to video recorders produced video tape images which were digitized by computers (Gardel et al., 2005). These implementations were limited by their

The term **"Micro"** refers to the length scale of the microfluidic environment ranging between 1μm and 1000 μm. The word "environment" is a general term for every possible

This chapter is a medium size review on **Digital micro PIV (μPIV)** and its applications on the velocity profiles *in vitro* and *in vivo*. Parts of sections 6 and 7 come from a mini review

microstructure inside which the fluid under study flows.

**1. Introduction** 

the operator.

spatial correlation techniques.

analog components.

paper (Koutsiaris, 2010b).

Zimmer, M. E., Williams, H. A. R. and Gaver III, D. P. (2005). The pulsatile motion of a semiinfinite bubble in a channel: flow fields, and transport of an inactive surfaceassociated contaminant. *Journal of Fluid Mechanics*, Vol.537. pp.1-33.

## **Digital Micro PIV (μPIV) and Velocity Profiles**  *In Vitro* **and** *In Vivo*

Aristotle G. Koutsiaris

*Bioinformatics Lab, School of Health Sciences, Technological Educational Institute (TEI) of Larissa, Larissa, Greece* 

### **1. Introduction**

282 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

Zimmer, M. E., Williams, H. A. R. and Gaver III, D. P. (2005). The pulsatile motion of a semi-

associated contaminant. *Journal of Fluid Mechanics*, Vol.537. pp.1-33.

infinite bubble in a channel: flow fields, and transport of an inactive surface-

The term **Particle Image Velocimetry (PIV)**, in the technical world, is used to describe a powerful, automated flow visualization method which quantifies the instantaneous flow velocity field in 2 dimensions. PIV gives valuable information on how velocity field changes at a specific measurement plane, at regular time intervals, selected by the operator.

Correlation techniques were used extensively for the measurement of fluid velocity. In temporal correlation techniques, velocity is inversely proportional to the transit time for flow tracers to cross a fixed distance. In **spatial correlation techniques**, the velocity is directly proportional to the displacement of flow tracers in a fixed time interval. In this sense, many video techniques, high speed cinematography and PIV can be classified as spatial correlation techniques.

The term "**Digital**" refers to the fully digital implementation of the method, namely the use of a digital camera connected directly to a digital electronic computer in order to acquire flow images and then to estimate the correlation function. This may seem a common place today, but a lot of early implementations used to have special electrooptical and electromechanical hardware for the estimation of the correlation function (optical correlation) or film cameras with laser scanners (optical – digital correlation). Later, fully electronic PIV implementations appeared using analog together with digital hardware: analog CCD cameras connected to video recorders produced video tape images which were digitized by computers (Gardel et al., 2005). These implementations were limited by their analog components.

The term **"Micro"** refers to the length scale of the microfluidic environment ranging between 1μm and 1000 μm. The word "environment" is a general term for every possible microstructure inside which the fluid under study flows.

This chapter is a medium size review on **Digital micro PIV (μPIV)** and its applications on the velocity profiles *in vitro* and *in vivo*. Parts of sections 6 and 7 come from a mini review paper (Koutsiaris, 2010b).

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 285

microdevices such as micropumps can be integrated easily in a PDMS device. A more detailed discussion on PDMS advantages can be found in the paper of Lima et al. (2008).

The microfluidic system can be a part of a MicroElectroMechanical Systems (MEMS) device. Other typical microdevices are microheat sinks, micropumps, microturbines, microengines, micromixers and microsensors. More details on the design, fabrication and applications of MEMS devices can be found in review papers (Hassan, 2006) and in books edited by Gad-el-

Hak (2005) and Breuer (2005) and written by Nguyen and Wereley (2002).

Objective Lens

> Objective Lens

Fig. 2. A typical microfluidic circuit with a syringe pump, on an inverted microscope.

way a more economic set up is possible.

DH

Container

Capillary

force is provided by the height difference DH.

Capillary

Container

in the textbook edited by Breuer (2005).

When the experimental conditions are right, the syringe pump is not needed since the necessary driving force can be controlled with the height difference (DH, figure 3). In this

Syringe Pump

Plastic Tube

Fig. 3. A microfluidic circuit without any syringe pump (Koutsiaris et al., 1999). The driving

The basic characteristic of a successful flow tracer is that it should accurately follow the flow with an appropriate specific gravity matching (Stokes equation, Raffel et al., 2007). Flow tracers are usually made of fluorescent **P**oly**S**tyrene **L**atex (**PSL**) particles but the final choice depends on the fluid. When the particle diameter is less than ≈ 0.5 μm and characteristic velocities are less than ≈ 1mm/s, the Brownian motion should be taken into account (Werely and Meinhart 2010). More details on Brownian motion and the Saffman effect can be found

### **2. Components of a Digital μPIV system**

A complete PIV implementation is subdivided into four steps (Koutsiaris et al., 1999): 1) seeding of the flow, 2) illumination of the flow plane of interest with a light sheet, 3) image capture by a camera placed at right angles to the illuminated flow plane, and 4) data processing.

There are **three principal differences** between an ordinary macroscopic and a μPIV system. **First**, as it was mentioned in the introduction, it is the **length scale** of the fluidic circuit under study (hence the name "micro"). **Second**, as a consequence of the first difference, it is the design of the optical system, which has as a minimum requirement some kind of a **microscope** objective lens. **Third**, the thickness of the measurement plane is defined by the optical system using **volume illumination** and not by the thickness of an illuminating light sheet. Forming a light sheet with a thickness between 1 and 20 μm and aligning it properly in the microfluidic circuit is very difficult.

In this section, the main components of a Digital μPIV system are described: **1)** the microfluidic circuit with appropriate flow tracers, **2)** the optical system, **3)** the digital electronics system and **4)** the computer software. These components are presented in schematic form in figure 1.

Fig. 1. The four main components of a Digital μPIV system.

### **2.1 Microfluidic circuit and flow tracers**

The usual implementation of the microfluidic system comprises some kind of a microstructure-microchannel (microduct, microtube, capillary) connected to a syringe pump (figure 2). The microchannel can be made of various materials such as glass (Koutsiaris et al., 1999; Meinhart et al., 1999), biocompatible polymers and collagen gel inside silicone elastomer (Chrobak et al., 2006; Potter & Damiano, 2008). Biocompatible polymers can be classified to thermoplastic polymers such as **P**oly **M**ethyl **M**eth**A**crylate (**PMMA**, Timgren et al., 2008) and to elastomeric polymers such as **P**oly **D**i**M**ethi**S**iloxane (**PDMS**, Lima et al., 2008).

A lot of research was directed during the past 10 years to **biocompatible polymers**, due to their advantages over glass. PDMS in particular is permeable to gases such as oxygen and there is no need to use a refractive index matching liquid. The ultimate tensile stress and Young's elastic modulus are much closer to those of blood vessels in comparison to glass and sealing does not require any complex bonding technique. In addition, various

A complete PIV implementation is subdivided into four steps (Koutsiaris et al., 1999): 1) seeding of the flow, 2) illumination of the flow plane of interest with a light sheet, 3) image capture by a camera placed at right angles to the illuminated flow plane, and 4) data

There are **three principal differences** between an ordinary macroscopic and a μPIV system. **First**, as it was mentioned in the introduction, it is the **length scale** of the fluidic circuit under study (hence the name "micro"). **Second**, as a consequence of the first difference, it is the design of the optical system, which has as a minimum requirement some kind of a **microscope** objective lens. **Third**, the thickness of the measurement plane is defined by the optical system using **volume illumination** and not by the thickness of an illuminating light sheet. Forming a light sheet with a thickness between 1 and 20 μm and aligning it properly

In this section, the main components of a Digital μPIV system are described: **1)** the microfluidic circuit with appropriate flow tracers, **2)** the optical system, **3)** the digital electronics system and **4)** the computer software. These components are presented in

The usual implementation of the microfluidic system comprises some kind of a microstructure-microchannel (microduct, microtube, capillary) connected to a syringe pump (figure 2). The microchannel can be made of various materials such as glass (Koutsiaris et al., 1999; Meinhart et al., 1999), biocompatible polymers and collagen gel inside silicone elastomer (Chrobak et al., 2006; Potter & Damiano, 2008). Biocompatible polymers can be classified to thermoplastic polymers such as **P**oly **M**ethyl **M**eth**A**crylate (**PMMA**, Timgren et al., 2008) and to elastomeric polymers such as **P**oly **D**i**M**ethi**S**iloxane (**PDMS**, Lima et al.,

**3 Digital Electronics System** 

**Optical Images Digital Images** 

**4 Software** 

**2D Velocity Field** 

A lot of research was directed during the past 10 years to **biocompatible polymers**, due to their advantages over glass. PDMS in particular is permeable to gases such as oxygen and there is no need to use a refractive index matching liquid. The ultimate tensile stress and Young's elastic modulus are much closer to those of blood vessels in comparison to glass and sealing does not require any complex bonding technique. In addition, various

**2. Components of a Digital μPIV system** 

in the microfluidic circuit is very difficult.

Fig. 1. The four main components of a Digital μPIV system.

**2 Optical System** 

**2.1 Microfluidic circuit and flow tracers** 

2008).

schematic form in figure 1.

**Desired Measurement Plane** 

**1 Microfluidic Circuit** 

processing.

microdevices such as micropumps can be integrated easily in a PDMS device. A more detailed discussion on PDMS advantages can be found in the paper of Lima et al. (2008).

The microfluidic system can be a part of a MicroElectroMechanical Systems (MEMS) device. Other typical microdevices are microheat sinks, micropumps, microturbines, microengines, micromixers and microsensors. More details on the design, fabrication and applications of MEMS devices can be found in review papers (Hassan, 2006) and in books edited by Gad-el-Hak (2005) and Breuer (2005) and written by Nguyen and Wereley (2002).

Fig. 2. A typical microfluidic circuit with a syringe pump, on an inverted microscope.

When the experimental conditions are right, the syringe pump is not needed since the necessary driving force can be controlled with the height difference (DH, figure 3). In this way a more economic set up is possible.

Fig. 3. A microfluidic circuit without any syringe pump (Koutsiaris et al., 1999). The driving force is provided by the height difference DH.

The basic characteristic of a successful flow tracer is that it should accurately follow the flow with an appropriate specific gravity matching (Stokes equation, Raffel et al., 2007). Flow tracers are usually made of fluorescent **P**oly**S**tyrene **L**atex (**PSL**) particles but the final choice depends on the fluid. When the particle diameter is less than ≈ 0.5 μm and characteristic velocities are less than ≈ 1mm/s, the Brownian motion should be taken into account (Werely and Meinhart 2010). More details on Brownian motion and the Saffman effect can be found in the textbook edited by Breuer (2005).

In addition, the particle diameter distribution should be monodispersive (diameter values distributed over a very limited range around the mean value). We shall see later that this makes easier the design and error evaluation.

#### **2.2 Optical system**

#### **2.2.1 Basics**

The basic optical characteristics carved on the metallic surface of every microscope objective lens are magnification (M) and **numerical aperture (NA)**. In simple terms, M shows how many times the perpendicular to the optical axis dimension of an object lying in the object plane is enlarged in the image plane on the other side of the lens. A schematic diagram of these planes is shown in figure 4.

Magnification is a characteristic easily perceived by the majority of people who often seem to neglect the second equally important optical characteristic of a microscope objective lens, the NA:

$$\text{NA} = \mathfrak{n} \sin \Theta \tag{1}$$

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 287

**G**

Flow Tracers

**DoF** 

**Objective Lens**

Fig. 4. The object and image planes of a microscope objective lens have a finite depth along the optical axis. The object plane depth is called **Depth of Focus (DoF)**. Θ is the half cone angle of the objective light rays focused on a **focal point G** inside the object plane. OG is the

**Optical Axis** 

**Θ**

 **O B**

Where px is the pixel size of the video camera. The difference in the DoF estimations given

Another optical characteristic of the microscope objective lens, used frequently in photographic cameras, is called f number (f#). The f# is closely related to the NA, but is

OG f #

**DoFV (Video) (μm)** 

**Relative Difference** 

**V DoF DoF % DoF** 

<sup>D</sup> (5)

**<sup>V</sup>**

**Object Plane** 

**Image Plane** 

by the 2 formulas becomes important for NA > 0.5, as it is shown in Table 1.

**A**

10/0.25 8.5 9.3 - 9 20/0.5 1.9 2.3 - 17 40/0.6 1.2 1.6 - 25 40/0.75 0.6 1 - 35 60/1.4 Not defined 0.3 - Table 1. The Depth of Field (DoF) and the video Depth of Field (DoFV) depend on the objective lens. Numbers were estimated assuming: λa = 0.55 μm, η = 1, pixel size px = 16 μm.

focal distance of the objective lens and AB is its diameter D.

Microdevice Flow Field

Flow Direction

**Z** 

**DoF (Shillaber) (μm)** 

**Objective Lens (M/NA)** 

defined in purely geometrical terms:

Where η is the refraction index of the material between the lens and the specimen and Θ is the half angle of the cone of light received by the objective lens (figure 4). It should be noted that η is by definition always greater or equal to 1 and is a function of the light wavelength λ (η = f(λ)).

The NA is a very important lens specification for μPIV applications because of the following reasons: **First**, it determines in a non-linear way the light gathering ability of the objective lens: the higher the NA the much higher the light gathering capacity. **Second**, it specifies, in an inversely proportional way, the resolving ability (RA) or simply "resolution" of the objective lens, i.e. the smallest discernible distance between two objects (points) in the object plane:

$$\text{RA} = 0.61 \,\lambda\_\text{u} / \text{NA} \tag{2}$$

The above formula was derived using the Rayleigh criterion and assuming paraxial conditions (optical rays close to the optical axis). λa is the wavelength of light in the air.

**Third**, the NA specifies in a non-linear way, the depth of field or depth of focus DoF (figure 4) of an objective lens: the higher the NA the much lower the DoF. A typical "simple" equation quantifying the DoF of an objective lens was proposed by Shillaber (1944, as cited in Delly, 1988):

$$\text{DoF} = \lambda\_a \frac{\sqrt{\text{n}^2 - \text{NA}^2}}{\text{NA}^2} \tag{3}$$

However, there seems to be a difference between the DoF seen by an observer through an eyepiece and the DoFV when a video camera is attached on the microscope (Nakano et al., 2005):

α V 2 λη η px DoF NA Μ ΝΑ (4)

In addition, the particle diameter distribution should be monodispersive (diameter values distributed over a very limited range around the mean value). We shall see later that this

The basic optical characteristics carved on the metallic surface of every microscope objective lens are magnification (M) and **numerical aperture (NA)**. In simple terms, M shows how many times the perpendicular to the optical axis dimension of an object lying in the object plane is enlarged in the image plane on the other side of the lens. A schematic diagram of

Magnification is a characteristic easily perceived by the majority of people who often seem to neglect the second equally important optical characteristic of a microscope objective lens,

Where η is the refraction index of the material between the lens and the specimen and Θ is the half angle of the cone of light received by the objective lens (figure 4). It should be noted that η is by definition always greater or equal to 1 and is a function of the light wavelength λ

The NA is a very important lens specification for μPIV applications because of the following reasons: **First**, it determines in a non-linear way the light gathering ability of the objective lens: the higher the NA the much higher the light gathering capacity. **Second**, it specifies, in an inversely proportional way, the resolving ability (RA) or simply "resolution" of the objective lens, i.e. the smallest discernible distance between two objects (points) in the object plane:

The above formula was derived using the Rayleigh criterion and assuming paraxial conditions (optical rays close to the optical axis). λa is the wavelength of light in the air.

**Third**, the NA specifies in a non-linear way, the depth of field or depth of focus DoF (figure 4) of an objective lens: the higher the NA the much lower the DoF. A typical "simple" equation quantifying the DoF of an objective lens was proposed by Shillaber (1944, as cited

However, there seems to be a difference between the DoF seen by an observer through an eyepiece and the DoFV when a video camera is attached on the microscope (Nakano et al.,

> α V 2 λη η px DoF

DoF λ

α 2 η NA

NA Μ ΝΑ 

2 2

ΝΑ = η sinΘ (1)

RA = 0.61 λa/NA (2)

NA (3)

(4)

makes easier the design and error evaluation.

**2.2 Optical system** 

these planes is shown in figure 4.

**2.2.1 Basics** 

the NA:

(η = f(λ)).

in Delly, 1988):

2005):

Fig. 4. The object and image planes of a microscope objective lens have a finite depth along the optical axis. The object plane depth is called **Depth of Focus (DoF)**. Θ is the half cone angle of the objective light rays focused on a **focal point G** inside the object plane. OG is the focal distance of the objective lens and AB is its diameter D.

Where px is the pixel size of the video camera. The difference in the DoF estimations given by the 2 formulas becomes important for NA > 0.5, as it is shown in Table 1.


Table 1. The Depth of Field (DoF) and the video Depth of Field (DoFV) depend on the objective lens. Numbers were estimated assuming: λa = 0.55 μm, η = 1, pixel size px = 16 μm.

Another optical characteristic of the microscope objective lens, used frequently in photographic cameras, is called f number (f#). The f# is closely related to the NA, but is defined in purely geometrical terms:

$$\text{If } \# = \frac{\text{OG}}{\text{D}} \tag{5}$$

Where OG is the focal distance of the objective lens and D is its diameter (figure 4). The mathematical relationship between NA and f# can be derived from equations 1 and 5:

$$\text{If } \# = \frac{1}{2} \sqrt{\left(\frac{\eta}{\text{NA}}\right)^2 - 1} \tag{6}$$

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 289

In an attempt to quantify the contribution of out of focus particles in the velocity result, Olsen & Adrian (2000) introduced the concept of the "correlation depth". The correlation depth (Zcor) was defined as the axial distance from the object plane in which a particle becomes sufficiently out of focus so that it no longer contributes significantly to the velocity estimation (Werely & Meinhart, 2005). The **measurement plane width MPW** (proposed by Werely et al., (2000), as cited in Olsen & Adrian, (2000)) can be defined as double the Zcor:

MPW 2 Zcor 2 f # d 5.95

experiments than when using the exact f number relationship (equation 6).

DoFV is **higher than 300%** for all kinds of objective lenses.

**(μm) fp**

**DoFV (Video)** 

effect of particle diameter on MPW when dp < 0.5 μm.

**2.2.3 Effective Diameter (dE)** 

force microscopy and electron microscopy.

**Objective Lens (M/NA)** 

22 4

(8)

**Relative Difference** 

**V MPW DoF % DoF** 

**<sup>V</sup>**

2 2 a p p p 2 1 ε (M 1) λ f #

> **MPW (μm)**

ε 16 Μ

Where ε is the relative contribution of a particle located at a distance Zcor from the object plane, f#P is the f number with paraxial approximation (equation 7), dp is the particle diameter in the object plane, M is the objective lens magnification and λa is the wavelength of light in the air. According to Werely & Meinhart (2010), equation 8 agrees more closely to

A series of MPW values for various objective lenses and for a dp = 1μm are shown in Table 2 (ε = 0.01, λa = 0.55 μm, η = 1, px = 16 μm). The relative difference between the MPW and the

10/0.25 9.3 2 37.4 302 20/0.50 2.3 1 10.4 352 40/0.60 1.6 0.83 7.5 367 40/0.75 1 0.66 5.35 435 60/1.4 0.3 0.36 2.40 700 Table 2. Video Depth of Filed (DoFV) in comparison to the Measurement Plane Width (MPW).

In order to see the effect of the particle diameter dp on the MPW given by equation 8, the reader can see table 1 in Bourdon et al. (2004) and in Werely & Meinhart (2010), even though there seems to exist a discrepancy in the values given by the 2 groups (in addition, Werely & Meinhart (2010) do not mention the light wavelength used in their calculations). For the effect of dp on MPW using the exact definition of f number, the reader can see table 2.2 in Werely & Meinhart (2005) where it is shown that, for "dry" lenses, there is not a significant

The recorded image of a tracer particle is the convolution result between the geometric image of the particle and the point response function of the imaging system, given diffraction limited optics. The diameter of the geometric image of a particle is MdP. The particle diameter dP needed for determining the geometric image dimension is usually measured using an optical microscope and an object micrometer (micrometric ruler). For particle diameters less than about 0.2 μm other techniques must be used such as atomic

This is a strong non linear relationship which can be significantly simplified assuming paraxial conditions (tanΘ ≈ sinΘ ≈ Θ, Bown et al., 2005):

$$\text{If } \#\_{\mathbb{P}} = \frac{\text{\tiny n}}{\text{2NA}} \tag{7}$$

The assumption of paraxial conditions in equation 7, leads to a relative error less than 12% when f# > 1 or (NA/η) < 0.45.

#### **2.2.2 Measurement Plane Width (MPW)**

In classical PIV the measurement plane width (MPW) is defined by a laser light sheet because outside particles do not influence the result. However in μPIV, there is not any laser light sheet and most of the flow field is illuminated in a situation commonly referred to as "**volume illumination**" (figure 5). This means that an unknown amount of particles below and above the level of the object plane contributes to the position of the maximum of the correlation function and consequently to the velocity result (see Section 2.4). These particles are shown in the areas between the 2 solid lines and the 2 dashed lines of figure 5. The position of the 2 solid lines, depending on many factors related to the experimental set up (but primarily on the objective lens NA), can not be located accurately and therefore the MPW can not be determined in a rigorous way.

Fig. 5. The μPIV volume illumination principle: the depth of focus (DoF) is always much lower than the measurement plane width (MPW).

Where OG is the focal distance of the objective lens and D is its diameter (figure 4). The mathematical relationship between NA and f# can be derived from equations 1 and 5:

> <sup>2</sup> <sup>1</sup> <sup>η</sup> f # <sup>1</sup> 2 ΝΑ

This is a strong non linear relationship which can be significantly simplified assuming

The assumption of paraxial conditions in equation 7, leads to a relative error less than 12%

In classical PIV the measurement plane width (MPW) is defined by a laser light sheet because outside particles do not influence the result. However in μPIV, there is not any laser light sheet and most of the flow field is illuminated in a situation commonly referred to as "**volume illumination**" (figure 5). This means that an unknown amount of particles below and above the level of the object plane contributes to the position of the maximum of the correlation function and consequently to the velocity result (see Section 2.4). These particles are shown in the areas between the 2 solid lines and the 2 dashed lines of figure 5. The position of the 2 solid lines, depending on many factors related to the experimental set up (but primarily on the objective lens NA), can not be located accurately and therefore the

Fig. 5. The μPIV volume illumination principle: the depth of focus (DoF) is always much

**Optical Axis** 

P <sup>η</sup> f #

paraxial conditions (tanΘ ≈ sinΘ ≈ Θ, Bown et al., 2005):

when f# > 1 or (NA/η) < 0.45.

Flow Direction

**2.2.2 Measurement Plane Width (MPW)** 

MPW can not be determined in a rigorous way.

Microdevice Flow Field

lower than the measurement plane width (MPW).

**Z** 

(6)

<sup>2</sup>ΝΑ (7)

Flow Tracers

**MPW** 

**DoF**

**Measurement Plane** 

**Object Plane** 

**Image Plane** 

**Objective Lens**

In an attempt to quantify the contribution of out of focus particles in the velocity result, Olsen & Adrian (2000) introduced the concept of the "correlation depth". The correlation depth (Zcor) was defined as the axial distance from the object plane in which a particle becomes sufficiently out of focus so that it no longer contributes significantly to the velocity estimation (Werely & Meinhart, 2005). The **measurement plane width MPW** (proposed by Werely et al., (2000), as cited in Olsen & Adrian, (2000)) can be defined as double the Zcor:

$$\text{MPW} = 2 \cdot \text{Zcor} = 2 \cdot \sqrt{\frac{1 - \sqrt{\varepsilon} \left[ \left\| \text{\#}\_{\text{p}}{}^{2} \text{d}\_{\text{p}}{}^{2} + 5.95 \frac{(\text{M} + 1)^{2} \lambda\_{\text{a}}{}^{2} \text{f} \#\_{\text{p}}{}^{4} \right]}{16 \cdot \text{M}^{2}}} \right] \tag{8}$$

Where ε is the relative contribution of a particle located at a distance Zcor from the object plane, f#P is the f number with paraxial approximation (equation 7), dp is the particle diameter in the object plane, M is the objective lens magnification and λa is the wavelength of light in the air. According to Werely & Meinhart (2010), equation 8 agrees more closely to experiments than when using the exact f number relationship (equation 6).

A series of MPW values for various objective lenses and for a dp = 1μm are shown in Table 2 (ε = 0.01, λa = 0.55 μm, η = 1, px = 16 μm). The relative difference between the MPW and the DoFV is **higher than 300%** for all kinds of objective lenses.


Table 2. Video Depth of Filed (DoFV) in comparison to the Measurement Plane Width (MPW).

In order to see the effect of the particle diameter dp on the MPW given by equation 8, the reader can see table 1 in Bourdon et al. (2004) and in Werely & Meinhart (2010), even though there seems to exist a discrepancy in the values given by the 2 groups (in addition, Werely & Meinhart (2010) do not mention the light wavelength used in their calculations). For the effect of dp on MPW using the exact definition of f number, the reader can see table 2.2 in Werely & Meinhart (2005) where it is shown that, for "dry" lenses, there is not a significant effect of particle diameter on MPW when dp < 0.5 μm.

#### **2.2.3 Effective Diameter (dE)**

The recorded image of a tracer particle is the convolution result between the geometric image of the particle and the point response function of the imaging system, given diffraction limited optics. The diameter of the geometric image of a particle is MdP. The particle diameter dP needed for determining the geometric image dimension is usually measured using an optical microscope and an object micrometer (micrometric ruler). For particle diameters less than about 0.2 μm other techniques must be used such as atomic force microscopy and electron microscopy.

The diameter of the point response function dS is given by the Airy function:

$$\mathrm{d}\_{\mathbb{S}} = 2.44 \,\mathrm{(M+1)} \,\mathrm{f} \# \lambda\_u \tag{9}$$

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 291

The effective diameter dE is very important because it contributes to the random and bias error components (Section 3) in the displacement and velocity estimation. It has been shown (Prasad et al., 1992) that, when the centroiding technique is chosen for locating the autocorrelation peak, the total displacement error is minimized by selecting dE ≈ 2 pixels. The same result was obtained when a Gaussian peak fit estimator was used (Westerweel 1997). Since the pixel size is usually fixed, depending on the CCD camera, the number of pixels corresponding to the effective diameter dE can be arranged by selecting the appropriate optics and flow tracers. It should be noted however, that later authors preferred a design of dE ≈ 4 pixels (Buffone et al., 2005; Koutsiaris et al., 1999; Meinhart et al., 1999).

Finally, it should be noted that dE depends also on the vertical distance in the z direction from the object plane (figure 5). So, for out of focus particles located outside the object plane, there is a z dependent third term added in equation 10. This is beyond the scope of this

Volume illumination can be implemented with 2 different experimental set ups: **fluorescence** and **brightfield** illumination. In the experimental set ups with fluorescence, **darkfield images** are produced by the camera and are sent to the PC for off line processing (figure 6). In a darkfield image the tracers appear bright in a dark background, as in the

**MPW** 

**PC** 

Fluorescent Tracers

Dichromatic Mirror

8 to 16 bit

**Objective Lens**

Barrier Filter

**CCD camera** 

Microdevice Flow Field

Fig. 6. Digital μPIV set up with fluorescence. MPW: Measurement Plane Width.

Band Filter

chapter (see Bown et al., 2005).

**2.2.4 Fluorescence μPIV** 

Broad Spectrum Light Source

Flow Direction

Adrian and Yao (1985, as cited in Werely & Meinhart, 2005) found that the Airy function can be approximated accurately by a Gaussian function. Given spherical particles and diffraction limited optics the geometric image can also be approximated accurately by a Gaussian function and the total diameter dE (effective diameter in microns) of the particle in the image plane can be approximated by:

$$\mathbf{d}\_{\rm E} = \sqrt{\left(\mathbf{M}\mathbf{d}\_{\rm P}\right)^{2} + \mathbf{d}\_{\rm S}^{\rm 2}} \tag{10}$$

Then effective diameter can be converted to pixels by using the pixel size of the video camera. The contribution of the geometric and the point response components in the final dE is shown in Table 3 for various particle diameters, in the case of a 10/0.25 objective lens (λa = 0.55 μm).


Table 3. The geometric and the point response component of the effective particle diameter dE.

As it can be observed in the gray line of table 3, when the geometric component is **less than one third of dS**, then it contributes by less than 5% in the final effective diameter dE. In practice this means that for an objective lens 10/0.25, all particles with diameters dP < 1μm will have an effective diameter approximately equal to dS .

In Table 4, the point response diameter dS is given for commonly used objective lenses and λa = 0.55μm. It should be noted that in the case of oil immersion objectives (60/1.4) the NA is equal to the refraction index of the medium and using equation 6 this gives f# = 0 (hence dS = 0, which is not true). In this case, the f# should be estimated by its original definition (equation 5). In Table 4, for the case 60/1.4 it was assumed that f# = 0.2.


Table 4. Point response diameter dS for various objective lenses.

The effective diameter dE is very important because it contributes to the random and bias error components (Section 3) in the displacement and velocity estimation. It has been shown (Prasad et al., 1992) that, when the centroiding technique is chosen for locating the autocorrelation peak, the total displacement error is minimized by selecting dE ≈ 2 pixels. The same result was obtained when a Gaussian peak fit estimator was used (Westerweel 1997). Since the pixel size is usually fixed, depending on the CCD camera, the number of pixels corresponding to the effective diameter dE can be arranged by selecting the appropriate optics and flow tracers. It should be noted however, that later authors preferred a design of dE ≈ 4 pixels (Buffone et al., 2005; Koutsiaris et al., 1999; Meinhart et al., 1999).

Finally, it should be noted that dE depends also on the vertical distance in the z direction from the object plane (figure 5). So, for out of focus particles located outside the object plane, there is a z dependent third term added in equation 10. This is beyond the scope of this chapter (see Bown et al., 2005).

### **2.2.4 Fluorescence μPIV**

290 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

 dS = 2.44 (M+1) f# λa (9) Adrian and Yao (1985, as cited in Werely & Meinhart, 2005) found that the Airy function can be approximated accurately by a Gaussian function. Given spherical particles and diffraction limited optics the geometric image can also be approximated accurately by a Gaussian function and the total diameter dE (effective diameter in microns) of the particle in

Then effective diameter can be converted to pixels by using the pixel size of the video camera. The contribution of the geometric and the point response components in the final dE is shown in Table 3 for various particle diameters, in the case of a 10/0.25 objective lens (λa =

> **Point Response Component dS (μm)**

> > 28.6

0.5 5 29.0 - 1.4 0.7 7 29.4 - 2.7 1.0 10 30.3 - 5.6 3.0 30 41.4 - 31.0 5.0 50 57.6 - 50.3 Table 3. The geometric and the point response component of the effective particle diameter dE.

As it can be observed in the gray line of table 3, when the geometric component is **less than one third of dS**, then it contributes by less than 5% in the final effective diameter dE. In practice this means that for an objective lens 10/0.25, all particles with diameters dP < 1μm

In Table 4, the point response diameter dS is given for commonly used objective lenses and λa = 0.55μm. It should be noted that in the case of oil immersion objectives (60/1.4) the NA is equal to the refraction index of the medium and using equation 6 this gives f# = 0 (hence dS = 0, which is not true). In this case, the f# should be estimated by its original definition

**F#** 1.94 0.87 0.66 0.44 0.2 **dS (μm)** 28.6 24.5 36.3 24.2 16.4

10/0.25 20/0.50 40/0.60 40/0.75 60/1.4

<sup>2</sup> <sup>2</sup> d Md d E PS (10)

**Effective Diameter dE (μm)** 

28.6 0

**Relative Difference S E E d d % d** 

The diameter of the point response function dS is given by the Airy function:

the image plane can be approximated by:

**Geometric Component M dP (μm)** 

will have an effective diameter approximately equal to dS .

(equation 5). In Table 4, for the case 60/1.4 it was assumed that f# = 0.2.

Table 4. Point response diameter dS for various objective lenses.

0.55 μm).

**Particle Diameter dP (μm)** 

Objective Lens (M/NA)

0.1 1

Volume illumination can be implemented with 2 different experimental set ups: **fluorescence** and **brightfield** illumination. In the experimental set ups with fluorescence, **darkfield images** are produced by the camera and are sent to the PC for off line processing (figure 6). In a darkfield image the tracers appear bright in a dark background, as in the

Fig. 6. Digital μPIV set up with fluorescence. MPW: Measurement Plane Width.

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 293

Broad Spectrum Light Source

**Condenser Lens** 

Tracers

**Objective Lens**

8 to 16 bit

**MPW** 

**PC** 

Microdevice Flow Field

Fig. 7. Digital μPIV set up with brightfield illumination. MPW: Measurement Plane Width.

**CCD camera** 

**e**

Fig. 8. Glass cylindrical capillaries with internal diameters of ≈ 275 μm. (a) Glass particles suspended in water: in the diametric plane, approximately 41% of the internal diameter is not visible (black band e ≈ 57 μm). (b) The black bands disappeared when the glass particles

(a) (b)

were suspended in a mixture of 75% glycerol and 25% water.

classical film negatives. When a monochromatic light source (laser) is used, the band pass filter is not necessary.

The first μPIV system using an upright **epi-fluorescent** microscope was reported by Santiago et al. (1998). The vast majority of fluorescent microscopes are epi-fluorescent (figure 6), meaning that image sensors detect the back scattered (reflected) fluorescence from the object plane and not the transmitted fluorescence. Santiago et al. (1998) used 300 nm in diameter, fluorescently labeled, PSL particles in the flow field between a microscope slide and a 170 μm thick coverslip. The liquid thickness between the slide and the coverslip was ≈ 5 μm and the spatial resolution was 6.9 x 6.9 x 1.5 μm. Because of the large time delay between successive images, they managed to measure only low velocities of the order of 35μm/s. One year later, Meinhart et al. (1999), using an inverted epi-fluorescent microscope, and a different digital camera illuminated by 2 Nd:YAG lasers, reduced the time delay between images by more than a factor of 100 and managed to measure velocities of the order of 10 mm/s.

### **2.2.5 Brightfield μPIV**

In brightfield μPIV images, the tracers appear dark in a **bright background**, as the objects in the positive photos of everyday photographic albums. This happens because particles are not fluorescent and instead of emitting they actually absorb light.

The first μPIV system without fluorescence, using an inverted brightfield microscope (transmission mode) was reported by Koutsiaris et al. (1999). The vast majority of the brightfield microscopes work in **transmission mode**, meaning that video cameras detect the transmitted (forward scattered) light from the object plane (figure 7).

Koutsiaris et al. (1999) used borosilicate glass particles with a mean diameter of 10 μm to seed the flow of a suspension consisting of glycerol and water. The distinctive optical characteristic of this suspension was the similar refractive index with the glass capillary (figure 8). They demonstrated for the first time that μPIV is possible in cylindrical microtubes (150 to 300 μm internal diameter) by using the aforementioned suspension and by surrounding the capillary with a fluid having a similar refractive index with the capillary. The spatial resolution of their velocity fields was 26.2 x 335 x 10 μm, optimized for the velocity profile measurement inside the capillaries and velocities up to the order of 5 mm/s were measured. In addition, the application of the μPIV technique at the microvessels of a living animal was proposed for the first time and a discussion on possible obstacles of such an attempt was presented.

A brightfield μPIV set up can be considered as the dual counterpart of the fluorescence set up, but without requiring complex and expensive fluorescence hardware such as a special light source, filters and a dichromatic mirror. It seems that a brightfield set up has a higher in focus noise in comparison to a fluorescent set up but a smaller contribution to noise from out of focus particles. In addition, dark particles with diameters lower than about 0.5 μm can not be easily resolved by an optical microscope. It seems that these topics as well as the MPW and the dE in the case of a brightfield set up have not been fully exploited by the research community yet.

classical film negatives. When a monochromatic light source (laser) is used, the band pass

The first μPIV system using an upright **epi-fluorescent** microscope was reported by Santiago et al. (1998). The vast majority of fluorescent microscopes are epi-fluorescent (figure 6), meaning that image sensors detect the back scattered (reflected) fluorescence from the object plane and not the transmitted fluorescence. Santiago et al. (1998) used 300 nm in diameter, fluorescently labeled, PSL particles in the flow field between a microscope slide and a 170 μm thick coverslip. The liquid thickness between the slide and the coverslip was ≈ 5 μm and the spatial resolution was 6.9 x 6.9 x 1.5 μm. Because of the large time delay between successive images, they managed to measure only low velocities of the order of 35μm/s. One year later, Meinhart et al. (1999), using an inverted epi-fluorescent microscope, and a different digital camera illuminated by 2 Nd:YAG lasers, reduced the time delay between images by more than

In brightfield μPIV images, the tracers appear dark in a **bright background**, as the objects in the positive photos of everyday photographic albums. This happens because particles are

The first μPIV system without fluorescence, using an inverted brightfield microscope (transmission mode) was reported by Koutsiaris et al. (1999). The vast majority of the brightfield microscopes work in **transmission mode**, meaning that video cameras detect the

Koutsiaris et al. (1999) used borosilicate glass particles with a mean diameter of 10 μm to seed the flow of a suspension consisting of glycerol and water. The distinctive optical characteristic of this suspension was the similar refractive index with the glass capillary (figure 8). They demonstrated for the first time that μPIV is possible in cylindrical microtubes (150 to 300 μm internal diameter) by using the aforementioned suspension and by surrounding the capillary with a fluid having a similar refractive index with the capillary. The spatial resolution of their velocity fields was 26.2 x 335 x 10 μm, optimized for the velocity profile measurement inside the capillaries and velocities up to the order of 5 mm/s were measured. In addition, the application of the μPIV technique at the microvessels of a living animal was proposed for the first time and a discussion on possible obstacles of

A brightfield μPIV set up can be considered as the dual counterpart of the fluorescence set up, but without requiring complex and expensive fluorescence hardware such as a special light source, filters and a dichromatic mirror. It seems that a brightfield set up has a higher in focus noise in comparison to a fluorescent set up but a smaller contribution to noise from out of focus particles. In addition, dark particles with diameters lower than about 0.5 μm can not be easily resolved by an optical microscope. It seems that these topics as well as the MPW and the dE in the case of a brightfield set up have not been fully exploited by the

a factor of 100 and managed to measure velocities of the order of 10 mm/s.

not fluorescent and instead of emitting they actually absorb light.

transmitted (forward scattered) light from the object plane (figure 7).

filter is not necessary.

**2.2.5 Brightfield μPIV** 

such an attempt was presented.

research community yet.

Fig. 7. Digital μPIV set up with brightfield illumination. MPW: Measurement Plane Width.

Fig. 8. Glass cylindrical capillaries with internal diameters of ≈ 275 μm. (a) Glass particles suspended in water: in the diametric plane, approximately 41% of the internal diameter is not visible (black band e ≈ 57 μm). (b) The black bands disappeared when the glass particles were suspended in a mixture of 75% glycerol and 25% water.

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 295

potential well of the camera corresponds to a pixel. Therefore, the higher the light intensity on the camera sensor, the higher the amount of electrons trapped inside the potential wells, and the higher the gray value of the corresponding pixel. In fact it is the product of the light intensity and the exposure time which affects the final gray value of a pixel. The most important characteristics of a CCD camera are: **1)** the quality of the CCD sensor, **2)** the architecture of the CCD sensor, **3)** the sensitivity (lowest detectable light intensity), **4)** the frame rate capacity (frames per second, fps) and **5)** the gray level dynamic range where the

Monochrome CCD cameras are preferable to color CCD cameras (Breuer 2005), because colors usually increase the complexity and the cost of a camera at the expense of frame rate, sensitivity and dynamic range. In addition pixels should be square to avoid complexities

For μPIV systems, non interlaced high speed digital cameras are preferred. A camera is of the "**high speed**" type, when it can acquire more than 25 (EUROPE) or 30 (USA and JAPAN) full frames per second (fps). But in special μPIV applications, speeds up to 2000 fps may be necessary. A high speed camera is a prerequisite in μPIV applications because of the magnified measurement plane causing the virtual magnification of the real velocities.

In the interlaced format, first all the odd rows of the image frame are read out and then all the even rows. This introduces a series of complications in PIV applications. In order to avoid these complications, other architectures are recommended such as the frame transfer and the full frame interline transfer architecture. In the **frame transfer architecture** the camera sensor is divided into two different rectangular areas: 1) the active or light sensitive area used for image acquisition and 2) the inactive or masked storage area used for the temporal storage of each acquired image. In the **full frame interline transfer architecture**

The original advantage of the frame transfer architecture was the 100% fill factor i.e. the absence of gaps between pixels. In contrast, full frame interline transfer cameras had always fill factors much less than 100%. Later, this disadvantage was almost eliminated by using

The **sensitivity** of a Digital μPIV camera should be enough to acquire images of the tracer particles flowing inside the microstructure. This is not so trivial to estimate because it depends on many factors such as frame rate, exposure time and the wavelength depended

In **CMOS (Complementary Metal Oxide Semiconductor)** cameras, photodiodes are used for detecting light instead of potential wells. A relatively new development is active pixel sensor (APS) technology which allows the integration of amplification on each pixel with an appropriate MOS-FET transistor. In a typical APS implementation **each pixel** consists of a photodiode and 3 transistors: a reset transistor to control integration time, a readout

Advantages of the **CMOS sensors in comparison to the CCD sensors** are the recording of high contrast images without blooming, higher pixel rates (less clock pulses per pixel read out) leading to higher frame rates at the same resolution, electronic shuttering integrated in each pixel (shutter transistor) and windowing (reading smaller windows of the sensor array

the masked area is composed of columns between the active columns of the sensor.

factors of quantum efficiency (QE) and noise equivalent exposure (NEE).

amplifier transistor (source follower) and a row select transistor.

related to the conversion from image domain (pixels) to real dimensions.

camera operates linearly.

micro lenses in front of the sensor.

### **2.2.6 Confocal μPIV**

The incorporation of confocal imaging in a μPIV experimental set up provides a powerful experimental tool introduced by Park et al. (2004). In a confocal optical system the object plane of interest is scanned point by point by a laser beam. Each scanned point of the measurement plane is the optical conjugate of a pinhole located in the image plane of the objective lens. This fact reduces the signal intensity passing through the pinhole, but also reduces dramatically the out of focus background light, producing a rigorously defined optical slice in the object plane with a thickness much smaller than that in ordinary optical systems.

The confocal μPIV has the following advantages over the classical μPIV: **first**, the difference between the depth of focus (DoF) and the measurement plane width (MPW) is significantly smaller due to the confocal superiority over classical optics in terms of axial resolution.

**Second,** the increased axial resolution implies sharp reduction of background light from out of focus images and higher signal to noise ratios for the correlation operation. **Third**, there are no different effective particle diameters produced from their different distances from the object plane.

Despite the numerous advantages of the confocal μPIV, there are some disadvantages stemming out from the operating principle of confocal imaging according to which a single point can only be imaged at one instance in time. This means that each image is produced by scanning a 2D plane point by point, which implies restrictions in the frame rate and increased cost due to complex hardware. Restrictions in the frame rate (hence in the maximum measurable velocity) can be overcome by using a superfast Nipkow disk (Lima et al., 2006; Park et al., 2004). However, this action further increases complexity and cost.

It seems that, confocal μPIV has not been applied without fluorescence. This would perhaps be feasible in relatively transparent media which do not attenuate light intensity significantly. In addition, image processing of confocal images could increase even more the image quality (signal to noise ratio).

Combining 2D velocity fields at different z positions (figure 5), confocal data can be used in steady flows to calculate the 3D velocity field by applying the continuity equation. Other methods for the quantification of the 3D velocity field are digital holography, stereo μPIV and particle image defocusing. In stereo μPIV (Bown et al., 2006; Lindken et al., 2006) all 3 velocity components in space can be extracted from a single 2D plane. More details on the 3D μPIV techniques can be found in the review papers of Lee & Kim (2009) and Werely & Meinhart (2010) and a comparison between stereo μPIV and the multiple 2D velocity field technique was presented in the paper of Bown et al. (2006).

### **2.3 Digital Electronics System (camera)**

The digital electronics component of μPIV set up comprises a digital video camera, a frame grabber and a personal computer. The usual way is to put emphasis on the camera design, but its performance depends heavily on the frame grabber design so, they usually come together.

Most digital cameras are based on the **CCD (Charge-Coupled Device)** technology. Briefly, photons from the optical image of the measurement plane hit on the surface of the camera producing free electrons, which in their turn are trapped inside potential wells. Each

The incorporation of confocal imaging in a μPIV experimental set up provides a powerful experimental tool introduced by Park et al. (2004). In a confocal optical system the object plane of interest is scanned point by point by a laser beam. Each scanned point of the measurement plane is the optical conjugate of a pinhole located in the image plane of the objective lens. This fact reduces the signal intensity passing through the pinhole, but also reduces dramatically the out of focus background light, producing a rigorously defined optical slice in the object plane

The confocal μPIV has the following advantages over the classical μPIV: **first**, the difference between the depth of focus (DoF) and the measurement plane width (MPW) is significantly smaller due to the confocal superiority over classical optics in terms of axial resolution.

**Second,** the increased axial resolution implies sharp reduction of background light from out of focus images and higher signal to noise ratios for the correlation operation. **Third**, there are no different effective particle diameters produced from their different distances from the

Despite the numerous advantages of the confocal μPIV, there are some disadvantages stemming out from the operating principle of confocal imaging according to which a single point can only be imaged at one instance in time. This means that each image is produced by scanning a 2D plane point by point, which implies restrictions in the frame rate and increased cost due to complex hardware. Restrictions in the frame rate (hence in the maximum measurable velocity) can be overcome by using a superfast Nipkow disk (Lima et al., 2006; Park et al., 2004). However, this action further increases complexity and cost.

It seems that, confocal μPIV has not been applied without fluorescence. This would perhaps be feasible in relatively transparent media which do not attenuate light intensity significantly. In addition, image processing of confocal images could increase even more the

Combining 2D velocity fields at different z positions (figure 5), confocal data can be used in steady flows to calculate the 3D velocity field by applying the continuity equation. Other methods for the quantification of the 3D velocity field are digital holography, stereo μPIV and particle image defocusing. In stereo μPIV (Bown et al., 2006; Lindken et al., 2006) all 3 velocity components in space can be extracted from a single 2D plane. More details on the 3D μPIV techniques can be found in the review papers of Lee & Kim (2009) and Werely & Meinhart (2010) and a comparison between stereo μPIV and the multiple 2D velocity field

The digital electronics component of μPIV set up comprises a digital video camera, a frame grabber and a personal computer. The usual way is to put emphasis on the camera design, but its performance depends heavily on the frame grabber design so, they usually come together. Most digital cameras are based on the **CCD (Charge-Coupled Device)** technology. Briefly, photons from the optical image of the measurement plane hit on the surface of the camera producing free electrons, which in their turn are trapped inside potential wells. Each

with a thickness much smaller than that in ordinary optical systems.

**2.2.6 Confocal μPIV** 

object plane.

image quality (signal to noise ratio).

**2.3 Digital Electronics System (camera)** 

technique was presented in the paper of Bown et al. (2006).

potential well of the camera corresponds to a pixel. Therefore, the higher the light intensity on the camera sensor, the higher the amount of electrons trapped inside the potential wells, and the higher the gray value of the corresponding pixel. In fact it is the product of the light intensity and the exposure time which affects the final gray value of a pixel. The most important characteristics of a CCD camera are: **1)** the quality of the CCD sensor, **2)** the architecture of the CCD sensor, **3)** the sensitivity (lowest detectable light intensity), **4)** the frame rate capacity (frames per second, fps) and **5)** the gray level dynamic range where the camera operates linearly.

Monochrome CCD cameras are preferable to color CCD cameras (Breuer 2005), because colors usually increase the complexity and the cost of a camera at the expense of frame rate, sensitivity and dynamic range. In addition pixels should be square to avoid complexities related to the conversion from image domain (pixels) to real dimensions.

For μPIV systems, non interlaced high speed digital cameras are preferred. A camera is of the "**high speed**" type, when it can acquire more than 25 (EUROPE) or 30 (USA and JAPAN) full frames per second (fps). But in special μPIV applications, speeds up to 2000 fps may be necessary. A high speed camera is a prerequisite in μPIV applications because of the magnified measurement plane causing the virtual magnification of the real velocities.

In the interlaced format, first all the odd rows of the image frame are read out and then all the even rows. This introduces a series of complications in PIV applications. In order to avoid these complications, other architectures are recommended such as the frame transfer and the full frame interline transfer architecture. In the **frame transfer architecture** the camera sensor is divided into two different rectangular areas: 1) the active or light sensitive area used for image acquisition and 2) the inactive or masked storage area used for the temporal storage of each acquired image. In the **full frame interline transfer architecture** the masked area is composed of columns between the active columns of the sensor.

The original advantage of the frame transfer architecture was the 100% fill factor i.e. the absence of gaps between pixels. In contrast, full frame interline transfer cameras had always fill factors much less than 100%. Later, this disadvantage was almost eliminated by using micro lenses in front of the sensor.

The **sensitivity** of a Digital μPIV camera should be enough to acquire images of the tracer particles flowing inside the microstructure. This is not so trivial to estimate because it depends on many factors such as frame rate, exposure time and the wavelength depended factors of quantum efficiency (QE) and noise equivalent exposure (NEE).

In **CMOS (Complementary Metal Oxide Semiconductor)** cameras, photodiodes are used for detecting light instead of potential wells. A relatively new development is active pixel sensor (APS) technology which allows the integration of amplification on each pixel with an appropriate MOS-FET transistor. In a typical APS implementation **each pixel** consists of a photodiode and 3 transistors: a reset transistor to control integration time, a readout amplifier transistor (source follower) and a row select transistor.

Advantages of the **CMOS sensors in comparison to the CCD sensors** are the recording of high contrast images without blooming, higher pixel rates (less clock pulses per pixel read out) leading to higher frame rates at the same resolution, electronic shuttering integrated in each pixel (shutter transistor) and windowing (reading smaller windows of the sensor array

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 297

In more detail, let's take an interrogation window pair and assume that f(x,y) is the luminous intensity distribution of the first window and g(x,y) the distribution in the second.

Where (sx, sy) is the variable vector **s** coordinates of the new CCOR window (figure 10). Assuming that the interrogation windows of the first and second image have the same dimensions M x N pixels (Fig. 9(b)), then the CCOR result window will have dimensions (M+M-1) x (N+N-1) = (2M-1) x (2N-1) pixels. For negative images, the CCOR function will have a maximum value (peak) at position (sxMAX, syMAX) where the image of the particles in the first window coincides with the image of the particles in the second window. The CCOR peak is shown in white color in figure 10. The **vector distance SM between the geometrical center of the CCOR window and the peak of the CCOR function** corresponds to the

Fig. 10. The displacement vector **SM**, starts from the geometrical center of the **CCOR window** and ends at the peak of the CCOR function shown in white. In the rest area of the window various values of the CCOR function are shown in dark color. Any other peak of the CCOR function giving a false estimate of the vector S is considered as "noise''. The higher the difference of the "white" CCOR peak from the second highest peak, the higher

geometrical center of the CCOR window and the minimum of the CCOR function.

By analogy, when the original images are **positive** (Fig. 7 & 8), we are interested in the location of the **CCOR minimum** in order to estimate the vector distance S between the

In a perfect situation of a white particle on a completely black background οf the first window, the size of the CCOR window permits the detection of a displacement equal to M-1 pixels in the x direction and to N-1 pixels in the y direction. However, these conditions are never met in real experimental conditions with many "gray" particles from which some are lost between the first and second window. Therefore, the statistical correlation estimator

CCOR(s ,s ) f(x, x y <sup>y</sup> x y )g(x s ,y s )dxdy (11)

**SM** 

Then, the cross correlation function is given by the formula:

statistical mean displacement of the window particles.

the signal to noise ratio.

**sY**

**sX**

CCOR has 3 components (Keane & Adrian 1992):

at higher frame rates). More details on digital cameras can be found elsewhere (Holst, 1998; Raffel et al., 2007).

#### **2.4 Software**

According to the PIV method, successive recorded images of the flow field in the (x,y) measurement plane are divided into rectangular areas called "interrogation windows" (figure 9). The time interval Δt between the recorded images is defined by the frame rate of the digital camera.

The record of the successive images of the flow in the measurement plane can form "pairs": the first pair includes the first image and the second image after Δt, the second pair includes the second and third image, etc. Each image pair corresponds to a collection of interrogation window pairs.

Fig. 9. **(a)** Side view of the measurement plane (x,y). The measurement plane width (MPW) here is defined along the z axis. **(b)** Top view of the measurement plane (x,y) with the interrogation windows shown in dashed line. The size of each interrogation window in this figure is M x N pixels.

The PIV method is based on the following assumptions: **1)** the average velocity of the fluid inside every interrogation window is accurately described by the average velocity of the particle tracers inside the same window, **2)** the average particle velocity inside every window can be found by calculating the average particle displacement **S** caused by the flow in and **3)** the average particle displacement S can be estimated using the correlation function on the 2 window particle images.

at higher frame rates). More details on digital cameras can be found elsewhere (Holst, 1998;

According to the PIV method, successive recorded images of the flow field in the (x,y) measurement plane are divided into rectangular areas called "interrogation windows" (figure 9). The time interval Δt between the recorded images is defined by the frame rate of

The record of the successive images of the flow in the measurement plane can form "pairs": the first pair includes the first image and the second image after Δt, the second pair includes the second and third image, etc. Each image pair corresponds to a collection of interrogation

**(a)**

Tracers

**MPW** 

Microdevice Flow Field

**M** 

**N** 

Fig. 9. **(a)** Side view of the measurement plane (x,y). The measurement plane width (MPW) here is defined along the z axis. **(b)** Top view of the measurement plane (x,y) with the interrogation windows shown in dashed line. The size of each interrogation window in this

**(b)**

The PIV method is based on the following assumptions: **1)** the average velocity of the fluid inside every interrogation window is accurately described by the average velocity of the particle tracers inside the same window, **2)** the average particle velocity inside every window can be found by calculating the average particle displacement **S** caused by the flow in and **3)** the average particle displacement S can be estimated using the correlation function on the 2

Raffel et al., 2007).

the digital camera.

window pairs.

**Z** 

**Y** 

**Y** 

**X** 

figure is M x N pixels.

**X** 

window particle images.

**2.4 Software** 

In more detail, let's take an interrogation window pair and assume that f(x,y) is the luminous intensity distribution of the first window and g(x,y) the distribution in the second. Then, the cross correlation function is given by the formula:

$$\text{CCOR}(\mathbf{s}\_{\mathbf{x'}} \mathbf{s}\_{\mathbf{y}}) = \iint \mathbf{f}(\mathbf{x}, \mathbf{y}) \mathbf{g}(\mathbf{x} + \mathbf{s}\_{\mathbf{x'}} \mathbf{y} + \mathbf{s}\_{\mathbf{y}}) \text{dxdy} \tag{11}$$

Where (sx, sy) is the variable vector **s** coordinates of the new CCOR window (figure 10). Assuming that the interrogation windows of the first and second image have the same dimensions M x N pixels (Fig. 9(b)), then the CCOR result window will have dimensions (M+M-1) x (N+N-1) = (2M-1) x (2N-1) pixels. For negative images, the CCOR function will have a maximum value (peak) at position (sxMAX, syMAX) where the image of the particles in the first window coincides with the image of the particles in the second window. The CCOR peak is shown in white color in figure 10. The **vector distance SM between the geometrical center of the CCOR window and the peak of the CCOR function** corresponds to the statistical mean displacement of the window particles.

Fig. 10. The displacement vector **SM**, starts from the geometrical center of the **CCOR window** and ends at the peak of the CCOR function shown in white. In the rest area of the window various values of the CCOR function are shown in dark color. Any other peak of the CCOR function giving a false estimate of the vector S is considered as "noise''. The higher the difference of the "white" CCOR peak from the second highest peak, the higher the signal to noise ratio.

By analogy, when the original images are **positive** (Fig. 7 & 8), we are interested in the location of the **CCOR minimum** in order to estimate the vector distance S between the geometrical center of the CCOR window and the minimum of the CCOR function.

In a perfect situation of a white particle on a completely black background οf the first window, the size of the CCOR window permits the detection of a displacement equal to M-1 pixels in the x direction and to N-1 pixels in the y direction. However, these conditions are never met in real experimental conditions with many "gray" particles from which some are lost between the first and second window. Therefore, the statistical correlation estimator CCOR has 3 components (Keane & Adrian 1992):

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 299

low so, some kind of image processing is usually required in order to reduce the noise level

Using the velocity definition equation 13, there are two major error sources contributing to the total velocity measurement error: the error Δte in the estimation of the time interval between two images and the error ΔSe of the displacement calculation. The time interval error is considered negligible hence we can focus on ΔSe. Generally, ΔSe can be considered equal to the square root of the sum of the squares of a random (RAN) and a mean bias (BS)

RAN or precision is considered proportional to the effective particle image diameter dE and

Where c is a proportionality constant ranging between 1% and 10% depending on various experimental factors such as flow tracing, velocity gradients, non uniform illumination,

Most of the factors contributing to the random component can also be sources of error for the mean bias component BS. In more detail, BS could have the following error components: **1)** flow tracing error, **2)** flow structure error, **3)** particle image generation error and **4)**

**Flow tracing error** is determined by the quality of density matching between particles and

**Flow structure error** is caused by fluid accelerations in Δt and from velocity spatial gradients inside the interrogation windows. Starting from fluid acceleration and assuming it causes a critical velocity change in time τ inside the interrogation window, then, if Δt > τ, the result will be an integration of **V**(t) over the time difference Δt of successive images. For a proper PIV quantification of the **instantaneous velocity field**, Δt should be less than τ in all interrogation windows. The definition of the **time scale τ** depends on the application and the wanted quantification quality (temporal resolution). It should be noted that in the case of linear fluid acceleration, Δt can be equal or greater than τ as long as an average estimation

In analog terms with the above paragraph, assuming that a velocity gradient causes a critical velocity change in distance δ less than the size of the window, the result would be by definition an average velocity value over the surface area of the window. For a proper PIV quantification of the **spatial velocity field**, window size should be less than δ in all interrogation windows. The definition of the **space scale δ** depends on the application and the wanted quantification quality (spatial resolution). It should be noted that in the case of a linear gradient along only a certain direction (x or y) the selection criteria of δ may be less strict.

2 2 ΔSe RAN BS (14)

RAN c d E S λ (15)

or in other words to remove the background noise (Koutsiaris et al., 1999).

the streak length s (Adrian, 1991) according to the formula:

CCD camera electronics, the cable and digitization noise.

**3. Error analysis (Uncertainty)** 

interrogation procedure error.

fluid and the Brown motion.

of the velocity is acceptable.

component:

$$\text{CCOR}(\mathbf{s}) = \text{CCOR}\_{\text{D}}(\mathbf{s}) + \text{CCOR}\_{\text{C}}(\mathbf{s}) + \text{CCOR}\_{\text{f}}(\mathbf{s}) \tag{12}$$

Where CCORD is the displacement component (the peak of which we want), CCORC is the mean intensity convolution component and CCORF is the component of the convolution of the mean intensity of the first window with the fluctuating intensity of the second window. The components CCORC and CCORF are considered as "noise" creating a fluctuating background shown as a dark background in figure 10.

Since the computation of the cross correlation function in the space domain is time consuming, it is usually estimated in the frequency domain by using the **Fast Fourier Transform (FFT)**. Using the FFT algorithmic technique, the calculation of the CCOR is at least 10 times faster, depending on the information content of the interrogation windows. In some applications it can be 100 times faster. The shortcoming is that the CCOR window has now the same dimensions with the interrogation windows and consequently the dynamic range of the measured displacements is reduced.

Using a Gaussian interpolation in the determination of the cross correlation peak, **subpixel accuracy** can be achieved (Willert & Gharib, 1991) in the estimation of the **SM** magnitude. Then a **conversion factor (CF)** measured in μm/pixel is needed to transform the pixel units of **SM** to micrometers. Since the nominal magnification of a video microscopic system often deviates from reality, an object micrometer is the best way for the CF determination.

Knowing the time interval Δt between the two successive images from the frame rate of the camera, the statistical mean velocity **V** corresponding to each interrogation window pair can be estimated from the classical velocity definition:

$$\mathbf{V} = \frac{\mathbf{S}\_{\text{M}}}{\Delta t} \tag{13}$$

Repeating the procedure described in the above paragraphs for all the interrogation window pairs belonging to an image pair, a computer software program can calculate the **whole velocity field**.

In the early PIV implementations many scientists preferred using the **autocorrelation (ACOR)** function on a single image with double exposure. This technique is not used frequently any more, mainly due to the fact that ACOR is a 5 component estimator (Adrian, 1991, as cited in Keane & Adrian, 1992). Two of the five components are displacement components at symmetrical positions with respect to the correlation window center. This has the following implications: **1)** directional ambiguity, **2)** increased hardware complexity to select the right displacement component and **3)** approximately double noise level in comparison to CCOR. In addition, the CCOR technique permits the second window to be larger than the first window in order to reduce the in plane loss of particles Fi. This is not possible with the ACOR function.

In a **bright field μPIV set up**, the images are positive and consequently the displacement vector SM can be estimated by two different ways: **1)** images are inverted to their negative version and the same software algorithm described above is used and **2)** positive images are used but now there should be a difference in the algorithm: the minimum of the CCOR function is detected. In either case, the typical signal to noise ratio in a brightfield set up is low so, some kind of image processing is usually required in order to reduce the noise level or in other words to remove the background noise (Koutsiaris et al., 1999).

### **3. Error analysis (Uncertainty)**

298 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

Where CCORD is the displacement component (the peak of which we want), CCORC is the mean intensity convolution component and CCORF is the component of the convolution of the mean intensity of the first window with the fluctuating intensity of the second window. The components CCORC and CCORF are considered as "noise" creating a fluctuating

Since the computation of the cross correlation function in the space domain is time consuming, it is usually estimated in the frequency domain by using the **Fast Fourier Transform (FFT)**. Using the FFT algorithmic technique, the calculation of the CCOR is at least 10 times faster, depending on the information content of the interrogation windows. In some applications it can be 100 times faster. The shortcoming is that the CCOR window has now the same dimensions with the interrogation windows and consequently the dynamic

Using a Gaussian interpolation in the determination of the cross correlation peak, **subpixel accuracy** can be achieved (Willert & Gharib, 1991) in the estimation of the **SM** magnitude. Then a **conversion factor (CF)** measured in μm/pixel is needed to transform the pixel units of **SM** to micrometers. Since the nominal magnification of a video microscopic system often

Knowing the time interval Δt between the two successive images from the frame rate of the camera, the statistical mean velocity **V** corresponding to each interrogation window pair can

> <sup>M</sup> Δt

Repeating the procedure described in the above paragraphs for all the interrogation window pairs belonging to an image pair, a computer software program can calculate the **whole** 

In the early PIV implementations many scientists preferred using the **autocorrelation (ACOR)** function on a single image with double exposure. This technique is not used frequently any more, mainly due to the fact that ACOR is a 5 component estimator (Adrian, 1991, as cited in Keane & Adrian, 1992). Two of the five components are displacement components at symmetrical positions with respect to the correlation window center. This has the following implications: **1)** directional ambiguity, **2)** increased hardware complexity to select the right displacement component and **3)** approximately double noise level in comparison to CCOR. In addition, the CCOR technique permits the second window to be larger than the first window in order to reduce the in plane loss of particles Fi. This is not

In a **bright field μPIV set up**, the images are positive and consequently the displacement vector SM can be estimated by two different ways: **1)** images are inverted to their negative version and the same software algorithm described above is used and **2)** positive images are used but now there should be a difference in the algorithm: the minimum of the CCOR function is detected. In either case, the typical signal to noise ratio in a brightfield set up is

**<sup>S</sup> <sup>V</sup>** (13)

deviates from reality, an object micrometer is the best way for the CF determination.

background shown as a dark background in figure 10.

range of the measured displacements is reduced.

be estimated from the classical velocity definition:

**velocity field**.

possible with the ACOR function.

CCOR(s) CCOR (s) CCOR (s) CCOR (s) DCF (12)

Using the velocity definition equation 13, there are two major error sources contributing to the total velocity measurement error: the error Δte in the estimation of the time interval between two images and the error ΔSe of the displacement calculation. The time interval error is considered negligible hence we can focus on ΔSe. Generally, ΔSe can be considered equal to the square root of the sum of the squares of a random (RAN) and a mean bias (BS) component:

$$
\Delta \mathbf{S} \mathbf{e} = \sqrt{\mathbf{R} \mathbf{A} \mathbf{N}^2 + \mathbf{B} \mathbf{S}^2} \tag{14}
$$

RAN or precision is considered proportional to the effective particle image diameter dE and the streak length s (Adrian, 1991) according to the formula:

$$\text{RAN} = \mathbf{c} \left( \mathbf{d}\_{\text{E}} + \lambda\_{\text{s}} \right) \tag{15}$$

Where c is a proportionality constant ranging between 1% and 10% depending on various experimental factors such as flow tracing, velocity gradients, non uniform illumination, CCD camera electronics, the cable and digitization noise.

Most of the factors contributing to the random component can also be sources of error for the mean bias component BS. In more detail, BS could have the following error components: **1)** flow tracing error, **2)** flow structure error, **3)** particle image generation error and **4)** interrogation procedure error.

**Flow tracing error** is determined by the quality of density matching between particles and fluid and the Brown motion.

**Flow structure error** is caused by fluid accelerations in Δt and from velocity spatial gradients inside the interrogation windows. Starting from fluid acceleration and assuming it causes a critical velocity change in time τ inside the interrogation window, then, if Δt > τ, the result will be an integration of **V**(t) over the time difference Δt of successive images. For a proper PIV quantification of the **instantaneous velocity field**, Δt should be less than τ in all interrogation windows. The definition of the **time scale τ** depends on the application and the wanted quantification quality (temporal resolution). It should be noted that in the case of linear fluid acceleration, Δt can be equal or greater than τ as long as an average estimation of the velocity is acceptable.

In analog terms with the above paragraph, assuming that a velocity gradient causes a critical velocity change in distance δ less than the size of the window, the result would be by definition an average velocity value over the surface area of the window. For a proper PIV quantification of the **spatial velocity field**, window size should be less than δ in all interrogation windows. The definition of the **space scale δ** depends on the application and the wanted quantification quality (spatial resolution). It should be noted that in the case of a linear gradient along only a certain direction (x or y) the selection criteria of δ may be less strict.

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 301

The **dynamic velocity range (DVR)** of a μPIV system can be defined in a similar way with a macroscopic PIV system, i.e. the ratio of the maximum to the lowest velocity which can be measured (Adrian, 1997). A higher frame rate digital camera, can record images from faster flows increasing linearly the dynamic range of the system, but in μPIV applications care should be taken with exposure time. As the frame rate increases, the exposure time should decrease accordingly to avoid streaking but there is a down limit in the exposure time depending on the power of the illumination system and the sensitivity of the digital camera. From the above paragraphs it is evident that the size of the interrogation windows can not be reduced indefinitely. There is a lower size limit depending on many factors. Similarly, the DVR can not increase indefinitely. More details on the spatial resolution and the DVR can be

The overall performance of a μPIV system can be improved by using **appropriate software techniques** such as overlapping, averaging, single-pixel resolution, background removal,

With the **overlapping** technique, new windows are defined which overlap up to a point with the old ones. For example, a 50% overlapping means that new windows occupying half the area of each old window, were introduced, doubling the number of interrogation windows along each direction (double minus one). One could argue that in this case the window size is now half, but we should keep in mind that the new windows produced by

The **correlation averaging** technique (or **ensemble correlation**) improves dramatically the signal to noise ratio, but it requires a steady laminar flow. The technique permits also the formation of a **background image** which can be used to remove the background noise by subtracting it from the image sample pairs. An extension of the ensemble correlation technique is the **single-pixel resolution ensemble correlation** (Westerweel et al., 2004) but it requires 1000 images or more in contrast to the 10-30 image pairs of the correlation

The PIV bias error can be reduced using the **adaptive window shifting** technique which requires iteration for optimum results. In adaptive window shifting, the second interrogation window of each pair is shifted proportionally to the expected average particle displacement (Forward Difference Interrogation). In an improvement of this technique called CDI (Central Difference Interrogation, Werely & Meinhart, 2001) both windows are shifted by half the expected average particle displacement: the first interrogation window is shifted backwards and the second window is shifted forwards. Using CDI the bias error can

 The random error can be reduced using **image correction** techniques. In image correction techniques (Huang et al., 1993) image patterns in the interrogation windows are deformed in a way depending on the spatial velocity gradients. In this way, the random error is

More details on software techniques can be found in other textbooks (Breuer, 2005; Nguyen

overlapping do not give new information. It is actually an interpolation technique.

found in the work of Adrian (1997).

averaging technique.

adaptive window shifting and image correction.

be neglected in comparison to the random error.

& Wereley, 2002; Raffel et al., 2007).

reduced and the total error becomes approximately half.

**Particle image generation error** can be produced by many factors such as non-uniform illumination, out of focus particles, non-uniform scattering cross section, optical aberrations, electronic and digitization noise.

**Interrogation procedure error** can be produced by the size of the interrogation window, the displacement SM estimation error and the interpolation technique for the location of the CCOR peak.

The above analysis was based on the first error quantification analysis on a μPIV application published by Koutsiaris et al. (1999). More details on PIV uncertainty can be found in other chapters of this textbook.

### **4. Performance of a μPIV system**

From section 2.4 it should be obvious by now that the **spatial resolution** of the μPIV technique is defined by the size of the interrogation windows. So, which are the factors affecting window size? **First** of all, it is the size of the flow tracer particles. The smaller the particles are the smaller the interrogation windows and the higher the spatial resolution of the μPIV technique.

**Second**, it is the resolution capability of the optical system and the digital camera (electrooptical system). The higher the resolution of the electro-optical system is, the smaller the interrogation window. But the resolution of the optical system depends on its numerical aperture and the resolution of the digital camera on its pixel size. So, the higher the numerical aperture and the smaller the pixel size, the smaller the interrogation window.

**Third**, it is the image particle density. If window density Ni is defined as the mean number of particles per interrogation window, Fi the in plane loss of particles and Fo the out of plane loss of particles, both Fi and Fo ranging between 0 and 1, then **effective image density equals NiFiFo** (Keane & Adrian, 1992). Since PIV is a statistical method calculating the mean velocity over the entire interrogation window, the NiFiFo corresponds to a detection probability. The detection probability takes maximum values for NiFiFo > 7. For example, a NiFiFo = 5.6 corresponds to an approximate 92% detection probability.

Ni depends on the **particle concentration** (**Nc**) of the fluid, assuming that particles are dispersed homogeneously in the entire volume. It has been shown empirically that a volume per volume particle concentration between 1% and 2% gives an acceptable image density. When concentration is higher than say ≈ 5% agglomerates start to form and when it is lower than ≈ 0.5% effective image density becomes extremely low to give an acceptable detection probability and we have a situation called low image density (LID). However, as we are going to see later in the *in vitro* and *in vivo* applications of the technique, the researchers have found clever ways to overcome these limitations.

The values of the Fi and Fo depend on the **nature of the velocity field**. Fast flows cause large displacements and "aliasing" (Westerweel, 1997) reducing the Fi and the signal to noise ratio. In addition, spatial velocity gradients cause deformations influencing detection probability (Huang et al., 1993). As a starting rule of thumb the maximum particle displacement should be less than 25% the window dimension (for both directions).

**Particle image generation error** can be produced by many factors such as non-uniform illumination, out of focus particles, non-uniform scattering cross section, optical aberrations,

**Interrogation procedure error** can be produced by the size of the interrogation window, the displacement SM estimation error and the interpolation technique for the location of the

The above analysis was based on the first error quantification analysis on a μPIV application published by Koutsiaris et al. (1999). More details on PIV uncertainty can be found in other

From section 2.4 it should be obvious by now that the **spatial resolution** of the μPIV technique is defined by the size of the interrogation windows. So, which are the factors affecting window size? **First** of all, it is the size of the flow tracer particles. The smaller the particles are the smaller the interrogation windows and the higher the spatial resolution of

**Second**, it is the resolution capability of the optical system and the digital camera (electrooptical system). The higher the resolution of the electro-optical system is, the smaller the interrogation window. But the resolution of the optical system depends on its numerical aperture and the resolution of the digital camera on its pixel size. So, the higher the numerical aperture and the smaller the pixel size, the smaller the interrogation window.

**Third**, it is the image particle density. If window density Ni is defined as the mean number of particles per interrogation window, Fi the in plane loss of particles and Fo the out of plane loss of particles, both Fi and Fo ranging between 0 and 1, then **effective image density equals NiFiFo** (Keane & Adrian, 1992). Since PIV is a statistical method calculating the mean velocity over the entire interrogation window, the NiFiFo corresponds to a detection probability. The detection probability takes maximum values for NiFiFo > 7. For example, a

Ni depends on the **particle concentration** (**Nc**) of the fluid, assuming that particles are dispersed homogeneously in the entire volume. It has been shown empirically that a volume per volume particle concentration between 1% and 2% gives an acceptable image density. When concentration is higher than say ≈ 5% agglomerates start to form and when it is lower than ≈ 0.5% effective image density becomes extremely low to give an acceptable detection probability and we have a situation called low image density (LID). However, as we are going to see later in the *in vitro* and *in vivo* applications of the technique, the researchers

The values of the Fi and Fo depend on the **nature of the velocity field**. Fast flows cause large displacements and "aliasing" (Westerweel, 1997) reducing the Fi and the signal to noise ratio. In addition, spatial velocity gradients cause deformations influencing detection probability (Huang et al., 1993). As a starting rule of thumb the maximum particle

displacement should be less than 25% the window dimension (for both directions).

NiFiFo = 5.6 corresponds to an approximate 92% detection probability.

have found clever ways to overcome these limitations.

electronic and digitization noise.

chapters of this textbook.

the μPIV technique.

**4. Performance of a μPIV system** 

CCOR peak.

The **dynamic velocity range (DVR)** of a μPIV system can be defined in a similar way with a macroscopic PIV system, i.e. the ratio of the maximum to the lowest velocity which can be measured (Adrian, 1997). A higher frame rate digital camera, can record images from faster flows increasing linearly the dynamic range of the system, but in μPIV applications care should be taken with exposure time. As the frame rate increases, the exposure time should decrease accordingly to avoid streaking but there is a down limit in the exposure time depending on the power of the illumination system and the sensitivity of the digital camera.

From the above paragraphs it is evident that the size of the interrogation windows can not be reduced indefinitely. There is a lower size limit depending on many factors. Similarly, the DVR can not increase indefinitely. More details on the spatial resolution and the DVR can be found in the work of Adrian (1997).

The overall performance of a μPIV system can be improved by using **appropriate software techniques** such as overlapping, averaging, single-pixel resolution, background removal, adaptive window shifting and image correction.

With the **overlapping** technique, new windows are defined which overlap up to a point with the old ones. For example, a 50% overlapping means that new windows occupying half the area of each old window, were introduced, doubling the number of interrogation windows along each direction (double minus one). One could argue that in this case the window size is now half, but we should keep in mind that the new windows produced by overlapping do not give new information. It is actually an interpolation technique.

The **correlation averaging** technique (or **ensemble correlation**) improves dramatically the signal to noise ratio, but it requires a steady laminar flow. The technique permits also the formation of a **background image** which can be used to remove the background noise by subtracting it from the image sample pairs. An extension of the ensemble correlation technique is the **single-pixel resolution ensemble correlation** (Westerweel et al., 2004) but it requires 1000 images or more in contrast to the 10-30 image pairs of the correlation averaging technique.

The PIV bias error can be reduced using the **adaptive window shifting** technique which requires iteration for optimum results. In adaptive window shifting, the second interrogation window of each pair is shifted proportionally to the expected average particle displacement (Forward Difference Interrogation). In an improvement of this technique called CDI (Central Difference Interrogation, Werely & Meinhart, 2001) both windows are shifted by half the expected average particle displacement: the first interrogation window is shifted backwards and the second window is shifted forwards. Using CDI the bias error can be neglected in comparison to the random error.

 The random error can be reduced using **image correction** techniques. In image correction techniques (Huang et al., 1993) image patterns in the interrogation windows are deformed in a way depending on the spatial velocity gradients. In this way, the random error is reduced and the total error becomes approximately half.

More details on software techniques can be found in other textbooks (Breuer, 2005; Nguyen & Wereley, 2002; Raffel et al., 2007).

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 303

(a) (b)







Soon after the first μPIV measurements on Newtonian flows, researchers started the flow study of **red blood cell (RBC) suspensions**. Okuda et al. (2003) measured in round tubes with internal diameter of 100μm the flow of rabbit blood seeded with fluorescent particles; Bitch et al., (2005) measured in specially flattened tubes the flow of a RBC suspension with

Lima et al. (2006) were the first to measure three-dimensional velocity profiles of human RBC suspensions inside a square glass microchannel (100 x 100 μm) using a special confocal experimental set up. One year later (Lima et al., 2007), using the same microchannel dimensions, found that low hematocrit (up to 17%) suspensions have parabolic averaged velocity profiles. In 2008 Lima et al. compared the velocity profile of physiologic saline with the profile of human blood with 20% heamatocrit inside a rectangular high aspect ratio (W = 300 μm, H = 45 μm) PDMS microchannel; microturbulences were encountered on averaged blood flow profiles. Next year (Lima et al., 2009), they combined a particle tracking velocimetry (PTV) system with a confocal microscope in order to quantify the RBCs

When the tube dimension is greater than 40-60 μm it is difficult for the light rays to penetrate blood at physiologic hematocrits both in transmission and reflectance mode. Even when a confocal set up is used, the microchannel dimension parallel to the optical axis should be less than ≈ 100 μm and the hematocrit less than ≈ 20%. In order to overcome these limitations, Kim and Lee (2006) tried a completely different approach using X-rays. The Fresnel diffraction pattern images can be used to calculate the blood velocity field at high

ratio, after the application of the kernel shown in (c). (From Koutsiaris et al., 1999)

60% hematocrit using RBCs as natural flow tracers (brightfield set up).

trajectories in suspensions up to 20% in heamatocrit.

### **5. Research** *IN VITRO*

As it is the usual practice, the first applications of the μPIV technique were *in vitro*. The fluorescence μPIV set up introduced by Santiago et al. (1998) produced negative images in accordance with the classical PIV systems. The μPIV set up introduced by Koutsiaris et al. (1999) produced positive images i.e. the background was brighter than the particles (figure 11 (a)) similar to the ordinary daylight photographs. This meant that images should be inverted before calculating the cross correlation or the software should be modified to detect the minimum of the correlation function. However, this set up was much simpler and cheaper than fluorescence set ups since it did not require the use of fluorescence apparatus (special particles, light sources, optics and low light CCD cameras).

With the use of the appropriate **image processing digital filters** one can have image inversion and simultaneous increase of the signal to noise ratio. For example, the Laplace filter (a 6 x 6 Kernel) shown in figure 11(c) enhances particle boundaries and removes slowly varying background shading. In addition, the same kernel helps in eliminating the out of focus particles, since the spatial frequencies corresponding to the in focus flow tracers can be maximized by adjusting the size of the filter (Koutsiaris et al., 1999). The determination of thresholds and optimum filter variable values could be the object of further research in digital image processing and digital filter design. The effects of the possible variable combinations on the μPIV flow field accuracy have not yet been examined thoroughly.

**Cylindrical microtubes** (Koutsiaris et al., 1999) simulate better the flow geometry of microvessels but their construction is demanding. In addition, they require a good optical matching otherwise image optical distortions must be corrected.

**Rectangular microchannels** are not good models for simulating animal microcirculation, but they possess a simple geometry with minimum optical distortions. The aspect ratio (AR) of a television screen is defined as the ratio of the longest (horizontal) over the shortest (vertical) side and is always greater than 1. Keeping the same definition in rectangular microchannels, the longest (horizontal) side of the cross section is usually referred to as "width" (W) and the shortest (vertical) as "height" (H). Research groups all over the world have studied flows inside microchannels with various ARs: 1 (W = 100μm, H = 100μm, Lima et al., 2006), 1.7 (W = 80μm, H = 48μm, Kuang et al., 2009), 4 (W = 800μm, H = 200μm, Lindken et al., 2006; W = 20mm, H = 5mm, Timgren et al., 2008), 6.7 (W = 300mm, H = 45mm, Lima et al., 2008) and 10 (W = 300μm, H = 30μm, Meinhart et al., 1999).

There are several analytical solutions for the steady Newtonian flow inside a rectangular channel such as those shown by Werely & Meinhart (2005), Lima et al. (2006) and Lindken et al. (2006). All these solutions contain infinite sum terms. In addition, Werely & Meinhart (2005) reported that their analytical solution failed to capture the trends of the measured profile near the wall and that in order to amend this they used a second order polynomial fit. Lima et al. (2008) reported results in the middle plane with analytical solution errors of less than 5%. However, it seems that these errors can be reduced to less than 1.6% (more than 3 times) using an alternative model equation discussed below (see figure 15 in section 7).

In 2001, Werely and Meinhart measured the flow of deionized water around human red blood cells placed in the gap between a microscope slide and a coverslip. The same year, Gomez et al. measured for the first time the flow of water based suspensions inside a microfluidic biochip designed for impedance spectroscopy.

As it is the usual practice, the first applications of the μPIV technique were *in vitro*. The fluorescence μPIV set up introduced by Santiago et al. (1998) produced negative images in accordance with the classical PIV systems. The μPIV set up introduced by Koutsiaris et al. (1999) produced positive images i.e. the background was brighter than the particles (figure 11 (a)) similar to the ordinary daylight photographs. This meant that images should be inverted before calculating the cross correlation or the software should be modified to detect the minimum of the correlation function. However, this set up was much simpler and cheaper than fluorescence set ups since it did not require the use of fluorescence apparatus

With the use of the appropriate **image processing digital filters** one can have image inversion and simultaneous increase of the signal to noise ratio. For example, the Laplace filter (a 6 x 6 Kernel) shown in figure 11(c) enhances particle boundaries and removes slowly varying background shading. In addition, the same kernel helps in eliminating the out of focus particles, since the spatial frequencies corresponding to the in focus flow tracers can be maximized by adjusting the size of the filter (Koutsiaris et al., 1999). The determination of thresholds and optimum filter variable values could be the object of further research in digital image processing and digital filter design. The effects of the possible variable combinations on the μPIV flow field accuracy have not yet been examined thoroughly.

**Cylindrical microtubes** (Koutsiaris et al., 1999) simulate better the flow geometry of microvessels but their construction is demanding. In addition, they require a good optical

**Rectangular microchannels** are not good models for simulating animal microcirculation, but they possess a simple geometry with minimum optical distortions. The aspect ratio (AR) of a television screen is defined as the ratio of the longest (horizontal) over the shortest (vertical) side and is always greater than 1. Keeping the same definition in rectangular microchannels, the longest (horizontal) side of the cross section is usually referred to as "width" (W) and the shortest (vertical) as "height" (H). Research groups all over the world have studied flows inside microchannels with various ARs: 1 (W = 100μm, H = 100μm, Lima et al., 2006), 1.7 (W = 80μm, H = 48μm, Kuang et al., 2009), 4 (W = 800μm, H = 200μm, Lindken et al., 2006; W = 20mm, H = 5mm, Timgren et al., 2008), 6.7 (W = 300mm, H =

There are several analytical solutions for the steady Newtonian flow inside a rectangular channel such as those shown by Werely & Meinhart (2005), Lima et al. (2006) and Lindken et al. (2006). All these solutions contain infinite sum terms. In addition, Werely & Meinhart (2005) reported that their analytical solution failed to capture the trends of the measured profile near the wall and that in order to amend this they used a second order polynomial fit. Lima et al. (2008) reported results in the middle plane with analytical solution errors of less than 5%. However, it seems that these errors can be reduced to less than 1.6% (more than 3 times) using an alternative model equation discussed below (see figure 15 in section 7). In 2001, Werely and Meinhart measured the flow of deionized water around human red blood cells placed in the gap between a microscope slide and a coverslip. The same year, Gomez et al. measured for the first time the flow of water based suspensions inside a

45mm, Lima et al., 2008) and 10 (W = 300μm, H = 30μm, Meinhart et al., 1999).

(special particles, light sources, optics and low light CCD cameras).

matching otherwise image optical distortions must be corrected.

microfluidic biochip designed for impedance spectroscopy.

**5. Research** *IN VITRO*


Fig. 11. (a) An original positive image from the diametric plane of a cylindrical glass tube with internal diameter of 262 μm. Numbers 1, 2 & 3 correspond to different positions downstream the flow. (b) The negative of the original image with improved signal to noise ratio, after the application of the kernel shown in (c). (From Koutsiaris et al., 1999)

Soon after the first μPIV measurements on Newtonian flows, researchers started the flow study of **red blood cell (RBC) suspensions**. Okuda et al. (2003) measured in round tubes with internal diameter of 100μm the flow of rabbit blood seeded with fluorescent particles; Bitch et al., (2005) measured in specially flattened tubes the flow of a RBC suspension with 60% hematocrit using RBCs as natural flow tracers (brightfield set up).

Lima et al. (2006) were the first to measure three-dimensional velocity profiles of human RBC suspensions inside a square glass microchannel (100 x 100 μm) using a special confocal experimental set up. One year later (Lima et al., 2007), using the same microchannel dimensions, found that low hematocrit (up to 17%) suspensions have parabolic averaged velocity profiles. In 2008 Lima et al. compared the velocity profile of physiologic saline with the profile of human blood with 20% heamatocrit inside a rectangular high aspect ratio (W = 300 μm, H = 45 μm) PDMS microchannel; microturbulences were encountered on averaged blood flow profiles. Next year (Lima et al., 2009), they combined a particle tracking velocimetry (PTV) system with a confocal microscope in order to quantify the RBCs trajectories in suspensions up to 20% in heamatocrit.

When the tube dimension is greater than 40-60 μm it is difficult for the light rays to penetrate blood at physiologic hematocrits both in transmission and reflectance mode. Even when a confocal set up is used, the microchannel dimension parallel to the optical axis should be less than ≈ 100 μm and the hematocrit less than ≈ 20%. In order to overcome these limitations, Kim and Lee (2006) tried a completely different approach using X-rays. The Fresnel diffraction pattern images can be used to calculate the blood velocity field at high

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 305

cooperate and in part due to the expensive experimental set up. Therefore it is not surprising that apart from some preliminary efforts in the 70's (Schoenbein & Zweifach, 1975), the **first** *in vivo* quality velocity profile measurements were presented in 1986 by the group of professor Reneman (Tangelder et al., 1986). They measured velocity profiles in the arterioles of the rabbit mesentery using as flow tracers platelets labeled with a special

More than 15 years later, Sugii et al. (2002) and Nakano et al. (2003) measured the velocity profile in arterioles of the rat mesentery using a technique introduced some years earlier by Sugii et al. (2000) under the name "**High Resolution Particle Image Velocimetry" (HR-PIV)**. Regarding the software, this technique was a combination of the iterative crosscorrelation method (Raffel et al., 2007) and the optical flow (or gradient or spatio-temporal derivative) method, providing excellent accuracy (as little as 0.01 pixels). Their hardware was a brightfield μPIV set up with the exceptional advantage of using natural blood flow thus avoiding any toxic effects from fluorescent materials and complex-expensive fluorescent equipment. The final velocity field spatial resolution in the object plane was 0.8 μm. The only drawback is that being a **fully automated** technique it is difficult to validate the results. Another fully automated technique was presented by Tsukada et al. (2000) based

In 2003, Hove et al. (2003) mapped the flow field inside the developing zebrafish heart 37 hours and 4.5 days post fertilization using RBCs as flow tracers. They found the presence of higher shear vertical flow than expected and evidence that **blood flow-induced forces act as a key epigenetic factor** in embryonic cardiogenesis. Later, Vennemann et al. (2006) improved the resolution of the flow field maps and boundaries, using fluorescent, longcirculating liposomes with a diameter of 400 nm, as flow tracers, in the embryonic avian heart. They noted the potential of μPIV to become a general tool in complex geometries in cardiovascular research. Both groups underlined the importance of examining the interplay between genetics and fluid shear forces in analyzing not only normal development but also

In 2004, Long et al. (12 venules from male mice, 24 μm ≤ D ≤ 42.9 μm) and Damiano et al (9 light-dye treated venules from 3 mice, 24 μm ≤ D ≤ 42.9 μm) provided the most complete **manual** velocity profile measurements until now, with the best spatial resolution and the assumption of steady axisymmetric flow. They measured in the cremaster muscle of mice

In 2005, Nakano et al. (2005) were the first to measure the effect of an arteriolar bifurcation and confluence on the red blood cell velocity profile on the rat mesentery. More recently, Potter & Damiano, (2008) performed measurements in mice venules up to diameters of 101 μm but they mainly concentrated on the properties of the endothelium glycocalyx layer both

The accurate quantification of the velocity profile in a cylindrical axisymmetric flow is very important because it is the **first and unique step** required for the estimation of the wall

on circular correlation windows reduced down to the size of the erythrocytes.

the pathogenesis of embryonic cardiovascular defects.

using fluorescent microspheres (0.47 ± 0.01 μm) as blood flow tracers.

fluorescence technique.

*in vivo* and *in vitro*.

**7.1 Introduction** 

**7. Velocity profile equations** *IN VIVO*

haematocrits (20-80%) without tracer particles, in microchannels with dimensions higher than ≈ 500 μm. A disadvantage of the method is that sample thickness and heamatocrit affect image quality so more work is required to define the limits inside which valid measurements can be taken.

In 2011, Kaliviotis et al. used brightfield μPIV to measure the velocity field of 45% heamatocrit human blood samples inside an optical shearing system consisted of 2 circular parallel glass plates set apart by a gap h = 30 μm. The shear rate derived from the blood velocity field was used in their non-Newtonian (shear rate, time and aggregation depended) blood viscosity model.

Except for the biological flows, *in vitro* μPIV has a lot of other useful applications such as those regarding the **computer industry**. Meinhart and Zhang (2000) measured the evolution of the meniscus and the detailed flow fields inside a nozzle of an inkjet printhead. Buffone et al. (2005) investigated the thermocapillary Marangoni convection in the proximity of the liquid-vapor interface for an evaporating meniscus in horizontal capillary tubes (600, 900 and 1630 μm). Today, air cooling limitations are responsible for a barrier in the total power consumed by a processor chip (a power wall of approximately 100 Watts) and ultimately in the chip performance. However, this situation can change using microchannels for liquid flow cooling (either single phase cooling with water, or two phase cooling with refrigerant). This could be a revolution in the microelectronics industry since the maximum heat dissipation can increase approximately 10 times from 37 W/cm2 (air cooling) to 314 W/cm2 (Thome & Marcinichen, 2011). Typical components of a two phase microcircuit are a liquid micropump or vapor compressor, a microevaporator and a microcondenser.

Among **other applications**, Bown et al., (2005) demonstrated the application of μPIV to complex microchannel geometries and introduced a method of estimating the out of plane effects on the velocity measurements. Lindken et al. (2006) measured for the first time in the mixing region of a T-shaped micromixer. King et al. (2007) demonstrated the ability to perform μPIV measurements of aqueous plugs in two phase flow within circular tubing with a 762 μm internal diameter. Such two phase flows are encountered in lab-on-chip devices designed for various biological applications such as the Polymerase Chain Reaction (PCR). Similarly, Timgren et al. (2008) measured the velocity field inside silicon oil drops forming in a mixture of water and glycerol flowing in a rectangular channel.

Kuang et al. (2009) presented a **molecular tracer method** (Molecular Tracers Velocimetry, MTV) for measuring the velocity profile in cylindrical and rectangular microchannels with dimensions less than 100 μm. Their method was based on the Laser Induced Fluorescence Photobleaching Anemometry (LIFPA) technique.

More information on the **biological applications** of μPIV can be found in the review paper of Lindken et al. (2009) and more details on the numerical and experimental analysis of flows inside microdiffusers and valveless micropumps are presented in the review paper of Nabavi (2009).

### **6. Velocity profile measurements** *IN VIVO*

The actual measurement of the blood velocity profile in microvessels is a known difficult task to accomplish. This is in part due to the many different scientific fields that need to

haematocrits (20-80%) without tracer particles, in microchannels with dimensions higher than ≈ 500 μm. A disadvantage of the method is that sample thickness and heamatocrit affect image quality so more work is required to define the limits inside which valid

In 2011, Kaliviotis et al. used brightfield μPIV to measure the velocity field of 45% heamatocrit human blood samples inside an optical shearing system consisted of 2 circular parallel glass plates set apart by a gap h = 30 μm. The shear rate derived from the blood velocity field was used in their non-Newtonian (shear rate, time and aggregation depended)

Except for the biological flows, *in vitro* μPIV has a lot of other useful applications such as those regarding the **computer industry**. Meinhart and Zhang (2000) measured the evolution of the meniscus and the detailed flow fields inside a nozzle of an inkjet printhead. Buffone et al. (2005) investigated the thermocapillary Marangoni convection in the proximity of the liquid-vapor interface for an evaporating meniscus in horizontal capillary tubes (600, 900 and 1630 μm). Today, air cooling limitations are responsible for a barrier in the total power consumed by a processor chip (a power wall of approximately 100 Watts) and ultimately in the chip performance. However, this situation can change using microchannels for liquid flow cooling (either single phase cooling with water, or two phase cooling with refrigerant). This could be a revolution in the microelectronics industry since the maximum heat dissipation can increase approximately 10 times from 37 W/cm2 (air cooling) to 314 W/cm2 (Thome & Marcinichen, 2011). Typical components of a two phase microcircuit are a liquid

Among **other applications**, Bown et al., (2005) demonstrated the application of μPIV to complex microchannel geometries and introduced a method of estimating the out of plane effects on the velocity measurements. Lindken et al. (2006) measured for the first time in the mixing region of a T-shaped micromixer. King et al. (2007) demonstrated the ability to perform μPIV measurements of aqueous plugs in two phase flow within circular tubing with a 762 μm internal diameter. Such two phase flows are encountered in lab-on-chip devices designed for various biological applications such as the Polymerase Chain Reaction (PCR). Similarly, Timgren et al. (2008) measured the velocity field inside silicon oil drops

Kuang et al. (2009) presented a **molecular tracer method** (Molecular Tracers Velocimetry, MTV) for measuring the velocity profile in cylindrical and rectangular microchannels with dimensions less than 100 μm. Their method was based on the Laser Induced Fluorescence

More information on the **biological applications** of μPIV can be found in the review paper of Lindken et al. (2009) and more details on the numerical and experimental analysis of flows inside microdiffusers and valveless micropumps are presented in the review paper of

The actual measurement of the blood velocity profile in microvessels is a known difficult task to accomplish. This is in part due to the many different scientific fields that need to

micropump or vapor compressor, a microevaporator and a microcondenser.

forming in a mixture of water and glycerol flowing in a rectangular channel.

Photobleaching Anemometry (LIFPA) technique.

**6. Velocity profile measurements** *IN VIVO*

Nabavi (2009).

measurements can be taken.

blood viscosity model.

cooperate and in part due to the expensive experimental set up. Therefore it is not surprising that apart from some preliminary efforts in the 70's (Schoenbein & Zweifach, 1975), the **first** *in vivo* quality velocity profile measurements were presented in 1986 by the group of professor Reneman (Tangelder et al., 1986). They measured velocity profiles in the arterioles of the rabbit mesentery using as flow tracers platelets labeled with a special fluorescence technique.

More than 15 years later, Sugii et al. (2002) and Nakano et al. (2003) measured the velocity profile in arterioles of the rat mesentery using a technique introduced some years earlier by Sugii et al. (2000) under the name "**High Resolution Particle Image Velocimetry" (HR-PIV)**. Regarding the software, this technique was a combination of the iterative crosscorrelation method (Raffel et al., 2007) and the optical flow (or gradient or spatio-temporal derivative) method, providing excellent accuracy (as little as 0.01 pixels). Their hardware was a brightfield μPIV set up with the exceptional advantage of using natural blood flow thus avoiding any toxic effects from fluorescent materials and complex-expensive fluorescent equipment. The final velocity field spatial resolution in the object plane was 0.8 μm. The only drawback is that being a **fully automated** technique it is difficult to validate the results. Another fully automated technique was presented by Tsukada et al. (2000) based on circular correlation windows reduced down to the size of the erythrocytes.

In 2003, Hove et al. (2003) mapped the flow field inside the developing zebrafish heart 37 hours and 4.5 days post fertilization using RBCs as flow tracers. They found the presence of higher shear vertical flow than expected and evidence that **blood flow-induced forces act as a key epigenetic factor** in embryonic cardiogenesis. Later, Vennemann et al. (2006) improved the resolution of the flow field maps and boundaries, using fluorescent, longcirculating liposomes with a diameter of 400 nm, as flow tracers, in the embryonic avian heart. They noted the potential of μPIV to become a general tool in complex geometries in cardiovascular research. Both groups underlined the importance of examining the interplay between genetics and fluid shear forces in analyzing not only normal development but also the pathogenesis of embryonic cardiovascular defects.

In 2004, Long et al. (12 venules from male mice, 24 μm ≤ D ≤ 42.9 μm) and Damiano et al (9 light-dye treated venules from 3 mice, 24 μm ≤ D ≤ 42.9 μm) provided the most complete **manual** velocity profile measurements until now, with the best spatial resolution and the assumption of steady axisymmetric flow. They measured in the cremaster muscle of mice using fluorescent microspheres (0.47 ± 0.01 μm) as blood flow tracers.

In 2005, Nakano et al. (2005) were the first to measure the effect of an arteriolar bifurcation and confluence on the red blood cell velocity profile on the rat mesentery. More recently, Potter & Damiano, (2008) performed measurements in mice venules up to diameters of 101 μm but they mainly concentrated on the properties of the endothelium glycocalyx layer both *in vivo* and *in vitro*.

### **7. Velocity profile equations** *IN VIVO*

#### **7.1 Introduction**

The accurate quantification of the velocity profile in a cylindrical axisymmetric flow is very important because it is the **first and unique step** required for the estimation of the wall

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 307

All the above conditions are satisfied by the equations presented below except for the parabolic equation which can not satisfy the non-Newtonian condition, as it will be shown

> V ( ) = V 1- P m <sup>R</sup> *<sup>r</sup> <sup>r</sup>*

V ( ) = V 1- RS <sup>m</sup> <sup>R</sup> *<sup>r</sup> <sup>r</sup>*

V ( ) = V 1- KS m 1 κ 1-

2

κ

<sup>2</sup> 2 κ

R R

*r r <sup>r</sup>*

Where VP(r), VRS(r), VKS(r) is the velocity at radial position r, for the parabolic (equation 16), the Roevros (equation 17, Roevros 1974) and the Koutsiaris (equation 18, Koutsiaris 2009)

The parameters κ and κ1, κ<sup>2</sup> **affect the velocity profile shape** of equations 17 and 18 respectively. For a velocity profile blunter than the parabolic one, with the same Vm, the following conditions must be satisfied: κ > 2 (equation 17), 0 < κ1 < 1, κ2 > 2 and (1-κ1) κ2 ≥ 2

In **equation 17**, the higher the κ, the flatter the profile near the vessel axis and the higher the wall shear rate (Roevros 1974). Equation 17 reduces to parabolic when κ = 2. It should be noted that a modified version of equation 17 with 2 more parameters (a and b) was proposed in the 80s (Tangelder et al., 1986), but it does not satisfy the zero slip condition on

In **equation 18**, the advantage is that the bluntness of the profile can be controlled near the axis and the wall: generally, as κ1 approaches zero the profile becomes flatter near the axis and as κ2 takes values higher than 2 the profile becomes flatter near the wall (Koutsiaris,

Damiano et al. (2004) made significant contributions in theory and experimental measurements and provided a way to estimate the viscosity profile as well as the effective viscosity *in vivo*. They proposed the following velocity profile equation which identically

0

R

f( )d

f( )d

r/R m R

2009). Equation 18 reduces to the parabolic equation when κ1 = 0, κ2 =2.

satisfies the momentum equation and boundary conditions (Long et al., 2004):

V(r) V

(16)

(17)

(19)

(18)

below.

**7.2.1 Group A** 

equation, respectively.

(equation 18).

**7.2.2 Group B** 

This group comprises 3 velocity profile equations:

the vessel wall which is true for any viscous flow.

shear rate (WSR) and volume flow (Q). In addition, the viscosity profile (and hence the apparent viscosity), the axial pressure gradient and the shear stress profile (and hence wall shear stress, WSS) can be estimated **under the assumptions** of a locally Newtonian fluid and the existence of plasma between red blood cells (RBCs) and vessel walls (Damiano et al., 2004).

Before the last third of the 20th century, the only equation available to the researchers studying laminar flows inside cylindrical tubes was the parabolic one. In the seventies (70s) it became evident that the flow of blood is quite different from simple Newtonian flows like that of water. Blood exhibits special shear thinning properties due to reasons which are still partly unexplained. For example the molecular and biochemical basis of the rouleaux (structures resembling coin piles) formation is still unknown. The shear thinning property means that blood viscosity diminishes (blood becomes thinner) as shear rate increases. For the case of blood, this property is quite evident taking into account that at high shear rates (> 100 s-1) its viscosity is many times lower than at shear rates < 10 s-1. This means that near the vessel axis where there are such low shear rates, blood is much more viscous, causing a characteristic "blunting" of the velocity profile (Bugliarello & Sevilla, 1970; Damiano et al., 2004; Gaehtgens et al., 1970; Long et al., 2004; Nakano et al., 2003; Schoenbein & Zweifach, 1975; Tangelder et al., 1986).

After 1970, the researchers proposed equations trying to describe the blunting of the velocity profile in the microvasculature with diameters (D) higher than ≈ 20 μm. The approximate diametric **down size limit of the 20 μm** (Cokelet, 1999) is imposed by the manifestation of the biphasic nature of blood in the smallest arterioles and venules and in the capillaries. In these microvessels RBCs flow separately, constituting a different liquid phase from plasma and therefore the flow medium can not be considered as a "continuum" and a velocity profile can not be defined in the ordinary sense. However, **averages of WSR, Q and WSS** can be estimated *in vivo* using empirical equations (Koutsiaris, 2005; Koutsiaris et al., 2007) requiring only axial RBC velocity measurements.

The available velocity profile equations today, could be divided in many ways, but in this section the criterion was whether they can be easily reduced to the classic parabolic equation (Group A) or not (Group B).

#### **7.2 Available equations**

**Realistic assumptions** of the blood flow in straight sections of microvessels with D > 20μm, several diameters downstream their entrance, are (Koutsiaris, 2009): 1) incompressible flow, 2) continuous medium, 3) viscous flow with Reynolds number less than one, 5) cylindrical vessel geometry with a radius R, 5) non-Newtonian medium with a time averaged velocity profile blunter than the parabolic with the same maximum velocity Vm, 6) the blood velocity is zero on the vessel wall (zero slip condition: V(r) = 0, at radial position r = R) and 7) axisymmetric velocity profile with maximum velocity Vm on the vessel axis.

The assumption of steady flow can be accepted for venules with D > 20μm (Koutsiaris et al., 2011), but not for arterioles. Recently, it was verified for the first time in humans, that the velocity pulse in arterioles is quite strong, even at the precapillary level (Koutsiaris et al., 2010c). Despite the strong pulse, the velocity profile can be measured at the same cardiac cycle phase taking advantage of the periodic nature of the flow. So, the flow can be considered as "steady" for the same phase.

All the above conditions are satisfied by the equations presented below except for the parabolic equation which can not satisfy the non-Newtonian condition, as it will be shown below.

#### **7.2.1 Group A**

306 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

shear rate (WSR) and volume flow (Q). In addition, the viscosity profile (and hence the apparent viscosity), the axial pressure gradient and the shear stress profile (and hence wall shear stress, WSS) can be estimated **under the assumptions** of a locally Newtonian fluid and the existence of plasma between red blood cells (RBCs) and vessel walls (Damiano et al., 2004). Before the last third of the 20th century, the only equation available to the researchers studying laminar flows inside cylindrical tubes was the parabolic one. In the seventies (70s) it became evident that the flow of blood is quite different from simple Newtonian flows like that of water. Blood exhibits special shear thinning properties due to reasons which are still partly unexplained. For example the molecular and biochemical basis of the rouleaux (structures resembling coin piles) formation is still unknown. The shear thinning property means that blood viscosity diminishes (blood becomes thinner) as shear rate increases. For the case of blood, this property is quite evident taking into account that at high shear rates (> 100 s-1) its viscosity is many times lower than at shear rates < 10 s-1. This means that near the vessel axis where there are such low shear rates, blood is much more viscous, causing a characteristic "blunting" of the velocity profile (Bugliarello & Sevilla, 1970; Damiano et al., 2004; Gaehtgens et al., 1970; Long et al., 2004; Nakano et al., 2003; Schoenbein & Zweifach,

After 1970, the researchers proposed equations trying to describe the blunting of the velocity profile in the microvasculature with diameters (D) higher than ≈ 20 μm. The approximate diametric **down size limit of the 20 μm** (Cokelet, 1999) is imposed by the manifestation of the biphasic nature of blood in the smallest arterioles and venules and in the capillaries. In these microvessels RBCs flow separately, constituting a different liquid phase from plasma and therefore the flow medium can not be considered as a "continuum" and a velocity profile can not be defined in the ordinary sense. However, **averages of WSR, Q and WSS** can be estimated *in vivo* using empirical equations (Koutsiaris, 2005; Koutsiaris et al., 2007)

The available velocity profile equations today, could be divided in many ways, but in this section the criterion was whether they can be easily reduced to the classic parabolic equation

**Realistic assumptions** of the blood flow in straight sections of microvessels with D > 20μm, several diameters downstream their entrance, are (Koutsiaris, 2009): 1) incompressible flow, 2) continuous medium, 3) viscous flow with Reynolds number less than one, 5) cylindrical vessel geometry with a radius R, 5) non-Newtonian medium with a time averaged velocity profile blunter than the parabolic with the same maximum velocity Vm, 6) the blood velocity is zero on the vessel wall (zero slip condition: V(r) = 0, at radial position r = R) and 7)

The assumption of steady flow can be accepted for venules with D > 20μm (Koutsiaris et al., 2011), but not for arterioles. Recently, it was verified for the first time in humans, that the velocity pulse in arterioles is quite strong, even at the precapillary level (Koutsiaris et al., 2010c). Despite the strong pulse, the velocity profile can be measured at the same cardiac cycle phase taking advantage of the periodic nature of the flow. So, the flow can be

axisymmetric velocity profile with maximum velocity Vm on the vessel axis.

1975; Tangelder et al., 1986).

(Group A) or not (Group B).

**7.2 Available equations** 

requiring only axial RBC velocity measurements.

considered as "steady" for the same phase.

This group comprises 3 velocity profile equations:

$$\mathbf{V}\_p(r) = \mathbf{V}\_m \left[ 1 \cdot \left( \frac{r}{\mathbf{R}} \right)^2 \right] \tag{16}$$

$$\mathbf{V}\_{\rm RS}(r) = \mathbf{V}\_{\rm m} \left[ 1 \cdot \left( \frac{r}{\mathbf{R}} \right)^{\kappa} \right] \tag{17}$$

$$\mathbf{V}\_{\mathbf{KS}}(r) = \mathbf{V}\_{\mathbf{m}} \left[ 1 \cdot \mathbf{x}\_1 \left( \frac{r}{\mathbf{R}} \right)^2 \right] \left[ 1 \cdot \left( \frac{r}{\mathbf{R}} \right)^{\kappa\_1} \right] \tag{18}$$

Where VP(r), VRS(r), VKS(r) is the velocity at radial position r, for the parabolic (equation 16), the Roevros (equation 17, Roevros 1974) and the Koutsiaris (equation 18, Koutsiaris 2009) equation, respectively.

The parameters κ and κ1, κ<sup>2</sup> **affect the velocity profile shape** of equations 17 and 18 respectively. For a velocity profile blunter than the parabolic one, with the same Vm, the following conditions must be satisfied: κ > 2 (equation 17), 0 < κ1 < 1, κ2 > 2 and (1-κ1) κ2 ≥ 2 (equation 18).

In **equation 17**, the higher the κ, the flatter the profile near the vessel axis and the higher the wall shear rate (Roevros 1974). Equation 17 reduces to parabolic when κ = 2. It should be noted that a modified version of equation 17 with 2 more parameters (a and b) was proposed in the 80s (Tangelder et al., 1986), but it does not satisfy the zero slip condition on the vessel wall which is true for any viscous flow.

In **equation 18**, the advantage is that the bluntness of the profile can be controlled near the axis and the wall: generally, as κ1 approaches zero the profile becomes flatter near the axis and as κ2 takes values higher than 2 the profile becomes flatter near the wall (Koutsiaris, 2009). Equation 18 reduces to the parabolic equation when κ1 = 0, κ2 =2.

#### **7.2.2 Group B**

Damiano et al. (2004) made significant contributions in theory and experimental measurements and provided a way to estimate the viscosity profile as well as the effective viscosity *in vivo*. They proposed the following velocity profile equation which identically satisfies the momentum equation and boundary conditions (Long et al., 2004):

$$\mathbf{V}(\mathbf{r}) = \mathbf{V}\_{\text{m}} \frac{\int\_{\mathbf{r}}^{\mathbb{R}} \mathbf{f}(\sigma) d\sigma}{\int\_{\mathbf{r}}^{\mathbb{R}} \mathbf{f}(\sigma) d\sigma} \tag{19}$$

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 309

Instead of using the same maximum velocity and fixed parametric values (axial fit), the classical approach would be to apply the **best fit**, i.e. finding the parametric values producing the minimum sum square error on each experimental velocity profile. Then statistics could be applied to the velocity relative errors of all the profiles, dividing the

Where j is an integer index (1 ≤ j ≤ 10). Working in this way, Koutsiaris et al. (2011) compared statistically the best fits of equations 17 and 18 and the axial fit of equation 18 on the **original experimental data of 12 velocity profiles from mouse venules** between 21 and 39 μm in diameter (Long et al., 2004). As it is shown in figure 13, the most efficient fit is the best fit of equation 18 with average relative errors (REj) between -1% and +2% in all radial segments, but it requires the complete velocity profile data from each vessel. The axial fit of equation 18 gives results with acceptable error (REj less than 11%) and requires only one

Here, it should be noted that a lot of researchers working in the area of micro blood flow still use the parabolic equation. As it is proved by figures 12 and 13, according to the current experimental data, the parabolic equation can lead to serious errors, especially near the

R (20)

1 10 10 j j <sup>r</sup>

velocity measurement near the vessel axis (Koutsiaris, 2009; Koutsiaris et al., 2011).

normalized radial position (r/R) at 10 different radial segments:

vessel wall.

**-70**

**-60**

**-50**

**-40**

**-30**

**-20**

**-10**

**REj (%)**

**0**

**1** **2** **3**

Parabolic Best Fit

**4** **5**

Equation 18 (Koutsiaris 2009) Axial Fit

Equation 18 (Koutsiaris 2009) Best Fit

Fig. 13. Velocity **relative error (RE)** statistics on original experimental data from the mouse cremaster muscle (12 velocity profiles, Long et al., 2004). **Average RE of each segment j (REj)** is shown in columns and standard error of the mean is shown with black bars on each column. Gray, white and black columns represent the parabolic best fit, the equation 18 axial fit and the equation 18 best fit respectively. Data were taken from Koutsiaris et al. (2011).

**6**

**Radial segment (j)**

**7** **8** **9** **10**

**10**

**20**

Where *f* (σ) is a function of R and of two independent parameters c1 and c2 which can be found through non linear regression analysis that uses equation 19 to minimize the leastsquares error (SSE) of the fit to the experimental velocity profile data sets (Long et al., 2004). With a suitable modification the equation can take into account the infinitesimal flow inside the microvascular glycocalyx layer. This is important for the transcapillary exchange and endothelium studies but from the volume flow estimation point of view it contributes little due to the very low velocities near the vessel wall. The fitting of this equation to experimental data from mouse venules can be seen in the relevant papers (Damiano et al., 2004; Long et al., 2004).

#### **7.3 Fitting efficiency**

At a preliminary evaluation of the **group A equations** (Koutsiaris et al., 2010a), fixed values for the parameters were selected: κ = 9 (equation 17) and κ1 = 0.58, κ2 =22 (equation 18) assuming they all have the same axial velocity estimated from the nearest experimental point to the vessel axis (**axial fit**). Eight profiles from **mouse venules** were estimated **graphically** from the literature (Long et al., 2004). According to the results, the parabolic equation tends to underestimate blood velocity, reaching a maximum relative error of - 72% near the vessel wall. The Roevros equation tends to overestimate blood velocity reaching a maximum relative error of + 48% at a radial position between 70% and 80% of the vessel radius R. Equation 18 tends to approximate blood velocity with a relative error between – 8% and + 7%, for all radial positions, leading to an average volume flow error of less than 0.5%. An axial fit example of the 3 equations is shown in figure 12.

**Radial Position (r/R)**

Fig. 12. Velocity profile equation 16, 17 and 18 (with the same axial velocity Vm) is shown in squares, triangles and solid black line respectively (Koutsiaris et al., 2010a). Velocity profile data from a 38.6 μm mouse venule are shown in black dots. Data were estimated graphically from Long et al. (2004).

Where *f* (σ) is a function of R and of two independent parameters c1 and c2 which can be found through non linear regression analysis that uses equation 19 to minimize the leastsquares error (SSE) of the fit to the experimental velocity profile data sets (Long et al., 2004). With a suitable modification the equation can take into account the infinitesimal flow inside the microvascular glycocalyx layer. This is important for the transcapillary exchange and endothelium studies but from the volume flow estimation point of view it contributes little due to the very low velocities near the vessel wall. The fitting of this equation to experimental data from mouse venules can be seen in the relevant papers (Damiano et al.,

At a preliminary evaluation of the **group A equations** (Koutsiaris et al., 2010a), fixed values for the parameters were selected: κ = 9 (equation 17) and κ1 = 0.58, κ2 =22 (equation 18) assuming they all have the same axial velocity estimated from the nearest experimental point to the vessel axis (**axial fit**). Eight profiles from **mouse venules** were estimated **graphically** from the literature (Long et al., 2004). According to the results, the parabolic equation tends to underestimate blood velocity, reaching a maximum relative error of - 72% near the vessel wall. The Roevros equation tends to overestimate blood velocity reaching a maximum relative error of + 48% at a radial position between 70% and 80% of the vessel radius R. Equation 18 tends to approximate blood velocity with a relative error between – 8% and + 7%, for all radial positions, leading to an average volume flow error of less than

**0.0 0.2 0.4 0.6 0.8 1.0**

**Radial Position (r/R)**

Fig. 12. Velocity profile equation 16, 17 and 18 (with the same axial velocity Vm) is shown in squares, triangles and solid black line respectively (Koutsiaris et al., 2010a). Velocity profile data from a 38.6 μm mouse venule are shown in black dots. Data were estimated graphically

0.5%. An axial fit example of the 3 equations is shown in figure 12.

2004; Long et al., 2004).

**7.3 Fitting efficiency** 

from Long et al. (2004).

**Velocity (**

**μm/s)**

Instead of using the same maximum velocity and fixed parametric values (axial fit), the classical approach would be to apply the **best fit**, i.e. finding the parametric values producing the minimum sum square error on each experimental velocity profile. Then statistics could be applied to the velocity relative errors of all the profiles, dividing the normalized radial position (r/R) at 10 different radial segments:

$$\frac{\mathbf{j} - \mathbf{l}}{10} \le \frac{\mathbf{r}}{\mathbf{R}} \le \frac{\mathbf{j}}{10} \tag{20}$$

Where j is an integer index (1 ≤ j ≤ 10). Working in this way, Koutsiaris et al. (2011) compared statistically the best fits of equations 17 and 18 and the axial fit of equation 18 on the **original experimental data of 12 velocity profiles from mouse venules** between 21 and 39 μm in diameter (Long et al., 2004). As it is shown in figure 13, the most efficient fit is the best fit of equation 18 with average relative errors (REj) between -1% and +2% in all radial segments, but it requires the complete velocity profile data from each vessel. The axial fit of equation 18 gives results with acceptable error (REj less than 11%) and requires only one velocity measurement near the vessel axis (Koutsiaris, 2009; Koutsiaris et al., 2011).

Here, it should be noted that a lot of researchers working in the area of micro blood flow still use the parabolic equation. As it is proved by figures 12 and 13, according to the current experimental data, the parabolic equation can lead to serious errors, especially near the vessel wall.

Fig. 13. Velocity **relative error (RE)** statistics on original experimental data from the mouse cremaster muscle (12 velocity profiles, Long et al., 2004). **Average RE of each segment j (REj)** is shown in columns and standard error of the mean is shown with black bars on each column. Gray, white and black columns represent the parabolic best fit, the equation 18 axial fit and the equation 18 best fit respectively. Data were taken from Koutsiaris et al. (2011).

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 311

**0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0**

**Radial Position (r/R)**

**0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0**

**Radial Position (r/R)**

(b)

Fig. 14. Best fit of equation 18 to original velocity profile data from a 25 μm rabbit arteriole at the diastolic phase (Tangelder et al., 1986). **(a)** 151 experimental points. **(b)** 11 experimental

(a)

points after filtering.

**Velocity (**

**μm/s)**

**Velocity (**

**μm/s)**

In addition, it should be noted that the best fit of the Roevros equation was not examined here, because it has already been reported (Tangelder et al., 1986) that it tends to underestimate velocity in the center of the vessel and near the wall and to overestimate velocity in the range 0.5 ≤ (r/R) ≤ 0.8.

As it was mentioned in the beginning of section 7.2, equations 16 to 19 could also be applied to the same phase of the **arteriolar blood flow**. The best fit of equation 18 to the **original velocity profile data** from a 25 μm rabbit arteriole at the diastolic phase (Tangelder et al., 1986) is shown in figure 14. The dispersion of the 151 experimental points around the black line in figure 14 (a) was caused by at least two factors: **1)** the inability of a volume illuminated system to define the measurement plane (out of focus effects) and **2)** small irregularities in the periodic arteriolar flow.

The first obstacle can now be overcome with modern confocal systems (section 2.2.6). An off-line way to overcome the out of focus effects is the use of the filtering criterion proposed by Damiano et al. (2004). The best fit of equation 18 on the 11 experimental points left after applying this criterion is shown in figure 14 (b).

Closing this section, it should be reported that equation 18 seems also to provide good fits, to velocity profile data coming from **Newtonian fluids inside rectangular microchannels**. It appears that rectangular cross sections with aspect ratios >> 1 (or << 1 depending on the definition; here the definition described in section 5 was accepted) distort the parabolic velocity profile of a Newtonian fluid producing blunt profiles similar to those of shear thinning fluids, such as blood, flowing inside cylindrical microchannels. The blunt profiles of the Newtonian fluids appear along the greatest side of the rectangular cross section.

An example of velocity profile along the greatest dimension (width W) of a rectangular cross section microchannel is shown in figure 15. The width was defined along the y direction, the height (H) was defined along the z direction and the length along the x direction (the direction of flow). The experimental velocity profile data shown in black dots, were measured in the central plane (z = (H/2) = 22.5 μm, Lima et al., 2008) and the width position y here was normalized with (W/2) = 150μm. The line represents the best fit approximation of equation 18. The parametric values of equation 18 giving the best fit were: Vm = 0.451 mm/s, κ1 = 0.109 and κ2 =12. The κ2 value was rounded down to the nearest even number, because a non-positive number can not be raised to a fractional power. Even with this approximating κ2 value, the absolute relative error (|RE|) was less than 1.6% and the average |RE| was 0.5%.

Perhaps, the parameters κ1 and κ2 could be expressed as functions of the aspect ratio (W/H) and the z position in order to use equation 18 for the velocity profile expression of a Newtonian fluid in every rectangular channel, but this requires more experimental data at various aspect ratios in order to be verified.

#### **7.4 Application to humans**

A fundamental remaining question is whether equation 18, which seems to approximate efficiently the blood velocity profile in the mouse and rabbit microcirculation, can be applied to the human microcirculation also. Taking into account the current state of technology, it would be rather difficult now, or in the near future, to measure the velocity profile of blood in human microvessels.

In addition, it should be noted that the best fit of the Roevros equation was not examined here, because it has already been reported (Tangelder et al., 1986) that it tends to underestimate velocity in the center of the vessel and near the wall and to overestimate

As it was mentioned in the beginning of section 7.2, equations 16 to 19 could also be applied to the same phase of the **arteriolar blood flow**. The best fit of equation 18 to the **original velocity profile data** from a 25 μm rabbit arteriole at the diastolic phase (Tangelder et al., 1986) is shown in figure 14. The dispersion of the 151 experimental points around the black line in figure 14 (a) was caused by at least two factors: **1)** the inability of a volume illuminated system to define the measurement plane (out of focus effects) and **2)** small

The first obstacle can now be overcome with modern confocal systems (section 2.2.6). An off-line way to overcome the out of focus effects is the use of the filtering criterion proposed by Damiano et al. (2004). The best fit of equation 18 on the 11 experimental points left after

Closing this section, it should be reported that equation 18 seems also to provide good fits, to velocity profile data coming from **Newtonian fluids inside rectangular microchannels**. It appears that rectangular cross sections with aspect ratios >> 1 (or << 1 depending on the definition; here the definition described in section 5 was accepted) distort the parabolic velocity profile of a Newtonian fluid producing blunt profiles similar to those of shear thinning fluids, such as blood, flowing inside cylindrical microchannels. The blunt profiles of the Newtonian fluids appear along the greatest side of the rectangular cross section.

An example of velocity profile along the greatest dimension (width W) of a rectangular cross section microchannel is shown in figure 15. The width was defined along the y direction, the height (H) was defined along the z direction and the length along the x direction (the direction of flow). The experimental velocity profile data shown in black dots, were measured in the central plane (z = (H/2) = 22.5 μm, Lima et al., 2008) and the width position y here was normalized with (W/2) = 150μm. The line represents the best fit approximation of equation 18. The parametric values of equation 18 giving the best fit were: Vm = 0.451 mm/s, κ1 = 0.109 and κ2 =12. The κ2 value was rounded down to the nearest even number, because a non-positive number can not be raised to a fractional power. Even with this approximating κ2 value, the absolute relative error (|RE|) was less than 1.6% and the

Perhaps, the parameters κ1 and κ2 could be expressed as functions of the aspect ratio (W/H) and the z position in order to use equation 18 for the velocity profile expression of a Newtonian fluid in every rectangular channel, but this requires more experimental data at

A fundamental remaining question is whether equation 18, which seems to approximate efficiently the blood velocity profile in the mouse and rabbit microcirculation, can be applied to the human microcirculation also. Taking into account the current state of technology, it would be rather difficult now, or in the near future, to measure the velocity

velocity in the range 0.5 ≤ (r/R) ≤ 0.8.

irregularities in the periodic arteriolar flow.

applying this criterion is shown in figure 14 (b).

average |RE| was 0.5%.

**7.4 Application to humans** 

various aspect ratios in order to be verified.

profile of blood in human microvessels.

Fig. 14. Best fit of equation 18 to original velocity profile data from a 25 μm rabbit arteriole at the diastolic phase (Tangelder et al., 1986). **(a)** 151 experimental points. **(b)** 11 experimental points after filtering.

(b)

Digital Micro PIV (PIV) and Velocity Profiles *In Vitro* and *In Vivo* 313

In this chapter a medium size review was given on digital micro particle image velocimetry (μPIV). The four main components of a Digital μPIV system were described in subsections

In the optics subsection, important insight was given into the concepts of volume illumination, depth of focus (DoF), f number (f#), measurement plane width (MPW) and effective diameter (dE). In addition, the distinction between fluorescent and brightfield μPIV

The latest development in μPIV optics is the "confocal" experimental set up which has the advantage of defining the width of the measurement plane (optical slice thickness). It seems that this will be the long term future of the digital μPIV set ups. However, at the moment, this is an expensive solution and there is always the drawback of the single point scanning, meaning that the image of the measurement plane is not strictly acquired at the same time. It is the view of the writer that low cost brightfield systems have not been examined

In the electronics subsection some hinds were given on digital camera species and architecture. In the software subsection the basic algorithm was described together with the

In addition, a brief but incisive description was given of the error (uncertainty, section 3) and performance (section 4) of a μPIV system, two subjects that often are not given the

The promising future of the Digital μPIV technique stems from the wide range of applications in micromechanics and microelectronics industry and research. Separate sections (sections 5 and 6) were devoted to the *in vitro* and *in vivo* experiments with a

Special emphasis was given on the microflows of biological fluids and especially in the velocity profiles of blood *in vivo*. A separate section (section 7) was dedicated on the velocity

All current experimental evidence suggests that the classical parabolic velocity profile is inappropriate for describing blood flow in the mammalian microvasculature. As it was shown in section 7, there are now **new equations** and **fitting techniques** for the expression of the average velocity profile of small mammals *in vivo* with acceptable error (figures 12, 13 and 14). In conclusion these new equations are at the moment the best choice for the description of blood flow in the human microcirculation. It should also be noted that equation 18 seems to describe well the Newtonian flow inside rectangular microchannels.

The author of this chapter would like to thank Professor Edward Damiano from Boston University, USA, Professor Geert Tangelder from VU University Medical Center, Amsterdam, The Netherlands and Professor Rui Lima from Polytechnic Institute of

Braganca, Portugal, for kindly sending the necessary original experimental data.

profile equations *in vivo* and their evaluation based on original experimental data.

basic assumptions and differences between fluorescent and brightfield set ups.

of section 2: 2.1) microfluidics, 2.2) optics, 2.3) electronics and 2.4) software.

adequately together with the use of image processing techniques.

**8. Conclusion** 

systems was clarified.

proper attention.

historical research overview.

**9. Acknowledgments** 

**Width Position (μm)**

Fig. 15. Best fit of equation 18 (shown with a line) to velocity profile data (shown with black dots) from a rectangular microchannel (Lima et al., 2008, Fig. 5) with a Height (H) = 45 μm and a Width (W) = 300 μm. Here, the width position was normalized with (W/2) = 150μm. The absolute relative error of the fit was less than 1.6% at all experimental points.

An indirect way of finding the answer would be to measure the rheological differences between mouse and human blood and more specifically the viscosity differences at low shear rates. In case these differences prove to be high enough, presumably the profiles would be different and a change of the equation fixed parametric values would be required.

It is already known (Windberger et al., 2003; Windberger & Baskurt, 2007) that in humans and other athletic species like horses, **whole blood viscosity (WBV)** is higher than in mice. However, this WBV difference becomes important at very low shear rates (< 10 s-1) occurring close to the vessel axis. Using the fixed parametric form of equation 18, the shear rate of 10 s-1 corresponds to a radial position r = 0.18 R, or to a surface area of only 3.3% of the total cross sectional area of the vessel. Therefore, it would be logical to assume that the fixed parametric form of equation 18 could be applied to the human microvessels as well. However, one could argue that this region near the vessel axis was responsible for the profile blunting in the first place.

A more detailed viscometric experiment comparing mouse and human blood samples would involve WBV measurements at many different shear rates < 10 s-1, at physiologic temperatures (human blood at 36.6 o C and mouse blood at 38 o C). Even so, there would be some remaining issues such as the use of anticoagulants in the blood samples and the selection of the appropriate hematocrit level, since according to the Fahraeus effect, the average microcirculatory hematocrit is lower than the systemic hematocrit (Hs). As it was proved by Lipowsky et al. (1980), for diameters of approximately 20 μm, the average hematocrit *in vivo* would be approximately 0.28Hs in the venous side. A suggested set of experiments would comprise WBV measurements at hematocrits of 0.28Hs, 0.38Hs and 0.50Hs.

### **8. Conclusion**

312 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications


**Width Position (μm)**

Fig. 15. Best fit of equation 18 (shown with a line) to velocity profile data (shown with black dots) from a rectangular microchannel (Lima et al., 2008, Fig. 5) with a Height (H) = 45 μm and a Width (W) = 300 μm. Here, the width position was normalized with (W/2) = 150μm.

An indirect way of finding the answer would be to measure the rheological differences between mouse and human blood and more specifically the viscosity differences at low shear rates. In case these differences prove to be high enough, presumably the profiles would be different and a change of the equation fixed parametric values would be required. It is already known (Windberger et al., 2003; Windberger & Baskurt, 2007) that in humans and other athletic species like horses, **whole blood viscosity (WBV)** is higher than in mice. However, this WBV difference becomes important at very low shear rates (< 10 s-1) occurring close to the vessel axis. Using the fixed parametric form of equation 18, the shear rate of 10 s-1 corresponds to a radial position r = 0.18 R, or to a surface area of only 3.3% of the total cross sectional area of the vessel. Therefore, it would be logical to assume that the fixed parametric form of equation 18 could be applied to the human microvessels as well. However, one could argue that this region near the vessel axis was responsible for the

A more detailed viscometric experiment comparing mouse and human blood samples would involve WBV measurements at many different shear rates < 10 s-1, at physiologic temperatures (human blood at 36.6 o C and mouse blood at 38 o C). Even so, there would be some remaining issues such as the use of anticoagulants in the blood samples and the selection of the appropriate hematocrit level, since according to the Fahraeus effect, the average microcirculatory hematocrit is lower than the systemic hematocrit (Hs). As it was proved by Lipowsky et al. (1980), for diameters of approximately 20 μm, the average hematocrit *in vivo* would be approximately 0.28Hs in the venous side. A suggested set of experiments would

comprise WBV measurements at hematocrits of 0.28Hs, 0.38Hs and 0.50Hs.

The absolute relative error of the fit was less than 1.6% at all experimental points.

**0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50**

profile blunting in the first place.

**Average Velocity (mm/s)**

In this chapter a medium size review was given on digital micro particle image velocimetry (μPIV). The four main components of a Digital μPIV system were described in subsections of section 2: 2.1) microfluidics, 2.2) optics, 2.3) electronics and 2.4) software.

In the optics subsection, important insight was given into the concepts of volume illumination, depth of focus (DoF), f number (f#), measurement plane width (MPW) and effective diameter (dE). In addition, the distinction between fluorescent and brightfield μPIV systems was clarified.

The latest development in μPIV optics is the "confocal" experimental set up which has the advantage of defining the width of the measurement plane (optical slice thickness). It seems that this will be the long term future of the digital μPIV set ups. However, at the moment, this is an expensive solution and there is always the drawback of the single point scanning, meaning that the image of the measurement plane is not strictly acquired at the same time. It is the view of the writer that low cost brightfield systems have not been examined adequately together with the use of image processing techniques.

In the electronics subsection some hinds were given on digital camera species and architecture. In the software subsection the basic algorithm was described together with the basic assumptions and differences between fluorescent and brightfield set ups.

In addition, a brief but incisive description was given of the error (uncertainty, section 3) and performance (section 4) of a μPIV system, two subjects that often are not given the proper attention.

The promising future of the Digital μPIV technique stems from the wide range of applications in micromechanics and microelectronics industry and research. Separate sections (sections 5 and 6) were devoted to the *in vitro* and *in vivo* experiments with a historical research overview.

Special emphasis was given on the microflows of biological fluids and especially in the velocity profiles of blood *in vivo*. A separate section (section 7) was dedicated on the velocity profile equations *in vivo* and their evaluation based on original experimental data.

All current experimental evidence suggests that the classical parabolic velocity profile is inappropriate for describing blood flow in the mammalian microvasculature. As it was shown in section 7, there are now **new equations** and **fitting techniques** for the expression of the average velocity profile of small mammals *in vivo* with acceptable error (figures 12, 13 and 14). In conclusion these new equations are at the moment the best choice for the description of blood flow in the human microcirculation. It should also be noted that equation 18 seems to describe well the Newtonian flow inside rectangular microchannels.

### **9. Acknowledgments**

The author of this chapter would like to thank Professor Edward Damiano from Boston University, USA, Professor Geert Tangelder from VU University Medical Center, Amsterdam, The Netherlands and Professor Rui Lima from Polytechnic Institute of Braganca, Portugal, for kindly sending the necessary original experimental data.

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## **Section 4**

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Werely, S.T. & Meinhart, C.D. (2010). Recent Advances in Micro-Particle Image Velocimetry.

Westerweel, J. (1997). Fundamentals of digital particle image velocimetry. *Meas. Sci. Technol.*,

Westerweel, J.; Geelhoed, P.F. & Lindken, R. (2004). Single-pixel resolution ensemble

Willert, C.E. & Gharib, M. (1991). Digital particle image velocimetry. *Exp. Fluids,* Vol.10, pp.

Windberger, U.; Bartholovitsch, A.; Plasenzotti, R.; Korak, K.J. & Heinze, G. (2003). Whole

Windberger, U. & Baskurt, O.K. (2007). Comparative Haemorheology, In: *Handbook of* 

velocimetry. *Exp Fluids*, Vol.31, pp. 258-268, ISSN 0723-4864.

*Annu. Rev. Fluid Mech.,* Vol.42, pp. 557-576, ISSN 0066-4189.

0967-3334.

23099-8, Heidelberg.

181-193, ISSN 0723-4864.

pp. 431-440, ISSN 0958-0670.

4864.

Netherlands.

Vol.8, pp. 1379-1392, ISSN 0957-0233.

simulation and *in vivo* image analysis. *Physiol. Meas.*, Vol.21, pp. 459-471, ISSN

T.L.M.; Ursem, N.T.C.; Poelmann, R.E.; Westerweel, J. & Hierck, B.P. (2006). In vivo micro particle image velocimetry measurements of blood-plasma in the embryonic

*Microscale Diagnostic Techniques*, Breuer K.S. (Ed.), pp. 51-112, Springer, ISBN 3-540-

correlation for micro-PIV applications. *Exp. Fluids,* Vol.37, pp. 375-384, ISSN 0723-

blood viscosity, plasma viscosity and erythrocyte aggregation in nine mammalian species: reference values and comparison of data. *Experimental Physiology*, Vol.88,

*Hemorheology and Hemodynamics*, Baskurt, O.K.; Hardeman, M.R.; Rampling, M. & Meiselman, H.J. (Eds), pp. 267-283, IOS Press, ISBN 978-1-58603-771-0, The **PIV and PTV** 

**12** 

*Japan* 

**Measurements of Particle Velocities and** 

Motohiko Umeyama, Tetsuya Shintani, Kim-Cuong Nguyen and Shogo Matsuki

**Trajectories for Internal Waves Propagating in a** 

**Density-Stratified Two-Layer Fluid on a Slope** 

*Department of Civil & Environmental Engineering, Tokyo Metropolitan University* 

The existence of internal waves was first recognized by a measurement of water temperature by Helland-Hansen and Nansen (1926). Later, the vertical structure of internal waves has been detected by observation of temperature, salinity, or ocean current, while the propagation of internal waves has been identified by images from radar or acoustic Doppler and echo sounder. Shand (1953) found internal wave fronts appearing on aerial photographs. From observation of offshore temperature variations, LaFond (1962) found that time-dependent isotherms are flattened for a shallower thermocline and peaked for a deeper thermocline on the wave crests. Apel et al. (1975, 1976, 1985) reported a series of research results for the internal waves observed in pictures from satellites, space shuttles, and aircraft. In addition to these indirect photographs, they also used various instruments such as the expendable bathythermograph (XBT), acoustic echo sounding, and ship radar. In contrast, numerous researchers have carried out laboratory experiments to examine the shoaling and breaking of internal waves on various topographic features. Thorpe (1968) studied the breaking and runup of internal waves in a two-layered system, and found that internal waves steepen at the front as the lower layer becomes shallow, but the crests break backwards unlike surface breakers. On the upper slope, the wave (bolus) behaves like the front of a gravity current, and the dense fluid returning down the slope from previous waves flows over the top of the overcoming waves. Using a hydrogen-bubble wiring system, Kao et al. (1985) measured the particle velocity profile during the passage of internal waves. Wallace and Wilkinson (1988) found that overturning is initiated by the interaction of an incident wave with the backflow from the preceding boluses. Helfrich (1992) performed experiments to observe the interaction of an internal wave of depression with a sloping bottom, and recognized the importance of the backflow that produces significant mixing. He found a rapid offshore flow of lower-layer water while the front face of the

There have been significant developments in measuring fluid velocities by using laboratory equipment, but the use of tools such as the electric‐magnetic current meter and laser Doppler anemometer has not solved kinetic problems for internal waves. Experimental studies for fluid

**1. Introduction** 

incident wave moved up the slope.

## **Measurements of Particle Velocities and Trajectories for Internal Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope**

Motohiko Umeyama, Tetsuya Shintani, Kim-Cuong Nguyen and Shogo Matsuki *Department of Civil & Environmental Engineering, Tokyo Metropolitan University Japan* 

### **1. Introduction**

The existence of internal waves was first recognized by a measurement of water temperature by Helland-Hansen and Nansen (1926). Later, the vertical structure of internal waves has been detected by observation of temperature, salinity, or ocean current, while the propagation of internal waves has been identified by images from radar or acoustic Doppler and echo sounder. Shand (1953) found internal wave fronts appearing on aerial photographs. From observation of offshore temperature variations, LaFond (1962) found that time-dependent isotherms are flattened for a shallower thermocline and peaked for a deeper thermocline on the wave crests. Apel et al. (1975, 1976, 1985) reported a series of research results for the internal waves observed in pictures from satellites, space shuttles, and aircraft. In addition to these indirect photographs, they also used various instruments such as the expendable bathythermograph (XBT), acoustic echo sounding, and ship radar.

In contrast, numerous researchers have carried out laboratory experiments to examine the shoaling and breaking of internal waves on various topographic features. Thorpe (1968) studied the breaking and runup of internal waves in a two-layered system, and found that internal waves steepen at the front as the lower layer becomes shallow, but the crests break backwards unlike surface breakers. On the upper slope, the wave (bolus) behaves like the front of a gravity current, and the dense fluid returning down the slope from previous waves flows over the top of the overcoming waves. Using a hydrogen-bubble wiring system, Kao et al. (1985) measured the particle velocity profile during the passage of internal waves. Wallace and Wilkinson (1988) found that overturning is initiated by the interaction of an incident wave with the backflow from the preceding boluses. Helfrich (1992) performed experiments to observe the interaction of an internal wave of depression with a sloping bottom, and recognized the importance of the backflow that produces significant mixing. He found a rapid offshore flow of lower-layer water while the front face of the incident wave moved up the slope.

There have been significant developments in measuring fluid velocities by using laboratory equipment, but the use of tools such as the electric‐magnetic current meter and laser Doppler anemometer has not solved kinetic problems for internal waves. Experimental studies for fluid

Measurements of Particle Velocities and Trajectories for Internal

system to those of the electromagnetic current (EC) meter.

theoretically by the method of characteristics.

**2. Experiments and data analysis** 

**2.1 Wave tank and wavemakers** 

and its photograph.

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 323

array of velocity vectors, it is convenient to define the Eulerian velocity based upon the average particle motion in the possible space. In contrast, PTV traces the individual particle path from a sequence of images in a system. From a Lagrangian viewpoint, PTV is better suited than PIV for handling unsteady flow. Quantitative results for Lagrangian fluid motion can be obtained through computerized analyses of the particle images in the modern PTV technique. Generally, PIV has determined the Eulerian velocity field from a sequence of images, while PTV has estimated the Lagrangian velocity by tracing individual particle paths. Umeyama (2011) employed a PTV system with single-exposure images to track particle displacements for surface waves with or without a steady current. In addition to the basic use of PTV, an alternative measurement technique was proposed to describe particle trajectories in a Eulerian scheme through PIV analysis. Later, Umeyama et al. (2011) made similar measurement and analysis for the water particle velocity and trajectory using a PIV system with two Nd:YAG lasers of 50 mW. In this experiment, DIAION and micro bubbles were chosen as tracer. More recently, Umeyama (2012) measured the water particle velocity and trajectory in a pure wave motion using a new PIV system with an 8 W Nd:YAG laser. These previous validation results are presented by comparing the measurements of the PIV

This article investigates the spatial and temporal variations of the density interface, wave height, celerity and setup due to shoaling and breaking of internal waves, using an image processing technique, and the velocity and trajectory of water particles in an internal wave motion, using particle image velocimetry (PIV). The writers illustrate 2D instantaneous displacements of density interface from the observed data, and analyse them to obtain the wave height, celerity, and setup. These results are compared with the calculated values by the method of characteristics, the simple shoaling model with energy dissipation, and the momentum balance equation based on a radiation stress concept. The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The PIV technique's ability to measure both temporal and spatial variations of the velocity is proven after a series of attempts. This technique is applied to the prediction of particle trajectory in a Eulerian scheme. The measured particle path is compared to the positions found

Experiments on internal waves were carried out in the 6.0-m-long, 0.15-m-wide, and 0.35-mdeep wave tank. It was constructed of 12 Plexiglas panels, 10 stainless flanges, and a stainless bottom. Each glass panel was 91.0 cm long, 27.0 cm high and 1.0 cm thick. A wave generator was placed at one end. Fig. 1 shows a sketch of the apparatus for the wave tank

In the earlier stages of experiments, Umeyama (2002) and Umeyama & Shintani (2004, 2006) used a horizontal flap-type wavemaker. Recently, experimental studies were undertaken to test several types of wave-generating paddles, and a different kind of wavemaker was set at one end of the wave tank. The sketch of the new wavemaker is presented in Fig.2. This slidetype wavemaker consists of a D-shaped paddle and a linear actuator that moves smoothly and programmatically within a given stroke length. As the D-shaped paddle limits the mixing of the upper and lower waters, the intermediate density layer does not grow quickly

velocities have generally relied on point measurement techniques. However, recent advances in technology provide two and three‐dimensional features of the velocity field for several flow problems. Visualization techniques have played an essential role in fluid flows during the previous decade, because they yield both qualitative and quantitative insights in geophysical or environmental fluid mechanics. Now, imaging techniques enable high‐resolution images of several kinds of unsteady flows. The latest developments in particle image velocimetry (PIV) and particle tracking velocimetry (PTV) have led to the visualization of velocity fields and particle paths. Both techniques are analysis methods for image pairs taken in a seeded flow field with known temporal separation. Water velocities due to the propagation of internal waves have been measured by Michallet and Ivey (1999), and Walker et al. (2003) using PIV, and by Grue et al. (1999, 2000) using PTV.

The mechanism of internal waves in a two-layer system comprising homogeneous fluids of slightly different densities has been studied using visualization techniques in the Hydraulic Laboratory at Tokyo Metropolitan University. In the research of Umeyama (2002), a digital video camera was first used to illustrate the internal waves propagating in a fluid of finite depth over a flat bed. After analysing continuous pictures recorded on a DV tape, the density interface was determined from a set of luminance values using image-processing software. The temporal and spatial variations of the density interface were compared with the analytical results based on the third-order finite amplitude approximation. Umeyama and Shintani (2004) installed a Plexiglas plate in the same wave tank to observe the runup and breaking of long internal waves over an artificial slope. The profile of internal waves and the mixing between upper and lower layers, were visualized by adding a blue dye (Anilin Blue) in lower salt water. Later, Umeyama and Shintani (2006) performed more precise laboratory tests, by considering additional aspects such as transformation, attenuation, set-down, and setup during the shoaling and breaking events. The method of characteristics, energy dissipation model with radiation stress, and momentum balance equation were used to confirm the experimental results. To study the transformation processes using instantaneous and mean velocity fields and nonlinear properties using interfacial displacements over a uniform slope, Shimizu et al. (2005) developed a PIV system that consisted of a Nd:YAG pulsed laser and a CCD camera. The analysis, however, highlighted the limitations in the measuring range. This PIV system of the laser sheet could not measure a large area while maintaining a fine resolution. The PIV measurements were repeated three times to cover one wavelength and the total depth in adjoining areas for each case. In contrast, Umeyama (2008) and Umeyama and Shinomiya (2009) developed a new PIV system that utilized halogen lamps and three high-definition digital video cameras in which the maximum resolution was 2,016×1,134 pixels and the images were recorded on a hard disk. Each video camera, operating simultaneously side by side, covered a larger area with a frame rate 16:9. Since the water surface was almost flat during all experiments, the halogen lamps were set in a line along the wave tank at its top, and the light sheet of 3 mm width was emitted from the upper side of the wave tank. Umeyama and Matsuki (2011) recently measured the similar physical quantities with two frequency-doubled Nd:YAG lasers of 50 mW energy at 532 nm as the illumination sources. In addition to the common use of the PIV technique, the knowledge has been extended to visualize water particle paths and mass transport variations due to the propagation of internal waves in the tank.

From a Eulerian prospective, the motion of an incompressible fluid is distinctive if the velocity vectors occupy an instantaneous velocity field. As PIV is used to represent a regular

velocities have generally relied on point measurement techniques. However, recent advances in technology provide two and three‐dimensional features of the velocity field for several flow problems. Visualization techniques have played an essential role in fluid flows during the previous decade, because they yield both qualitative and quantitative insights in geophysical or environmental fluid mechanics. Now, imaging techniques enable high‐resolution images of several kinds of unsteady flows. The latest developments in particle image velocimetry (PIV) and particle tracking velocimetry (PTV) have led to the visualization of velocity fields and particle paths. Both techniques are analysis methods for image pairs taken in a seeded flow field with known temporal separation. Water velocities due to the propagation of internal waves have been measured by Michallet and Ivey (1999), and Walker et al. (2003) using PIV,

The mechanism of internal waves in a two-layer system comprising homogeneous fluids of slightly different densities has been studied using visualization techniques in the Hydraulic Laboratory at Tokyo Metropolitan University. In the research of Umeyama (2002), a digital video camera was first used to illustrate the internal waves propagating in a fluid of finite depth over a flat bed. After analysing continuous pictures recorded on a DV tape, the density interface was determined from a set of luminance values using image-processing software. The temporal and spatial variations of the density interface were compared with the analytical results based on the third-order finite amplitude approximation. Umeyama and Shintani (2004) installed a Plexiglas plate in the same wave tank to observe the runup and breaking of long internal waves over an artificial slope. The profile of internal waves and the mixing between upper and lower layers, were visualized by adding a blue dye (Anilin Blue) in lower salt water. Later, Umeyama and Shintani (2006) performed more precise laboratory tests, by considering additional aspects such as transformation, attenuation, set-down, and setup during the shoaling and breaking events. The method of characteristics, energy dissipation model with radiation stress, and momentum balance equation were used to confirm the experimental results. To study the transformation processes using instantaneous and mean velocity fields and nonlinear properties using interfacial displacements over a uniform slope, Shimizu et al. (2005) developed a PIV system that consisted of a Nd:YAG pulsed laser and a CCD camera. The analysis, however, highlighted the limitations in the measuring range. This PIV system of the laser sheet could not measure a large area while maintaining a fine resolution. The PIV measurements were repeated three times to cover one wavelength and the total depth in adjoining areas for each case. In contrast, Umeyama (2008) and Umeyama and Shinomiya (2009) developed a new PIV system that utilized halogen lamps and three high-definition digital video cameras in which the maximum resolution was 2,016×1,134 pixels and the images were recorded on a hard disk. Each video camera, operating simultaneously side by side, covered a larger area with a frame rate 16:9. Since the water surface was almost flat during all experiments, the halogen lamps were set in a line along the wave tank at its top, and the light sheet of 3 mm width was emitted from the upper side of the wave tank. Umeyama and Matsuki (2011) recently measured the similar physical quantities with two frequency-doubled Nd:YAG lasers of 50 mW energy at 532 nm as the illumination sources. In addition to the common use of the PIV technique, the knowledge has been extended to visualize water particle paths

and mass transport variations due to the propagation of internal waves in the tank.

From a Eulerian prospective, the motion of an incompressible fluid is distinctive if the velocity vectors occupy an instantaneous velocity field. As PIV is used to represent a regular

and by Grue et al. (1999, 2000) using PTV.

array of velocity vectors, it is convenient to define the Eulerian velocity based upon the average particle motion in the possible space. In contrast, PTV traces the individual particle path from a sequence of images in a system. From a Lagrangian viewpoint, PTV is better suited than PIV for handling unsteady flow. Quantitative results for Lagrangian fluid motion can be obtained through computerized analyses of the particle images in the modern PTV technique. Generally, PIV has determined the Eulerian velocity field from a sequence of images, while PTV has estimated the Lagrangian velocity by tracing individual particle paths. Umeyama (2011) employed a PTV system with single-exposure images to track particle displacements for surface waves with or without a steady current. In addition to the basic use of PTV, an alternative measurement technique was proposed to describe particle trajectories in a Eulerian scheme through PIV analysis. Later, Umeyama et al. (2011) made similar measurement and analysis for the water particle velocity and trajectory using a PIV system with two Nd:YAG lasers of 50 mW. In this experiment, DIAION and micro bubbles were chosen as tracer. More recently, Umeyama (2012) measured the water particle velocity and trajectory in a pure wave motion using a new PIV system with an 8 W Nd:YAG laser. These previous validation results are presented by comparing the measurements of the PIV system to those of the electromagnetic current (EC) meter.

This article investigates the spatial and temporal variations of the density interface, wave height, celerity and setup due to shoaling and breaking of internal waves, using an image processing technique, and the velocity and trajectory of water particles in an internal wave motion, using particle image velocimetry (PIV). The writers illustrate 2D instantaneous displacements of density interface from the observed data, and analyse them to obtain the wave height, celerity, and setup. These results are compared with the calculated values by the method of characteristics, the simple shoaling model with energy dissipation, and the momentum balance equation based on a radiation stress concept. The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The PIV technique's ability to measure both temporal and spatial variations of the velocity is proven after a series of attempts. This technique is applied to the prediction of particle trajectory in a Eulerian scheme. The measured particle path is compared to the positions found theoretically by the method of characteristics.

### **2. Experiments and data analysis**

### **2.1 Wave tank and wavemakers**

Experiments on internal waves were carried out in the 6.0-m-long, 0.15-m-wide, and 0.35-mdeep wave tank. It was constructed of 12 Plexiglas panels, 10 stainless flanges, and a stainless bottom. Each glass panel was 91.0 cm long, 27.0 cm high and 1.0 cm thick. A wave generator was placed at one end. Fig. 1 shows a sketch of the apparatus for the wave tank and its photograph.

In the earlier stages of experiments, Umeyama (2002) and Umeyama & Shintani (2004, 2006) used a horizontal flap-type wavemaker. Recently, experimental studies were undertaken to test several types of wave-generating paddles, and a different kind of wavemaker was set at one end of the wave tank. The sketch of the new wavemaker is presented in Fig.2. This slidetype wavemaker consists of a D-shaped paddle and a linear actuator that moves smoothly and programmatically within a given stroke length. As the D-shaped paddle limits the mixing of the upper and lower waters, the intermediate density layer does not grow quickly

Measurements of Particle Velocities and Trajectories for Internal

disturbances produced deviations from the original density value.

properties are expected to change in the wave tank.

**2.2 Flow visualization** 

frequency of 47 Hz.

**2.3 PIV technique** 

displacement.

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 325

In the present study, a 1-cm-thick Plexiglas plate, which served as the plane seabed, was fabricated between 100 and 600 m from the wavemaker. A density-stratified fluid consisting of fresh water and salt water was prepared for the experiments, and the density of the salt water was 1,030 mg/cm3. The total water depth from the bottom of the wave tank was kept at 30 cm. The density of the salt water was assumed to be constant initially, but subsequent

Using an image processing technique, Umeyama & Shintani (2004) illustrated the temporal and spatial variations of the density interface and the mixture of upper and lower layer waters in the density-stratified two-layer fluid on a sloping bed. The numerically predicted density variation due to mixing was compared with a set of luminance data analyzed by the image processing technique. Later, Umeyama & Shintani (2006) and Umeyama (2008) extended the aspects of internal wave mechanics during shoaling and breaking events. The objective of these studies was to observe internal waves approaching an upper slope in a wave tank using a video recording system, convert the measured data to the wave profile, celerity, height and setup, and compare the experimental values with theoretical ones. For the flow visualization and video recording technique in detail, refer to Umeyama (2008). The colour image file from the video recorder was transferred to an 8-bit (256 grades) grayscale image file. Using the method of image segmentation, individual pixels in a grayscale image were marked as object or background pixels. The density interface was estimated from the spatial distribution of the threshold. Finally, the temporal displacements of the density interface were obtained at several points, and the wave height and mean level were estimated by averaging these displacements about 10 wave periods. This duration may be assumed stationary at the location where data are gathered, because artificial internal waves are considered approximately stationary only for a few minutes. Beyond the duration, their

An internal wave gauge was also used to measure the vertical displacement of density interface at a location 100 cm from the wave maker. A salinity sensor at the tip of the internal wave gauge could run after the position of the prescribed salt density layer. Under each set of experimental conditions, experimental data were collected continuously at a

The instantaneous water particle velocities induced by internal waves were measured using PIV. The basic principle of PIV is evaluating the instantaneous velocities through recording the position of images of small tracers, suspended in the fluid, at successive instants in time. In practice, when two successive images of tracers illuminated in a thin and intense light sheet are acquired, the velocity is calculated from the known time difference and measured

In this study, the water particle velocity was measured using a single-exposure image PIV system. The instantaneous vector field was trapped in the 91-cm-long and 27-cm-high glass panel using a frequency-doubled Nd:YAG laser of 8-W energy at 532 nm. A 2-mm-thick light sheet was emitted from the upper side: this light sheet had a very uniform

during each test. Umeyama (2008), Umeyama & Shinomiya (2009), and Umeyama & Matsuki (2011) examined internal waves generated by the slide-type wavemaker to obtain insight into the nonlinear properties and kinematics.

Fig. 1. A schematic diagram of experimental arrangements and a photograph of wave tank

Fig. 2. A slide-type wavemaker with a D-shaped paddle

In the present study, a 1-cm-thick Plexiglas plate, which served as the plane seabed, was fabricated between 100 and 600 m from the wavemaker. A density-stratified fluid consisting of fresh water and salt water was prepared for the experiments, and the density of the salt water was 1,030 mg/cm3. The total water depth from the bottom of the wave tank was kept at 30 cm. The density of the salt water was assumed to be constant initially, but subsequent disturbances produced deviations from the original density value.

### **2.2 Flow visualization**

35

324 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

during each test. Umeyama (2008), Umeyama & Shinomiya (2009), and Umeyama & Matsuki (2011) examined internal waves generated by the slide-type wavemaker to obtain

Upper layer

Fig. 1. A schematic diagram of experimental arrangements and a photograph of wave tank

linear actuater

D-shaped paddle

Fig. 2. A slide-type wavemaker with a D-shaped paddle

insight into the nonlinear properties and kinematics.

PIV region <sup>x</sup>

z 0

Plexiglas plate

(Unit cm) 500 100

Lower layer Sloping bottom

Using an image processing technique, Umeyama & Shintani (2004) illustrated the temporal and spatial variations of the density interface and the mixture of upper and lower layer waters in the density-stratified two-layer fluid on a sloping bed. The numerically predicted density variation due to mixing was compared with a set of luminance data analyzed by the image processing technique. Later, Umeyama & Shintani (2006) and Umeyama (2008) extended the aspects of internal wave mechanics during shoaling and breaking events. The objective of these studies was to observe internal waves approaching an upper slope in a wave tank using a video recording system, convert the measured data to the wave profile, celerity, height and setup, and compare the experimental values with theoretical ones. For the flow visualization and video recording technique in detail, refer to Umeyama (2008). The colour image file from the video recorder was transferred to an 8-bit (256 grades) grayscale image file. Using the method of image segmentation, individual pixels in a grayscale image were marked as object or background pixels. The density interface was estimated from the spatial distribution of the threshold. Finally, the temporal displacements of the density interface were obtained at several points, and the wave height and mean level were estimated by averaging these displacements about 10 wave periods. This duration may be assumed stationary at the location where data are gathered, because artificial internal waves are considered approximately stationary only for a few minutes. Beyond the duration, their properties are expected to change in the wave tank.

An internal wave gauge was also used to measure the vertical displacement of density interface at a location 100 cm from the wave maker. A salinity sensor at the tip of the internal wave gauge could run after the position of the prescribed salt density layer. Under each set of experimental conditions, experimental data were collected continuously at a frequency of 47 Hz.

### **2.3 PIV technique**

The instantaneous water particle velocities induced by internal waves were measured using PIV. The basic principle of PIV is evaluating the instantaneous velocities through recording the position of images of small tracers, suspended in the fluid, at successive instants in time. In practice, when two successive images of tracers illuminated in a thin and intense light sheet are acquired, the velocity is calculated from the known time difference and measured displacement.

In this study, the water particle velocity was measured using a single-exposure image PIV system. The instantaneous vector field was trapped in the 91-cm-long and 27-cm-high glass panel using a frequency-doubled Nd:YAG laser of 8-W energy at 532 nm. A 2-mm-thick light sheet was emitted from the upper side: this light sheet had a very uniform

Measurements of Particle Velocities and Trajectories for Internal

P4

Fig. 3. Lagrangian particle trajectory on Eulerian grids

Hydraulic Laboratory of Tokyo Metropolitan University.

Case Slope Density hI:hII

\* Wave height was measured using wave gauge at 100 cm from the wavemaker.

potentials in the upper and lower layers, so that the Laplace equations are

u2

u4

P1 P2

l3 l4

A

u

A'

l2

l1

**2.5 Experimental conditions** 

Table 1. Experimental cases

**3.1 Stokes internal waves** 

boundary conditions at the free surface are

**3. Theory** 

u3

P3

u1

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 327

The experimental conditions are listed in Table 1 that includes the present results in the

1 3/50 1,030 mg/cm3 15 cm:15 cm 2.6 cm 5.2 s 2 2.7 cm 7.2 s 3 3/50 1,030 mg/cm3 10 cm:20 cm 2.8 cm 5.2 s 4 2.4 cm 7.2 s

First, we consider Stokes internal waves propagating along the interface between two homogeneous incompressible and inviscid fluids of different density in a constant depth. The origin of the axes is located in the undisturbed interface. The density and depth of the upper layer are *I* and *<sup>I</sup> h* , respectively, and those of the lower layer are *II* and *II h* , respectively. The vertical displacements of the free surface and the density interface are ( ,) *<sup>I</sup> x t* and ( ,) *II x t* , respectively. Let ( , ,) *<sup>I</sup> xzt* , and ( , ,) *II xzt* denote the velocity

where *x* =horizontal coordinate; and *z* =vertical coordinate. The kinematical and dynamical

t=t t=t+Δt

P'1 P'2

l'1

u'3

P'3

u'

l'3 l'4

u'1 u'2

l'2 A'

P'4

Wave height\*

0 *Ixx Izz* (1)

0 *IIxx IIzz* (2)

Wave period

u'4

intensity and covered the total area in the glass panel. The system included two highdefinition digital video cameras (SONY HXR-NX5J) with a maximum resolution of 1920×1080 pixels. The video camera was arranged linearly 1.28 m from the sidewall of the wave tank. The camera image area was centered in the light sheet; consequently, the corresponding viewing area up to 100.0 cm×28.0 cm was chosen using the optical arrangement. According to Austin and Halikas (1976), the index of refraction of clear water is 1.335, while that of salt water with a density of 1,030 mg/cm3 is 1.341. As the index of refraction varies by less than 0.5% (the maximum difference in angle of refraction is approximately 0.1 degree), the difference in geometric distortion was not corrected. DIAION (DK-FINE HP20SS) was used to capture the high-contrast images with the particle tracer in both layers. It consisted of ion-exchange resin with the homogeneous matrix structure inside the particle. This kind of matrix gave micropores formed by the polymeric networks, so that water could pass through these pores. Before each experiment, DIAION was mixed in the salt water. Analysis of the displacement of images in each interrogation window by means of the cross-correlation method leads to an estimated average displacement of particles. The resolution is directly related to the size of the interrogation window. The displacement vector computed at any location is the spatially averaged transitional motion of particles. Vector fields could be obtained with the PIV system processing a pair of images, using an interrogation window of 64×64 pixels in a candidate region of 128×128 pixels. Since the internal wave topography does not change significantly over 0.1 s, the resultant displacement of topographic features for two images spaced in *t* =0.1 s was chosen for a direct calculation of the velocity vectors.

#### **2.4 Eulerian/Lagrangian method**

A cross-correlation method was performed to calculate the water particle displacement and local velocity by processing a pair of image frames. Although the representation of the velocity vector field in a Eulerian system is a typical example of the PIV method, the result can be applied to a particle tracking process in a Lagrangian system. Umeyama & Matsuki (2011) used the velocity given at the spatially discrete nodal point to estimate the imaginary velocity and location of a particle.

The following explains the particle motion within a tracking time step *t* along an arbitrary trajectory across a general mesh of quadrilateral cells (Fig.3). The algorithm has two steps: (1) the velocity value of a Lagrangian point A where *t* is obtained by interpolating the neighboring velocity values ( *u*<sup>1</sup> at *P*<sup>1</sup> , *u*2 at *P*<sup>2</sup> , *u*3 at *P*<sup>3</sup> , and *u*4 at *P*<sup>4</sup> , where *P*<sup>1</sup> , *P*<sup>2</sup> , *P*<sup>3</sup> , and *P*4 are corners of the mesh), and (2) the particle associated with the Lagrangian point at *t* is traced to a hypothetical location (A') at *t t* . Thus, these Lagrangian velocities *uL* at *t* and ' *uL* at *t t* are

$$\mu = \frac{\frac{\mu\_1}{l\_1} + \frac{\mu\_2}{l\_2} + \frac{\mu\_3}{l\_3} + \frac{\mu\_4}{l\_4}}{\frac{1}{l\_1} + \frac{1}{l\_2} + \frac{1}{l\_3} + \frac{1}{l\_4}} \quad \text{at } t = t \text{, and } \mu' = \frac{\frac{\mu\_1}{l\_1}' + \frac{\mu\_2}{l\_2}' + \frac{\mu\_3}{l\_3}' + \frac{\mu\_4}{l\_4}'}{\frac{1}{l\_1} + \frac{1}{l\_2} + \frac{1}{l\_3} + \frac{1}{l\_4}} \text{ at } t = t + \Delta t$$

where 1*l* , 2*l* , 3*l* , 4*l* , 1 *l* ' , 2*l* ' , 3*l* ' , and 4*l* ' are distances to the imaginary location of a particle from the Eulerian grid points.

Fig. 3. Lagrangian particle trajectory on Eulerian grids

### **2.5 Experimental conditions**

The experimental conditions are listed in Table 1 that includes the present results in the Hydraulic Laboratory of Tokyo Metropolitan University.


\* Wave height was measured using wave gauge at 100 cm from the wavemaker.

Table 1. Experimental cases

### **3. Theory**

326 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

intensity and covered the total area in the glass panel. The system included two highdefinition digital video cameras (SONY HXR-NX5J) with a maximum resolution of 1920×1080 pixels. The video camera was arranged linearly 1.28 m from the sidewall of the wave tank. The camera image area was centered in the light sheet; consequently, the corresponding viewing area up to 100.0 cm×28.0 cm was chosen using the optical arrangement. According to Austin and Halikas (1976), the index of refraction of clear water is 1.335, while that of salt water with a density of 1,030 mg/cm3 is 1.341. As the index of refraction varies by less than 0.5% (the maximum difference in angle of refraction is approximately 0.1 degree), the difference in geometric distortion was not corrected. DIAION (DK-FINE HP20SS) was used to capture the high-contrast images with the particle tracer in both layers. It consisted of ion-exchange resin with the homogeneous matrix structure inside the particle. This kind of matrix gave micropores formed by the polymeric networks, so that water could pass through these pores. Before each experiment, DIAION was mixed in the salt water. Analysis of the displacement of images in each interrogation window by means of the cross-correlation method leads to an estimated average displacement of particles. The resolution is directly related to the size of the interrogation window. The displacement vector computed at any location is the spatially averaged transitional motion of particles. Vector fields could be obtained with the PIV system processing a pair of images, using an interrogation window of 64×64 pixels in a candidate region of 128×128 pixels. Since the internal wave topography does not change significantly over 0.1 s, the resultant displacement of topographic features for two images spaced in *t* =0.1 s was chosen for a

A cross-correlation method was performed to calculate the water particle displacement and local velocity by processing a pair of image frames. Although the representation of the velocity vector field in a Eulerian system is a typical example of the PIV method, the result can be applied to a particle tracking process in a Lagrangian system. Umeyama & Matsuki (2011) used the velocity given at the spatially discrete nodal point to estimate the imaginary

The following explains the particle motion within a tracking time step *t* along an arbitrary trajectory across a general mesh of quadrilateral cells (Fig.3). The algorithm has two steps: (1) the velocity value of a Lagrangian point A where *t* is obtained by interpolating the neighboring velocity values ( *u*<sup>1</sup> at *P*<sup>1</sup> , *u*2 at *P*<sup>2</sup> , *u*3 at *P*<sup>3</sup> , and *u*4 at *P*<sup>4</sup> , where *P*<sup>1</sup> , *P*<sup>2</sup> , *P*<sup>3</sup> , and *P*4 are corners of the mesh), and (2) the particle associated with the Lagrangian point at *t* is traced to a hypothetical location (A') at *t t* . Thus, these Lagrangian velocities *uL* at

*u*

12 4 3 1 2 3 14

*uu u u ll ll*

'' ' ' ''' ' ' 1111 ''''

at *tt t*

1234

*llll*

*l* ' , 2*l* ' , 3*l* ' , and 4*l* ' are distances to the imaginary location of a particle

at *t t* , and

direct calculation of the velocity vectors.

**2.4 Eulerian/Lagrangian method** 

velocity and location of a particle.

12 4 3 1234

*uu u u llll*

1234 1111

*llll*

*t* and ' *uL* at *t t* are

*u*

where 1*l* , 2*l* , 3*l* , 4*l* , 1

from the Eulerian grid points.

#### **3.1 Stokes internal waves**

First, we consider Stokes internal waves propagating along the interface between two homogeneous incompressible and inviscid fluids of different density in a constant depth. The origin of the axes is located in the undisturbed interface. The density and depth of the upper layer are *I* and *<sup>I</sup> h* , respectively, and those of the lower layer are *II* and *II h* , respectively. The vertical displacements of the free surface and the density interface are ( ,) *<sup>I</sup> x t* and ( ,) *II x t* , respectively. Let ( , ,) *<sup>I</sup> xzt* , and ( , ,) *II xzt* denote the velocity potentials in the upper and lower layers, so that the Laplace equations are

$$
\Phi\_{l\ge x} + \Phi\_{l\ge x} = \mathbf{0} \tag{1}
$$

$$
\Phi\_{IIxx} + \Phi\_{IIzz} = 0 \tag{2}
$$

where *x* =horizontal coordinate; and *z* =vertical coordinate. The kinematical and dynamical boundary conditions at the free surface are

$$\log(\eta\_I + h\_I) + \phi\_{It} + \frac{1}{2}(\phi\_{Ix}^2 + \phi\_{Iz}^2) = 0 \quad \text{on} \quad z = h\_I + \eta\_I \tag{3}$$

$$
\eta\_{ll} + \eta\_{lx}\phi\_{lx} - \phi\_{lz} = 0 \text{ on } \ z = h\_I + \eta\_I \tag{4}
$$

Measurements of Particle Velocities and Trajectories for Internal

Solving Eq.(13) for *C* = /*k* and assuming *II I* , it becomes

*C*

Thus the group velocity for internal waves is given by

*g*

**3.2 The method of characteristics for long internal waves on a slope** 

It is convenient to define the lower-layer thickness for a uniform slope as

*II II*

*II I h h* , the results can be written in the familiar form:

where *<sup>g</sup>* = *II I*

*I <sup>g</sup>* .

the governing equations are

2

*II*

*I*

*I*

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 329

4 2 <sup>2</sup> (coth coth ) (coth coth ) () 0 *<sup>I</sup> II I*

*kh kh kh kh gk gk*

*II I*

1 (coth coth ) *<sup>g</sup>*

*k kh kh*

2 2 sinh sinh ( 1 ) 2 coth coth

*<sup>C</sup> kh kh <sup>C</sup>*

Umeyama and Shintani (2004) investigated the runup of internal waves on a plane impermeable slope. A reliable solution for the displacement of the density interface and the horizontal velocity of the internal waves was derived by means of the method of characteristics. Let ( , ,) *u xzt II* denotes the horizontal velocity for long internal waves so that

2(1 ) 2(1 ) 0 *II II II II*

*I I h h C uC <sup>C</sup>*

*h u uu CC g h <sup>h</sup>* 

*h h*

*t II x x*

<sup>2</sup> 2(1 ) *II II II I IIt II II x x IIx*

> ( ) ( ) *I*

*h hx m x g* 

where *m* =constant. By adding and subtracting Eqs.(16) and (17), and assuming

[ ( ) ]( 2 ) 0 *u C u C mt II II t x*

Use of the method of characteristics will make it possible to describe *II* and *uII* such as

1 2 1 0 0 1 ( ) [ ( )cos { ( ) }sin ] { ( )sin ( )cos } <sup>2</sup>

*A h sx J X J X T J X T AJ X T J X T h sx <sup>X</sup>* (19)

*I II*

*II I*

(16)

(18)

*I II I II*

*kh kh*

*I II*

*kh kh*

*I II*

(14)

(15)

(17)

(13)

*I II I II*

where *g* = gravity acceleration; and *t* = time. The boundary conditions at the density interface are

$$
\eta\_{\rm IIt} + \eta\_{\rm Itx} \phi\_{\rm Ix} - \phi\_{\rm Iz} = 0 \quad \text{on} \ z = \eta\_{\rm II} \tag{5}
$$

$$
\eta\_{\rm IIt} + \eta\_{\rm IIx} \phi\_{\rm IIx} - \phi\_{\rm IIz} = 0 \quad \text{on} \quad z = \eta\_{\rm II} \tag{6}
$$

$$\left\{\mathfrak{p}\_{I}\left\{\mathfrak{g}\eta\_{\mathrm{II}}+\phi\_{\mathrm{II}}+\frac{1}{2}(\phi\_{\mathrm{Ix}}^{2}+\phi\_{\mathrm{Iz}}^{2})\right\}\right\}=\mathfrak{p}\_{II}\left\{\mathfrak{g}\eta\_{\mathrm{II}}+\phi\_{\mathrm{II}}+\frac{1}{2}(\phi\_{\mathrm{IIx}}^{2}+\phi\_{\mathrm{IIz}}^{2})\right\}\text{ on }\;z=\eta\_{\mathrm{II}}\tag{7}$$

The bottom boundary condition is

$$
\Phi\_{llz} = 0 \quad \text{on} \quad z = -h\_{ll} \tag{8}
$$

In the finite-amplitude wave theory, the perturbation method is used to solve the above basic equations and boundary conditions. These solutions have been obtained to the second order by Umeyama (1998), and to the third order by Umeyama (2000).

When the displacement of fluid interface is given by a linear profile such as ( , ) cos( ) *II x t a kx t* , the horizontal and vertical velocity components for the water particle can be obtained from the velocity potentials where *u x I I* / , *w z I I* / , *u x II II* / , and *w z II II* / . Therefore, the velocity components in both layers are expressed as

$$u\_1 = \frac{ak}{\sigma} (a \cosh kz - \frac{\sigma^2}{k} \sinh kz) \cos(kz - \sigma t) \tag{9}$$

$$w\_I = -\frac{ak}{\sigma}(a\sinh kz - \frac{\sigma^2}{k}\cosh kz)\sin(kx - \sigma t) \tag{10}$$

$$
\mu\_{\rm II} = -\frac{a\sigma}{\sinh kh\_{\rm II}} \cosh k(z + h\_{\rm II}) \cos(kx - \sigma t) \tag{11}
$$

$$w\_{\rm II} = \frac{a\sigma}{\sinh kh\_{\rm II}} \sinh k(z + h\_{\rm II}) \sin(k\pi - \sigma t) \tag{12}$$

where *a* =amplitude of internal waves; *k* =wave number; and =constant that is given by

$$\alpha = \frac{\mathfrak{p}\_{II} - \mathfrak{p}\_{I}}{\mathfrak{p}\_{I}} \mathcal{g} - \frac{\mathfrak{p}\_{II}}{\mathfrak{p}\_{I}} \frac{\sigma^{2}}{k} \coth k h\_{II}$$

The dispersion relation may be written as

$$\sigma^4 \text{(coth } k\text{h}\_I \text{coth } k\text{h}\_{\text{II}} + \frac{\rho\_I}{\rho\_{\text{II}}} \text{)} - \sigma^2 \text{(coth } k\text{h}\_I + \text{coth } k\text{h}\_{\text{II}} \text{)} \text{gk} + \frac{\rho\_{\text{II}} - \rho\_I}{\rho\_I} \text{(gk)}^2 = 0 \tag{13}$$

Solving Eq.(13) for *C* = /*k* and assuming *II I* , it becomes

$$C = \varepsilon\_{\mathcal{g}} \sqrt{\frac{1}{k(\coth kh\_l + \coth kh\_{ll})}} \tag{14}$$

where *<sup>g</sup>* = *II I I <sup>g</sup>* .

328 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

where *g* = gravity acceleration; and *t* = time. The boundary conditions at the density

In the finite-amplitude wave theory, the perturbation method is used to solve the above basic equations and boundary conditions. These solutions have been obtained to the second

When the displacement of fluid interface is given by a linear profile such as ( , ) cos( ) *II x t a kx t* , the horizontal and vertical velocity components for the water particle can be obtained from the velocity potentials where *u x I I* / , *w z I I* / , *u x II II* / , and *w z II II* / . Therefore, the velocity components in both layers are

> 2 ( cosh sinh )cos( ) *<sup>I</sup>*

2 ( sinh cosh )sin( ) *<sup>I</sup>*

cosh ( )cos( ) sinh *II II*

sinh ( )sin( ) sinh *II II*

2 coth *II I II II*

*g kh k*

*w k z h kx t*

where *a* =amplitude of internal waves; *k* =wave number; and =constant that is given by

*I I*

 

*u k z h kx t*

*II*

*II*

*kh*

*kh*

*u kz kz kx t k* 

*w kz kz kx t k* 

order by Umeyama (1998), and to the third order by Umeyama (2000).

*ak*

*ak*

The dispersion relation may be written as

*a*

*a*

interface are

expressed as

The bottom boundary condition is

<sup>1</sup> 2 2 ( ) ( )0 <sup>2</sup> *I I It Ix Iz g h* on *I I z h* (3)

0 *It Ix Ix Iz* on *I I z h* (4)

0 *IIt IIx Ix Iz* on *II z* (5)

0 *IIt IIx IIx IIz* on *II z* (6)

0 *IIz* on *II z h* (8)

(11)

(12)

(9)

(10)

1 1 2 2 2 2 { ( )} { ( )} 2 2 *I II It Ix Iz II II IIt IIx IIz g g* on *II <sup>z</sup>* (7)

Thus the group velocity for internal waves is given by

$$C\_g = \frac{C}{2} (1 + \frac{\sinh^2 k l\_I}{\coth k l\_I + \coth^2 k l\_{II}}) \tag{15}$$

#### **3.2 The method of characteristics for long internal waves on a slope**

Umeyama and Shintani (2004) investigated the runup of internal waves on a plane impermeable slope. A reliable solution for the displacement of the density interface and the horizontal velocity of the internal waves was derived by means of the method of characteristics. Let ( , ,) *u xzt II* denotes the horizontal velocity for long internal waves so that the governing equations are

$$\mathbf{2(1+\frac{\eta\_{II}+h\_{II}}{h\_I})\mathbf{C}\_t+\imath\iota\_{I\text{tr}}\mathbf{C}+\mathbf{2(1+\frac{\eta\_{II}+h\_{II}}{h\_I})\mathbf{C}\_x=\mathbf{0}}{h\_I}\tag{16}$$

$$\left(\mu\_{\rm IIt} + \mu\_{\rm IIt}\mu\_{\rm IIx} + \mathbf{2}\{1 + \frac{\eta\_{\rm II} + h\_{\rm II}}{h\_{\rm I}}\}^2 \mathbf{C} \mathbf{C}\_x = \mathbf{g} \frac{\boldsymbol{\rho}\_{\rm II} - \boldsymbol{\rho}\_{\rm I}}{\boldsymbol{\rho}\_{\rm II}}\boldsymbol{h}\_{\rm Ilx} \tag{17}$$

It is convenient to define the lower-layer thickness for a uniform slope as

$$h\_{II} = h\_{II}(\boldsymbol{\pi}) = m \frac{\boldsymbol{\rho}\_I}{\operatorname{g}(\boldsymbol{\rho}\_{II} - \boldsymbol{\rho}\_I)} \boldsymbol{\pi}\_I$$

where *m* =constant. By adding and subtracting Eqs.(16) and (17), and assuming *II I h h* , the results can be written in the familiar form:

$$\mathbb{E}\left[\frac{\partial}{\partial t} + (\mu\_{\text{II}} \pm \mathbb{C})\frac{\partial}{\partial \mathbf{x}}\right](\mu\_{\text{II}} \pm 2\mathbb{C} - mt) = 0\tag{18}$$

Use of the method of characteristics will make it possible to describe *II* and *uII* such as

$$\eta\_{\rm II} = -\frac{A^2}{2} \frac{h\_l + \text{sx}}{h\_l \text{sx}} [f\_1(X) \cos T + \{f\_0(X) - \frac{f\_1(X)}{X}\} \sin T]^2 + A \{f\_0(X) \sin T + f\_1(X) \cos T\} \tag{19}$$

Measurements of Particle Velocities and Trajectories for Internal

change and average slope of the density interface yields

**3.4 Theoretical water particle trajectory** 

2

*I*

*I*

*I I*

*I*

0 1

*AC J TJ T <sup>h</sup>*

( cos sin )

0

*I*

*h*

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 331

*xx I I I II II II*

Substituting Eqs.(9)-(12) into Eq.(25), the radiation stress of internal waves becomes

*xx I I*

*S u w dz u w dz* 

> 2 2 2 2 2 2 2 { ( ) } <sup>2</sup> sinh *I II II*

The change in radiation stress leads to a change in the mean level of the density interface when internal waves encounter a sloping beach. The equilibrium between radiation stress

> { }( ) 0 *xx I II II dS <sup>d</sup> g h dx dx*

Generally, the attenuation of internal waves in the continental slope is a complicated hydrodynamic process. For the purpose of the present study it may be helpful to use a model in which the divergence of the energy flux is balanced by the dissipation. Therefore,

> 3 2 ( ) ( ) ( ) 3 sinh 4 2 *<sup>g</sup> I II I II <sup>w</sup>*

*dF d EC <sup>a</sup> <sup>g</sup> <sup>f</sup> <sup>a</sup>*

where *F* =energy flux per unit of width; *E* =depth-integrated, time-averaged wave energy

In the case of internal waves on a slop, we denote *xtzt I I* ( ), ( ) and *x tz t II II* ( ), ( ) the instantaneous water particle positions at time *t* in the upper and lower layers, respectively. The corresponding horizontal and vertical velocities become *uxt I I* / , *wzt I I* / , *uxt II II* / , and *wzt II II* / . When the mean position of a water particle is given at (,) *I I x z* for the upper layer or at (,) *II II x z* for the lower layer, the instantaneous water particle position is denoted as () () *I II xt x t* and () () *I II zt z t* , or () () *II II II xt x t* and () () *II II II zt z t* , where *<sup>I</sup>* , *<sup>I</sup>* and *II* , *II* are the horizontal and vertical displacements in the upper layer and lower layer, respectively. Thus, expansion of velocities

> 2 2 1 1 01 01

sin 2 cos2 sin 2 {( ) ( )} 2 24 2 24

*A C h sx T T T T T <sup>J</sup> JJ J h h sx*

*II*

the equation of energy conservation can be expressed as (Umeyama & Shintani 2006)

*dx dx kh*

per unit area; *wf* =friction coefficient; and =energy dissipation coefficient.

in the Taylor series and integration of those velocities with respect to time yield

*a kh <sup>h</sup> S h*

0 2 2 2 2

() ( )

*II*

(25)

*II*

(27)

(28)

(29)

(26)

*kh*

*h*

$$\mu\_{II} = A\varepsilon\_{\mathcal{S}} \sqrt{\frac{h\_l + \text{sx}}{h\_l \text{sx}}} \left[ f\_1(X) \cos T + \{ f\_0(X) - \frac{f\_1(X)}{X} \} \sin T \right] \tag{20}$$

where *A* =constant; and *pJ* =the Bessel function of order *p* . The dependent variables are given by

$$X = \frac{2\sigma}{\mathrm{s}\varepsilon\_{\mathrm{g}}} \sqrt{\frac{h\_{\mathrm{l}}\mathrm{s}\mathbf{x}}{h\_{\mathrm{l}} + \mathrm{s}\mathbf{x}}} \text{, and } \quad T = -\sigma t$$

For convenience, the dependent variable *X* will not be shown hereafter.

A displacement of the interface will cause an associated surface displacement. In the upper layer, the linearized momentum equation may be simply given by

$$\frac{\partial \mathfrak{u}\_{\mathrm{I}}}{\partial t} = -\mathbf{g} \frac{\partial \mathfrak{n}\_{\mathrm{I}}}{\partial \mathbf{x}} \tag{21}$$

The continuity equation can be determined in the same manner:

$$
\mu\_I = \frac{C(\eta\_I - \eta\_{II})}{h\_I + (\eta\_I - \eta\_{II})} \approx -\frac{C}{h\_I}\eta\_{II} \tag{22}
$$

Combining Eqs.(21) and (22), the following differential results:

$$\begin{split} \eta\_{l} &= -\frac{A^{2}\sigma\mathbb{C}}{g} \Big[ \frac{h\_{l} + \mathrm{sx}}{h\_{l}^{2}\mathrm{sx}} [I\_{1}\sin T - \{I\_{0} - \frac{I\_{1}}{X}\}\cos T] [I\_{1}\cos T + \{I\_{0} - \frac{I\_{1}}{X}\}\sin T] dt \\ &- \frac{A\sigma\mathbb{C}}{g h\_{l}} \Big[ \{I\_{0}\cos T - I\_{1}\sin T\} dt \end{split} \tag{23}$$

#### **3.3 Radiation stress, setup, and attenuation for internal waves**

During the passage of surface waves, there are mean transport of water upward the shoreline and depression of the mean water level from the still water level. Longuet-Higgins and Stewart (1964) introduced the radiation stress concept to prove these mechanisms, and Umeyama (2006) applied it to internal waves. The principal component of the radiation stress for internal waves can be defined as

$$S\_{\rm xx} = \overbrace{\underset{\eta\_{\rm II}}{\overset{\eta\_{\rm I} + h\_{\rm I}}{\rightleftharpoons}}^{\eta\_{\rm I} + h\_{\rm I}} (p\_{\rm I} + \mathfrak{p}\_{\rm I} \mu\_{\rm I}^2) dz - \overbrace{\underset{\eta\_{\rm II}}{\overset{\eta\_{\rm II}}{\rightleftharpoons}} (p\_{\rm II} + \mathfrak{p}\_{\rm II} \mu\_{\rm II}^2)}^{h\_{\rm I}} - \overbrace{\underset{-h\_{\rm I}}{\overset{\circ}{\rightleftharpoons}} p\_{\rm II 0}}^0 \tag{24}$$

where *Sxx* =radiation stress for internal waves; *<sup>I</sup>*<sup>0</sup> *p* =hydrostatic pressure in the upper layer; *II*<sup>0</sup> *p* =hydrostatic pressure in the lower layer; and the over-bar denotes averaging in time over a wave period. Assuming that the upper limit of integration may be replaced by *<sup>I</sup> z h ,* the displacement of the density interface is small relative to the wavelength, and the mean mass flux of vertical momentum across a horizontal plane balances with the weight of the water above it, Eq.(24) reduces to

1 0

where *A* =constant; and *pJ* =the Bessel function of order *p* . The dependent variables are

A displacement of the interface will cause an associated surface displacement. In the upper

*uI I <sup>g</sup> t x*

( ) ( ) *I II I II I I II I C C*

*h h* 

2 10 1 0

During the passage of surface waves, there are mean transport of water upward the shoreline and depression of the mean water level from the still water level. Longuet-Higgins and Stewart (1964) introduced the radiation stress concept to prove these mechanisms, and Umeyama (2006) applied it to internal waves. The principal component of the radiation

2 2

*II II II*

where *Sxx* =radiation stress for internal waves; *<sup>I</sup>*<sup>0</sup> *p* =hydrostatic pressure in the upper layer; *II*<sup>0</sup> *p* =hydrostatic pressure in the lower layer; and the over-bar denotes averaging in time over a wave period. Assuming that the upper limit of integration may be replaced by *<sup>I</sup> z h ,* the displacement of the density interface is small relative to the wavelength, and the mean mass flux of vertical momentum across a horizontal plane balances with the weight of the

() ( )

*xx I II I II II II II*

*S p u dz p dz p u dz p dz*

0

*I I I II*

*h h*

*A C h sx <sup>J</sup> <sup>J</sup> J T J T J T J T dt g XX h sx*

*h sx J X u A JX T JX T h sx <sup>X</sup>*

*II g*

given by

*I*

2 *<sup>I</sup> g I h sx <sup>X</sup> s h sx* 

For convenience, the dependent variable *X* will not be shown hereafter.

layer, the linearized momentum equation may be simply given by

The continuity equation can be determined in the same manner:

Combining Eqs.(21) and (22), the following differential results:

0 1

*A C J T J T dt gh*

*I*

*I*

{ cos sin }

**3.3 Radiation stress, setup, and attenuation for internal waves** 

2

*I*

stress for internal waves can be defined as

water above it, Eq.(24) reduces to

*I*

*u*

( ) [ ( )cos { ( ) }sin ] *<sup>I</sup>*

, and *T t*

1

(21)

0

1 1

0 0

(24)

*h h*

[ sin { } cos ][ cos { }sin ]

(22)

(23)

(20)

$$S\_{\rm xx} = \int\_0^{h\_l} \overline{\rho\_I \overline{(u\_I^2 - w\_I^2)}} dz + \int\_{-h\_{ll}}^0 \overline{\rho\_{II} \overline{(u\_{II}^2 - w\_{II}^2)}} dz \tag{25}$$

Substituting Eqs.(9)-(12) into Eq.(25), the radiation stress of internal waves becomes

$$S\_{xx} = \frac{a^2}{2} \{ \rho\_I (\frac{k^2 h\_I}{\sigma^2} \alpha^2 - \sigma^2 h\_I) + \frac{\rho\_{II} \sigma^2 h\_{II}}{\sinh^2 kh\_{II}} \} \tag{26}$$

The change in radiation stress leads to a change in the mean level of the density interface when internal waves encounter a sloping beach. The equilibrium between radiation stress change and average slope of the density interface yields

$$\frac{d S\_{\text{xx}}}{d \mathbf{x}} - \{\boldsymbol{\rho}\_{I} - \boldsymbol{\rho}\_{II}\} \mathbf{g}(\overline{\boldsymbol{\eta}} + \boldsymbol{h}\_{II}) \frac{d \overline{\boldsymbol{\eta}}}{d \mathbf{x}} = \mathbf{0} \tag{27}$$

Generally, the attenuation of internal waves in the continental slope is a complicated hydrodynamic process. For the purpose of the present study it may be helpful to use a model in which the divergence of the energy flux is balanced by the dissipation. Therefore, the equation of energy conservation can be expressed as (Umeyama & Shintani 2006)

$$\frac{dF}{d\mathbf{x}} = \frac{d(EC\_g)}{d\mathbf{x}} = -f\_w \frac{\mathbf{p}\_I + \mathbf{p}\_{II}}{3\pi} (\frac{\sigma a}{\sinh kh\_{ll}})^3 - \beta \frac{(\mathbf{p}\_I + \mathbf{p}\_{II})\mathbf{g}}{4\pi\sqrt{2}} \sigma a^2 \tag{28}$$

where *F* =energy flux per unit of width; *E* =depth-integrated, time-averaged wave energy per unit area; *wf* =friction coefficient; and =energy dissipation coefficient.

#### **3.4 Theoretical water particle trajectory**

In the case of internal waves on a slop, we denote *xtzt I I* ( ), ( ) and *x tz t II II* ( ), ( ) the instantaneous water particle positions at time *t* in the upper and lower layers, respectively. The corresponding horizontal and vertical velocities become *uxt I I* / , *wzt I I* / , *uxt II II* / , and *wzt II II* / . When the mean position of a water particle is given at (,) *I I x z* for the upper layer or at (,) *II II x z* for the lower layer, the instantaneous water particle position is denoted as () () *I II xt x t* and () () *I II zt z t* , or () () *II II II xt x t* and () () *II II II zt z t* , where *<sup>I</sup>* , *<sup>I</sup>* and *II* , *II* are the horizontal and vertical displacements in the upper layer and lower layer, respectively. Thus, expansion of velocities in the Taylor series and integration of those velocities with respect to time yield

$$\begin{aligned} \mathbf{c}\_{l} &= \frac{A^{2}\mathbf{C}}{2\sigma h\_{l}} \frac{h\_{l} + \mathbf{s}x}{h\_{l}\mathbf{s}x} \{-f\_{1}^{2}(\frac{T}{2} + \frac{\sin 2T}{4}) + f\_{1}I\_{01}\frac{\cos 2T}{2} + f\_{01}^{2}(-\frac{T}{2} + \frac{\sin 2T}{4})\} \\ &- \frac{A\mathbf{C}}{\sigma h\_{l}} (f\_{0}\cos T - f\_{1}\sin T) \end{aligned} \tag{29}$$

Measurements of Particle Velocities and Trajectories for Internal

0 10 20 30 40 50 60 70

(a) Case 1

0 10 20 30 40 50 60 70

0 10 20 30 40 50 60 70

0 10 20 30 40 50 60 70 Distance (cm)

0 10 20 30 40 50 60 70 Distance (cm)

Fig. 4. Spatial displacements of density interface of : *h h I II* =15 cm:15 cm





cm (a) Case 1

Fig. 5. Spatial profiles of celerity

0

5

10

0

5 cm

0

5 cm

0

5 cm

0

5 cm

from the wavemaker and a slope between 100 and 600 cm from it.

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 333

obtained over a different topography consisting of a constant depth between 0 and 100 cm

t / T= 0.0

t / T = 0.25


0

5

0 10 20 30 40 50 60 70

0 10 20 30 40 50 60 70

0 10 20 30 40 50 60 70

0 10 20 30 40 50 60 70 Distance (cm)

(b) Case 2

0 10 20 30 40 50 60 70 Distance (cm)

(b) Case 2

t / T = 0.5




Measured Method of characteristics

0

Measured Eq. (14) Method of characteristics

5

10

0

5 t / T = 0.75

0

5

0

5

$$\begin{split} \mathfrak{L}\_{ll} &= -\frac{A\mathfrak{s}\_{\mathcal{S}}}{\sigma} \sqrt{\frac{h\_{l} + \mathrm{sx}}{h\_{l}\mathrm{sx}}} (I\_{1} \sin T + I\_{01} \cos T) \\ &+ \frac{A^{2}\mathfrak{s}\_{\mathcal{S}}^{2}}{\sigma^{2}} (\frac{h\_{l} + \mathrm{sx}}{h\_{l}\mathrm{sx}}) \mathbf{I} \frac{1}{2\mathrm{sx}^{2}} \frac{h\_{l}\mathrm{sx}}{h\_{l} + \mathrm{sx}} (I\_{1}^{2} \frac{\cos 2T}{4} + I\_{1} \boldsymbol{I}\_{01} \frac{\sin 2T}{2} - I\_{01}^{2} \frac{\cos 2T}{4}) \\ &- I\_{1} \boldsymbol{I}\_{01} \frac{d\boldsymbol{X}}{d\mathbf{x}} \frac{\cos 2T}{4} + I\_{0} \boldsymbol{I}\_{1} \frac{d\boldsymbol{X}}{d\mathbf{x}} - \frac{1}{\boldsymbol{X}} (\frac{1}{2\mathrm{sx}^{2}} \frac{h\_{l} \mathrm{sx}}{h\_{l} + \mathrm{sx}} I\_{1} - I\_{01} \frac{d\boldsymbol{X}}{d\mathbf{x}}) (\mathrm{-} \frac{T}{2} + \frac{\sin 2T}{4}) \\ &- I\_{01}^{2} \frac{d\boldsymbol{X}}{d\mathbf{x}} (\frac{T}{2} + \frac{\sin 2T}{4}) - I\_{01} \{I\_{1} \frac{d\boldsymbol{X}}{d\mathbf{x}} - \frac{1}{\boldsymbol{X}} (\frac{1}{2\mathrm{sx}^{2}} \frac{h\_{l} \mathrm{sx}}{h\_{l} + \mathrm{sx}} I\_{01} \frac{d\boldsymbol{X}}{d\mathbf{x}}) \frac{\cos 2T}{4\sigma} \mathrm{l} \} \end{split} \tag{30}$$

where *J JJX* 01 0 1 / .

#### **4. Results**

#### **4.1 Interfacial displacement and celerity distribution**

Fig.4 shows the spatial displacements of the density interface for two different experiments, i.e. (a) Case 1 and (b) Case 2. The interval between two panels is *T* /4 for each case. The abscissa is the distance from the intersection between the sloping bed and stationary level of the density interface, and the ordinate is the elevation above that level. The circular symbols show the density interface by using the image processing technique. The solid curve shows the analytical solution based on Eq.(19). For Case 1, the absolute value of the crest level is larger than that of the trough level, and this tendency is prominent in the upperslope region. Inspecting the four figures reveals that the test data agree with the theoretical displacement in the horizontal range of 15 *x* 50 cm. To obtain closer agreement in the rest of range, several appropriate assumptions such as breaking, bottom friction, reflection and return flow may be proposed to account for the observed wave profiles. For Case 2, the experimental waveform is peaked near the crest but declined near the trough except in the upper-slope region, when comparing it to the theoretical profile. The method of characteristics appears to adequately predict the details of the runup profile on the sloping bottom. Umeyama and Shintani (2006) examined the similar measured distributions with the *k* model and the method of characteristics, and found that the former is quantitatively superior to the latter in the upper-slope region.

Fig.5 depicts the corresponding variations of celerity for Cases 1 and 2. The celerity distributions obtained from the linear wave theory (Eq.14) and the method of characteristics by Umeyama & Shintani (2004) are presented to compare with the experimental data. The measured celerity is smaller than these predicted ones except in the upper-slope region where most measured values exceed the predicted ones by the linear wave theory for Case 1 and those by the method of characteristics for Case 2. In the present cases, i.e. the linear bottom slope of 3:50, the solution by the linear wave theory shows a fair agreement with the measured celerity when compared with the solution by the method of characteristics. According to Umeyama and Shintani (2006), the former underestimates the measurements but the latter overestimates them by about 0-30% in some experimental cases for the bottom slope of 1:28. These quantitative discrepancies could be due to the difference of boundary conditions of the experiment and the theory. The theoretical solution was derived for a topography consisting of a plane sloping beach, although the experimental data were

2 2 1 1 01 01

Fig.4 shows the spatial displacements of the density interface for two different experiments, i.e. (a) Case 1 and (b) Case 2. The interval between two panels is *T* /4 for each case. The abscissa is the distance from the intersection between the sloping bed and stationary level of the density interface, and the ordinate is the elevation above that level. The circular symbols show the density interface by using the image processing technique. The solid curve shows the analytical solution based on Eq.(19). For Case 1, the absolute value of the crest level is larger than that of the trough level, and this tendency is prominent in the upperslope region. Inspecting the four figures reveals that the test data agree with the theoretical displacement in the horizontal range of 15 *x* 50 cm. To obtain closer agreement in the rest of range, several appropriate assumptions such as breaking, bottom friction, reflection and return flow may be proposed to account for the observed wave profiles. For Case 2, the experimental waveform is peaked near the crest but declined near the trough except in the upper-slope region, when comparing it to the theoretical profile. The method of characteristics appears to adequately predict the details of the runup profile on the sloping bottom. Umeyama and Shintani (2006) examined the similar measured distributions with the *k* model and the method of characteristics, and found that the former is

Fig.5 depicts the corresponding variations of celerity for Cases 1 and 2. The celerity distributions obtained from the linear wave theory (Eq.14) and the method of characteristics by Umeyama & Shintani (2004) are presented to compare with the experimental data. The measured celerity is smaller than these predicted ones except in the upper-slope region where most measured values exceed the predicted ones by the linear wave theory for Case 1 and those by the method of characteristics for Case 2. In the present cases, i.e. the linear bottom slope of 3:50, the solution by the linear wave theory shows a fair agreement with the measured celerity when compared with the solution by the method of characteristics. According to Umeyama and Shintani (2006), the former underestimates the measurements but the latter overestimates them by about 0-30% in some experimental cases for the bottom slope of 1:28. These quantitative discrepancies could be due to the difference of boundary conditions of the experiment and the theory. The theoretical solution was derived for a topography consisting of a plane sloping beach, although the experimental data were

*<sup>A</sup> h sx h sx T T T J JJ J h sx h sx sx*

<sup>1</sup> cos2 sin 2 cos2 ( )[ ( ) <sup>2</sup> 4 24

*dX T dX h sx dX T T J J J J J J dx dx X h sx dx sx*

1 01 0 1 2 1 01

2 2

2 01 1

1 1 cos2 ( ) }] <sup>2</sup> <sup>4</sup> *h sx dX T <sup>J</sup> x X h sx dx sx*

(30)

1

cos2 1 1 sin 2 { ( )}( ) <sup>4</sup> <sup>2</sup> 2 4

1

1 01

<sup>1</sup>

( sin cos )

01 01 1

**4.1 Interfacial displacement and celerity distribution** 

quantitatively superior to the latter in the upper-slope region.

*g I I I I*

*<sup>A</sup> h sx J TJ T h sx*

sin 2 ( ){ 2 4

*dX T T dX <sup>J</sup> J J dx <sup>d</sup>*

2 2

*II*

where *J JJX* 01 0 1 / .

**4. Results** 

*g I*

 

*I*

2

obtained over a different topography consisting of a constant depth between 0 and 100 cm from the wavemaker and a slope between 100 and 600 cm from it.

Fig. 4. Spatial displacements of density interface of : *h h I II* =15 cm:15 cm

Fig. 5. Spatial profiles of celerity

Measurements of Particle Velocities and Trajectories for Internal

mean interfacial displacement agrees with the measured setup.

0 10 20 30 40 50 60 70 Distance (cm)

Fig. 7. Attenuation and setup of internal waves on a slope

**4.3 Instantaneous velocity fields of internal waves** 

Wave setup and height (cm)

height

Case 1 Case 2

setup

Measured Energy dissipation model

Fig.8 depicts the experimental velocity fields of internal waves for the layer thickness ratio of : *I II h h* =15 cm:15 cm by a PIV measurement. Each vector image consists of two pictures taken simultaneously using two high-definition digital video cameras. Internal waves propagate from right to left. Fig.8 (a) indicates four velocity fields at an interval of *T* /4 for Case 1, in which the internal waves were generated with a period of *T* = 5.2 s, and the measured wave height was *H* =2.6 cm at a location 100 cm from the wavemaker. In these experimental images, an array of asymmetric vortices forms along the wave tank and their scale decreases as waves progress into the shallow-water region. The mean velocity in the lower layer appears to be relatively larger than that in the upper layer. The thinner clockwise vortex alternates with the thicker counterclockwise vortex, and the array of

> 0 10 20 30 40 50 60 70 Distance (cm)

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 335

For shoaling waves on a given bottom slope, the wave height decreases gradually with decreasing water depth but does not vanish at the origin. Good agreement is found between the measured and calculated values of wave height in the recorded region. The discrepancy between these measured and calculated distributions is probably due to the neglect of the reflection or the overestimation of shear stress parameters. The radiation stress for partial standing waves differs from that for incident waves; it is presented by the sum of the incident and reflected waves. For surface waves, Longuet-Higgins and Stewart (1964) found that the mean surface level for a standing wave train slightly increases at the antinodes and correspondingly decreases at the nodes, having twice the frequency of an incident wave train. A somewhat similar relationship was found in the experimental result by Umeyama (2008) for partial standing internal waves. Partial standing internal waves develop a longitudinal mean interfacial oscillation that is a half period out of phase. Although it is difficult to detect these oscillations from the observation data, generally, the theoretical

#### **4.2 Attenuation and setup for internal waves**

The laboratory data in this section were obtained for the upper and lower thickness ratio of : *I II h h* = 15 cm:15 cm. Fig.6 represents a series of temporal displacements of the density interface for Case 1 at six horizontal locations along the wave tank. All waveforms differ considerably from a sinusoidal profile, but the general characteristics at any given location are quite similar. The interfacial displacements show strong nonlinearity. These internal waves exhibit a higher rise at the crest and a depression near the trough in the upper-slope region. When waves are moving closer to the origin, a prominent feature of the cnoidal-type fluctuations continues from one wave to the next. The wave height abruptly decreases, while its mean density interface slowly increases.

Fig. 6. Temporal displacement of density interface for Case 1

Fig.7 shows comparisons of predicted and observed variations of the local wave height and the mean density interface for Cases 1 and 2. Illustrated in the solid curve are the wave transformation predicted using Eq.(28) and the wave setup or set-down using Eq.(27). A portion of the incident wave motion is converted to the forward translation of the water mass by the breaking process. This results in forming a bolus that runs further up the face of the slope. The maximum runup elevation depends on the wave steepness and the bottom angle. Although the reflection coefficient should be determined in advance of the calculations of attenuation and setup, the reflection was neglected. In order to calculate the wave-height distribution, the value of in Eq.(28) was determined using a trial-and-error procedure. In the present computation, it was equal to 0.020 for Case 1 and 0.025 for Case 2.

The laboratory data in this section were obtained for the upper and lower thickness ratio of : *I II h h* = 15 cm:15 cm. Fig.6 represents a series of temporal displacements of the density interface for Case 1 at six horizontal locations along the wave tank. All waveforms differ considerably from a sinusoidal profile, but the general characteristics at any given location are quite similar. The interfacial displacements show strong nonlinearity. These internal waves exhibit a higher rise at the crest and a depression near the trough in the upper-slope region. When waves are moving closer to the origin, a prominent feature of the cnoidal-type fluctuations continues from one wave to the next. The wave height abruptly decreases,

> -2 -1 0 1 2

> -2 -1 0 1 2

> -2 -1 0 1 2

Fig.7 shows comparisons of predicted and observed variations of the local wave height and the mean density interface for Cases 1 and 2. Illustrated in the solid curve are the wave transformation predicted using Eq.(28) and the wave setup or set-down using Eq.(27). A portion of the incident wave motion is converted to the forward translation of the water mass by the breaking process. This results in forming a bolus that runs further up the face of the slope. The maximum runup elevation depends on the wave steepness and the bottom angle. Although the reflection coefficient should be determined in advance of the calculations of attenuation and setup, the reflection was neglected. In order to calculate the wave-height distribution, the value of in Eq.(28) was determined using a trial-and-error procedure. In the present computation, it was equal to 0.020 for Case 1 and 0.025 for Case 2.

0 5 10 15

x= 85 cm

x= 115 cm

x= 145 cm

0 5 10 15

0 5 10 15 Time (sec)

**4.2 Attenuation and setup for internal waves** 

while its mean density interface slowly increases.

x= 5 cm

x = 35 cm

x = 65 cm

0 5 10 15

0 5 10 15

0 5 10 15 Time (sec)

Fig. 6. Temporal displacement of density interface for Case 1




Fig. 7. Attenuation and setup of internal waves on a slope

### **4.3 Instantaneous velocity fields of internal waves**

Fig.8 depicts the experimental velocity fields of internal waves for the layer thickness ratio of : *I II h h* =15 cm:15 cm by a PIV measurement. Each vector image consists of two pictures taken simultaneously using two high-definition digital video cameras. Internal waves propagate from right to left. Fig.8 (a) indicates four velocity fields at an interval of *T* /4 for Case 1, in which the internal waves were generated with a period of *T* = 5.2 s, and the measured wave height was *H* =2.6 cm at a location 100 cm from the wavemaker. In these experimental images, an array of asymmetric vortices forms along the wave tank and their scale decreases as waves progress into the shallow-water region. The mean velocity in the lower layer appears to be relatively larger than that in the upper layer. The thinner clockwise vortex alternates with the thicker counterclockwise vortex, and the array of

Measurements of Particle Velocities and Trajectories for Internal

90 120 150 180

90 120 150 180

90 120 150 180

90 120 150 180 Distance (cm)

in these cases.

0.5 cm/s

5 cm/s

(a) Case 3





Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 337

an increase in the stability of vortices that gradually decrease the size with distance up the slope. From a pair of counterrotating vortices, one can expect the nonlinearity of internal wave, although the difference of two vertical positions for the counterrotating vortices is relatively small. The flow is no more symmetric with respect to the vertical line at the node

Fig.9 shows a similar comparison for the generated internal waves in the density-stratified water where the upper and lower thickness ratio is : *I II h h* = 10 cm:20 cm (Cases 3 and 4).

t / T= 0.0

t / T = 0.25


90 120 150 180

90 120 150 180

90 120 150 180

90 120 150 180 Distance (cm)

(b) Case 4

t / T = 0.5



Fig. 9. Instantaneous velocity fields of internal waves ( : *I II h h* = 10 cm:20 cm)


vortices sakes vertically from the mean density interface ( *z* =0). Although the distortion to the pair of vortices occurs in the upper slope, the velocities still show quasi-elliptical trends. Closer the density interface, the magnitude of the velocity vector reaches its maximum. The center of vortex located within a zone between the crest and trough of internal waves. Generally, the center of ellipse starts to depart upward from the density interface before the wave crest arrives, while it deviates downward slightly from the mean interface level before the wave trough arrives. The flow under the density interface converges in the front of the wave crest and diverges behind it. This contributes to creating trajectory systems in the upper and lower layers, without crossing the density interface. Fig.8 (b) depicts four velocity fields for Case 2. The clockwise and counterclockwise vortices are in an orderly line when compared with those in Fig.8 (a). This fact suggests that an increase of wave period leads to

Fig. 8. Instantaneous velocity fields of internal waves ( : *I II h h* = 15 cm:15 cm)

vortices sakes vertically from the mean density interface ( *z* =0). Although the distortion to the pair of vortices occurs in the upper slope, the velocities still show quasi-elliptical trends. Closer the density interface, the magnitude of the velocity vector reaches its maximum. The center of vortex located within a zone between the crest and trough of internal waves. Generally, the center of ellipse starts to depart upward from the density interface before the wave crest arrives, while it deviates downward slightly from the mean interface level before the wave trough arrives. The flow under the density interface converges in the front of the wave crest and diverges behind it. This contributes to creating trajectory systems in the upper and lower layers, without crossing the density interface. Fig.8 (b) depicts four velocity fields for Case 2. The clockwise and counterclockwise vortices are in an orderly line when compared with those in Fig.8 (a). This fact suggests that an increase of wave period leads to

t / T= 0.0

t / T = 0.25

80 90 100 110 120 130 140 150 160 170

80 90 100 110 120 130 140 150 160 170

80 90 100 110 120 130 140 150 160 170

80 90 100 110 120 130 140 150 160 170 Distance (cm)

(b) Case 2

t / T = 0.5


Fig. 8. Instantaneous velocity fields of internal waves ( : *I II h h* = 15 cm:15 cm)

80 90 100 110 120 130 140 150 160 170

80 90 100 110 120 130 140 150 160 170

80 90 100 110 120 130 140 150 160 170

80 90 100 110 120 130 140 150 160 170 Distance (cm)


0.5 cm/s

5 cm/s

(a) Case 1




Fig.9 shows a similar comparison for the generated internal waves in the density-stratified water where the upper and lower thickness ratio is : *I II h h* = 10 cm:20 cm (Cases 3 and 4).

Fig. 9. Instantaneous velocity fields of internal waves ( : *I II h h* = 10 cm:20 cm)

Measurements of Particle Velocities and Trajectories for Internal






0

5

10 cm


0

5

10 cm

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 339

The PIV data at *x* =145 cm are exhibited individually for four different phase values: i.e., *t T*/ =0.0, 0.25, 0.5, and 0.75. The horizontal solid line indicates the density interface, while the dash line indicates the bottom at this cross-section. The wave direction is from right to left in the horizontal velocity panel. The time-marching exhibitions were performed to examine the application of the PIV method to the velocity variations in a total depth. Under the crest of an internal wave at *t T*/ =0.0, the vertical velocity is nearly zero over the depth. The horizontal velocity in the wave direction appears in the total lower layer, and reaches the maximum slightly below the wave trough level ( *z* -2.0 cm). In the upper layer, the horizontal velocity is opposed to the wave direction. It increases from the density interface until the wave crest level *z* -1.0 cm, and slowly decreases to the surface. Under the node of an internal wave at /*t T* =0.25, the upward velocity starts to increase from the bottom,

t/T = 0.0 t/T = 0.25 t/T = 0.5 t/T = 0.75

Horizontal velocity

Case 4

Vertical velocity

Fig. 11. Vertical distributions of velocity components at *x* =170 cm for Case 4




0

5

10



0

5

10


The experimental data points are missing due to the flume flange in the range of 135 cm< *x* <145 cm. A pair of counterrotating vortices in the experiment shows still a satisfactory pattern. Umeyama & Matsuki (2011) found that the vortex pair turns inconspicuous by changing the thickness rate from : *I II h h* =15 cm:15 cm to : *I II h h* =5 cm:25 cm in a fluid of finite depth over a flat bed. The present improvement may be attributed to the replacement of the PIV system from two frequency doubled Nd:YAG lasers of 50-mW energy to a frequency-doubled Nd:YAG laser of 8-W energy. It could be confirmed from a series of experiments that the water particle movement in clockwise vortices is stretched in the horizontal direction while the anticlockwise vortices become less elliptical in the longitudinal direction over the slope.

#### **4.4 Vertical distributions of velocity components**

In this section, the measured profiles of the horizontal and vertical components of velocity at a cross-section are examined. An example of these profiles is shown in Fig.10 for Case 2.

Fig. 10. Vertical distributions of velocity components at *x* =145 cm for Case 2

The experimental data points are missing due to the flume flange in the range of 135 cm< *x* <145 cm. A pair of counterrotating vortices in the experiment shows still a satisfactory pattern. Umeyama & Matsuki (2011) found that the vortex pair turns inconspicuous by changing the thickness rate from : *I II h h* =15 cm:15 cm to : *I II h h* =5 cm:25 cm in a fluid of finite depth over a flat bed. The present improvement may be attributed to the replacement of the PIV system from two frequency doubled Nd:YAG lasers of 50-mW energy to a frequency-doubled Nd:YAG laser of 8-W energy. It could be confirmed from a series of experiments that the water particle movement in clockwise vortices is stretched in the horizontal direction while the anticlockwise vortices become less elliptical in the

In this section, the measured profiles of the horizontal and vertical components of velocity at a cross-section are examined. An example of these profiles is shown in Fig.10 for Case 2.

t/T = 0.0 t/T = 0.25 t/T = 0.5 t/T = 0.75

Horizontal velocity

Case 2

Vertical velocity

Fig. 10. Vertical distributions of velocity components at *x* =145 cm for Case 2




0

5

10

15



0

5

10

15


longitudinal direction over the slope.

**4.4 Vertical distributions of velocity components** 






0

5

10

15 cm


0

5

10

15 cm The PIV data at *x* =145 cm are exhibited individually for four different phase values: i.e., *t T*/ =0.0, 0.25, 0.5, and 0.75. The horizontal solid line indicates the density interface, while the dash line indicates the bottom at this cross-section. The wave direction is from right to left in the horizontal velocity panel. The time-marching exhibitions were performed to examine the application of the PIV method to the velocity variations in a total depth. Under the crest of an internal wave at *t T*/ =0.0, the vertical velocity is nearly zero over the depth. The horizontal velocity in the wave direction appears in the total lower layer, and reaches the maximum slightly below the wave trough level ( *z* -2.0 cm). In the upper layer, the horizontal velocity is opposed to the wave direction. It increases from the density interface until the wave crest level *z* -1.0 cm, and slowly decreases to the surface. Under the node of an internal wave at /*t T* =0.25, the upward velocity starts to increase from the bottom,

Fig. 11. Vertical distributions of velocity components at *x* =170 cm for Case 4

Measurements of Particle Velocities and Trajectories for Internal

110 115 120 125 Distance (x cm)

110 115 120 125 x (cm)


Fig. 12. Water particle trajectories by PIV/PTV method



**5. Conclusion** 

0.0

z cm 3.0

Particle reajectries (cm)

z cm

Waves Propagating in a Density-Stratified Two-Layer Fluid on a Slope 341

110 115 120 125 Distance (x cm)

110 115 120 125 x cm

(b) x=120 cm

Fig. 13. Calculated particle paths by the Method of characteristics


(a) x= 120 cm for Case 1 (b) x=135 cm for Case 2 (c) x=170 cm for Case 3 (d) x=170 cm for Case 4

In the present study, an image processing technique was used to quantify the spatial and temporal displacements of the density interface, and a PIV system was examined to illustrate the velocity fields in layers of fresh and salt water over a slowly varying water depth. The wave generation was made by a slide-type wavemaker. Wave celerity, attenuation and setup of internal waves were investigated theoretically and experimentally. The method of characteristics was adapted to express the internal waves at the interface of two fluids of slightly different densities on a sloped topography. A comparison of theoretical and measured variations of internal waves indicated that the agreement with


0.0

5.0

10.0

(a) x= 120 cm for Case 1 (b) x=120 cm for Case 2 (c) x=170 cm for Case 3 (d) x=170 cm for Case 4

160 165 170 175 Distance (x cm)

160 165 170 175 x cm



0.0

5.0

10.0

160 165 170 175 Distance (x cm)

160 165 170 175 x cm

becomes the peak at an elevation slightly below the density interface, and decreases to the surface. The horizontal velocity is zero except in the region where there is a slight rise of velocity in the wave direction near the density interface. Under the trough at /*t T* =0.5, the direction of horizontal velocity changes in the lower layer. The velocity peak occurs at *z* -1.0 cm in the wave direction and *z* -5.5 cm in the direction opposing to the wave. The velocity decreases slowly toward the surface in the upper layer but it keeps a relatively large value at the bottom. Under the other node at /*t T* =0.75, the downward velocity dominants the phase. The vertical velocity profile is reverse to that at /*t T* =0.25. The horizontal velocity in the wave direction can be only found in the region from -1.0 cm *z* 0.0 cm.

Fig.11 depicts similar distributions of the horizontal and vertical components of velocity for Case 4, in which the experiment was performed for the layer thickness ratio of : *I II h h* =10 cm:20 cm. Plotted are two velocity components at *x* =170 cm. Under the crest and trough, the horizontal velocities are maxima, while the vertical velocities are zero, and under the nodes, the opposite is true. At *t T*/ =0.0 and 0.5, the horizontal velocity decreases slowly to the surface in the upper layer or the bottom in the lower layer but does not vanish near these boundaries. In contrast, the horizontal velocity is zero over the depth at *t T*/ =0.25 and 0.75 when the velocity peak in the vertical direction appears slightly below the mean density interface.

#### **4.5 Water particle trajectories**

Fig.12 displays a plot of the particle orbit geometries for : *I II h h* = 15 cm:15 cm and : *I II h h* = 10 cm:20 cm. Shown in the diagram are attained for four wave conditions: i.e. (a) Case 1; (b) Case 2; (c) Case 3; and (d) Case 4. The data were taken approximately at the center of the frame in the digital video camera. The circular symbol indicates the instantaneous position of a water particle based on the PIV technique in which each Lagrangian point was determined using the present algorithm (see Fig.3). All trajectories are not elliptical and not closed for each case. Near the density interface in the lower layer, the horizontal and vertical displacements of the water particle are large relative to those near the mid-depth and surface region. The particle tends to take less distance to complete one wave cycle in the wave direction for larger wave period. Generally, the vertical excursion of the particle becomes smaller than its horizontal excursion with distance up in the water column. At these elevations, the particle moves backward from the wave direction to maintain a balance between the following and opposing fluxes in the wave tank. In contrast, the particle marches forward in a large nonclosed loop at the density interface, implying that each particle has a periodic motion per wave cycle but yields a maximum forward drift. The horizontal particle displacement in the direction opposing to the wave propagation increases with distance down in the water column for Cases 3 and 4. Fig.13 shows the theoretical trajectory calculated for Cases 1, 2, 3, and 4 by equations (19), (29) and (30) whose higher terms lead to an asymmetry of the particle orbit. Note that ideal trajectory data cannot be obtained without removing extraneous effects such as reflection from the wall and higher harmonics generated by the wavemaker, although the size of the wave tank restricts these effects. Inspecting the present comparisons for internal waves, however, the experimental path is qualitatively in good agreement with the theoretical trajectory just above and below the density interface.

Fig. 12. Water particle trajectories by PIV/PTV method

Fig. 13. Calculated particle paths by the Method of characteristics

### **5. Conclusion**

340 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

becomes the peak at an elevation slightly below the density interface, and decreases to the surface. The horizontal velocity is zero except in the region where there is a slight rise of velocity in the wave direction near the density interface. Under the trough at /*t T* =0.5, the direction of horizontal velocity changes in the lower layer. The velocity peak occurs at *z* -1.0 cm in the wave direction and *z* -5.5 cm in the direction opposing to the wave. The velocity decreases slowly toward the surface in the upper layer but it keeps a relatively large value at the bottom. Under the other node at /*t T* =0.75, the downward velocity dominants the phase. The vertical velocity profile is reverse to that at /*t T* =0.25. The horizontal velocity in the wave direction can be only found in the region from -1.0

Fig.11 depicts similar distributions of the horizontal and vertical components of velocity for Case 4, in which the experiment was performed for the layer thickness ratio of : *I II h h* =10 cm:20 cm. Plotted are two velocity components at *x* =170 cm. Under the crest and trough, the horizontal velocities are maxima, while the vertical velocities are zero, and under the nodes, the opposite is true. At *t T*/ =0.0 and 0.5, the horizontal velocity decreases slowly to the surface in the upper layer or the bottom in the lower layer but does not vanish near these boundaries. In contrast, the horizontal velocity is zero over the depth at *t T*/ =0.25 and 0.75 when the velocity peak in the vertical direction appears slightly below the mean density

Fig.12 displays a plot of the particle orbit geometries for : *I II h h* = 15 cm:15 cm and : *I II h h* = 10 cm:20 cm. Shown in the diagram are attained for four wave conditions: i.e. (a) Case 1; (b) Case 2; (c) Case 3; and (d) Case 4. The data were taken approximately at the center of the frame in the digital video camera. The circular symbol indicates the instantaneous position of a water particle based on the PIV technique in which each Lagrangian point was determined using the present algorithm (see Fig.3). All trajectories are not elliptical and not closed for each case. Near the density interface in the lower layer, the horizontal and vertical displacements of the water particle are large relative to those near the mid-depth and surface region. The particle tends to take less distance to complete one wave cycle in the wave direction for larger wave period. Generally, the vertical excursion of the particle becomes smaller than its horizontal excursion with distance up in the water column. At these elevations, the particle moves backward from the wave direction to maintain a balance between the following and opposing fluxes in the wave tank. In contrast, the particle marches forward in a large nonclosed loop at the density interface, implying that each particle has a periodic motion per wave cycle but yields a maximum forward drift. The horizontal particle displacement in the direction opposing to the wave propagation increases with distance down in the water column for Cases 3 and 4. Fig.13 shows the theoretical trajectory calculated for Cases 1, 2, 3, and 4 by equations (19), (29) and (30) whose higher terms lead to an asymmetry of the particle orbit. Note that ideal trajectory data cannot be obtained without removing extraneous effects such as reflection from the wall and higher harmonics generated by the wavemaker, although the size of the wave tank restricts these effects. Inspecting the present comparisons for internal waves, however, the experimental path is qualitatively in good agreement with the theoretical trajectory just

cm *z* 0.0 cm.

interface.

**4.5 Water particle trajectories** 

above and below the density interface.

In the present study, an image processing technique was used to quantify the spatial and temporal displacements of the density interface, and a PIV system was examined to illustrate the velocity fields in layers of fresh and salt water over a slowly varying water depth. The wave generation was made by a slide-type wavemaker. Wave celerity, attenuation and setup of internal waves were investigated theoretically and experimentally. The method of characteristics was adapted to express the internal waves at the interface of two fluids of slightly different densities on a sloped topography. A comparison of theoretical and measured variations of internal waves indicated that the agreement with

Measurements of Particle Velocities and Trajectories for Internal

Vol.169, pp.19-53, ISSN: 0022-1120.

Annu. *J. Coastal Eng.*, Vol.52, pp.1-5.

Vol.263, pp.563–614, ISSN: 1471-2962.

Vol.134, No.5, pp.286-298, ISSN:0733-950X.

370(1964), pp.1687-1702, ISSN: 1471-2962.

No.2, pp.89-97, ISSN:0733-950X.

No.6, pp.477-486, ISSN:0733-950X.

141, ISSN:0733-950X.

No.3, L03612.

L06603.

No.2.

1, pp.731–751.

0967-0637.

0227.

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Helland-Hansen, B., and Nansen, F. (1926). The eastern North Atlantic. *Geofys. Publ.*, Vol.4,

Kao, T. W., Pan, F.-S., and Renouard, D. (1985). Internal solitons on the pycnocline:

LaFond, C. (1962). Internal waves, Part 1, In: *The sea*, M. N. Hill, ed., Interscience, New York,

Longuet-Higgins, M. S., and Stewart, R. W. (1964). Radiation stress in water waves: A

Michallet, H., and Ivey G. N. (1999). Experiments on mixing due to internal solitary waves

Shand, J. A. (1953). Internal waves on Georgia Strait. *Trans.*, AGU, Vol.34, No.6, pp.849–856. Shimizu, R., Shintani, T. and Umeyama, M. (2005). Instantaneous and Lagragian velocity

Thorpe, S. A. (1968). On the shape of progressive internal waves. *Phil. Trans. the Royal Soc. A*,

Umeyama, M. (2002). Experimental and theoretical analyses of internal waves of finite

Umeyama, M. (2008). PIV techniques for velocity fields of internal waves over a slowly

Umeyama, M. (2011). Coupled PIV and PTV measurements of particle velocities and

Umeyama, M. (2012). Eulerian/Lagrangian analysis for particle velocities and trajectories in

Umeyama, M. and Matsuki, S. (2011). Measurements of velocity and trajectory of water

Umeyama, M. and Shinomiya, H. (2009) Particle image velocimetry measurements for

Umeyama, M. and Shintani, T. (2004). Visualization analysis of runup and mixing of internal

Umeyama, M. and Shintani, T. (2006). Transformation, attenuation, setup and undertow of

Umeyama, M., Shintani, T. and Watanabe, S. (2011). Measurements of particle velocities and

*Conf. of Coastal Eng.*, ASCE, ISSN: 2156-1028, Shanghai, July, 2010.

*and Ocean Eng.*, ASCE, Vol.137, No.2, pp.85-94, ISSN:0733-950X.

Generation, propagation, and shoaling and breaking over a slope. *J. Fluid Mech.*,

physical discussion, with applications. *Deep-Sea Res.*, Vol.11, pp.529–562, ISSN:

breaking on uniform slopes. *J. Geophys. Res.*, 104(C6), pp.13467-13477, ISSN: 0148–

fields of internal waves on a slope by PIV measurement and numerical simulation.

amplitude. *J. Waterway, Port, Coastal, and Ocean Eng.*, ASCE, Vol.128, No.3, pp.133-

varying bottom topography. *J. Waterway, Port, Coastal, and Ocean Eng.*, ASCE,

trajectories for surface waves following a steady current. *J. Waterway, Port, Coastal,* 

a pure wave motion using particle image velocimetry. *Phil. Trans. the Royal Soc. A*,

particle for internal waves in two density layers. *Geophysical Res. Lett.*, AGU, Vol.38,

Stokes progressive internal waves. *Geophysical Res. Lett.*, AGU, Vol.36, No.6,

waves on an upper slope. *J. Waterway, Port, Coastal, and Ocean Eng.*, ASCE, Vol.130,

internal waves on a gentle slope. *J. Waterway, Port, Coastal, and Ocean Eng.*, Vol.132,

trajectories in a wave-current motion using PIV and PTV. *Proceedings of 32nd Inter.* 

these values improves when the target area is located in the region slightly apart from the origin. Over the range of interest, the spatial variations of internal waves were well predicted by the nonlinear long-wave equation. In addition, the wave celerity was obtained by analyzing the experimental data and compared with the result by the method of characteristics. To predict the local wave-height attenuation and the setup of density interface, we used the energy dissipation model, the energy conservation equation, and the momentum balance equation based on the radiation stress concept for internal waves by Umeyama and Shintani (2006). Note that the spatial variations of wave height and setup for all experimental conditions were well reproduced by the theoretical solution.

Using a PIV system, we measured the water particle velocity to obtain successive velocity fields over one wave cycle. The instantaneous velocity vector map clearly illustrated a vortex pair when the thickness ratio was relatively large in a fluid of two density layers. The vertical distributions of velocities analyzed from the PIV data were also presented at different phases. In addition to the common use of the PIV technique, we extended the knowledge to the visualization of the mass transport due to the propagation of internal waves. The algorithm for PIV was employed to compute Lagrangian velocity and track water particle displacements in Eulerian grids. The particle trajectories in a cross-section were simulated using a solution based on the definition of the Lagrangian approach to the method of characteristics. The agreement between the computed and measured results near the density interface was reasonable, apart from the restriction resulting from the apparatus. Thus, the proposed approach of the PIV can be applied to the Lagrangian description of the trajectory of a water particle when internal waves propagate above a sloping bottom.

### **6. Acknowledgment**

The authors wish to thank Shinya Watanabe, Yasuhiro Takei and Ryota Kobayashi for preparing all experimental data.

### **7. References**


these values improves when the target area is located in the region slightly apart from the origin. Over the range of interest, the spatial variations of internal waves were well predicted by the nonlinear long-wave equation. In addition, the wave celerity was obtained by analyzing the experimental data and compared with the result by the method of characteristics. To predict the local wave-height attenuation and the setup of density interface, we used the energy dissipation model, the energy conservation equation, and the momentum balance equation based on the radiation stress concept for internal waves by Umeyama and Shintani (2006). Note that the spatial variations of wave height and setup for

Using a PIV system, we measured the water particle velocity to obtain successive velocity fields over one wave cycle. The instantaneous velocity vector map clearly illustrated a vortex pair when the thickness ratio was relatively large in a fluid of two density layers. The vertical distributions of velocities analyzed from the PIV data were also presented at different phases. In addition to the common use of the PIV technique, we extended the knowledge to the visualization of the mass transport due to the propagation of internal waves. The algorithm for PIV was employed to compute Lagrangian velocity and track water particle displacements in Eulerian grids. The particle trajectories in a cross-section were simulated using a solution based on the definition of the Lagrangian approach to the method of characteristics. The agreement between the computed and measured results near the density interface was reasonable, apart from the restriction resulting from the apparatus. Thus, the proposed approach of the PIV can be applied to the Lagrangian description of the

trajectory of a water particle when internal waves propagate above a sloping bottom.

The authors wish to thank Shinya Watanabe, Yasuhiro Takei and Ryota Kobayashi for

Apel, J. R., Byrne, H. M., Proni, J. R., and Charnell, R. L. (1975). Observations of oceanic

Apel, J. R., Byrne, H. M., Proni, J. R., and Sellers, R. L. (1976). A study of oceanic internal

Apel, J. R., Holbrook, J. R., Liu, A. K., and Tsi, J. (1985). The Sulu Sea internal soliton experiment. J. Phys. Oceanogr., Vol.15, No.12, pp.1625–1651, ISSN: 0022-3670. Austin, R.W. and Halikas, G. (1976). "The index of refraction of seawater." Scripps

Grue, F., Jensen, A., Rusas, P.-O. and Sveen, J.K. (1999). Properties of large-amplitude

Grue, F., Jensen, A., Rusas, P.-O. and Sveen, J.K. (2000). Breaking and broadening of internal

Helfrich, K. R. (1992). Internal solitary wave breaking and run-up on a uniform slope. *J.* 

internal waves. *J. Fluid Mech.*, Vol.380, pp.257-278, ISSN: 0022-1120.

solitary waves. *J. Fluid Mech.*, Vol.413, pp.181-217, ISSN: 0022-1120.

*Res.*, Vol.80, No.6, pp.865–881, ISSN: 0148–0227.

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internal and surface waves from the earth resources technology satellite. *J. Geophys.* 

waves using satellite imagery and ship data. *Remote Sens. Environ.*, Vol.5, pp.125–

**6. Acknowledgment** 

**7. References** 

preparing all experimental data.

135, ISSN: 0034-4257.

all experimental conditions were well reproduced by the theoretical solution.


**13** 

*Russia* 

**Applying of PIV/PTV Methods for** 

**Buoyant Jets in a Stratified Fluid** 

*2Institute of Applied Physics Russian Academy of Sciences* 

**Physical Modeling of the Turbulent** 

Valery Bondur1, Yurii Grebenyuk1, Ekaterina Ezhova2,

Alexander Kandaurov2, Daniil Sergeev2 and Yuliya Troitskaya2 *1AEROCOSMOS Institute for Scientific Research of Aerospace Monitoring* 

Modern optical methods of flow visualization: Particle Tracking Velocimetry (PTV) and Particle Image Velocimetry (PIV) (see (Adrian, 1981)) are widely used in experimental investigations of air and liquid flows for scientific and industrial purposes. They are common in exploration of such processes as heat and mass transfer in power plants, flows in aircraft and shipbuilding, and medico-biological applications. Nowadays this technique is also employed in the laboratory modeling of geophysical flows (Sergeev Troitskaya, 2011) including air-sea interaction (Reul et al., 1999; Veron et al., 2007); flows in water column and their interaction with bottom topography (Umeyama, 2008; Zhang et al., 2007); vortex flows

The present work is devoted to the investigation of the new class of flows by PIV/PTVmethods – oscillating buoyant jets (fountains) in stratified fluid. (Bondur Grebenyuk, 2001; Bondur 2004, 2011; Bondur et al. 2006, 2009). Among the applications of these flows are heat and moisture exchange in the atmosphere and cloud formation (Turner, 1966). The investigation of buoyant jets in stratified fluid is extremely important for the development of new technologies of sewage disposal by coastal cities (Koh Brooks, 1975). The end body of such systems is a submerged collector. A typical diffuser of a modern collector is a pipe with lots of outlets. Sewage water (which has almost the density of fresh water after sewage disposal plants) is discharged into ambient salt water to produce buoyant jets (Bondur, 2011; Bondur et al, 2006, 2009). One of the main questions when constructing diffusers of these collectors is a regime of jet flows when they are trapped by pycnocline and don't reach the

Sewage disposal to the ocean is an example of the man's impact, influencing mass transfer, hydrodynamics, hydrobiology and coastal ecosystem state as a whole (Bondur, 2011). The complex investigation of these processes includes mathematic modeling of jets dynamics (Bondur, 2011; Bondur et al, 2006, 2009; Bondur Grebenyuk, 2001; Koh Brooks, 1975; Ozmidov 1986), contact methods (Bondur 2006; Bondur Tsidilina, 2006; Gibson et al., 2006 a), and airborne and spaceborne remote sensing (Bondur, 2004, 2006, 2011; Bondur

**1. Introduction** 

surface.

(Beckers et al., 2002; Heist et al., 2003).


## **Applying of PIV/PTV Methods for Physical Modeling of the Turbulent Buoyant Jets in a Stratified Fluid**

Valery Bondur1, Yurii Grebenyuk1, Ekaterina Ezhova2, Alexander Kandaurov2, Daniil Sergeev2 and Yuliya Troitskaya2 *1AEROCOSMOS Institute for Scientific Research of Aerospace Monitoring 2Institute of Applied Physics Russian Academy of Sciences Russia* 

### **1. Introduction**

344 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

Walker, S. A., Martin, A. J., Easson, W. J., and Evans, W. A. B. (2003). Comparison of

Wallace, B. C., and Wilkinson, D. L. (1988). Run-up of internal waves on a gentle slope in a two-layered system. *J. Fluid Mech.*, Vol.191, pp.419–442, ISSN: 0022-1120.

*Ocean Eng.*, ASCE, Vol.129, No.5, pp.210–218, ISSN:0733-950X.

laboratory and theoretical solitary wave kinematics. *J. Waterway, Port, Coastal, and* 

Modern optical methods of flow visualization: Particle Tracking Velocimetry (PTV) and Particle Image Velocimetry (PIV) (see (Adrian, 1981)) are widely used in experimental investigations of air and liquid flows for scientific and industrial purposes. They are common in exploration of such processes as heat and mass transfer in power plants, flows in aircraft and shipbuilding, and medico-biological applications. Nowadays this technique is also employed in the laboratory modeling of geophysical flows (Sergeev Troitskaya, 2011) including air-sea interaction (Reul et al., 1999; Veron et al., 2007); flows in water column and their interaction with bottom topography (Umeyama, 2008; Zhang et al., 2007); vortex flows (Beckers et al., 2002; Heist et al., 2003).

The present work is devoted to the investigation of the new class of flows by PIV/PTVmethods – oscillating buoyant jets (fountains) in stratified fluid. (Bondur Grebenyuk, 2001; Bondur 2004, 2011; Bondur et al. 2006, 2009). Among the applications of these flows are heat and moisture exchange in the atmosphere and cloud formation (Turner, 1966). The investigation of buoyant jets in stratified fluid is extremely important for the development of new technologies of sewage disposal by coastal cities (Koh Brooks, 1975). The end body of such systems is a submerged collector. A typical diffuser of a modern collector is a pipe with lots of outlets. Sewage water (which has almost the density of fresh water after sewage disposal plants) is discharged into ambient salt water to produce buoyant jets (Bondur, 2011; Bondur et al, 2006, 2009). One of the main questions when constructing diffusers of these collectors is a regime of jet flows when they are trapped by pycnocline and don't reach the surface.

Sewage disposal to the ocean is an example of the man's impact, influencing mass transfer, hydrodynamics, hydrobiology and coastal ecosystem state as a whole (Bondur, 2011). The complex investigation of these processes includes mathematic modeling of jets dynamics (Bondur, 2011; Bondur et al, 2006, 2009; Bondur Grebenyuk, 2001; Koh Brooks, 1975; Ozmidov 1986), contact methods (Bondur 2006; Bondur Tsidilina, 2006; Gibson et al., 2006 a), and airborne and spaceborne remote sensing (Bondur, 2004, 2006, 2011; Bondur

Applying of PIV/PTV Methods for Physical Modeling

of the Turbulent Buoyant Jets in a Stratified Fluid 347

(a)

(b)

Fig. 1. General scheme of LTST IAP RAS experiments with the location of temperature and velocity sensors before the area of surface PTV measurements series *S1 -* (*a*)*,* and behind

*S2 -* (*b*)

Grebenyuk, 2001). The investigation of physical mechanisms, responsible for surface manifestations of sewage flows, is a challenging problem. In the papers (Bondur, 2004, 2006, 2011; Bondur Grebenyuk 2001) mechanisms, resulting from surface deformation by rising vortices or internal waves are suggested, and in works (Bondur et al., 2005; Gibson et al., 2006 b, 2007a,b) surface manifestations are explained by the complex interaction between turbulence, internal waves, tides and bottom topography.

The intensive generation of internal waves by buoyant jets from submerged wastewater outfalls in stratified fluid was investigated by contact methods in experiments on the laboratory scale modeling of these systems (Bondur et al, 2009, 2010 a, 2010 b; Troitskaya et al., 2008). However, in order to explore the possibility of internal waves manifestation and mechanisms of their generation by buoyant jets, the additional experiments were needed which allowed high-precision measurements of velocity fields of flows on the surface and in the water column. Contact sensors are not applicable for such systems since they cause essential perturbations in the investigated flow. Thus, in new experimental series noninvasive methods were employed, based on the flow visualization (modified PIV/PTVmethods), that allowed the effective solution to this problem.

The Chapter is organised as follows. The laboratory scale modeling of buoyant jets and the investigation of surface flows induced by these jets with the application of PIV-technique is described in Section 2. Section 3 is devoted to the testing of PIV-methods for the measurement of velocity fields in buoyant jets in stratified fluid. The last Section deals with the application of this method for the laboratory scale modeling. The parameters of oscillating jets are compared with the characteristics of internal waves. Special methods of video processing are employed to investigate the structure of jet perturbation modes.

### **2. Experimental studies on measurements of the surface flows induced by submerged buoyant jets in the thermostratified tank with the modified PTVmethod**

The main purpose of investigations, described in this part, is to assess the possibility of internal waves manifestation caused by a submerged sewer system on the sea surface. To solve this complicated problem it is necessary to obtain the properties of inhomogeneous flow fields created on the sea surface.

The experimental study of these processes was carried out on the basis of laboratory scale modeling at the Large Thermally Stratified Tank (LTST) of the Institute of Applied Physics, Russian Academy of Sciences (IAP RAS). The experiments included measurements in the water, and the main attention was drawn to the measurements of the surface flow, where the PTV- method was used.

#### **2.1 Experimental setup for the scale laboratory modeling of the surface flows induced by the typical submerged sewer system in the LTST**

The principal scheme of experiments is shown in Fig1. The LTST dimensions are as follows: 20 m in length, 4 m in width, and 2 m in depth. The temperature (density) stratification in the LTST is generated through liquid heating and cooling with heat exchangers installed along the tank walls (Arabadzhi et al., 1999; Bondur et al., 2009). It results in the formation of the inhomogeneous vertical distribution of the temperature (density) in the tank.

Grebenyuk, 2001). The investigation of physical mechanisms, responsible for surface manifestations of sewage flows, is a challenging problem. In the papers (Bondur, 2004, 2006, 2011; Bondur Grebenyuk 2001) mechanisms, resulting from surface deformation by rising vortices or internal waves are suggested, and in works (Bondur et al., 2005; Gibson et al., 2006 b, 2007a,b) surface manifestations are explained by the complex interaction between

The intensive generation of internal waves by buoyant jets from submerged wastewater outfalls in stratified fluid was investigated by contact methods in experiments on the laboratory scale modeling of these systems (Bondur et al, 2009, 2010 a, 2010 b; Troitskaya et al., 2008). However, in order to explore the possibility of internal waves manifestation and mechanisms of their generation by buoyant jets, the additional experiments were needed which allowed high-precision measurements of velocity fields of flows on the surface and in the water column. Contact sensors are not applicable for such systems since they cause essential perturbations in the investigated flow. Thus, in new experimental series noninvasive methods were employed, based on the flow visualization (modified PIV/PTV-

The Chapter is organised as follows. The laboratory scale modeling of buoyant jets and the investigation of surface flows induced by these jets with the application of PIV-technique is described in Section 2. Section 3 is devoted to the testing of PIV-methods for the measurement of velocity fields in buoyant jets in stratified fluid. The last Section deals with the application of this method for the laboratory scale modeling. The parameters of oscillating jets are compared with the characteristics of internal waves. Special methods of

video processing are employed to investigate the structure of jet perturbation modes.

**2. Experimental studies on measurements of the surface flows induced by submerged buoyant jets in the thermostratified tank with the modified PTV-**

The main purpose of investigations, described in this part, is to assess the possibility of internal waves manifestation caused by a submerged sewer system on the sea surface. To solve this complicated problem it is necessary to obtain the properties of inhomogeneous

The experimental study of these processes was carried out on the basis of laboratory scale modeling at the Large Thermally Stratified Tank (LTST) of the Institute of Applied Physics, Russian Academy of Sciences (IAP RAS). The experiments included measurements in the water, and the main attention was drawn to the measurements of the surface flow, where

**2.1 Experimental setup for the scale laboratory modeling of the surface flows induced** 

The principal scheme of experiments is shown in Fig1. The LTST dimensions are as follows: 20 m in length, 4 m in width, and 2 m in depth. The temperature (density) stratification in the LTST is generated through liquid heating and cooling with heat exchangers installed along the tank walls (Arabadzhi et al., 1999; Bondur et al., 2009). It results in the formation

of the inhomogeneous vertical distribution of the temperature (density) in the tank.

turbulence, internal waves, tides and bottom topography.

methods), that allowed the effective solution to this problem.

**method** 

flow fields created on the sea surface.

**by the typical submerged sewer system in the LTST** 

the PTV- method was used.

Fig. 1. General scheme of LTST IAP RAS experiments with the location of temperature and velocity sensors before the area of surface PTV measurements series *S1 -* (*a*)*,* and behind *S2 -* (*b*)

(b)

Applying of PIV/PTV Methods for Physical Modeling

**2.2 Measuring technique** 

by internal waves.

removed.

of the Turbulent Buoyant Jets in a Stratified Fluid 349

where ρ0 – mean density of ambient fluid, N0 – maximum buoyancy frequency of the ambient stratification, g – gravitational acceleration, and a geometric similarity on the scale of 1:27. In this case, the Reynolds number at the output was around 3000, which ensures the

Preliminary estimates indicated that the amplitudes of surface flows induced by internal waves would be only few mm/s. For these conditions, the modified Particle Tracking Velocimetry (PTV) method was used to measure the velocities of the surface flows induced

Thus, the limited area of basin surface under observation was seeded by particles of black polyethylene (density 0.98 g/cm3) with a characteristic size of about 1.5 mm for creating a contrast to the white background of the bottom (see the experimental setups in Figs. 1 a, b). The motion of particles was recorded by a ССD camera from above (25 frames/sec), and the resulting time series of images were then processed on the computer. It turned out to be impossible to combine the particle observation region with the sensor allocation area (the distance between sensors and the observation area center is a minimum) in the conditions of this experiment, because the sensor images hindered the correct identification of particles on the images. That is why, two series of experiments were carried out with the sensors and the

The series *S1* (see Fig. 1 *a*) included the installation of 13 temperature sensors vertically at a distance of 200 cm from the diffuser model for measuring proprieties of internal waves; a scanning 3D ultrasound doppler anemometer (ADV) (at a distance of 260 cm); and the center of the observation area (at a distance of 400 cm), which is a 6048 cm2 rectangle was

During the series *S2* (see Fig. 1 *b*), the surface observation area was located at a distance of 200 cm from the model. The area had dimensions 10080 cm2 and was oriented perpendicular to the flow motion. Further, at a distance of 300 cm from the collector model,

Two important problems concerning the measurements of surface flows in the LTST appeared during these experiments. The first one was that, when the temperature stratification with a shallow thermocline is created (Fig. 2), large-scale flows as a system of cyclonic and anticyclonic vortexes occurred on the surface layer. The measurements performed by the PTV method indicated that the scale of an individual vortex was 1.5–2.5 m, the maximum velocities of flows in it reached 1.3 cm/s, and the average velocities were about 4 mm/s. These values were calculated approximately, because the size of the observed area in both series of experiments did not allow one to cover the whole area at least one vortex. It can be assumed that vortexes appeared by inhomogeneous horizontal heating of the fine upper layer of thermocline. The presence of the large-scale flows made a low frequency trend in the dependence of the velocity on time, which was eliminated by the

The second factor making it difficult to perform velocity measurements of surface flows is the presence of a Surface active substance (SAS) or dust film, which could not be completely

temperature sensors were located and, at a distance of 360 cm, an ADV was located.

developed turbulence mode of buoyant jets in the laboratory experiment.

observation area allocated differently relative to the diffuser model.

oriented by its longer side along the direction of the jet flow.

low frequency filtering of the results (see Subsection 2.3).

The experiments were carried out using distribution of temperature with shallow thermocline depth of 13–15 cm on the average (profile 1 in Fig.2), with the total water depth of 130 cm.

Fig. 2. Operating profiles of temperature stratification in the LTST. 1) shallow thermocline 2) deep thermocline. Two curves for each case indicates borders of stratification changing during experiments.

The scaled model of the diffuser of the sewer system was a metallic blanked-off tube at one end with the length of 1.3 m and the diameter *d* of 1.2 cm; the model includes 5 holes with the diameter of 3 mm located at a distance of 30 cm from each other at the same level. The tube is oriented horizontally across and in the middle of the tank (Fig. 1). The holes axes are oriented horizontally. The model is connected by a hose with a tank containing the solution of ethyl alcohol, the density of which during the experiments was kept constant (0.93 g/cm3). Thus initial difference in density between jet and ambient fluid ∆ρ0 was 0.07 g/cm3. The outflow rate *V*0 from the diffuser model was: 40, 70, 100, and 150 cm/s (controlled by measuring the volumetric time rate). The variation of the flow rate through the change in the tank-solution level during the experiment does not exceed 10% (the average value was 5%).

The parameters of the induced jet flow and stratification in the LTST, enable us to simulate the typical conditions of the coastal area parameters of the submerged disposal system (Koh Brooks, 1975) with respect to the Ri, Str numbers (Bondur et al., 2009):

$$\begin{aligned} Ri &= \frac{g \Delta \mathfrak{p}\_o d}{\mathfrak{p}\_o V\_o^z} \text{ - global Richstandon number,} \\\\Str &= \frac{N\_o^z d \mathfrak{p}\_o}{g \Delta \mathfrak{p}\_o} \text{ - parameter of ambient stratification,} \end{aligned}$$

0

where ρ0 – mean density of ambient fluid, N0 – maximum buoyancy frequency of the ambient stratification, g – gravitational acceleration, and a geometric similarity on the scale of 1:27. In this case, the Reynolds number at the output was around 3000, which ensures the developed turbulence mode of buoyant jets in the laboratory experiment.

### **2.2 Measuring technique**

348 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

The experiments were carried out using distribution of temperature with shallow thermocline depth of 13–15 cm on the average (profile 1 in Fig.2), with the total water depth

Fig. 2. Operating profiles of temperature stratification in the LTST. 1) shallow thermocline 2) deep thermocline. Two curves for each case indicates borders of stratification changing

The scaled model of the diffuser of the sewer system was a metallic blanked-off tube at one end with the length of 1.3 m and the diameter *d* of 1.2 cm; the model includes 5 holes with the diameter of 3 mm located at a distance of 30 cm from each other at the same level. The tube is oriented horizontally across and in the middle of the tank (Fig. 1). The holes axes are oriented horizontally. The model is connected by a hose with a tank containing the solution of ethyl alcohol, the density of which during the experiments was kept constant (0.93 g/cm3). Thus initial difference in density between jet and ambient fluid ∆ρ0 was 0.07 g/cm3. The outflow rate *V*0 from the diffuser model was: 40, 70, 100, and 150 cm/s (controlled by measuring the volumetric time rate). The variation of the flow rate through the change in the tank-solution

The parameters of the induced jet flow and stratification in the LTST, enable us to simulate the typical conditions of the coastal area parameters of the submerged disposal system (Koh



level during the experiment does not exceed 10% (the average value was 5%).

Brooks, 1975) with respect to the Ri, Str numbers (Bondur et al., 2009):

*<sup>g</sup> <sup>d</sup> Ri V* 

*N d Str g* 

of 130 cm.

during experiments.

Preliminary estimates indicated that the amplitudes of surface flows induced by internal waves would be only few mm/s. For these conditions, the modified Particle Tracking Velocimetry (PTV) method was used to measure the velocities of the surface flows induced by internal waves.

Thus, the limited area of basin surface under observation was seeded by particles of black polyethylene (density 0.98 g/cm3) with a characteristic size of about 1.5 mm for creating a contrast to the white background of the bottom (see the experimental setups in Figs. 1 a, b).

The motion of particles was recorded by a ССD camera from above (25 frames/sec), and the resulting time series of images were then processed on the computer. It turned out to be impossible to combine the particle observation region with the sensor allocation area (the distance between sensors and the observation area center is a minimum) in the conditions of this experiment, because the sensor images hindered the correct identification of particles on the images. That is why, two series of experiments were carried out with the sensors and the observation area allocated differently relative to the diffuser model.

The series *S1* (see Fig. 1 *a*) included the installation of 13 temperature sensors vertically at a distance of 200 cm from the diffuser model for measuring proprieties of internal waves; a scanning 3D ultrasound doppler anemometer (ADV) (at a distance of 260 cm); and the center of the observation area (at a distance of 400 cm), which is a 6048 cm2 rectangle was oriented by its longer side along the direction of the jet flow.

During the series *S2* (see Fig. 1 *b*), the surface observation area was located at a distance of 200 cm from the model. The area had dimensions 10080 cm2 and was oriented perpendicular to the flow motion. Further, at a distance of 300 cm from the collector model, temperature sensors were located and, at a distance of 360 cm, an ADV was located.

Two important problems concerning the measurements of surface flows in the LTST appeared during these experiments. The first one was that, when the temperature stratification with a shallow thermocline is created (Fig. 2), large-scale flows as a system of cyclonic and anticyclonic vortexes occurred on the surface layer. The measurements performed by the PTV method indicated that the scale of an individual vortex was 1.5–2.5 m, the maximum velocities of flows in it reached 1.3 cm/s, and the average velocities were about 4 mm/s. These values were calculated approximately, because the size of the observed area in both series of experiments did not allow one to cover the whole area at least one vortex. It can be assumed that vortexes appeared by inhomogeneous horizontal heating of the fine upper layer of thermocline. The presence of the large-scale flows made a low frequency trend in the dependence of the velocity on time, which was eliminated by the low frequency filtering of the results (see Subsection 2.3).

The second factor making it difficult to perform velocity measurements of surface flows is the presence of a Surface active substance (SAS) or dust film, which could not be completely removed.

Applying of PIV/PTV Methods for Physical Modeling

**2.4 Results - Comparing with theory forecasts** 

of the Turbulent Buoyant Jets in a Stratified Fluid 351

Basing on measured time realizations, we calculated the rms values of the surface velocity 1/2 <sup>2</sup> *<sup>V</sup>* . The dependence of 1/2 <sup>2</sup> *<sup>V</sup>* on the outflow rate from the diffuser model is shown in

Fig. 4. It can be seen from here that 1/2 <sup>2</sup> *<sup>V</sup>* varies in the range between 0.1 and 0.3 cm/s.

Fig. 4. Amplitudes of surface flow velocities (series *S1* left and series *S2* right): the black diamonds indicate theoretical estimates while accounting for the influence of the film and the light diamonds indicate the measurement results obtained by the PTV- method. Error bars corresponding to the uncertainty of the PTV measurements 10%, and uncertainty

The experimental data were compared with theoretical estimations of the value of the velocity on the surface according the theory of internal wave propagation proposed in (Bondur et al., 2010 а). Estimations were obtained taking into account the influence of the SAS films. The estimate for the error in theoretical values was determined by the measurement error (constituted 20%) (Ermakov Kijashko, 2006). It is well seen from the

Thus, the experiments revealed that in the presence of internal waves induced by jets during outflow from the submerged sewer system model, surface flows with spatial periods controlled by the properties these waves appeared. The wavelength was from 30 to 160 cm. The standard deviations of velocities in the presence of a SAS film at the water surface varied in the range from 0.1 to 0.3 mm/s, corresponding to the amplitudes from 0.15 to 0.45 mm/s. For pure water the surface would constitute 1 to 2 mm/s. It should be pointed out

In view of this, using the coefficients of scale modeling, one can estimate the flows created near the submerged sewer system in nature conditions: the parameters of internal waves (induced by jets), and the prosperities of their surface manifestations, as well as make conclusions on the possibility of remote diagnostics of these waves. In our laboratory experiment the coefficient of scale modeling with respect to the velocity value constitutes 1:3 and the coefficient of

of theoretical estimations (determined by the accuracy of SAS films properties

that these experiments were performed for the conditions of scaled modeling.

measurements 20 %).

figures that the results are in good agreement.

We measured the parameters of the SAS film using the technique proposed in (Ermakov Kijashko, 2006).

#### **2.3 Modified algorithms of the PTV-method for studying weak surface flows**

A classical PTV-method measures the velocity of each particle with respect to its motion on frames separated by a time interval and then reconstructs the velocity field by the velocity values at the points of the particle location. In these experiments, due to the presence of a background flow (see Subsection 2.2), the number of seeding particles in the observation area quickly decreased with time. For this reason we were able to determine only the averaged (over the observation area) value of the flow velocity. We found the trajectories of particles passing through this area and calculated their velocity at each moment. Then we calculated the velocity value averaged over all particles that were found in the observation area at the given time moment. The uncertainty of the PTV measurements was defined by the accuracy of the center of particle determination. It was about 10 % (based on results of special test experiments). To exclude the background low-frequency trends in the particle velocity, caused by large-scale flows in the LTST, we performed the low-frequency filtering of distributions of signals at frequencies below 0.02 Hz. The examples of such time dependences of the averaged surface flow velocity are shown in Fig. 3. These data were compared with oscillations of isotherms obtained from the temperature measurements (see Bondur et al., 2010 а).

Fig. 3. Amplitudes of disturbances at the surface measured by the PTV method for rates of outflow from the diffuser model: *a*, 40 cm/s, *b*, 70 cm/s, *c*, 100 cm/s, and *d*, 150 cm/s.

We measured the parameters of the SAS film using the technique proposed in (Ermakov

A classical PTV-method measures the velocity of each particle with respect to its motion on frames separated by a time interval and then reconstructs the velocity field by the velocity values at the points of the particle location. In these experiments, due to the presence of a background flow (see Subsection 2.2), the number of seeding particles in the observation area quickly decreased with time. For this reason we were able to determine only the averaged (over the observation area) value of the flow velocity. We found the trajectories of particles passing through this area and calculated their velocity at each moment. Then we calculated the velocity value averaged over all particles that were found in the observation area at the given time moment. The uncertainty of the PTV measurements was defined by the accuracy of the center of particle determination. It was about 10 % (based on results of special test experiments). To exclude the background low-frequency trends in the particle velocity, caused by large-scale flows in the LTST, we performed the low-frequency filtering of distributions of signals at frequencies below 0.02 Hz. The examples of such time dependences of the averaged surface flow velocity are shown in Fig. 3. These data were compared with oscillations of isotherms obtained from the temperature measurements (see

Fig. 3. Amplitudes of disturbances at the surface measured by the PTV method for rates of outflow from the diffuser model: *a*, 40 cm/s, *b*, 70 cm/s, *c*, 100 cm/s, and *d*, 150 cm/s.

**2.3 Modified algorithms of the PTV-method for studying weak surface flows** 

Kijashko, 2006).

Bondur et al., 2010 а).

### **2.4 Results - Comparing with theory forecasts**

Basing on measured time realizations, we calculated the rms values of the surface velocity 1/2 <sup>2</sup> *<sup>V</sup>* . The dependence of 1/2 <sup>2</sup> *<sup>V</sup>* on the outflow rate from the diffuser model is shown in Fig. 4. It can be seen from here that 1/2 <sup>2</sup> *<sup>V</sup>* varies in the range between 0.1 and 0.3 cm/s.

Fig. 4. Amplitudes of surface flow velocities (series *S1* left and series *S2* right): the black diamonds indicate theoretical estimates while accounting for the influence of the film and the light diamonds indicate the measurement results obtained by the PTV- method. Error bars corresponding to the uncertainty of the PTV measurements 10%, and uncertainty of theoretical estimations (determined by the accuracy of SAS films properties measurements 20 %).

The experimental data were compared with theoretical estimations of the value of the velocity on the surface according the theory of internal wave propagation proposed in (Bondur et al., 2010 а). Estimations were obtained taking into account the influence of the SAS films. The estimate for the error in theoretical values was determined by the measurement error (constituted 20%) (Ermakov Kijashko, 2006). It is well seen from the figures that the results are in good agreement.

Thus, the experiments revealed that in the presence of internal waves induced by jets during outflow from the submerged sewer system model, surface flows with spatial periods controlled by the properties these waves appeared. The wavelength was from 30 to 160 cm. The standard deviations of velocities in the presence of a SAS film at the water surface varied in the range from 0.1 to 0.3 mm/s, corresponding to the amplitudes from 0.15 to 0.45 mm/s. For pure water the surface would constitute 1 to 2 mm/s. It should be pointed out that these experiments were performed for the conditions of scaled modeling.

In view of this, using the coefficients of scale modeling, one can estimate the flows created near the submerged sewer system in nature conditions: the parameters of internal waves (induced by jets), and the prosperities of their surface manifestations, as well as make conclusions on the possibility of remote diagnostics of these waves. In our laboratory experiment the coefficient of scale modeling with respect to the velocity value constitutes 1:3 and the coefficient of

Applying of PIV/PTV Methods for Physical Modeling

the small reservoir.

during time exposure.

Fig. 7. Example of the buoyant plume.

of the Turbulent Buoyant Jets in a Stratified Fluid 353

Fig. 6. Distributions of density (solid line) and buoyancy frequency *g d <sup>N</sup>*

The PIV method was used to study the jet flow. Polyamide particles 50 μm were added to the reservoir with freshwater. We put particles only in the jet, because we want to see and measure the form and boundary of the jet precisely (oscillations of the top of the jet). The motion of particles in the jet was visualized by a vertical laser sheet along the jet axis. The source – CW NdYag laser (532 nm wavelength, 0.5 Wt power). The lateral view was recorded on a CCD-camera (example of the buoyant plume is shown in Fig. 7) with the rate of 25 frames per second and exposure time of 5 ms. The displacement was less than 1 pxl

*dz* 

(dashed line) in

geometric similarity was 1:27. In view of this, we revealed the fact that this experiment simulated stratification with a pycnocline thickness of about 4 m, an internal wave with the length from 8 to 43 m, celerity from 5 to 10 cm/s, and the surface flow velocity from 0.3 to 0.6 cm/s. For such flows it yielded an estimate (see (Bondur et al., 2010 b)) for the contrast in the field of short waves of 0.12–0.3, which can be confidently detected by modern remote sensing methods (Bondur, 2004, 2006, 2011; Bondur, Grebenuyk, 2001).

### **3. The experimental study of the interaction of buoyant turbulent jet with pycnocline stratification with the PIV-method**

A theory describing the relation of characteristics of surface manifestations with the operational parameters of sewer systems should be made. For this propose it is necessary to investigate the dynamics of the buoyant jets in the pycnocline region, where the trapping of the jets by stratification occurred. The PIV-method is widely used for studying the velocity fields of the jet flows. However, there are several problems of carrying out measurements by PIV-methods in LTST (see Section 4). That is why preliminary test experiments of applying PIV-methods were provided in a small reservoir with saline stratification.

#### **3.1 Experimental setup in saline stratification**

To study the properties of the buoyant turbulent jets and ambient stratified liquid interaction, we performed preliminary test experiments in a small plexiglas basin with saline stratification. The scheme of the experiment is shown in Fig.5.

Here, a salt stratification of the pycnocline type is created. The distributions of density and buoyancy frequency are shown in Fig. 6.

In this experiment, the diffuser model had only a single vent with a diameter of 1.2 mm that allowed fresh water to flow out with the rate of 50 cm/s and form buoyant jet in ambient salt water.

Fig. 5. Principal scheme of experimental setup.

the small reservoir.

352 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

geometric similarity was 1:27. In view of this, we revealed the fact that this experiment simulated stratification with a pycnocline thickness of about 4 m, an internal wave with the length from 8 to 43 m, celerity from 5 to 10 cm/s, and the surface flow velocity from 0.3 to 0.6 cm/s. For such flows it yielded an estimate (see (Bondur et al., 2010 b)) for the contrast in the field of short waves of 0.12–0.3, which can be confidently detected by modern remote sensing

**3. The experimental study of the interaction of buoyant turbulent jet with** 

PIV-methods were provided in a small reservoir with saline stratification.

saline stratification. The scheme of the experiment is shown in Fig.5.

Water Surface

Tank with saline stratification

reservoir with fresh water and particles

z

(z)

density profile

Model of diffusor

50 cm

Fig. 5. Principal scheme of experimental setup.

50 cm

A theory describing the relation of characteristics of surface manifestations with the operational parameters of sewer systems should be made. For this propose it is necessary to investigate the dynamics of the buoyant jets in the pycnocline region, where the trapping of the jets by stratification occurred. The PIV-method is widely used for studying the velocity fields of the jet flows. However, there are several problems of carrying out measurements by PIV-methods in LTST (see Section 4). That is why preliminary test experiments of applying

To study the properties of the buoyant turbulent jets and ambient stratified liquid interaction, we performed preliminary test experiments in a small plexiglas basin with

Here, a salt stratification of the pycnocline type is created. The distributions of density and

In this experiment, the diffuser model had only a single vent with a diameter of 1.2 mm that allowed fresh water to flow out with the rate of 50 cm/s and form buoyant jet in ambient

Model of diffusor Bottom

V =100 cm/s <sup>0</sup>

jet

120 cm

1 3 hole d= mm

Field of laser knife

Side view

Field of laser knife

laser

Top view

CCD camerа

methods (Bondur, 2004, 2006, 2011; Bondur, Grebenuyk, 2001).

**pycnocline stratification with the PIV-method** 

**3.1 Experimental setup in saline stratification** 

buoyancy frequency are shown in Fig. 6.

salt water.

The PIV method was used to study the jet flow. Polyamide particles 50 μm were added to the reservoir with freshwater. We put particles only in the jet, because we want to see and measure the form and boundary of the jet precisely (oscillations of the top of the jet). The motion of particles in the jet was visualized by a vertical laser sheet along the jet axis. The source – CW NdYag laser (532 nm wavelength, 0.5 Wt power). The lateral view was recorded on a CCD-camera (example of the buoyant plume is shown in Fig. 7) with the rate of 25 frames per second and exposure time of 5 ms. The displacement was less than 1 pxl during time exposure.

Fig. 7. Example of the buoyant plume.

Applying of PIV/PTV Methods for Physical Modeling

analysis (semi-logarithmic scale)

of the Turbulent Buoyant Jets in a Stratified Fluid 355

current is divided into parts, each of which is taken to be quasi-parallel and treated by the method of normal modes. It testifies to the fact that the globally instable mode (Monkewitz et al., 1993) is actuated. The estimates for oscillation frequencies of the globally instable mode are well consistent quantitatively with the measured spectrum of jet oscillations (see. Fig 9).

Fig. 9. Spectrum of oscillations of the upper boundary of the jet, the gray field indicates boundaries of theoretically predicted frequency of oscillations basing on the stability

Thus, the following mechanism of internal wave generation by buoyant plume is proposed. (Huerre et al., 1990). Self induced oscillations of the globally unstable mode appear during the interaction of a buoyant plume with the pycnocline. Internal waves are intensely generated if the frequency of these oscillations turns out to be lower than the maximal

Fig. 10. Profiles of jet rate in cross sections *1*, *2*, and *3* (see Fig. 8).

buoyancy frequency in the pycnocline.

#### **3.2 PIV-processing**

The main attention was drawn to the area of the front of the fountain. The processing of the resulting frame sequences by PIV algorithms made it possible to obtain the velocity field in the laser-sheet cross section at consecutive time points with a step of 0.25 s by the way of cross correlation processing successive pairs of frames. The interrogation window size was 32\* 32 pix, with 50 % overlapping. The Gaussian approximation of the correlation function was used to avoid the effect of peak locking. The measurements uncertainty by PIV-method was about 3 %. It was obtained from the processing of synthetic images with determined displacement. Fig. 8 shows examples of measured instantaneous velocity fields.

Fig. 8. Velocity field of buoyant turbulent jet.

It can be clearly seen that the jet is trapped by the stratification and propagates at the neutral buoyancy level, which is located on the lower boundary of the pycnocline. The video recording also indicated that the upper boundary of the jet oscillates in the vertical plane; the oscillation spectrum of the front clearly expressed peak at a frequency of 0.1 Hz (Fig. 9).

### **3.3 Main results of the experiment**

Fig. 10 shows the instantaneous velocity profiles in different cross sections of the jet. To smooth the turbulent fluctuations that arise on these profiles, averaging by the coordinate along the jet axis over three domains shown in Fig. 8 was used. This includes the calculation of the mean profile of velocity on the basis of three adjacent profiles located 4.8 mm away from each another. It can be seen from the Fig. 10 that the counterflow exists in the region of pycnocline.

A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet with the counterflow region, the condition of absolute instability by the Briggs criterion (Briggs, 1964) for axisymmetric jet oscillations is satisfied. The stability of nonparallel currents is normally analyzed in the following way: the

The main attention was drawn to the area of the front of the fountain. The processing of the resulting frame sequences by PIV algorithms made it possible to obtain the velocity field in the laser-sheet cross section at consecutive time points with a step of 0.25 s by the way of cross correlation processing successive pairs of frames. The interrogation window size was 32\* 32 pix, with 50 % overlapping. The Gaussian approximation of the correlation function was used to avoid the effect of peak locking. The measurements uncertainty by PIV-method was about 3 %. It was obtained from the processing of synthetic images with determined

It can be clearly seen that the jet is trapped by the stratification and propagates at the neutral buoyancy level, which is located on the lower boundary of the pycnocline. The video recording also indicated that the upper boundary of the jet oscillates in the vertical plane; the oscillation spectrum of the front clearly expressed peak at a frequency of 0.1 Hz (Fig. 9).

Fig. 10 shows the instantaneous velocity profiles in different cross sections of the jet. To smooth the turbulent fluctuations that arise on these profiles, averaging by the coordinate along the jet axis over three domains shown in Fig. 8 was used. This includes the calculation of the mean profile of velocity on the basis of three adjacent profiles located 4.8 mm away from each another. It can be seen from the Fig. 10 that the counterflow exists in the region of

A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet with the counterflow region, the condition of absolute instability by the Briggs criterion (Briggs, 1964) for axisymmetric jet oscillations is satisfied. The stability of nonparallel currents is normally analyzed in the following way: the

displacement. Fig. 8 shows examples of measured instantaneous velocity fields.

**3.2 PIV-processing** 

Fig. 8. Velocity field of buoyant turbulent jet.

**3.3 Main results of the experiment** 

pycnocline.

current is divided into parts, each of which is taken to be quasi-parallel and treated by the method of normal modes. It testifies to the fact that the globally instable mode (Monkewitz et al., 1993) is actuated. The estimates for oscillation frequencies of the globally instable mode are well consistent quantitatively with the measured spectrum of jet oscillations (see. Fig 9).

Fig. 9. Spectrum of oscillations of the upper boundary of the jet, the gray field indicates boundaries of theoretically predicted frequency of oscillations basing on the stability analysis (semi-logarithmic scale)

Fig. 10. Profiles of jet rate in cross sections *1*, *2*, and *3* (see Fig. 8).

Thus, the following mechanism of internal wave generation by buoyant plume is proposed. (Huerre et al., 1990). Self induced oscillations of the globally unstable mode appear during the interaction of a buoyant plume with the pycnocline. Internal waves are intensely generated if the frequency of these oscillations turns out to be lower than the maximal buoyancy frequency in the pycnocline.

Applying of PIV/PTV Methods for Physical Modeling


integral model (thermocline center is at 44 cm depth). Side view.

thermocline measured experimentally are shown in Fig.13.


z, cm



equipment positioning

of the Turbulent Buoyant Jets in a Stratified Fluid 357

technique in LTST were a very complicated task. Horizontally discharged buoyant jet comes to the pycnocline nearly vertically at some distance from the nozzle (see the jet photo from the experiment in Fig. 7, and calculations result in Fig. 12). In order to perform successful jetthermocline interaction survey of a high space resolution we have to know this distance with a very high accuracy just to place the camera and the laser system correctly. It should be noted, that this distance depends strongly on a jet flow rate resulting in difficulties with

> 0 10 20 30 40 50 x, cm

Fig. 12. Jet trajectory (boundaries) calculated for typical stratification in LTST basing on the

Alcohol solutions also cause problems for visualization (chemical interaction with polyamide particles). Thus, in the new experimental series we used one jet of neutral buoyancy, discharged vertically at several rates. Jet exit velocity and a distance from the nozzle to the thermocline were chosen to provide jet parameters in the thermocline coincident with those in the previous series on the laboratory scale modeling of sewage disposal systems (see Section 2). Jet parameters in the thermocline for the series with buoyant liquid were determined from the direct numerical solutions to the system of equations for integral parameters of a turbulent jet in ideal incompressible liquid (Fan 1968). New series consisted of 10 experiments: 2 for each flow rate. Jet parameters in the

Velocity fields in a jet were studied by the PIV-method. For jet visualization 20 m polyamide particles were added to jet liquid. Only jet was seeded, for precise measurements of boundary oscillations. Particles were put to a reservoir 5 minutes after the beginning of each experiment. The laser sheet was produced by the same laser we used in the previous

### **4. Investigation of the mechanisms of internal waves generation by buoyant jets within the laboratory modeling of submerged sewage in a stratified ocean with the PIV-methods**

Basing on the results of successful applying of the PIV-methods in small reservoir with saline stratification a series of similar experiments in the LTST for the conditions of scale modeling of the typical sewer system (see Section 2) were carried out for approving the hypothesis offered in section 3. In these experiments for the first time simultaneous measurements of the jet characteristics (source of oscillations) with PIV-method and the properties of internal waves by contact methods were performed.

### **4.1 Experiments in LTST with the application of the PIV-technique**

The simplified general experimental scheme is shown in Fig. 11. This scheme is similar to the one we used for the experimental investigation of surface flows (see Section 2). In this experimental series the temperature stratification was created in LTST with the thermocline center located at the depth of 43-45 cm. Full water depth in the Tank was 160 cm (profile 2 in Fig. 2).

Fig. 11. Experimental setup: visualization of a turbulent jet in LTST

Opposite to the previous experimental series in LTST (see Section 2), a jet was discharged vertically from a П-shaped round pipe of 6 mm diameter (see Fig. 11), i.e. only one nozzle was used. Previously we worked with several buoyant jets (alcohol solution) discharged horizontally from a diffuser model at different rates.

The laboratory modeling of the jets from disposal systems showed that jets do not merge until they reach pycnocline. The visualization of such flows and the application of the PIV-

**4. Investigation of the mechanisms of internal waves generation by buoyant jets within the laboratory modeling of submerged sewage in a stratified** 

Basing on the results of successful applying of the PIV-methods in small reservoir with saline stratification a series of similar experiments in the LTST for the conditions of scale modeling of the typical sewer system (see Section 2) were carried out for approving the hypothesis offered in section 3. In these experiments for the first time simultaneous measurements of the jet characteristics (source of oscillations) with PIV-method and the

The simplified general experimental scheme is shown in Fig. 11. This scheme is similar to the one we used for the experimental investigation of surface flows (see Section 2). In this experimental series the temperature stratification was created in LTST with the thermocline center located at the depth of 43-45 cm. Full water depth in the Tank was 160 cm (profile 2 in

properties of internal waves by contact methods were performed.

**4.1 Experiments in LTST with the application of the PIV-technique** 

Fig. 11. Experimental setup: visualization of a turbulent jet in LTST

horizontally from a diffuser model at different rates.

Opposite to the previous experimental series in LTST (see Section 2), a jet was discharged vertically from a П-shaped round pipe of 6 mm diameter (see Fig. 11), i.e. only one nozzle was used. Previously we worked with several buoyant jets (alcohol solution) discharged

The laboratory modeling of the jets from disposal systems showed that jets do not merge until they reach pycnocline. The visualization of such flows and the application of the PIV-

**ocean with the PIV-methods** 

Fig. 2).

technique in LTST were a very complicated task. Horizontally discharged buoyant jet comes to the pycnocline nearly vertically at some distance from the nozzle (see the jet photo from the experiment in Fig. 7, and calculations result in Fig. 12). In order to perform successful jetthermocline interaction survey of a high space resolution we have to know this distance with a very high accuracy just to place the camera and the laser system correctly. It should be noted, that this distance depends strongly on a jet flow rate resulting in difficulties with equipment positioning

Fig. 12. Jet trajectory (boundaries) calculated for typical stratification in LTST basing on the integral model (thermocline center is at 44 cm depth). Side view.

Alcohol solutions also cause problems for visualization (chemical interaction with polyamide particles). Thus, in the new experimental series we used one jet of neutral buoyancy, discharged vertically at several rates. Jet exit velocity and a distance from the nozzle to the thermocline were chosen to provide jet parameters in the thermocline coincident with those in the previous series on the laboratory scale modeling of sewage disposal systems (see Section 2). Jet parameters in the thermocline for the series with buoyant liquid were determined from the direct numerical solutions to the system of equations for integral parameters of a turbulent jet in ideal incompressible liquid (Fan 1968).

New series consisted of 10 experiments: 2 for each flow rate. Jet parameters in the thermocline measured experimentally are shown in Fig.13.

Velocity fields in a jet were studied by the PIV-method. For jet visualization 20 m polyamide particles were added to jet liquid. Only jet was seeded, for precise measurements of boundary oscillations. Particles were put to a reservoir 5 minutes after the beginning of each experiment. The laser sheet was produced by the same laser we used in the previous

Applying of PIV/PTV Methods for Physical Modeling

calculated for each experiment (an example is shown in Fig. 15a).

particles injection moments would be the most powerful.

velocity field is calculated on the PIV-measurements base.

high-frequency oscillations were filtered from *I(t)*.

a formula

trend).

of the Turbulent Buoyant Jets in a Stratified Fluid 359

modes, one rectangular side was chosen along the jet axis and the other side separated the area with particles from the rest, simply black area (see Fig. 14). Upper and bottom rectangular sides indicated the maximum and minimum jet top positions. Jet top oscillations were

It should be noted, however, that particles concentration in a jet changed in time causing changes in average intensity. This resulted in the average intensity trend. At the moments of particles injection in the reservoir one could observe sudden changes of intensity. Besides, slow intensity decrease due to decreasing particles concentration could also lead to incorrect ratio of power spectral peaks, and oscillations corresponding to the film beginning or

Fig. 14. An example of rectangular area for investigation of jet top oscillations. Mean

Thus, the calculated intensity had to be corrected. For each experiment we found the intensity trend due to varying particles concentration in a jet. This was performed by choosing a maximum possible rectangular area in a jet fully occupied by particles and calculating its average intensity dependency on time (Fig.15 b). The bigger this area is, the smaller high-frequency pulsations of intensity are. Jet top oscillations can be represented by

*y(t)=I(t)\*f(t),*  where *f(t)* – is jet oscillations function, as it would be for the constant particles density; *I(t)–* function, corresponding to the average intensity trend (or particles concentration

Then a desired function is *f(t)=y(t)/I(t)* (see example in Fig. 15 c). When processing data out,

experimental series. Since LTST walls are not transparent, the digital camera (frame rate 25 frames/sec, time exposure 10 ms) was placed into a specially designed waterproof box (we performed underwater survey). The time exposure was 2 ms. Displacement of the particles less 1 pxl during one frame. The camera was submerged to the thermocline level at the distance 3 m from the nozzle (a maximum possible distance). The digital data from the camera were processed out with "Vortex" program which was also used previously to calculate the velocity fields, and a specially developed "SMPD" algorithm for simultaneous work with the survey data and calculated velocity fields.

Fig. 13. Experimental jet parameters (maximum longitudinal velocity and radius): O – calculated in the framework of the integral model for discharge rates of buoyant jets 40, 70, 100 and 150 cm/s; ◊ - parameters, measured in the experiments with one jet.

Temperature oscillations in the LTST during jet discharge were measured as in previous experiments by contact methods (a string of 13 thermistors was employed). The string was placed at 50 cm distance from the nozzle. Using the data from thermistors we calculated isotherms.

The underwater survey in each experiment lasted 20 min (during this time particles were added to the reservoir from time to time) and temperature oscillations were measured during the whole time of the experiment – 1 h.

#### **4.2 Processing technique for video and velocity fields**

We studied jet oscillations in the thermocline using the SMPD algorithm. It allows calculating the average intensity of a frame in the user-defined rectangular area, thus, intensity dependence on time can be easily derived. If a rectangular area is chosen in the jet oscillations region, the intensity dependence detects these oscillations due to the light particles in the jet. We also employed the next considerations when chose the area. One could expect 2 types of unstable jet modes to develop: the first was axisymmetric and the second was spiral or helical. An axisymmetric mode results in the jet top oscillations in the vertical plane, and a spiral one in the laser sheet plane looks like jet oscillations from left to right. In order to detect both

experimental series. Since LTST walls are not transparent, the digital camera (frame rate 25 frames/sec, time exposure 10 ms) was placed into a specially designed waterproof box (we performed underwater survey). The time exposure was 2 ms. Displacement of the particles less 1 pxl during one frame. The camera was submerged to the thermocline level at the distance 3 m from the nozzle (a maximum possible distance). The digital data from the camera were processed out with "Vortex" program which was also used previously to calculate the velocity fields, and a specially developed "SMPD" algorithm for simultaneous

> 4 5 6 7 8 9 10 up, cm/s

Fig. 13. Experimental jet parameters (maximum longitudinal velocity and radius): O – calculated in the framework of the integral model for discharge rates of buoyant jets 40, 70,

Temperature oscillations in the LTST during jet discharge were measured as in previous experiments by contact methods (a string of 13 thermistors was employed). The string was placed at 50 cm distance from the nozzle. Using the data from thermistors we calculated

The underwater survey in each experiment lasted 20 min (during this time particles were added to the reservoir from time to time) and temperature oscillations were measured

We studied jet oscillations in the thermocline using the SMPD algorithm. It allows calculating the average intensity of a frame in the user-defined rectangular area, thus, intensity dependence on time can be easily derived. If a rectangular area is chosen in the jet oscillations region, the intensity dependence detects these oscillations due to the light particles in the jet. We also employed the next considerations when chose the area. One could expect 2 types of unstable jet modes to develop: the first was axisymmetric and the second was spiral or helical. An axisymmetric mode results in the jet top oscillations in the vertical plane, and a spiral one in the laser sheet plane looks like jet oscillations from left to right. In order to detect both

100 and 150 cm/s; ◊ - parameters, measured in the experiments with one jet.

work with the survey data and calculated velocity fields.

6

during the whole time of the experiment – 1 h.

**4.2 Processing technique for video and velocity fields** 

8

rp, cm

isotherms.

10

12

modes, one rectangular side was chosen along the jet axis and the other side separated the area with particles from the rest, simply black area (see Fig. 14). Upper and bottom rectangular sides indicated the maximum and minimum jet top positions. Jet top oscillations were calculated for each experiment (an example is shown in Fig. 15a).

It should be noted, however, that particles concentration in a jet changed in time causing changes in average intensity. This resulted in the average intensity trend. At the moments of particles injection in the reservoir one could observe sudden changes of intensity. Besides, slow intensity decrease due to decreasing particles concentration could also lead to incorrect ratio of power spectral peaks, and oscillations corresponding to the film beginning or particles injection moments would be the most powerful.

Fig. 14. An example of rectangular area for investigation of jet top oscillations. Mean velocity field is calculated on the PIV-measurements base.

Thus, the calculated intensity had to be corrected. For each experiment we found the intensity trend due to varying particles concentration in a jet. This was performed by choosing a maximum possible rectangular area in a jet fully occupied by particles and calculating its average intensity dependency on time (Fig.15 b). The bigger this area is, the smaller high-frequency pulsations of intensity are. Jet top oscillations can be represented by a formula

$$y(t) = I(t)"\!^\*f(t)"\!^\prime$$

where *f(t)* – is jet oscillations function, as it would be for the constant particles density; *I(t)–* function, corresponding to the average intensity trend (or particles concentration trend).

Then a desired function is *f(t)=y(t)/I(t)* (see example in Fig. 15 c). When processing data out, high-frequency oscillations were filtered from *I(t)*.

Applying of PIV/PTV Methods for Physical Modeling

0.016

0

dependence of the internal waves excitation coefficient.

0.004

0.008

Sp, ar b.

prevailing jet mode was determined.

function has a minimum at *t*=0.

un.

0.012

of the Turbulent Buoyant Jets in a Stratified Fluid 361

0 0.04 0.08 0.12 f, Hz

Fig. 16 Jet top oscillations spectrum (hatch line) and spectrum of isotherm (solid line), corresponding to the thermocline center for the experiment with discharge rate 150 cm/s. The straight line marks the maximum buoyancy frequency. The smooth curve is a frequency

**4.4 Jet mode structure investigation with the application of the PIV-method** 

In this Subsection we determine an unstable jet mode type generating internal waves. For this purpose we used a modified method, developed in (Yoda et al., 1992), where the jet mode structure was investigated basing on the experimental data for a turbulent round jet at a distance *x d* / 1 (*x* is a distance from the nozzle, *d* is a nozzle diameter). The method is based on cross-correlation processing of the digital survey data. First, in each frame from the film jet boundaries were determined – areas of the same intensity defined by the authors. Then for several jet cross sections they obtained jet boundaries dependencies on time (2 for every cross section) and calculated their cross-correlations. Basing on these data, a

Let's illustrate this method application on the example. Let the axisymmetric jet mode dominate. Jet boundaries dependencies for this case are shown in Fig. 17. If one of them is reflected with respect to the jet axis, the curves *a* and *b* coincide. Their cross correlation function is periodic and has a maximum in zero. If a spiral mode prevails (Fig. 17), the

We modified this method: jet boundaries were determined using longitudinal jet velocity profiles, calculated by means of the PIV-method. In order to reduce high-frequency fluctuations, we averaged velocity fields by time and coordinate along the jet axis. The averaging time and length were chosen small as compared to characteristic time and spatial scales. Characteristic time corresponding to the frequency 0.7*N*0 was 25 s. The averaging

Fig. 15. Average intensity oscillations of the digital image (the gradations of grey color - 12 bit) (a), intensity change due to varying particles concentration (b); jet top oscillations (c). All taken from rectangular area in Fig 14

#### **4.3 Experimental results. The comparison between internal waves and jet top oscillations spectra**

During the experiments the turbulent jet, as in previous series, spread at the level of neutral buoyancy, forming a horizontal shear flow under the thermocline, and generated intensive internal waves. We calculated internal waves spectra for all experiments and revealed pronounced peaks in the frequency interval between *fmin*=0.02 Hz и *fmax*=0.05 Hz, with maximum buoyancy frequency being 0.07 Hz.

Jet top oscillations spectra (spectra of functions *f(t)*) were found for all experiments and compared to spectra of isotherms *T*=16°С, close to the thermocline center (from the 1h realization we cut 20 min corresponding to survey time). The examples of such spectra are shown in Fig. 16 for experiment with discharge rate 150 cm/s. There exists a pronounced peak at the frequency close to 0.7*N*0 in the internal waves spectrum. It can be seen from the figure, that jet oscillations at frequency 0.7*N*0 generate internal waves most effectively. Theoretical analysis performed basing on the work [Bondur et al, 2010а] for source parameters taken from our experiments confirms the most effective generation of internal waves at this particular frequency.

Fig. 15. Average intensity oscillations of the digital image (the gradations of grey color - 12 bit) (a), intensity change due to varying particles concentration (b); jet top oscillations (c). All

During the experiments the turbulent jet, as in previous series, spread at the level of neutral buoyancy, forming a horizontal shear flow under the thermocline, and generated intensive internal waves. We calculated internal waves spectra for all experiments and revealed pronounced peaks in the frequency interval between *fmin*=0.02 Hz и *fmax*=0.05 Hz, with

Jet top oscillations spectra (spectra of functions *f(t)*) were found for all experiments and compared to spectra of isotherms *T*=16°С, close to the thermocline center (from the 1h realization we cut 20 min corresponding to survey time). The examples of such spectra are shown in Fig. 16 for experiment with discharge rate 150 cm/s. There exists a pronounced peak at the frequency close to 0.7*N*0 in the internal waves spectrum. It can be seen from the figure, that jet oscillations at frequency 0.7*N*0 generate internal waves most effectively. Theoretical analysis performed basing on the work [Bondur et al, 2010а] for source parameters taken from our experiments confirms the most effective generation of internal

**4.3 Experimental results. The comparison between internal waves and jet top** 

taken from rectangular area in Fig 14

maximum buoyancy frequency being 0.07 Hz.

waves at this particular frequency.

**oscillations spectra** 

Fig. 16 Jet top oscillations spectrum (hatch line) and spectrum of isotherm (solid line), corresponding to the thermocline center for the experiment with discharge rate 150 cm/s. The straight line marks the maximum buoyancy frequency. The smooth curve is a frequency dependence of the internal waves excitation coefficient.

### **4.4 Jet mode structure investigation with the application of the PIV-method**

In this Subsection we determine an unstable jet mode type generating internal waves. For this purpose we used a modified method, developed in (Yoda et al., 1992), where the jet mode structure was investigated basing on the experimental data for a turbulent round jet at a distance *x d* / 1 (*x* is a distance from the nozzle, *d* is a nozzle diameter). The method is based on cross-correlation processing of the digital survey data. First, in each frame from the film jet boundaries were determined – areas of the same intensity defined by the authors. Then for several jet cross sections they obtained jet boundaries dependencies on time (2 for every cross section) and calculated their cross-correlations. Basing on these data, a prevailing jet mode was determined.

Let's illustrate this method application on the example. Let the axisymmetric jet mode dominate. Jet boundaries dependencies for this case are shown in Fig. 17. If one of them is reflected with respect to the jet axis, the curves *a* and *b* coincide. Their cross correlation function is periodic and has a maximum in zero. If a spiral mode prevails (Fig. 17), the function has a minimum at *t*=0.

We modified this method: jet boundaries were determined using longitudinal jet velocity profiles, calculated by means of the PIV-method. In order to reduce high-frequency fluctuations, we averaged velocity fields by time and coordinate along the jet axis. The averaging time and length were chosen small as compared to characteristic time and spatial scales. Characteristic time corresponding to the frequency 0.7*N*0 was 25 s. The averaging

Applying of PIV/PTV Methods for Physical Modeling


**5. Conclusion** 

mode prevails at generation frequency of internal waves.

of the Turbulent Buoyant Jets in a Stratified Fluid 363

In order to determine a mode, generating internal waves, every jet boundaries function was filtered with cut-off frequencies 0.02 Hz and 0.05 Hz. For each rectangular area we calculated jet boundaries cross-correlation functions, see Fig. 19 as an example. It can be seen from this figure, that functions has maxima at *t* = 0, consequently, the axisymmetric

> -100 0 100 t, s

Fig. 19. Example of cross-correlation functions of jet boundaries for 5 rectangular areas in

Investigation of hydrodynamic processes near submerged wastewater outfalls is an important scientific and engineering problem. Method of dye colouring for jet visualization has been extensively used both in laboratory and field conditions. It allowed observing and investigating evolution of jet integral parameters, in particular, jet spread and dilution laws, oscillations of buoyant jet fronts, both in homogeneous and stratified liquid. At the same time, precise and very specific experiments were needed to clarify the possibility of surface manifestations of the jets from submerged wastewater outfalls. This task demanded

Fig. 18 in the same order – experiment with discharge rate 150 cm/s.

time was *tavg* = 2 с. The wavelength of the unstable jet mode had to be of jet diameter order, which was 15-16 cm in the thermocline. Thus, 5 neighbour jet velocity profiles were averaged, located at a distance 1 cm from each other and the average length was, consequently, *lavg* = 4 сm (see Fig. 18).

For each experimental frame sequence consisting of 30000 frames, 5 rectangular areas were chosen, as a rule, 2 of them were in thermocline, 2 - above it and 1 – below (see Fig. 18). For each rectangular area the SMPD algorithm was employed to make a file containing averaged by *tavg* and *lavg* longitudinal velocity profiles for successive time moments at interval *tavg*. Using these data we obtained the maximum velocity and jet boundaries dependencies on time for each rectangular area. Jet boundaries were determined by *е* times velocity decrease from the maximal meaning.

Fig. 17. Jet boundary dependencies on time for some jet cross-section: left – axisymmetric mode, right – spiral mode.

Fig. 18. An example of rectangular areas for velocity profiles averaging

time was *tavg* = 2 с. The wavelength of the unstable jet mode had to be of jet diameter order, which was 15-16 cm in the thermocline. Thus, 5 neighbour jet velocity profiles were averaged, located at a distance 1 cm from each other and the average length was,

For each experimental frame sequence consisting of 30000 frames, 5 rectangular areas were chosen, as a rule, 2 of them were in thermocline, 2 - above it and 1 – below (see Fig. 18). For each rectangular area the SMPD algorithm was employed to make a file containing averaged by *tavg* and *lavg* longitudinal velocity profiles for successive time moments at interval *tavg*. Using these data we obtained the maximum velocity and jet boundaries dependencies on time for each rectangular area. Jet boundaries were determined by *е* times

Fig. 17. Jet boundary dependencies on time for some jet cross-section: left – axisymmetric

consequently, *lavg* = 4 сm (see Fig. 18).

velocity decrease from the maximal meaning.

Fig. 18. An example of rectangular areas for velocity profiles averaging

mode, right – spiral mode.

In order to determine a mode, generating internal waves, every jet boundaries function was filtered with cut-off frequencies 0.02 Hz and 0.05 Hz. For each rectangular area we calculated jet boundaries cross-correlation functions, see Fig. 19 as an example. It can be seen from this figure, that functions has maxima at *t* = 0, consequently, the axisymmetric mode prevails at generation frequency of internal waves.

Fig. 19. Example of cross-correlation functions of jet boundaries for 5 rectangular areas in Fig. 18 in the same order – experiment with discharge rate 150 cm/s.

### **5. Conclusion**

Investigation of hydrodynamic processes near submerged wastewater outfalls is an important scientific and engineering problem. Method of dye colouring for jet visualization has been extensively used both in laboratory and field conditions. It allowed observing and investigating evolution of jet integral parameters, in particular, jet spread and dilution laws, oscillations of buoyant jet fronts, both in homogeneous and stratified liquid. At the same time, precise and very specific experiments were needed to clarify the possibility of surface manifestations of the jets from submerged wastewater outfalls. This task demanded

Applying of PIV/PTV Methods for Physical Modeling

*Kosmosa*, No. 6, pp. 1-12 [in Russian].

*Environment, ISRSE*, pp. 192-195.

doi:10.1029/2005GL022390.

Vol. 46, No. 6, pp. 757–771.

*Physics*: Vol. 46, pp. 768 - 779.

*Oceanology*, Vol. 49, No. 5, pp. 595–606.

1045.

of the Turbulent Buoyant Jets in a Stratified Fluid 365

Beckers, M.R, Clercx, H., Heijst van G.J.F. & Verzicco, H.J.H. (2003) Evolution and

Bondur V. G., (2004) Aerospace Methods in Modern Oceanology, in *New Ideas in Oceanology, Vol. 1: Physics. Chemistry. Biology*, pp. 55–117, Nauka Press, Moscow, [in Russian]. Bondur, V., (2006) Complex Satellite Monitoring of Coastal Water Areas *Proceedings of 31st International Symposium on Remote Sensing of Environment, ISRSE*, pp. 31 – 35. Bondur, V.G. (2011) Satellite monitoring and mathematical modelling of deep runoff

pp. 231–251, IAP RAS Press, Nizhnii Novgorod, [in Russian].

Institute of Applied Physics, Russian Academy of Sciences), in *Near-Surface Ocean Layer. Physical Processes of Remote Probing,* V. I. Talanov and E. N. Pelinovskii, Vol. 2,

instability of monopolar vortices in a stratified fluid. *Phys. Fluids,* Vol. 15, pp. 1033-

turbulent jets in coastal water areas In *Waste Water.* http:// www.intechopen.com/articles/show/title/satellite-monitoring-and-mathematicalmodelling-of-deep-runoff-turbulent-jets-in-coastal-water-areas, pp. 26-32, Intech. Bondur, V. G. and Grebenyuk, Yu. V., (2001) Remote Indication of Anthropogenic Impacts

on the Marine Environment Caused by Deep-Water Sewage Discharge *Issl. Zemli* 

Databases for The Monitoring of Anthropogenic Impact on Ecosystems of Coastal Water Areas. *Proceedings of 31st International Symposium on Remote Sensing of* 

effects from a submerged turbulent outfall in the stratified ocean *GRL*, 32, L12610,

Turbulent Jets of Deep- Water Sewage Discharge into Coastal Basins, *Oceanology*,

of Turbulent Jet Propagation in the Stratified Environment of Coastal Water Areas

Troitskaya Yu.I. (2009) Surface Manifestations of Internal Waves Investigated by a Subsurface Buoyant Jet: 1. The Mechanism of Internal-Wave Generation *Izvestiya,* 

Troitskaya Yu.I. (2010) Surface Manifestations of Internal Waves Investigated by a Subsurface Buoyant Jet: 2. Internal Wave Field *Izvestiya, Atmospheric and Oceanic* 

Troitskaya Yu.I. (2010) Surface Manifestations of Internal Waves Investigated by a Subsurface Buoyant Jet: 3. Surface Manifestations of Internal Waves *Izvestiya,* 

Bondur. V., Tsidilina M. (2006) Features of Formation of Remote Sensing and Sea truth

Bondur V., Keeler R., Gibson C. (2005) Optical satellite imagery detection of internal wave

Bondur, V. G., Zhurbas, V. M., and Grebenyuk, Yu. V. (2006), Mathematical Modeling of

Bondur, V.G., Zhurbas, V.M., Grebenuk Yu.V. (2009) Modeling and Experimental Research

Bondur V.G., Grebenyuk Yu.V., Ezhova E.V., Kazakov V.I., Sergeev D.A., Soustova I.A. and

Bondur V.G., Grebenyuk Yu.V., Ezhova E.V., Kazakov V.I., Sergeev D.A., Soustova I.A. and

Bondur V.G., Grebenyuk Yu.V., Ezhova E.V., Kazakov V.I., Sergeev D.A., Soustova I.A. and

Ermakov, S.A., Kijashko, S.V. (2006). Laboratory study of the damping of parametric ripples due to surfactant films In *Marine surface films*. pp.113-128. Springer. Germany.

*Atmospheric and Oceanic Physics*: Vol. 45, No 6, pp. 779-790.

*Atmospheric and Oceanic Physics*: Vol. 46, No. 4, pp. 482-491. Briggs, R. J.(1964) *Electron-Stream Interaction with Plasmas* MIT Press, Cambridge.

measurements of velocity fields of surface flows and in water column with high time and spatial resolution. Thus, optical PIV/PTV methods were optimal. This Chapter is devoted to application of these methods for investigation of dynamics of flows from submerged wastewater outfalls and their surface manifestations.

For this purpose a physical scale modeling of internal waves generation by the turbulent buoyant jets induced by submerged sewer in conditions of temperature stratification with shallow thermocline in LTST IAP RAS was performed. Velocity fields of the surface flows induced by internal waves were measured by the modified PTV-method. The modified method allowed to identify these very weak surface flows in the presence of large-scale background flows. The obtained experimental data are in good agreement with theoretical forecasts taking into account presence of a SAS film, which could not be eliminated completely. For the known parameters of the film and coefficients of scale modeling, we estimated the parameters of internal waves generated by a submerged sewer jet flows and the values of their surface manifestations for the nature conditions. The estimations of hydrodynamic contrasts (caused by manifestations) in the field of surface waves obtained in [Bondur 2004, 2006, 2011, Bondur Grebenyuk 2001], show that such contrast could be detected with confidence by the modern remote sensing methods.

The experiments on measurements of submerged flows with PIV-methods were carried out for the purpose of studying mechanisms of internal waves generation by buoyant jets. At first preliminary test experiments were performed in small reservoir with saline stratification. It turned out that, when the jet approaches the pycnocline, a counterflow is generated at the edges. A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet portions with counterflow, the condition of absolute instability criterion for axisymmetric jet oscillations is satisfied. The estimates for oscillation frequencies of the globally unstable mode are in good agreement with measured spectrum of the jet oscillations.

These experiments were continued as a laboratory scale modeling of submerged wastewater outfalls in LTST with application of PIV-technique for measurements of jets' parameters and contact methods for investigation of internal waves. It allowed to compare jet oscillations spectra, obtained by modified video images processing, with spectra of internal waves. The comparison confirmed that self-sustained jet oscillations serve as a source of internal waves. The investigation of mode structure of jet perturbations with application of modified PIVmethod showed that the axisymmetric mode prevails and it effectively generates internal waves.

Within the framework of this study modified methods of using PIV/PTV technique were developed for the complicated investigations of turbulent submerged flows and its surface manifestations in the conditions of ambient stratification together with contact methods.

### **6. References**

Adrian, R. J., (1991) Particle Imaging techniques for experimental fluid mechanics. *Annu. Rev. Fluid Mech.*, Vol. 23, p. 261–304.

Arabadzhi, V. V., Bogatyrev, S. D., Bakhanov, V. V, et al (1999) Laboratory Modeling of Hydrophysical processes in the Upper Ocean Layer (Large Thermostratified Tank

measurements of velocity fields of surface flows and in water column with high time and spatial resolution. Thus, optical PIV/PTV methods were optimal. This Chapter is devoted to application of these methods for investigation of dynamics of flows from submerged

For this purpose a physical scale modeling of internal waves generation by the turbulent buoyant jets induced by submerged sewer in conditions of temperature stratification with shallow thermocline in LTST IAP RAS was performed. Velocity fields of the surface flows induced by internal waves were measured by the modified PTV-method. The modified method allowed to identify these very weak surface flows in the presence of large-scale background flows. The obtained experimental data are in good agreement with theoretical forecasts taking into account presence of a SAS film, which could not be eliminated completely. For the known parameters of the film and coefficients of scale modeling, we estimated the parameters of internal waves generated by a submerged sewer jet flows and the values of their surface manifestations for the nature conditions. The estimations of hydrodynamic contrasts (caused by manifestations) in the field of surface waves obtained in [Bondur 2004, 2006, 2011, Bondur Grebenyuk 2001], show that such contrast could be

The experiments on measurements of submerged flows with PIV-methods were carried out for the purpose of studying mechanisms of internal waves generation by buoyant jets. At first preliminary test experiments were performed in small reservoir with saline stratification. It turned out that, when the jet approaches the pycnocline, a counterflow is generated at the edges. A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet portions with counterflow, the condition of absolute instability criterion for axisymmetric jet oscillations is satisfied. The estimates for oscillation frequencies of the globally unstable mode are in good

These experiments were continued as a laboratory scale modeling of submerged wastewater outfalls in LTST with application of PIV-technique for measurements of jets' parameters and contact methods for investigation of internal waves. It allowed to compare jet oscillations spectra, obtained by modified video images processing, with spectra of internal waves. The comparison confirmed that self-sustained jet oscillations serve as a source of internal waves. The investigation of mode structure of jet perturbations with application of modified PIVmethod showed that the axisymmetric mode prevails and it effectively generates internal

Within the framework of this study modified methods of using PIV/PTV technique were developed for the complicated investigations of turbulent submerged flows and its surface manifestations in the conditions of ambient stratification together with contact methods.

Adrian, R. J., (1991) Particle Imaging techniques for experimental fluid mechanics. *Annu.* 

Arabadzhi, V. V., Bogatyrev, S. D., Bakhanov, V. V, et al (1999) Laboratory Modeling of

Hydrophysical processes in the Upper Ocean Layer (Large Thermostratified Tank

wastewater outfalls and their surface manifestations.

detected with confidence by the modern remote sensing methods.

agreement with measured spectrum of the jet oscillations.

*Rev. Fluid Mech.*, Vol. 23, p. 261–304.

waves.

**6. References** 

Institute of Applied Physics, Russian Academy of Sciences), in *Near-Surface Ocean Layer. Physical Processes of Remote Probing,* V. I. Talanov and E. N. Pelinovskii, Vol. 2, pp. 231–251, IAP RAS Press, Nizhnii Novgorod, [in Russian].


**14** 

*Italy* 

**Full Field Measurements in a River Mouth** 

**by Means of Particle Tracking Velocimetry** 

The measurement of marine streams is a difficult task even for well tested velocimetry methods based on advanced image analysis. The wide size of the measurement domain (from hundreds to thousands meters), the extended range of flow velocities (from mm/s to several m/s), the long time-scales (from minutes to weeks) and the related length and time scales of vortical structures involved in marine dynamics do not allow a straightforward application of Particle Image Velocimetry (PIV) and related methods. Due to the previous requirements, a natural choice is to consider Lagrangian "tracers" to be introduced in the fluid as candidates to sample the flow field in time. Therefore, the most useful measurement technique which enables to derive global velocity data from Lagrangian "tracers" is Particle Tracking Velocimetry, PTV (Tropea & Foss, 2007). As will be outlined in section 3, a large variety of Lagrangian buoys have been designed in the past to probe large-scale marine motion (larger than 50 km), whereas a lot of work is still necessary regarding the measurements at smaller scales. This aspect must be also considered within the debate on the effective role of mesoscales (around 10 km) and small-scales (100 m) in generating the "local" geophysical turbulence field (submesoscales) in the sea and how this dynamics is also dependent on the large-scales (Kanarska *et al*. 2007, Özgökmen 2011). Therefore, on-site measurements of flow at submesoscale level by using effective Lagrangian buoys are

Moreover, there are also many specific questions to be solved at small-scale levels regarding for example the diffusion of pollutants into the sea. The general question to be solved is usually related to the spreading of a polluted river water into the marine water and how such spreading can be improved, from the point of view of water quality along the shoreline. The problem is complex, due to the interactions of the river flow with the sea stream and with marine structures. The major phenomena are the interactions between the flow from the river and the harbor structures. Thus, a classical river mouth configuration can be considered as the combination of two flow fields frequently encountered in fluid

mechanics, known as the "jet in a cross-flow" and the "impact jet on a wall".

needed (Griffa *et al*. 2007, Haza *et al*. 2010, Wang 2010).

**1. Introduction** 

A. Ciarravano1, E. Binotti1, A. Bruschi2, V. Pesarino2, F. Lalli2 and G.P. Romano3

*2ISPRA – Italian Agency for Environment, Roma 3Department of Mechanical and Aerospace Engineering,* 

*1Fluid Solutions – alternative Srl, Roma* 

*University "La Sapienza", Roma* 


## **Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry**

A. Ciarravano1, E. Binotti1, A. Bruschi2,

V. Pesarino2, F. Lalli2 and G.P. Romano3 *1Fluid Solutions – alternative Srl, Roma 2ISPRA – Italian Agency for Environment, Roma 3Department of Mechanical and Aerospace Engineering, University "La Sapienza", Roma Italy* 

#### **1. Introduction**

366 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

Fan, L.N. (1968) Turbulent buoyant jet problems. In *Rep. № KH-R-18* Calif. Inst.

Gibson C.H., Bondur V.G., Keeler R.N., Leung P.T. Energetics of the Beamed Zombie

Turbulence. *Journal of Applied Fluid Mechanics*, Vol. 1, No. 1, pp. 11-42, 2006. Gibson C.H., Bondur V.G., Keeler R.N., Leung P.T. Remote sensing of submerged oceanic

Gibson C.H., Keeler R.N., Bondur V.G. (2007) Vertical stratified turbulent transport

Gibson, C.H., Bondur, V.G., Keeler, R.N., Leung, P.T., Prandke, H., Vithanage, D. (2007).

Koh, C.Y. and Brooks, H.N. (1975) Fluid mechanics of waste-water disposal in the ocean

Monkewitz, P. A., Huerre P., Chomaz J.-M., (1993) Global Linear Stability Analysis of

Ozmidov R. V., (1986) Diffusion of Admixture in the Ocean. Gidrometeoizdat, Leningrad,

Reul, N., Branger, H., Giovanangeli, J.P. (1999) Air flow separation over unsteady breaking

Sergeev, D.A., Troitskaya, Yu.I., (2011) APPLYING OF PIV/PTV-methods in Laboratory

Troitskaya, Yu. I. , Sergeev, D. A., Ezhova, E. V., Soustova, I. A., and Kazakov, V. I. (2008)

Turner, J. S. (1966) Jets and plumes with negative or reversing buoyancy *Journal Fluid. Mech.*,

Umeyama M., (2008) PIV Techniques for Velocity Fields of Internal Waves over a Slowly

Veron, F., Saxena, G., Misra, S.K. (2007) Measurements of the viscous tangential stress in the

Zhang H. P., King B., and Harry L. Swinney Experimental study of internal gravity waves generated by supercritical Topography // *Physics of Fluids* (2007) 19, 096602 Yoda M., Hesselink L., Mungal M.D. The evolution and nature of large-scale structures in

the turbulent jet // *Phys Fluids A*. 1992. V.4. No.4. P. 803-811.

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Varying Bottom Topography *Journal of Waterway Port Coastal and Ocean Engineering*

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turbulence and fossil turbulence. *International Journal of Dynamics of Fluids*, Vol.2,

mechanism indicated by remote sensing. *Proceedings of SPIE, Coastal Remote Sensing.* 

Submerged turbulence detection with optical satellites, *Proceedings of SPIE, Coastal Remote Sensing. SPIE*, Vol. 6680, 6680X1-8. doi: 10.1117/12.732257 Aug. 26-27 2007 Heijst van G.J.F., Beckers, M., R. Verzicco, H.J.H. (2002) Dynamics of pancake-like vortices in

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Rinkavichus B.S. pp. 330-347, Overley Press. Moscow.

*Doklady Earth Sciences,* Vol. 419A, pp. 506 -510.

The measurement of marine streams is a difficult task even for well tested velocimetry methods based on advanced image analysis. The wide size of the measurement domain (from hundreds to thousands meters), the extended range of flow velocities (from mm/s to several m/s), the long time-scales (from minutes to weeks) and the related length and time scales of vortical structures involved in marine dynamics do not allow a straightforward application of Particle Image Velocimetry (PIV) and related methods. Due to the previous requirements, a natural choice is to consider Lagrangian "tracers" to be introduced in the fluid as candidates to sample the flow field in time. Therefore, the most useful measurement technique which enables to derive global velocity data from Lagrangian "tracers" is Particle Tracking Velocimetry, PTV (Tropea & Foss, 2007). As will be outlined in section 3, a large variety of Lagrangian buoys have been designed in the past to probe large-scale marine motion (larger than 50 km), whereas a lot of work is still necessary regarding the measurements at smaller scales. This aspect must be also considered within the debate on the effective role of mesoscales (around 10 km) and small-scales (100 m) in generating the "local" geophysical turbulence field (submesoscales) in the sea and how this dynamics is also dependent on the large-scales (Kanarska *et al*. 2007, Özgökmen 2011). Therefore, on-site measurements of flow at submesoscale level by using effective Lagrangian buoys are needed (Griffa *et al*. 2007, Haza *et al*. 2010, Wang 2010).

Moreover, there are also many specific questions to be solved at small-scale levels regarding for example the diffusion of pollutants into the sea. The general question to be solved is usually related to the spreading of a polluted river water into the marine water and how such spreading can be improved, from the point of view of water quality along the shoreline. The problem is complex, due to the interactions of the river flow with the sea stream and with marine structures. The major phenomena are the interactions between the flow from the river and the harbor structures. Thus, a classical river mouth configuration can be considered as the combination of two flow fields frequently encountered in fluid mechanics, known as the "jet in a cross-flow" and the "impact jet on a wall".

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 369

of these are based on the two fluid dynamics frameworks, *i.e.* Eulerian or Lagrangian (Munson, 1994). In the Lagrangian methods, the variables are described in time following the trajectories of fluid elements, thus the observer is moving with the fluid particle motion. In the Eulerian approach, a control volume in a fixed reference system is defined within the

In the present study the Lagrangian framework was preferred because it is straightforward to assess for local fluid elements behavior. Otherwise, it would be necessary to install a large

In recent years, different types of Lagrangian buoys have been designed and manufactured with the aim of studying marine flows both in the open ocean and near to the coastline (Selsor, 1993). These devices were differentiated over the years depending on the purpose for which they were designed: some buoys were able to follow deep currents, whereas other types have been designed to follow the surface current. One of the most important parameter is the scale of the observed phenomenon, ocean large-scale, mesoscale, submesoscale and small-scale where sea bed effects must be also taken into account (Lalli *et al*. 2001). The design of a buoy must also take into account the residence time in water which can reach in some cases even more than a year for studies at oceanic scale (in general less in the Mediterranean sea and near the coastline). The Lagrangian buoys also differ depending on the type of on board sensor defining the range of use. Some are used to measure only the temperature, some only for the velocity field, while the most complex have onboard chemical and biological parameter sensors such as salinity, dissolved oxygen, pH *etc*. Series of Lagrangian buoys have been developed in different national and international research programs such as SVP (Surface Velocity Program) in the United States, for the investigation of ocean streams, or those within the European community concerning the observation of the Mediterranean sea. Hereafter, examples of developed Lagrangian buoy are reported.

At present, there are two basic sizes of SVP drifters: the original, relatively heavy SVP drifter and the new "mini" version (Figure 1). The less expensive, easier-to-deploy mini design was proposed in 2002 and is currently produced alongside original SVP drifters by several manufacturers. The surface float ranges from 30.5 cm to 40 cm in diameter. It contains: batteries in 4-5 packs, each with 7-9 alkaline D-cell batteries; a transmitter; a thermistor to measure sea surface temperature; and possibly other instruments measuring barometric pressure, wind speed and direction, salinity, and/or ocean color. They also have a submergence sensor or a tether strain sensor to verify the presence of the drogue. The drogue is centered at 15 meters beneath the surface to measure mixed layer currents in the upper ocean. The outer surface of the drogue is made of nylon cloth. In the original design, it has seven sections, each 92 cm long and 92 cm in diameter, for a total length of 6.44 m. Mini drogues are not yet standardized among the manufacturers: they are 4 (Pacific Gyre) or 5 (Marlin-Yug) sections of original dimensions, or 4 (Clearwater) or 5 (Technocean) redesigned sections of diameter 61 cm, length 1.22 m per section. Throughout the drogue, rigid rings with spokes support the drogue's cylindrical shape. The drogue is a "holey-sock" and each drogue section contains two opposing holes, which are rotated 90 degrees from

fluid and its properties are measured as functions of space and time.

number of devices fixed in space, to be checked continuously in time.

**3. A survey of Lagrangian buoys** 

*SVP and "mini" SVP (Lumpkin & Pazos, 2006)* 

The relevance of the present work is that real field measurements are performed by using almost completely submerged floating buoys which have been designed for the following specific purpose: to measure the velocity of the water stream close to the free-surface by minimizing the sensitivity to wind contributions. Here, the interest is focused on barotropic features, *i.e*. stratification effects are not considered, even if the design of the floating buoys was conceived to consider submerged streams also. The buoys are designed, built and setup to test the Pescara river mouth spreading into the Adriatic Sea. The river outlet and harbor have been recently modified and faced by a large breakwater which gave rise to several significant environmental effects, as for example concentrating fresh water along the near shore and changing the sea water quality along the shoreline. The aim of the present analysis is to test, by field experiments, the effective velocity field at the channel-harbor outlet to investigate some possible lay-out improvements of the situation.

### **2. Experimental studies on coastal dynamics**

The study of the coastal dynamics is very complex and has been faced during the last decade to understand a number of phenomena of different nature (Shibayama, 2009). The focus, regarding the action of the sea on the coastline, is directed not only to the study of waves and sea currents, but also to aspects related to chemical and biological parameters, especially in recent years in which the human activity has led to effects both in the open sea and near the coastline. Some examples of these effects are coastal erosion, dispersion of pollutants, effects on marine biodiversity (Mc Nealy *et al*. 1995) and influence of marine works on the sedimentation (Wang *et al*. 2011).

In this framework, it is really important to understand the fluid dynamics of the coastal flows, firstly to evaluate in advance what would be the effects of human activity on this area, but also to derive solutions to existing problems. An example is that of harbors where it is necessary to modify and adapt the marine structures to solve problems of sedimentation and pollution of the surrounding area (Shibayama, 2011).

This type of study is performed in recent years by two complementary approaches: numerical models, *i.e.* by simulating with computer dedicated algorithms the coastal area (Apsley & Hu 2003, Hillman *et al*. 2007), or field experiments with sensors detecting kinematic, chemical and physical parameters directly in the sea to correlate the results with scale models of the area (Lacorata *et al*. 2001, Lalli *et al*. 2010).

Numerical simulations bring significant advantages in terms of costs and allow to reproduce different environmental conditions, such as the analysis of critical conditions. However, there is still a lot of work to be done to connect among them the different scales in the ocean dynamics and to correctly modeling the fully three-dimensional phenomena involved (Özgökmen 2011, Balas & Ozhan 2000, Lalli *et al.* 2001). The combination of numerical simulations with laboratory experiments is a very interesting and promising opportunity (Lalli *et al.* 2001, Miozzi *et al*. 2010). Nevertheless, the experimental approach on the field has the strong advantage to directly measure the values of interest. Considering the costs of the tests and the fact that the devices are sometimes very complex in terms of setup and data handling, in most cases the use of a work team made up of many people is required (as in the present activity).

Regarding such experiments, different techniques have been used by many years to measure the speed of marine streams and to detect physical and biological parameters. All of these are based on the two fluid dynamics frameworks, *i.e.* Eulerian or Lagrangian (Munson, 1994). In the Lagrangian methods, the variables are described in time following the trajectories of fluid elements, thus the observer is moving with the fluid particle motion. In the Eulerian approach, a control volume in a fixed reference system is defined within the fluid and its properties are measured as functions of space and time.

In the present study the Lagrangian framework was preferred because it is straightforward to assess for local fluid elements behavior. Otherwise, it would be necessary to install a large number of devices fixed in space, to be checked continuously in time.

### **3. A survey of Lagrangian buoys**

368 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

The relevance of the present work is that real field measurements are performed by using almost completely submerged floating buoys which have been designed for the following specific purpose: to measure the velocity of the water stream close to the free-surface by minimizing the sensitivity to wind contributions. Here, the interest is focused on barotropic features, *i.e*. stratification effects are not considered, even if the design of the floating buoys was conceived to consider submerged streams also. The buoys are designed, built and setup to test the Pescara river mouth spreading into the Adriatic Sea. The river outlet and harbor have been recently modified and faced by a large breakwater which gave rise to several significant environmental effects, as for example concentrating fresh water along the near shore and changing the sea water quality along the shoreline. The aim of the present analysis is to test, by field experiments, the effective velocity field at the channel-harbor

The study of the coastal dynamics is very complex and has been faced during the last decade to understand a number of phenomena of different nature (Shibayama, 2009). The focus, regarding the action of the sea on the coastline, is directed not only to the study of waves and sea currents, but also to aspects related to chemical and biological parameters, especially in recent years in which the human activity has led to effects both in the open sea and near the coastline. Some examples of these effects are coastal erosion, dispersion of pollutants, effects on marine biodiversity (Mc Nealy *et al*. 1995) and influence of marine

In this framework, it is really important to understand the fluid dynamics of the coastal flows, firstly to evaluate in advance what would be the effects of human activity on this area, but also to derive solutions to existing problems. An example is that of harbors where it is necessary to modify and adapt the marine structures to solve problems of sedimentation

This type of study is performed in recent years by two complementary approaches: numerical models, *i.e.* by simulating with computer dedicated algorithms the coastal area (Apsley & Hu 2003, Hillman *et al*. 2007), or field experiments with sensors detecting kinematic, chemical and physical parameters directly in the sea to correlate the results with

Numerical simulations bring significant advantages in terms of costs and allow to reproduce different environmental conditions, such as the analysis of critical conditions. However, there is still a lot of work to be done to connect among them the different scales in the ocean dynamics and to correctly modeling the fully three-dimensional phenomena involved (Özgökmen 2011, Balas & Ozhan 2000, Lalli *et al.* 2001). The combination of numerical simulations with laboratory experiments is a very interesting and promising opportunity (Lalli *et al.* 2001, Miozzi *et al*. 2010). Nevertheless, the experimental approach on the field has the strong advantage to directly measure the values of interest. Considering the costs of the tests and the fact that the devices are sometimes very complex in terms of setup and data handling, in most cases the use of a work team made up of many people is required (as in

Regarding such experiments, different techniques have been used by many years to measure the speed of marine streams and to detect physical and biological parameters. All

outlet to investigate some possible lay-out improvements of the situation.

**2. Experimental studies on coastal dynamics** 

works on the sedimentation (Wang *et al*. 2011).

the present activity).

and pollution of the surrounding area (Shibayama, 2011).

scale models of the area (Lacorata *et al*. 2001, Lalli *et al*. 2010).

In recent years, different types of Lagrangian buoys have been designed and manufactured with the aim of studying marine flows both in the open ocean and near to the coastline (Selsor, 1993). These devices were differentiated over the years depending on the purpose for which they were designed: some buoys were able to follow deep currents, whereas other types have been designed to follow the surface current. One of the most important parameter is the scale of the observed phenomenon, ocean large-scale, mesoscale, submesoscale and small-scale where sea bed effects must be also taken into account (Lalli *et al*. 2001). The design of a buoy must also take into account the residence time in water which can reach in some cases even more than a year for studies at oceanic scale (in general less in the Mediterranean sea and near the coastline). The Lagrangian buoys also differ depending on the type of on board sensor defining the range of use. Some are used to measure only the temperature, some only for the velocity field, while the most complex have onboard chemical and biological parameter sensors such as salinity, dissolved oxygen, pH *etc*. Series of Lagrangian buoys have been developed in different national and international research programs such as SVP (Surface Velocity Program) in the United States, for the investigation of ocean streams, or those within the European community concerning the observation of the Mediterranean sea. Hereafter, examples of developed Lagrangian buoy are reported.

#### *SVP and "mini" SVP (Lumpkin & Pazos, 2006)*

At present, there are two basic sizes of SVP drifters: the original, relatively heavy SVP drifter and the new "mini" version (Figure 1). The less expensive, easier-to-deploy mini design was proposed in 2002 and is currently produced alongside original SVP drifters by several manufacturers. The surface float ranges from 30.5 cm to 40 cm in diameter. It contains: batteries in 4-5 packs, each with 7-9 alkaline D-cell batteries; a transmitter; a thermistor to measure sea surface temperature; and possibly other instruments measuring barometric pressure, wind speed and direction, salinity, and/or ocean color. They also have a submergence sensor or a tether strain sensor to verify the presence of the drogue. The drogue is centered at 15 meters beneath the surface to measure mixed layer currents in the upper ocean. The outer surface of the drogue is made of nylon cloth. In the original design, it has seven sections, each 92 cm long and 92 cm in diameter, for a total length of 6.44 m. Mini drogues are not yet standardized among the manufacturers: they are 4 (Pacific Gyre) or 5 (Marlin-Yug) sections of original dimensions, or 4 (Clearwater) or 5 (Technocean) redesigned sections of diameter 61 cm, length 1.22 m per section. Throughout the drogue, rigid rings with spokes support the drogue's cylindrical shape. The drogue is a "holey-sock" and each drogue section contains two opposing holes, which are rotated 90 degrees from

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 371

The Compact Meteorological and Oceanographic Drifter (CMOD) (Figure 2) consists of a 60 cm-long aluminum cylindrical hull with a floatation collar (35-cm overall diameter). This is equipped with the sonobuoy case (62-cm-long and 12-cm-diameter) on a 100-m-long (4-m for a few of them) 0.5-in-diameter tether, resulting in a wet to dry area ratio of about 5 to 1. Air temperature is measured with a thermistor located in a radiation shield which houses the inlet for the barometer port and the Argos transmitting antenna and ground plane. This housing is on top of the mast about 50.8 cm above the surface. The sea surface temperature

The Lagrangian drifter used in the MELBA project is dedicated to the study in the Mediterranean Sea, in particular near the coastline (Figure 3). The body of the drifter consists of an aluminum tube, capable of withstanding up to 2000 meters deep, and containing the engine of the ascent and descent (single movement allowed to the buoy), the satellite communications system (active surface) and the mission control system. The accessory instrumentation sensors varies depending on the type of mission to perform: it may include measures of conductivity, salinity, temperature, chlorophyll, etc. The communication system, used to send the measurement data and to receive new subsequent missions is supported by two-way satellite constellation Orbcom. A GPS (Global Position System) is integrated for the geo-referencing of the measured data, once the drifter has

*CMOD (Gerin et al. 2007)* 

*MELBA (Dell'Erba, 2002)* 

emerged.

Fig. 3. MELBA Buoy.

is measured at a subsurface depth of 44.5 cm.

one section to the next. These holes act like the dimples of a golf ball by disrupting the formation of organized lee vortices. While the size of the surface float and drogue vary, the manufacturers all aim for a specific non-dimensional goal: a drag area ratio of 40. This ratio is the drag area (drag coefficient times cross-sectional area) of the drogue, divided by the drag area of all other components. At a drag area ratio of 40, the resulting downwind slip (defined later) is 0.7 cm/s in 10 m/s winds (Niiler and Paduan, 1995). Once deployed, a modern SVP drifter lives an average of around 400 days before ceasing transmission. Occasionally, drifters are picked up by fishermen or lose their drogue and run aground.

Fig. 1. SVP and Mini SVP Drifter Buoy.

Fig. 2. CMOD Buoy.

#### *CMOD (Gerin et al. 2007)*

370 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

one section to the next. These holes act like the dimples of a golf ball by disrupting the formation of organized lee vortices. While the size of the surface float and drogue vary, the manufacturers all aim for a specific non-dimensional goal: a drag area ratio of 40. This ratio is the drag area (drag coefficient times cross-sectional area) of the drogue, divided by the drag area of all other components. At a drag area ratio of 40, the resulting downwind slip (defined later) is 0.7 cm/s in 10 m/s winds (Niiler and Paduan, 1995). Once deployed, a modern SVP drifter lives an average of around 400 days before ceasing transmission. Occasionally, drifters are picked up by fishermen or lose their drogue and run aground.

Fig. 1. SVP and Mini SVP Drifter Buoy.

Fig. 2. CMOD Buoy.

The Compact Meteorological and Oceanographic Drifter (CMOD) (Figure 2) consists of a 60 cm-long aluminum cylindrical hull with a floatation collar (35-cm overall diameter). This is equipped with the sonobuoy case (62-cm-long and 12-cm-diameter) on a 100-m-long (4-m for a few of them) 0.5-in-diameter tether, resulting in a wet to dry area ratio of about 5 to 1. Air temperature is measured with a thermistor located in a radiation shield which houses the inlet for the barometer port and the Argos transmitting antenna and ground plane. This housing is on top of the mast about 50.8 cm above the surface. The sea surface temperature is measured at a subsurface depth of 44.5 cm.

#### *MELBA (Dell'Erba, 2002)*

The Lagrangian drifter used in the MELBA project is dedicated to the study in the Mediterranean Sea, in particular near the coastline (Figure 3). The body of the drifter consists of an aluminum tube, capable of withstanding up to 2000 meters deep, and containing the engine of the ascent and descent (single movement allowed to the buoy), the satellite communications system (active surface) and the mission control system. The accessory instrumentation sensors varies depending on the type of mission to perform: it may include measures of conductivity, salinity, temperature, chlorophyll, etc. The communication system, used to send the measurement data and to receive new subsequent missions is supported by two-way satellite constellation Orbcom. A GPS (Global Position System) is integrated for the geo-referencing of the measured data, once the drifter has emerged.

Fig. 3. MELBA Buoy.

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 373

related to coastal hydrodynamics (Griffa *et al.*, 2007). Basically, the possible uses and implications related to the above issues can be classified into two approaches, diagnostic

The diagnostic approach is related to problems regarding monitoring of ocean streams, river plumes and discharges into the sea and analysis of biological and chemical parameters. The mark plume discharge into rivers and open waters is a typical phenomenon which can be investigated by a Lagrangian technique as Particle Tracking Velocimetry, PTV (Tropea & Foss, 2007). Simultaneously, with a prognostic approach the experimental tests are carried out also to validate the numerical models and codes used to simulate the phenomena. An example is given in this study in which the river freshwater flows into the sea having a different temperature and the determination of Lagrangian trajectories, provided by PTV,

Thus, the experimental investigation and the resulting data can be used in different ways and may be part of a process of analysis in which many aspects are involved, as numerical models validation, coastal erosion, sediments transport and deposition, marine works pre-

The proximal sensing device used to derive the flow trajectories into the open field is a halfsubmerged buoy. The geometric and physical characterization have been defined to satisfy the main requirement, *i.e*. to follow the flow and to determine the trajectories close to the sea surface. The Lagrangian point of view allows to consider the buoys as macro-particles representing the flow behavior and transported by it while continuously acquiring the position with the on board electronics (GPS Data Logger). In order to verify the Lagrangian behavior, a system based on central fins has been designed with the objective of increasing as much as possible the wetted surface of the buoy, and consequently the drag produced by

A specific problem for the open sea measurements is to reduce the effects of the free surface where wind breeze effects are dominant. To minimize this disturb, the buoy have been weighted to reduce the area exposed to the wind, and the fins have been located about 20cm in depth, as displayed in Figure 5. The main dimensions of the buoy are reported in Table 1.

> Height 41 cm Width 50 cm Cabinet Diameter 8 cm Fins 25x25 cm Optical Target 20x20 cm Total Weight 1550 g Cabinet Weight 1375 g Appendages 175 g

planning, analysis for marine generators (renewable energy solutions).

and prognostic which are also complementary.

are also used to validate the numerical models.

Table 1. The designed buoy dimensions and weight.

**5. Setup description** 

the flow.

**a. Drifter Buoy Description** 

#### *"Code" Davis Drifter (Davis, 1985)*

The "Code" Davis Drifter (conceived by Dr. Russ Davis of Scripps Institute of Oceanography) or "ARGODRIFTER" is a surface current monitoring Lagrangian drifter (Figure 4). It reports its position by several means, from a calculated position through the ARGOS/CLS system, or by transmitting a GPS location through either ARGOS/CLS or the IRIDIUM satellite system. The surrounding water temperature can also be monitored. Data transmissions can be varied through a wide spectrum of options at the selection of the user. The ARGODRIFTER consists of two orthogonal 1 meter cloth planes oriented vertically around a central instrument containing core. Four 10cm. diameter polyethylene foam floats provide positive buoyancy and are tethered at the end of the arms on Dacron lines 25cms long. These floats insure that the antennas, sometimes two are used when GPS is required, are sufficiently clear of seawater to insure adequate electronic transmissions. The antennas are mounted on 316 stainless steel springs to protect them in case of contact with foreign bodies, or they can "flex" in very high seas.

Fig. 4. "CODE" Davis Drifter.

In the present study, a Lagrangian buoy has been designed and tested by taking inspiration from the drifter "Code" Davis, since it was evaluated as a solution which meets the criteria of reliability and flexibility, especially in a measurement campaign carried out in a short period and close to the coastline. Starting from this configuration, some structural changes have been applied to allow a successful measurements of the sea surface stream (as detailed in section 5a).

#### **4. Use and applications of experimental data**

The experimental tests presented in this study represent a first approach to an important problem, *i.e*. the study of the coastal flows to highlight possible solutions to problems related to coastal hydrodynamics (Griffa *et al.*, 2007). Basically, the possible uses and implications related to the above issues can be classified into two approaches, diagnostic and prognostic which are also complementary.

The diagnostic approach is related to problems regarding monitoring of ocean streams, river plumes and discharges into the sea and analysis of biological and chemical parameters. The mark plume discharge into rivers and open waters is a typical phenomenon which can be investigated by a Lagrangian technique as Particle Tracking Velocimetry, PTV (Tropea & Foss, 2007). Simultaneously, with a prognostic approach the experimental tests are carried out also to validate the numerical models and codes used to simulate the phenomena. An example is given in this study in which the river freshwater flows into the sea having a different temperature and the determination of Lagrangian trajectories, provided by PTV, are also used to validate the numerical models.

Thus, the experimental investigation and the resulting data can be used in different ways and may be part of a process of analysis in which many aspects are involved, as numerical models validation, coastal erosion, sediments transport and deposition, marine works preplanning, analysis for marine generators (renewable energy solutions).

### **5. Setup description**

372 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

The "Code" Davis Drifter (conceived by Dr. Russ Davis of Scripps Institute of Oceanography) or "ARGODRIFTER" is a surface current monitoring Lagrangian drifter (Figure 4). It reports its position by several means, from a calculated position through the ARGOS/CLS system, or by transmitting a GPS location through either ARGOS/CLS or the IRIDIUM satellite system. The surrounding water temperature can also be monitored. Data transmissions can be varied through a wide spectrum of options at the selection of the user. The ARGODRIFTER consists of two orthogonal 1 meter cloth planes oriented vertically around a central instrument containing core. Four 10cm. diameter polyethylene foam floats provide positive buoyancy and are tethered at the end of the arms on Dacron lines 25cms long. These floats insure that the antennas, sometimes two are used when GPS is required, are sufficiently clear of seawater to insure adequate electronic transmissions. The antennas are mounted on 316 stainless steel springs to protect them in case of contact with foreign

In the present study, a Lagrangian buoy has been designed and tested by taking inspiration from the drifter "Code" Davis, since it was evaluated as a solution which meets the criteria of reliability and flexibility, especially in a measurement campaign carried out in a short period and close to the coastline. Starting from this configuration, some structural changes have been applied to allow a successful measurements of the sea surface stream (as detailed

The experimental tests presented in this study represent a first approach to an important problem, *i.e*. the study of the coastal flows to highlight possible solutions to problems

*"Code" Davis Drifter (Davis, 1985)* 

bodies, or they can "flex" in very high seas.

Fig. 4. "CODE" Davis Drifter.

**4. Use and applications of experimental data** 

in section 5a).

#### **a. Drifter Buoy Description**

The proximal sensing device used to derive the flow trajectories into the open field is a halfsubmerged buoy. The geometric and physical characterization have been defined to satisfy the main requirement, *i.e*. to follow the flow and to determine the trajectories close to the sea surface. The Lagrangian point of view allows to consider the buoys as macro-particles representing the flow behavior and transported by it while continuously acquiring the position with the on board electronics (GPS Data Logger). In order to verify the Lagrangian behavior, a system based on central fins has been designed with the objective of increasing as much as possible the wetted surface of the buoy, and consequently the drag produced by the flow.

A specific problem for the open sea measurements is to reduce the effects of the free surface where wind breeze effects are dominant. To minimize this disturb, the buoy have been weighted to reduce the area exposed to the wind, and the fins have been located about 20cm in depth, as displayed in Figure 5. The main dimensions of the buoy are reported in Table 1.


Table 1. The designed buoy dimensions and weight.

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 375

The preliminary tests have been performed on two buoy models aiming primarily to verify the feasibility of the measurement campaign and to highlight possible critical points regarding the devices used and logistical activities related to the release and recovery of the Lagrangian buoys. The buoys have been released in marine water to verify their stability, floating level, flow traceability, data acquisition, visibility and handling. A picture of the floating buoys during the tests is given in Figure 7, while the measured trajectories are overlapped to those derived during the final tests and reported in Figure 10. As a result of

the buoys are very stable in marine water (even in presence of waves) and seem to

 the floating level is so that almost 90% of the buoy is submerged; the part coming out of water surface is required to recover the buoy after the end of the measurements;

the tests, the following specific aspects have been pointed out:

follow very well the local flow direction;

Fig. 7. Two drifting buoys during the preliminary tests.

Fig. 6. GPS Data logger.

**c. Preliminary Tests** 

Fig. 5. Sketch of the Lagrangian buoy used in the present measurements.


Table 2. GPS Data Logger technical specifications

#### **b. Electronic Transmission**

The buoys are equipped with a GPS (Kaplan & Hegarty 2002) antenna Transystem i-Blue 747 which is an economic and functional satellite navigation system with storage of positions in time of the buoys on the on board data logger (maximum number of points equal to 1,25105, one every second). This device is shown in Figure 6, while in table 2 the technical specifications are summarized. It uses a GPS Chip MTK with Frequency L1, 1575.42 MHz C/A Code 1.023MHz chip rate Channels 51 CH for tracking and Antenna Built-in patch antenna with LNA Datum WGS-84. The recording is performed switching the instrument to mode Nav-Log and storing the position data calculated by the GPS with an internal memory. The data are exported in ASCII format NMEA-0183 by connecting the device to the USB port of the PC.

Fig. 6. GPS Data logger.

374 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

1

2

3

4

5

1 – Optical Target 2 - Cabinet with GPS System 3 – Air 4 - Ballast 5 - Fins System

Fig. 5. Sketch of the Lagrangian buoy used in the present measurements.

BatteryLi-Ion, Charging time 3 h Battery, Operation Time 32 h Operating Conditions: temperature -10°C to +60°C Operating Conditions: humidity 5% to 90% Accuracy on position 3.0 m Accuracy on velocity 0.1 m/s Velocity range 0 m/s to 515 m/s Maximum acceleration 4 g

Data bit 8

Weight 64 g

Table 2. GPS Data Logger technical specifications

**b. Electronic Transmission** 

device to the USB port of the PC.

Protocols NMEA-0183 (V3.01) - GGA,

Size 46.5W x 72.2L x 20H mm

Data Log up to 125,000 way points

The buoys are equipped with a GPS (Kaplan & Hegarty 2002) antenna Transystem i-Blue 747 which is an economic and functional satellite navigation system with storage of positions in time of the buoys on the on board data logger (maximum number of points equal to 1,25105, one every second). This device is shown in Figure 6, while in table 2 the technical specifications are summarized. It uses a GPS Chip MTK with Frequency L1, 1575.42 MHz C/A Code 1.023MHz chip rate Channels 51 CH for tracking and Antenna Built-in patch antenna with LNA Datum WGS-84. The recording is performed switching the instrument to mode Nav-Log and storing the position data calculated by the GPS with an internal memory. The data are exported in ASCII format NMEA-0183 by connecting the

GSA, GSV, RMC (default)

### **c. Preliminary Tests**

The preliminary tests have been performed on two buoy models aiming primarily to verify the feasibility of the measurement campaign and to highlight possible critical points regarding the devices used and logistical activities related to the release and recovery of the Lagrangian buoys. The buoys have been released in marine water to verify their stability, floating level, flow traceability, data acquisition, visibility and handling. A picture of the floating buoys during the tests is given in Figure 7, while the measured trajectories are overlapped to those derived during the final tests and reported in Figure 10. As a result of the tests, the following specific aspects have been pointed out:


Fig. 7. Two drifting buoys during the preliminary tests.

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 377

*Test preparation.* The first part of the test was dedicated to the preparation and mounting of the buoys and to the set up of the logistics with port authorities to stop vessels during the test period. At the end about 100 Lagrangian buoys were set-up, 30 of them mounting the GPS (plus fins and targets), while the other 70 are used for visual inspection of the

*Buoy Release and data acquisition.* After the preparation phase, the buoys were released at about 200 meters from the mouth of the river from the stern of the support boat as displayed in Figure 9 and data acquisition of their positions started. To measure the displacements of

*Buoy Recovery.* After a period of about 3 hours, the buoys have been led back on board and all the devices were switched off. All the GPS were ready to be transported into the

At this stage, data download and processing is performed in order to derive the buoys trajectories. In particular, the sequential steps of analysis consist of downloading GPS data, creating a comprehensive data set, data pre-processing, correcting GPS by reference position, data processing and filtering, deriving velocity fields and comparisons. To this end, GPS are connected to PC and the tracks downloaded in the format defined in the initial configuration. In our case, the format used was NMEA-0183 (National Marine Electronics Association). This format allows to obtain the position data including the altitude and speed. As mentioned above, scripts are used for data analysis as the software supplied with the GPS data logger was unable to handle a big amount of data. Once exported in ASCII

*Raw data acquisition.* Once connected to the PC at USB port, the GPS devices allow to view the raw tracks stored in the data-logger and to store the data in the desired format. With the included software the downloaded raw tracks can be viewed as presented in Figure 10. The GPS data given in ASCII format (NMEA type), are easily exported into spreadsheet form, extracting only the fields of interest (sample number, latitude, longitude, altitude and

The final test was split into three different phases:

laboratory to start the processing phase.

**7. Data analysis and results** 

format data are analyzed as follows:

phenomenon. All these buoys were led onto the supporting boats.

the buoys the devices have acquired samples at a data rate equal to 1Hz.

Fig. 9. Buoys release along the river mouth at about 200 m from the outlet.


### **6. Measurement campaign**

The measurement campaign was performed at the Pescara river mouth located in the shallow coastal environment of the Adriatic Sea. In Figure 8, a satellite image of the region considered in this campaign is presented. The main characteristics of this area are the presence of the harbor on the right side of the river mouth, the shoreline on the left and the big breakwater recently built, which influences the flow outcome and gives rise to significant environmental effects. Specifically, the dispersion of polluted water from the river, the possible increase of sediments and the loss of biodiversity should be addressed.

Fig. 8. Measurement region with the river mouth, the breakwater and the harbor.

The present activity aims to setup a method to measure the effective velocity field in order to investigate some possible change or modifications of the harbor and related structures. From the geometrical and dynamical point of views, such a problem is complex, due to the interactions of the river flow with the sea stream and with marine structure, as it is well visible by the satellite image. However, this activity has also a much general validity which can be adapted to similar conditions.

The final test was split into three different phases:

376 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

 the position where buoys are released is crucial and the best place is as close as possible to the center of the river, because close to the boundaries they move into the boundary layer, thus decreasing their speed and increasing the risk to stop somewhere under the

the time scale for the whole phenomenon to be completed, from the river mouth to the

 to avoid unnecessary and difficult interpretation of data, it is useful to acquire the GPS signal only for the time required by the test, therefore to turn-on the GPS just before

the management program bundled with the GPS (GPS Photo Tagger) cannot handle

The measurement campaign was performed at the Pescara river mouth located in the shallow coastal environment of the Adriatic Sea. In Figure 8, a satellite image of the region considered in this campaign is presented. The main characteristics of this area are the presence of the harbor on the right side of the river mouth, the shoreline on the left and the big breakwater recently built, which influences the flow outcome and gives rise to significant environmental effects. Specifically, the dispersion of polluted water from the river, the possible increase of sediments and the loss of biodiversity should be addressed.

putting the buoy into the water and turn-off immediately after recovering;

Fig. 8. Measurement region with the river mouth, the breakwater and the harbor.

The present activity aims to setup a method to measure the effective velocity field in order to investigate some possible change or modifications of the harbor and related structures. From the geometrical and dynamical point of views, such a problem is complex, due to the interactions of the river flow with the sea stream and with marine structure, as it is well visible by the satellite image. However, this activity has also a much general validity which

main breakwater, is at least 30 minutes and no more than 3 hours;

many tracks simultaneously, so an appropriate script is needed.

docks;

**6. Measurement campaign** 

can be adapted to similar conditions.

*Test preparation.* The first part of the test was dedicated to the preparation and mounting of the buoys and to the set up of the logistics with port authorities to stop vessels during the test period. At the end about 100 Lagrangian buoys were set-up, 30 of them mounting the GPS (plus fins and targets), while the other 70 are used for visual inspection of the phenomenon. All these buoys were led onto the supporting boats.

*Buoy Release and data acquisition.* After the preparation phase, the buoys were released at about 200 meters from the mouth of the river from the stern of the support boat as displayed in Figure 9 and data acquisition of their positions started. To measure the displacements of the buoys the devices have acquired samples at a data rate equal to 1Hz.

*Buoy Recovery.* After a period of about 3 hours, the buoys have been led back on board and all the devices were switched off. All the GPS were ready to be transported into the laboratory to start the processing phase.

Fig. 9. Buoys release along the river mouth at about 200 m from the outlet.

### **7. Data analysis and results**

At this stage, data download and processing is performed in order to derive the buoys trajectories. In particular, the sequential steps of analysis consist of downloading GPS data, creating a comprehensive data set, data pre-processing, correcting GPS by reference position, data processing and filtering, deriving velocity fields and comparisons. To this end, GPS are connected to PC and the tracks downloaded in the format defined in the initial configuration. In our case, the format used was NMEA-0183 (National Marine Electronics Association). This format allows to obtain the position data including the altitude and speed. As mentioned above, scripts are used for data analysis as the software supplied with the GPS data logger was unable to handle a big amount of data. Once exported in ASCII format data are analyzed as follows:

*Raw data acquisition.* Once connected to the PC at USB port, the GPS devices allow to view the raw tracks stored in the data-logger and to store the data in the desired format. With the included software the downloaded raw tracks can be viewed as presented in Figure 10. The GPS data given in ASCII format (NMEA type), are easily exported into spreadsheet form, extracting only the fields of interest (sample number, latitude, longitude, altitude and

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 379

Fig. 11. Reference fixed positions along the harbor dock and coordinates.

even if the correction is smaller than 0.3 m.

1

Indeed, when analyzing the sample distribution of the position of the fixed point GPS in UTM coordinates, it is not possible to recover a well defined probability density distribution. Rather, data are largely scattered and the mean value does not represent the most probable or a meaningful value. In Figure 12, at the top, the coordinates on the (*latitude, longitude*) plane are presented showing that none of the acquired data coincides with the mean value, thus indicating the fact that different ensemble of data are grouped together. Considering that the GPS is linked to a given satellite configuration for time intervals not longer than a few minutes, it can be argued that the observed scattering id due to the change of such a configuration in time. This is confirmed by the probability density distributions of the latitude and longitude given in Figure 12 at the bottom, where the overlapping of two distinct almost Gaussian distributions is noticed for both. So far, the mean value is simply the one among the two distributions. It is possible to correct this additional bias error by selecting which of the distribution is related to each period of time,

*Processing and data filtering (smoothing spline).* The data acquired by GPS once corrected by the geographical reference are still subject to random errors due to the factors previously mentioned. These errors give rise to some noise in the derived buoy trajectories. Graphically, this is represented in Figure 13 where all raw measured trajectories are shown. Although the general features of the flow field can be derived, these errors could give strong oscillations especially when differentiating the data to derive the buoy velocity. Therefore, a smoothing

where *Y*i are the measured data (at time *x*i), is the smoothing spline estimator (to be determined), '' is its second-order derivative and is a positive coefficient taken equal to 2103. The result of this spline is presented in Figure 14. The trajectories are now much smoother than before and the fluid-mechanics information can now be derived easily.

spline filter among the acquired *n* data has been applied by minimizing the quantity

1 2 2

( ( )) ''( ) . ˆ ˆ *<sup>n</sup>*

*Y x x dx*

*<sup>n</sup> <sup>x</sup> i i <sup>x</sup> <sup>i</sup>*

speed). For each GPS a file containing the tracks of the stored trajectory is exported. *Differential correction of GPS data with reference position.* The GPS signal is affected both by random and bias errors. The main causes of failure are usually the variations of the orbits of satellites, the timing error of the satellites (different stages) and the atmospheric effects on the signal (weather, ionosphere disturbances). To reduce such bias errors, thus improving the precision, a differential GPS is used which provides a correction by referring to another reference GPS placed at a known position. In this way, it is possible to correct data to attain an accuracy up to 10 cm. The possible drawback is that this reference correction can be used only in conditions in which the position of the reference location is known very well.

Fig. 10. Raw trajectories of the Lagrangian buoys as measured by the GPS. The white and yellow line represent the two buoys trajectories during the preliminary tests.

In the present experiments, a fixed GPS, of the same type as those on board, has been placed at a point with known coordinates, and the position was acquired for the whole duration of the experiment. The chosen location has been identified on the outer edge of the dock of the river Pescara on the right side as displayed in Figure 11. It has the following WGS84 coordinates:

Reference position: coord\_rif Latitude: 42.469628 ° Longitude: 14.229803 °

Simultaneously to the GPS released with the buoys, also the acquisition of about 3500 samples of the fixed-point GPS position was performed and the results were analyzed in post-processing to make bias corrections. The measured positions by reference GPS were also corrected by knowing the exact point where the reference GPS is placed (differences around 1-10 m as displayed in Figure 11). Lastly, all the GPS position were computed as the difference between the true location and the median value of samples of fixed point reference. As a result, with this correction the effective accuracy of GPS data is under 1 m. It should be emphasized as the only possible correction on the data position is relative to the average of samples collected, thus reducing only the bias error. On the other hand, the use of the instantaneous data to correct even random errors (e.g. timing satellites) is not possible because it would require information on the phases of the satellites, currently not available with this low-cost technology.

speed). For each GPS a file containing the tracks of the stored trajectory is exported. *Differential correction of GPS data with reference position.* The GPS signal is affected both by random and bias errors. The main causes of failure are usually the variations of the orbits of satellites, the timing error of the satellites (different stages) and the atmospheric effects on the signal (weather, ionosphere disturbances). To reduce such bias errors, thus improving the precision, a differential GPS is used which provides a correction by referring to another reference GPS placed at a known position. In this way, it is possible to correct data to attain an accuracy up to 10 cm. The possible drawback is that this reference correction can be used

only in conditions in which the position of the reference location is known very well.

Fig. 10. Raw trajectories of the Lagrangian buoys as measured by the GPS. The white and

In the present experiments, a fixed GPS, of the same type as those on board, has been placed at a point with known coordinates, and the position was acquired for the whole duration of the experiment. The chosen location has been identified on the outer edge of the dock of the river Pescara on the right side as displayed in Figure 11. It has the following WGS84

Simultaneously to the GPS released with the buoys, also the acquisition of about 3500 samples of the fixed-point GPS position was performed and the results were analyzed in post-processing to make bias corrections. The measured positions by reference GPS were also corrected by knowing the exact point where the reference GPS is placed (differences around 1-10 m as displayed in Figure 11). Lastly, all the GPS position were computed as the difference between the true location and the median value of samples of fixed point reference. As a result, with this correction the effective accuracy of GPS data is under 1 m. It should be emphasized as the only possible correction on the data position is relative to the average of samples collected, thus reducing only the bias error. On the other hand, the use of the instantaneous data to correct even random errors (e.g. timing satellites) is not possible because it would require information on the phases of the satellites, currently not available

yellow line represent the two buoys trajectories during the preliminary tests.

coordinates:

Reference position: coord\_rif

Latitude: 42.469628 ° Longitude: 14.229803 °

with this low-cost technology.

Fig. 11. Reference fixed positions along the harbor dock and coordinates.

Indeed, when analyzing the sample distribution of the position of the fixed point GPS in UTM coordinates, it is not possible to recover a well defined probability density distribution. Rather, data are largely scattered and the mean value does not represent the most probable or a meaningful value. In Figure 12, at the top, the coordinates on the (*latitude, longitude*) plane are presented showing that none of the acquired data coincides with the mean value, thus indicating the fact that different ensemble of data are grouped together. Considering that the GPS is linked to a given satellite configuration for time intervals not longer than a few minutes, it can be argued that the observed scattering id due to the change of such a configuration in time. This is confirmed by the probability density distributions of the latitude and longitude given in Figure 12 at the bottom, where the overlapping of two distinct almost Gaussian distributions is noticed for both. So far, the mean value is simply the one among the two distributions. It is possible to correct this additional bias error by selecting which of the distribution is related to each period of time, even if the correction is smaller than 0.3 m.

*Processing and data filtering (smoothing spline).* The data acquired by GPS once corrected by the geographical reference are still subject to random errors due to the factors previously mentioned. These errors give rise to some noise in the derived buoy trajectories. Graphically, this is represented in Figure 13 where all raw measured trajectories are shown. Although the general features of the flow field can be derived, these errors could give strong oscillations especially when differentiating the data to derive the buoy velocity. Therefore, a smoothing spline filter among the acquired *n* data has been applied by minimizing the quantity

$$\sum\_{i=1}^{n} (Y\_i - \hat{\mu}(\alpha\_i))^2 + \lambda \int\_{x\_1}^{x\_n} \hat{\mu}"(\alpha)^2 \,d\alpha.$$

where *Y*i are the measured data (at time *x*i), is the smoothing spline estimator (to be determined), '' is its second-order derivative and is a positive coefficient taken equal to 2103. The result of this spline is presented in Figure 14. The trajectories are now much smoother than before and the fluid-mechanics information can now be derived easily.

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 381

Fig. 13. Raw trajectories of the GPS buoys, before filtering.

Fig. 14. Trajectories of the GPS buoys, after filtering.

Fig. 12. Spatial distributions of the data acquired at the fixed reference GPS position (at the top) and statistical distributions of latitude and longitude of these data.

*Coordinate transformation from WGS84 to UTM*. After completing the previous differential correction, the coordinates of the GPS have been converted from WGS84 to UTM format (Universal Traverse Mercator).

Fig. 12. Spatial distributions of the data acquired at the fixed reference GPS position (at the top) and statistical distributions of latitude and longitude of these data.

(Universal Traverse Mercator).

*Coordinate transformation from WGS84 to UTM*. After completing the previous differential correction, the coordinates of the GPS have been converted from WGS84 to UTM format

Fig. 13. Raw trajectories of the GPS buoys, before filtering.

Fig. 14. Trajectories of the GPS buoys, after filtering.

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 383

Fig. 16. Modules of the buoy velocity for x and y components (in m/s) *vs* time (in seconds),

Fig. 17. Absolute value of the buoy velocity (in m/s) over time (in seconds), GPS raw data

GPS raw data and interpolating lines.

and interpolating line.

Once obtained the final filtered coordinate data, these can be displayed in space (as in Figures 13 and 14) or in time as given in Figure 15 for one specific buoy. In this case the two coordinates are increasing in time with a similar behavior thus indicating that the buoy moved along a diagonal as the one colored in yellow in Figure 10. For increasing time, the horizontal coordinate has a maximum and then decreases, thus indicating that the buoy is turning on the left side of the field, whereas the vertical coordinate continues to increase departing from the river mouth. A displacement equal to several hundred meters is attained after about 1500s, thus indicating an average velocity equal to 0.3 m/s for both velocity components. Similar information can be derived for the other buoys. From plots like that given in Figure 15, it is possible to derive the velocity of the buoy. The two velocity components in the measurement plane can be computed by centered differences on the positions dividing by the time interval among data acquisition (1 s). An example is given in Figures 16 for the two velocity components separately and in Figure 17 for the absolute value of the velocity (the trajectory is the one displayed in Figure 15). At a first sight, the velocity behavior appears very noise regardless of the filtering applied to the data in position. However, it is still possible to derive meaningful behaviors if interpolation are performed as reported in the figure (consider that the large oscillations are on a time scale of 1 s, whereas the useful information are on time scales one or two order of magnitude larger, so that averaging over 10-100 samples is reasonable). As expected from the previous raw computation, the velocity components have values ranging in the interval (0 - 0.9) m/s and the maximum value is observed just after 500 s as in Figure 15. After about 2000 s the horizontal velocity is almost vanished, whereas the vertical one attains a constant value around 0.5 m/s. Similar information can be derived from the plot given in Figure 17.

Fig. 15. Values of x and y position in time (in meters) of GPS buoys *vs* time (in seconds) with interpolating fits.

Once obtained the final filtered coordinate data, these can be displayed in space (as in Figures 13 and 14) or in time as given in Figure 15 for one specific buoy. In this case the two coordinates are increasing in time with a similar behavior thus indicating that the buoy moved along a diagonal as the one colored in yellow in Figure 10. For increasing time, the horizontal coordinate has a maximum and then decreases, thus indicating that the buoy is turning on the left side of the field, whereas the vertical coordinate continues to increase departing from the river mouth. A displacement equal to several hundred meters is attained after about 1500s, thus indicating an average velocity equal to 0.3 m/s for both velocity components. Similar information can be derived for the other buoys. From plots like that given in Figure 15, it is possible to derive the velocity of the buoy. The two velocity components in the measurement plane can be computed by centered differences on the positions dividing by the time interval among data acquisition (1 s). An example is given in Figures 16 for the two velocity components separately and in Figure 17 for the absolute value of the velocity (the trajectory is the one displayed in Figure 15). At a first sight, the velocity behavior appears very noise regardless of the filtering applied to the data in position. However, it is still possible to derive meaningful behaviors if interpolation are performed as reported in the figure (consider that the large oscillations are on a time scale of 1 s, whereas the useful information are on time scales one or two order of magnitude larger, so that averaging over 10-100 samples is reasonable). As expected from the previous raw computation, the velocity components have values ranging in the interval (0 - 0.9) m/s and the maximum value is observed just after 500 s as in Figure 15. After about 2000 s the horizontal velocity is almost vanished, whereas the vertical one attains a constant value

around 0.5 m/s. Similar information can be derived from the plot given in Figure 17.

Fig. 15. Values of x and y position in time (in meters) of GPS buoys *vs* time (in seconds) with

interpolating fits.

Fig. 16. Modules of the buoy velocity for x and y components (in m/s) *vs* time (in seconds), GPS raw data and interpolating lines.

Fig. 17. Absolute value of the buoy velocity (in m/s) over time (in seconds), GPS raw data and interpolating line.

Full Field Measurements in a River Mouth by Means of Particle Tracking Velocimetry 385

The hydrodynamic field of the mouth of the river Pescara has been investigated, covering an area of 2 km x 1 km and performing measurement on floating buoys in order to get

The Particle Tracking Velocimetry (PTV) technique has been successfully applied to this phenomenology, by using a set of drifting buoy equipped with GPS system measuring consecutive positions in time. The determination of the best buoy to be used for this specific

 Once tested, the buoys have been released into the sea for a measurement campaign, obtaining a characterization of the hydrodynamic field in terms of trajectories and velocity

After data pre and post-processing, the reconstructed field allows to derive information on the behavior close or far from the river mouth and so on the possible consequences on the

Specifically, the velocity is clearly larger at the river mouth, decreasing when the river water spreads into the sea. Other two important features to be pointed out, are that the tracer are mostly directed towards the left part of the field and this could depend on the sea stream and waves during the experiments, as well on the curved breakwater placed in front of the river. Secondly, probably independently on the sea conditions, there is a considerable number of tracers which are trapped on the right part of the field and start recirculating with also negative velocities as an effect of the recently added harbor docks and structures. The experimental setup together with the methodology have demonstrated the possibility to derive the fluid dynamics features of the mouth of the river using very simple and low cost devices (drifting buoys) that have been studied and designed for the specific survey. In this context important conclusions have been achieved especially observing the interactions between the flow and the marine structures, thus representing a high value result to

The increase of the number of buoys (thus increasing the spatial resolution of the measurement), the possible additional simultaneous measurement of temperature and other atmospheric and sea parameters, the possibility of using a variable height of the fins to measure also the flow stream at different depths are some of the possible improvements that

Apsley, D. and Hu, W., 2003, CFD simulation of two- and three-dimensional free-surface flow. International *Journal for Numerical Methods in Fluids*, vol. 42, pp. 465–491. Balas L., Ozhan E., 2000: "An Implicit three-Dimensional Numerical Model to Simulate

Davis, R. E., 1985, Drifter observations of coastal currents during CODE. The method and descriptive view, *Journal of Geophysical Research*, vol. 90, pp. 4741-4755.

Transport Processes in Coastal Water Bodies", *Journal of Computational Physics*, vol.

purpose, the consequent set-up and tests have been performed step by step.

**8. Conclusions and future developments** 

improve the harbor impact on the coastal zone.

the authors are going to test in the near future.

34, pp. 307-339.

components in the plane.

environment.

**9. References** 

information on flow diffusion from the river onto the sea.

Fig. 18. Trajectories of buoys and geographical distribution of the absolute value of the velocity (in m/s) calculated on filtered data.

Therefore, it is possible to establish that after about 500 s, this specific buoy felt an increase of the velocity which is then decreasing slowly to a constant value after about 2000 s.

To connect this behavior in time to the spatial position and to a general view of the flow field, the buoy trajectories have been reported on the geographical reference of the river mouth. This has been performed in Figure 18, where the entire set of buoy trajectories is displaced. The color code represents the velocity absolute value. It is possible to notice several aspects:


The quality of these results is high and the data contains a large quantity of information, so that the measurement of Lagrangian trajectories by means of floating boys equipped with GPS fulfills all the initial requirements. Therefore, from such an analysis it is clear how large are the potential applications of the tested technique in similar or different conditions.

### **8. Conclusions and future developments**

384 The Particle Image Velocimetry – Characteristics, Limits and Possible Applications

Fig. 18. Trajectories of buoys and geographical distribution of the absolute value of the

of the velocity which is then decreasing slowly to a constant value after about 2000 s.

Therefore, it is possible to establish that after about 500 s, this specific buoy felt an increase

To connect this behavior in time to the spatial position and to a general view of the flow field, the buoy trajectories have been reported on the geographical reference of the river mouth. This has been performed in Figure 18, where the entire set of buoy trajectories is displaced. The color code represents the velocity absolute value. It is possible to notice





The quality of these results is high and the data contains a large quantity of information, so that the measurement of Lagrangian trajectories by means of floating boys equipped with GPS fulfills all the initial requirements. Therefore, from such an analysis it is clear how large are the potential applications of the tested technique in similar or different conditions.

trapped into the recirculation region close to the harbor dock.

velocity (in m/s) calculated on filtered data.

several aspects:

buoys;

the left part of the field;

as in jet flows;

The hydrodynamic field of the mouth of the river Pescara has been investigated, covering an area of 2 km x 1 km and performing measurement on floating buoys in order to get information on flow diffusion from the river onto the sea.

The Particle Tracking Velocimetry (PTV) technique has been successfully applied to this phenomenology, by using a set of drifting buoy equipped with GPS system measuring consecutive positions in time. The determination of the best buoy to be used for this specific purpose, the consequent set-up and tests have been performed step by step.

 Once tested, the buoys have been released into the sea for a measurement campaign, obtaining a characterization of the hydrodynamic field in terms of trajectories and velocity components in the plane.

After data pre and post-processing, the reconstructed field allows to derive information on the behavior close or far from the river mouth and so on the possible consequences on the environment.

Specifically, the velocity is clearly larger at the river mouth, decreasing when the river water spreads into the sea. Other two important features to be pointed out, are that the tracer are mostly directed towards the left part of the field and this could depend on the sea stream and waves during the experiments, as well on the curved breakwater placed in front of the river. Secondly, probably independently on the sea conditions, there is a considerable number of tracers which are trapped on the right part of the field and start recirculating with also negative velocities as an effect of the recently added harbor docks and structures.

The experimental setup together with the methodology have demonstrated the possibility to derive the fluid dynamics features of the mouth of the river using very simple and low cost devices (drifting buoys) that have been studied and designed for the specific survey. In this context important conclusions have been achieved especially observing the interactions between the flow and the marine structures, thus representing a high value result to improve the harbor impact on the coastal zone.

The increase of the number of buoys (thus increasing the spatial resolution of the measurement), the possible additional simultaneous measurement of temperature and other atmospheric and sea parameters, the possibility of using a variable height of the fins to measure also the flow stream at different depths are some of the possible improvements that the authors are going to test in the near future.

### **9. References**


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Griffa, A., A.D. Kirwan, A.J. Mariano, T.M. Özgökmen and T. Rossby, 2007: *Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics.* Cambridge University Press Haza, A.C., T.M. Özgökmen, A. Griffa, A. Molcard, P.M. Poulain, and G. Peggion, 2010:

Lumpkin, R. and M. Pazos, 2006, Measuring surface currents with Surface Velocity Program

Kanarska Y, Shchepetkin A, & McWilliams JC, 2007: Algorithm for non-hydrostatic dynamics in the Regional Oceanic Modeling System, *Ocean Modelling*, vol. 18, pp. 143-174. Kaplan E and Hegarty C, 2002, *Understanding GPS: Principles and Applications*, Second

Lacorata, G., Aurell, E., Vulpiani, A (2001) Drifter dispersion in the Adriatic Sea: Lagrangian

Lalli F., Berti D., Miozzi M., Miscione F., Porfidia B., Serva L., Vittori E., Romano G.P. (2001),

Lalli F, Bruschi A, Lama R, Liberti L, Mandrone S, Pesarino V, 2010, Coanda effect in coastal

McNeely J. A., Gadgil M., Leveque C., Padock C., Redford K., 1995, Human influence on

Miozzi M, Lalli F, Romano GP, 2010, Experimental investigation of a free-surface turbulent

Özgökmen T, 2011, *Large Eddy Simulations of Submesoscale Flows,* La Londe Coastal

Selsor, H. D., 1993. Data from the sea: Navy drift buoy program. *Sea Technology,* vol. 34(12),

Shibayama T, (2009), *Coastal Processes—Concepts in Coastal Engineering and their Applications* 

Tropea C and Foss JF, 2007, *Handbook of Experimental Fluid Mechanics*, Springer- Verlag. Wang Y, 2009, *Remote Sensing of Coastal Environment*, CRC Press Taylor & Francis Group. Wang Y, Yuan D, Nie H, 2011, Numerical simulation of sediment transport in Bohai Bay,

*Water Resource and Environmental Protection* (ISWREP), 2011

Analysis of Breakwater-Induced Environmental Effects at Pescara (Adriatic Sea, Italy) Channel-Harbor, *11th International Offshore and Polar Engineering Conference*,

biodiversity. In *Global biodiversity assessment*. (V. H. Heywood and R. T. Watson,

data and chaotic model. *Annales Geophysicae* vol. 19(1), pp. 121-9.

ed.), pp. 771–821. Cambridge University Press, Cambridge.

jet with Coanda effect. *Experiments in Fluids*, vol. 49(1) pp. 341-343. Munson BR, Young DF, Okiishi TH, 1994, *Fundamentals of Fluid Mechanics*, Wiley and Sons. Niiler, P. P. , J. D. Paduan, 1995, Wind-driven motions in the northeast Pacific as measured

by Lagrangian drifters. *J. Phys. Oceanogr.* Vol. 25, pp. 2819-2830.

*Report Istituto Nazionale di Oceanografia e di Geofisica*, vol. 38

*More Sustainable Development,* pp. 108 – 115.

Edition, Artech House.

Stavanger, Norway.

pp. 53-58.

Kirwan, A. J. Mariano, T. Ozgokmen, and T. Rossby.

flows, *Coastal Engineering*, vol. 57, pp. 278-289.

Oceanography Summer School, September 2011.

*to Multifarious Environments*, World Scientific.

Surface circulation in the Eastern Mediterranean using Lagrangian drifters. *Internal* 

Transport properties in small scale coastal flows: relative dispersion from VHF radar measurements in the Gulf of La Spezia. O*cean Dynamics*, vol. 60, pp. 861-882. Hillman G, Rodriguez A, Pagot M, Tyrrell D, Corral M, Oroná C, and Möller O, 2007, 2D

Numerical Simulation of Mangueira Bay Hydrodynamics. Journal of Coastal Research: *Special Issue 47 - ECOSUD: Estuaries & Coastal Areas: Basis and Tools for a* 

drifters: the instrument, its data, and some recent results. *Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics* (LAPCOD), Chapter 2, ed. A. Griffa, A. D.

## *Edited by Giovanna Cavazzini*

The Particle Image Velocimetry is undoubtedly one of the most important technique in Fluid-dynamics since it allows to obtain a direct and instantaneous visualization of the flow field in a non-intrusive way. This innovative technique spreads in a wide number of research fields, from aerodynamics to medicine, from biology to turbulence researches, from aerodynamics to combustion processes. The book is aimed at presenting the PIV technique and its wide range of possible applications so as to provide a reference for researchers who intended to exploit this innovative technique in their research fields. Several aspects and possible problems in the analysis of large- and micro-scale turbulent phenomena, two-phase flows and polymer melts, combustion processes and turbo-machinery flow fields, internal waves and river/ocean flows were considered.

Photo by idrutu / iStock

The Particle Image Velocimetry - Characteristics, Limits and Possible Applications

The Particle Image

Velocimetry

Characteristics, Limits

and Possible Applications

*Edited by Giovanna Cavazzini*