**2. Boundary layer flows at the UNNE wind tunnel**

Next, measurement results obtained at the Prof. Jacek Gorecki wind tunnel of the UNNE (**Figure 1**) in three different boundary layer flows are analyzed. The UNNE wind tunnel is a 39.56-m-long channel where the air enters through a contraction to reach the test section. This is connected to the velocity regulator and to the blower, and then, the air passes through a diffuser before leaving the wind tunnel. The contraction has a honeycomb and a screen to uniform the airflow. The test section is a 22.8-m-long rectangular channel (2.40 m width, 1.80 m height) where two rotating tables are located to place test models. Conditions of zero-pressure-gradient boundary layers can be obtained by the vertical displacement of the upper wall. The blower has a 2.25 m diameter and is driven by a 92 kW electric motor at 720 rpm.

The first of these flows correspond to a boundary layer developed on the smooth floor of the wind tunnel test section. Then, the results obtained for two ABL simulations are analyzed. The first model corresponds to a full-depth simulation of the neutrally stable ABL and the second to a part-depth model.

**Figure 1.** *The Prof. Jacek Gorecki boundary layer wind tunnel of the UNNE.*

*Boundary Layer Flows - Theory, Applications and Numerical Methods*

the case of a neutral boundary layer.

\_\_\_\_

\_\_\_\_\_

longitudinal pressure gradient [3].

for atmospheric boundary layer [2].

effects are negligible.

topographical features could cause highly complex flows. The depth of the atmospheric boundary layer is typically 100 m during the nighttime stable conditions, and this could reach 1 km in daytime unstable conditions [2]. The Prandtl logarithmic law (Eq. (1)), proposed from similarity theories, can be used near the surface in

> 0.4 ln\_\_\_\_ *z* − *zd*

where *U* is the mean velocity, *u\** is the friction velocity, *z*0 is known as the roughness height, and *zd* is defined as the zero-plane displacement for very rough surface. The potential law (Eq. (2)) is also widely used in wind engineering to characterize the vertical velocity distribution. The values for the exponent *α* vary between 0.10 and 0.43 and the boundary layer thickness *zg* between 250 and 500 m, according to the terrain type [2]. This law is verifiable in the case of strong winds and neutral stability conditions that must be considered for structural analysis.

*<sup>z</sup>*<sup>0</sup> (1)

<sup>α</sup> (2)

*U*(*z*) *<sup>u</sup>* <sup>∗</sup> <sup>=</sup> \_\_\_1

> *U*(*z*) *U*(*zg*) = ( \_\_*z zg*)

Similarity requirements corresponding to studies of atmospheric flow in the laboratory can be obtained by the dimensional analysis. The equations are expressed in dimensionless form by means of reference parameters that lead to the following set of non-dimensional groups or numbers: Reynolds number, Prandtl number, Rossby number, and Richardson number. These dimensionless parameters must be in the same value with the model and prototype to obtain the exact similarity, and, in addition, there must be geometric similarity and similarity of the boundary conditions, including incident flow, surface temperature, heat flow, and

Geometric scales defined between the simulated laboratory boundary layer and the atmospheric boundary layer are generally <1:200, velocities in the model and prototype have values of the same order, and the viscosity is the same for both cases. This results in the impossibility of reproducing the Reynolds number in low-speed wind tunnels; however, the effects of Reynolds number variation can be taken into account according to the type of wind tunnel test. On the other hand, the equality of the Prandtl number is obtained simply by using the same fluid in model and prototype, as in this case. The equality of the Rossby and Richardson numbers may not be considered for simulation of neutral ABL since Coriolis forces and thermal

In most laboratories it is more common to simulate the neutrally stratified boundary layer. This implies modeling the distribution of mean velocities, turbulence scales, and atmospheric spectrum [4]. The quality of these approximate models is simply evaluated by comparing the results expressed in dimensionless form with design values. Turbulence intensity distribution is commonly compared with values obtained by other authors [5] and by using Harris-Davenport formula

Atmospheric velocity fluctuations with frequencies upper than 0.0015 Hz define the micrometeorological spectral region. Interest of wind engineering is concentrated on this spectral turbulence region. von Kármán suggested an expression for the turbulence spectrum in 1948, and today this spectral formula is still used for wind engineering applications. According to Reference [2], the expression for the dimensionless spectrum of the longitudinal component of atmospheric turbulence

**126**

is given by Eq. (3):

Velocity and longitudinal velocity fluctuations were measured by a Dantec 56C constant temperature hot-wire anemometer connected to a Stanford amplifier with low- and high-pass analogic filters. Hot-wire signals were digitalized by a DAS-1600 A/D converter board controlled by a computer which was also used for the analysis of the results. Voltage output from hot wires was converted in mean velocity and velocity fluctuations [6, 7] by the probe calibration curves previously determined. Full spectra from longitudinal velocity fluctuations were obtained by juxtaposing three different partial spectra from three different sampling series, registered in the same location, each with a specific sampling frequency, designed as low, mean, and high frequencies. Then, the fast Fourier transform (FFT) algorithm was applied to each numerical series, and the corresponding longitudinal turbulence spectra were obtained.

### **2.1 The boundary layer obtained with empty tunnel**

The uniformity of the flow corresponding to the empty boundary layer wind tunnel is evaluated previously to implement physical models of turbulent flows. Deviations of mean velocity and turbulence intensity are measured to determine uniform flow zones and boundary layer thickness in the test section. Finally, longitudinal component of the turbulence spectrum is obtained from the boundary layer flow and from the uniform flow.

Dimensionless velocity profiles measured with the empty tunnel along a vertical line on the center of the rotating table of the test section (see reference [8]) and at positions 0.6 m to the right and left of this line are presented in **Figure 2**. The vertical coordinate *z* is measured from the floor, and *H* is the test section height equal to 1.80 m. Measurements are presented only for the lower half of the test section. The depth of the boundary layer is of about 0.3 m, and a good uniformity can be observed from the vertical velocity distributions. A maximal deviation of the mean velocity of about 3% is verified outside the boundary layer, by taking the velocity at the center of the channel as reference.

**129**

**Figure 3.**

*Physical Models of Atmospheric Boundary Layer Flows: Some Developments and Recent…*

Turbulence intensity distribution at the same locations shows values around 1% outside the boundary layer increasing, as expected, inside the boundary layer. Reference velocity for these tests was the velocity at the center of the channel, 27 m/s. The value of Reynolds number calculated with the hydraulic diameter of the

Turbulence spectra obtained inside and outside the boundary layer with the empty tunnel are presented in **Figure 3**. Inside the boundary layer, it is possible to observe higher values of fluctuation energy and a clear definition of the 5/3 declivity, characterizing Kolmogorov's inertial subrange. Outside the boundary layer, low turbulence levels produce a spectral definition only for frequencies

The complete boundary layer thickness of the ABL is simulated when a fulldepth simulation is developed. The Counihan method [9] was applied at the UNNE wind tunnel, and four 1.42-m-high elliptic vortex generators and a 0.23 m (b) barrier were used, together with prismatic roughness elements placed on the test

Velocity and longitudinal velocity fluctuations were measured by the same hot-wire anemometer system described above. Measurements of the mean velocity distribution were made along a vertical line on the center of rotating table and along lines 0.30 m to the right and left of this line. **Figure 5** shows the vertical velocity distribution, and at center, the same measured values are presented in a log-graph to verify the low part of the profile where the distribution of mean speeds is logarithmic. There is a good similarity among the three measured velocity profiles, and

Turbulence intensity distribution at the same locations is also shown in **Figure 5** on the right. The values are lower than those obtained by using Harris-Davenport formula for atmospheric boundary layer [2]. This behavior was verified by other authors

*DOI: http://dx.doi.org/10.5772/intechopen.86483*

section floor along 17 m (see **Figure 4**).

.

**2.2 Full-depth simulation of the atmospheric boundary layer**

the value of the exponent α obtained by fitting to Eq. (2) is 0.24.

[5] mainly in the points located above (*z*/*H* > 0.5).

*Spectral density function with the empty wind tunnel.*

test section was 3.67 × 106

minor than 70 Hz.

**Figure 2.** *Vertical profiles of mean velocity and turbulence intensity with the empty wind tunnel.*

*Physical Models of Atmospheric Boundary Layer Flows: Some Developments and Recent… DOI: http://dx.doi.org/10.5772/intechopen.86483*

Turbulence intensity distribution at the same locations shows values around 1% outside the boundary layer increasing, as expected, inside the boundary layer. Reference velocity for these tests was the velocity at the center of the channel, 27 m/s. The value of Reynolds number calculated with the hydraulic diameter of the test section was 3.67 × 106 .

Turbulence spectra obtained inside and outside the boundary layer with the empty tunnel are presented in **Figure 3**. Inside the boundary layer, it is possible to observe higher values of fluctuation energy and a clear definition of the 5/3 declivity, characterizing Kolmogorov's inertial subrange. Outside the boundary layer, low turbulence levels produce a spectral definition only for frequencies minor than 70 Hz.

#### **2.2 Full-depth simulation of the atmospheric boundary layer**

The complete boundary layer thickness of the ABL is simulated when a fulldepth simulation is developed. The Counihan method [9] was applied at the UNNE wind tunnel, and four 1.42-m-high elliptic vortex generators and a 0.23 m (b) barrier were used, together with prismatic roughness elements placed on the test section floor along 17 m (see **Figure 4**).

Velocity and longitudinal velocity fluctuations were measured by the same hot-wire anemometer system described above. Measurements of the mean velocity distribution were made along a vertical line on the center of rotating table and along lines 0.30 m to the right and left of this line. **Figure 5** shows the vertical velocity distribution, and at center, the same measured values are presented in a log-graph to verify the low part of the profile where the distribution of mean speeds is logarithmic. There is a good similarity among the three measured velocity profiles, and the value of the exponent α obtained by fitting to Eq. (2) is 0.24.

Turbulence intensity distribution at the same locations is also shown in **Figure 5** on the right. The values are lower than those obtained by using Harris-Davenport formula for atmospheric boundary layer [2]. This behavior was verified by other authors [5] mainly in the points located above (*z*/*H* > 0.5).

**Figure 3.** *Spectral density function with the empty wind tunnel.*

*Boundary Layer Flows - Theory, Applications and Numerical Methods*

**2.1 The boundary layer obtained with empty tunnel**

flow and from the uniform flow.

the channel as reference.

Velocity and longitudinal velocity fluctuations were measured by a Dantec 56C constant temperature hot-wire anemometer connected to a Stanford amplifier with low- and high-pass analogic filters. Hot-wire signals were digitalized by a DAS-1600 A/D converter board controlled by a computer which was also used for the analysis of the results. Voltage output from hot wires was converted in mean velocity and velocity fluctuations [6, 7] by the probe calibration curves previously determined. Full spectra from longitudinal velocity fluctuations were obtained by juxtaposing three different partial spectra from three different sampling series, registered in the same location, each with a specific sampling frequency, designed as low, mean, and high frequencies. Then, the fast Fourier transform (FFT) algorithm was applied to each numerical

series, and the corresponding longitudinal turbulence spectra were obtained.

The uniformity of the flow corresponding to the empty boundary layer wind tunnel is evaluated previously to implement physical models of turbulent flows. Deviations of mean velocity and turbulence intensity are measured to determine uniform flow zones and boundary layer thickness in the test section. Finally, longitudinal component of the turbulence spectrum is obtained from the boundary layer

Dimensionless velocity profiles measured with the empty tunnel along a vertical line on the center of the rotating table of the test section (see reference [8]) and at positions 0.6 m to the right and left of this line are presented in **Figure 2**. The vertical coordinate *z* is measured from the floor, and *H* is the test section height equal to 1.80 m. Measurements are presented only for the lower half of the test section. The depth of the boundary layer is of about 0.3 m, and a good uniformity can be observed from the vertical velocity distributions. A maximal deviation of the mean velocity of about 3% is verified outside the boundary layer, by taking the velocity at the center of

*Vertical profiles of mean velocity and turbulence intensity with the empty wind tunnel.*

**128**

**Figure 2.**

**Figure 4.** *Counihan vortex generators, barrier, and roughness elements of the full-depth boundary layer simulation.*

**Figure 5.** *Vertical mean velocity and turbulence intensity profiles measured for the full-depth boundary layer simulation.*

Three spectra obtained at positions *z* = 0.23, 0.58, and 0.97 m are presented in **Figure 6**. An important characteristic of the spectra is the presence of a clear region of the Kolmogorov's inertial subrange. The comparison of the results obtained through the simulations with the atmospheric boundary layer is made by means of dimensionless variables of the auto-spectral density and of the frequency using the von Kármán spectrum (Eq. (3)). A good agreement is observed at *z* = 0.23 m, but this agreement diminishes at positions *z* = 0.58 and 0.97 m, and this behavior is coincident with the behavior observed for the turbulence intensities.

These measurements were realized at velocity *Uref* ≈ 27 m/s, being *Uref* measured at gradient height *zg* = 1.16 and the corresponding Reynolds number value of Re ≈ 2.10 × 106 . A scale factor of 250 was calculated through the Cook's procedure [5], using the roughness length *z*0 and the integral scale *Lu* as key parameters. The

**131**

**Figure 7.**

**Figure 6.**

*Kármán spectrum.*

*Physical Models of Atmospheric Boundary Layer Flows: Some Developments and Recent…*

value of the roughness length was obtained by fitting mean velocity values to the logarithmic law, and the integral scale values were determined through the fitting of

Two Irwin-type generators separated 1.5 m were used to simulate the part-depth boundary layer by means of the Standen method [10]. The windward plate of the

*Dimensionless spectra obtained at different heights for the full-depth boundary layer simulation and the von* 

*Irwin vortex generators and roughness elements of the part-depth boundary layer simulation.*

*DOI: http://dx.doi.org/10.5772/intechopen.86483*

the measured spectrum to the design spectrum.

**2.3 Part-depth simulation of the atmospheric boundary layer**

*Physical Models of Atmospheric Boundary Layer Flows: Some Developments and Recent… DOI: http://dx.doi.org/10.5772/intechopen.86483*

value of the roughness length was obtained by fitting mean velocity values to the logarithmic law, and the integral scale values were determined through the fitting of the measured spectrum to the design spectrum.
