**1. Introduction**

Spray cooling of a hot body takes place when a dispersion of fine droplets impinges upon its surface to remove a large amount of heat by evaporation and convection (Deb & Yao, 1989). In metallurgical processes such as continuous casting of steel (Camporredondo et al., 2004) the surface temperature, Tw, of the hot steel strand exceeds considerably the saturation temperature, Ts, of the cooling liquid (water), i.e., Tw-Ts ranges between ~600 to 1100°C. These harsh temperature conditions have traditionally called for the use of high water impact fluxes (w, L/m2s) to remove the heat arriving to the surface as a result of the solidification of the liquid or semi-liquid core of the strand. The boundary between dilute and dense sprays has been specified at w= 2 L/m2s (Deb & Yao, 1989, Sozbir et al., 2003). In modern continuous casting machines the w found are well above this value. Most of the impingement area of the spray or mist jets will have w 10 L/m2s, with regions where w can be as large as ~110 L/m2s. Heat treatment of alloys requiring the rapid removal of large amounts of heat also makes use of dense sprays or mists (Totten & Bates, 1993).

Sprays and air-mists are dispersions of drops produced by single-fluid (e.g., water) and twin-fluid (e.g. water-air) nozzles, respectively. In sprays, the energy to fragment the water into drops is provided by the pressure drop generated across the narrow exit orifice, while in air-mists nozzles a high speed air-stream breaks the water-stream generating fine, fastmoving droplets (Lefebvre, 1989; Nasr et al., 2002). In air-mist nozzles with internal mixing and perpendicular inlets for the fluids, as those shown in Fig. 1, the water splatters against a deflector surface and the resulting splashes are further split by the shear forces exerted by the axial air-stream, which also accelerates the drops as they move along the mixing chamber toward the exit port. Thus, the liquid emerges in the form of drops with different sizes and velocities and with a non-uniform spatial distribution (Hernández et al., 2008).

In addition to w, the size, dd, and velocity, u, of the drops in dense air-mists play a crucial role in the cooling of highly superheated surfaces (Bendig et al., 1995; Jenkins et al., 1991; Hernández et al., 2011). This behavior stresses the important relationship between the heat transfer process and the droplet impact or deformation and break-up behavior. Since, for a specified fluid those two parameters, dd and u, determine the local impingement Weber number (Wezs= duzs2dd/), which in general has been agreed to characterize the impact behavior (Wachters & Westerling, 1966; Araki & Moriyama, 1981; Issa & Yao, 2005). As the

<sup>\*</sup> Corresponding Author

An Experimental and Computational Study of the Fluid Dynamics of Dense Cooling Air-Mists 3

the impingement region (Hatta et al., 1991a, 1991b). The researchers considered monodisperse drops with sizes of 1 and 10 µm and found that the motion of both phases depended strongly on the particle size. More recently, a computational model was developed to calculate the in-flight and impingement motion of air and droplets with a size distribution (Issa & Yao, 2005). The rebounding of multiple drops from the surface was simulated by extending empirical information regarding the variation of the normal coefficient of restitution of single droplets with the impingement Wezs. The authors claimed that large drops with high momentum tended to impinge closer to the stagnation point, whereas smaller drops tended to collision farther away because they were entrained by the air. In another study, the equation of motion for drops projected horizontally in quiescent air was solved considering sizes ranging from 100 to 1000 µm and velocities of 20 m/s and 50 m/s (Ciofalo et al., 2007). It was found that drops smaller than 100 µm would experience

large deflections due to gravity, and would never reach a plane beyond 0.25 m.

whole range of practical interest.

system for the nozzle.

following expression,

smaller than ±10 %.

**2. Experimental methods and conditions** 

The sprays and mists that have been studied experimentally and computationally are far apart from those used in important metallurgical processes. In recent studies the authors presented a 3-D computational fluid dynamic (CFD) Eulerian-Lagrangian model for free dense air-mist jets (Hernández et al., 2008). However, since new and rigorous experimental information has been generated the model has been refined in regard to the size distribution imposed at the nozzle orifice. The experimental information generated in this work has also enabled to carry out a detailed validation of the model. The model predicts very well the correlation between drop velocity and particle size, the velocity and trajectory of the drops and the water impact density as a function of the nozzle operating conditions, over the

A schematic of the experimental set-up used for measuring the mist parameters is displayed in Figure 1. It consists of: (a) a patternator for measuring water impact density distribution, (b) a particle/droplet image analysis, PDIA, system for acquiring and analyzing the images of fine moving droplets to determine their size and velocity and (c) a water and air supply

To determine w the nozzle was oriented horizontally and this parameter was evaluated collecting the drops entering tubes with an area a, to measure the total volume of water v accumulated during a period of time t in the bottles connected to the tubes. The collecting tubes were arranged forming a grid and their diameter and spacing are given in Figure 1. Hence, the local water impact flux at a position x-y-z was calculated according to the

)z,y,x(v )z,y,x(w

where (cos is the direction cosine of the angle formed between the nozzle axis and the line connecting the centers of the nozzle orifice and of a given tube, i.e., (a cos gives the projected area of a tube perpendicular to the direction of motion of the drops. The accuracy of the measured w distributions was verified by integrating w over the impingement area to compare it with the total water flow rate, W. In general, the computed W had an error

tcosa

(1)

impingement Weber number increases the drops tend to deform more widely, break more profusely, stay closer to the surface and agitate more intensively the liquid film formed by previous drops. Thus, it is clear that knowledge of the local parameters characterizing free mist-jets is needed to arrive to a quantitative description of the fluid dynamic interaction of drops with a surface and of the boiling-convection heat transfer that would result.

Experimentally, the water impact flux has been the parameter most frequently determined, using a patternator (Camporredondo et al., 2004; Puschmann & Specht, 2004). The drop size distribution in mists has often been measured by: (a) laser diffraction (Jenkins et al., 1991; Bul, 2001), (b) phase Doppler particle analysis, PDPA (Bendig et al., 1995; Puschmann & Specht, 2004) and (c) particle/droplet image analysis, PDIA (Minchaca et al., 2011). The last two methods allow the simultaneous determination of the droplet velocity and hence of the correlation between both parameters. To the best knowledge of the authors only PDIA has been used for the characterization of dense sprays and mists. Particle image velocimetry, PIV, has been employed for measuring the velocity of drops in dense mists, but the technique did not allow the simultaneous determination of size (Hernández et al., 2008). Recent works have presented a detailed experimental characterization of the local variation of w, dd and u obtained with typical air-mist nozzles, operating over a wide range of conditions of practical interest (Minchaca et al., 2011; Hernández et al., 2011).

The phenomena involved in the atomization of a liquid stream are very complex and therefore the generation of drops and their motion are generally treated separately. Knowledge of the influence of the fluid physical properties, nozzle design and operating conditions on atomization is crucial to generate drops with the size distribution that would perform better the task for which they are intended. The best well-known method for modeling drop size distributions is the empirical method (Babinski & Sojka, 2002). This consists in fitting a curve to data collected over a wide range of nozzles and operating conditions. In the case of nozzles with internal mixing and 90° intersecting streams of air and water, the number and volume frequency distributions of drop size have been adequately modeled by log-normal and Nukiyama-Tanasawa, NT, distribution functions (Minchaca et al., 2011), respectively. The statistical parameters of the distributions have been correlated with the water and air inlet pressures allowing the prediction of different characteristic mean diameters, over a wide range of operating conditions. Alternative modeling approaches are the maximum entropy and the discrete probability function methods (Babinski & Sojka, 2002).

Two-phase flow models generally treat the continuous phase (e.g., air) in an Eulerian frame of reference while the disperse phase (e.g., water droplets) is considered by either one of two approaches: (a) Eulerian representation, which treats it as a continuum whose characteristics (e.g., velocity, concentration, etc) are declared and updated at grid cells shared with the continuous phase, and (b) Lagrangian representation, where the drops characteristics (e.g., position, velocity, concentration, etc) are tracked along their path-lines (Crowe et al., 1998). The Eulerian-Eulerian approach is best suited for flows of monodisperse or narrow size range drops. But models have been developed to handle efficiently polydisperse sprays by describing the distribution of sizes through the moments of the droplet distribution function (Beck & Watkins, 2002). The Eulerian-Lagrangian approach can handle more efficiently a large range of particle sizes and give more details of the behavior of individual particles and of their interaction with walls. Both approaches use submodels to represent phenomena such as droplet break-up, droplet-droplet collisions, droplets-wall interaction, etc.

A two-dimensional (2-D) transient Eulerian-Lagrangian model was developed to describe the motion of air and drops in a domain that included the nozzle chamber, the free jet and the impingement region (Hatta et al., 1991a, 1991b). The researchers considered monodisperse drops with sizes of 1 and 10 µm and found that the motion of both phases depended strongly on the particle size. More recently, a computational model was developed to calculate the in-flight and impingement motion of air and droplets with a size distribution (Issa & Yao, 2005). The rebounding of multiple drops from the surface was simulated by extending empirical information regarding the variation of the normal coefficient of restitution of single droplets with the impingement Wezs. The authors claimed that large drops with high momentum tended to impinge closer to the stagnation point, whereas smaller drops tended to collision farther away because they were entrained by the air. In another study, the equation of motion for drops projected horizontally in quiescent air was solved considering sizes ranging from 100 to 1000 µm and velocities of 20 m/s and 50 m/s (Ciofalo et al., 2007). It was found that drops smaller than 100 µm would experience large deflections due to gravity, and would never reach a plane beyond 0.25 m.

The sprays and mists that have been studied experimentally and computationally are far apart from those used in important metallurgical processes. In recent studies the authors presented a 3-D computational fluid dynamic (CFD) Eulerian-Lagrangian model for free dense air-mist jets (Hernández et al., 2008). However, since new and rigorous experimental information has been generated the model has been refined in regard to the size distribution imposed at the nozzle orifice. The experimental information generated in this work has also enabled to carry out a detailed validation of the model. The model predicts very well the correlation between drop velocity and particle size, the velocity and trajectory of the drops and the water impact density as a function of the nozzle operating conditions, over the whole range of practical interest.

## **2. Experimental methods and conditions**

2 Advanced Fluid Dynamics

impingement Weber number increases the drops tend to deform more widely, break more profusely, stay closer to the surface and agitate more intensively the liquid film formed by previous drops. Thus, it is clear that knowledge of the local parameters characterizing free mist-jets is needed to arrive to a quantitative description of the fluid dynamic interaction of

Experimentally, the water impact flux has been the parameter most frequently determined, using a patternator (Camporredondo et al., 2004; Puschmann & Specht, 2004). The drop size distribution in mists has often been measured by: (a) laser diffraction (Jenkins et al., 1991; Bul, 2001), (b) phase Doppler particle analysis, PDPA (Bendig et al., 1995; Puschmann & Specht, 2004) and (c) particle/droplet image analysis, PDIA (Minchaca et al., 2011). The last two methods allow the simultaneous determination of the droplet velocity and hence of the correlation between both parameters. To the best knowledge of the authors only PDIA has been used for the characterization of dense sprays and mists. Particle image velocimetry, PIV, has been employed for measuring the velocity of drops in dense mists, but the technique did not allow the simultaneous determination of size (Hernández et al., 2008). Recent works have presented a detailed experimental characterization of the local variation of w, dd and u obtained with typical air-mist nozzles, operating over a wide range of

The phenomena involved in the atomization of a liquid stream are very complex and therefore the generation of drops and their motion are generally treated separately. Knowledge of the influence of the fluid physical properties, nozzle design and operating conditions on atomization is crucial to generate drops with the size distribution that would perform better the task for which they are intended. The best well-known method for modeling drop size distributions is the empirical method (Babinski & Sojka, 2002). This consists in fitting a curve to data collected over a wide range of nozzles and operating conditions. In the case of nozzles with internal mixing and 90° intersecting streams of air and water, the number and volume frequency distributions of drop size have been adequately modeled by log-normal and Nukiyama-Tanasawa, NT, distribution functions (Minchaca et al., 2011), respectively. The statistical parameters of the distributions have been correlated with the water and air inlet pressures allowing the prediction of different characteristic mean diameters, over a wide range of operating conditions. Alternative modeling approaches are the maximum entropy and the

Two-phase flow models generally treat the continuous phase (e.g., air) in an Eulerian frame of reference while the disperse phase (e.g., water droplets) is considered by either one of two approaches: (a) Eulerian representation, which treats it as a continuum whose characteristics (e.g., velocity, concentration, etc) are declared and updated at grid cells shared with the continuous phase, and (b) Lagrangian representation, where the drops characteristics (e.g., position, velocity, concentration, etc) are tracked along their path-lines (Crowe et al., 1998). The Eulerian-Eulerian approach is best suited for flows of monodisperse or narrow size range drops. But models have been developed to handle efficiently polydisperse sprays by describing the distribution of sizes through the moments of the droplet distribution function (Beck & Watkins, 2002). The Eulerian-Lagrangian approach can handle more efficiently a large range of particle sizes and give more details of the behavior of individual particles and of their interaction with walls. Both approaches use submodels to represent phenomena

such as droplet break-up, droplet-droplet collisions, droplets-wall interaction, etc.

A two-dimensional (2-D) transient Eulerian-Lagrangian model was developed to describe the motion of air and drops in a domain that included the nozzle chamber, the free jet and

drops with a surface and of the boiling-convection heat transfer that would result.

conditions of practical interest (Minchaca et al., 2011; Hernández et al., 2011).

discrete probability function methods (Babinski & Sojka, 2002).

A schematic of the experimental set-up used for measuring the mist parameters is displayed in Figure 1. It consists of: (a) a patternator for measuring water impact density distribution, (b) a particle/droplet image analysis, PDIA, system for acquiring and analyzing the images of fine moving droplets to determine their size and velocity and (c) a water and air supply system for the nozzle.

To determine w the nozzle was oriented horizontally and this parameter was evaluated collecting the drops entering tubes with an area a, to measure the total volume of water v accumulated during a period of time t in the bottles connected to the tubes. The collecting tubes were arranged forming a grid and their diameter and spacing are given in Figure 1. Hence, the local water impact flux at a position x-y-z was calculated according to the following expression,

$$\mathbf{w}(\mathbf{x}, \mathbf{y}, \mathbf{z}) = \frac{\mathbf{v}(\mathbf{x}, \mathbf{y}, \mathbf{z})}{\left(\mathbf{a} \cos \gamma\right)\mathbf{t}} \tag{1}$$

where (cos is the direction cosine of the angle formed between the nozzle axis and the line connecting the centers of the nozzle orifice and of a given tube, i.e., (a cos gives the projected area of a tube perpendicular to the direction of motion of the drops. The accuracy of the measured w distributions was verified by integrating w over the impingement area to compare it with the total water flow rate, W. In general, the computed W had an error smaller than ±10 %.

An Experimental and Computational Study of the Fluid Dynamics of Dense Cooling Air-Mists 5

controlled valve, to minimize flow rate variations, a mass flow-meter and a digital manometer. The results reported in this article are for a Casterjet 1/2-6.5-90 nozzle (Spraying Systems Co., Chicago, IL), whose operating diagram is displayed in Figure 2. The conditions investigated are indicated by the triangles drawn in the plot, and it is seen that

The 3-D system domain considered in the model is shown in Fig. 3(a), it includes the twophase free-jet issuing from a pneumatic nozzle and the surrounding environment; the mixing chamber is excluded from the analysis. Since the visualization of the jets and the

Fig. 3. (a) Schematic of system considered and computational domain, (b) quadruple exposure PIV image of drops in the neighborhood of the nozzle orifice, (c) schematic of assumed air-velocity profiles at nozzle exit and (d) schematic of assumed drop velocity

(c)

they correspond to constant W with different air inlet pressures, pa, and vice versa.

Fig. 2. Measured operating diagram of a Casterjet 1/2-6.5-90 nozzle

**3. Mathematical model and computational procedure** 

**3.1 System considered and assumptions** 

profiles and water flux distribution at nozzle exit

(a) (b)

(d)

Fig. 1. Schematic of experimental setup

The PDIA system (VisiSizer N60V, Oxford Laser Ltd. Didcot, United Kingdom) schematically illustrated in Fig. 1 is a spatial multiple counting apparatus that captures instantaneously (i.e., in 4 ns) shadow images of the droplets moving through a thin (~400 m) sampling volume and analyzes them in real time (Minchaca et al., 2011). A dual head Nd:YAG laser sends light pulses (15 mJ at 532 nm) through a fluorescent diffuser to illuminate the region of interest from behind while a high resolution camera placed in front captures the shadow images of the objects passing in between. The disposition of these elements is illustrated in the figure. Operating in dual pulse mode the laser and camera are triggered to capture image pairs separated by a time interval of 1.7 s, the figure displays a single pair extracted from superposed frames. The analysis of single and superposed frames allows, respectively, the simultaneous determination of the size and velocity of the drops appearing. The criteria employed for the consideration of single drops and drop pairs have been described elsewhere and were validated by off-line analysis of single and superposed frames (Minchaca, 2011; Minchaca et al., 2011). Lenses with two magnifications (2×, 4×) were employed to resolve the whole spectrum of drop sizes. With each magnification 1000 frames were captured to obtain samples with over 5500 drops that ensured statistical confidence limits of 95 % (Bowen & Davies, 1951). The magnifications allowed resolving drops with sizes ranging from 5 m to 366 m and velocities of up to 185 m/s. The field of view with both magnifications was 2.561×2.561 mm2, which allowed combination of the samples obtained from both to carry out statistical analysis of the data. The calibration (i.e., m/pixel) provided for the camera, lens and magnifications used was validated measuring standard circles in a reticule and standard line spacings in a grating and the agreement was better than 0.5 %. The traversing rail shown in the figure moved the diffuser and camera to 7 prescribed x-positions (0.0013, 0.030, 0.059, 0.088, 0.116, 0.145 and 0.174 m), while the y and zs positions where maintained constant at 0 m and 0.175 m, respectively. Differently from the measurements with the patternator the measurements with the PDIA system were carried out with the nozzle oriented vertically downward, but it was experimentally verified that the distributions of dd and u obtained with both orientations were not significantly different.

The water for the pneumatic nozzle was supplied from a reservoir using an immersion pump instrumented with a digital turbine flow-meter, a valve and a digital pressure gauge. A compressor provided the air and this line was instrumented with an automatically controlled valve, to minimize flow rate variations, a mass flow-meter and a digital manometer. The results reported in this article are for a Casterjet 1/2-6.5-90 nozzle (Spraying Systems Co., Chicago, IL), whose operating diagram is displayed in Figure 2. The conditions investigated are indicated by the triangles drawn in the plot, and it is seen that they correspond to constant W with different air inlet pressures, pa, and vice versa.

Fig. 2. Measured operating diagram of a Casterjet 1/2-6.5-90 nozzle
