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

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


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, T w , of the hot steel strand exceeds considerably the saturation temperature, T s , of the cooling liquid (water), i.e., T w -T s ranges between ~600 to 1100°C.These harsh temperature conditions have traditionally called for the use of high water impact fluxes (w, L/m 2 s) 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/m 2 s (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/m 2 s, with regions where w can be as large as ~110 L/m 2 s.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, d d , 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, d d and u, determine the local impingement Weber number (We zs =  d u zs 2 d d /), which in general has been agreed to characterize the impact behavior (Wachters & Westerling, 1966;Araki & Moriyama, 1981;Issa & Yao, 2005).As the the impingement region (Hatta et al., 1991a(Hatta et al., , 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 We zs .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.

Experimental methods and conditions
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, 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 %. 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 2.561×2.561mm 2 , 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 z s 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 d d 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 1/2-6.5-90nozzle (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, p a , and vice versa.

System considered and assumptions
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 measurements of their impact footprints indicated double symmetry over the x-z and y-z planes the computational domain involved just one quarter of the physical domain, as seen in the figure.Additionally, since the air-and water-flow rates were stable it was assumed that on a time average basis, the flow characteristics of the two-phase jet could be simulated in steady-state conditions.For their treatment the continuous air-phase was considered in an Eulerian frame of reference and the discrete droplets were regarded in a Lagrangian frame.
The assumptions for the model were: (a) the liquid emerges from the nozzle as drops.This is supported by PIV observations done close of the nozzle orifice, as that displayed in Figure 3 (b).This figure shows a quadruple-exposure photograph with trails of 4-images of droplets.Additionally and in agreement with PDIA observations the drops are assumed spherical; (b) the size distribution of the drops exiting the orifice is equal to the distribution measured at a distance z= z s (i.e., at the typical working distance of a given nozzle).This is reasonable since drop coalescence and break-up are rare events.The low volume fraction,  d  of the drops prevents coalescence and the PDIA images, taken at different positions in the free mists, rarely show droplet break-up; (c) drops of all the specified sizes leave the orifice at the terminal velocity reached in the mixing chamber while dragged by the air.Calculations indicate that this would be the case for individual drops and since  d is low the assumption would seem reasonable for the dilute multi-drop system moving within the chamber; in the mixing chamber  d < 0.08; (d) the droplets in the jet do not interact with each other and only interact with the air through interfacial drag, and (e) the air and the droplets are at room temperature and condensation and vaporization are negligible.

Governing equations
Under the considerations just described, the governing equations for the motion of the air are: the continuity equation ( 2), the Navier-Stokes equations (3) and the turbulence transport equations ( 4) and ( 5), which are expressed as follows, 3) is the source term expressing the i-direction momentum transferred between the air and the drops in a given cell of the fixed Eulerian grid over a Lagrangian time step.It is equal to the change in the momentum (only due to interfacial drag) of the drops following all the trajectories traversing a cell over that time step (Crowe et al., 1977) and it is given as, The meaning of the symbols appearing in the equations is given in Section 7. The turbulence of the air was treated by the k- model for low Reynolds flows of Lam-Bremhorst modified by Yap, 1987.The constants and functionsappearing in Eqs. ( 4) and ( 5) are listed in Table 1.Also, under the considerations done in Sec.3.1 the equation of motion for individual drops in the mist and under the effects of aerodynamic drag and gravity is expressed as, The drag coefficient C D was assumed to vary with the particle Reynolds number, Re d , according to the expressions given in Table 1.The trajectory of the drops was computed from the variation with time of the components of the position-vectors, according to, Constants and functions involved in the turbulence model

Boundary and initial conditions
At the boundaries of the calculation domain shown in Fig. 3(a), Eqs.
(2) through ( 5) describing the turbulent motion for the air-phase were solved imposing the following conditions: -Ambient conditions at boundaries ABCD, A'B'C'D', ABB'A' and BCC'B', specified as, To approach these conditions, the boundaries were located far away from the jet.
-Symmetry conditions at the boundaries ADD'A', DCC'D', given as: where j represents the index for the coordinate normal to the respective symmetry plane.
-Non-penetration and non-slip conditions were specified at the external wall of the nozzle, -Air velocity profiles as those shown in Fig. 3(c) were specified at the nozzle orifice, which corresponds to an internal boundary.Along the x-direction these profiles were uniform over the length l x ' of the flat hollow portion of the flanged orifice, in the rest of the orifice the profiles decreased to zero varying in angle from 0 deg to  deg at the edge; the distributions were the same throughout the whole thickness (y-)direction of the orifice.These velocity profiles were suggested by the geometry of the flanged orifice and are supported by the results presented in Section 4. The expressions describing the profiles are listed in Table 1, together with the expressions for the turbulence kinetic energy and the dissipation rate of turbulence kinetic energy at this boundary, k o and  o , respectively.-Positions and velocities were specified to the droplets as initial conditions for the solution of their motion (7) and trajectory (8) equations.For doing this, a first step was to decide a series of criteria to distribute throughout the orifice drops of different size and velocity in a random fashion that reflected that the water flux profile decreases from its center to its edges.To do this, the orifice was simulated as a grid of ports, k, releasing drops satisfying the diameter distribution measured at z= z s (according with the assumption indicated in Section 3.1) for the particular set of nozzle operating conditions under consideration.For deciding the number of ports assigned to each drop size category it is important to establish what type of distribution to use, number or volume frequency?Figure 4 shows both size distributions measured for a representative set of operating conditions W and p a .The number frequency distribution shows that droplets smaller than 25 m account for a large number percentage of the drops (82.85 % of them), but that they represent only 6.82 % of the volume of the drops in the sample.Since the number of ports that can be used cannot be excessively large the assignment of the ports according to the number frequency distribution would leave many sizes unrepresented.The volume frequency distribution does not present this disadvantage and was chosen to designate the number of ports for each size category.The size assigned to each port was done through a random number generator to simulate the stochastic emergence of drops with different characteristics from distinct sites of the orifice.The drops with volume v d,k = (d d 3 ) k /6 exiting the ports k with a number frequency, N d,k , had to satisfy the water-flow rate, W, according to the following expression, ,, 1 Furthermore, based on the form of the mist footprint obtained with a patternator the water flow was assumed to be distributed in the orifice according to an obelisk-shaped distribution (Camporredondo et al., 2004), as that shown schematically in Figure 3(d).With the criteria given, the initial conditions for Eqs. ( 7) and ( 8) were assigned to each port of the nozzle orifice, such that at t = 0 the position and velocity of the drop are specified as follows, As mentioned in Sec.3.1, the initial velocity, (u i ) k , of the drops was prescribed by assuming that the drops exit with the terminal velocity that they reach in the mixing chamber (Minchaca et al., 2010).As suggested by the observed drop trajectories (Hernández et al., 2008), according to the position assigned to the drop the angle of the velocity varied from 0 deg to  deg in the x-direction and from 0 deg to  deg in the y-direction.A schematic representation of the velocity vectors of the drops is displayed in Fig. 3(d), and the expressions for the u x,k , u y,k and u z,k velocity components are given in Table 1.Also, the physical properties of the fluid, the dimensions of the orifice and the angles of expansion of the jet are given in the table.

Solution procedure
The Eulerian and Lagrangian equations of the model were solved using the control volume method and the particle tracking facility implemented in Phoenics.The mesh used had 128×25×99 control volumes to achieve mesh independent results and the number of ports was 100×12 in the x-y directions.The convergence criterion specified a total residual for all the dependent variables ≤ 10 -3 .

Drop velocity and size correlation
As indicated in Sec. 2 the drop size and velocity measurements were done at 7 sampling volumes spaced along the x-direction at y= 0 and z= z s .Figure 5 shows the correlation between drop velocity and diameter for the set of measurements done over all the sampling volumes.Droplets of all sizes exhibit a wide range of velocities when they arrive to the measuring positions.It is noticed that as the droplet diameter decreases their velocities exhibit a broader range, many small drops arrive at the measuring axis with small velocities and this causes a weak positive correlation between droplet velocity and diameter, i.e., the results denote a slight trend in the velocities to be larger as the size of the drops increases.
Correlation coefficients, for several conditions and positions, were evaluated quantitatively in another work and confirm the weak positive correlation appreciated for the particular case illustrated in the figure (Minchaca et al., 2011).In agreement with the experiments, the results of the model reveal that the small drops exhibit a broader spectrum of velocities than the larger ones, causing the development of a weak positive correlation of velocity with size.Considering that the model assumes that all drops of each size leave the nozzle at the particular terminal velocity that they reach in the mixing chamber, as a result of the drag exerted by the air, the results of the figure indicate that the smaller droplets are more susceptible to lose their momentum while moving in the mist jet interacting with the air.This is evidenced by comparing the dispersion results with the calculated terminal velocity curve included in the figure .From the nozzle exit the drops follow ballistic nearly rectilinear trajectories and drops of the same size, which according to the model exit at the same velocity, will decelerate more when leaving from external than from internal positions of the nozzle orifice, so that they travel in the periphery of the jet interacting with the quiescent environment.This statement is supported by the experimental and computational results displayed in Fig. 6, which shows the variation of the normal and tangential velocity components of drops of different size traversing the sampling volumes located at the different x-positions.The regression curves fitted to the experimental and computational results show an excellent agreement.The dispersion exhibited by the computed results displayed in Figs. 5 and 6 is smaller than the experimental due to the very different number of drop trajectories traversing the sampling volumes, thousands in the experimental case versus a few tens in the computational case.Despite of this the model is able to represent very well the trend in the behavior of the actual system.In the application of air-mist nozzles for the cooling of surfaces at high temperature it is common to vary the water flow rate maintaining constant the air inlet pressure.This procedure would be equivalent to move along the curves of constant p a appearing in the operating diagram of Figure 2. The reason behind this is that the spray cooling intensity is commonly associated only to the flux of water impinging upon the hot surface, when actually there is another mist parameter that plays an important role and this is the velocity of the drops (Hernández et al., 2011).Experimentally, it has been found that the velocity of the drops increases with W up to a certain value, but once this value is exceeded the opposite effect takes place and the drop velocity decreases markedly (Minchaca et al., 2011).With the increase in W at constant p a the drops generated by the nozzle become larger (Minchaca et al., 2011) and the air flow rate, A, gets smaller as indicated by Figure 2.Both factors will alter the terminal velocities that the drops will reach at the nozzle exit and also their behavior in the free jet.
The multivariate effects that the droplet velocity experiences when changing W at constant p a are complex.Therefore, it was important to examine the predictions of the CFD model in 12 this regard.Figure 7 shows experimental and computational profiles of the normal and tangential volume weighed mean velocity components defined as, for four different water flow rates and a constant p a = 205 kPa.It is seen that both, experimental and computational results, indicate that the increase in W from 0.1 to 0.3 L/s causes an increase in the normal and tangential velocity components and that further increase leads to a decrease in the velocities.The drop velocities obtained with W equal to 0.30 L/s and 0.58 L/s are considerably different, being substantially smaller for the higher W.This behavior could be one of the factors of why the heat transfer does not augment considerably when W and hence w do it (Montes et al., 2008).The computed velocities are somewhat larger than the experimental because the volume frequency distribution of sizes, chosen to establish the model, generates a greater number of large drops than small drops.

Effect of air inlet pressure at constant water flow rate
The computed and measured x-and z-components of the volume weighed mean velocity are shown in Fig. 8, for conditions involving a constant W and different p a .The agreement between computed and experimental results is quite reasonable and the curves show that as p a increases both velocity components become larger.This behavior suggests that if the drops were to impinge over a surface, a more intimate contact would take place as p a increases; this as a consequence of the higher impingement Weber numbers that would result.The larger tangential velocity component of the drops hints a faster renewal of the liquid on the surface as p a increases.In fact, heat transfer experiments have shown a substantial increase in the heat flux with the increase in p a at constant W (Montes et al., 2008;Hernández et al., 2011), suggesting that the change in the fluid dynamic behavior of the drops with the increase in p a favors heat transfer.The phenomena occurring during the impingement of dense air-mist jets with solid surfaces is being investigated.The effect of p a on the intensity of heat extraction could have important implications to achieve water savings during cooling operations.Similar to the results in Fig. 7, the computed velocities in Fig. 8 are somewhat larger than the experimental because the volume frequency distribution of sizes tends to generate a greater number of large drops than small drops.

Effect of air inlet pressure on droplet volume fraction and water impact flux
As mentioned in Sec. 1 the mists have been classified in dense or dilute according to the value of the water impact density.However, little has been investigated about the actual mist density defined as the volume of liquid of the drops per unit volume of space; which is equivalent to the local liquid volume fraction,  d .This parameter would give an indication of how critical could be to the model the assumption that the drops in the free jet do not interact as a consequence that they are far apart from each other.Although, the direct experimental measurement of this parameter is difficult the validity of the computational estimation of  d can be tested by its relation with the water impact density.The local water volume fraction can be defined by the following expression, and the water impact density can be evaluated as, Figure 9 shows computed contour plots of  d over the x-z symmetry plane of mist jets generated with a constant water flow rate and different air nozzle pressures.It is appreciated that as the air inlet pressure decreases the region close to the nozzle exhibits a higher liquid fraction.This behavior arises from the larger size and smaller velocities of the drops generated as p a decreases.For conservation of mass this last factor would imply that the drops travel more closely spaced as p a decreases, leading this to a higher particle packing.This behavior continues up to z= z s where regions of higher liquid volume fraction are more widely spread in the case of smaller p a .
The predicted liquid fraction contours indicate that the increase in p a at constant W causes a redistribution of the liquid in the free jet that could affect the water impact density.In previous w measurements no effect was detected (Hernández et al., 2008).Thus, it was decided to refine the patternator to try to reveal if there was an influence of p a on the water impact density for a constant W. Figure 10 shows measured and computed water impact density maps for p a of 257 kPa and 320 kPa with W= 0.50 L/s.It is seen that both results agree very well and indicate an increase of the water impact density with the increase in p a , in the central region.Based on the model, this result points out that although at higher p a the drops tend to travel more widely spaced from each other, having a lower volume fraction, their higher velocities causes them to arrive more frequently to the collecting cells of the patternator or equivalently to the virtual impingement plane (in the case of the model), leading this to higher w in the central region of the footprint.The differences observed in the figure between experimental and computed results are mainly in the sizes of the footprint.This discrepancy arises because the model considers the nominal value of the expansion semi-angle  and a semi-angle = 10 deg.However, the w maps and the visualization of the jets indicate that the actual angles were slightly larger than the nominal values.

Summary and conclusions
A comprehensive experimental and computational study of the fluid dynamics of air-mist jets generated under conditions of interest in the cooling of surfaces found in metallurgical processes and in other high temperature processes was carried out.The work analyzes the variation of droplet velocity and water impact density as a function of droplet size and nozzle operating conditions.The rigorous determination of statistically meaningful samples of droplet size to establish that a relatively small numeric proportion (~0.17) of 'large´ drops (between ~25 m and 370 m) are responsible for transporting a large fraction of the water in the mist.The smaller drops transport only a small proportion of the liquid volume.This fact, which is typical of the different nozzles and operating conditions, suggested that the description of the drop sizes mainly responsible for carrying the water arriving at a given distance from the nozzle orifice would be crucial for formulating a 3-D turbulent Eulerian-Lagrangian model for simulating the dynamics of fan-shaped air-mists.Thus, the present model considers the volume frequency distribution of sizes, instead of the number frequency distribution, to prescribe the inlet ports assigned to the different sizes.This specification, together with those for the distributions of the velocity of the air and drops and of the water volume flux at the orifice, was critical in the results of the model.The model predicts very well the correlation between drop velocity and size, indicating that the finest drops tend to decelerate rapidly when traveling in the periphery of the mist.Also, it gives an accurate description of the influence that the variation in water flow rate at constant air inlet pressure, and of the variation in air inlet pressure at constant water flow rate, has on the velocity of the drops and on the water impact density distribution.The results on the fluid dynamics of free mist jets are being very useful to develop models for simulating the interaction of dense mists with solid surfaces.

Acknowledgments
The

Fig. 3 .
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 profiles and water flux distribution at nozzle exit Drag coefficient expressions Stokes law region, Re d  2 C D = 24/Re d Intermediate region, 2 ≤ Re d ≤ 500C k = u z,t sin(x/l x ) u y,k = u z,t sin(y/l y ) 02 kg/m 3 ; = 1.8×10 -5 Pa s;  d = 998 kg/m 3 Nozzle dimensions and parameters l x = 0.01 m; l y = 0.00325 m; l x '= 0.00585 m z s = 0.175 m; = 45°; = 10° *A is computed at local conditions: 25°C, 86 kPa.

Fig. 4 .
Fig. 4. Numeric and volume frequency drop size distributions measured for W= 0.58 L/s and p a = 279 kPa.The log-normal and Nukiyama-Tanasawa, NT, distributions fitted to the respective data are included

Fig. 5 .
Fig. 5. Measured and calculated velocities for drops of different sizes reaching the x-axis at y= 0 and z= z s .The results are for W= 0.58 L/s and p a = 279 kPa Figure 5 also shows results of computed velocities for drops arriving at the measuring axis.In agreement with the experiments, the results of the model reveal that the small drops exhibit a broader spectrum of velocities than the larger ones, causing the development of a weak positive correlation of velocity with size.Considering that the model assumes that all drops of each size leave the nozzle at the particular terminal velocity that they reach in the mixing chamber, as a result of the drag exerted by the air, the results of the figure indicate that the smaller droplets are more susceptible to lose their momentum while moving in the mist jet interacting with the air.This is evidenced by comparing the dispersion results with the calculated terminal velocity curve included in the figure.From the nozzle exit the drops follow ballistic nearly rectilinear trajectories and drops of the same size, which according to the model exit at the same velocity, will decelerate more when leaving from external than from internal positions of the nozzle orifice, so that they travel in the periphery of the jet interacting with the quiescent environment.This statement is supported by the experimental and computational results displayed in Fig.6, which shows the variation of the normal and tangential velocity components of drops of different size traversing the sampling volumes

Fig. 6 .
Fig. 6.Measured and computed velocity components as a function of x-position for drops of all sizes: (a) tangential velocity component and (b) normal velocity component.The results are for W= 0.58 L/s and p a = 279 kPa

Fig. 7 .
Fig. 7. Measured and computed volume weighed mean velocity components as a function of x-position for different W and a constant p a .Normal velocity components: (a) measured, (b) computed.Tangential velocity components: (c) measured, (d) computed

Fig. 8 .
Fig. 8. Measured and computed volume weighed mean velocity components as a function of x-position for different p a and constant W. Normal velocity components: (a) measured, (b) computed.Tangential velocity components: (c) measured, (d) computed

Fig. 9 .
Fig. 9. Computed contour maps of  d over the main symmetry plane of the mist jet for a W= 0.50 L/s and p a of: (a) 205 kPa, (b) 257 kPa and (c) 320 kPa

Fig. 10 .
Fig. 10.Contour maps of w at z= z s for a W= 0.50 L/s with p a = 257 kPa: (a) experimental, (b) computational and with p a = 320 kPa: (c) experimental, (d) computational

Table 1 .
Auxiliary equations, properties and dimensions www.intechopen.com authors are grateful to the National Council of Science and Technology of Mexico (CONACYT) for financial support through grant No. 57836.JIMM wish to thank CONACYT for his Ph.D scholarship grant.