**4.1 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= zs. 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).

Fig. 5. Measured and calculated velocities for drops of different sizes reaching the x-axis at y= 0 and z= zs. The results are for W= 0.58 L/s and pa= 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 10 Advanced Fluid Dynamics

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= zs. 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

Fig. 5. Measured and calculated velocities for drops of different sizes reaching the x-axis at

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

y= 0 and z= zs. The results are for W= 0.58 L/s and pa= 279 kPa

**4. Experimental and computational results and discussion** 

**4.1 Drop velocity and size correlation** 

case illustrated in the figure (Minchaca et al., 2011).

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.

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 pa= 279 kPa

#### **4.2 Effect of nozzle operating conditions on the velocity of the drops 4.2.1 Effect of water flow rate at constant air inlet pressure**

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 pa 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 pa 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 pa are complex. Therefore, it was important to examine the predictions of the CFD model in

An Experimental and Computational Study of the Fluid Dynamics of Dense Cooling Air-Mists 13

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 pa. The agreement between computed and experimental results is quite reasonable and the curves show that as pa 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 pa 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 pa increases. In fact, heat transfer experiments have shown a substantial increase in the heat flux with the increase in pa 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 pa favors heat transfer. The phenomena occurring during the impingement of dense air-mist jets with solid surfaces is being investigated. The effect of pa 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

**4.2.2 Effect of air inlet pressure at constant water flow rate** 

of sizes tends to generate a greater number of large drops than small drops.

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

(c) (d)

(a) (b)

computed. Tangential velocity components: (c) measured, (d) computed

this regard. Figure 7 shows experimental and computational profiles of the normal and tangential volume weighed mean velocity components defined as,

$$\mathbf{u}\_{\mathbf{z},\mathbf{v}} = \sum\_{\mathbf{i}=1}^{\mathrm{N}} \mathbf{u}\_{\mathbf{z},\mathbf{i}} \mathbf{d}\_{\mathrm{d},\mathrm{i}}^{3} \Big/ \sum\_{\mathbf{i}=1}^{\mathrm{N}} \mathbf{d}\_{\mathrm{d},\mathrm{i}}^{3} \quad ; \ \mathbf{u}\_{\mathbf{x},\mathbf{v}} = \sum\_{\mathbf{i}=1}^{\mathrm{N}} \mathbf{u}\_{\mathbf{x},\mathbf{i}} \mathbf{d}\_{\mathrm{d},\mathrm{i}}^{3} \Big/ \sum\_{\mathbf{i}=1}^{\mathrm{N}} \mathbf{d}\_{\mathrm{d},\mathrm{i}}^{3} \tag{14}$$

for four different water flow rates and a constant pa= 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.

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

#### **4.2.2 Effect of air inlet pressure at constant water flow rate**

12 Advanced Fluid Dynamics

this regard. Figure 7 shows experimental and computational profiles of the normal and

 

for four different water flow rates and a constant pa= 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.

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

(c) (d)

(a) (b)

computed. Tangential velocity components: (c) measured, (d) computed

1i

i,zv,z i,d u d/duu;d/du (14)

i,xv,x i,d

N 1i

3

3 i,d

<sup>N</sup>

3 i,d

N 1i

tangential volume weighed mean velocity components defined as,

3

N 1i 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 pa. The agreement between computed and experimental results is quite reasonable and the curves show that as pa 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 pa 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 pa increases. In fact, heat transfer experiments have shown a substantial increase in the heat flux with the increase in pa 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 pa favors heat transfer. The phenomena occurring during the impingement of dense air-mist jets with solid surfaces is being investigated. The effect of pa 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.

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

An Experimental and Computational Study of the Fluid Dynamics of Dense Cooling Air-Mists 15

the drops travel more closely spaced as pa decreases, leading this to a higher particle packing. This behavior continues up to z= zs where regions of higher liquid volume fraction

The predicted liquid fraction contours indicate that the increase in pa 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 pa on the water impact density for a constant W. Figure 10 shows measured and computed water impact density maps for pa 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 pa, in the central region. Based on the model, this result points out that although at higher pa 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

Fig. 10. Contour maps of w at z= zs for a W= 0.50 L/s with pa= 257 kPa: (a) experimental, (b)

(b)

(d)

computational and with pa= 320 kPa: (c) experimental, (d) computational

are more widely spread in the case of smaller pa.

angles were slightly larger than the nominal values.

(a)

(c)

#### **4.3 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,

$$\alpha\_{\rm d} = \frac{\sum\_{\rm l=1}^{n\_{\rm cell}} (\mathbf{N\_{d}} \mathbf{v\_{d}} \Delta \mathbf{t})\_{\rm k}}{\mathbf{v\_{cell}}} \tag{15}$$

and the water impact density can be evaluated as,

$$\mathbf{w}(\mathbf{x}, \mathbf{y}) = \frac{\sum\_{\mathbf{k}=1}^{\mathrm{n}\_{\mathrm{d}}} (\mathbf{N}\_{\mathrm{d}} \mathbf{v}\_{\mathrm{d}})\_{\mathrm{k}}}{\mathrm{A}(\mathbf{x}, \mathbf{y})} \tag{16}$$

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 pa decreases. For conservation of mass this last factor would imply that

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

14 Advanced Fluid Dynamics

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

cell

)y,x(A

)vN(

d

kd

d

)tvN( cell 

v

n

A 

1k

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 pa decreases. For conservation of mass this last factor would imply that

Fig. 9. Computed contour maps of d over the main symmetry plane of the mist jet for a W=

0.50 L/s and pa of: (a) 205 kPa, (b) 257 kPa and (c) 320 kPa

(a) (b) (c)

kd

(15)

(16)

**4.3 Effect of air inlet pressure on droplet volume fraction and water impact flux** 

n

d

)y,x(w

1k

volume fraction can be defined by the following expression,

and the water impact density can be evaluated as,

the drops travel more closely spaced as pa decreases, leading this to a higher particle packing. This behavior continues up to z= zs where regions of higher liquid volume fraction are more widely spread in the case of smaller pa.

The predicted liquid fraction contours indicate that the increase in pa 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 pa on the water impact density for a constant W. Figure 10 shows measured and computed water impact density maps for pa 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 pa, in the central region. Based on the model, this result points out that although at higher pa 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.

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

An Experimental and Computational Study of the Fluid Dynamics of Dense Cooling Air-Mists 17

S Source term for momentum transfer interaction between the drops and the

lx, ly, lx' Half length; half width nozzle orifice; half length of hollow portion of

nozzle orifice, m

 air, m s-2 t Time, s

n Number of drop trajectories np Port number or number of ports Nd Number frequency of drops, s-1 p, P Pressure in Ecs. (3); in Eq. (9), kPa pa, pw Air-; water nozzle inlet pressures, kPa Red, Ret, Rez' Reynolds number defined in Table 1

Ts Saturation temperature of water, °C

uzs Normal drop velocity at z= zs, m s-1

Wezs Impinging droplet Weber number

x, y, z Rectangular coordinates, m

Angle defined in Eq. (1)

Kinematic viscosity, m2 s-1

Surface tension of drop phase, N m-1

i, j Indexes for coordinate directions in, out Input, output to control volume

amb Ambient conditions, P = 86 kPa, T = 25 °C

t Time interval, s

cell Discretization cell

k Ports or trajectories

max Maximum

U Velocity of the continuous phase (air), m s-1 Uz,max Velocity of air phase defined in Table 1

w Water impact flux or water impact density, L m-2s-1

zs Setback distance of nozzle tip from plane of interest, m

, Jet expansion half angles in x and y directions, deg

d Continuous; discontinuous-phase density, kg m-3

k Laminar and turbulent Schmidt numbers for k and

d Volume fraction of drops, dimensionless

ux,v, uz,v Tangential; normal volume weighed mean velocity, m s-1

v Volume of water collected in bottles of patternator, L; volume, m3

; o Dissipation rate of turbulence kinetic energy; at nozzle orifice, m2 s-3 μ, μt Continuous-phase molecular; turbulent dynamic viscosity, Pa s

Tw Surface temperature, °C u Velocity of drops, m s-1

vd Volume of drop, m3

W Water flow rate, L s-1

x Coordinate, m

Greek symbols

Subscripts
