AIAA-95-2103 Thickness of Film Procllrced by Pressure Atomizing Nozzles

X.Q. Chen, L.C. Chow, and M.S. Sehmbey, University of Kentucky Lexington, KY

30th AlAA Thermophysics Conference

June I9=22,1995/San Diego, CA For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 370 L'Enfant Promenade, S.W., Washington, D.C. 20024

THICKNESS OF FILM PRODUCED BY PRESSURE ATOMIZING NOZZLES

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Xiang-Qun Chen*, Louis C. Chow ’, and Maninder S. Sehmbey *

Department of Mechanical Engineering University of Kentucky Lexington, KY 40506

The film thickness is one of the most important parameters in heat transfer analysis of spray cooling. The liquid film created by the pressure atomizing spray impacting on a flat surface is studied in this paper. Measurements ofthe water film thicknesses using the point gauge method is performed using two pressure atomizing nozzles with different orifice diameters at two diffcrcnt nozzle heights. Results show the film thickness remains at almost SO pnunder all situations tested. The nozzle height ( I O mm and IS nun) has little effect on the film thickness. An integral method incorporating the radial mass flow rate distribution is employed in the analysis of the film thickness. The pressure distribution in the film is assumed to be directly caused by the droplet impingement. Laminar flow model is used in the analysis. The numerical results agree well with the experiment and reveal more details about the liquid film. The results show thc mean droplet velocity and the mass flow rate distribution are the dominant factors that affect the film thickness of the pressure atomizing nozzles. The film.thickness decreases with increase of the nozzle operating pressure and liquid flow rate for each nozzle; nozzles with a larger diameter produce thicker film at the same nozzle operating pressure or at the same liquid flow rate; radial and circumferential mass flow rate distribution affects the film thickness and the shape of the film surface. The numerical results also show the independence of film thickness with the l lolz~c height.

Nomcnclaturc h m

nozzle orifice to target suiface distance, m local liquid flow rate, kgim” s

* Graduatc Research Assistant

M P pressure, Pa r radial position, m R radius, m

Re, U liquid local velocity, m/s

U, V average droplet velocity, d s

total liquid flow rate, kgis

Reynolds number, Re, = U, - 8 I p

liquid velocity at film surface, d s

a 8 film thickness, m P liquid density, kgim’ P dynamic viscosity, Ndm’

droplet attacking angle, cosa = h I (?+h’)’’

Introduction Spray cooling is the method of using small-size,

high-velocity droplets impinging on a heated surface to remove the heat. Spray cooling can be divided into two categories based on the method of spay generation. A pressure atomizing nozzle can be used to atomize the liquid using the pressure difference across the nozzle. A higl- velocity gas stream can also break up a liquid jet into a spray. Because of the different atomizing method used and the different flow field around and on the heated surface, these two kinds of spray cooling have dEerent heat transfer mechanisms. Experiments have shown both methods can achieve high critical heat flux (CHF) and high heat transfer cceficient [ 1 - 41. At heat fluxes lower than CHF, a steady film can always be observed on the surface. The thickness of the film and its flow are very important for heat transfer analysis of spray cooling. Most heat transfer mechanisms involved in spray cooling (such as forced convection, surface evaporation, nucleation boiling, secondary nucleation hoiling and cven dry out at CHF) are directly or ’ Professor, Assoc. Fellow AIAA indirectly related to the film thickness and film flow.

Assoc. Engineer, Member AIM. Yang et 81. [ 5 ] measured the film thickness of an

Copyrighi 0 1995 by the Amaric.m lnrtiliitc of Aeronautics Nld Astronautics. Inc. All ridils rescrvcd

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air atomizing nozzle using the Fresnel diffraction method. The experiment was carried out on a 10x10 nun glass d a c e with an air atomizing nozzle situated 20 mm above. They showed that with a fixed air pressure, the film thickness is vety sensitive to the liquid flow rate, the film thickness changes from 85t15 pm at I literih to 235+75 p at 4 lit& when the air pressure is at I38 kPa (20 psi). No result was shown concerning the effect of the air pressure and air velocity which could he vety important for the air atomizing nozzle. Yang et a1.[6] also used an analytical model to analyze the film thickness of the air atomizing nozzles. They assumed a laminar film llow and used the stagnation flow pressure gradient of the air llow field in their model. The liquid film thickness prediction agrees well with theexperimental data [ 5 ] .

Tilton [3] measured the film thickless of the pressure atomizing nozzle. He measured tlie film tliichicss after the hydraulic jump and calculated the film thickness before the jump using the hydraulic jump theoiy. This methcd may not be accurate in predicting the film thickness in the spray core because the hydraulic jump occurs some distance away from the spray core and the film tluckncss may change within that distance.

In the present work, the film thickness produced hy a pressure atomizing nozzle is studied experin~entally and numerically. The point gauge method is riscd to measure the film thickness. An integral method incorporating the mass flow rate distrihution is uscd in Uie modeling of the film flow.

Exneriment Descrintion Needle probes have heen used to measui-e the film

thickness in the past [3,7]. One of the concerns using this method to measure the film thickness in the spray core is that the entire d a c e is kimg impinged hy the droplets, and the presence of the needle probe may interfere with the integrity of the flow field. Since the liquid is llowing outwards in the radial direction in the spray coi-c, thc probe only interfers with the flow in the area hehind i t . By setting the prohe along the radial direction and set it with an angle to the surface the interference of the probe for tlie area ahead ofit can be reduced and the measurenient donc at that point couldbe considered reliahle. Previous measiircnicnts of the film thickness are hased on the sudden and signilicant change in resistance as the prohe leaves or toochcs tlie

I 0.025

o . w o I - - - - - 1 , , , L_I.I., , . , , , I 1 2 3 4 5 6 0

Time(M)

Fig. I Raw Signal Near Film Surface

liquid surface. Unfortunately, this sudden change in resistance is not apparent in the spray core. Figure 1 is a typical signal when the probe tip is near the film suface. The y axis is the current in the circuit shown in Fig. 2 that rcflccts the resistance of water hetween the needle tip and the surface. This signal form maintains the same characteristics and no abrupt resistance change can he ohsnved as the probe moves up and down in the spray core. The reason is that the film in the spray core has a wavy d a c e that yields oscillating signals near the surface. Also, since the needle is constantly hit by the droplets in the spray core, even when the tip is already above the liquid surface

F ig2 Experimental Setup

there will still he liquid dripping down at the needle tip which provides a conductive path (see Fig. 3). Instead of a conspicuous resistance change at the liquid surface, this hipping liquid makes the resistance change gradually with thc distance between the needle tip and the surface.

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However, the rate of resistance change will he different when the needle tip is at Merent positions (in the film, near the wavy film d a c e and above the film stuface) due to the different conductive paths (see Fig. 3). The difference of

.-..--‘

Nccdls Prctbc.

W

Fig. 3 Conductive Path at the Needle Tip

resistance change rates is more repeatable when the time average of the signal is used. Figure 4 is a trpical current- distance curve measured in the experiments. Thc X-axis is the distance hetween the needle tip and the surface. The Y- axis is the current in the circuit shown in Fig. 2. Time average is used for the current. At both ends of the curves there are always two linear sections with diffcrent slopes. These arc the sections when the needle tip is in and out of the film. The middle point of thc mid section ( point A in Fig. 4) gives the average position of the film surface,

Electrolvsis Pronertv of Water The voltage corresponding to Gihhs’ free energy

of water at r w m temperature is nhout 1.22 V [SI. Water molecules will dissociate if thc voltage across the two electrodes is larger than this voltage. Preliminary measurements show that if the voltage drop on the water is less than I .22 V, the signal is too weak and the relation between the resistance and the distance hetween the electrodes cannot he used reliably to measure the film thickness. If the voltage on the water film is higher than 1.22 V, ions begin to be generated and the resistance changes significantly with the distance hetween electrodes in the flowing water film. This is the property needed in the film thickness measurement. The resistance also changes with the velocity of water for a fixed electrode distance when using a high voltage. This is hecause morc ions will be washed away when water velocity is higher. This makes the resistance higher when generated ions fomi the main conductive medium. This phenomenon prevcnted us from using the calibrated resistance-distance table to measure the film thickness. However it is not a problem if we use !lie

d

0.012

0.010

,-O.W8

g 0.m

E .., .- c

3 0

0.W4

0.W2

Distance Between the Needle Tip and the Surface (pm) Fig. 4 Method of Finding Film Swface

method described above to find the film thickness.

Exneriment Setun and Procedure The schematic diagram of the experiment setup is

presented in Fig. 2. The surface on which film thickness is measured is the polished flat end of a stainless steel cylinder with a diamcter of 62 mm. The surface has a mirror finish reducing the effect of surface roughness on film flow. ‘The cylinder sits on an adjustable platform to keep it horizontal. This platform is attached firmly to a micrometer with a resolution of 2 pm. The prohe is made of a stainless steel sewing needle covered with dielectric paint. Only the tip of the needle is e s p o d . The needle is attached to a f m stand and is set at an angle of 45” with the surface. Before each experiment the surface is cleaned and adjusted to the horizontal position. For each test run the cylinder is first moved upwards until the needle tip touches the solid surface. This point is set to zero. Then the surface is moved down with a 5 p interval. To obtain a longer linear section out of the film, the increment is increased to I O pm when the needle tip is 75 pm away from the surface. The time average voltage on the resistor is recorded at every step. Thccurrcut versus distance hetween the needle tip and the mface is then plotted. The method described above is then used to determine the film thickness. Because of the reasons discussed in the previous section, a stabilized 5 V DC power supply and a 120 K resistor are used to form the circuit. The actual voltage drop on water is around 3.2 - 5 V. The voltage output on the resistor is connected to an

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adjustable lowpass filter. The filtered signals are mcasurcd by the data acquisition system and monitored by an oscilloscope at the m e time. Because the film has a wavy surface and the resistance changes with the velocity, the current in the circuit oscillates violently when the needle tip is near the film surface (see Fig. I). The data acquisition system with a maximum data acquisition speed of 50 kIIz cannot provide enough resolution for the signal So a lowpass filter is used to eliminate the high frequencies in the signal. The data acquisition system is then used to give the time average of the voltage output.

The surface tension does not affect the film thickness measurement because the liquid film is flowing. This is proven by the identical results when the film thickness is measured by moving the surfacc ripwards (reversed direction compared with the way rlcscrihcd above).

An adjustable speed gear pump is used to provide stable liquid pressure. The liquid flow rate is measiitcd with an orifice meter and a pressure transducer.

The droplet speed is measured using Phase Doppler Particle Analyzer (PDPA). A small orifice collector is used to measure the mass flow rate distrihution in the spray core. Water at room temperature is used in the experiment.

Exneriment Results Two nozzles TG4 and TG6 with orifice diameter

0.559 nun and 0.686 mm respectively from Spray Systems are used in the experiment. The spray characteristics are listed in Table 1. The velocity is generally unifomi across the spray core. So only the mean velocity listed in Table I The mass flow rate distribution varies dramatically hetween the two nozzles. Figure 5 shows the mass flow rate distributions of TG4 and TG6 along one radial direction at 276 kPa (40 psi). Since only the distribution is of conceiii, the Y-axis is plotted in a relative scale. As the measurements show, the shapes of distribution c iwes are similar. The liquid flow rate is low near the cciitci ofthe core and most of the liquid flow is concentrated near the edge.

The results of the film thickless m e a ~ u r c ~ ~ i e i ~ t are shown in Table 2. The measurements are done iicar fhc outer edge of the spray core (R = 3 mm when thc n ~ ~ ~ l e is IO nun high and R = 5 nun when !lie nozzle is I5 m i high). The results show that for the liquid flow rate tested. there is

Eq IO "'1 0 T G 4 o /

0.02

0.W 0.0 1.0 2.0 3.0 4.0 5.0 6.0

R ( m m ) Fig. 5 Mass Flow Rate Distribution

only a slight decrease ofthe film thickness with the increase of liquid flow rate and nozzle operating pressure. Different nozzle heights ( I O mm and I5 mm) do not affect the film thickness. For the two kinds of nozzles used in the cxpcriment (TG6 and TG4). experiment results show no obvious relation between the film thickness and nozzle oritice diameter. The film thickness remains at about 50 pm in most of the experiments. Radial film thickness profile measurement is also performed. Table 3 lists one set of the results. Within the tolerance the present method can provide, no obvious film thickness change is observed across the spray core.

Uncertaintv Analvsis The uncertainty in droplet velocity measurement

depends on the PDPA system. The velocity distribution of the droplets for any location is always Gaussian with a standard deviation of 2-4 m / s and is reasonably repeatable. The overall uncertainty in the mean droplet velocity is helow 8 percent for the velocity range measured. The liquid flow rate measured from the orifice meter and the transducer is calibrated using a graduated cylinder and a stop watch. The uncertainty in the measured volume is i 2 cc and the uncertainty in the time is + 0.8 s. This gives an

average uncertainty of i 0.2 ccls in the volumetric flow rate measmemeut. The uncertainty in the nozzle inlet pressure is about 2 percent as read from a grade gauge. Several procedures are followed to measure the film thickness as shown in Fig. 4. The steps that determine the positions of

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Table 1 Droplet Velocitv Measurement Results

Pressure ("a)

l 0 m TG4

TG6 Film Nozzle Freight '

(W 15 m TG4

'TG6

Thickness

Nozzle Height

Tahlc 2. Film Thickness Measurement Results

207 276 348 414

54 41 44 43

80 80 47 42

62 46 46 46

60 84 84 52

Table 3. Cross Section Film Thickness (TG4.276 Wa, 15 nun Nozzle Height)

core is still laminar. When the droplets hit the surface, the vertical

Thickness(pm) il point B and C and the step to set the initial point in the

experiment are most importmt for the accuracy. The uncertainty in finding the positions of points I? and C arc about f 5 pn and the error in finding thc initial point is about f 3 p. This gives an avcragc unccilainty off 13 pin in the film thickness results.

Hvdraulic Modeling of Film Flow Low Reynolds numkr flow (Re6 < I8 IO) has been

proven to have a strong damping factor and it can remain laminar under strong disturbance [9]. Even under unfavorable pressure gradient, low Reynolds nrunher flow can still be stable [9].

component of the velocity is converted to pressure. Because of the dense spray (ahout 60,000 droplets/mm*.s with a TG6 nozzle, liquid pressure 275 kPa and 15 mm nozzle height) and die high kequency of droplets impingement (60 k1-Izlmm' for the same situation), the transient process of single droplet impingement will not be sigificant in the low Rcynolds numkr film with a strong damping factor. So we assume thc average pressure can he used in the analysis:

V

Q

I - I I I

lL_,

For the nozzles and the flow ratc range tested in the present study, the maximum Rcynulds number based on the film thickness is about Rc, = 580 ( 'Ki6, 482 kPa ) when the linear vclocity profile is assumed. This is far

despite the strong disturhance caused hy droplet impingement, it is very likely that the film flow in the spray

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below thc critical Reynolds number Re,,,, = 1510 [9]. So b

Fig. 6 Control Volume for Momentum Equation

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usually not sensitive to the velocity profile. So we only use a third order polynomial for the velocity profile :

L j The pressure gradient caused by the impingement

angle and mass flow rate distribution is: - 3 q - 3q’ + q’, U _ -

U. hV din

(2) +-.- dp = -mVbr

The mass flow rate profiles of TG6 and TG4 dr fl dr

obtained from the experiments are as follow: Figure 6 illustrates the pressure and shear hrce on

the control volume and the mass flow across the boundary. The momentum change of liquid across the control volrune

m=M.(0.037 - 17.23r+2.38x104r’

is: -1 .132~106r’ ~ 1.355x109r4) (9)

TG6, h=15mm, r = 0 - 5 . 5 m m

rif = M.(0.044 - 16.03r + 2.883xIO4r2

8 d -[pZnr/ u’dy].dr - m2rrrdrVsina (3) dr 0

The net force on the control volume is:

d dr 2 n [ - - ( r 6 p ) ~ ~ ~ r ] d r

where T~ is the surface shear force when y = 0:

So the momentum equation for thc control \ olunie IS.

d dr

- - ( rSp) - Tor =

6 (6 ) p i ( . / u’dy) - ritrVsina 0

The continuity equation can be ohtaincd on a disc with a radius of r :

(10) - 4.983 x 106r’)

TGB, h = 15mm. r = 0 - 5mm

The mass flow rata distribution will affect the pressure profile [ eq. ( I ) 1, and thus affect the film flow. But gctting a unique equation for the mass flow rate profile is impossihle. Reference I O provides a more detailed discusion on radial and circumferential liquid distribution in dic spray core. Ortman and Lefehvre [I I ] examined the sQray characteristics of several n o d e s of different design They found the circumferential maldistrihutions can he seen in most of the nozzles. For the TG4 and TG6 nozzles used in thc experiment, the radial mass flow rate distribution is diffqmt and the circumferential maldistrihutions were also obscrved. So in order to get better comparison between dilfercnt nozzles, the mass flow rate profile as eq. ( I O ) is uscd in most of the film thickness calculations except when spccifiai DBerent mass flow distributions are also used in order to see their effect on the film thickness.

The effect of nozzle height is very important for application. Nozzle heights of IO mm and 15 mm are used for comparison with the experimental results.

When the velocity and the mass flow rate profile are substituted into equation (Z), (6) and (7). we can’get a diRerential equation of the form :

dS dr /I ( ~ k V h . r 3 w ) - =f, ( ~ , f i , V , h , r , p . f i ) (11)

For the laminar integral method, thc results are

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60 80

70

-Eo. E E - 50 5 40

413kPa --.- / * . E i 40 -

d

5 - 8 < M -

E 20 . .-

Y ._ 30: - E .

20

10

0 0

c . I-

y. Y

TG4 I5 mmNozzle Height 10 -

R ( m m )

Fig. 7 Numerical Film Thickness Rcsillts of TG4

Runge-Kutta method of the sixth order is used to integrate eq. (1 I). This equation is unstahle for a small radius. So integration starts at about r = 2 mm for I5 mm n o d e height and at 1.5 mm for 10 mm nozzle height. Thc factory specification of the spray angle of TG4 and TG6 is 54” - 63” dcpending on the nozzle inlet pressure. However, the mass flow rate profile measurements show most of the m a s flow is concentrated within 40” (see Figure 5). so the integrations are also done within that angle. Water properties at the room temperature and the droplet velocities listed in Table 1 are used in the analysis. ~d

Results and Discussion Figures 7 to 12 present some of the numerical

results. F iy rcs 7 and 8 show the film thiclaicss results of TG4 and TF6 at I5 mm nozzle heights. Because of the hollow spray core center, the pressure gradient caused by droplet impingement (Eq. 2) is unfavorahle near the ccnter (up to 3.5 mm for TG4, I5 mm nozzle heights). So the film

- . 206kPa

275 kPa - 413kPa

.

. TG6 15 mrn Nozzle Height

-

d

€ 4 -

E 50- I .

5 4 0 -

5 30-

,-. - 2 - E

20

1 T G 6 / ‘“1 .+ 50 T G 4 / :

-

40

20

10 I S nun Nouls Height 276 kPa

1 .O 2.0 3.0 4 0 5.0 6.0

R ( m m )

Fig. 8 Numerical Film Thickness Results of TG6

thicknes decreases to provide the pressure gradient to keep the liquid flowing out. This is reflected in Figs. 7 and 8. Superficially, it would appear that higher mass flow rate will make the film thicker. But with the increase of the mass flow rate, the n o d e inlet pressure and therefore the droplet velocity also increases. Higher droplet velocity causes higher pressure on the film (Eq. 1) which makes film thinner. Combining these two factors, the film thickness decreases slightly with the increase of liquid flow rate and nozzle inlet pressure as shown in Figs. 7 and 8.

The effect of the nozzle orifice diameter on the film thickness is also directly related to the mean droplet velocity and the liquid flow rate, and the results show the droplet velocity has a significant effect on the film thickness. Figures 9 and 10 illustrate the comparison of film thickness results of TG4 and TG6 at same nozzle inlet pressure (Fig. 9) and same liquid flow rate (Fig. 10). When the nozzle operating pressure is fixed, nozzles with a larger orifice (TC6) have lower droplet velocity and higher flow

70, . I , I . . , I

Liquid Flow Rate 6.7 cch 1 I5 mm Nozzle Height 10

0 1 .o 2.0 3.0 4.0 5.0 6.0

R (mm)

Fig. 9 Comparison of Film Thickness Rcsults Fig. IO Effect ofDroplet Velocity on Film Thickness Results

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Fig. 11 The Effect ofNozzle Height on Film ~lliic!aess

rate (Table I). This results in a thicker film compared with that of the nozzle with a smaller orifice as shown in Fig. 9. While for a fixed liquid flow rate (Fig. IO), nozzlcs with a smaller orifice have higher droplet velocity and thcrcfore thinner liquid film as shown in Fig. 10.

The effects of nozzle height are not as sigiiiiicnt. The mean droplet velocity drops only about 5?4 for the distance from I O mm to IS nun. This is not cnoogh I o iiiakc a perceptible difference. So despite the change oflhe local liquid flow rate for different nozzle height, the film thickness remains almost unchanged. Figure 1 I sliow~s the comparison of numerical results of TG4 at I O nini and 15

- . .- Effects of mass flow rate distribution iiii film

thickness are further presented in Figure 13 \ v i t h the comparison of numerical solutions with the expcriinental results. The numerical results we ohtained at R = 5 mm since the film thickness is also mcasured at that riiilius. For

20

10

ro - Eq 10 -

E 60 - 1 . - c - y-: 2 M -

Eq 9 r P 40

& 30

- t -

-

TG4 Eq. 9 :

0 TG4 1

t A TG6 I5 mm Nozzle Height :

-

0- " ' ' ' I " " "

ro - Eq. 10 -

E 60 - 1 . - c - y-: 2 M -

t . Eq. 9 r

P 40 -

TGG I5 mm Nozzle liaight 276 kPa : : I , , , , , , , , , I 0 1.0 2.0 3.0 4.0 5.0 6.0

R ( m m ) Fig. 12 The Effect of Mass Flow Rate Profile on Film Tliickness

given by Eq. I O gives better results However, both can give a prediction of the film thickness within * 20% while thc results with Eq. 10 have an accuracy about * 10%. Considering the inevitable circumferential mal-distribution and its effect on the film thickness, this accuracy can he considered acceptable. Figure 13 also shows the decrease of the film thickness with the increase of the nozzle operating pressure as discussed above. The film thickness u f T M with a larger orifice is also always thicker than that ofTG4 ifthe same flow rate profile is used for both nozzles.

Since there is only a slight change in the Sauter meal diameter of the droplets ( from I20 pm to I32 pm )

concentrated near the edge, the iiunierical solutioii @Js slightly thinner film coniparcd with thc experimental rusults. While the numerical solution with tlic flow rate prdile

Fig. 13 Film Thickness Results with Different Flow Rate Distnbutiou and Uie Coinparisoil with

Experimental Results 4'

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Aincrican Instilutc of Aeronautics and Astronautics

thickness remains unclear in the present study

Conclusions A method using the point gauge is developed to

measure the water film thickness in the spray core. Experimental results show the film thickness is around 50 pm for the two nozzles tested. The effcct of thc nozzle height on the film thickness is insignificant for the two hcights ( I 0 mm and I5 mm) tested.

An integral method that incorporates the effect of mass flow rate distribution is used in the numerical analysis. The results agree well with the experiment and show the following properties of the film in the spray core: the mean droplet velocity and the radial mass flow rate distribution are the main factors that affect the liquid film thickncss in the spray core of pressure atomizing noulcs; for each nozzle, the film thickness decreases with the incrcase of thc nozzle inlet pressure and liquid flow rate; nozzles with a smaller orifice diameter have thinncr liquid films at the w e nozzle operating pressure or the same liquid flow rate; the radial and circumferential mass llow rate disti-ibution affects the film thickness and also tlic shapc of the film surface. The numcncal method incoi-porating the two correlations of mass flow rate distrihution provided in the paper can give the prediction of thc watcr film thickness with an accuracy of I 20%. Equation 10 achieved hctter accwacy for the two novlcs testcd.

The numerical methcd developed in this paper can provide a solid base for hcat transfer analysis of spray cooling.

Refcrences I M.S. Sehmhey, L.C. Chow, M.R. Pais and E.T.

Mahefkey, "High heat flux spray cooling," Heat Transfer in High Heat Flux Systems, HTD-Vol. 301, pp. 39 - 46, ASME 1994.

2 M.R. Pais, L.C. Chow and E.T. Mahefkey, "Suiface roughness and its effects on heat transfer nieclianism i n spray cooling," J. ofHeat Tr.an/er, Vol I 14. pi). 2 1 I - 219, 1992.

3 D.E. Tilton, "Spray cooling," P1i.D. dissertation, University ofKentucky, Lexington, KY, 1989.

4 J.D.Yang, "Spraycooling with an air atomizing nozzle,"

P1i.D. dissertation, University of Kentucb, Lexington, KY, 1993.

J.D. Ymg, L.C. Chow and M.R. Pais, "Liquid film thickness and topography determination using Fresnel diffraction and holography," Experimenkd Heat Transfer., Vol. 5, pp. 239-252, 1992.

G J.D. Yang, L.C. Chow and M.R. Pais, "An analytical model to determine the liquid film thickncss produced by gas atomized sprays," 29th ASME/AIChE National Neat Transfer Cod.. , ASME Paper No. 93-HT-30, Atlanta, GA., 1993.

7 T. Azuma a id T. Hoshino, "The radial flow of a thin liquid film," Bde t in ofJSME, Vol. 27, No. 234, pp. 2747-2754, 1984.

8 A.P. Fickett and F.R. Kalhammer, "Water electrolysis," liydrogen: its technology and implications, Vol. 1,

CRC Press Inc., pp. 3 - 44, 1977.

9 El. Schlichting, Boundaiy Layer Theoiy, 7th Edition, McGraw-Hill Book Company, pp. 449-488, 1979.

5

0 A.H. Lcfcbvrc, Arornization and sprays, Hemisphere Publishing Corporation, pp.298, 1989.

1 J. O m a n and A.H. Lefebvre, "Fuel distribution from prcssure-swirl atomizers," AlAA J. Propul. Power, Vol. I,No. l ,pp. I I - 15, 1985.

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