Experimental Thermal and Fluid Science 34 (2010) 933–942

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Experimental Thermal and Fluid Science

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Experimental study on the effects of spray inclination on water spray coolingperformance in non-boiling regime

Yaqing Wang, Minghou Liu *, Dong Liu, Kan Xu, Yiliang ChenDepartment of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui 230027, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 14 September 2008Received in revised form 14 January 2010Accepted 19 February 2010

Keywords:Spray coolingInclination angleNon-boiling regime

0894-1777/$ - see front matter � 2010 Elsevier Inc. Adoi:10.1016/j.expthermflusci.2010.02.010

* Corresponding author. Tel.: +86 551 3603127.E-mail address: mhliu@ustc.edu.cn (M. Liu).

Experiments were performed to study the effects of spray inclination angle (the angle between the nor-mal of the square test surface and the axis of symmetry of the spray), the mass flux as well as the surfacetemperature on the heat transfer performance in non-boiling regime by using water sprays. A swirl semi-solid nozzle was used with mass flux of 15.7 kg/m2 s, 18.1 kg/m2 s and 24.9 kg/m2 s, respectively. Thespray parameters were measured by PDPA. It was found that there was a recirculating zone due to astrong rotational flow at the center of the spray. By varying the orifice-to-surface distance for the sameinclination angle, the optimum distance was found, corresponding to the best heat flux, when the majoraxis of the elliptical spray impact area intersects the square test surface. With the optimum distance foreach different inclination angle, the heat flux, heat transfer coefficient and cooling efficiencies wereobtained and the results showed that as the inclination angle increased, the heat transfer performanceand utilization efficiency of liquid were both enhanced gradually, with an increased rate as the surfacetemperature approaches the saturation temperature of the liquid spray. Generalized correlations weredeveloped for local Nusselt number as a function of the spray Reynolds number and the non-dimensionaltemperature in non-boiling regime of vertical and inclined sprays.

� 2010 Elsevier Inc. All rights reserved.

1. Introduction

1.1. Background and literature review

Many emerging technologies with higher transistor integrationdensities, such as microwave systems, defense laser, modern elec-tronics and power devices, have increased the chip level heatfluxes that may reach the range of more than 100 W/cm2 in nearfuture [1,2]. Traditional cooling technologies such as air coolingcould not be adequately satisfy such high-flux heat removal, andwill have to be replaced or supplemented by other effective coolingsolutions. Alternative cooling technologies involving jet impinge-ment, micro-channel flow, droplets and sprays, are receiving great-er attentions from researchers. Each of those schemes hasadvantages and drawbacks which must be carefully evaluatedwhen selecting a heat removal system. Micro-channel cooling de-vices offer compactness and reduced coolant inventory. However,they also have potentially high pressure drop and temperature dif-ference between the inlet and the outlet within the heat source. Jetimpingement is especially desirable for cooling very high-fluxdevices, but may lead to large spatial temperature gradients unlessimplemented in a carefully configured multi-jet array [1–8]. Of the

ll rights reserved.

above cooling technologies, spray cooling may be the best compet-ing option for thermal management of high heat flux systems,which could provide high heat flux in excess of 1000 W/cm2 withwater as coolant while allowing uniformity of heat removal atsmall fluid inventory. Despite those advantages, spray coolingcould not be widespread in the industrial applications because ofpoor understanding of the underlying mechanism and the keyparameters that influence cooling performance [7–9].

The physical, as well as the geometrical, parameters that affectspray cooling performance include mean droplet size, droplet flux,droplet velocity [10,11] and volumetric flux [12,13] while the latterare composed of cone angle, orifice-to-surface distance, and sur-face type and inclination angle. Besides those, the subcooling ofcoolant [6,10,14,15] and nozzle type [6,8] also influences coolingperformance.

Compared to the above factors, geometrical parameters gainedmuch less attention from researchers and the corresponding liter-atures were quite sparse. The existing studies and literaturesmainly focused on orifice-to-surface distance and surface type.Mudawar and Estes [16] experimentally illustrated the optimumdistance between the orifice and the heater surface at which CHFwas maximized for a given volumetric flux. And this occurredwhen the spray was configured such that the impact area just in-scribed a square test surface. Too small orifice-to-surface distanceswould result in only a small fraction of the test surface impacted by

Nomenclature

V droplet velocityd32 Sauter mean diameterk thermal conductivityTw surface temperatureQ volumetric flow ratecl specific heat of waterg cooling efficiencym mass flow rate (L/h)h inclination angle between spray axis and normal to test

surfaceN droplet fluxq00

heat fluxDT temperature gradienth heat transfer coefficient

q the destiny of waterA the area of test surfacee error toleranceG mass fluxa spray cone angler surface tension

SubscriptsT temperatureSpray sprayWall wallTest testx distance between thermocouplesInclined inclined

934 Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942

the spray, while too large a distance causes a substantial fraction ofthe spray liquid falling wastefully outside the test surface. Both ex-tremes made CHF small. From above, it was concluded that the ori-fice-to-surface distance was essential to the cooling performanceand influenced the heat transfer directly. Concerning the surfacetype, it has been widely accepted that increasing surface roughnessand using structured surface enhancements could benefit heat fluxand offer better nucleation characteristics, however, in recentyears, most of studies have been performed using the latter[6,8,17].

There are very few published literatures available on the effectsof spray inclination on spray cooling performance. Using a singlenozzle whose spray inclination angles varied between 0� and 60�with the orifice-to-surface distance kept 1.4 cm to cool a heat sur-face, Li et al. [18] revealed that there was little effect unless theinclination angle exceeded 40�. Shedd et al. [19] used inclinedsprays to assist with fluid drainage and mitigation of heat flux deg-radation because of the multi-nozzle configuration and assertedthat inclined sprays also provided orientation-independent heatflux performance. Recent studies conducted by Silk et al. [20]examined the effects of spray inclination using PF-5060 as workingfluid to both flat and enhanced surface with multiple nozzles.Spray angles in their test were 0�, 30�, and 45�. The orifice-to-sur-face was constant and heat flux was based on the projected area ofthe test surface. For both the flat and enhanced surface, the opti-mum heat transfer performance was achieved at an inclination an-gle of 30�.

As suggested previously, in the review of past investigations,works focused on the boiling regime and the conclusion was onlyappropriate for high temperature and high heat flux. The non-boil-ing regime’s spray cooling performances, as an important part ofthe spray cooling process, has been investigated by very fewresearchers. In the non-boiling regime, the surface temperature isbelow the boiling point of coolant. During spray, droplets accumu-late to form a moving liquid film on the heater surface. As moredroplets come in, the film swept away by fresh cold coolant movestowards the edge of the heater and becomes turbulent gradually,removing large amounts of heat flux due to the latent heat of evap-oration in addition to substantial forced convection. The mecha-nism of heat transfer in non-boiling regime consists of forcedconvection and liquid film evaporation. Oliphant et al. [7] studiedthe heat transfer of non-boiling regime using air-assist nozzle.The author suggested that mass flux determined heat transfer per-formance and droplet velocity also affected the heat transfer, butfurther studies was required to verify and quantify this effect. Nitinet al. [21] studied the heat transfer of non-boiling regime usingpressure atomization nozzle and developed an empirical correla-

tion, which related the dimensionless parameters: the averageNusselt number and the spray Reynolds number. The two men-tioned representative studies in the non-boiling regime did notconsider the effect of film evaporation and the authors held thatthe evaporation of the film can be neglected. As one of the signifi-cant mechanisms, liquid film evaporation takes up low proportionin the heat transfer but can not be neglected, especially in the non-boiling regime.

1.2. Objectives of present work

Unlike the published studies discussed antecedently, whichconcern inclined sprays in the boiling regime, the primary purposeof the present study is to develop comprehensive design tools vitalto the implementation of spray cooling at different inclination an-gles, and to explore the variations in cooling performance and cool-ing efficiencies as the inclination angle increased from 0� to 49� innon-boiling regime. The heat transfer of non-boiling regime con-sideration for film evaporation will be also studied. The results ofthe experiments will be utilized to develop an empirical dimen-sional correlation to completely reflect the characteristics of heattransfer in non-boiling regime. A modified model is developed topredict the heat transfer of inclined sprays. Experiments were per-formed using a semi-solid swirl nozzle with a spray cone angle of60� with the mass flux ranged from 15.7 kg/m2 s to 24.9 kg/m2 sand distilled water was used as coolant.

2. Experimental apparatus

In order to maintain the atmospheric pressure, an open flowloop was designed, as shown in Fig. 1. The experimental apparatusconsisted of a spray system, a data acquisition system and a heatersource. The experimental setup provided the opportunity to varythe surface heat flux, the water mass flux, the droplet diameterand velocity, the spray inclination angles, the distance betweenorifice and surface as well.

In the spray system, the liquid coolant was supplied from a lowtemperature sink which was used prior to heat and cool the cool-ant to desired nozzle inlet temperature. By the side of the low tem-perature sink was a variable-speed, magnetically-coupledcentrifugal pump which could supply a maximum pressure of8.6 bar and a maximum flow rate of 4 L/min. The pumped liquidfirstly passed through a filter, to remove any entrained impurities,followed by rotameters, a pressure transducer and a temperaturetransducer where rate flow, tube pressure and nozzle inlet temper-ature were measured respectively. The fluid then entered into thenozzle and sprayed downwards at different inclination angles.

Fig. 1. Experimental setup.

Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942 935

After the heat exchanger, the fluid was drained to the lower por-tion of a large reservoir by gravity. The coolant lastly passedthrough the heat exchanger to bring the surplus heat by the tapwater and returned liquid to the low temperature sink.

In order to adjust the nozzle position, the nozzle positioningsystem was designed, shown in Fig. 2. With the aid of nuts in thevertical direction, the orifice-to-surface distance could be adjustedto a desired value and the inclination angle cloud be controlled bythe horizontal nuts and the rotation stage where a series of holeswere drilled and spanned 0–70� from normal in 7� increments.

The heater source was made of a pure copper block and washeated by five 300 W cartridge heaters bored under the side ofthe copper, as show in Fig. 3. The copper block trapped off nearthe top to a 10 mm � 10 mm crown, was a solid cylinder, whichwas 57 mm in diameter and 110 mm in height. To minimize heatloss, all surfaces of the copper block were insulated by Durablanketinsulation (thermal conductivity, k = 0.013 W/m k) except the testsurface and were supported by an aluminum enclosure. The heaterwas integrated into the spray chamber using standard flat faced

Fig. 2. Nozzle positioning system.

flanges. Before fabricating the heater, a three-dimensional heat dif-fusion model using FLUENT showed that the heater exhibited agood one-dimensional heat transfer characteristic (as shownFig. 4). Six K-type (Chromel–Alumel) thermocouples with a0.127 mm wire diameter and 0.25 mm bead diameter was embed-ded 10 mm below the test surface to measure the surface temper-ature, accounting for the temperature gradient between thethermocouple head and the surface(as shown in Fig. 3). Knowingthe distance between the thermocouples and those between thethermocouple and the heater surface (both 10 mm), it was possibleto predict the heat flux and the surface temperature using the one-dimensional Fourier law of heat conduction. Thermal analysisusing FLUENT showed that the surface temperature was very closeto that inferred using one-dimensional heat conduction betweenthe planes of thermocouples and the test surface.

The data acquisition system was comprised of an Agilent34970A digital acquisition/control system and a personal com-puter, which recorded and processed the signal from the thermo-couples as well as the temperature and pressure sensorsthroughout the loop.

Fig. 3. Schematic diagram of heat-target.

XZ

Nozzle

measurement plane 1

measurement plane 2

measurement plane 3

Fig. 6. Spray cone measurement planes.

Fig. 4. Schematic diagram of simulated temperature.

Table 1The parameters of nozzles atomization (measurement plane 3).

Pressure (MPa) Mass flux(kg/m2 s1)

Diameter d32

(lm)Velocity V(m/s)

0.4 15.7 45–113 �0.1–13.60.45 18.1 45–107 �0.1–14.70.5 24.9 45–100 �0.3–15.9

ty o

f dr

ople

t (m

/s)

-10 -5 0 5 10

10 10

20 20

4.8 mm8.66 mm12 mm

936 Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942

3. Spray parameters

The spray parameters, mainly the droplet diameter, velocity andthe spray pattern, were measured by a Dantec Phase Doppler Par-ticle Analyzer (PDPA). The PDPA system determined the spraycharacteristics via photo-detection of scattered light. As shown inFig. 5, measurements were made at the control volume formedby intersection of the two beams from emitter. The interferencefringe pattern produced by light scattered by individual drops asthey passed through the control volume was captured by opticaldetector. The oscillation intensity of the scattered light corre-sponds to particles passing through the fringes and has a frequencywhich is proportional to the velocity of the component at right an-gle to the fringe. The phase difference between the signals fromdetectors was proportional to the droplet size. Detailed explana-tion to this measurement can refer to the work by Estes et al.[12] and Silk et al. [22]. In these tests, data were obtained alongthe x axis at three different planes with known distances fromthe nozzle (schematic shown in Fig. 6). In the horizontal axis atthe same measurements heights, the velocity and diameter ofdroplets were also measured by PDPA every 0.5 mm. Measuringrange was �10 mm < x < 10 mm from the spray cone one edge toanother as described by Silk in detail [22]. The centerline axiswas taken as x = 0 and the edge of measured spray cone was takenas x = ±10 mm.

measured volume

nozzle

emitter detector

Fig. 5. PDPA system measurement schematic.

In the experiment, through the semi-solid swirl nozzle, the dis-tilled water mass flux is ranged from 15.7 kg/m2 s to 24.9 kg/m2 s.Key hydrodynamic parameters are shown in Table 1.

Figs. 7 and 8 present the cross-stream distribution of thestreamwise mean velocity and Sauter mean diameter (SMD) ofdroplet at position of z = 4.8 mm, 8.66 mm, and 12.0 mm, respec-tively (Fig. 6). The mass flux is 24.9 kg/m2 s. As z increases, themultiple peaks in Figs. 7 and 8 did not merge into one. Fig. 7 showsthat there are two local peaks and one local valley across the spraycone in each measurement and as the distance from the nozzle (z)increased, the local peaks speed decreased. Regardless of the dis-tance from the nozzle, the distribution plot showed that the localvalleys are all located at the center of the spray cone. Whenz = 4.8 mm, the streamwise mean velocity of droplet in the spraycone center (�2 mm < x < 2 mm) is negative. This may be attrib-uted to the effect of the recirculating zone resulting from thestrong rotational flow. However, when z = 8.66 mm, the negative

X location

The

mea

n ve

loci

-10 -5 0 5 10-20 -20

-10 -10

0 0

Fig. 7. Schematic of mean droplet velocity distribution (24.9 kg/m2 s).

X location (mm)

The

dia

met

er o

f dr

ople

t (μ

m)

-10

-10

-5

-5

0

0

5

5

10

10

30 30

60 60

90 90

120 120

150 1504.80 mm8.66 mm12.0 mm

Fig. 8. Schematic of SMD distribution (24.9 Kg/m2 s).

Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942 937

streamwise velocities appear only at x = 0 mm; when z = 12 mm,all the streamwise velocities become positive. In other words, therecirculating zone resulting from the strong rotational flow be-comes weaker and weaker when z increased gradually. Near theouter edge of the spray in each measurement plane, the stream-wise velocities are continuously approaching zero. The maximumdroplet velocity for this flow flux is 18.9 m/s when z = 4.8 mm.

The diameter of droplet distribution (Fig. 8) shows that in therecirculating zone the SMD is minimum (approximately 35 lm),while at outer side of the spray zone, the SMD is comparativelylarge (approximately 35–130 lm). The main reason is due to thelow odds that droplets converge with new larger ones due to rota-tional flow which causes a smaller density of droplets at the centerof spray cone.

Fig. 9 shows the distribution of transverse mean velocity ofdroplet. It is found that the figure is anti-symmetric in each mea-surement plane. The velocities are zero at the center of the spraycone. The values of velocities at both sides are nearly equal whilethe directions are opposite. Hence, it could be concluded that thespray fluid structure (spray pattern) exhibits axis symmetric well.

X location (mm)

The

mea

n ve

loci

ty o

f dr

ople

t (m

/s)

-10

-10

-5

-5

0

0

5

5

10

10

-20 -20

-10 -10

0 0

10 10

20 20

4.8 mm8.66 mm12 mm

Fig. 9. Schematic of transverse mean velocity of droplet (the horizontal axis).

4. Data and uncertainty analysis

4.1. Data analysis

In the experiment, the main parameter measured is the temper-atures in the heated element. The surface temperature and heatflux are both calculated using those temperature readings assum-ing one-dimensional heat transfer using Fourier’s law. The heatflux is

q00 ¼ kDTDx

ð1Þ

where k is the thermal conductivity of the heater plate, DT is thetemperature difference between the thermocouple measurementsand Dx is the distance between the thermocouples used. The aver-age surface temperature on the hot surface Twall, can be attained by:

Twall ¼ T1m �q00Dx1�wall

kð2Þ

where T1m is the arithmetic means of the temperatures indicated bythe two thermocouples closest to the upper surface and Dx1�wall isthe distance between the first thermocouple and the test surface.The average heat transfer coefficient is a very important parameterand was calculated by:

h ¼ q00

Twall � Tsprayð3Þ

To appraise how efficiently the coolant used in spray cooling,the single phase cooling efficiency, characterized by the ratio ofthe real heat flux to the theoretical maximum heat flux in non-boiling regime, is generally defined as:

g ¼ q00AqQðc1ðTwall � TsprayÞÞ

ð4Þ

An empirical correlation was developed for all the data in theterms of dimensionless groups. The Reynolds number was de-scribed based on the length L of the target surface and mass fluxas [7]:

Re ¼ GLl

ð5Þ

where the mass flux G can be calculated by the followingexpression:

G ¼ m3600Atest

ð6Þ

And the Nusselt number was defined in the light of the length Lof the target surface and heat transfer coefficient as [7]:

Nu ¼ hLk

ð7Þ

To reflect the influence of droplet diameter and velocity on heattransfer, a dimensionless number known as Weber number is de-fined as:

We ¼ qv2d32

rð8Þ

And this is a measure of the relative strengths of the competingeffect of droplets’ kinetic energy and the surface energy.

4.2. Measurement uncertainty

All measurements in the experiment have extra fine error toler-ance. The data acquisition has a resolution of 0.5 �C. This deviceand the thermocouples were compared to a precision mercurythermometer with ±0.05 �C rated accuracy before used at the range

30 40 50 60 70 80 90 10025000 25000

938 Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942

of 0–300 �C. The system accuracy is found to be within 0.25 �C overthe range of test, so the steady state is reached when the temper-ature fluctuate within 0.25 �C. The rotameter was calibrated byweighing on an electronic scale with an accuracy of 0.1 g. The accu-racy of the distance between thermocouples and the cooling sur-face area of the heater are 0.1 mm and 0.05 cm2, respectively.The PDPA Manual gave the maximum measurement uncertaintiesof ±0.5% and ±0.25% for droplet and velocity, respectively. ThePDPA measurements also yield the mass flow rate and detailedexplanation can refer to the work by Chen et al. [10]. In order totest and verify the accuracy of this measurements, in light of themethods given by Chen et al. [10], the comparison with the directmeasured flowrate by rotameter indicated excellent agreement, towithin 7.3%. According the method proposed by Kim and Kiger[23], it showed that the uncertainty of Tw was estimated within±2.9 �C, at q = 160 W/cm2 and the power removed by the spraywas typically 94.7% of input to the cartridge heater which is iden-tical with the analytical calculation using fluent.

According to the traditional methods of error analysis, theuncertainty of the heat flux can be calculated by:

dq ¼ �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi@q@x

dx

� �2

þ @q@k

dk

� �2

þ @q@ðDTÞ dDT

� �2s

ð9Þ

The conductivity value used was 398 ± 4 W/mk. When the heatflux is 150 W/cm2, the uncertainty dq is less than ±6.0%. Followingthe same procedure, the estimated uncertainties in the variousparameters are: mass flux ±3.2%, Reynolds number ±5.61%, andNusselt number ±7.1% over the range of experiments.

Wall temperature ( oC )

Hea

ttra

nsfe

rco

effi

cien

t(W

/m2

K)

30 40 50 60 70 80 90 1005000 5000

10000 10000

15000 15000

20000 20000

15.7 kg/m2s18.1 kg/m2s24.9 kg/m2s

Fig. 10. Heat coefficient vs. wall temperature (inclination angle 0� and standoffdistance of 8.66 mm).

5. Operating procedure

Before commencing the experiment, the distilled water waspumped into the pipe without the nozzle to remove impuritiesadhering to the pipe. To ensure consistency in the surface proper-ties of the heater, the surface was cleaned with acetone to removeoxides and residues and then polished with 360-grit sandpaper.

To achieve the optimum orifice-to-surface distance where thesystem has maximum heat flux in a given inclination angle, theexperiments were conducted in the condition of different orifice-to-surface distances and inclination angles.

Experiment curves are produced by raising the electrical powerinput to the heater in small increments and recording the heat fluxfrom the test surface and the surface temperature. Although thetemperature of the heater block changed with the increasing ofheat input, the temperature at the crown reached a quasi-steadystate due to the fact that the amount of heat stored in the crownregion are small. But this was validated by the fact all the thermo-couples fluctuated within 0.25 �C over 20 min periods, in the otherwords, the linearity of the temperature gradient are approximatelyconstant. The data were recorded only after the system reachedsteady state. The steady state for each run was obtained in about1–4 h and experiments showed that the larger inclination anglehas a longer time to reach the steady state.

Fig. 11. Image of nozzle spray in stagnation zone (inclination angle 0� and standoffdistance of 8.66 mm).

6. Results and discussion

6.1. Surface temperature results

The heat transfer mechanism in the non-boiling regime mainlyincludes forced convection and film evaporation. At the surfacetemperatures below the saturation temperature of coolant, theheat is mainly transferred by the sensible heating of the fluid flow-ing over the surface and the latent heat because of the evaporationof the thin film on the surface. The variation of heat transfer coef-

ficient vs. surface temperature at the different mass flux is shownin Fig. 10.

From Fig. 10, it can be seen that the heat transfer coefficient in-creased slowly with the wall temperature at all mass flux workcondition. It is abnormal compared to other convective heat trans-fer techniques where the heat transfer coefficient is irrelevant tothe wall temperature and mainly depends on the properties andthe motion state of coolant. Such abnormal phenomena can beattributed to the factor that the increase of the wall temperatureenhanced the evaporation of the water film resulting from thedroplet coalescence on the test surface. And the conclusion wasalso drawn by Kim and Kiger [23]. However, the conclusion wasinconsistent with the study by Nitin et al. [21] and Oliphantet al. [7] who ignored the evaporation of the liquid film.

Revisiting the experimental results, Fig. 10 shows that therewas an inflexion point in the curves around 85–90 �C, beyondwhich the heat flux, heat transfer coefficient increased quickly. Itmay be attributed to the fact that the local temperature exceededthe boiling temperature in the stagnation zone which leads tosome bubble formation and enhancement in the heat transferdue to boiling (shown in Fig. 11).

6.2. Spray inclination angle

To explore the performance of spray cooling, non-boiling curveswere measured using the semi-solid nozzle at a mass flux of

Fig. 12. Schematic representation of spray impact patterns for different orifice-to-surface distances (at 14� inclination angle).

Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942 939

24.9 kg/m2 s and subcooling of 80 �C in the condition of differentinclination angles and orifice-to-surface distances. Fig. 13 showsthe effect of orifice-to-surface distances with the inclination angleof 14�. The major axis of the elliptical impact area inscribes, inter-sects, and circumscribes the square test surface at the distances of7 mm, 8 mm, 9 mm, respectively, as shown in Fig. 12. Each of thesedistances is hereafter denoted as cases 1, 2 and 3, respectively.

Fig. 13 shows that when the major axis of the elliptical impactarea is intersecting the square test surface (case 2), the heat trans-fer performance is the best. This is degraded when the orifice ismoved toward or away from the surface. The main reason for suchperformance can be explained as follows. In case 1, only a smallfraction of the heated area is directly impacted by the spray drops,yielding small heat flux, while, a substantial portion of the spray li-quid falls wastefully outside the test surface in case 3. However, incase 2, the contact region is maximized under the constraint offully utilizing the spray liquid, which, therefore, optimizes the heattransfer performance. So the height in case 2 was determined asthe optimum orifice-to-surface distance.

All the next experiments in current studies were obtained withthe major axis of the elliptical impact area just inscribing thesquare teat surface. Under this constraint, increasing the inclina-tion angle causes a pronounced decrease in both the distance be-tween orifice and test surface and the area of impact ellipse, asshown in Figs. 14 and 15. As illustrated in Fig. 15, distance H is re-lated to length L of the test surface by the relation.

Wall temperature ( oC )

Hea

tfl

ux(

W/c

m2

)

30

30

40

40

50

50

60

60

70

70

80

80

90

90

100

100

3030

6060

9090

120120

150150

1801809.00mm7.00mm8.00mm

Fig. 13. Heat flux vs. wall temperature at 14� inclination angle.

H ¼ Lsin 60

sinð60� hÞ sinð120� hÞ ð10Þ

And the area of ellipse is given by:

Aellipse ¼p4

L2 cos hð1� tan2 h tan2ða=2ÞÞ1=2 ð11Þ

Calculated from relation 8, the optimum distances are 6 mm,3.5 mm, 2.1 mm, respectively at the inclination angle of 28�,42�and 49�. Fig. 16 shows the effect of inclination angle on the heattransfer characteristics. All the tests are conducted with the opti-mum orifice-to-surface distance. It could be found that increasingthe inclination angle leads to a better heat transfer performance,which is not in agreement with previous studies (Li et al. [18];Visaria and Mudawar [2]). The difference between the current re-sults and the studies proposed by Li et al. [18] which indicated thatthere was little effect unless the inclination angle exceeded 40�,might be attributed to the stringent geometrical constraints in thisstudy. As mentioned earlier, nozzle to heater surface distances forcurrent studies must be reduced gradually as the inclination in-creased to insure that all the liquids are impacting the surfaceand that the major axis of the elliptical spray impact area is inter-secting the square test surface. However, it was kept at a constant

Fig. 14. Schematic of impact patterns for different inclination angle.

Fig. 15. Nomenclature for inclined model.

iii

iii

ii

i

i

i

Wall temperature ( oC )

Hea

tfl

ux(

W/c

m2

)

30

30

40

40

50

50

60

60

70

70

80

80

90

90

100

100

0303

0606

0909

021021

051051

081081

0120120o

14o

28o

42o

49oi

Fig. 16. Heat flux vs. wall temperature.

940 Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942

in Schwarzkopf studies. So when the inclination increased to a cer-tain value, it could create overspray and heat flux decreased.

The tests conducted by Visaria and Mudawar [2] suggested thatinclination angle has little effect on the heat transfer in the non-boiling regime, on the condition that all the tests were performedwith the major axis of the elliptical impact area just inscribing thesquare test surface and the range of inclination angle is from 0� to55� with full cone nozzles. The reason for such conflict might beowing to the exceptional spray nozzle used in the experiment. Asmentioned previously, in the semi-solid swirl nozzle, there is arecirculation in the center of the spray cone which creates a stag-nation zone at the center of the heated surface, resulting in theaccumulation of an unsteady liquid pool in the center of the sur-

Fig. 17. Image of nozzle spray at

face as shown in Fig. 17. It also shows that the larger the inclinationangle, the smaller the stagnation area, which disappears in any ofthe heat flux regimes as the inclination angle reaches 49�. It meansthat the inclined sprays could foster better liquid drainage from thetest surface by washing out the stagnation zone and this determi-nation was also experimentally shown in the study by Silk et al.[20]. This factor can also illuminate the phenomenon that the heattransfer increased with the increasing of inclination angle as[10,20].

Despite the increase in the heat transfer, it takes a longer timeat larger inclination angles for the test surface to reach steady statebetween power increments. One possible reason is the fact that theheat transfer is highly uneven in the current studies, thus the heatis not conducted uniformly through the copper and it may take along time for the thermocouples to reach a stable state. And thisstable effect would be more evident at larger inclination angles.

The cooling efficiencies are shown as a function of temperaturein Figs. 18 and 19. On account of the splashing and the shorter li-quid residence time on the heater surface due to the high speedimpinging droplets, the heat exchange between the surface andthe liquid is generally quite small and the cooling efficiencies arecharacteristically low, less than 50% [24].

In Fig. 18, the cooling efficiencies decreases in the sequence ofcase 2 then cases 1 and 3, this was consistent with the analysisof the heat transfer performance. As for the inclination angle cool-ing efficiencies (shown in Fig. 17), 49� gives the optimum coolingefficiency corresponding to the maximum heat flux, followed by42�, 28�, 14� and 0� sequentially.

6.3. Theoretical models

In this part, a new analytical model is constructed to determinerelations between the various geometrical parameters of an in-clined spray. From intuitive judgment, one can argue that heat fluxdepends on the Weber which characterizes the impacting dynam-ics of the droplet. In present studies, the mass flux is ranged from15.1 kg/m2 s to 24.7 kg/m2 s and Weber number is less than 350.However, Bernardin’s study [25] suggested that liquid mass fluxranged from 0.2 to 3.5 Kg/m2 s was regard as the boundary condi-tion between the dilute and dense sprays. Furthermore, Choi andYao [26] experimentally found that droplet Weber number didnot affect the heat transfer in dense spray. Since all the results ofcurrent studies are based on the mass flux above 3.5 kg/m2 s, theeffect of Weber number on heat transfer must be marginal. Earlierstudies [7,21] have demonstrated that mass flux is the key hydro-dynamic parameter that governs spray cooling performance in thenon-boiling regime. However, the authors did not consider the ef-fect of surface temperature on the heat transfer performance. Asone of the significant mechanisms, liquid film evaporation takesup low proportion in the heat transfer but can not be neglected,especially in the non-boiling regime. The speed of film evaporationwas mainly influenced by the surface temperature Tw and environ-ment temperature Te and increased with the increasing of them. To

different inclination angles.

Wall temperature ( oC )

Coo

ling

effi

cien

cy

30

30

40

40

50

50

60

60

70

70

80

80

90

90

100

100

1.01.0

2.02.0

3.03.0

4.04.0

5.05.09.0mm7.00mm8.00mm

Fig. 18. Cooling efficiency vs. wall temperature at 14� inclination angle.

i i ii i i

i i i i i

Wall temperature ( oC )

Coo

ling

effi

cien

cy

30

30

40

40

50

50

60

60

70

70

80

80

90

90

100

100

1.01.0

2.02.0

3.03.0

4.04.0

5.05.00o

14o

28o

42o

49oi

Fig. 19. Cooling efficiency vs. wall temperature.

Non-dimensional temperature ξ

Nus

selt

num

ber

Nu

3.8

3.8

4

4

4.2

4.2

4.4

4.4

4.6

4.6

12012 0

542542

82082 0

513513

53053 0

Nu=7.1449Re0.438ξ0.9016

Re=248

Re=180

Re=156

Fig. 20. Nusselt number vs. no-dimensional temperature.

Non-dimensional temperature ξ

Nus

selt

num

ber

Nu

3.8

3.8

4

4

4.2

4.2

4.4

4.4

4.6

4.6

002002

003003

004004

005005

00600614 correlation14 Exp28 correlation28 Exp42 correlation42 Exp49 correlation49 Exp

Fig. 21. Nusselt number vs. Reynolds number (inclined sprays).

Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942 941

appraise the liquid film evaporation rate, in this study, a non-dimensional temperature n is defined. The dimensionless temper-ature is the ratio of wall temperature Tw to the temperature differ-ence between the boiling of the liquid and environmenttemperature, as follows:

n ¼ Tw

Tboiling � Teð12Þ

where Te is 293 K in this experiment. The boiling temperature Tboiling

of the water is 393 K. Because the wall temperature is ranged fromthe sprayed liquid temperature Tin to the boiling temperature ofthe coolant Tboiling, the non-dimensional temperature n is betweenTin/(373 � Te) and Tboiling/(373 � Te). Bigger n represents more heattransfer contribution from liquid film evaporation.

The analysis above suggests that mass flux and wall tempera-ture both influences the heat transfer performance in the non-boil-ing regime. To study the effect factor comprehensively, theexperimental data are utilized to develop an empirical correlation,which relates the Nusselt number to the spray Reynolds numberand non-dimensional temperature n. The expression obtained isas follows:

Nu ¼ 7:144Re0:438n0:9016 ð13Þ

Fig. 20 showed that the local Nusselt number at different Rey-nolds number vs. the non-dimensional temperature n with a meanabsolute error of ±2.5%. It is found that Nusselt number increaseswith the increasing of Reynolds number and non-dimensional tem-perature n. Compared with the previous studies [7,21], relation 11may accurately reflect the process of heat transfer in the non-boil-ing regime of spray cooling.

As mentioned earlier, inclined sprays produce an elliptical area.Furthermore, with the increasing of inclination angle, the area ofellipse decreased which resulted in a rise of average mass flux G.And the G is given in inclined spray by:

Ginclined sprays ¼m

3600Aellipseð14Þ

And the Reynolds number can be defined at inclined sprays, as:

Re ¼ Ginclined spraysDl

ð15Þ

942 Y. Wang et al. / Experimental Thermal and Fluid Science 34 (2010) 933–942

Comparison of predicted data and experimental data shown inFig. 21, it is found that both data are shown good agreement witheach other when inclination angle is small (<14�). However, thelarger inclination angle, the bigger difference between predictedand experimental data. It is interesting that predicted data are low-er than the experimental results in general. When inclination anglereaches 49�, the maximum difference is about 10%. This may bedue to the fact that the relation 11 could not reflect the influencefrom the gradual decreasing of stagnation zone area on heat trans-fer, especially in larger inclination angles.

7. Conclusions

Spray cooling heat transfer is a complex phenomenon. In thispaper, the effect of heat surface and inclination angle on spraycooling in the non-boiling regime was studied. The experimentswere conducted using distilled water as coolant for the semi-solidswirl nozzle at different inclination angles with subcooling of 80�.The mass flux is ranged from 15.7 kg/m2 s to 24.9 kg/m2 s. Keyfindings from this study are as follows:

1. Film evaporation is very important to heat transfer in non-boiling regime of spray cooling. As test surface temperatureincreased, film evaporation increased as well and heat trans-fer performance enhanced. There is an inflexion point in theheat transfer curves when the temperature reached 85–90 �C. After that point, the heat flux as well as the heat trans-fer coefficient and the cooling efficiencies increased quicklydue to boiling.

2. Inclination angle strongly affect the heat transfer performancein non-boiling regime. Experiments revealed that there is anoptimal orifice-to-surface distance where heat transfer perfor-mance is best. And this occurred when the major axis of theelliptical spray impact area is just intersecting the square testsurface at inclined sprays. Knowing the inclination angle andspray cone angle as well as the test size, the optimum orifice-to-surface distance can be easily determined. Too small ori-fice-to-surface distances would result in only a small fractionof the test surface impacted by the spray, while too large a dis-tance causes a substantial fraction of the spray liquid fallingwastefully outside the test surface. Both extremes made heattransfer performance decrease.

3. A stagnation zone at the center of the heated surface resultingfrom the impingement flow was found. Heat transfer can beincreased by increasing the inclination angle which canstrengthen the effect of washing and reduce the area of stagna-tion zone.

4. The heat transfer performance and the cooling efficienciesincreased with increasing inclination angle from 0� to 49�.Despite the increased heat transfer, it takes longer time at largerinclination angles for the test surface to reach a steady statebetween power increments.

5. An empirical correlation which relates the average Nusseltnumber to Reynolds number and non-dimensional temperaturehas been developed for swirl semi-solid nozzle.

Acknowledgements

The authors thank Steinen Inc., for providing the semi-solidnozzles. The authors would like to acknowledge the EngineeringCenter of USTC for their assistance in the experiments.

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