International Journal of Heat and Mass Transfer 108 (2017) 1068–1077

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Heat transfer of single drop impact on a film flow cooling a hot surface

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.12.1060017-9310/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: sunny.li@ubc.ca (R. Li).

Xuan Gao a, Lingjian Kong a,b, Ri Li a,⇑, Jitian Han b

aUniversity of British Columbia, Kelowna, British Columbia V1V 1V7, Canadab Shandong University, Jinan, Shandong Province 250061, China

a r t i c l e i n f o

Article history:Received 4 August 2016Received in revised form 25 December 2016Accepted 27 December 2016

Keywords:Drop impactFilm flowSpray coolingHeat transfer enhancement

a b s t r a c t

A water drop impacts a thin heated wafer which is being cooled by a film flow generated from water jetimpingement. The drop impact breaks the steady-state cooling and causes the local temperature aroundthe drop landing location to change. This transient heat transfer process is experimentally investigatedusing an IR camera to record the surface temperature (Ts) of the wafer’s underneath. The measured tem-perature shows two stages of the process: a response stage when the temperature quickly decreases as aresult of the drop impact, followed by a recovery stage during which the temperature returns to thesteady state. It is found the recovery time decreases with increasing the film flow rate. Although duringthe entire process Ts is lower than the steady state, the heat transfer coefficient (ht) is revealed to changeby three steps. The first step is the increase of ht across the impact area, which indicates enhanced con-vection. In the second step, ht decreases toward and eventually below the steady state. In the third stepthe heat transfer coefficient increases toward and returns to the steady state. An enhancement factorbased on the change of heat transfer coefficient rather than the temperature change is introduced to eval-uate the enhancement of convection. The distribution of local maximum enhancement (gmax) along thecenter line of the impact area and the peak value of gmax are used to investigate the enhancement effectsof film flow rate, drop diameter, and drop impact velocity. It is found gmax does not follow a monotonictrend with increasing the impact velocity. The peak enhancement is found to be proportional to thesquare root of the ratio of the drop flow rate to the film flow rate.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Spray cooling has been considered as an important coolingmethod for high heat flux applications. In spray cooling, a largenumber of drops impinge on a hot surface which is covered by aflowing liquid film. Extensive research [1–7] has been conductedto study the heat transfer performance of spray cooling in relationto parameters such as drop size, drop velocity, drop flux, volumet-ric flux, nozzle-surface distance, spray angle, and enhanced sur-face. Chen et al. [1] showed the drop velocity is the mostdominant parameter in affecting CHF (critical heat flux). Xie et al.[2] demonstrated that the surface temperature distributiondepends solely on the drop flux distribution in the non-boilingregime. Mudawar and Estes [3] found that the optimal nozzle-surface distance for maximum CHF is determined when the sprayfootprint is exactly enclosed within the cooling surface. Wanget al. [5] found that inclined sprays with optimal orifice-surfacedistances provide better cooling performance. Bostanci et al. [6]examined the effects of enhanced surfaces on CHF with ammonia

as the working fluid, and showed that the enhanced surfaces couldincrease CHF by 18% over the smooth surface.

Most of the parameters have been revealed to have significantrelationships to the spray cooling performance. The physics behindthe relationships are the effects of the parameters on the drop andfilm flow conditions. The drop and film flow conditions are the flowparameters that directly determine the spray cooling performancefor two reasons. First, in spray cooling heat transfers from the sur-face to the fluid on the surface. Second, the flow dynamics of thefluid on the surface is determined by the film flow and also thedrops impacting the film.

The fluid dynamics involved in the drop impacting a flowingfilm is complicated. Fig. 1 shows a water drop impacting a radiallyflowing water film generated by a vertical jet impinging on a trans-parent surface. High speed images are taken from the side andunder the surface. Fig. 1a shows the interaction of the drop andfilm produces a crown-like rising liquid sheet. For cooling applica-tions, the rising liquid sheet can be considered as local loss of cool-ant, which does not contribute to local convection heat transfer onthe surface. From Fig. 1b, the drop impact generates a spreadingarea, where local flow spreads downstream and upstream. Thespreading area deforms and moves over time. Fig. 1 clearly shows

Fig. 1. A water drop impacting a water film radially flowing on a transparentsubstrate: (a) high speed images taken from the side and (b) high speed imagestaken under the substrate.

Fig. 2. Schematic of test setup for studying a liquid drop impacting a radiallyflowing film generated by jet impingement on a silicon wafer. The lower surface ofthe wafer is coated with a thin gold film as electrical heater. Only half of the wafer isshown.

X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077 1069

a transient development of the flow as a result of the drop impact.The flow development must cause transient change of the localconvection heat transfer, which will eventually affect cooling per-formance. Unfortunately, there is very limited study on this topic.

Most previous studies of drop impact on liquid films focus onthe fluid mechanics aspects. There has been a few studies on thefluid dynamics of drop impacting stationary liquid films [8–10],and flowing liquid films [11–13] under isothermal conditions.Most of previous studies on the heat transfer of drop impact areonly for dry surfaces [14–19]. Pasandideh-Fard et al. [14] experi-mentally and numerically found that increasing drop impact veloc-ity enhances heat flux around the impact area. Bernardin et al. [16]showed that the surface roughness has small effects on the CHFtemperature but significantly affects the Leidenfrost point temper-ature. Tran et al. [18] showed that the maximum spreading of adrop impacting a heated surface follows a universal scaling withthe Weber number. Adera et al. [19] reported the formation ofnon-wetting droplets on a super-hydrophilic micro-structured sur-face by heating the surface above the saturation temperature of thedroplet fluid.

Recently, a few studies have been reported on the heat transferof continuous droplets impinging on hot surfaces [20–22]. Qiuet al. [20] found that the surface temperature above the boilingtemperature enhances the spreading rate of flowing film signifi-cantly and affects the splashing angle. Soriano et al. [21] presentedexperimental observation of multiple droplet train impingement.The impact spacing between multiple droplet streams affectsspreading and splashing, and the optimal cooling performance is

achieved when the film velocity is not disturbed by adjacent dro-plet streams. The simulation results [22] also demonstrated theimpact velocity played a dominant role in promoting local heattransfer.

Despite plenty of previous work on drop impact, very limitedwork has been done to investigate the heat transfer of drop impacton flowing films. There is lack of information and understandingregarding the effects of the drop and film flows on the heat transferof spray cooling. Therefore, the focus of the present work is on theheat transfer involved in the impact of a single drop on a flowingfilm.

2. Experimental methodology

Tests were conducted using the experimental setup shownschematically in Fig. 2. It is composed five components: (1) a sub-strate with uniform surface heat flux; (2) a circular water jet whichimpinges on the substrate to generate radially flowing film; (3) adrop generator to generate water drops impacting the film flow;(4) a HS (high speed) camera for recording flow dynamics; (5) aninfrared camera for recording temperature distribution andchange.

The substrate is a silicon wafer with a diameter of 76 mm and athickness b = 380 lm. The properties of the silicon are: thermalconductivity k = 149W/m K, density q = 2329 kg/m3, specific heatcp = 705 J/kg K. As shown in Fig. 2, the upper surface of the waferis exposed to the spray, while the underneath is coated with a goldlayer, which serves as an electrical heater. Between the wafer andthe gold layer are a dielectric layer and an adhesive layer. The goldlayer is painted black which has high radiative emissivity cali-brated to be 0.95. All the layers have a total thickness less than2 lm, which has negligible resistance to heat conduction. The elec-trical resistance of the gold layer is �1 O. The heater power isdetermined based on the electrical current read from the DC powersupply (Model 62050P, Chroma System Solutions) and the voltagemeasured across the gold-coated area.

Heat loss includes the free air convection and radiation from thecoated underneath and conduction through the wafer edge andelectrical connections. For the free convection, a heat transfer coef-ficient of 10 W/m2 K and an ambient air temperature of 20 �C areused. A large surrounding with temperature 20 �C is used for calcu-lating the radiation. Due to the high heat transfer coefficient of thefilm flow, the heat loss accounts for less than 0.3% of the total hea-ter power. The coated area and the electrical connection are

1070 X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077

designed such that uniform electrical current throughout the goldlayer. Hence, a uniform heat flux (q00) is calculated using the heaterpower divided by the coated area, which ranges from 34.1 W/cm2

to 34.6 W/cm2 for all the conducted tests.Water at room temperature is used as the working fluid for both

jet impingement and drop impact, and its temperature, denoted byTl, is measured using a calibrated T-type thermocouple. Water jetfrom a large jet nozzle with radius a = 1.91 mm impinges on thecenter of the wafer. The volumetric flow rates of the jet, denotedby Q , ranges from 20 to 60 cm3/s. There is no hydraulic jump onthe wafer surface. Depending on the jet flow rate Q and the landinglocation X (the distance from the stagnation point of jet impinge-ment to the drop impact point), the local film flow at the landinglocation can be characterized by

Q 0 ¼ Q2pX

ð1Þ

Here Q 0 is referred to as the film flow rate, which is the productof local film thickness and mean velocity.

Water drops are generated from stainless steel capillary tubesconnected to a syringe pump. The plunger advances very slowlyto form a drop at the tip of the tube, which finally detaches fromthe tube under its own weight. Drop diameter, denoted by D0,ranges from 2.2 to 4.3 mm by using different tube sizes. The heightof the tube orifice above the wafer surface is adjusted to changedrop impact velocity, denoted by U0, which ranges from 0.17 to4.5 m/s determined from the high speed video.

A high speed camera (Phantom Miro M310, Vision Research) isused to capture the impact dynamics of water drops on flowingfilms. To capture the change of the surface temperature (Ts), aninfrared (IR) camera (SC660, FLIR Direct) is positioned underneaththe wafer and operated at 240 fps. The high emissivity of the blackpaint on the lower surface of the wafer is to increase the measure-ment accuracy of the IR camera.

The resolution of the IR images is �3.3 pixels/mm2. Hence, theIR camera provides a detailed temperature distribution on thelower surface of the wafer. We use the measured temperature tostudy the convection cooling on the upper surface of the wafer.Two concerns need to be addressed. One is regarding the lagbetween the observation from the underneath and the actualdevelopment on the other side. The other concern is regardingthe difference between the measured underneath temperatureand the temperature of the spray-cooled surface.

To address the first concern, we consider a Fourier numberdefined as

Fo ¼ aD0

U0b2 ð2Þ

where a is the thermal diffusivity of the silicon wafer, b is the thick-ness of the silicon wafer. Here Fo compares the drop impact timescale to the thermal diffusion time scale through the wafer thick-ness. For the tested ranges D0 and U0, Fo ranges roughly from 1 to10. As will be shown later, the entire thermal process related tothe drop impact is actually much longer than D0=U0. So the lagdue to heat transfer across the wafer thickness is insignificant ascompared to the entire time period.

To address the temperature measurement, we evaluate the Biotnumber defined as

Bi ¼ hbk

ð3Þ

where h is the heat transfer coefficient. In the present work,h � 1 W/cm2 K, which gives Bi � 0:03. Hence, the temperature mea-sured on the lower side is the same as the upper side at the samelocation.

During the drop impact, heat transfer coefficient can be calcu-lated based in the measured temperature. Since the heat loss isnegligible, and also Bi < 0:1, an energy balance on the thin filmheater can be written as

q00 ¼ bqcpdTs

dtþ htðTs � TlÞ ð4Þ

Here ht is transient heat transfer coefficient. The heat transfercoefficient is further written as

ht ¼ q00 � bqcpdTs

dt

� �1

Ts � Tlð5Þ

The IR camera records surface temperature at a constant framerate. For any location and any transient point, the term dTs=dt canbe approximately calculated using the local temperature changebetween two consecutive images multiplied by the frame rate.Without drop impact, the cooling is at steady state, and Eq. (5)reduces to

hss ¼ q00

Tss � Tlð6Þ

Here hss and Tss represent the heat transfer coefficient and sur-face temperature at steady state, respectively. It should be notedthat Tl in Eqs. (5) and (6) is the fluid temperature of the dropand jet. However, the free surface temperature of the local flowduring the impact process and at the steady state could be higherthan Tl.

3. Uncertainty analysis

In the present work, the surface temperature (Ts, and Tss) ismeasured by the IR camera, which has a measurement error±0.5 �C associated with the accuracy of the IR camera and theuncertainty of the emissivity calibration. The water temperature(Tl) is measured using a calibrated T-type thermocouple whichhas a measurement error ±0.1 �C.

The heat flux q00 is calculated based on the heater power andheater area (A), and the heater power is calculated based on themeasured voltage (V) and current (I). The uncertainty of the heatflux can be obtained from

dq00

q00

�������� ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidUU

� �2

þ dII

� �2

þ dAA

� �2s

ð7Þ

In the present work, jdq00=q00j � 2%.The uncertainty of the steady-state heat transfer coefficients

(hss) is evaluated using

dhss

hss

�������� ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidq00

q00

� �2

þ dTss

Tss � Tl

� �2

þ dTl

Tss � Tl

� �2s

ð8Þ

In the present work, jdhss=hssj ranges from �2.5% to �2.8%.Replacing Tss with Ts, Eq. (8) can also be used to approximatelyevaluate the uncertainty of ht . For each test, the lowest value Ts

is chosen for the uncertainty analysis. As a result, jdht=htj rangesfrom �2.8% to �3.2%.

4. Results and discussion

The influence of drop impact on heat transfer should be inves-tigated by determining the difference between the steady coolingof the film flow and the transient cooling during the drop impact.The steady-state cooling of the film flow is shown in Fig. 3 whenthe drop is about to land on the film. The temperature increasesfrom the center toward the edge, showing a concentric distribu-tion. The center is the stagnation of the jet impingement, and is

Fig. 3. (a) A drop (U0 = 3.24 m/s, D0 = 3.2 mm) impacting flowing film (Q 0 ¼ 2:49 cm2=s) at X ¼ 16 mm; (b) contour of surface temperature Tss at the steady state prior to dropimpact (b1); contours of temperature change DTs (b2, b3); and (c) temperature change along the center line.

X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077 1071

used as the origin point of the coordinates system. The locationwhere the drop lands on the film flow is the impact point. InFig. 3, the distance between the impact point and the stagnationpoint X ¼ 16 mm.

At the early stage of the drop impact such as t ¼ 1:6 and 4.8 msshown in Fig. 3a, the drop impact results in a rising crown sheetwhich expands and breaks up over time. At the same time, localtemperature starts decreasing due to the change of the local flow.To highlight the temperature change, we can subtract the transientthermal images from the steady-state image, and the resultedimages show the temperature change DTs = Ts � Tss. The contourof the temperature difference is plotted in Fig. 3b, which roughlyis concentric with a cold spot in the center. Fig. 3c shows the dis-tribution of the temperature difference along the center line, whichis the line crossing the jet stagnation point and the drop impactpoint.

The temperature difference profile shown in Fig. 3c is like a val-ley. At t = 1.6 ms, a small jag appears at the valley bottom, and dis-appears in the following images. This is also visible in thetemperature change contour shown in Fig. 3b. This phenomenonhas been observed consistently in many tests at the very earlystage of impact. A possible reason could be a thin layer of airtrapped between the drop and the flowing film [23–25].

Fig. 3a also shows that the center of the spreading area movesdownstream from the impact point, which is consistent with theobservations in Fig. 1. As a result, the center of the temperature

change contour moves downstream from the impact point (com-paring t = 1.6 ms and 5.8 ms in Fig. 3b), which can also be seenfrom the valley bottom of temperature change profile in Fig. 3c.This is due to the interaction of the drop and the film flow duringthe drop impact, which results in a higher film flow downstream ofthe impact point. This can be easily determined by comparing thespreading extents downstream and upstream of the impact point[10–12].

The drop impact on the film flow breaks the steady-state cool-ing. As a result the temperature within the spreading area changeswith time, as shown by Fig. 3. The transient process can be charac-terized by monitoring the local temperature at the impact point ofthe drop. The temperature is plotted in Fig. 4, where t ¼ 0 ms iswhen the drop lands on the film flow. The transient process is com-posed of two stages. In the first stage, the temperature quicklydecreases, showing quick response to the drop impact. The timetaken for this stage, denoted by Dt1, is referred to as response time.From Fig. 1, it is reasonable to believe that in the first stage thecooling is dominated by the impacting and spreading flows drivenby the drop impact. In the second stage, after reaching the lowestpoint, the temperature starts rising toward the steady state. Thetime taken for this stage, denoted by Dt2, is referred to as recoverytime. During the second stage, the film flow is taking over whilethe spreading flow is diminishing. For the test shown in Fig. 4,Dt1 � 40 ms, while Dt2 � 160 ms, both are much longer than thetime scale D0/U0 = 1 ms.

Fig. 4. The local temperature measured at the impact point (Q 0 ¼ 2:49 cm2=s,U0 ¼ 3:5 m=s, D0 = 3.5 mm). The drop impact starts at t = 0 ms. The first stage of thedrop impact is Dt1, and the second stage is Dt2.

1072 X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077

Fig. 3 has shown that the temperature change valley deepensfrom t = 1.6 to 5.8 ms. To have more information about the evolu-tion of temperature change in the entire transient process, thetemperature change along the center line is plotted for a longertime period from t ¼ 13 to 196 ms, which is much longer than

Fig. 5. (a) The temperature change along the center line after the drop impact (Q 0 ¼ 2:49line including the steady state (t ¼ 0 ms) hss and transient state ht . The inset plot showsmaximum enhancement curve gmax , and its peak is the peak enhancement gp .

the drop impact time scale D0/U0 � 1 ms. It can be seen that thevalley continues to deepen until t ¼ 38 ms, and then comes backuntil it almost disappears at t ¼ 196 ms. This is consistent withthe response and recovery stages observed in Fig. 4. It also showsthat the valley bottom moves in the direction of the film flow.

Without the drop impact, the heat transfer coefficient of thesteady-state cooling is the highest in the center and decreasestoward the edge. This trend can be seen in Fig. 4b, where the heattransfer coefficient prior to the drop impact is calculated using Eq.(6). When a drop impacts, the interaction of the drop and the filmflow significantly affects the local heat transfer coefficient aroundthe impact area, which can be calculated using Eq. (5). The tran-sient term in Eq. (5) is approximately calculated using the temper-ature change from the previous thermal image multiplied by theframe rate of the IR camera. The heat transfer coefficient alongthe center line is plotted for a few transient points in comparisonwith the heat transfer coefficients at the steady state. To bettershow the change of heat transfer coefficient, the differencebetween the local steady state and transient heat transfer coeffi-cients, Dh = ht � hss, is plotted as an inset in Fig. 5b.

A few interesting points can be observed by comparingFig. 5a and b. At the early stage, along the center line Ts decreasesand ht increases. The temperature Ts reaches the maximumdecrease at t ¼ 38 ms, while ht reaches its maximum increase att ¼ 21 ms. In other words, although Ts continues to decrease fromt = 21 to 38 ms, the heat transfer coefficient already starts decreas-

cm2=s, U0 ¼ 3:5 m=s, D0 = 3.5 mm). (b) The heat transfer coefficient along the centerDh = ht � hss. (c) Cooling enhancement calculated using Eq. (9). The top curve is the

X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077 1073

ing as ht=21 ms > ht=38 ms. This is because the temperature decreasesat a faster rate during the early stage of drop impact, i.e. �(dTs/dt)t=21 ms > �(dTs/dt)t=38 ms. Second, after reaching the maximumat t = 21 ms, the heat transfer coefficient continues to decrease,and passed the steady-state curve at t = 63 ms (the curve fort = 63 ms is not shown). At t = 75 ms when the temperature changecurve is still rising toward the steady state, the heat transfer coef-ficient curve reduces below the steady state, showing Dh < 0. Att = 125 ms, the heat transfer coefficient has almost recovered tothe steady state, while the temperature is still on the way to thesteady state.

The discussion above can be summarized as follows. The changeof the temperature shows two steps: decrease and recovery. Thechange of the heat transfer coefficient shows three steps: increase,decrease, and recovery. The differences between the trends for Ts

and ht is due to the existence of the transient term in Eq. (5). Inother words, if the cooling target had zero thermal mass, thechange of Ts would also be three steps in directions opposite tothe change of ht .

The three-step change of heat transfer coefficient shown inFig. 5b can be explained from both hydrodynamic and thermal per-spectives. From the hydrodynamic perspective, the drop impactresults in a fast spreading flow which slows down before beingreplaced by the film flow. Particularly, at some location the floweventually switches from flowing upstream to flowing down-stream. From the thermal perspective, the arrival of the dropbreaks the local steady-state thermal boundary layer, and a newthermal boundary layer develops in the spreading flow. Before

Fig. 6. (a) The maximum enhancement along the centerline caused by the dropimpact (U0 ¼ 3:5 m=s, D0 = 3.5 mm) on films with varied flow rates. (b) The peakenhancement versus film flow rate.

the takeover by the film flow, it could be possible that the thermalboundary layer encompasses the spreading flow thickness, andconsequently the free surface temperature is higher than Tl. Thechange of heat transfer coefficient represents the change of theconvection, which can be quantified by introducing an enhance-ment factor defined as

g ¼ ðht � hssÞ=hss ð9ÞFor the enhancement analysis, instead of Eq. (9) based on the

heat transfer coefficient, one might choose to use a temperatureratio given by DTs/(Tss � Tl). However, from Eqs. (5) and (6), theconvective heat flux during the drop impact is different from thatat the steady state. Therefore, the temperature ratio shows theenhancement of cooling performance, while the ratio of heat trans-fer coefficient evaluates the capability of the convective heattransfer.

Base on the uncertainties of ht and hss discussed in Section 3, theuncertainty of the enhancement jdg=gj ranges from �4% to �4.5%.Eq. (9) is plotted in Fig. 5c, which clearly shows the enhancementdevelops over time. At t = 21 ms, except a small region aroundX � 25 mm, most of the impact region has reached local maximumenhancement, denoted by gmax. Hence, for the drop impact shownin Fig. 5, the curve at t = 21 ms shows the distribution of local max-imum enhancement, and therefore is referred to as the maximumenhancement curve. The maximum enhancement occurs in thefirst stage of the drop impact when the flow driven by the dropimpact is dominant. On the gmax curve, there is a peak enhance-ment gp ¼� 55% which occurs at a location close to the impactpoint at t ¼ 21 ms. At t ¼ 75 ms, there is �10% decrease of convec-tion close to the impact point. This occurs when the film flow istaking over from the spreading flow. The trends of the enhance-ment factor shown in Fig. 5c can be explained by the discussionabove from both hydrodynamic and thermal perspectives.

The observed temperature change during the drop impact is theresult of the change of convection heat transfer. The change of con-vection heat transfer is caused by the change of fluid dynamics,which is driven by the interaction of the drop and film flows. Inthe following we will evaluate the effects of film flow rate Q 0, dropdiameter D0, and impact velocity U0.

4.1. Changing film flow rate Q 0

A series of tests are conducted to investigate the effect of thefilm flow when the drop parameters are maintained constant(U0 ¼ 3:5 m=s, D0 = 3.5 mm). The film flow rate Q 0 is varied from

Fig. 7. The response time and recovery time versus the film flow rate underconstant drop conditions (U0 ¼ 3:5 m=s, D0 = 3.5 mm).

1074 X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077

2.49 to 6.63 cm2/s by changing the jet flow rate Q while the droplanding location is maintained constant at X ¼ 16 mm. The maxi-mum enhancement curves of a few tests are presented in Fig. 6a,which shows the local maximum enhancement gmax along the cen-ter line. Generally, the curves with lower film flow rates encom-pass the curves with higher film flow rates. This can be clearlyobserved from the two curves with the lowest and highest filmflow rates (Q 0 ¼ 2:49 and 6.63 cm2/s). Hence, the film flow ratehas two major effects. First, drop impact tends to cause significantlocal enhancement if the film flow rate is low. Second, theenhancement tends to occur in a large area if the film flow rateis low.

A close look at Fig. 6a also shows that the location of the peakenhancement gp shifts downstream of the impact point. Interest-ingly, the higher the film flow rate, the less shift from the impactpoint. For example the peak location almost coincides with theimpact point for Q0 = 6.63 cm2/s. When the film flow rate is high,the drop impact can cause appreciable effect only at the early stageof the impact. When the film flow rate is low, the flow driven bythe drop impact has more time to develop, and at the same timethe center of the spreading area is moving downstream [11].Fig. 6a also shows that gmax decreases with increasing Q 0. To clearlyshow the trend, gp is plotted versus Q 0 in Fig. 6b. For the film flowrate increasing from 2.49 to 6.63 cm2/s, the peak enhancementdecreases from �55% to �10%.

Changing the film flow while keeping the drop flow constantalso affects the time duration of the impact process. The tempera-ture at the impact point is recorded for all the tests with constantdrop conditions (U0 ¼ 3:5 m=s, D0 = 3.5 mm), and the same patternas shown by Fig. 4 is observed for all the tests. Fig. 7 shows that the

Fig. 8. Drop spreading and splashing at different drop velocities: (a) U0 ¼ 1:67 m=s, (bconditions (Q 0 ¼ 2:49 cm2=s) are the same for all the three tests.

recovery time Dt2 decreases with increasing Q0. This is understand-able as a strong film flow is expected to quickly remove the dropimpact flow and recover the flow in the spreading area to thesteady state. In contrast, the response time Dt1 is almost indepen-dent of Q 0, as the fluid dynamics in the early stage is dominated bythe drop impact. Since Dt1 + Dt2 is the time duration of the entiretransient thermal process, Fig. 7 also shows that the transient pro-cess shortens as Q 0 increases.

4.2. Changing drop velocity U0

Tests are conducted to investigate the effects of drop impactvelocity U0 while the film flow rate (Q 0 ¼ 2:49 cm2=s) is main-tained constant. Three groups of tests are carried out for three dropdiameters: D0 ¼ 2:6, 3.5 and 4.3 mm. The impact velocity isobserved to affect the spreading and splashing. Fig. 8 shows highspeed video images of three drops impacting the flowing film,which have different velocities but the same drop diameterD0 ¼ 3:5 mm. At any transient point from t = 1 to 7 ms, a higherimpact velocity always shows a larger spreading area. This indi-cates that a higher impact velocity results in a faster spreadingflow, which is expected to enhance the local convection. Fig. 8 alsoshows that a higher impact velocity results in higher rising sheet.The rising sheet can be considered as local loss of coolant, as theejected fluid does not contribute to local cooling. It is reasonableto believe the rising sheet has negative effect on local cooling.

The maximum enhancement curve, gmax, is plotted in Fig. 9a forfive tests with D0 ¼ 3:5 mm and different impact velocities. Gener-ally, Fig. 9a shows a higher impact velocity results in a larger areato be thermally affected, both upstream and downstream of the

) U0 ¼ 3:50 m=s, (c) U0 ¼ 4:38 m=s. The drop size (D0 ¼ 3:5 mm) and flowing film

Fig. 9. (a) The maximum enhancement with varied drop impact velocities from0.16 m/s to 4.38 and constant drop diameter (D0 ¼ 3:5 mm) and film flow rate(Q 0 ¼ 2:49 cm2=s). (b) The peak enhancement of drop impact (Q 0 ¼ 2:49 cm2=s)versus the drop impact velocity.

Fig. 10. The drop impact (U0 ¼ 3:01 m=s, Q 0 ¼ 2:49 cm2=s) with varied dro

X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077 1075

impact point. Consistent to the observation discussed above, thelocation the peak enhancement shifts away from the impact point.For the two low impact velocities, U0 ¼ 0:16 and 1.13 m/s, the peakenhancement is closer to the impact point. The possible reason isthat if the drop flow is relative weak and the film flow is dominant,the maximum enhancement can occurs only at the early stage ofthe impact when the center of the impact region is still very closeto the impact point.

The most interesting observation from Fig. 9a is regarding theposition of the gmax curve for the highest velocity U0 ¼ 4:38 m=s.Rather than being the top, the curve is between the gmax curvesfor U0 ¼ 1:13 m=s and 3.37 m/s. This indicates that the maximumenchantment does not follow a monotonic trend with the impactvelocity. In other words, faster impact does not necessarily causehigher enhancement.

To further investigate the trend of enhancement with dropimpact velocity, the peak enhancement gp is plotted versus theimpact velocity U0 in Fig. 9b for all the conducted tests. Each datacurve in Fig. 9b represents a constant drop diameter. From eachdata curve, the following can be observed. The peak enhancementfirst increases with increasing the impact velocity for a relativelylarge portion of the tested range of U0 (see region-I in Fig. 9b). Fur-ther increasing U0 causes gp to decrease (see region-II in Fig. 9b).Then gp becomes relatively stable and shows low dependency onU0 (see region-III in Fig. 10b). In region-I, the convection isenhanced as the drop impact velocity increases. In region-II,increasing U0 could significantly increases rising sheet and splash-ing causes more loss of coolant, and as a result the enhancement isnegatively affected. Fig. 9b also shows the effect of the drop diam-eter, which will be discussed in the following section.

4.3. Changing drop diameter D0

The focus of this section is on the drop diameter D0, which ischanged from 2.2 to 4.3 mm. Three groups of tests are conductedwith constant film flow (Q 0 ¼ 2:49 cm2=s) and three differentimpact velocities U0 ¼ 1:39, 3.01, and 3.50 m/s. Fig. 10 shows three

p diameters: (a) D0 ¼ 2:2 mm; (b) D0 ¼ 3:2 mm; and (c) D0 ¼ 4:3 mm.

Fig. 12. The peak enchancement versus the ratio of drop flow rate to the film flowrate plotted in a log-log scale. The tests shown in regions-II & III in Fig. 9b areexcluded.

1076 X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077

drops with D0 ¼ 2:2, 3.2, and 4.3 mm and the same velocityU0 ¼ 3:01 m=s impacting the film flow. A larger drop results in lar-ger spreading area and higher rising sheet. The shift of the spread-ing center from the impact point is clear for each case.

In Fig. 11a, the maximum enhancement curve is plotted for thetests with U0 ¼ 3:01 m=s. Increasing D0 extends the enhanced areaboth upstream and downstream of the impact point. The peakenhancement takes place downstream of the impact point. The lar-ger the drop size, the more shift from the impact point. The effectof the drop diameter is significant. The peak enhancementgp � 35% for D0 ¼ 2:2 mm, while gp � 60% for D0 ¼ 4:3 mm.

The peak enhancement gp is plotted versus the drop diameterD0 in Fig. 11b for all the tests conducted in this section. Each datacurve represents a constant impact velocity. For each case, the peakenhancement increases with increasing the drop size, showing amonotonic trend within the tested range of D0. Although Fig. 10shows that increasing D0 also promotes the rising sheet andsplashing similar to the effect of increasing U0, it should be notedthat a larger drop increases the amount flow added to the impactarea. This could be the reason that gp is not observed to decreasewith increasing D0.

4.4. Discussion on peak enhancement gp

Three important parameters including the film flow rate Q 0, thedrop impact velocity U0, and the drop diameter D0 have beenexperimentally tested. Their effects on the maximum enhance-ment along the center line has been shown in

Fig. 11. (a) The maximum enhancement of drop impact (U0 ¼ 3:01 m=s,) withvaried drop diameters and (b) the peak enhancement of drop impact(Q 0 ¼ 2:49 cm2=s) versus the drop diameter.

Figs. 6a, 9a, and 11a. Each test has a value of peak enhancement,gp, which has been plotted versus the three parameters inFigs. 6b, 9b, and 11b, respectively. Fig. 6b shows that gp decreases

with increasing Q 0. Fig. 9b shows that for a large portion of thetested range of U0, gp increases with increasing U0. Fig. 11b showsthat gp increases with increasing D0. Therefore, if we exclude theregions-II and III in Fig. 9b, the three parameters can be groupedinto U0D0=Q

0, and we expect an increasing trend of gp with respect

to U0D0=Q0. It should be noted that U0D0 and Q 0 are the two-

dimensional flow rates for the drop and the film flow, respectively.All the tests (except the tests in regions-II and III in Fig. 9b) are

presented in Fig. 12, which shows gp versus U0D0=Q0 in a log-log

plot. The data points show a general trend that the peak enhance-ment increases with increasing the ratio of the drop flow rate andfilm flow rate. Since the least mean square linear fitting has a slope

of 1/2, the relationship can be expressed as gp / ðU0D0=Q0Þ1=2. It

should be noted that the grouped parameter U0D0=Q0 can also be

replaced with the ratio of two Reynolds numbers: one for the drop,and the other one for the film flow.

5. Conclusions

An experimental study is presented to analyze the heat transferinvolved in the impact of single water drops on a water film flowcooling a hot surface. The surface is made of a thin silicon waferwith a thin film heater coated on one side while the other side iscooled for the water flow. IR camera is used to capture temperaturewith high spatiotemporal resolutions. Focus is put on the change ofconvection heat transfer in relation to the observation of flowdynamics during the drop impact. Based on the temperature mea-surement, the drop impact causes the surface temperature to firstdecrease and then return to the steady state, showing a thermalresponse process followed by a recovery process. It is found thatthe recovery time decreases with increasing the film flow rate,while the response time is negligibly affected by the film flow.

Different from the surface temperature change, the transientheat transfer coefficient (htÞ presents three steps compared tothe steady state: the increase step, the decrease step, and therecovery step. After drop impact, ht continuously increases untilreaching a maximum value, indicating enhancement of convection,and then decreases toward and eventually below the steady state.In the recovery step ht increases toward and returns to the steadystate. To evaluate the change of convection, an enhancement factor

X. Gao et al. / International Journal of Heat and Mass Transfer 108 (2017) 1068–1077 1077

(g) based on the change of heat transfer coefficient, is introduced.In the increase step, when most of the impact area reaches its localmaximum enhancement (gmax), the distribution of gmax along thecenterline of the impact area is referred as the maximum enhance-ment curve, and the peak value of the curve is referred to as thepeak enhancement (gp).

It is shown that the relation of gp with drop velocity does notfollow a monotonic trend. With increasing drop velocity, the peakenhancement first increases, then decreases, and eventuallybecomes relatively stable, showing low dependency on U0. How-ever, the peak enhancement increases with the increase of dropsize in the current experimental range, since a larger dropincreases the amount flow added to the impact area. Combiningthe effects of the drop flow and film flow, the parameters can begrouped into the ratio of the drop flow rate and film flow rate asU0D0=Q

0. The least mean square linear fitting shows

gp / ðU0D0=Q0Þ1=2.

Acknowledgment

The authors would like to thank the Natural Sciences and Engi-neering Research Council of Canada (NSERC) for support. Theauthors also would like to thank Dr. Xian Jin for his help in fabricat-ing the heater on the silicon wafer.

References

[1] R.H. Chen, L.C. Chow, J.E. Navedo, Effects of spray characteristics on criticalheat flux in subcooled water spray cooling, Int. J. Heat Mass Transfer 45 (2002)4033–4043.

[2] J.L. Xie, Z.W. Gan, F. Duan, T.N. Wong, S.C.M. Yu, R. Zhao, Characterization ofspray atomization and heat transfer of pressure swirl nozzles, Int. J. Therm. Sci.68 (2013) 94–102.

[3] I. Mudawar, K. Estes, Optimizing and predicting CHF in spray cooling of asquare surface, J. Heat Transfer 118 (1996) 672–679.

[4] E.A. Silk, J. Kim, K. Kiger, Spray cooling of enhanced surfaces: impact ofstructured surface geometry and spray axis inclination, Int. J. Heat MassTransfer 49 (2006) 4910–4920.

[5] Y.Q. Wang, M.H. Liu, D. Liu, K. Xu, Y.L. Chen, Experimental study on the effectsof spray inclination on water spray cooling performance in non-boiling regime,Exp. Therm. Fluid Sci. 34 (2010) 933–942.

[6] H. Bostanci, D.P. Rini, J.P. Kizito, V. Singh, S. Seal, L.C. Chow, High heat fluxspray cooling with ammonia: Investigation of enhanced surfaces for CHF, Int. J.Heat. Mass Transfer 55 (2012) 3849–3856.

[7] J.L. Xie, Z.W. Gan, T.N. Wong, F. Duan, S.C.M. Yu, Y.H. Wu, Thermal effects on apressure swirl nozzle in spray cooling, Int. J. Heat. Mass Transfer 73 (2014)130–140.

[8] G.T. Liang, I. Mudawar, Review of mass and momentum interactions duringdrop impact on a liquid film, Int. J. Heat. Mass Transfer 101 (2016) 577–599.

[9] G.E. Cossali, M. Marengo, A. Coghe, S. Zhdanov, The role of time in single dropsplash on thin film, Exp. Fluids 36 (2004) 888–900.

[10] I.V. Roisman, C. Tropea, Impact of a drop onto a wetted wall: description ofcrown formation and propagation, J. Fluid Mech. 472 (2002) 373–397.

[11] X. Gao, R. Li, Impact of a single drop on a flowing liquid film, Phys. Rev. E 92(2015) 053005.

[12] Z.Z. Che, A. Deygas, O.K. Matar, Impact of droplets on inclined flowing liquidfilms, Phys. Rev. E 92 (2015) 023032.

[13] S.K. Alghoul, C.N. Eastwick, D.B. Hann, Normal droplet impact on horizontalmoving films: an investigation of impact behaviour and regimes, Exp. Fluids.50 (2011) 1305–1316.

[14] M. Pasandideh-Fard, S.D. Aziz, S. Chandra, J. Mostaghimi, Cooling effectivenessof a water drop impinging on a hot surface, Int. J. Heat Fluid Fl. 22 (2001) 201–210.

[15] Y.M. Qian, S. Chandra, Experiments on adding a surfactant to water dropsboiling on a hot surface, Proc. R. Soc. Lond. A 453 (1997) 673–689.

[16] J.D. Bernardin, C.J. Stebbins, I. Mudawar, Mapping of impact and heat transferregimes of water drops impinging on a polished surface, Int. J. Heat MassTransfer 40 (1997) 247–267.

[17] S. Herbert, S. Fischer, T. Gambaryan-Roisman, P. Stephan, Local heat transferand phase change phenomena during single drop impingement on a hotsurface, Int. J. Heat Mass Transfer 61 (2013) 605–614.

[18] T. Tran, H.J.J. Staat, A. Prosperetti, C. Sun, D. Lohse, Drop impact on superheatedsurfaces, Phys. Rev. Lett. 108 (2012) 036101.

[19] S. Adera, R. Raj, R. Enright, E.N. Wang, Non-wetting droplets on hotsuperhydrophilic surfaces, Nat. Commun. 4 (2013) 2518.

[20] L. Qiu, S. Dubey, F.H. Choo, F. Duan, Splashing of high speed droplet trainimpinging on a hot surface, Appl. Phys. Lett. 107 (2015) 164102.

[21] G.E. Soriano, T.L. Zhang, J.L. Alvarado, Study of the effects of single and multipleperiodic droplet impingements on liquid film heat transfer, Int. J. Heat. MassTransfer 77 (2014) 449–463.

[22] M.F. Trujillo, S.R. Lewis, Thermal boundary layer analysis corresponding todroplet train impingement, Phys. Fluids 24 (2012) 112102.

[23] M.M. Driscoll, S.R. Nagel, Ultrafast interference imaging of air in splashingdynamics, Phys. Rev. Lett. 107 (2011) 154502.

[24] T. Tran, H. De Maleprade, C. Sun, D. Lohse, Air entrainment during impact ofdroplets on liquid surfaces, J. Fluid Mech. 726 (2013) R3.

[25] M.J. Thoraval, K. Takehara, T.G. Etoh, S.T. Thoroddsen, Drop impact entrapmentof bubble rings, J. Fluid Mech. 724 (2013) 234–258.