Experimental Thermal and Fluid Science 54 (2014) 179–188

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Experimental Thermal and Fluid Science

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Liquid volume measurements in the cavity formed by single dropletimpacts into a thin, static liquid film

0894-1777/$ - see front matter � 2014 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.expthermflusci.2013.12.007

⇑ Corresponding author. Tel.: +1 304 293 3180; fax: +1 304 293 6689.E-mail address: john.kuhlman@mail.wvu.edu (J.M. Kuhlman).

John M. Kuhlman a,⇑, Nicholas L. Hillen b, Murat Dinc c, Donald D. Gray d

a West Virginia University, Mechanical & Aerospace Engineering Dept., ESB 317, P.O. Box 6106, Morgantown, WV 26506, United Statesb West Virginia University, Mechanical & Aerospace Engineering Dept., ERB 120A, P.O. Box 6106, Morgantown, WV 26506, United Statesc West Virginia University, Civil and Environmental Engineering Dept., ESB 641, P.O. Box 6103, Morgantown, WV 26506, United Statesd West Virginia University, Civil and Environmental Engineering Dept., ESB 641A, P.O. Box 6103, Morgantown, WV 26506, United States

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

Article history:Received 13 July 2013Received in revised form 9 December 2013Accepted 10 December 2013Available online 4 January 2014

Keywords:Droplet impingementDrop impact sub-cavity liquid volumeCavity dry outHeat flux

The time variation of the liquid volume beneath the cavity formed by the impact of a single droplet into astatic liquid film (termed the ‘‘sub-cavity volume’’) over an unheated, horizontal surface has been mea-sured for the first time, using water as the test liquid. Droplet Weber numbers, Reynolds numbers, andinitial liquid film thickness-to-drop diameter ratios were studied that are representative of the impactconditions that are expected for typical sprays. The thin liquid film thickness beneath the droplet impactcavity (the ‘‘sub-cavity liquid film thickness’’) was measured using a non-contacting optical thicknesssensor, as a function of both time and radial distance away from the impact cavity centerline. These datahave been numerically integrated to determine the time variation of the sub-cavity liquid volume. Themeasured liquid film thickness decreases away from the cavity centerline in the immediate vicinity ofthe inner crown wall. The sub-cavity volume is typically between 30% and 35% of the droplet volume,and remains near this plateau value over much of the cavity lifetime. The measured sub-cavity liquid vol-ume and cavity lifetime are used for one example case to demonstrate the predicted values of both thelocal heat flux averaged over an individual cavity, and the overall heater average heat flux, that would berequired to dry out the cavity prior to cavity fill in. The computed average heat flux value for this firstexample case, on the order of 4–6 MW/m2, is the same order of magnitude as the range of measured over-all critical heat flux values referenced in the spray cooling literature.

� 2014 Elsevier Inc. All rights reserved.

1. Introduction

Spray cooling has been developed for practical cooling applica-tions for many years [1,2], and is attractive for a range of applica-tions due to demonstrated high heat fluxes (critical heat flux, or‘‘CHF’’, upwards of 5 MW/m2 using water) [3] at relatively low sur-face temperatures (heat flux of 1 MW/m2 at (Twall–Tsat) � 12 K,again using water) [3]. However, a fundamental understanding ofspray cooling is as yet incomplete. This is largely due to the com-plex interactions of large numbers of spray droplets (order of 106 -drops/s/cm2) primarily with the cooled surface, but also with otherimpacting and splashed droplets. A full simulation of spray coolingvia Computational Fluid Dynamics (CFD) is infeasible for the samereasons. Thus, a simplified phenomenological model of the spraycooling process which would maintain enough of the relevantphysics to enable accurate performance calculations to be madefor design purposes in reasonable simulation run times would beextremely valuable.

One approach to develop such a model is described in Kreitzer[4], where a preliminary Monte Carlo model focusing on spray cool-ing at surface temperatures below the Leidenfrost point is described.Although greatly simplified, this model did capture qualitativelysome of the observed trends for the single full cone spray nozzlethat was modeled, such as the onset of dry out of the heated surfacenear the circular heater’s outer edge. Also, this initial model pre-dicted that different processes would govern the lifetimes of the im-pact ‘‘craters’’, or cavities, formed when individual droplets impactthe residual liquid film that forms on the heated surface. The cavi-ties formed by the larger droplets (greater than approximately50 lm) were predicted to be covered over primarily by liquid fromsubsequent nearby droplet impacts before being re-filled by capil-lary action upon crown collapse. The cavities formed by dropletssmaller than 50 lm were predicted to fill in due primarily to capil-lary effects before being covered over by subsequent droplet im-pacts [4–6]. However, this preliminary model could not makequantitative predictions of either the average heat flux versus wallsurface temperature, or of the conditions for the onset of CHF.

The present work is part of an ongoing effort to improve thispreliminary Monte Carlo spray cooling model [4–6], in order to

Nomenclature

A areaCp specific heat at constant pressureD droplet diameterF VOF indicator functionFr Froude number = V2/(gD)h local cavity liquid film thicknesshfg latent heatH initial liquid layer thickness; crown heightq’’ heat fluxR radial locationRe Reynolds number = qVD/lt timeT temperatureV droplet impact velocityVol sub-cavity liquid volumeWe Weber number = qV2D/r

Greek Symbols

Ds dimensionless cavity lifetimeg index of refractionl viscosity

q densityr surface tensions dimensionless time = t/(D/V)

Superscripts

⁄ dimensionless quantity

Subscripts

b bottomc cavitycrown crown valuedry dry outf filmFluid fluidGlass glassi time indexMax maximumSat saturationw wall

180 J.M. Kuhlman et al. / Experimental Thermal and Fluid Science 54 (2014) 179–188

develop it into a predictive design tool. The detailed time historiesof the volume of liquid remaining beneath the droplet impact cav-ities that form upon single droplet impact are being studied bothexperimentally and via CFD simulation over the ranges of Weberand Reynolds numbers expected for a spray nozzle of interest.Sample laboratory experiments and CFD simulations are brieflycompared, to gain confidence in the experimental methods and re-sults, and these initial results are then used for one typical case tocompute an estimate of the average heat flux for onset of dry out ofthe droplet impact cavity. This occurrence would be expected tocontribute to the onset of CHF. Simplified statistical methods havebeen used previously to model spray behavior. These previousmethods either focused on droplet impacts with a dry surface[7], or on the contributions of nucleate boiling and secondary bub-ble formation to the overall spray cooling heat flux [8]. The presentwork is an initial step towards quantifying the contribution of theenhanced heat transfer in the thin liquid films formed in the spraydroplet impact cavities.

Experimental methods first developed by van Hinsberg et al. [9]have been used in the present work, in conjunction with a CFDsimulation approach partially based on the work of Josserandand Zaleski [10], to study the time evolution of the thin liquid filmbeneath the droplet impact cavity. We have used the same opticalinstrument as van Hinsberg et al. [9] (but here with a thicknessmeasurement range of 3 mm) to measure the thickness of the li-quid film beneath the droplet impact cavity, versus both timeand radial distance from the drop impact centerline. Using thistechnique the total volume of liquid in the film (termed the‘‘sub-cavity volume’’) has been computed by integration. Van Hins-berg et al. utilized a commercial optical sensor based on chromaticconfocal imaging [11] to measure the history of the thickness ofthe thin film that remains beneath the droplet impact cavity onthe impact centerline. The present work has extended this tech-nique to again measure film thickness versus time in the impactcavity, but away from the centerline of droplet impact; this thick-ness has been found to decrease somewhat at large cavity radius.Van Hinsberg et al. found that the centerline minimum film thick-ness approached a constant value at high Weber and Froude num-bers, depending only on the nondimensional liquid layer thicknessand the droplet Reynolds numbers. This dependence also became

relatively weak at high Reynolds number. The ranges of the dropletWeber number and initial liquid film thickness-to-drop diameterratio that have been studied herein are similar to those of vanHinsberg et al. These ranges were selected because they are theranges expected for the spray nozzle of current interest, and be-cause lower Weber numbers or thicker initial liquid layers arenot expected to form as thin a film beneath the droplet impactcavity.

The temperature of the liquid in the residual liquid film on theheated surface is expected to be at, or significantly closer to, satu-ration conditions than the impinging spray liquid. So for a sub-cooled spray liquid, the time to heat to saturation and then boilaway the liquid that remains in the impact cavity will be influ-enced by what portion of that total sub-cavity liquid volume orig-inated from the droplet versus the residual liquid layer.Identification of the droplet liquid and the layer liquid as two dif-ferent ‘‘fluids’’ having identical properties, as in the CFD simula-tions of Josserand and Zaleski [10], is being used to determinethese percentages. These percentages cannot be determined fromexperiments. Also, the spray cooling CFD simulations by Sarkarand Selvam [12] that showed significant increases in the transientlocal heat flux in the thin film in the droplet impact cavities rela-tive to the average heat flux have given impetus to the presentstudy. The percent increase calculated from the results of Sarkarand Selvam in this local heat flux was comparable to, but some-what less than, the corresponding percent increase over the aver-age heat flux in the vicinity of the contact line [12,13] that formswhen bubbles nucleate on the heater surface and move along thesurface. This indicates that heat transfer in the sub-cavity liquidfilm should make a significant contribution to the overall heattransfer in spray cooling.

Some of the present results have been reported previously inpreliminary form, along with further details of the experimentalapparatus, experimental procedures, and CFD methods, in Hillenet al. [14]. This paper gave initial comparisons between sub-cavityvolumes that were computed using experimental and CFD results,but the agreement was only qualitative due to the relatively crudeintegration method that was used. The present work has focusedprimarily on thin preexisting liquid films, following the terminol-ogy of Cossalli et al. [15] (H/D < 1), or on thin and intermediate

Fiber Optics Cable

Optical Probe

Liquid Layer

Impact Stand

0.152mm Thick Glass Disc

Measuring Range

Acrylic Enclosure

Fig. 2. Schematic of the impact support with the CHR optical sensor.

Fig. 3. Definitions of crown height and bottom radius.

J.M. Kuhlman et al. / Experimental Thermal and Fluid Science 54 (2014) 179–188 181

films, using the classification of Vander Wal et al. [16] (H/D < 0.1and H/D � 1, respectively). This is because it is for this range ofH/D values that significant increases in the localized transient heatflux are expected beneath the droplet impact cavities. These thinfilms, in addition to being regions of high local transient heat flux,should also be especially susceptible to localized dry out as thethin film boils away, which should then influence both the CHFand the average heat flux values below CHF.

2. Experimental apparatus and procedure

The experimental apparatus is shown schematically in Fig. 1. A15.2 � 15.2 � 5.1 cm acrylic tank open to the atmosphere was usedto contain the impact surface and to provide the capacity for a li-quid pool. The tank was sufficiently large so that surface wavesfrom drop impacts did not reflect from the walls during the timesof interest. The droplet impact surface was secured to the transpar-ent floor of the acrylic tank as shown in Fig. 2. Also shown is theoptical liquid film thickness sensor (CHRocodile SE electronicsmodule with a 3.3 mm full-range probe) that was mounted belowthe 152 lm thick, 25 mm diameter optically transparent glass im-pact surface. The CHR sensor had a sampling rate of 4 kHz and±0.1 lm thickness resolution. A Photron FASTCAM SA5 high speedvideo camera was utilized to record the droplet impacts for de-tailed analysis. The high-speed camera was positioned perpendic-ular to the tank sidewall and was backlit by a single 250 Whalogen lamp as shown in Fig. 1. A Nikon ED AF MICRO NIKKOR200 mm 1:4 D camera lens was used to image with the high speedcamera. Further details of the experimental apparatus have beengiven by Hillen et al. [14]. Individual liquid droplets were createdby a gravity-driven drop generator (Fig. 1) in which the droplet sizewas controlled by the nozzle orifice size and the solenoid valveopening time. The liquid drop impact velocity was controlled byvarying the height of the droplet generator above the surface ofthe liquid pool. The fluid used for both the droplets and the initialliquid pool for the present work was distilled water. To create apreexisting liquid film of the desired thickness over the impact sur-face, the enclosure was filled with distilled water until a static li-quid film of the desired thickness covered the surface. The liquidfilm thickness was initially measured using a machinist’s scaleand was confirmed and refined to the targeted thickness for a spe-cific case with the use of the CHR optical thickness measuring sys-tem. Immediately prior to each test case the nozzle was wipedwith a sterile cloth to remove excess fluid buildup at the tip andto remove any contaminants, to improve repeatability.

Fig. 1. Schematic of experimental ap

Time histories of the dimensions of the crowns that formedupon droplet impact, as defined in Fig. 3, were obtained byanalyzing the backlit high-speed videos images via automatedimage processing methods. The crown height Hcrown was definedas the vertical distance from the undisturbed free surface to thebase of the fingering of the crown, and the bottom crown radius,RB, was defined as half the distance between the outer edges ofthe crown in contact with the free surface (Fig. 3). The imageprocessing utilized the MATLAB Image Processing Toolbox; detailshave been provided by Hillen et al. [14]. These experimental datahave been used to determine the range of cavity radii at whichto measure the time histories of the sub-cavity film thickness, aswell as in validation work with the present CFD simulation results.

Droplet size and velocity immediately prior to impact weredetermined by an automated image processing code which fitted

paratus, set up for backlit video.

182 J.M. Kuhlman et al. / Experimental Thermal and Fluid Science 54 (2014) 179–188

an ellipse to the drop image. This method was adopted because thelarger droplets were rarely observed to be spherical at impact.Droplet diameter has been taken as the average of the major andminor diameters of the fitted ellipse. Time has been measured rel-ative to when the drop first contacted the static surface of the pre-existing liquid pool.

It should be noted that the CHR sensor measures the total thick-ness of the liquid and the glass. To obtain the true liquid film mea-surements the thickness of the glass was subtracted from the CHRreadings using the following equation to account for the differ-ences in the indices of refraction:

hFluid ¼ hTotal �hGlass

gGlass

� �gFluid ð1Þ

To acquire liquid film thickness measurements away from the cav-ity centerline the target surface was mounted to a micro traversethat allowed it to move independently from the droplet generator.This allowed the droplets to impinge at a fixed location in labora-tory coordinates, but permitted the entire tank, including the opti-cal probe, to be traversed radially so that thickness versus time datacould be collected at different radii, measured from the center of thedrop impact point. These data were synchronized to the video re-cords, in order to synchronize the time histories at different radiiwith one another. Measurements were obtained at 0%, 25%, 50%,62.5%, 75%, 87.5%, and 100% of the maximum bottom crown radius,Rb, for the specific case (Fig. 3), where maximum values of Rb weredetermined from analysis of the backlit video images. Since the li-quid film thickness data were acquired using a point measurementmethod, the data were acquired for different droplet impacts ateach radial location. Thus, it is expected that the largest source ofuncertainty in the current results is due to the drop-to-drop vari-ability of the point of drop impact. At present the magnitude of thiserror source has not yet been carefully documented, but it is esti-mated to be a relatively small fraction of the impacting dropletdiameter. Hillen et al. [14] have given further details of both theexperimental procedures and data reduction methods.

Sub-cavity volumes for specific times have been computed viaintegration, evaluated using the trapezoidal rule:

Voli ¼ 2pZ Rci

0ðR � hÞdR; ð2Þ

where the i subscript indicates the time index for which the volumeis computed, and R is the radial coordinate measured from the cav-ity center.

Limitations of the CHR instrumentation required post-process-ing of the sub-cavity thickness profiles prior to evaluating theabove integral. Thickness values that were beyond the sensormeasuring range, as well as complex curvature of the free surface,would cause data drop out or inaccurate measured film thicknessvalues. Sub-cavity thickness readings are generally quite repeat-able and reliable, but difficulties were observed particularly atthe times of initial droplet contact with the liquid layer, as wellas during the collapse of the crown, and the complex events dur-ing and after fill in of the cavity during the retraction phase. Bymanually referring to the corresponding high-speed videos anyinaccurate readings were filtered out, and missing data pointswere then added in using cubic interpolation. Additionally, to in-crease the resolution of the sub-cavity volume calculations, thick-ness values at intermediate radii between the actual radialmeasurement locations have been linearly interpolated for eachtime step.

In order to compute the sub-cavity volume at any time step,two assumptions had to be made: the choice of the radial locationat which to end the integration near the base of the inside crownwall, Rc, and the initial time at which to begin to compute a sub-cavity volume. The liquid film thickness at a point within the cavity

decreases rapidly versus time as the cavity initially forms and thethickness transitions into a (nearly) uniform film thickness afterdroplet impact. The liquid film thickness also changes rapidly ver-sus radius at a fixed time at the inside crown wall. These regions ofrapid variation of the film thickness are easily seen in the final car-pet plots of the smoothed data to be presented below. The desiredsub-cavity liquid volume at each time is computed as the integralof the measured h(R), as in Eq. (2), in the ‘‘floor’’ of the surface con-tour plots shown below. The ending cavity radius for the numericalintegration has been determined through an iterative process de-scribed in Hillen et al. [17]. Generally, the value of Rc in Eq. (2)has been selected to be the radial location where the local liquidfilm thickness is between 1.2 and 1.6 times the average sub-cavityliquid film thickness computed for R < Rc. Noting that the measuredsub-cavity film thickness values are on the order of 100 lm or less,it was noted that varying this value of Rc such that the local filmthickness changes by 10 lm changes the computed sub-cavity vol-ume by only about 1.3–1.5%. Hillen et al. [17] also describe analternate method that was used for one of their cases as a checkon this direct integration method, where good agreement wasfound between the two integration methods.

3. Computational method

All of the current CFD simulations reported have been per-formed using the commercial CFD code ANSYS FLUENT on aquad-core desktop computer. FLUENT solves the fluid dynamicsconservation equations using the finite volume approximation. Inorder to simulate a drop impact, it is essential to be able to accu-rately compute the location of the free surface of the liquid. Thishas been accomplished by using the explicit Volume of Fluid(VOF) method [18]. The VOF multiphase model was implementedsuch that the drop liquid and the layer liquid could be distin-guished [10], even though they are physically identical. For each li-quid an advective transport equation was solved for an indicatorfunction defined as the fraction of a computational grid cell occu-pied by that liquid. If the sum of these liquid indicator functionswas less than 1, the cell contained an air–water interface at whichsurface tension acted. Each fluid was treated as incompressible,and volume weighted fluid properties were used in cells whichcontained both air and water. In these simulations, the surround-ing gas is air at atmospheric conditions while the liquid is purewater. In every case the drop and layer liquids are the same(water). Surface tension is incorporated into the Navier–Stokesequation by using the Continuum Surface Force (CSF) [19] modelwhich accounts for the curvature of the interface. The sharpnessof the interface is enhanced by use of the geo-reconstruct (Piece-wise Linear Interface Calculation, PLIC [20]) scheme. Velocity andpressure coupling is achieved with the Pressure Implicit with Split-ting of Operators (PISO) [21] algorithm. Discretization of the advec-tive terms in the momentum equations is obtained via secondorder upwinding.

The initial conditions for the axisymmetric simulations areshown in Fig. 4. The spherical drop has been initially located1.5D above the free surface of the initial liquid film, but the simu-lation time has been set to zero when the drop first makes contactwith the film surface to be consistent with the experiments. Theinitial drop diameter, D; the original liquid layer thickness, H;and the drop velocity, V, have been defined as initial conditions.Pressure outlet boundary conditions were defined on the upperand the maximum radius outer boundaries. The impermeable no-slip wall boundary condition was applied on the bottom boundary,and the centerline was set as a symmetry boundary. Solutionswere initially obtained using a zonally uniform quadrilateral meshwith a total of 325,000 cells without grid refinement for the 2D-Axi

D/2

V

H

Fig. 4. Schematic for CFD of a single drop above a thin liquid film before the impact.(Note that only half of the axisymmetric domain is shown; blue represents theliquid while white represents the surrounding gas). (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)

J.M. Kuhlman et al. / Experimental Thermal and Fluid Science 54 (2014) 179–188 183

(Axi refers to axisymmetric) model. A great improvement in compu-tational speed was achieved without sacrificing accuracy by usingthe adaptive mesh refinement option in which the grid is refinedonly in critical areas of rapid change, such as the liquid–gas inter-face. In each level of refinement, the mesh length (both in verticaland horizontal directions) is divided by two. If the initial mesh sizeis D/5.25, a Level-4 (D/84) adaptive mesh reduces the number ofcells to around 25,000 for the 2D-Axi case. Similarly, a 1.8 millioncell 3D grid can be reduced to about 400,000 cells using Level-3(D/42) refinement. An example of the adaptive dynamic meshrefinement is illustrated in Fig. 5. Based on initial 2D-Axi and 3Dsimulations, it was concluded that Level-3 (D/42) and Level-4 (D/84) results did not differ significantly in the important impactcharacteristics (e.g. upper crown diameter). The 2D-Axi presentedresults used adaptive mesh refinement where the mesh size is D/5.25 in the outer zone and D/84 (for Level-4) at the liquid gas inter-face. Further details of the simulation method and several valida-tion results have been presented in Hillen et al. [14].

Fig. 5. Dynamic mesh refinement at the interface of liquid and air at 3 ms for case 2(H/D = 0.113) (Note: Blue refers to drop liquid, green refers to layer liquid, and redrefers to air). (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)

4. Results

4.1. Comparisons between simulation and experiment

Hillen et al. [14] have compared their CFD simulations andexperimental results to validate their methods for two differentcases: one near to the drop splashing threshold (case 1), and a sec-ond that is significantly above this threshold (case 2). An addi-tional, higher Weber number case is presented below in a similarfashion (case 3). The three cases used in efforts to validate the pres-ent experimental methods are defined in Table 1. Froude numbersfor the present single drop experiments are large compared to a va-lue of Fr = 1 (Table 1), indicating that body forces are relativelysmall compared to inertial effects. However, it is not possible toproperly match the much larger values of the Froude numberbased on drop diameter that would be expected for the much smal-ler droplets produced by a typical spray (order of 50–100 lm),since the present drops have diameters of between 3 and 6 mm.

Fig. 6 shows the present simulations compared against thehigh-speed video images from experimental results for case 3 atnominally the same times. The interfaces between the experimentand simulation show clear agreement at the first two times, withsome differences in the shape of the crown at later times. The mostnoticeable difference is that at 69.1 ms the simulation shows a col-lapsed crown, but the experiment shows the crown to be nearingcollapse, yet still largely intact. Upon inspection of the high-speedvideo image, it was found that the crown has been torn in a com-plicated, three-dimensional fashion, and is a very short distancefrom the free surface. This implies imminent crown collapse. Thus,the lack of a crown in the simulation results is expected to be lar-gely due to the limitations of the present 2D simulations, wherethe experimental crown collapse is altered significantly by athree-dimensional instability and jets that form around the cir-cumference. This discrepancy between experiment and CFD simu-lation at later times (earlier onset and completion of the cavityretraction phase in the CFD) is seen consistently for the currentsimulations, and is probably due to this strong departure from axi-symmetry observed in the experiments during retraction. As a re-sult, it is the experimental sub-cavity film thickness data that havebeen used to compute the sub-cavity liquid volume rather than theCFD simulation results.

To compare liquid film thickness results for case 3, the center-line values for the first portion of the droplet impact event areshown in dimensional form in Fig. 7. The CFD results are in closeagreement with the experimental results for the first 30 ms. How-ever, between 30 ms and approximately 75 ms the simulationover-predicts the centerline film thickness. Further, beyondapproximately 80 ms, the CFD simulations significantly over-pre-dict the centerline film thickness, due to earlier onset of retractionof the cavity for the CFD. The dimensionless outer bottom crownradius results obtained from the experiments and simulations havebeen compared for case 3 for 0 < t/(D/V) < 40 in Fig. 8. In this figureit is seen that the simulation consistently overpredicts Rb for t/(D/V) > 2. Differences between the experiment and simulation are aslarge as 8% at t/(D/V) = 28 and 12% at t/(D/V) = 32. These differencesmay be put in perspective by noting that in earlier work by Hillen

Table 1Dimensional and dimensionless parameters for cases for which detailed data wasobtained.

Case D (mm) V (m/s) We Re H/D Fr

1 3.19 1.79 141 5700 0.614 1032 6.39 2.69 633 17,100 0.113 1153 6.48 4.21 1580 27,100 0.463 279

Fig. 6. Example of comparisons of the high-speed video images (top) and the CFD simulations (bottom) for case 3 at times t � 0, 4.42, 33.2, and 69.1 ms.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

0 10 20 30 40 50 60 70 80 90

h 0 (µ

m)

t (ms)

Experiment

2D Simulation

Fig. 7. Case 3 centerline film thickness comparisons between the average exper-imental results and simulation results.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 4 8 12 16 20 24 28 32 36 40

RB

/D

t/(D/V)

Experiment

2D Simulation

Fig. 8. Comparison of bottom outer crown diameter experimental and simulationresults for case 3.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 10 20 30 40 50 60 70

h/h 0

ττ

We=137; Re=6,690; and Fr=51We=457; Re=12,300; and Fr=165We=1,690; Re=23,600; and Fr=619

Fig. 9. Experimental dimensionless centerline cavity film thickness history for awetted surface at varying We and Re numbers with H/D � 0.73.

184 J.M. Kuhlman et al. / Experimental Thermal and Fluid Science 54 (2014) 179–188

et al. [14], the variability of experimental bottom crown radius re-sults for five repeat runs was as large as ±12–14%. Since the dropswere observed to be non-spherical (See Fig. 6 for an extreme case),variability in droplet shape at impact likely contributed to this var-iability in Rb. These differences were also attributed partially to dif-ficulties in the image processing in detecting the full bottom crownradius, due to a meniscus effect on the near wall of the tank. Com-parisons between simulations and experiments presented by Hil-len et al. [14] for cases 1 and 2 were generally comparable to, orin some instances better than, those presented here for case 3.The current bottom crown radius experimental data have been uti-lized to determine how far away from the cavity centerline to mea-sure the sub-cavity liquid film thickness.

4.2. Liquid film thickness measurements

Comparisons between the CFD simulation and the experimentin the previous section, and similar comparisons presented by Hil-len et al. [14] for other (We, Re) values, show reasonable agreementand give some confidence that either may be used to determine thedetailed time evolution of the sub-cavity liquid film volume up tothe beginning of the retraction phase when the crown collapsesand the cavity begins to refill. Previous experimental data [14] ata nearly constant nondimensional initial liquid layer thickness ofH/D = 0.73 have been re-plotted nondimensionally versus dimen-sionless time, s = t/(D/V) in Fig. 9. The centerline cavity film thick-ness decreases slightly as Weber number is increased, from about2.6% of the initial layer thickness (or 2% of the droplet diameter) at(We = 137, Re = 6690), to 1.85% of the initial layer thickness (1.3%of the droplet diameter) at (We = 1690, Re = 23,600). However,the nondimensional lifetime of the cavity, Ds, increases dramati-cally as Weber number increases, from Ds � 5–10 at We = 137 toDs � 50 at We = 1690. Noting that the actual dimensional cavitylifetimes increase modestly, from approximately 22 ms atWe = 137 to 42 ms at We = 1690, indicates that a significant portionof the increase in Ds is due to the shortening of the droplet char-acteristic interaction time, D/V, with increased We. Similar resultsfor the three present cases for which detailed cavity film thicknessdata versus both time and radius have been obtained (Table 1) arepresented in Fig. 10. Similar trends are observed in this figure. Thecenterline cavity film thickness is approximately 2.3% of the dropdiameter for case 1, at We = 141, Re = 5700, and consistently de-creases to 1.8% of D for case 2, at We = 633, Re = 15,700, and to1% of D for case 3, at We = 1580, Re = 27,100. However, note thatwhen plotted normalized by the initial liquid layer thickness, thecomputed plateau value of dimensionless cavity film thickness is0.11 at We = 633 (case 2), as opposed to only 0.037 at We = 141

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60

h/h 0

ττ

We=141; Re=5,710; =0.61We=598; Re=15,700; =0.11We=1,580; Re=27,200; =0.46

h0*

h0*

h0*

Fig. 10. Experimental dimensionless centerline cavity film thickness history(normalized by h0) for case 1, case 2, and case 3.

J.M. Kuhlman et al. / Experimental Thermal and Fluid Science 54 (2014) 179–188 185

and 0.022 at We = 1580. This is due to the very thin initial liquidlayer thickness for case 2 (H/D = 0.113). These observations areconsistent with the general conclusions by van Hinsberg et al. [9]and Berberovic et al. [22]. These authors determined that the pla-teau value of the centerline sub-cavity film thickness depends onboth the initial nondimensional liquid layer thickness, H/D, as wellas the Reynolds number for high Weber numbers and Froudenumbers.

The sub-cavity film thicknesses versus both time and the radiusare summarized in carpet plot form for case 1 and case 2 in Figs. 11and 12, respectively. It is these data that have been integrated radi-ally at different times to compute the sub-cavity volume versustime. These figures show pictorially the differences in size and life-time of the thin film regions formed beneath each droplet impactcavity. For case 1, the thin film lifetime is seen to be no longer thanabout 15 to 20 ms (Fig. 11a), with a maximum radius of approxi-mately 5 mm. For case 2, lifetime is significantly larger (about50 ms; see Fig. 12a), as is the maximum radius (between 13 and15 mm). Similarly, case 3 (not shown) has both the longest lifetime(about 80 ms) and the largest maximum radius (about 15 mm).Note that for the experiments, the film thickness values beyondthe maximum cavity radius and after the lifetime of the thin filmare incomplete, due to limitations of the CHR sensor. For both casesshown, there is clear evidence that the sub-cavity film becomesthinner at later times near the maximum cavity radius; see Figs. 11and 12. An example of this is shown more clearly for case 2 in

(a)Fig. 11. Carpet plot of measured liquid film thickness versus time for case 1 (Tar

Fig. 13, where the dimensional sub-cavity film thickness is shownversus radius at several times between t = 15 ms and t = 35 ms. Re-sults have been shown using solid lines to connect the data duringthe establishment of the cavity and dotted curves with open sym-bols during the onset of the retraction phase. The plot has beenzoomed-in to emphasize the decreases in the film thickness thatoccur near to the inner crown wall. (The thickness of the undis-turbed liquid layer was nominally 725 lm). Between t = 20 msand t = 35 ms the sub-cavity film thickness is nearly constant ver-sus radius until around R = 8 to 10 mm (equaling between nomi-nally 80 lm and 90 lm), and then decreases between R = 10 and12 mm (from about 90 lm to as little as 60 lm). This phenomenoncould be partially due to the viscous nature of the flow in the film;the liquid at the cavity centerline does not have sufficient time toflow radially outwards before the retraction phase begins. How-ever, surface tension is also believed to influence this phenomenon,forming a reflexive thickness versus radius profile in an effort tolessen the sharp increase in curvature of the profile as the crownbegins to collapse. Similar sub-cavity film thickness results com-puted from CFD match the experiments well during initial cavityformation, yielding very similar sub-cavity film thicknesses, butshow an earlier onset of the cavity retraction, and more gradualretraction phase. The cause of this discrepancy between experi-ment and CFD is uncertain at present, and is under investigation.Again, it is believed to be a result of the departure from axisymme-try during this phase of the experiments. However, Berberovicet al. [22] have developed an improved numerical method thatled to sharper air–liquid interfaces for the cavity retraction phasein their work; it is also possible that this improved method mightbe necessary in order to obtain more accurate predictions of theretraction phase for the current application.

4.3. Sub-cavity volume results

The sub-cavity volume versus time results are presented inFig. 14 for case 1 and Fig. 15 for case 2. Results for case 3 havenot been presented since this Weber number (Table 1) is abovethose that have recently been measured for a full cone spray of cur-rent interest [23]. The sub-cavity volume histories shown inFigs. 14 and 15 have been computed using the experimental filmthickness data from Figs. 11a and 12a, respectively. The computedsub-cavity volume has been nondimensionalized by dividing bythe original droplet volume, and s is the dimensionless time sinceinitial contact of the drop with the liquid layer. Three similarcurves are shown in each figure. The sub-cavity volume computed

0

2

4

6

00.250.5

0.751

1.251.5

1.752

2.252.5

2.753

0 10 20 30 40

R (m

m)

h (m

m)

t (ms)

2.75-32.5-2.752.25-2.52-2.251.75-21.5-1.751.25-1.51-1.250.75-10.5-0.750.25-0.50-0.25

(b)get values of We = 141, Re = 5700, H/D = 0.614): (a) experiment and (b) CFD.

01.53.556.589.511

0

0.25

0.5

0.75

1

1.25

1.5

0 20 40 60 80

R (m

m)

h (m

m)

t (ms)

1.25-1.51-1.250.75-10.5-0.750.25-0.50-0.25

(a) (b)Fig. 12. Carpet plot of measured liquid film thickness versus time for case 2 (Target values of We = 598, Re = 15,650, H/D = 0.116): (a) experiment and (b) CFD.

Fig. 13. Experimental sub-cavity film thickness versus radius at several times during establishment of cavity (solid lines) and during start of retraction phase (dotted lines)for case 2 (We = 598, Re = 15,650, H/D = 0.116).

Fig. 14. Computed sub-cavity volume versus time for case 1 (We = 141, Re = 5700,Fr = 103, H/D = 0.614). Volume has been normalized by the droplet volume, whiletime has been normalized by (D/V).

Fig. 15. Computed sub-cavity volume versus time for case 2 (We = 633, Re = 17,100,Fr = 115, H/D = 0.113). Volume has been normalized by the droplet volume, whiletime has been normalized by (D/V).

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Table 2Percentages of sub-cavity liquid from the droplet and from the original layer,averaged over the sub-cavity volume and cavity lifetime (from CFD simulations).

Case H*=H/D Drop liquid (%) Film liquid (%)

1 0.614 52.80 47.202 0.113 92.17 7.833 0.463 48.30 51.70

J.M. Kuhlman et al. / Experimental Thermal and Fluid Science 54 (2014) 179–188 187

using the optimized maximum film thickness at which the integra-tion is ended [17], hmax (135 lm for case 1, and 130 lm for case 2),is the middle (solid) curve. Also shown are two additional curves,showing calculated sub-cavity volume time histories if the hmax va-lue is increased or decreased by nominally 17%. Differences are rel-atively small (variations of 1% for case 1 and 3% for case 2, averagedover 7.5 6 s 6 15), except for the early times during the establish-ment of the thin film.

For both cases, the sub-cavity volume remains at a relativelyconstant value of nominally 30% of the original droplet volumefor a significant portion of the cavity lifetime. For example, for case1 (Fig. 14), the dimensionless sub-cavity liquid volume, Vol*, re-mains above approximately 0.3 for dimensionless times in therange 5.33 < s < 10.80, corresponding to a characteristic lifetimeof 9.75 ms. The computed average value of Vol* over this thin filmlifetime is 0.30. Similar analysis of Fig. 15 for case 2 indicates thataveraging over the times of 6.32 < s < 17.68 (corresponding to athin film lifetime of 27 ms) yields an average value of Vol* of 0.35.

These computed values of the sub-cavity liquid volume andsub-cavity thin film lifetimes are the key results of the presentwork, since they enable estimates to be made of the value of thelocal average heat flux that would be required to dry out the sur-face beneath the cavity. From another perspective, for a given localheat flux, if the sub-cavity thin film lifetime is sufficiently long,then the sub-cavity liquid will be boiled away before the cavityis filled in by the surrounding liquid. If this occurs with sufficientfrequency, then these localized dry areas could be a significantcontributor to the onset of critical heat flux (CHF), because the lo-cal dry areas would be likely to result in even higher local surfacetemperatures, thereby leading to decreases in the local transientheat flux.

4.4. Example of use of present sub-cavity volume data to compute heatflux required to dry out a droplet impact cavity

A simple energy balance between the heat flux from the heatedsurface to the sub-cavity liquid volume may be written as:

tdryðq00wAcÞ ¼ qVolc½CpðT � TsatÞ þ hfg � ð3Þ

where Ac is the heated surface area covered by the drop impact cav-ity, Volc is the sub-cavity liquid volume, q00w is the average sub-cavitywall heat flux, and tdry is the time required to dry out the heater sur-face covered by the cavity. This relation can be used to estimate therequired cavity average wall heat flux that would be required to boilaway all of the sub-cavity liquid volume during the sub-cavity thinfilm lifetime:

ðq00wÞdry ¼ qVolc½CpðT � TsatÞ þ hfg �=ðActfilmÞ ð4Þ

where tfilm now is the sub-cavity thin film lifetime.The results in Fig. 15 for case 2 in Table 1 (We = 633,

Re = 15,700, H/D = 0.113) [14] have been selected to illustrate themethod, since the Weber number for case 2 is representative ofvalues expected for a Spraying Systems 1/8-G full cone spray noz-zle for which detailed Phase Doppler Particle Analyzer (PDPA) datahave been measured [23]. From this PDPA data, it was found thatdroplets with diameters in the range of 0.95Dmax < D < Dmax com-prise approximately 40% of the total spray mass, and have Webernumbers prior to impact of between We = 500 and We = 800. Theselarger, higher Weber number droplets are expected to have suffi-cient inertia to form the thin sub-cavity liquid films and to havelong enough sub-cavity thin film lifetimes that would lead to sig-nificantly enhanced local transient heat transfer. They also wouldbe susceptible to localized dry out at sufficiently high average localheat fluxes. Using the computed sub-cavity thin film lifetime forcase 2 of tfilm = 0.027 s, and the sub-cavity average liquid volume

of Volc = 4.73 � 10�7 m3, with q = 988 kg/m3, Cp = 4.2 kJ/kg K,hfg = 2257 kJ/kg for water, and a droplet subcooling of 50 �C, Eq.(4) predicts ðq00wÞdry ¼ 33:93 MW=m2. The numerical simulationsof Sarkar and Selvam [12] indicate the local transient heat flux inthe droplet impact cavity to be approximately six to seven timeshigher than the average wall heat flux to the surrounding liquidlayer. Thus, the predicted overall heat flux, averaged over the en-tire heater surface, that would be required in order to dry outthe cavity for this example would be between 4.8 MW/m2 and5.6 MW/m2. These values are near to the maximum heat flux val-ues achieved by Lin and Ponnappan [3] using water as theircoolant.

This level of consistency in this initial example is quite encour-aging, but the method must now be implemented into the MonteCarlo spray cooling heat transfer model [4–6] for the full range ofrelevant droplet diameters and velocities in order to fully assessthe importance of this phenomenon on spray cooling heat transferbehavior. It is expected that the effects will be significant, since forthe spray nozzle of interest, almost 40% of the liquid mass impactsthe heated surface with Weber numbers of around 500 or above[23], and further the preliminary version of the Monte Carlo model[4–6] predicted that at all times, over 65% of the heater surfacearea was covered by droplet impact cavities that were in somephase of the processes of being heated up to saturation tempera-ture, or boiling, or being filled in due to either capillary action orsubsequent, nearby droplet impacts.

Also, similar calculations may be made to predict the localcavity heat flux that would be required for onset of localizedboiling of the sub-cavity liquid volume by including only thesensible heating in Eq. (4). For the same conditions as above thisyields the prediction that ðq00wÞ ¼ 0:0083 [Twall–Tsat] for the onsetof boiling, where the heat flux is the value averaged over theheater surface, taken as one-seventh of the sub-cavity heat flux,in MW/m2. For example, for 30 �C subcooling, this modelpredicts the onset of boiling within the cavity for an averageheat flux of 0.25 MW/m2.

One further complication related to predicting the level ofheating required to initiate boiling of the sub-cavity liquid isthe relative composition of this liquid volume: a portion of thisliquid will have originated from the impacting droplet, whilethe remainder will have come from the liquid layer which wasalready in contact with the surface to be cooled. This liquid alreadycontacting the heated surface will likely be at or near to saturationconditions, so the fraction of the sub-cavity liquid volume notoriginating from the impacting droplet will reduce the requiredheat flux for onset of boiling in the cavity. The current CFDsimulations have been used to compute the relative percentagesof the sub-cavity liquid volume originating from the droplet andfrom the liquid layer for cases 1–3, as summarized in Table 2. Itis seen that for the very thin liquid layer of case 2 (H/D = 0.113),the sub-cavity liquid volume consists almost entirely of dropliquid. On the other hand, for the other two cases, with(We = 141, H/D = 0.614) and (We = 1580, H/D = 0.463), the relativepercentages are nearly 50–50%. Thus, it is concluded that very thinliquid layers should contribute to the highest possible transientheat fluxes for onset of boiling, and for CHF.

188 J.M. Kuhlman et al. / Experimental Thermal and Fluid Science 54 (2014) 179–188

5. Conclusions

The detailed temporal and radial dependence of the thickness ofthe liquid film beneath the cavity formed due to the impact of asingle water droplet into a static water layer over an unheated,horizontal, flat surface has been measured for the first time. Theseresults were obtained in the ranges of Weber and Reynolds num-bers and dimensionless liquid layer thicknesses, H/D, expectedfor sprays. This sub-cavity liquid film thickness decreased relativeto the centerline thickness value in the outer portion of the cavity,especially once the cavity was fully established. The centerlinesub-cavity film thickness was seen to decrease slightly as Webernumber (and Reynolds number) increased, and to increase slightlyfor very small H/D (Figs. 9 and 10), consistent with previous resultsfrom the literature. The measured sub-cavity liquid film thick-nesses generally were very close to those predicted by the presentCFD simulations, but only up to the onset of the cavity retractionphase. The present CFD simulations consistently predict retractionto occur earlier than is observed in the experiments. The cause ofthis discrepancy is currently under investigation, but is believedto be primarily due to the onset of significant three-dimensionalityduring retraction. Because of this discrepancy, only the experimen-tal sub-cavity film thickness results have been used to determinethe sub-cavity liquid volume and the cavity lifetime. The presentCFD simulations predict that the sub-cavity liquid volume consistsof nominally 50% droplet liquid and 50% liquid from the original li-quid layer for the two cases (We = 141 and We = 1580) with H/Daround 0.5. However, for the intermediate Weber number case(We = 633), with H/D = 0.113, the sub-cavity liquid volume consistsalmost entirely of droplet liquid. It is expected that transient heattransfer will be increased for droplet impacts onto these very thininitial liquid layers.

The sub-cavity liquid film thickness data have been integratedradially at several times spanning the cavity lifetime, to computethe sub-cavity liquid volume history. Sub-cavity volumes arenearly constant in magnitude over a significant portion of the cav-ity lifetime. The sub-cavity volume is around 30–35% of the initialdrop volume over the current ranges of We and Re values. The mea-sured cavity lifetime and sub-cavity volume were used in an exam-ple to estimate the local average heat flux values that would berequired to: (a) bring the liquid in the sub-cavity volume to satu-ration temperature, and to (b) dry out the cavity, for the presentintermediate Weber number case (We = 630, Re = 17,000,H* = 0.11). For water the heat flux to dry out the cavity is signifi-cantly higher than the value required for the onset of boiling.The computed heat flux averaged over the heater surface thatwould be required to dry out the cavity was estimated to be onthe order of 4–6 MW/m2, over a range of subcooling of 20–80 �C,which is the same order of magnitude as the maximum overallheat flux achieved in spray cooling experiments using water asthe coolant [3]. These calculations support the hypothesis thatdry out of droplet impact cavities is a significant contributor tothe onset of critical heat flux for the spray cooling process.

Acknowledgements

The authors gratefully acknowledge the financial support of thiswork under NASA Cooperative Agreement NNX10AN0YA. Initial

development of the Monte Carlo model was partially supportedby the West Virginia NASA Space Grant Consortium. The currentviews and conclusions are those of the authors and should not beinterpreted as necessarily representing the official policies, orendorsements, whether expressed or implied, of NASA or the WestVirginia NASA Space Grant Consortium.

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