Spray cooling with phase change offers the means to achieve the highest rates of heat transfer from microelectronic components and other high energy density devices. The extreme complexity of the flow created by the impact of millions of droplets per second per cm 2 creates a need for a heat transfer design model which incorporates enough physical detail to yield accurate predictions while being sufficiently simplified to allow its use in routine design computations. The spray cooling group at West Virginia University is pursuing a coordinated program of laboratory experiments and computational simulations to develop a Monte Carlo-based spray cooling model that will satisfy this requirement. This paper reports progress in both the laboratory and computational fluid dynamics (CFD) phases of this study, including comparisons between single droplet impact results at We values of 161 and 633 to validate the CFD simulations and experimental measurements. A key goal of the present work is to determine the thickness of the thin liquid layer remaining in the crater formed when a liquid droplet impacts a surface covered by a preexisting liquid film. The volume of liquid in this thin liquid film in the droplet impact crater is one factor that will influence the onset of critical heat flux (CHF). Based on the present data the preexisting static film thickness is observed to have more of an effect than the initial drop parameters on the minimum liquid volume under the crater, but the crater lifetime depends on the initial drop conditions. The comparisons between experiments and simulations for these two cases show promise, but more refinement in experimental and computational technique are needed to achieve more consistent determinations of the volume of liquid under a crater. NomenclatureD = Drop diameter D U = upper crown diameter D V = Initial drop volume Fr = Froude number = H = Preexisting static liquid pool thickness H crown = Height of droplet impact crown h o = Centerline liquid film thickness h avg = Average liquid film thickness Oh = Ohnesorge number = Re = Reynolds number = 2 r = radius, measured from center of droplet impact R B = Radius of outside bottom of crown t = Time We = Weber number = V = Impact velocity Vol = Volume liquid under the impact crater Y = splashing-deposition criteria ρ = Density μ = Viscosity σ = Surface tension

Spray cooling is a topic of current interest for its ability to uniformly remove high levels of waste heat for densely packed microelectronics. A Monte-Carlo (MC) spray cooling simulation model is under development that is based on empirical data to be a cost effective design tool that will predict accurate heat fluxes based on nozzle conditions and heater geometry. This work reports spray and single drop experiments with the goal of computing the volume beneath a drop impact cavity (sub-cavity volume) created by a single impinging droplet on an initial liquid layer. A relevant test plan for the single drop experiments in terms of We and Re numbers was created through utilization of Phase Doppler Anemometry to characterize a water spray generated by a nozzle of interest for varying flow conditions. Liquid thickness profiles of the sub-cavity formed by a single impinging drop onto a range of initial liquid film thicknesses were measured versus time via a non-contact optical thickness sensor. Time dependent sub-cavity volumes were computed by integrating these sub-cavity liquid film thickness profiles measured radially outward from the impact centerline. It is found that higher We and lower h 0 * result in a more radially uniform sub-cavity surface contour versus time, except for regions near the outer bottom cavity radius, where the liquid film was thinner. The sub-cavity volume was found to be nearly constant for a majority of the cavity lifetime and increased with We and h 0 * . These results will be incorporated in future work into the MC model to improve its predictive capability. Nomenclatured = Drop diameter Greek Letters D = Arithmetic mean droplet diameter ρ = Density D 32 = Sauter mean droplet diameter η = Index of refraction Fr = Froude number = μ = Dynamic viscosity h = Liquid film thickness σ = Surface tension R = Radial location τ = Dimensionless time (t•V axial /d) Re = Reynolds number = Superscripts T = Temperature * = Dimensionless parameter t = Time Subscripts V = Arithmetic mean velocity 0 = Initial condition Vol = Sub-cavity volume axial = Axial velocity component We = Weber number = c = Cavity z = Axial standoff distance from the nozzle tip r = Radial velocity component s = Spray

Spray cooling is a topic of current interest for its ability to uniformly remove high levels of waste heat from densely packed microelectronics. It has demonstrated the ability to achieve very high heat fluxes, up to 500 W/cm 2 with water as the coolant, making it an attractive active thermal management tool. Full Computational Fluid Dynamic (CFD) simulations of spray cooling are infeasible due to the complexity of the spray (drops fluxes of 10 6 drops/cm 2-sec) and heater surface physics requiring impractical resources. Thus a Monte-Carlo (MC) spray cooling simulation model based on empirical data is under development to serve as a cost effective design tool. The initial MC model shows promise, but it lacks additional physics necessary to predict accurate heat fluxes based on nozzle conditions and heated surface geometry. This work reports spray and single drop experiments with the goal of computing the volume beneath a droplet impact cavity (the sub-cavity volume) created by a single impinging droplet on an initial liquid layer. A Phase Doppler Particle Analyzer (PDPA) was utilized to characterize a spray of interest in terms of integrated global Weber, Reynolds, and Froude numbers for varying flow conditions. Results showed that the spray droplet diameters decreased and velocities increased with increasing nozzle gage pressure. A relevant test plan for the single drop experiments has been created from the measured PDPA spray profiles combined with residual spray film thickness measurements from literature resulting in: 140 ≤ We ≤ 1,000, 1,200 ≤ Re ≤ 3,300, and 0.2 ≤ h 0 * ≤ 1.0. Froude numbers were not able to be matched for the current single drop experiments (spray: 32,800 ≤ Fr ≤ 275,000). Liquid film thicknesses under the cavity formed by a single droplet have been measured versus radius and time via a non-contact optical thickness sensor for the selected range of dimensionless numbers (We, Re, and h 0 *). Sub-cavity radius histories have also been analyzed utilizing high-speed imagery techniques to create the cavity thickness traverse profiles. Time dependent sub-cavity volumes have been computed by integrating these subcavity liquid film thicknesses versus radius at various times. It is found that higher We and lower h 0 * result in a more radially uniform sub-cavity surface contour versus time, except for thinner liquid film regions which are observed near the outer bottom cavity radius. The subcavity volume was found to be nearly constant for a majority of the cavity lifetime and increased with We and h 0 *. These results will be incorporated into the MC model to improve its predictive capability in future work. In addition, splashed droplet diameters and velocities have been extracted from PDPA data for a spray impinging normal to a smooth surface. It was found that the splashed droplets had sizes which were similar to the impinging spray droplets, and had velocities that never exceeded 3 m/s. The splashed droplet results have a negligible contribution to cavity formations due to their low Weber number...

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Spray cooling is a crucial method for meeting today's thermal management challenges in many areas including space applications, high speed computers, microelectronic components and other high energy density devices. The extreme complexity of the flow created by the impact of millions of droplets per second creates a need for a heat transfer model which incorporates enough physical detail to yield accurate predictions while being sufficiently simplified to use in routine design computations. The spray cooling group at West Virginia University (WVU) is pursuing a coordinated program of computational simulations and laboratory experiments to develop a Monte Carlo-based spray cooling model that will satisfy this requirement. This paper reports our initial simulations of sprays. A companion paper focuses on progress in the laboratory. The results reported here include simulations of sprays generated by a pressure swirl nozzle and a full cone nozzle and their impact on surfaces. The goals of these simulations are to demonstrate that they can accurately reproduce the characteristics of sprays seen in previous numerical simulations and laboratory experiments and also to develop the capability to perform the simulations that will be needed in the development of the Monte Carlo spray cooling model. The computations have been performed using the commercial ANSYS FLUENT CFD software. The fully three dimensional and axisymmetric simulations use the Finite Volume Method (FVM) computational technique to solve the Navier-Stokes and continuity equations for the air and the Discrete Phase Model (DPM) to calculate the trajectories of discrete droplets. Sprays are injected using the pressure-swirl atomizer and full cone nozzle models which are sub-models of DPM in FLUENT. Inertial, gravity, viscous, and surface tension forces are accounted for but heat transfer has not yet been included.