Droplet Impact Sub-cavity Histories and PDPA Spray Experiments for Spray Cooling Modeling

Abstract

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...

Comparisons of Single Drop Impact Simulations with Experiments

“…Section 7.3 presents the CFD results for the sub-cavity liquid film thickness. These results are also compared with the experiments by Hillen (2013). Finally, the computed sub-cavity volumes are compared with these experiments in section 7.4.…”

“…In Figure 7.2-1, a sequence of images, organized vertically like film strips, are shown with their respective impact times displayed in red. The experimental images have been obtained from the videos within the thesis by Hillen, (2013). For the images to be compared, a common procedure was setup.…”

“…In these comparisons, for two cases, i.e. for case 1A and case 5A, the experimental sub-cavity volume calculations have been performed with Hillen's criterion (Hillen, 2013) applied to his experiment data of determining the sub-cavity cutoff height and calculating the sub-cavity volumes. In all five comparisons, calculations using two criteria are presented for the simulations.…”

“…Sprays consist of millions of droplets and one drop among them was taken for studying the properties of the sub-cavity region. By varying the non-dimensional parameters (We, Re and h*) of the liquid, the single drop impacts studied previously through experiments (Hillen, 2013) have been modeled using two different CFD simulation methods for comparisons with the experimental results.…”

“…Based on the expected range of spray droplet Reynolds number, Weber number, and Froude number. This thesis compares the isothermal single drop simulations, in both full 3D and in 2D axisymmetric cases, to experimental results from the thesis by Hillen (2013), and discusses the discrepancies that arise in the calculation of centerline film thickness and sub-cavity volumes. These discrepancies are possibly due to the variation in surface tension of the liquid in the experiments, as well as limits in grid resolution due to limited computational resources for the CFD.…”