Droplet impact time histories for a range of Weber numbers and liquid film thicknesses for spray cooling application

Abstract

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

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

“….1: Full cone water spray generated by a Spraying Systems FullJet 1/8-G nozzle on an unheated 5.08 cm diameter surface (Hillen et al 2013). __________________________________________________ 2 Figure 1.2: Single drop impingement into an unheated initial liquid surface and its components (Hillen et al 2013). 6 Figure 2.1: Simulated heater surface from the MC Spray Cooling model (Kreitzer, 2010).…”

“…_______________________________________________________________ 15 Figure 2.3: Incident beams crossing creating the measuring volume. ____________________________________ 27 Figure 3.1: Schematic of spray apparatus (Hillen et al, 2013). ________________________________________ 30 Figure 3.2: Spray testing 5.08 cm diameter impact surface apparatus with nozzle.…”

“…a) Intensity validation curve. b) Diameter difference validation (Hillen et al 2013). _______________________________________________________________________ 34 Figure 3.5: Coordinate system for spray axis and droplet coordinate system (Hillen et al, 2013).…”

“…b) Diameter difference validation (Hillen et al 2013). _______________________________________________________________________ 34 Figure 3.5: Coordinate system for spray axis and droplet coordinate system (Hillen et al, 2013). _____________ 35 Figure 3.11: Spray apparatus impinging onto the impact surface with the laser probe volume traversing along the z-axis to the side.…”

“…a) Side-view image of measured sub-cavity radius (red line indicates measured diameter). b) Bottom-view image of measured sub-cavity radius (red circle indicates measured diameter) (Hillen et al 2013). _______________________________________ 51 Figure 4.7: A basic overview for the side-view video image processing.…”