Thermal boundary layer analysis corresponding to droplet train impingement

Abstract

Simulations of droplet train impingement on a pre-wetted solid surface heated from below are used to study the thermal boundary layer behavior over a parameter space which includes variations in Reynolds, Peclet, and Weber numbers, as well as variations in inter-droplet spacing and initial liquid film thickness. Computationally, a modified version of the Volume-of-Fluid method is developed and employed in this study. The solver is validated against closed form solutions and additional experimental data from the literature. In combination with the simulations, an analytical representation is also developed and compared to the computations yielding favorable agreement. Results show that the boundary layer thickness is mostly affected by changes in inter-droplet spacing, Reynolds, and Peclet number, and influenced minimally by variations in Weber number and initial film thickness. In fact, it is explicitly demonstrated in the analysis that the impact velocity has the greatest effect in local heat transfer. An analytical expression for the Nusselt number radial profile is also developed. It shows that the Nusselt number scales as ∼ Re1/2, and its radial dependence is \documentclass[12pt]{minimal}\begin{document}$\sim \sqrt{r}$\end{document}∼r, which is the same as the circular jet impingement case. The notable difference in the present Nusselt number relationship is the role of inter-droplet spacing, which plays a significant role in the current configuration.