Heat transfer during condensing droplet coalescence

Abstract

Dropwise condensation can yield heat fluxes up to an order of magnitude higher than filmwise condensation. Coalescence is the primary mode of growth for condensing droplets above a small threshold size (e.g., radius r > 2 μm for water at 1 atm), but no prior studies have quantitatively assessed heat transfer during coalescence. Previous models of dropwise condensation have generally described coalescence as an instantaneous event, with a step reduction in heat transfer rate. However, coalescence and recovery of a quasi-steady droplet temperature profile requires a finite time, during which the direct droplet condensation heat transfer rate gradually decays. Additionally, during this period, the droplet may oscillate, repeatedly clearing the surrounding surface and resulting in high overall heat fluxes. This study employs Volume-of-Fluid (VOF) simulations to quantitatively assess these two transient heat transfer processes during droplet coalescence. It is shown that the direct mechanism of gradual heat transfer decay can be represented by a decaying exponential function with a time constant τ. Simulations are performed to determine τ(r1,Rt) for (1μm⩽r1⩽25μm;1⩽Rt⩽4) where r1 is the radius of the smaller droplet and Rt is the radius ratio between the two merging droplets. For water at atmospheric pressure this spans the range of droplet sizes through which most of the heat transfer occurs on a surface (∼80%). A simple correlation is proposed for τ(r1,Rt) for the studied droplet size range, fluid properties, and surface conditions. These simulations are also employed to determine the order of magnitude of heat transfer enhancement due to repeated clearing of the surrounding surface as droplets coalesce. Findings can inform improved models of dropwise condensation that more accurately predict transient heat transfer during coalescence events.