Simulating Heat Transfer During Transient Dropwise Condensation on a Low-Thermal-Conductivity Substrate

The instantaneous heat-transfer performance of a surface is dictated by the number and sizes of drops on the surface. While performance averaged over longer times is of interest from a technology standpoint, accurate simulation of the transient state is important in condenser design because the maximum heat rejection of the surface occurs in this range. Steady-state dropwise condensation can be thought of as a collection of transient dropwise condensation cycles occurring in parallel. Traditional simulation of dropwise condensation has focused on making comparisons with experimental drop-size distributions at later times, after the process has reached a statistical stationary phase where the heat transfer is lower. Understanding how to model and simulate transient dropwise condensation where a maximum in heat transfer occurs will help us design higher heat-rejecting surfaces. Additionally, a constant temperature difference between the steam and the surface below the drop is assumed. While often valid, there are some cases where this is not valid, and measuring the drop growth rate is required. We report a way to simulate transient dropwise condensation using a measured population averaged drop growth rate. The simulation reasonably predicts the time evolution of the number density of drops, fractional coverage, normalized condensate volume, and median drop radius for pendant mode dropwise condensation experiments on a cooled, horizontal, dodecyltrichlorosilane-coated glass surface. It was also found that assuming a constant temperature difference grossly underpredicts the heat transfer. Modification of the single-drop heat-transfer model to include substrate conduction and a thermal boundary layer shows that in the limit of low thermal conductivity the drop growth rate is constant for large drops. Additionally, a comparison between experiments and simulation shows that condensation might be initialized by nucleation onto fixed sites and then transitions to random nucleation as more sites become activated and more favorable. Understanding how a substrate's thermal properties affect the progression of dropwise condensation is important in determining the removal performance of the surface. With the commercialization of 3D printing, it is possible to fabricate low-cost, lightweight, plastic substrates with physical texturing for condensation applications where mass and cost savings are critical.