Physics-Based Surface Condition Discriminant for a Time-Efficient Roughness Model

The actual surface roughness has a multizone characteristic, including both smooth and rough regions, depending on the degree of droplet impingement and ice accretion rate. Droplets on smooth regions tend to run back due to low convective heat transfer, leading to ice formation on rough regions with relatively high convective heat transfer. Therefore, to accurately describe such phenomena in simulation, it is necessary to distinguish the surface conditions, especially the smooth regions. Previously, empirical formulas or thermodynamic equations have been used to define the surface conditions, but these have limited applicability or are computationally expensive. To address these issues, this study introduced a physics-based discriminant derived from the energy equation of a thin water film to distinguish surface conditions. In addition, a modified roughness model was applied to each identified region for local values. To validate the proposed methodology, the surface roughness distribution, convective heat transfer, and ice shape were compared with the experimental results. The results confirmed that the proposed model can discriminate the smooth regions more accurately than the existing models, significantly improving the predictions of convective heat transfer and ice shape.