Probability-Based Droplet Modeling for In-Flight Icing Problems

A probability-based model (PBM) is developed to predict the evolution of a population of impinging droplets on a solid substrate and the eventual transition between dropwise and filmwise regimes. A dedicated heat transfer model is designed, in order to estimate the evaporating mass flux when the solid substrate is heated. Statistical information such as the droplet size distribution and the influence of surface wettability, required by the PBM, are derived using a previously developed high-fidelity individual-based model (IBM). The PBM is verified with the high-fidelity model for a small patch of solid substrate. Then, validation with experimental evidence from the literature is carried out in the case of in-flight ice on the NACA0012 airfoil. Results show that the present PBM is capable of investigating in-flight ice problems and can be integrated with a CFD analysis of the air flow past an airfoil flying through a cloud of supercooled droplets to predict the possible onset of ice accretion on the airfoil surface. Compared to Messinger-like models, the influence of surface morphology on runback water flow is incorporated in the PBM through the modeling of a discontinuous wetting layer, contributing to the design of passive and active anti-icing systems.