Numerical Simulation of Supercooled Droplets Freezing During In-Flight Icing via a Hybrid Numerical-Analytical Method

This chapter deals with the mathematical modeling and computer simulation of the transient heat and mass transfer process with phase change in supercooled water droplets. The aim is to review the theoretical analysis of both a freely suspended droplet in a gas stream and a droplet lying on a cold substrate. First, a hybrid numerical-analytical methodology known as the Generalized Integral Transform Technique (GITT) is reviewed as an error-controlled simulation tool for moving boundary problems in transient nonlinear heat conduction with phase change, for a one-dimensional formulation of a suspended spherical droplet, and the supercooling with a two-dimensional formulation of a spherical droplet resting on a solid surface. Second, a mixed lumped-differential reformulation strategy known as the Coupled Integral Equations Approach (CIEA) is revisited to propose improved lumped models for the one-dimensional suspended droplet. The two approaches may be applied independently or in combination, for instance, in simplifying the multi-dimensional local models into a lumped-differential formulation through CIEA, which is then solved by the hybrid GITT methodology. The model reduction and simulation tools are then demonstrated for typical test cases available in the literature that include experimental campaign results for validation purposes. The relative merits of these alternative tools are then discussed, and their capabilities are employed in the physical interpretation of the fundamental transport phenomena involved.