A monolithic enthalpy-based model for the simulation of in-flight ice accretion on heated bodies using moving finite elements

With aircraft icing occurring in more and more complex environments, its modelling and simulation remains a challenging task. This is particularly the case for ice crystal icing on a heated substrate where effects such as liquid–solid phase change and imbibition can take place. In this work an unsteady model for ice accretion and melting on a heated substrate is presented. The model is based on an enthalpy formulation that accounts for temperature and liquid volume fraction gradients inside the accretion layer. It also takes into account heat conduction inside the considered substrate. The model is formulated in terms of a partial differential equation expressed on the time-evolving domain, that is solved using an existing moving finite element method. After describing the model and numerical resolution scheme, a verification case based on the Stefan problem is performed. The method is then used to simulate a heated flat plate configuration in ice crystal icing conditions, for which experimental data is available. The simulations are first performed in one dimension and several properties of the methodology are assessed. In particular, the effect of taking the imbibition process into account is investigated. The capabilities of the proposed methodology are then demonstrated with a two dimensional simulation of the heated plate. The results show that the methodology is an interesting way forward for the numerical investigation of icing on heated bodies.