Local Solution to the Unsteady Stefan Problem for In-Flight Ice Accretion Modeling

A new model for in-flight ice accretion is presented for both rime and glaze conditions. The model is based on the local, exact solution of the unsteady Stefan problem for the temperature profiles within the ice layer in glaze conditions. The new model moves from Myers’s formulation, and it includes an unsteady description of the heat diffusion problem within the ice layer. Moreover, the local value of the air temperature outside the boundary layer is used to compute convective heat fluxes, in place of the constant freestream temperature value considered in Myers’s model. A source term is introduced to take into account mass transfer at the boundary separating rime and glaze regions. The model was implemented in the ice accretion software PoliMIce to perform numerical simulations of inflight ice accretion over two-dimensional airfoils in both rime and glaze ice regimes. The open-source computational fluid dynamics software OpenFOAM was used to compute the aerodynamic flowfield and to reconstruct water droplet trajectories. Numerical results suggest that the modifications introduced with respect to the original Myers model improve significantly the accuracy of the predicted ice shapes for the considered test cases. The introduction of the local value of air temperature was found to be essential for the formation of the well-known two-horn ice shape, due to the occurrence of a local glaze to rime transition. The diverse contributions to the heat fluxes are discussed for both the proposed and the Myers models.