Stochastic ice accretion model using an unstructured advancing front technique

This paper describes a stochastic ice accretion method to model in-flight ice accretion. The approach consists in complementing the deterministic quasi-steady process generally used to simulate ice accretion by treating the effects of water-droplet deposition and freezing on the ice growth in a stochastic and unsteady manner. The baseline algorithm thus features an unstructured advancing front technique modeling the freezing of individual water particles. Stochasticity is introduced in the seeding process by generating a random initial position and diameter for each injected particle. The particles are treated sequentially and their impingement position is obtained from their trajectory, which is extracted as a streamline of the deterministic quasi-steady droplet velocity field computed by an Eulerian droplet impingement model. The thermodynamic state of the deposited water is then assessed and an advancing front algorithm is used to generate the corresponding elements of ice, which allows capturing the unsteady behavior of the ice growth. The mass of water to be frozen is given by the freezing fraction, computed by the deterministic quasi-steady approach, the remaining mass flowing downstream until the particle is completely frozen. Unlike deterministic approaches, the process treats the ice density as a dependent variable. The verification of the model shows its convergence according to the ice element size, which is the main computational parameter. An extended 2D model is presented to cater for 3D effects by introducing the concept of permeability of the ice front. Validation is performed by comparing the obtained ice shapes to the experimental results for four test cases of the literature. The method successfully captures both rime and glaze ice geometries. Finally, the stochasticity observed in the experimental ice shapes and the formation of discrete ice structures are well captured, which are usually missed by the state-of-the-art deterministic icing frameworks.