Comparison of turbulent Prandtl number correction models for the Stanton evaluation over rough surfaces

In-flight ice accretion code predictions depend on heat loss over rough surfaces. The equivalent sand grain roughness models the friction coefficient, but an additional model is needed for heat transfer predictions. In this paper, a two parameters model based on a turbulent Prandtl number correction is derived from the sublayer Stanton-based model. For flow over rough surfaces, the new model predictions will be compared to a three parameters model from the literature. First, the models are coupled with the Spalart-Allmaras turbulence model to predict heat transfers over rough surfaces. Thereafter, the two models are implemented in the open-source software, SU2, and then verified and validated for flow over rough flat plates. Lastly, the predictions of the two models are shown to be similar for ice accretion roughness on flat plates, aerofoils and a wing. Model discrepancies are always within the experimental 15% error margin.