Improvement of runback water film calculation and its impact on ice prediction

Over the past few decades, aircraft icing has been the subject of numerous studies. Ice accretion on an aircraft can damage its aerodynamic performance. It can also have a devastating affect on structures such as high voltage pylons. The simulation of ice accretion represents an important technological breakthrough in the understanding of ice behaviour as well as an alternative to expensive experiments. Although numerical models will probably never replace wind tunnel experiments, they continuously progress and benefit from the latest advances in computing techniques. ICECREMO2 is a new generation model and uses an unstructured grid approach. Unstructured meshes offer real advantages in the generation of complex grid structures but also provide support for grid adaptivity. Adaptivity consists in improving the resolution only in some aspects of the solution. It offers the benefits of the high resolution without the computational overhead of classical structured methods. Adaptive methods are usually more difficult to implement and the application to the equation coupling water film and ice growth has never been investigated before this work. The mathematical model used in ICECREMO describes both the water film flow and the ice growth. This allows us to better predict glaze ice accretion when a runback water film is present. The equation describing the thin film water flow is a complex non-linear fourth-order degenerate partial differential equation. To resolve complex features such as a moving front, high resolution numerical methods are necessary. Such a numerical scheme has been developed for this equation in a previous study on structured grid, and has proven to be reliable. In this work Sweby's scheme has been reformulated in a finite volume framework, an error estimator has been de ned for our adaptive mesh refinement method and a grid refinement strategy has been implemented which follows the water film front and keeps it under high resolution. Finally, the impact of the improved resolution of the water film on the glaze ice growth is investigated. Results obtained with first-order and high resolution methods have been compared on different model problems under various conditions. At the end an extension of the refinement strategy is proposed by defining error estimators with respect to the ice layer and by combining it with a multi-step procedure.