CFD-driven machine learning to ensure LES wall model consistency

Abstract: Large Eddy Simulation (LES) usage remains limited in industrial applications due to the high computational cost. The issue is intensified close to solid walls, where the grid must be fine enough to capture the small energetic eddies. Wall-modeled LES (WMLES) seeks to decrease the number of grid points close to the wall by modeling the effects of these small eddies. Classical wall models are mostly based on equilibrium laws of the wall and, therefore, inaccurate for cases featuring separation, high pressure gradients and other complex physical phenomena usually present in flows of industrial interest. We present a new machine learning (ML) framework to develop algebraic wall-shear stress models focused on using real WMLES results, i.e. Computational Fluid Dynamics (CFD) simulations with the potential candidates for wall-shear stress models implemented. The resulting flow field is then used as feedback to train the model. We use Gene-expression programming (GEP) to develop simple explicit mathematical models that are human-interpretable and straightforward to implement. The approach is tested for turbulent flow over periodic hills, a well-known case presenting separation, curved geometry and varying pressure gradient. The framework was capable of finding simple wall models that reconstructed the flow even with coarse grids close to the wall. Input features were analysed in order to improve the generalizability of the model. The GEP-based wall model was then applied to a periodic hills case which had a different Reynolds number, grid and geometry to the training one. The results obtained were in good agreement with high-fidelity simulations. Keywords: Machine learning, Large Eddy Simulation, Computational Fluid Dynamics, Wall models