Design and implementation of a data-driven wall function for the velocity in RANS simulations

A wall function approach makes simulations at high Reynolds numbers possible to yield reliable results even in the case of coarser meshes. However, it is difficult for the approach to obtain good results if boundary conditions are not valid for the law of the wall. This is why a data-driven approach is needed. A data-driven wall function can be applied to the boundary layer conditions where the law of the wall is not applicable such as adverse pressure gradient conditions, walls with porous media, etc.

This project aims to create a machine learning (ML) wall function that can be used for linear and non-linear flow conditions from a simple 1D geometry, which does not need any direct numerical simulation (DNS) data. The data is obtained from a 1D channel at Re = 1e7 , and three ML models that have the labels of slopes at wall, slopes at cell faces, and velocity at faces in wall normal direction are trained with the maximum relative error of 16%. The trained ML models are applied to flat plate cases at Re = 1e7 , 3e6 , and 6e6 . With the correction of diffusive fluxes, the skin friction of the scenarios for the ML models is compared to that of the standard wall function at y+ = 0.05, 1, 2, 5, 10, 30, 50, 100. The data-driven wall function yields a smaller confidence interval that corresponds to approximately 65% of the confidence interval for the standard wall function scenario, which means that the skin friction of the data-driven wall function is less mesh-dependent than that of the standard wall function. On the other hand, an airfoil case with a chord length of 1m at Re = 3e6 is also investigated. The skin friction and the pressure coefficient of the ML models compare to those of the standard wall function at y+ = 0.05, 1, 2, 3.5, 5, 10, 50, 100 with the correction of diffusive and convective fluxes. For the skin friction except at y+ = 3.5, the data-driven wall function yields slightly the longer confidence interval that is 108.4% of the confidence interval for the standard wall function scenario. This implies that the data-driven wall function is more mesh-dependent than the standard wall function for the airfoil case.