A Stress-equivalent Spalart-Allmaras Wall Model with Local Boundary Conditions for RANS, DES, and LES

Abstract

While high-fidelity, scale-resolving methods in Computational Fluid Dynamics (CFD) are increasingly applied, the cost of these methods remains a significant barrier to their effective use. In this thesis, a new wall model is developed based upon a modified version of the Spalart-Allmaras (SA) turbulence model that lessens the near-wall grid requirements. This is achieved by, below the log layer, making the eddy viscosity approach a constant, non-zero value, and the velocity, which has a non-zero slip, varying approximately linearly with distance from the wall while maintaining the same total shear stress. The wall model introduces one parameter which controls the near-wall behavior of the solution. Unlike typical wall models, this method avoids the need to query the interior solution by utilizing a boundary condition which only requires solution information present at the boundary, making it well-suited for unstructured grids and mesh adaptation. The new approach is combined with mesh adaptation and applied to ReynoldsAveraged Navier-Stokes (RANS), demonstrating accurate predictions of quantities of interest such as aerodynamic coefficients, surface pressure and temperature, skin friction, and heat transfer compared with standard RANS-SA, while requiring substantially less near-wall grid to resolve the solution. Additionally, the new wall model and modified turbulence model are applied to Detached Eddy Simulation (DES) in a hybrid RANS/LES framework, where it is demonstrated that the wall model allows for reliable solutions on near-wall grids that are significantly coarser in the wall-normal direction than those used typically for DES. Finally, the wall model boundary condition is applied to wall-stress Wall-Modeled Large Eddy Simulation (WMLES) and shown to produce similar results to the traditional equilibrium model, while avoiding the need to query the interior solution.