Quantification of Spalart-Allmaras Turbulence Modeling Uncertainties for Hypersonic Flows Utilizing Output-Based Grid Adaptation

Abstract

In this thesis, uncertainty in the Spalart-Allmaras (SA) turbulence model with the compressible Reynolds-averaged Navier-Stokes (RANS) equations is quantified for steady non-reacting hypersonic flows using a coarse-grained uncertainty metric. Output-based adaptation is utilized to guarantee negligible numerical error with complex flow features, such as shock wave-boundary-layer interactions (SBLI). The adapted meshes are generated using MIT Solution Adaptive Numerical Simulator (SANS) software, which is able to adapt high order unstructured meshes using a modified Continuous Galerkin (CG) finite element method (FEM) discretization. The meshes are iteratively adapted by minimizing the error estimate of a given output functional, such as integrated drag or heat flux, over a boundary. The goal of the study is to quantify the expected uncertainty bounds when using the SA model with modifications to the key assumptions of a linear eddy viscosity constitutive relation and incompressible flow. The uncertainty comparison is made between specific areas of hypersonic geometries such as the pre-compression flat plate region and the post-compression shocked-wedge region of a compression corner. Ultimately, this study improves the determination of uncertainty bounds in engineering design involving turbulent flow, provides more insight into exemplary meshing practices for high-speed flow involving SBLI, and highlights where additional work is needed for the development of turbulence models in the hypersonic regime.