Adjoint-based optimization of U-bend channel flow using a multi-fidelity eddy viscosity turbulence model

Abstract

Many fluid flows in engineering are turbulent and require the use of computational fluid dynamics (CFD) for design purposes. Optimization with CFD has largely been limited to low-fidelity simulation methods, such as Reynolds Averaged Navier Stokes (RANS), due to current computational capabilities. However, RANS has been shown to lack sufficient accuracy for certain flows. This thesis presents CFD simulation of a 180 degree U-bend square duct using low-fidelity steady RANS and high-fidelity wall-resolved Large Eddy Simulation (LES) models. The LES solution is shown to match experimental results, whereas the RANS solution is not sufficiently accurate. A process for training a RANS eddy viscosity field using the LES solution is provided. This approach is based on solving an inference problem by comparing the RANS calculations to the LES solution and tuning cell-based turbulent viscosity values. This multi-fidelity framework is intended to highlight that high-fidelity solutions can be used to improve even the simplest RANS turbulence models. The adjoint method is used for efficient gradient-based optimization of the turbulent viscosity on a U-bend channel to minimize the velocity solution error. Other objective functions are explored to check the uniqueness of the optimized turbulent viscosity. Sensitivity of the optimized result to the numerical convection scheme is presented to help provide insight for future optimization of turbulence models. The optimized turbulent viscosity is also used on a modified U-bend channel to demonstrate the applicability of the method on new geometries.