Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

The goal of this work is to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-averaged Navier–Stokes codes due to uncertainty in the values of closure coefficients for transonic wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients is performed for transonic flow over an axisymmetric bump and the RAE 2822 transonic airfoil. Three turbulence models are considered: the Spalart–Allmaras model, Wilcox (2006) k-ω model, and Menter shear-stress transport model. The FUN3D code developed by NASA Langley Research Center is used as the flow solver. The uncertainty quantification analysis employs stochastic expansions based on non-intrusive polynomial chaos for efficient uncertainty propagation. Several integrated and point quantities are considered as uncertain outputs for both computational fluid dynamics problems. Closure coefficients are treated as epistemic uncertain variables represented with intervals. Sobol indices are used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identifies a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic wall-bounded flows.