Uncertainty Quantification and Sensitivity Analysis of SA Turbulence Model Coefficients in Two and Three Dimensions

摘要

The goal of this work is to quantify the uncertainty and sensitivity of the Spalart-Allmaras turbulence model in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of model coefficients for three 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 coefficients is performed for a subsonic flat plate, the RAE 2822 transonic airfoil, and transonic flow over the NASA Common Research Model. The Boeing-developed BCFD code is used as the flow solver. The uncertainty quantification analysis employs stochastic expansions based on non-intrusive polynomial chaos for efficient uncertainty propagation. Integrated force coefficients, loads reports, pressure coefficient distributions, and skin friction coefficient distributions are considered as uncertain output quantities of interest. Turbulence model coefficients are treated as epistemic uncertain variables represented with intervals. Sobol indices are used to rank the relative contributions of each coefficient to the total uncertainty in the output quantities of interest. A new method of characterizing the Spalart-Allmaras coefficient uncertainties is discussed and comparisons are made with the old method. The new method employs relations between coefficients which were fundamental to the original development of the model, and in particular allows only a much narrower range for the variations of the logarithmic law.