Uncertainty Quantification of Spalart-Allmaras Turbulence Model Coefficients for Compressor Stall

Turbulence models in Reynolds-Averaged Navier-Stokes simulations have a crucial effect on the compressor stall margin. In this paper, a parametric uncertainty analysis of the Spalart-Allmaras (SA) turbulence model on compressor flows is performed by a metamodel-based Monte Carlo method. The 2D NACA airfoils series representing the compressor hub and tip sections are investigated first, followed by a detailed analysis of a single-passage model of the NASA Rotor 67 compressor. The SA model coefficients are represented by uniform distributions within intervals, and the quantities of interest include the compressor total pressure ratio and isentropic efficiency, radial and circumferential profiles of velocity components, tip leakage vortex trajectory, and turbulent viscosity. An artificial neural network from machine learning is applied as the metamodel, which is tuned, trained, and tested by databases from the flow solver to achieve high accuracy. The uncertainty of quantities of interest is determined by the range of the metamodel and the database samples from the flow solver. The sensitivity of model coefficients is quantified by calculating the gradient of quantities of interest from the metamodel. Results show that the level of uncertainty is stronger at high-incidence conditions than that at low-incidence conditions, indicating the deficiency of the SA turbulence model for separated flows. Crucial model coefficients on the quantities of interest are identified by a sensitivity analysis. However, the re-calibration of these coefficients is contradictory for different quantities of interest and flow regimes. This indicates the need for a modified Spalart-Allmaras turbulence model form to improve the accuracy for predicting compressor flows.