Uncertainty quantification of compressibility corrections on SA turbulence model for high Mach number flows

Abstract

Uncertainty quantification (UQ) of turbulence models for compressible flows with strong compressibility effects is crucial for accurately predicting the aerothermodynamic performance of hypersonic vehicles. In this paper, the Non-Intrusive Polynomial Chaos (NIPC) method is employed to quantify the uncertainties of the various compressibility correction terms of the Spalart-Allmaras(SA) turbulence model in high Mach number flows. Six correction terms are statistically assessed using Sobol indices, focusing on pressure profiles, heat flux profiles, and the separation region in hypersonic compression corner cases. Building upon the uncertainty quantification and dimensional analysis on the wall law of SA model with the compressibility correction term, a locally constrained correction is proposed by introducing a compression-expansion sensor on SA turbulence model. Re-quantification on constrained correction shows that the sensitivity rules of the six correction terms remain consistent across multiple Quantities of Interest (QoIs) at different corner cases. The proposed correction model significantly reduces the sensitivity coefficient of the correction term and improves the performance of SA model in high Mach number flows with strong compressibility effects. These results reveal the effects and mechanisms of the various correction terms, providing further understanding for future turbulence model development of hypersonic flows.