Uncertainty and sensitivity analysis of SST turbulence model on hypersonic flow heat transfer

Abstract

Due to the lacking of knowledge and incomplete information about the closure coefficients in Menter Shear Stress Transport (SST) turbulence model, numerical predictions of hypersonic flow heat transfer possess some uncertainties. The objective of this work is to investigate the uncertainty and identify the key parameters contributing most to the uncertainty in hypersonic aeroheating predictions. In the current study, the nine closure coefficients in SST turbulence model are treated as uncertainty variables represented with intervals, meanwhile stochastic expansion based on non-intrusive polynomial chaos (NIPC) expansion is utilized to represent and propagate the uncertainties, afterwards the Sobol indices evaluated by the polynomial chaos expansion coefficients are used to rank the relative contribution of each closure coefficient. Totally, 110 CFD evaluations are adopted to quantify the uncertainty and sensitivity in hypersonic flow heat transfer. Specifically, uncertainty and sensitivity analysis are performed for hypersonic flow over the double-ellipsoid model and the X-33 flight vehicle. The numerical results show that heat flux is more sensitive to uncertainty of closure coefficients compared to pressure. For the SST model, the coefficients which contribute most to uncertainty in hypersonic flow heat are σω1, κ and a1. While a1 is one of the dominant source of heat flux and pressure in the shock region near the wall.