Parametric uncertainty quantification of SST turbulence model for a shock train and pseudo-shock phenomenon

Computational fluid dynamics simulations are performed to identify the inadequacy of the Menter shear-stress transport (SST) turbulence model for the prediction of the shock train and pseudo-shock phenomenon in a square duct (M_r = 1.61, Re = 3 × 10⁷ m⁻¹), and the uncertainty of the SST model coefficients is quantified. Due to the underprediction of Reynolds stress and failures in predicting corner flow in a square duct, both two-dimensional and three-dimensional SST simulations tended to predict weaker first shock, more secondary shocks, and larger spacing between shocks. The static pressure of the wall fluctuates in the shock train region and suffers a greater loss after the shocks. Based on the two-dimensional simulations, parametric sensitivity analysis using Sobol indices is performed, and the SST model coefficients are classified into three groups according to their sensitivity and influence regions (before and within the shock train). Bayesian inference is conducted on three-dimensional simulations to quantify the uncertainty and calibrate the coefficients that mainly influence the shock train structure. After calibration using maximum a posteriori estimates, the eddy viscosity is greatly increased, and the prediction of the shock structures and the static pressure of the wall is significantly improved, while the prediction of the friction deteriorates.