Bayesian uncertainty quantification analysis of the SST model for transonic flow around airfoils simulation

Abstract

Transonic flow simulation is a common but complex task in engineering, and poses a great challenge to computational fluid dynamics using the Reynolds-averaged Navier–Stokes approach. One of the important factors influencing the complexity of this task is the uncertainty introduced by turbulence models. In this paper, to improve the performance of the shear stress transport model, a Bayesian uncertainty quantification analysis of turbulence model parameters is carried out on transonic flow around the RAE2822 airfoil and the ONERA M6 wing. First, the Sobol indices are obtained for sensitivity analysis, the results of which show that the pressure coefficients are mainly sensitive to four parameters a1, κ, β⁎, and β1. A posterior uncertainty analysis is then performed based on the pressure coefficients of two-dimensional sections. The maximum a posteriori estimates from the two examples indicate opposite trends for the predicted shock wave positions. In the predictions for RAE2822, the shock wave position is advanced, while in those for ONERA M6, it is delayed. The estimates from RAE2822 enable a better prediction capability at a small angle of attack, while those from ONERA M6 enables an ability to simulate flow with separation at a large angle of attack, mainly because of the increase in a1. In practical engineering applications, the choice between the two sets of calibrated parameters to achieve the best simulation results may be facilitated by reference to experimental data.