Bayesian uncertainty analysis of SA turbulence model for supersonic jet interaction simulations

作     者：Jinping LI Shusheng CHEN Fangjie CAI Sheng WANG Chao YAN Jinping LI;Shusheng CHEN;Fangjie CAI;Sheng WANG;Chao YAN

作者机构：School of Aeronautic Science and EngineeringBeihang UniversityBeijing 100083China School of AeronauticsNorthwestern Polytechnical UniversityXi'an 710072China AVIC The First Aircraft InstituteXi'an 710089China China Academy of Launch Vehicle TechnologyBeijing 100076China 

出 版 物：《Chinese Journal of Aeronautics》 (中国航空学报（英文版）)

年 卷 期：2022年第35卷第4期

页      面：185-201页

核心收录：

学科分类：080103[工学-流体力学] 08[工学] 080104[工学-工程力学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Numerical Windtunnel Project,China(No.NNW2019ZT1-A03) the National Natural Science Foundation of China(No.11721202) 

主　　题：Bayesian calibration MAP estimation SA turbulence model Supersonic jet interaction Uncertainty quantification 

摘      要：The Reynolds Averaged Navier-Stokes(RANS) models are still the workhorse in current engineering applications due to its high efficiency and robustness. However, the closure coefficients of RANS turbulence models are determined by model builders according to some simple fundamental flows, and the suggested values may not be applicable to complex flows, especially supersonic jet interaction flow. In this work, the Bayesian method is employed to recalibrate the closure coefficients of Spalart-Allmaras(SA) turbulence model to improve its performance in supersonic jet interaction problem and quantify the uncertainty of wall pressure and separation length. The embedded model error approach is applied to the Bayesian uncertainty analysis. Firstly, the total Sobol index is calculated by non-intrusive polynomial chaos method to represent the sensitivity of wall pressure and separation length to model parameters. Then, the pressure data and the separation length are respectively served as calibration data to get the posterior uncertainty of model parameters and Quantities of Interests(Qo Is). The results show that the relative error of the wall pressure predicted by the SA turbulence model can be reduced from 14.99% to 2.95% through effective Bayesian parameter estimation. Besides, the calibration effects of four likelihood functions are systematically evaluated. The posterior uncertainties of wall pressure and separation length estimated by different likelihood functions are significantly discrepant, and the Maximum a Posteriori(MAP) values of parameters inferred by all functions show better performance than the nominal values. Finally, the closure coefficients are also estimated at different jet total pressures. The similar posterior distributions of model parameters are obtained in different cases, and the MAP values of parameters calibrated in one case are also applicable to other cases.