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

Chinese Journal of Aeronautics 2022年第4期35卷 185-201页

作者： Jinping LI Shusheng CHEN Fangjie CAI Sheng WANG Chao YAN School of Aeronautic Science and Engineering Beihang UniversityBeijing 100083China School of Aeronautics Northwestern Polytechnical UniversityXi'an 710072China AVIC The First Aircraft Institute Xi'an 710089China China Academy of Launch Vehicle Technology Beijing 100076China

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.

关键词： Bayesian calibration MAP estimation SA turbulence model supersonic jet interaction Uncertainty quantification

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