In this study,Bayesian parameter calibration is applied to Saplart-Allmaras(SA)turbulence model,and the prediction improvement by the calibrated model is demonstrated.The quantity of interest(QOI)is the pitch-wise dis...In this study,Bayesian parameter calibration is applied to Saplart-Allmaras(SA)turbulence model,and the prediction improvement by the calibrated model is demonstrated.The quantity of interest(QOI)is the pitch-wise distribution of Mach number in the comer separation flow region.The 10 model parameters included in the SA model with Rotation-Curvature correction are considered as random variables obeying uniform prior probability distributions.The order of generalized Polynomial Chaos(gPC)used for sensitivity analysis and surrogate model in calibration is incrementally increased during the calibration process.Posterior convergence is obtained at the 3rd order expansion level in this study.At this final level,sensitivity analysis indicates 3 model parameters,cbl,k and cr3 are the most influential random variables,and 3-parameter Bayesian calibration is conducted.The likelihood function in the Bayesian theorem is specified in the form of Gaussian distribution,including experimental uncertainty.The combination of prior and likelihood brings the posterior distribution of model parameters,and Maximum A Posterior(MAP)value is selected as a calibrated parameter set.The flow simulation with calibrated parameters shows a significant increase in the accuracy of the Mach number profile in the comer separation region.The increase in accuracy is attributed to enlarged turbulent viscosity due to the parameter modification of the turbulent viscosity source term.The calibrated parameter is also tested in the off-design flow field,not included in the calibration process.The calibrated CFD again shows improved accuracy for comer separation prediction,and the effectiveness of the parameter set outside of the calibration field is demonstrated.展开更多
文摘In this study,Bayesian parameter calibration is applied to Saplart-Allmaras(SA)turbulence model,and the prediction improvement by the calibrated model is demonstrated.The quantity of interest(QOI)is the pitch-wise distribution of Mach number in the comer separation flow region.The 10 model parameters included in the SA model with Rotation-Curvature correction are considered as random variables obeying uniform prior probability distributions.The order of generalized Polynomial Chaos(gPC)used for sensitivity analysis and surrogate model in calibration is incrementally increased during the calibration process.Posterior convergence is obtained at the 3rd order expansion level in this study.At this final level,sensitivity analysis indicates 3 model parameters,cbl,k and cr3 are the most influential random variables,and 3-parameter Bayesian calibration is conducted.The likelihood function in the Bayesian theorem is specified in the form of Gaussian distribution,including experimental uncertainty.The combination of prior and likelihood brings the posterior distribution of model parameters,and Maximum A Posterior(MAP)value is selected as a calibrated parameter set.The flow simulation with calibrated parameters shows a significant increase in the accuracy of the Mach number profile in the comer separation region.The increase in accuracy is attributed to enlarged turbulent viscosity due to the parameter modification of the turbulent viscosity source term.The calibrated parameter is also tested in the off-design flow field,not included in the calibration process.The calibrated CFD again shows improved accuracy for comer separation prediction,and the effectiveness of the parameter set outside of the calibration field is demonstrated.
