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 d...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.展开更多
The Rotation and Curvature(RC)correction is an important turbulence model modifi-cation approach,and the Spalart-Allmaras model with the RC correction(SA-RC)has been exten-sively studied and used.As a multiplier of th...The Rotation and Curvature(RC)correction is an important turbulence model modifi-cation approach,and the Spalart-Allmaras model with the RC correction(SA-RC)has been exten-sively studied and used.As a multiplier of the modelling equation’s production term,the rotation function f_(r1)should have a cautiously designed value range,but its limit varies in different models and flow solvers.Therefore,the need of restriction is discussed theoretically,and the common range of f_(r1)is explored in Burgers vortexes.Afterwards,the SA-RC model with different limits is tested numerically.Negative f_(r1)always appears in the SA-RC model,and the difference between simula-tion results brought by the limits is not negligible.A lower limit of 0 enhances turbulence produc-tion,and therefore the vortex structures are dissipated faster and shrink in size,while an upper limit plays an opposite role.Considering that the lower limit of 0 usually promotes the simulation accu-racy and fixes the numerical defect,whereas the upper limit worsens the predictive performance in most cases,it is recommended to limit f_(r1)non-negative while utilizing the SA-RC model.In addi-tion,the RC-corrected model has a better prediction of the attached flow near curved walls,while the SA-Helicity model largely improves the simulation accuracy of three-dimensional large-scale vortices.The model combining both corrections has the potential to become more adaptive and more accurate.展开更多
基金supported by the National Numerical Windtunnel Project,China(No.NNW2019ZT1-A03)the National Natural Science Foundation of China(No.11721202)。
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.51976006,51790513)the Aeronautical Science Foundation of China(No.2018ZB51013)+1 种基金the National Science and Technology Major Project,China(2017-II-003-0015)the Open Fund from State Key Laboratory of Aerodynamics,China(No.SKLA2019A0101).
文摘The Rotation and Curvature(RC)correction is an important turbulence model modifi-cation approach,and the Spalart-Allmaras model with the RC correction(SA-RC)has been exten-sively studied and used.As a multiplier of the modelling equation’s production term,the rotation function f_(r1)should have a cautiously designed value range,but its limit varies in different models and flow solvers.Therefore,the need of restriction is discussed theoretically,and the common range of f_(r1)is explored in Burgers vortexes.Afterwards,the SA-RC model with different limits is tested numerically.Negative f_(r1)always appears in the SA-RC model,and the difference between simula-tion results brought by the limits is not negligible.A lower limit of 0 enhances turbulence produc-tion,and therefore the vortex structures are dissipated faster and shrink in size,while an upper limit plays an opposite role.Considering that the lower limit of 0 usually promotes the simulation accu-racy and fixes the numerical defect,whereas the upper limit worsens the predictive performance in most cases,it is recommended to limit f_(r1)non-negative while utilizing the SA-RC model.In addi-tion,the RC-corrected model has a better prediction of the attached flow near curved walls,while the SA-Helicity model largely improves the simulation accuracy of three-dimensional large-scale vortices.The model combining both corrections has the potential to become more adaptive and more accurate.
