A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is...A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw's assumption that the constant a1= 0.31 is recalibrated to a function based on a set of direct numerical simulation(DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.展开更多
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
We introduce a framework for statistical inference of the closure coefficients using machine learning methods.The objective of this framework is to quantify the epistemic uncertainty associated with the closure model ...We introduce a framework for statistical inference of the closure coefficients using machine learning methods.The objective of this framework is to quantify the epistemic uncertainty associated with the closure model by using experimental data via Bayesian statistics.The framework is tailored towards cases for which a limited amount of experimental data is available.It consists of two components.First,by treating all latent variables(non-observed variables)in the model as stochastic variables,all sources of uncertainty of the probabilistic closure model are quantified by a fully Bayesian approach.The probabilistic model is defined to consist of the closure coefficients as parameters and other parameters incorporating noise.Then,the uncertainty associated with the closure coefficients is extracted from the overall uncertainty by considering the noise being zero.The overall uncertainty is rigorously evaluated by using Markov-Chain Monte Carlo sampling assisted by surrogate models.We apply the framework to the Spalart-Allmars one-equation turbulence model.Two test cases are considered,including an industrially relevant full aircraft model at transonic flow conditions,the Airbus XRF1.Eventually,we demonstrate that epistemic uncertainties in the closure coefficients result into uncertainties in flow quantities of interest which are prominent around,and downstream,of the shock occurring over the XRF1 wing.This data-driven approach could help to enhance the predictive capabilities of CFD in terms of reliable turbulence modeling at extremes of the flight envelope if measured data is available,which is important in the context of robust design and towards virtual aircraft certification.The plentiful amount of information about the uncertainties could also assist when it comes to estimating the influence of the measured data on the inferred model coefficients.Finally,the developed framework is flexible and can be applied to different test cases and to various turbulence models.展开更多
The scale adaptive simulation(SAS) turbulence model is evaluated on a turbulent flow past a square cylinder using the open-source CFD package OpenF OAM 2.3.0. Two and three-dimensional simulations are performed to d...The scale adaptive simulation(SAS) turbulence model is evaluated on a turbulent flow past a square cylinder using the open-source CFD package OpenF OAM 2.3.0. Two and three-dimensional simulations are performed to determine global quantities like drag and lift coefficients and Strouhal number in addition to mean and fluctuating velocity profiles in the recirculation and wake regions. SAS model is evaluated against the Shear Stress Transport k-ω(SST) model and also compared with previously reported results based on DES, LES and DNS turbulence approaches. Results show that global quantities along with mean velocity profiles are well-captured by 2-D SAS model. The 3-D SAS model also succeeded in providing comparable results with recently published DES study on Reynolds shear stress and velocity fluctuation components using about 12 times lower computational cost. It is shown that large values of the SAS model constant result in too dissipative behavior, so that proper calibration of the SAS model constant for different turbulent flows is vital.展开更多
基金supported by the National Basic Research Program of China(Grant No.2014CB744804)
文摘A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw's assumption that the constant a1= 0.31 is recalibrated to a function based on a set of direct numerical simulation(DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.
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.
文摘We introduce a framework for statistical inference of the closure coefficients using machine learning methods.The objective of this framework is to quantify the epistemic uncertainty associated with the closure model by using experimental data via Bayesian statistics.The framework is tailored towards cases for which a limited amount of experimental data is available.It consists of two components.First,by treating all latent variables(non-observed variables)in the model as stochastic variables,all sources of uncertainty of the probabilistic closure model are quantified by a fully Bayesian approach.The probabilistic model is defined to consist of the closure coefficients as parameters and other parameters incorporating noise.Then,the uncertainty associated with the closure coefficients is extracted from the overall uncertainty by considering the noise being zero.The overall uncertainty is rigorously evaluated by using Markov-Chain Monte Carlo sampling assisted by surrogate models.We apply the framework to the Spalart-Allmars one-equation turbulence model.Two test cases are considered,including an industrially relevant full aircraft model at transonic flow conditions,the Airbus XRF1.Eventually,we demonstrate that epistemic uncertainties in the closure coefficients result into uncertainties in flow quantities of interest which are prominent around,and downstream,of the shock occurring over the XRF1 wing.This data-driven approach could help to enhance the predictive capabilities of CFD in terms of reliable turbulence modeling at extremes of the flight envelope if measured data is available,which is important in the context of robust design and towards virtual aircraft certification.The plentiful amount of information about the uncertainties could also assist when it comes to estimating the influence of the measured data on the inferred model coefficients.Finally,the developed framework is flexible and can be applied to different test cases and to various turbulence models.
基金Research Center of the Shahid Beheshti University (SBU)
文摘The scale adaptive simulation(SAS) turbulence model is evaluated on a turbulent flow past a square cylinder using the open-source CFD package OpenF OAM 2.3.0. Two and three-dimensional simulations are performed to determine global quantities like drag and lift coefficients and Strouhal number in addition to mean and fluctuating velocity profiles in the recirculation and wake regions. SAS model is evaluated against the Shear Stress Transport k-ω(SST) model and also compared with previously reported results based on DES, LES and DNS turbulence approaches. Results show that global quantities along with mean velocity profiles are well-captured by 2-D SAS model. The 3-D SAS model also succeeded in providing comparable results with recently published DES study on Reynolds shear stress and velocity fluctuation components using about 12 times lower computational cost. It is shown that large values of the SAS model constant result in too dissipative behavior, so that proper calibration of the SAS model constant for different turbulent flows is vital.