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
Helicity is an important quantity that represents the topological interpretation of vortices;however,helicity is not a Galilean invariant.In this study,VR helicity density(HVR)is derived via taking the dot product of ...Helicity is an important quantity that represents the topological interpretation of vortices;however,helicity is not a Galilean invariant.In this study,VR helicity density(HVR)is derived via taking the dot product of vorticity with the unit real eigen vector of the velocity gradient tensor when the complex eigenvalues exist.The analytical solution of HVR is derived to resolve it in a local pointwise manner,and the Galilean invariance of HVR is proved.Tip leakage flow structures in a direct numerical simulation of a tip leakage flow model and a delayed detached eddy simulation of a low-speed large-scale axial compressor rotor are extracted using helicity,eigen helicity density and HVR methods.Results show that the utilization of HVR permits the identification and accentuation of concentrated vortices.Vortices identified by HVR appear in more connective states.As in the case of helicity,the sign of HVR distinguishes between primary and secondary vortices,while eigen helicity density fails.The normalized HVR is superior to the normalized helicity density in locating the vortex axis,especially for the induced vortex structures.Hence,HVR is a strong candidate to replace the helicity density,especially when Galilean invariance is required.展开更多
基金supported by the National Natural Science Foundation of China (No. 51676007, No. 51376001, No. 51420105008)supported by the China Scholarship council (CSC)
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.
基金supported by the National Natural Science Foundation of China(Nos.52106039,51976006 and 51790513)the National Science and Technology Major Project,China(No.2017-Ⅱ-003-0015)+3 种基金the Aeronautical Science Foundation of China(No.2018ZB51013)the Open Fund from State Key Laboratory of Aerodynamics,China(No.SKLA2019A0101)the China Postdoctoral Science Foundation(Nos.2020M670097 and 2021T140037)also supported by the High-Performance Computing(HPC)resources at Beihang University,China。
文摘Helicity is an important quantity that represents the topological interpretation of vortices;however,helicity is not a Galilean invariant.In this study,VR helicity density(HVR)is derived via taking the dot product of vorticity with the unit real eigen vector of the velocity gradient tensor when the complex eigenvalues exist.The analytical solution of HVR is derived to resolve it in a local pointwise manner,and the Galilean invariance of HVR is proved.Tip leakage flow structures in a direct numerical simulation of a tip leakage flow model and a delayed detached eddy simulation of a low-speed large-scale axial compressor rotor are extracted using helicity,eigen helicity density and HVR methods.Results show that the utilization of HVR permits the identification and accentuation of concentrated vortices.Vortices identified by HVR appear in more connective states.As in the case of helicity,the sign of HVR distinguishes between primary and secondary vortices,while eigen helicity density fails.The normalized HVR is superior to the normalized helicity density in locating the vortex axis,especially for the induced vortex structures.Hence,HVR is a strong candidate to replace the helicity density,especially when Galilean invariance is required.
