Study Of ?-Re_? Transition Model And ? Transition Model Based On Nonlinear Eddy Viscosity Hypothesis

The prediction of flow transition is an important issue in the study of turbulence.The problem for prediction of viscous drag of the projectiles such as rockets and missiles and for many other technical applications stimulate broad numerical and experimental studies of transition prediction.Therefore,in order to better calculate laminar-turbulent transition,the article referenced the SST k-?turbulence model considering nonlinear eddy viscosity hypothesis through User-Defined Function method,and introduced the model into?-Re_?and?transition models to study the streamline curvature effect,the Reynolds stress anisotropy and rotation effect caused by the nonlinear eddy viscosity effect.Considering the transition prediction used the local variables to judge transition starting position,choosing the turbulence model that local simulation results was better can improve the prediction precision of transition position.Meanwhile,part of?-Re_?transition model coefficients associated with empirical correlations were not well suited for the current development of the transition model without the recalibration.And the effects of critical momentum thickness Reynolds numberempirical correlations were analyzed in the article with the transition starting positions,drag and lift coefficients,in order to calibrate the coefficients associated with empirical correlations and improve the prediction accuracy of?-Re_?transition model.Firstly,modifications of the nonlinear eddy viscosity and empirical correlations were studied.The nonlinear eddy viscosity modification was added by adding Reynolds stress nonlinear term to the source term of the different directions of the control equations momentum equations,the transport equations of turbulent kinetic energy k and dissipation rate?.The empirical correlations modification was adopted to replace the original values in existing program to the calibration values and to make thecritical momentum-thickness Reynolds number and its related coefficients join the existing program through the compiler interface of the User-Defined Function.Secondly,?-Re_?transition model based on eddy viscosity hypothesis was developed.Taking S809 airfoils for examples,the influences ofthe Reynolds stress nonlinear term expression and coefficients in the critical momentum thickness Reynolds number empirical correlations to the transition starting positions and aerodynamic characteristics were studied.On the basis of Reynolds number empirical correlations and its related coefficients calibrated with the S809 airfoils experimental results,the coefficients-revised nonlinear eddy viscosity?-Re_?transition model was built.Numerical simulations were conducted for transition on a two-dimensional plate at low speed and for the flows around the S809 airfoil.The numerical calculations indicated that,the coefficients-revised nonlinear eddy viscosity?-Re_?transition model's prediction precision of upper surface and lower surface increased by 5%and 1.5%relative to the nonlinear eddy viscosity?-Re_?transition model,and the simulation precision of drag and lift coefficients also got improved with the nonlinear eddy viscosity?-Re_?transition model with corrected coefficients,especially in large angle of attack.Considering the nonlinear effect,the flow field was more reasonable and the prediction precision of lift coefficient increased by 21.1%relative to the?-Re_?transition model.And finally,a?transition model based on the nonlinear eddy viscosity hypothesis was established.Numerical simulations were conducted for transition on a two-dimensional plate at low speed and for the flow around the S809 airfoil and the three-dimensional rotating sharp cone with the linear eddy viscosity?transition model and the nonlinear eddy viscosity?transition model.The comparison results of experiment and nonlinear eddy viscosity?-Re_?transition model indicated that,nonlinear eddy viscosity?transition can better predict transition position.Taking S809 airfoils for examples,transition prediction precision of upper surface was improved by 30%relative to the linear transition model,but transition prediction precision of upper and lower surface was lower than that with nonlinear eddy viscosity?-Re_?transition model;The three-dimensional rotating sharp cone starting positions of transition predicted were in good agreement with the experimental databecause of considering the flow transition effect,while the nonlinear eddy viscosity?-Re_?transition model can not capture the spinning cone boundary layer transition deflection accurately;The prediction accuracy of nonlinear eddy viscosity?transition model was higher than the linear transition model,and the precision of the lateral force coefficient increased by 6%relative to the linear transition model.