Analysis And Modelling Of Velocity Gradient Tensors In Compressible Turbulence

The velocity gradient tensor(VGT)provides a rich characterization of small-scale turbulence.In this dissertation,the evolution of the flow topology based on the VGT,the subgrid effects on the filtered VGT and the non-normality of the VGT are investigated by means of the direct numerical simulations.The results and conclusions are briefly given as follows:(1)The topological evolution near the turbulent/non-turbulent interface(TNTI)in turbulent mixing layer is studied by means of statistical analysis of the invariants of velocity gradient tensor(VGT)based on direct numerical simulation data.The dynamics of topological evolution is investigated in terms of the source terms of the evolution equations for the invariants,including the pressure effect term,viscous effect term and interaction term among the invariants.It is found that the local topology of fluid particles at the TNTI evolves from non-focal region to focal region in the plane of the second(Q)and the third(R)invariants of the VGT.The topological evolution is mainly associated with the pressure effect term in the TNTI region.According to the analysis of the evolution of enstrophy and dissipation,the enstrophy increase and the dissipation decrease are revealed in the TNTI region,which are caused by viscous vorticity diffusion near the TNTI.A weak correlation between the strain rate and the rotation rate is found in the TNTI region which is related to the reduction of enstrophy production.The alignments between vorticity and strain near the TNTI are investigated and a strong alignment of the vorticity with the extensive eigenvector direction is identified in the TNTI region.(2)The subgrid effects on the dynamics of the filtered VGT in compressible turbulence are studied by means of statistical analysis of the invariants of filtered VGT in compressible mixing layers.The evolution of the filtered VGT is determined by the interaction among the invariants,the pressure effects,the viscous effects and the subgrid effects.Based on the probability fluxes in the Q-R plane,it is found that the flux for the subgrid effect term changes most with the dilatation comparing to the other terms.Further,a Schur decomposition of the filtered VGT into its normal part and non-normal part,which represent the local effect and the non-local effect of the flow dynamics respectively,is used to deal with their effects of the velocity gradient.It is revealed that the compressibility is mainly related to the normal effect while the behaviour of the subgrid scale(SGS)energy dissipation is mainly associated with the non-normal effect.A backscattering region of the SGS energy dissipation in the Q-R plane is identified in the locally expanded regions which is determined by the non-normal effect.Further,a SGS model with the non-local effect is proposed to give a better prediction of the SGS energy dissipation.(3)The non-normality of the VGT in compressible turbulent boundary layer is studied by means of the Schur decomposition.The non-normal effect on the vortex stretching is investigated.It is revealed that the non-normal effect on the vortex stretching is extremely strong in the near-wall region.The pressure Hessian also significantly affects the vortex stretching process through different effects.The isotropic part of the pressure Hessian is associated with the normal effect and the deviatoric part of the pressure Hessian with the non-normal efect.Further,the non-normal effects on the strain rate tensor is analysed.The non-normality decreases the value of the intermediate eigenvalue of the strain rate tensor in the near-wall region.Moreover,in the non-normal effect dominated region,there exists a reinforced preference for the vorticity vector to align with the intermediate strain rate eigenvector and to be perpendicular to the extensive strain rate eigenvector and compressive strain rate eigenvector in the near-wall region.Finally,the SGS model with the non-local effect is proposed to give a better prediction of the SGS energy dissipation in the near-wall region of compressible turbulent boundary layer.