| Compressible turbulence is a major research topic in fluid dynamics. With the rapid developments of computational method and computer science, numerical simulation has become an important tool in studying compressible turbulent flows. In this thesis, the three-dimensional compressible Navier-Stokes equations are solved by finite different methods. Direct numerical simulation (DNS) and large-eddy simulation (LES) are employed to investigate several typical compressible shear turbulent flows, including a novel large-eddy simulation approach of compressible turbulent flow, compressible turbulent flow on a wavy wall, and compressible mixing layer. The results and conclusions are given as follows.(1) A new large-eddy simulation approach of compressible turbulent flow without density weighting is proposed. The work removes an inconsistent treatment including both the resolved and Favre-averaged variables. The subgrid-scale (SGS) terms in the resolved equations of mass, momentum and energy conservations are modeled reasonably and the model coefficients in the SGS terms are computed dynamically. The present LES approach is verified to be reliable and effective by comparing with direct simulation results of compressible turbulent channel flow.(2) A fully developed compressible turbulent flow in a channel with a lower wavy wall and an upper flat wall is numerically studied. Compressible turbulence characteristics for various amplitudes of the wavy wall and the dynamic behavior of the near-wall turbulence are investigated. We mainly attempt to deal with the curvature and compressible effects on the turbulent flow over the wavy wall. Results exhibit that the compressible effect of the flow is strengthened with increasing wave amplitude. Near the wavy wall, the turbulent kinetic energy budgets in the presence of wall curvature are significantly different from those in a plate channel. In addition, the near-wall turbulent structures are also changed by the curvature effect. The effects of stretching, dilatation and baroclinic play different roles in the vorticity dynamics with the distance away from the wall.(3) Two-dimensional compressible and three-dimensional binary-species mixing layers are studied. The influence of the convective Mach number and density stratification on the flow is discussed. Meanwhile, the behavior of the transition and evolution of the coherent structures is also analyzed. Results show that as the convective Mach number increases, the growth rate of the disturbances in the mixing layer decreases, the compressible effect becomes strengthened, and complex structures of vortex-shock interaction occur. In addition, the density stratification also plays an important role in the evolution of the mixing layer. The increasing density ratio suppresses the growth of the disturbances. In the early stage of the evolution in the binary-species mixing layer, the compressible effect, especially the baroclinic effect, dominates the dynamics of the vortex; in the later stage, the stretching effect plays as a dominate role. |
