Numerical Investigations Of Shock-Shock Interaction And Supersonic Turbulent Boundary Layer

Investigation of shock-shock interaction and supersonic turbulent boundary layer is of great importance for the development of high-speed vehicles and turbulence model-ing. In this dissertation, the unsteady shock-shock interaction and statistical properties of supersonic turbulent boundary layers are studied by means of direct numerical sim-ulation. The results and conclusions are briefly given as follows:(1) Characteristics of the unsteady type IV shock interaction of hypersonic blunt body flows are investigated. The intrinsic relations of flow structures to the shearing, compressing and thermal processes are studied and the physical mechanisms of the unsteady flow evolution are revealed. It is found that the instantaneous sur-face heating rate peak is caused by the fluid in the "hot spot" generated by an oscillating and deforming jet bow shock just ahead of the body surface. The features of local shock/boundary layer interaction and vortex/boundary layer in-teraction are clarified. Based on the analysis of flow evolution, it is identified that the upstream-propagating compression waves are associated with the inter-action of the jet bow shock and the shear-layers formed by a supersonic impinging jet, and then the interaction of the free-stream bow shocks and the compression waves results in the entropy waves and vortical waves propagating to the body surface. Further, the feedback mechanism of the inherent unsteadiness of flow field is revealed to be related to the impinging jet. A feedback model is proposed to reliably predict the dominant frequency of flow evolution. Moreover, the flow field will become steady for low Reynolds number flow.(2) Topological evolution of compressible turbulent boundary layers at Mach2is in-vestigated by means of statistical analysis of the invariants of the velocity gradient tensor. The probability density functions of the rate of change of the invariants exhibit the-3power law distribution in the region of large Lagrangian deriva-tive of the invariants in the inner and outer layers.The topological evolution is studied by conditional mean trajectories for the evolution of the invariants. The trajectories illustrate inward spiraling orbits around and converging to the origin of the space of invariants in the outer layer, while they are repelled by the vicinity of the origin and converge towards a limit cycle in the inner layer. The compressibility effect on the mean topological evolution is studied in terms of the’incompressible’, compressed and expanding regions. It is found that the mean evolution of flow topologies is altered by the compressibility. The evolution equations of the invariants are derived and the relevant dynamics of the mean topological evolution are analyzed. The compressibility effect is mainly related to the pressure effect. The mutual-interaction terms among the invariants are the root of the clockwise spiral behavior of the local flow topology in the space of invariants.(3) Turbulent boundary layers at Mach4.9with the ratio of wall temperature to re-covery temperature{Ts,/Tr) from0.5to1.5are investigated. The influence of wall temperature on Morkovin’s scaling, the standard and modified strong Reynolds analogies, turbulent kinetic energy budgets, coherent vortical structure and vor-tex stretching is assessed. The scaling relations proposed for cool and adiabatic cases, such as Morkovin’s scaling and the modified strong Reynolds analogy, are also applicable for the hot case. The approximate relations between the densi-ty fluctuations and temperature fluctuations as well as between the streamwise velocity fluctuations and temperature fluctuations are proposed. With the in-crease of wall temperature, the most probable inclination angle (the angle made in the streamwise and wall-normal plane) of coherent vortical structures increases in the inner layer and has little change in the outer layer. Moreover, in the in-ner layer, the enstrophy production is dominated by the intermediate strain-rate term and mainly comes from unstable node/saddle/saddle (UN/S/S) and stable focus/stretching (SF/S), and the vortex stretching of UN/S/S is stronger than SF/S; in the outer layer, the enstrophy production is dominated by the extensive strain-rate term and mainly comes from SF/S, and the vortex stretching of SF/S is stronger than UN/S/S.