Numerical Investigations Of The Compressible Turbulent Flow Around A Body Involving Shock Wave And Vortical Separation

The investigation of compressible turbulent flow around a body involving shock wave and vortical separation is of primary interest owing to its importance in a wide range of fundamentals and applications. In this dissertation, detached-and large-eddy simulations are employed to study three typical flows including transonic flow past a circular-arc aerofoil, transonic flow past a sphere and a jet from a blunt body opposing a supersonic flow. The results and conclusions are briefly given as follows:(1) Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach number M∞=0.76 and a Reynolds number Re=1.1×107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviors, turbulent boundary layer characteristics, kinematics of coherent structures, and dynamical processes in flow evolution, have been studied systematically. A feed-back model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock char-acteristics, three typical flow regimes are classified as attached boundary layer, moving shock/turbulent boundary layer interaction, and intermittent boundary layer separation. The turbulent statistical quantities have been analyzed in detail and different behaviors are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock/boundary layer inter-action. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analyzed. The speed of downstream propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the sepa-rated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region.(2) Large-eddy simulation of the compressible flow past a sphere was carried out for a free-stream Mach number M∞=0.8 and a Reynolds number Re=2×105. Based on the characteristics of shear layer, the turbulent wake is divided into four regions, i.e. initial stage, linear zone, recompression region, and wake region. Analysis of turbulence statistics indicates that the pressure-dilatation correlation and dilatational dissipation term are relatively small due to weak compressibility. In the shear layer separated from the sphere, the streamwise normal stress is dominated and is significantly enhanced by the onset of the recompression, which leads to a modification of the turbulence field. Within the recompression region of the shear layer, the joint probability density function (PDF) of the second and the third invariants exhibits a tear-drop shape. The growth of the tear-drop is associated with the development of the shear layer and the dissipation process. The PDF of side-load direction compares well with the uniform law and the PDF of its magnitude obeys Rayleigh's law. The vortex stretching/tilting term plays a dominated role in the vorticity transport equation. The double-layer structures of the separated shear layer are reasonably captured using the instantaneous Lamb vector divergence, which is associated with the momentum transport in the flow field. Furthermore, the proper orthogonal decomposition analysis of the pressure field reveals that the modes exhibit dipole, quadrupole, sextpole and octapole in the near wake, and core-shell double dipole and double quadrupole in the far downstream wake.(3) A supersonic flow past a hemispherical nose with an opposing jet placed on its axis has been investigated using large eddy simulation. It is found that the flow behaviors depend mainly on the jet total pressure ratio and can be classified into two typical states, i.e. the unstable and stable states. Analysis of turbulence statistics indicates that the evolution of the peak shear stress along the coni-cal shear layer exhibits two peaks, which are associated with the jet/oncoming flow interaction and the recompression process. The streamwise normal stress is dominated in the mixing process. The coherent structures in the shear layer are analyzed using generalized Lamb vector and the entropy change caused by shock wave is reasonably captured. The proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are antisymmetric for the unstable state and axisymmetric for the stable state. Side-loads have been analyzed from a statistical point of view. The PDF of side-load direction com-pares well with the uniform law and the PDF of magnitude obeys Rayleigh's law. Based on different flow characteristics of the two states, the corresponding feed-back models are proposed and can be used to reasonably predict the dominated frequencies. The results obtained in this study provide a physical insight into the understanding of the mechanisms underlying in this complex flow and will be of help in engineering application such as thermal protection, drag reduction and flow control.