Large eddy simulation of supersonic boundary layer transition over a flat-plate based on the spatial mode

The large eddy simulation (LES) of spatially evolving supersonic boundary layer transition over a flat-plate with freestream Mach number 4.5 is performed in the present work. The Favre-filtered Navier-Stokes equations are used to simulate large scales, while a dynamic mixed subgrid-scale (SGS) model is used to simulate subgrid stress. The convective terms are discretized with a fifth-order upwind compact difference scheme, while a sixth-order symmetric compact difference scheme is employed for the diffusive terms. The basic mean flow is obtained from the similarity solution of the compressible laminar boundary layer. In order to ensure the transition from the initial laminar flow to fully developed turbulence, a pair of oblique first-mode perturbation is imposed on the inflow boundary. The whole process of the spatial transition is obtained from the simulation. Through the space-time average, the variations of typical statistical quantities are analyzed. It is found that the distributions of turbulent Mach number, root-mean-square (rms) fluctuation quantities, and Reynolds stresses along the wall-normal direction at different streamwise locations exhibit self-similarity in fully developed turbulent region. Finally, the onset and development of large-scale coherent structures through the transition process are depicted.