Large Eddy Simulation of Flow Transition in a Compressible Flat-Plate Boundary Layer at Mach 4.5

Abstract

Large eddy simulation (LES) has been carried out to investigate the oblique transition process of a flat-plate boundary layer at a free-stream Mach number of M∞ = 4.5 and a Reynolds number of 10,000 based on the free-stream velocity and inflow displacement thickness. The numerical simulation is performed using a spatial approach to solve a full compressible Navier-Stokes system in the curvilinear coordinates. A compact sixth-order central difference scheme (Lele, 1992) is applied to the wall-normal direction and streamwise direction, the pseudo-spectral method is used in the spanwise direction. A compact storage third order Runge-Kutta scheme (Wray, 1986) is adopted for lime-integration. The sub-grid scales are formulated according to the filtered structure function model (Ducros et al., 1996). A pair of oblique first-mode perturbation is imposed on the inflow boundary. Several stages of transition process can be identified, i.e., the linear and weak nonlinear growth of disturbance, the appearance of staggered A-vortex pattern, the evolution of A-vortex into hairpin vortex, and the break-down of hairpin vortical structures. The organized motions during the transition are discussed in detail. The vortical and the shear layer structures are compared with the results obtained by Adams and Kleiser (1996) in their direct numerical simulation based on a temporal approach. The evolution of the averaged quantities, such as the boundary layer thickness are studied. The skin friction coefficient and the turbulent mean velocity profile obtained from the simulation agree well with the flat-plate theory of Van Driest (1956).