Large eddy simulation of flow transition in a compressible flat-plate boundary layer at Mach 4.5

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 nu mber of M proportional to = 4.5 and a Reynolds number of 10,000 based on th e free-stream velocity and inflow displacement thickness. The numerical sim ulation 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 direct ion and streamwise direction, the pseudo-spectral method is used in the spa nwise direction. A compact storage third order Runge-Kutta scheme (Wray, 19 86) is adopted for time-integration. The sub-grid scales are formulated acc ording to the filtered structure function model (Ducros et ai.: 1996). A pa ir of oblique first-mode perturbation is imposed on the inflow boundary. Se veral stages of transition process can be identified, i.e., the linear and weak nonlinear growth of disturbance, the appearance of staggered Lambda-vo rtex pattern, the evolution of Lambda-vortex into hairpin vortex, and the b reak-down of hairpin vortical structures. The organized motions during the transition are discussed in detail. The vortical and the shear layer struct ures are compared with the results obtained by Adams and Kleiser (1996) in their direct numerical simulation based on a temporal approach. The evoluti on of the averaged quantities, such as the boundary layer thickness are stu died. The skin friction coefficient and the turbulent mean velocity profile obtained from the simulation agree well with the Aat-plate theory of Van D riest (1956).