DNS for K- and H-Type flow transition over a flat plate

Abstract

In this paper, a direct numerical simulation (DNS) of flow transition over a flat plate at a free stream Mach number of 5 . 0 = ∞ M and a Reynolds number of 1000 based on the free stream velocity and inflow displacement thickness has been carried out. The time-dependent Navier-Stockes equations are solved directly by Runge-Kutta time advancement. A fourth order central compact scheme (Lele 1992) that facil itates high resolution of the flow field is used for spatial discretization together with a six th order implicit compact filter. To avoid possible non-physical wave reflection from the boun daries, the non-reflecting boundary conditions (Jiang et al . 1999b) are specified at the far field and the out flow boundaries. The inflow is specified by laminar flow profile with im posed eigenmodes of two-dimensional and three-dimensional Tollmien-Schlichting (T-S) waves and random noise. The parallel computation is accomplished through the Message Passing Interface (MPI) together with a domain decomposition approach. Computation is carried out currently in two different grid levels: 256x32x64 and 1536x128x64 in the streamwise ( x), spanwise ( y), and wall normal ( z) directions. In this paper for each grid level, two DNS cases are presented, which are distinguished by the inflow disturbance leading to the K-type (fundamental) or H-type (sub- harmonic) transition. The DNS results show the mean flow properties, such as the skin friction coefficients and the mean velocity profile . In addition, the velocity statistics, Reynolds shear stress and spectrum analysis of the turbulence region are also shown in this paper and are in good agreement with other reported work. Some of the structures appeared in the transition process are also studied.