Direct Numerical Simulation of Supersonic Turbulent Boundary Layer Flow

Direct numerical simulations of a spatially evolving supersonic flat-plate turbulent boundary layer flow with free Mach number M_∞=2.25 and Reynolds number Re=365000/in are performed. The transition process from laminar to turbulent flow is obtained by solving the three-dimensional compressible Navier--Stokes equations, using high-order accurate difference schemes. The obtained statistical results agree well with the experimental and theoretical data. From the numerical results it can be seen that the transition process under the considered conditions is the process which skips the Tollmien--Schlichting instability and the second instability through the instability of high gradient shear layer and becomes of laminar flow breakdown. This means that the transition process is a bypass-type transition process. The spanwise asymmetry of the disturbance locally upstream imposed is important to induce the bypass-type transition. Furthermore, with increasing the time disturbance frequency the transition will delay. When the time disturbance frequency is large enough, the transition will disappear.