SPATIAL DIRECT NUMERICAL-SIMULATION OF HIGH-SPEED BOUNDARY-LAYER FLOWS .2. TRANSITION ON A CONE IN MACH-8 FLOW

The laminar breakdown of the boundary-layer flow of an axisymmetric sh arp cone in a Mach 8 flow is simulated by a synergistic approach that combines the parabolized stability equation (PSE) method and spatial d irect numerical simulation (DNS). The transitional state is triggered by a symmetric pair of oblique second-mode disturbances whose nonlinea r interactions generate strong streamwise vorticity,which leads in tur n to severe spanwise variations in the flow and eventual laminar break down. The PSE method is used to compute the weakly and moderately nonl inear initial stages of the transition process and, thereby, to derive a harmonically rich inflow condition for the DNS. The strongly nonlin ear and laminar-breakdown stages of transition are then computed by we ll-resolved DNS, with a highly accurate algorithm that exploits spectr al collocation and high-order compact-difference methods. Evolution of the flow is presented in terms of modal energies, mean quantities (e. g., skin friction), Reynolds stresses, turbulent kinetic energy, and f low visualization. The numerical test case is an approximate computati onal analog of one of the few stability experiments performed for hype rsonic boundary-layer flows. Comparisons and contrasts are drawn betwe en the experimental and the computational results. ''Rope-like'' waves similar to those observed in schlieren images of high-speed transitio nal flows are also observed in the numerical experiment and are shown to be visual manifestations of second-mode instability waves.