Spatial direct numerical simulation of high-speed boundary-layer flows Part II: Transition on a cone in Mach 8 flow

Abstract

The laminar breakdown of the boundary-layer flow of an axisymmetric sharp cone in a Mach 8 flow is simulated by a synergistic approach that combines the parabolized stability equation (PSE) method and spatial direct numerical simulation (DNS). The transitional state is triggered by a symmetric pair of oblique second-mode disturbances whose nonlinear interactions generate strong streamwise vorticity, which leads in turn to severe spanwise variations in the flow and eventual laminar breakdown. The PSE method is used to compute the weakly and moderately nonlinear initial stages of the transition process and, thereby, to derive a harmonically rich inflow condition for the DNS. The strongly nonlinear and laminar-breakdown stages of transition are then computed by well-resolved DNS, with a highly accurate algorithm that exploits spectral 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 flow visualization. The numerical test case is an approximate computational analog of one of the few stability experiments performed for hypersonic boundary-layer flows. Comparisons and contrasts are drawn between the experimental and the computational results. “Rope-like” waves similar to those observed in schlieren images of high-speed transitional flows are also observed in the numerical experiment and are shown to be visual manifestations of second-mode instability waves.