Direct numerical simulation of hypersonic boundary-layer flow on a flared cone

The forced transition of the boundary layer on an axisymmetric flared cone in Mach 6 flow is simulated by the method of spatial direct numerical simulation (DNS). The full effects of the flared afterbody are incorporated into the governing equations and boundary conditions; these effects include nonzero streamwise surface curvature, adverse streamwise pressure gradient,and decreasing boundary-layer edge Mach number. Transition is precipitated by periodic forcing at the computational inflow boundary with perturbations derived from parabolized stability equation (PSE) methodology and based, in part, on frequency spectra available from physical experiments. Significant qualitative differences are shown to exist between the present results and those obtained previously for a cone without afterbody Bare. In both cases, the primary instability is of second-mode type; however, frequencies are much higher for the Bared cone because of the decrease in boundary-layer thickness in the flared region. Moreover, Goertler modes, which are linearly stable for the straight cone, are unstable in regions of concave body flare. Reynolds stresses, which peak near the critical layer for the straight cone, exhibit peaks close to the wall for the flared cone. The cumulative effect appears to be that transition onset is shifted upstream for the Bared cone. However, the length of the transition zone map possibly be greater because of the seemingly more gradual nature of the transition process on the flared cone.