Numerical Investigation of Boundary-Layer Transition for Cones at Mach 3.5 and 6.0

Abstract

Transition in high-speed boundary layers is investigated using direct numerical simulation (DNS). A compressible Navier-Stokes code that is specifically tailored towards accurate and efficient simulations of boundary layer stability and boundary layer transition was developed and thoroughly validated. Particular emphasis was put into the adoption of a high-order accurate spatial discretization including a boundary closure with the same stencil width as the interior scheme. Oblique breakdown has been shown, using both temporal and spatial DNS, to be a viable route to transition for the boundary layer of the sharp 7° cone at Mach 3.5 investigated by Corke 2002. A 'wedge-shaped' transitional regime was observed to be characteristic for this type of breakdown on the cone geometry. Furthermore, it was shown that the dominance of the longitudinal mode in the nonlinear transition regime of oblique breakdown is due to a continuously nonlinear forced transient growth. That is the primary pair of oblique waves permanently 'seeds' disturbances into the longitudinal mode, where these disturbances exhibit non-modal unstable behavior. In addition to the simulations of controlled transition via oblique breakdown, six simulations have been conducted and analyzed where transition is initiated by multiple primary waves. Despite the broader spectrum of primary waves, typical features of oblique breakdown are still apparent in these simulations and therefore, it may be conjectured, that oblique breakdown initiated by one primary pair of waves is a good model for the nonlinear processes in natural transition. Furthermore, hypersonic boundary layer stability and transition for a flared and a straight cone at Mach 6 was investigated. In particular, a comparative investigation between both geometries regarding the K-type breakdown was performed in order to give some indications towards the open question how strong the nonlinear transition processis altered by the cone flare.