Numerical Investigations of Receptivity, Stability and Transition for High-Speed Boundary Layers

Abstract

Numerical tools for receptivity and stability investigations in high-speed boundary layers were developed: A local Linear Stability Theory (LST) solver applicable for axisymmetric geometries as well as linear and nonlinear disturbance flow formulation solvers suitable for complex geometries. Explicit, implicit and time-spectral time-integration schemes were considered. Although explicit methods are comparatively simpler to implement for disturbance flow formulation solvers, the allowable time-step for stability reasons can be much smaller than that required by accuracy considerations. This is especially the case for receptivity problems involving sharp nose geometries, such as cones or wedges, because the resolution requirements in the nose region can lead to severe restrictions of the time-step for explicit schemes. The new solvers were verified and validated for a variety of flow conditions, geometries, and instabilities. Three investigations are presented. First, the effects of (small) leading edge bluntness on the linear stability of flat-plate boundary layers was investigated. For the conditions investigated, it was found that very small nose radii had already a significant effect on the stability characteristics. Second, the receptivity of a Mach 10 boundary layer on a 7 degree half-angle cone to freestream acoustic disturbances was considered. A detailed analysis as well as comparisons with LST are provided. For the case considered, slow acoustic waves converted rather naturally into the unstable mode S, while fast acoustic waves followed the trend of mode F until a specific downstream location where a switch occurred. Finally, linear and nonlinear cross-flow instability computations are presented for an infinite span swept wing with biconvex airfoil at Mach 2. The stability characteristics as well as flow structures associated with the linear, secondary instability and nonlinear regimes are presented and discussed.