Stability Analysis of Roughness Array Wake in a High-Speed Boundary Layer

Abstract

Computations are performed to examine the effects of both an isolated and spanwise periodic array of trip elements on a high-speed laminar boundary layer, so as to identify the potential physical mechanisms underlying an earlier transition to turbulence as a result of the trip(s). In the context of a 0.333 scale model of the Hyper-X forebody configuration, the time accurate solution for an array of ramp shaped trips asymptotes to a stationary field at large times, indicating the likely absence of a strong absolute instability in the mildly separated flow due to the trips. A prominent feature of the wake flow behind the trip array corresponds to streamwise streaks that are further amplified in passing through the compression corner. Stability analysis of the streaks using a spatial, 2D eigenvalue approach reveals the potential for a strong convective instability that might explain the earlier onset of turbulence within the array wake. The dominant modes of streak instability are primarily sustained by the spanwise gradients associated with the streaks and lead to integrated logarithmic amplification factors (N factors) approaching 7 over the first ramp of the scaled Hyper-X forebody, and substantially higher over the second ramp. Additional computations are presented to shed further light on the effects of both trip geometry and the presence of a compression corner on the evolution of the streaks.