Stationary cross-flow breakdown in a high-speed swept-wing boundary layer

Abstract

A new type-II secondary instability mode was recently identified in high-speed cross-flows using stability analysis, but its role in the transition process is not yet clear. Here, the breakdown of stationary cross-flow vortices at high speeds is examined using direct numerical simulation to determine differences from the low-speed case. The transition is achieved by disturbing stationary cross-flow vortices with unsteady blowing/suction in a swept-wing boundary layer with swept angle 45°, free-stream Mach number 6, and unit Reynolds number 8 $\times {10}^6$ . The results reveal that, as in low-speed cases, the type-I secondary instability mode (with frequency $\approx$ 190 kHz) is crucial to the breakdown, but neither the traditional nor the new type-II secondary instability play a role. The vortical structure induced by the type-I secondary instability mode has two counter-rotating tubes stretched along the spanwise direction and a footprint aligned normal to the mean flow direction. The composite vortex structures are similar to rolls/braids in plane free-shear layers arising from Kelvin–Helmholtz instability and they evolve into hairpins in the late stage of the transition. Some preliminary statistics from a three-dimensional turbulent boundary layer are provided as a comparison to the two-dimensional ones. The fluctuating cross-flow velocity does not contribute to the momentum and heat transfer on average, probably due to the very weak mean cross-flow profile. Thus, the obtained three-dimensional turbulent boundary layer is the same as the two-dimensional one but inclined by a swept angle. To the authors’ knowledge, this is the first in-depth analysis of the high-speed cross-flow transition to full turbulence.