Compressibility Effects on Boundary-Layer Transition Induced by an Isolated Roughness Element

Abstract

Direct numerical simulation has been used to study the transition to turbulence of a high-speed boundary layer over a flat plate with an isolated roughness element. The roughness element consists of a continuous bump that is approximately half the boundary-layer thickness in height. Simulations at Mach 3 and Mach 6 have been run over a range of Reynolds numbers for two fixed wall temperatures corresponding to either an adiabatic or a cooled wall condition. In each case a lift-up of low momentum fluid away from the wall is observed leading to the formation of a detached shear layer. Acoustic disturbances are imposed to stimulate the instability of this layer and breakdown to turbulence is observed in the simulations at the highest Reynolds number in all cases except for the Mach 6 cold wall condition. The magnitude of the streamwise vorticity behind the roughness element increases with roughness height Reynolds number and is relatively insensitive to Mach number and wall temperature. Strouhal numbers associated with hairpin vortex formation are generally lower than in incompressible flow. The critical roughness height Reynolds number for transition within the computational domain is found to increase as the Mach number increases and is higher for the cooled wall condition. A correlation based on roughness height Reynolds and Mach numbers and wall temperature is found to separate laminar from transitional cases for the range of flow conditions studied.