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

摘要

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