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Disturbance evolution in a Mach 4.8 boundary layer with two-dimensional roughness-induced separation and shock

Published online by Cambridge University Press:  07 April 2010

OLAF MARXEN ,
GIANLUCA IACCARINO  and
ERIC S. G. SHAQFEH
OLAF MARXEN*
Affiliation:
Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, USA
GIANLUCA IACCARINO
Affiliation:
Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, USA
ERIC S. G. SHAQFEH
Affiliation:
Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, USA
*
†Email address for correspondence: olaf.marxen@stanford.edu
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Abstract

A numerical investigation of the disturbance amplification in a Mach 4.8 flat-plate boundary layer with a localized two-dimensional roughness element is presented. The height of the roughness is varied and reaches up to approximately 70% of the boundary-layer thickness. Simulations are based on a time-accurate integration of the compressible Navier–Stokes equations, with a small disturbance of fixed frequency being triggered via blowing and suction upstream of the roughness element. The roughness element considerably alters the instability of the boundary layer, leading to increased amplification or damping of a modal wave depending on the frequency range. The roughness is also the source of an additional perturbation. Even though this additional mode is stable, the interaction with the unstable mode in the form of constructive and destructive interference behind the roughness element leads to a beating and therefore transiently increased disturbance amplitude. Far downstream of the roughness, the amplification rate of a flat-plate boundary layer is recovered. Overall, the two-dimensional roughness element behaves as disturbance amplifier with a limited bandwidth capable of filtering a range of frequencies and strongly amplifying only a selected range.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 435 - 469
Copyright
Copyright © Cambridge University Press 2010

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