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Mean flow deformation in a laminar separation bubble: separation and stability characteristics

Published online by Cambridge University Press:  17 August 2010

OLAF MARXEN  and
ULRICH RIST
OLAF MARXEN*
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Paffenwaldring 21, 70550 Stuttgart, Germany Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
ULRICH RIST
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Paffenwaldring 21, 70550 Stuttgart, Germany
*
†Email address for correspondence: olaf.marxen@stanford.edu
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Abstract

The mutual interaction of laminar–turbulent transition and mean flow evolution is studied in a pressure-induced laminar separation bubble on a flat plate. The flat-plate boundary layer is subjected to a sufficiently strong adverse pressure gradient that a separation bubble develops. Upstream of the bubble a small-amplitude disturbance is introduced which causes transition. Downstream of transition, the mean flow strongly changes and, due to viscous–inviscid interaction, the overall pressure distribution is changed as well. As a consequence, the mean flow also changes upstream of the transition location. The difference in the mean flow between the forced and the unforced flows is denoted the mean flow deformation. Two different effects are caused by the mean flow deformation in the upstream, laminar part: a reduction of the size of the separation region and a stabilization of the flow with respect to small, linear perturbations. By carrying out numerical simulations based on the original base flow and the time-averaged deformed base flow, we are able to distinguish between direct and indirect nonlinear effects. Direct effects are caused by the quadratic nonlinearity of the Navier–Stokes equations, are associated with the generation of higher harmonics and are predominantly local. In contrast, the stabilization of the flow is an indirect effect, because it is independent of the Reynolds stress terms in the laminar region and is solely governed by the non-local alteration of the mean flow via the pressure.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 660 , 10 October 2010 , pp. 37 - 54
Copyright
Copyright © Cambridge University Press 2010

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