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Three-dimensional instability of the flow over a forward-facing step

Published online by Cambridge University Press:  21 February 2012

Daniel Lanzerstorfer
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Resselgasse 3, 1040 Vienna, Austria
Hendrik C. Kuhlmann*
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Resselgasse 3, 1040 Vienna, Austria
*
Email address for correspondence: h.kuhlmann@tuwien.ac.at

Abstract

The global, temporal stability of the two-dimensional, incompressible flow over a forward-facing step in a plane channel is investigated numerically. The geometry is varied systematically covering constriction ratios (step-to-inlet height) from 0.23 to 0.965. A three-dimensional linear stability analysis shows that the stability boundary is a smooth continuous function of the constriction ratio. If the critical Reynolds and wavenumbers are scaled appropriately, they approach a linear asymptotic behaviour for large step heights. The critical mode is found to be stationary and confined to the region of separated flow downstream of the step for all constriction ratios. An energy-transfer analysis reveals that the basic flow becomes unstable due to a combined effect involving lift-up and flow deceleration, leading to a critical mode exhibiting steady streaks. Moreover, the receptivity of the flow to initial as well as to structural perturbations is studied by means of an adjoint analysis.

Type
Papers
Copyright
Copyright © Cambridge University Press 2012

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