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Global stability of multiple solutions in plane sudden-expansion flow

Published online by Cambridge University Press:  16 May 2012

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

The two-dimensional, incompressible flow in a plane sudden expansion is investigated numerically for a systematic variation of the geometry, covering expansion ratios (steps-to-outlet heights) from to . By means of a three-dimensional linear stability analysis global temporal modes are scrutinized. In a symmetric expansion the primary bifurcation is stationary and two-dimensional, breaking the mirror symmetry with respect to the mid-plane. The secondary asymmetric flow experiences a secondary instability to different three-dimensional modes, depending on the expansion ratio. For a moderately asymmetric expansion only one of the two secondary flows (the connected branch) is realized at low Reynolds numbers. Since the perturbed secondary flow does not deviate much from the symmetric secondary flow, both secondary stability boundaries are very close to each other. For very small and very large expansion ratios an asymptotic behaviour is found for suitably scaled critical Reynolds numbers and wavenumbers. Representative instabilities are analysed in detail using an a posteriori energy transfer analysis to reveal the physical nature of the instabilities. Depending on the geometry, pure centrifugal and elliptical amplification processes are identified. We also find that the basic flow can become unstable due to the effects of flow deceleration, streamline convergence and high shear stresses, respectively.

JFM classification

Instability: Instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 702 , 10 July 2012 , pp. 378 - 402
Copyright
Copyright © Cambridge University Press 2012

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