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Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step

Published online by Cambridge University Press:  26 April 2006

Lambros Kaiktsis ,
George Em Karniadakis  and
Steven A. Orszag
Lambros Kaiktsis
Affiliation:
Institut für Energietechnik, ETH-Zentrum, CH-8092 Zürich, Switzerland
George Em Karniadakis
Affiliation:
Center for Fluid Mechanics, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Steven A. Orszag
Affiliation:
Fluid Dynamics Research Center, Princeton University, Princeton, NJ 08544-0710, USA
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Abstract

A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds number Re = 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability analysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalues of a base flow state. The distinction is made between convectively and absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up to Re = 2500 are time-independent in the absence of any external excitation, whereas the flow is convectively unstable, in a large portion of the flow domain, for Reynolds numbers in the range 700 [les ] Re [les ] 2500. Consequently, upstream generated small disturbances propagate downstream at exponentially amplified amplitude with a space-dependent speed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, selective sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two different types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from the shear layer frequency; and (ii) random noise. It is found that for small-amplitude monochromatic excitation the flow acquires a time-periodic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequency. On the other hand, for the random noise as input, an unsteady behaviour is obtained with a fundamental frequency close to the shear layer frequency.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 321 , 25 August 1996 , pp. 157 - 187
Copyright
© 1996 Cambridge University Press

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