Journal of Fluid Mechanics



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


Lambros  Kaiktsis a1, George  Em Karniadakis a2 and Steven A.  Orszag a3
a1 Institut für Energietechnik, ETH-Zentrum, CH-8092 Zürich, Switzerland
a2 Center for Fluid Mechanics, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
a3 Fluid Dynamics Research Center, Princeton University, Princeton, NJ 08544-0710, USA

Article author query
kaiktsis l   [Google Scholar] 
em karniadakis g   [Google Scholar] 
orszag sa   [Google Scholar] 
 

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 [less-than-or-eq, slant] Re [less-than-or-eq, slant] 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.

(Published Online April 26 2006)
(Received June 6 1994)
(Revised April 9 1996)



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