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Flow dynamics and enhanced mixing in a converging–diverging channel

Published online by Cambridge University Press:  18 October 2016

S. W. Gepner  and
J. M. Floryan
S. W. Gepner*
Affiliation:
Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics, Nowowiejska 24, 00-665 Warsaw, Poland
J. M. Floryan
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada
*
†Email address for correspondence: sgepner@meil.pw.edu.pl
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Abstract

An analysis of flows in converging–diverging channels has been carried out with the primary goal of identifying geometries which result in increased mixing. The model geometry consists of a channel whose walls are fitted with spanwise grooves of moderate amplitudes (up to 10 % of the mean channel opening) and of sinusoidal shape. The groove systems on each wall are shifted by half of a wavelength with respect to each other, resulting in the formation of a converging–diverging conduit. The analysis is carried out up to Reynolds numbers resulting in the formation of secondary states. The first part of the analysis is based on a two-dimensional model and demonstrates that increasing the corrugation wavelength results in the appearance of an unsteady separation whose onset correlates with the onset of the travelling wave instability. The second part of the analysis is based on a three-dimensional model and demonstrates that the flow dynamics is dominated by the centrifugal instability over a large range of geometric parameters, resulting in the formation of streamwise vortices. It is shown that the onset of the vortices may lead to the elimination of the unsteady separation. The critical Reynolds number for the vortex onset initially decreases as the corrugation amplitude increases but an excessive increase leads to the stream lift up, reduction of the centrifugal forces and flow stabilization. The flow dynamics under such conditions is again dominated by the travelling wave instability. Conditions leading to the formation of streamwise vortices without interference from the travelling wave instability have been identified. The structure and the mixing properties of the saturated states are discussed.

JFM classification

Flow Control: Flow Control Flow Control: Mixing enhancement
Type
Papers
Information
Journal of Fluid Mechanics , Volume 807 , 25 November 2016 , pp. 167 - 204
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Copyright
© 2016 Cambridge University Press 

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