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Stability of flow in a channel with longitudinal grooves

Published online by Cambridge University Press:  25 September 2014

H. V. Moradi  and
J. M. Floryan
H. V. Moradi*
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada
J. M. Floryan
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada
*
†Email address for correspondence: hvafadar@uwo.ca
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Abstract

The travelling wave instability in a channel with small-amplitude longitudinal grooves of arbitrary shape has been studied. The disturbance velocity field is always three-dimensional with disturbances which connect to the two-dimensional waves in the limit of zero groove amplitude playing the critical role. The presence of grooves destabilizes the flow if the groove wavenumber $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\beta $ is larger than $\beta _{tran}\approx 4.22$ , but stabilizes the flow for smaller $\beta $ . It has been found that $\beta _{tran}$ does not depend on the groove amplitude. The dependence of the critical Reynolds number on the groove amplitude and wavenumber has been determined. Special attention has been paid to the drag-reducing long-wavelength grooves, including the optimal grooves. It has been demonstrated that such grooves slightly increase the critical Reynolds number, i.e. such grooves do not cause an early breakdown into turbulence.

JFM classification

Flow Control: Drag reduction Flow Control: Flow Control Flow Control: Instability control

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 757 , 25 October 2014 , pp. 613 - 648
Copyright
© 2014 Cambridge University Press 

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