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The influence of harmonic wall motion on transitional boundary layers

Published online by Cambridge University Press:  03 November 2014

M. J. Philipp Hack  and
Tamer A. Zaki
M. J. Philipp Hack
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
Tamer A. Zaki*
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Present address: Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA. Email address for correspondence: t.zaki@jhu.edu
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Abstract

The influence of harmonic spanwise wall motion on bypass transition in boundary layers is investigated using direct numerical simulations. It is shown that the appropriate choice of the forcing parameters can achieve a substantial stabilization of the laminar flow regime. However, an increase of the forcing amplitude or period beyond their optimal values diminishes the stabilizing effect, and leads to breakdown upstream of the unforced case. For the optimal wall-oscillation parameters, the reduction in propulsion power substantially outweighs the power requirement of the forcing. The mechanism of transition delay is examined in detail. Analysis of the pre-transitional streaks shows that the wall oscillation substantially reduces their average amplitude, and eliminates the most energetic streaks. As a result, the secondary instabilities that precede breakdown to turbulence are substantially weakened – an effect demonstrated by linear stability analyses of flow fields from direct numerical simulations. The outcome is transition delay owing to a significant reduction in the frequency of occurrence of turbulent spots and a downstream shift in their average inception location. Finally, it is shown that the efficiency of the forcing can be further improved by replacing the sinusoidal time dependence of the wall oscillation with a square wave.

JFM classification

Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 760 , 10 December 2014 , pp. 63 - 94
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© 2014 Cambridge University Press 

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