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Controlling the onset of turbulence by streamwise travelling waves. Part 2. Direct numerical simulation

Published online by Cambridge University Press:  08 September 2010

BINH K. LIEU ,
RASHAD MOARREF  and
MIHAILO R. JOVANOVIĆ
BINH K. LIEU
Affiliation:
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA
RASHAD MOARREF
Affiliation:
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA
MIHAILO R. JOVANOVIĆ*
Affiliation:
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: mihailo@umn.edu
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Abstract

This study builds on and confirms the theoretical findings of Part 1 of this paper (Moarref & Jovanović, J. Fluid Mech., 2010, doi:10.1017/S0022112010003393). We use direct numerical simulation of the Navier–Stokes equations to assess the efficacy of blowing and suction in the form of streamwise travelling waves for controlling the onset of turbulence in a channel flow. We highlight the effects of the modified base flow on the dynamics of velocity fluctuations and net power balance. Our simulations verify the theoretical predictions of Part 1 that the upstream travelling waves promote turbulence even when the uncontrolled flow stays laminar. On the other hand, the downstream travelling waves with parameters selected in Part 1 are capable of reducing the fluctuations' kinetic energy, thereby maintaining the laminar flow. In flows driven by a fixed pressure gradient, a positive net efficiency as large as 25 % relative to the uncontrolled turbulent flow can be achieved with downstream waves. Furthermore, we show that these waves can also relaminarize fully developed turbulent flows at low Reynolds numbers. We conclude that the theory developed in Part 1 for the linearized flow equations with uncertainty has considerable ability to predict full-scale phenomena.

JFM classification

Flow Control: Flow Control Instability: Transition to turbulence Turbulent Flows: Turbulence control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 100 - 119
Copyright
Copyright © Cambridge University Press 2010

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