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Changes in turbulent dissipation in a channel flow with oscillating walls

Published online by Cambridge University Press:  25 April 2012

Pierre Ricco ,
Claudio Ottonelli ,
Yosuke Hasegawa  and
Maurizio Quadrio
Pierre Ricco*
Affiliation:
Department of Mechanical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Claudio Ottonelli
Affiliation:
Dipartimento di Ingegneria Aerospaziale del Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Yosuke Hasegawa
Affiliation:
Center of Smart Interfaces, TU Darmstadt, Petersenstrasse 32, 64287, Darmstadt, Germany Department of Mechanical Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan
Maurizio Quadrio
Affiliation:
Dipartimento di Ingegneria Aerospaziale del Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: p.ricco@sheffield.ac.uk
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Abstract

Harmonic oscillations of the walls of a turbulent plane channel flow are studied by direct numerical simulations to improve our understanding of the physical mechanism for skin-friction drag reduction. The simulations are carried out at constant pressure gradient in order to define an unambiguous inner scaling: in this case, drag reduction manifests itself as an increase of mass flow rate. Energy and enstrophy balances, carried out to emphasize the role of the oscillating spanwise shear layer, show that the viscous dissipation of the mean flow and of the turbulent fluctuations increase with the mass flow rate, and the relative importance of the latter decreases. We then focus on the turbulent enstrophy: through an analysis of the temporal evolution from the beginning of the wall motion, the dominant, oscillation-related term in the turbulent enstrophy is shown to cause the turbulent dissipation to be enhanced in absolute terms, before the slow drift towards the new quasi-equilibrium condition. This mechanism is found to be responsible for the increase in mass flow rate. We finally show that the time-average volume integral of the dominant term is linearly related to the drag reduction.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulence control Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 77 - 104
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

‡

Present address: ONERA, Département d’Aérodynamique Fondamentale et Expérimentale, 8, rue des Vertugadins, 92190 Meudon, France.

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