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Global energy fluxes in turbulent channels with flow control

Published online by Cambridge University Press:  22 October 2018

Davide Gatti Open the ORCID record for Davide Gatti [Opens in a new window] ,
Andrea Cimarelli Open the ORCID record for Andrea Cimarelli [Opens in a new window] ,
Yosuke Hasegawa ,
Bettina Frohnapfel  and
Maurizio Quadrio
Davide Gatti*
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstraße 10, 76131 Karlsruhe, Germany
Andrea Cimarelli
Affiliation:
Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche 12, 60131 Ancona, Italy
Yosuke Hasegawa
Affiliation:
Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
Bettina Frohnapfel
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstraße 10, 76131 Karlsruhe, Germany
Maurizio Quadrio
Affiliation:
Department of Aerospace Science and Technologies, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: davide.gatti@kit.edu
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Abstract

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

JFM classification

Flow Control: Drag reduction Flow Control: Flow Control Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 857 , 25 December 2018 , pp. 345 - 373
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Copyright
© 2018 Cambridge University Press 

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Footnotes

‡

Mercator Fellow at Karlsruhe Institute of Technology

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