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Money versus time: evaluation of flow control in terms of energy consumption and convenience

Published online by Cambridge University Press:  30 April 2012

Bettina Frohnapfel ,
Yosuke Hasegawa  and
Maurizio Quadrio
Bettina Frohnapfel
Affiliation:
Center of Smart Interfaces, TU Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany
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: maurizio.quadrio@polimi.it
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Abstract

Flow control with the goal of reducing the skin-friction drag on the fluid–solid interface is an active fundamental research area, motivated by its potential for significant energy savings and reduced emissions in the transport sector. Customarily, the performance of drag reduction techniques in internal flows is evaluated under two alternative flow conditions, i.e. at constant mass flow rate or constant pressure gradient. Successful control leads to reduction of drag and pumping power within the former approach, whereas the latter leads to an increase of the mass flow rate and pumping power. In practical applications, however, money and time define the flow control challenge: a compromise between the energy expenditure (money) and the corresponding convenience (flow rate) achieved with that amount of energy has to be reached so as to accomplish a goal which in general depends on the specific application. Based on this idea, we derive two dimensionless parameters which quantify the total energy consumption and the required time (convenience) for transporting a given volume of fluid through a given duct. Performances of existing drag-reduction strategies as well as the influence of wall roughness are re-evaluated within the present framework; how to achieve the (application-dependent) optimum balance between energy consumption and convenience is addressed. It is also shown that these considerations can be extended to external flows.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulence control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 406 - 418
Copyright
Copyright © Cambridge University Press 2012

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