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A ‘win–win’ mechanism for low-drag transients in controlled two-dimensional channel flow and its implications for sustained drag reduction

Published online by Cambridge University Press:  27 January 2004

THOMAS R. BEWLEY
Affiliation:
Flow Control Lab, Department of MAE, University of California San Diego, La Jolla, CA 92093-0411, USA
OLE MORTEN AAMO
Affiliation:
Flow Control Lab, Department of MAE, University of California San Diego, La Jolla, CA 92093-0411, USA Department of Engineering Cybernetics, Norwegian University of Science and Technology, Norway

Abstract

A simple pressure-based feedback control strategy for wall-transpiration control of incompressible unsteady two-dimensional channel flow was recently investigated by Aamo, Krstic & Bewley (2003). Nonlinear two-dimensional channel flow simulations which implemented this control strategy resulted in flow transients with instantaneous drag far lower than that of the corresponding laminar flow. The present article examines the physical mechanism by which this very low level of instantaneous drag was attained. It then explores the possibility of achieving sustained drag reductions to below the laminar level by initiating such low-drag transients on a periodic basis. All attempts at sustaining the mean flow drag below the laminar level fail, perhaps providing indirect evidence in favour of the conjecture that the laminar state might provide a fundamental ‘performance limitation’ in such flows. Mathematical analysis of two-dimensional and three-dimensional channel-flow systems establishes a direct link between the average drag increase due to flow-field unsteadiness and a weighted space/time average of the Reynolds stress. Phenomenological justification of the conjecture is provided by a Reynolds analogy between convective momentum transport and convective heat transport. Proof of the conjecture remains an open problem.

Type
Papers
Copyright
© 2004 Cambridge University Press

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