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Opposition control within the resolvent analysis framework

Published online by Cambridge University Press:  19 May 2014

M. Luhar ,
A. S. Sharma  and
B. J. McKeon
M. Luhar*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
A. S. Sharma
Affiliation:
Engineering and the Environment, University of Southampton, Highfield, Southampton SO17 1BJ, UK
B. J. McKeon
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: mluhar@cantab.net
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Abstract

This paper extends the resolvent analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to consider flow control techniques that employ linear control laws, focusing on opposition control (Choi, Moin & Kim, J. Fluid Mech., vol. 262, 1994, pp. 75–110) as an example. Under this formulation, the velocity field for turbulent pipe flow is decomposed into a series of highly amplified (rank-1) response modes, identified from a gain analysis of the Fourier-transformed Navier–Stokes equations. These rank-1 velocity responses represent propagating structures of given streamwise/spanwise wavelength and temporal frequency, whose wall-normal footprint depends on the phase speed of the mode. Opposition control, introduced via the boundary condition on wall-normal velocity, affects the amplification characteristics (and wall-normal structure) of these response modes; a decrease in gain indicates mode suppression, which leads to a decrease in the drag contribution from that mode. With basic assumptions, this rank-1 model reproduces trends observed in previous direct numerical simulation and large eddy simulation, without requiring high-performance computing facilities. Further, a wavenumber–frequency breakdown of control explains the deterioration of opposition control performance with increasing sensor elevation and Reynolds number. It is shown that slower-moving modes localized near the wall (i.e. attached modes) are suppressed by opposition control. Faster-moving detached modes, which are more energetic at higher Reynolds number and more likely to be detected by sensors far from the wall, are further amplified. These faster-moving modes require a phase lag between sensor and actuator velocity for suppression. Thus, the effectiveness of opposition control is determined by a trade-off between the modes detected by the sensor. However, it may be possible to develop control strategies optimized for individual modes. A brief exploration of such mode-optimized control suggests the potential for significant performance improvement.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulence control Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 597 - 626
Copyright
© 2014 Cambridge University Press 

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