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Published June 2013 | public
Conference Paper

A systems approach to modeling opposition control in turbulent pipe flow


Despite being one of the earliest - and most studied - active control techniques proposed for wall-bounded turbulent flows, the opposition control method of Choi et al., [J.Fluid Mech., Vol. 262, 1994, pp. 75-110] remains to be fully understood. In this paper, we develop a simple model for opposition control by extending the forcing-response analysis presented in McKeon and Sharma [J. Fluid Mech., Vol. 658, 2010, pp. 336-382]. Based on a gain analysis of the Navier-Stokes equations, the velocity field in turbulent pipe flow is decomposed into a series of highly-amplified response modes (i.e., propagating helical waves). Opposition control, introduced via the boundary condition on wall-normal velocity, alters the amplification characteristics and structure of these response modes, whereby a reduction in gain (mode suppression) leads to a reduction in drag. With simple assumptions, and minimal computation, our model reproduces the leading-order integrated effects of opposition control predicted by DNS. By breaking down opposition control into modal subsystems, our analysis provides new physical insight into the deterioration of control performance with increasing sensor elevation and Reynolds number. We show that opposition control is only effective for specific wavenumber-frequency combinations; others require the introduction of a phase lag between sensed and actuated velocity. Moving forward, this mode-by-mode approach can enable the design and evaluation of targeted control techniques, as well as the definition of a theoretical limit for controller performance.

Additional Information

© 2013 AIAA. Financial support from the AFOSR under award FA9550-12-1-0469 (program manager Doug Smith) is gratefully acknowledged (ML, BJM).

Additional details

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