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Opposition control within the resolvent analysis framework

Opposition control within the resolvent analysis framework
Opposition control within the resolvent analysis framework
This paper extends the resolvent analysis of McKeon & Sharma (2010) to consider flow control techniques that employ linear control laws, focusing on opposition control (Choi et al. 1994) 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 DNS and LES, 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.
0022-1120
Luhar, M.
7972fd0e-2eb8-4c6d-aac0-8ef9b0540cff
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
McKeon, B. J.
4f338f42-224d-41f4-b3ac-c4ca1afc582f
Luhar, M.
7972fd0e-2eb8-4c6d-aac0-8ef9b0540cff
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
McKeon, B. J.
4f338f42-224d-41f4-b3ac-c4ca1afc582f

Luhar, M., Sharma, A.S. and McKeon, B. J. (2014) Opposition control within the resolvent analysis framework. Journal of Fluid Mechanics. (doi:10.1017/jfm.2014.209).

Record type: Article

Abstract

This paper extends the resolvent analysis of McKeon & Sharma (2010) to consider flow control techniques that employ linear control laws, focusing on opposition control (Choi et al. 1994) 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 DNS and LES, 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.

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Published date: 12 May 2014
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 364752
URI: https://eprints.soton.ac.uk/id/eprint/364752
ISSN: 0022-1120
PURE UUID: ec62433c-921b-4217-9efa-d1b985f8f912
ORCID for A.S. Sharma: ORCID iD orcid.org/0000-0002-7170-1627

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Date deposited: 12 May 2014 12:56
Last modified: 13 Jun 2018 00:29

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