Closed-loop control of vortex breakdown: a model study

doi:10.1017/S0022112004009498

Closed-loop control of vortex breakdown: a model study

2004-07-25

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DOI：10.1017/S0022112004009498

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The objective of the study is to develop a closed-loop control scheme that is capable of preserving the columnar swirling flow state in the finite-length pipe model of Wang & Rusak (1996a). The base state consists of a solid body rotation superimposed on axial plug flow, with two dimensionless parameters: the swirl Omega and the pipe aspect ratio L. The linear stability properties of the columnar base state are documented and shown to give rise to unstable global modes above a critical swirl level Omega(1), thereby triggering vortex breakdown. Our study focuses on the derivation of a control method in order to quench the linear development of the Wang & Rusak instability. An optimal control approach is then devised for a reduced-order system which is obtained by a suitable projection on a low-order subspace of the N least-stable eigenmodes. The actuator consists of perturbations of the inlet circulation and its time history is selected so as to minimize a cost-functional incorporating both the state energy and the control energy. A Riccati-based formulation leads to the determination of the optimal gain matrix for the low-order system. When applied to the full linear system, the feedback law for N = 4 succeeds in maintaining the columnar base state for swirl levels as high as 13% above global onset. The control scheme is found to be robust with respect to noise and to uncertainties in parameter settings. It remains effective even under partial-state information conditions.

Keywords:

TRACKING VELOCIMETRY PTV

REDUCED-ORDER CONTROLLER

FEEDBACK-CONTROL

SWIRLING FLOW

STABILITY

TRANSITION

DISTURBANCES

DYNAMICS

Closed-loop control of vortex breakdown: a model study

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