Nonlinear feedback control of the wake past a plate: From a low-order model to a higher-order model

Cortelezzi, Luca; Chen, Y.-C.; Chang, Herng-Hua

doi:10.1063/1.869320

Cited by 37 publications

(29 citation statements)

References 24 publications

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“…However, control laws need not necessarily depend on a single vortex position, but may be based on properties of an ensemble of vortices, of an ensemble of fluid particles, or of the instantaneous velocity field sensed at one or more locations. 23,24,46 For higher-dimensional vortex methods the receding horizon technique in which a quantity is optimized over a finite period of time, might be employed. In addition, optimization strategies for actuator positions may be carried out in the present framework.…”

Section: Discussionmentioning

confidence: 99%

Optimal mixing in recirculation zones

et al. 2004

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Coarse-scale mixing in a recirculation zone is described with a simple vortex model. Time-dependent forcing is employed to change the vortex motion and mixing properties. An optimal mixing problem is defined in which the flux across the recirculation region shall be maximized under the side-constraints of bounded vortex motion and bounded actuation. Concepts of control theory and chaotic advection are used to achieve this goal. In particular, controllability is proven with a transformation into flat coordinates. Thus, a feedforward law for the optimal trajectory and a feedback law for its stabilization are derived. Observability of the vortex motion is indicated by a dynamic observer. Mixing in the optimized flow is studied using Poincaré maps. The low-frequency modulations to vortex motion are shown to substantially increase mixing in the average. Generalizations of the mathematical framework for mixing optimization are suggested for a larger class of models and flows.

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Section: Discussionmentioning

confidence: 99%

Optimal mixing in recirculation zones

et al. 2004

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“…In the following, we simply refer to these vortices as unsteady point vortices. This method was previously used to study the vortex shedding past a finite or semi-infinite plate with prescribed orthogonal translation [14][15][16]-the purpose of the present work is to generalize the method to arbitrary motions of a general body, including rotation, and to formulate the fully coupled problem of the fluid and solid motions.…”

Section: Description Of the Point Vortex Methodsmentioning

confidence: 99%

“…A new vortex is shed when the intensity reaches a maximum, representing a new roll-up in the vortex sheet [16,20,27]. This method has been previously applied to study the shedding of vorticity from a finite or semi-infinite plate exposed to a prescribed uniform flow with no rotation [14,16] and compared to continuous shedding methods [15]. The originality of the present work is to generalize the method to arbitrary body shapes and motions and to couple the vortex model to the solid dynamics.…”

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confidence: 99%

An unsteady point vortex method for coupled fluid–solid problems

Michelin

Smith

2009

Theor. Comput. Fluid Dyn.

107

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A method is proposed for the study of the two-dimensional coupled motion of a general sharp-edged solid body and a surrounding inviscid flow. The formation of vorticity at the body's edges is accounted for by the shedding at each corner of point vortices whose intensity is adjusted at each time step to satisfy the regularity condition on the flow at the generating corner. The irreversible nature of vortex shedding is included in the model by requiring the vortices' intensity to vary monotonically in time. A conservation of linear momentum argument is provided for the equation of motion of these point vortices (Brown-Michael equation). The forces and torques applied on the solid body are computed as explicit functions of the solid body velocity and the vortices' position and intensity, thereby providing an explicit formulation of the vortex-solid coupled problem as a set of non-linear ordinary differential equations. The example of a falling card in a fluid initially at rest is then studied using this method. The stability of broadside-on fall is analysed and the shedding of vorticity from both plate edges is shown to destabilize this position, consistent with experimental studies and numerical simulations of this problem. The reduced-order representation of the fluid motion in terms of point vortices is used to understand the physical origin of this destabilization.

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“…[2,3]), methods of the control theory can be used to achieve various control objectives. The use of vortex methods in control of fluid flows has first been proposed by Cortelezzi et al [4][5][6]. Stabilization of vortex configurations [7], enhancement of mixing, [8,9] and improvement of airfoil lift [10] have been studied using vortex methods.…”

Section: Introductionmentioning

confidence: 99%