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Optimal rotary control of the cylinder wake using POD reduced order model

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierModélisation, contrôle et calcul [MC2]
dc.contributor.authorBERGMANN, Michel
hal.structure.identifierLaboratoire d'Études Aérodynamiques [LEA]
dc.contributor.authorCORDIER, Laurent
hal.structure.identifierLaboratoire d'Energétique et Mécanique Théorique et Appliquée [LEMTA ]
dc.contributor.authorBRANCHER, Jean-Pierre
dc.date.issued2005
dc.identifier.issn1070-6631
dc.description.abstractEnIn this paper we investigate the optimal control approach for the active control and drag optimization of incompressible viscous flow past circular cylinders. The control function is the time angular velocity of the rotating cylinder. The wake flow is solved in the laminar regime Re=200 with a finite-element method. Due to the CPU and memory costs related to the optimal control theory, a proper orthogonal decomposition (POD) reduced-order model (ROM) is used as the state equation. The key enablers to an accurate and robust POD ROM are the introduction of a time-dependent eddy-viscosity estimated for each POD mode as the solution of an auxiliary optimization problem and the use of a snapshot ensemble for POD based on chirp-forced transients. Since the POD basis represents only velocities, we minimize a drag-related cost functional characteristic of the wake unsteadiness. The optimization problem is solved using Lagrange multipliers to enforce the constraints. 25% of relative drag reduction is found when the Navier-Stokes equations are controlled using a harmonic control function deduced from the optimal solution determined with the POD ROM. Earlier numerical studies concerning mean drag reduction are confirmed: it is shown, in particular, that without a sufficient penalization of the control input, our approach is energetically inefficient. The main result is that cost-reduction factors of 100 and 760 are obtained for the CPU time and the memory, respectively. Finally, limits of the performance of our approach are discussed.
dc.language.isoen
dc.publisherAmerican Institute of Physics
dc.title.enOptimal rotary control of the cylinder wake using POD reduced order model
dc.typeArticle de revue
dc.identifier.doi10.1063/1.2033624
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
dc.subject.halInformatique [cs]/Modélisation et simulation
bordeaux.journalPhysics of Fluids
bordeaux.page097101
bordeaux.volume17
bordeaux.issue09
bordeaux.peerReviewedoui
hal.identifierinria-00338850
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//inria-00338850v1
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