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Closed-loop control of a free shear flow: a framework using the parabolized stability equations

Article dans une revue avec comité de lecture
Author
SASAKI, Kenzo
471029 Instituto Tecnológico de Aeronáutica [São José dos Campos] [ITA]
TISSOT, Gilles
75 Institut de Recherche Mathématique de Rennes [IRMAR]
961 Laboratoire d'Acoustique de l'Université du Mans [LAUM]
486012 Fluid Flow Analysis, Description and Control from Image Sequences [FLUMINANCE]
CAVALIERI, André V. G.
471029 Instituto Tecnológico de Aeronáutica [São José dos Campos] [ITA]
560912 Acoustique, Aérodynamique, Turbulence [Institut Pprime] [2AT ]
SILVESTRE, Flávio J.
471029 Instituto Tecnológico de Aeronáutica [São José dos Campos] [ITA]
JORDAN, Peter
300463 École Nationale Supérieure de Mécanique et d’Aérotechnique [Poitiers] [ISAE-ENSMA]
560912 Acoustique, Aérodynamique, Turbulence [Institut Pprime] [2AT ]
131861 University of Groningen [Groningen]
ccBIAU, Damien
134975 Laboratoire de Dynamique des Fluides [DynFluid]
118112 Institut Pprime [UPR 3346] [PPrime [Poitiers]]

URI
http://hdl.handle.net/10985/17783
DOI
10.1007/s00162-018-0477-x
Date
2018
Journal
Theoretical and Computational Fluid Dynamics

Abstract

In this study the parabolized stability equations (PSE) are used to build reduced-order-models (ROMs) given in terms of frequency and time-domain transfer functions (TFs) for application in closed-loop control. The control law is defined in two steps; first it is necessary to estimate the open-loop behaviour of the system from measurements, and subsequently the response of the flow to an actuation signal is determined. The theoretically derived PSE TFs are used to account for both of these effects. Besides its capability to derive simplified models of the flow dynamics, we explore the use of the TFs to provide an a priori determination of adequate positions for efficiently forcing along the direction transverse to the mean flow. The PSE TFs are also used to account for the relative position between sensors and actuators which defines two schemes, feedback and feedforward, the former presenting a lower effectiveness. Differences are understood in terms of the evaluation of the causality of the resulting gain, which is made without the need to perform computationally demanding simulations for each configuration. The ROMs are applied to a direct numerical simulation of a convectively unstable 2D mixing layer. The derived feedforward control law is shown to lead to a reduction in the mean square values of the objective fluctuation of more than one order of magnitude, at the output position, in the nonlinear simulation, which is accompanied by a significant delay in the vortex pairing and roll-up. A study of the robustness of the control law demonstrates that it is fairly insensitive to the amplitude of inflow perturbations and model uncertainties given in terms of Reynolds number variations.

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