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Reduced-order modelling of the flow around a high-lift configuration with unsteady Coanda blowing

Published online by Cambridge University Press:  29 June 2016

Richard Semaan ,
Pradeep Kumar ,
Marco Burnazzi ,
Gilles Tissot ,
Laurent Cordier  and
Bernd R. Noack
Richard Semaan*
Affiliation:
Institut für Strömungsmechanik, Technische Universität Braunschweig, Hermann-Blenk-Str. 37, D-38108 Braunschweig, Germany
Pradeep Kumar
Affiliation:
Institut für Strömungsmechanik, Technische Universität Braunschweig, Hermann-Blenk-Str. 37, D-38108 Braunschweig, Germany
Marco Burnazzi
Affiliation:
German Aerospace Center (DLR), Center for Computer Applications in AeroSpace Science and Engineering, Bunsenstrasse 10, D-37073 Göttingen, Germany
Gilles Tissot
Affiliation:
Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse CEDEX 9, France
Laurent Cordier
Affiliation:
Institut PPRIME, CNRS – Université de Poitiers – ISAE-ENSMA, F-86962 Futuroscope Chasseneuil, France
Bernd R. Noack
Affiliation:
Institut für Strömungsmechanik, Technische Universität Braunschweig, Hermann-Blenk-Str. 37, D-38108 Braunschweig, Germany Institut PPRIME, CNRS – Université de Poitiers – ISAE-ENSMA, F-86962 Futuroscope Chasseneuil, France LIMSI-CNRS, UPR 3251, Campus Universitaire d’Orsay, Bât 508, Rue John von Neumann, F-91405 Orsay CEDEX, France
*
†Email address for correspondence: r.semaan@tu-bs.de
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Abstract

We propose a hierarchy of low-dimensional proper orthogonal decomposition (POD) models for the transient and post-transient flow around a high-lift airfoil with unsteady Coanda blowing over the trailing edge. The modal expansion comprises actuation modes as a lifting method for wall actuation following Graham et al. (Intl J. Numer. Meth. Engng, vol. 44 (7), 1999, pp. 945–972) and Kasnakoğlu et al. (Intl J. Control, vol. 81 (9), 2008, pp. 1475–1492). A novel element is separate actuation modes for different frequencies. The structure of the dynamic model rests on a Galerkin projection using the Navier–Stokes equations, simplifying mean-field considerations, and a stochastic term representing the background turbulence. The model parameters are identified with a data assimilation (4D-Var) method. We propose a model hierarchy from a linear oscillator explaining the suppression of vortex shedding by blowing to a fully nonlinear model resolving unactuated and actuated transients with steady and high-frequency modulation of blowing. The models’ accuracy is assessed through the mode amplitudes and an estimator for the lift coefficient. The robustness of the model is physically justified, and then observed for the training and the validation dataset.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Turbulent Flows: Turbulence control

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Papers
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Journal of Fluid Mechanics , Volume 800 , 10 August 2016 , pp. 72 - 110
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© 2016 Cambridge University Press 

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