Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T03:26:27.387Z Has data issue: false hasContentIssue false
  • English
  • Français

A dynamic observer to capture and control perturbation energy in noise amplifiers

Published online by Cambridge University Press:  13 October 2014

Juan Guzmán Iñigo ,
Denis Sipp  and
Peter J. Schmid
Juan Guzmán Iñigo*
Affiliation:
Département d’Aérodynamique Fondamentale et Expérimentale, ONERA, 8 Rue des Vertugadins, 92190 Meudon, France
Denis Sipp
Affiliation:
Département d’Aérodynamique Fondamentale et Expérimentale, ONERA, 8 Rue des Vertugadins, 92190 Meudon, France
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we introduce techniques to build a reduced-order model of a fluid system that accurately predicts the dynamics of a flow from local wall measurements. This is particularly difficult in the case of noise amplifiers where the upstream noise environment, triggering the flow via a receptivity process, is not known. A system identification approach, rather than a classical Galerkin technique, is used to extract the model from time-synchronous velocity snapshots and wall shear-stress measurements. The technique will be illustrated for the case of a transitional flat-plate boundary layer, where the snapshots of the flow are obtained from direct numerical simulations. Particular attention is directed to limiting the processed data to data that would be readily available in experiments, thus making the technique applicable to an experimental set-up. The proposed approach combines a reduction of the degrees of freedom of the system by a projection of the velocity snapshots onto a proper orthogonal decomposition basis combined with a system identification technique to obtain a state-space model. This model is then used in a feedforward control set-up to significantly reduce the kinetic energy of the perturbation field and thus successfully delay transition.

JFM classification

Boundary Layers: Boundary layer control Flow Control: Control theory Flow Control: Instability control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 728 - 753
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. 1979 Conditional eddies in isotropic turbulence. Phys. Fluids 22, 2065–2070.CrossRefGoogle Scholar
Bagheri, S., Brandt, L. & Henningson, D. S. 2009 Input–output analysis, model reduction and control of the flat-plate boundary layer. J. Fluid Mech. 620 (1), 263–298.CrossRefGoogle Scholar
Barbagallo, A., Sipp, D. & Schmid, P. J. 2009 Closed-loop control of an open cavity flow using reduced-order models. J. Fluid Mech. 641 (1), 1–50.CrossRefGoogle Scholar
Bergmann, M., Bruneau, C.-H. & Iollo, A. 2009 Enablers for robust POD models. J. Comput. Phys. 228 (2), 516–538.CrossRefGoogle Scholar
Bonnet, J.-P., Cole, D. R., Delville, J., Glauser, M. N. & Ukeiley, L. S. 1994 Stochastic estimation and proper orthogonal decomposition: complementary techniques for identifying structure. Exp. Fluids 17, 307–314.CrossRefGoogle Scholar
Burl, J. B. 1999 Linear Optimal Control. Addison-Wesley Longman.Google Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A: Fluid Dyn. 4 (8), 1637–1650.CrossRefGoogle Scholar
Dergham, G., Sipp, D. & Robinet, J. C. 2013 Stochastic dynamics and model reduction of amplifier flows: the backward facing step flow. J. Fluid Mech. 719, 406–430.CrossRefGoogle Scholar
Guezennec, Y. G. 1989 Stochastic estimation of coherent structures in turbulent boundary layers. Phys. Fluids 1, 1054–1060.CrossRefGoogle Scholar
Hervé, A., Sipp, D., Schmid, P. J. & Samuelides, M. 2012 A physics-based approach to flow control using system identification. J. Fluid Mech. 702, 26–58.CrossRefGoogle Scholar
Hudy, L. M., Naguib, A. & Humphreys, W. M. 2007 Stochastic estimation of a separated flow field using wall-pressure array measurements. Phys. Fluids 19, 024103.CrossRefGoogle Scholar
Juillet, F., Schmid, P. J. & Huerre, P. 2013 Control of amplifier flows using subspace identification techniques. J. Fluid Mech. 725, 522–565.CrossRefGoogle Scholar
Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383–417.CrossRefGoogle Scholar
Lewis, J. M., Lakshmivarahan, S. & Dhall, S. 1989 Dynamic Data Assimilation: A Least Squares Approach, vol. 13, Encyclopedia of Mathematics and its Applications. Cambridge University Press.Google Scholar
Ljung, L. 1999 System Identification: Theory for the User. Prentice-Hall PTR.Google Scholar
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation, pp. 166–178. Nauka.Google Scholar
Moore, B. 1981 Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Autom. Control 26 (1), 17–32.CrossRefGoogle Scholar
Qin, S. J. 2006 An overview of subspace identification. Comput. Chem. Engng 30 (10), 1502–1513.CrossRefGoogle Scholar
Rowley, C. W. 2005 Model reduction for fluids, using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos 15 (3), 997–1013.CrossRefGoogle Scholar
Rowley, C. W. & Juttijudata, V. 2005 Model-based control and estimation of cavity flow oscillations. In Proceedings of the 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference (CDC-ECC’05), pp. 512–517. IEEE.Google Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Q. Appl. Maths 45, 561–571.CrossRefGoogle Scholar
Taylor, J. A. & Glauser, M. N. 2004 Towards practical flow sensing and control via POD and LSE based low-dimensional tools. Trans. ASME: J. Fluids Engng 126 (3), 337–345.Google Scholar
Tinney, C. E., Coiffet, F., Delville, J., Hall, A. M., Jordan, P. & Glauser, M. N. 2006 On spectral linear stochastic estimation. Exp. Fluids 41, 763–775.CrossRefGoogle Scholar
Tu, J. H., Griffin, J., Hart, A., Rowley, C. W., Cattafesta, L. N. III & Ukeiley, L. S. 2013 Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of velocity fields. Exp. Fluids 54 (2), 1–20.CrossRefGoogle Scholar
Van Overschee, P. & De Moor, B. 1994 N4SID: subspace algorithms for the identification of combined deterministic–stochastic systems. Automatica 30 (1), 75–93.CrossRefGoogle Scholar
Van Overschee, P. & De Moor, B. 1996 Subspace Identification for Linear Systems. Kluwer.CrossRefGoogle Scholar

Guzmán Iñigo et al. supplementary movie

Video of the streamwise disturbance component obtained from the DNS and the recover from signal s via the model.

Download Guzmán Iñigo et al. supplementary movie(Video)
Video 8.8 MB

Guzmán Iñigo et al. supplementary movie

Simulation of the LQR-control design based on the dynamic observer. The streamwise component of the disturbance velocity is showed together with the temporal evolution of the kinetic energy E(t), the control signal u(t) and the friction-sensor signal s(t).

Download Guzmán Iñigo et al. supplementary movie(Video)
Video 3.2 MB