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Frequency selection by feedback control in a turbulent shear flow

Published online by Cambridge University Press:  18 May 2016

Vladimir Parezanović ,
Laurent Cordier ,
Andreas Spohn ,
Thomas Duriez ,
Bernd R. Noack ,
Jean-Paul Bonnet ,
Marc Segond ,
Markus Abel  and
Steven L. Brunton
Vladimir Parezanović*
Affiliation:
Institut PPRIME - CNRS, Université de Poitiers, ISAE-ENSMA, 11 Boulevard Marie et Pierre Curie, F-86962 Futuroscope Chasseneuil, France ISAE-SUPAERO, Département d’Aérodynamique, Énergétique et Propulsion, 10 avenue Édouard Belin, F-31055 Toulouse, France
Laurent Cordier
Affiliation:
Institut PPRIME - CNRS, Université de Poitiers, ISAE-ENSMA, 11 Boulevard Marie et Pierre Curie, F-86962 Futuroscope Chasseneuil, France
Andreas Spohn
Affiliation:
Institut PPRIME - CNRS, Université de Poitiers, ISAE-ENSMA, 11 Boulevard Marie et Pierre Curie, F-86962 Futuroscope Chasseneuil, France
Thomas Duriez
Affiliation:
Institut PPRIME - CNRS, Université de Poitiers, ISAE-ENSMA, 11 Boulevard Marie et Pierre Curie, F-86962 Futuroscope Chasseneuil, France Laboratorio de FluidoDinamica - Facultad de Ingeneria CONICET - Universidad de Buenos Aires, Paseo Colon 850, Ciudad Autonoma de Buenos Aires, Argentina
Bernd R. Noack
Affiliation:
Institut PPRIME - CNRS, Université de Poitiers, ISAE-ENSMA, 11 Boulevard Marie et Pierre Curie, F-86962 Futuroscope Chasseneuil, France Institut für Strömungsmechanik Technische Universität Braunschweig, Hermann-Blenk-Str. 37, D-38108 Braunschweig, Germany LIMSI-CNRS, UPR 3251, Campus Universitaire d’Orsay, bât 508, F-91405 Orsay, France
Jean-Paul Bonnet
Affiliation:
Institut PPRIME - CNRS, Université de Poitiers, ISAE-ENSMA, 11 Boulevard Marie et Pierre Curie, F-86962 Futuroscope Chasseneuil, France
Marc Segond
Affiliation:
Phedes Lab, Calle Luis Fernandez Castañon, 4 - 2$^{\circ }$B, E-33013 Oviedo, Spain
Markus Abel
Affiliation:
Ambrosys GmbH, Albert-Einstein-Str. 1-5, D-14469 Potsdam, Germany University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam, Germany
Steven L. Brunton
Affiliation:
University of Washington, Mechanical Engineering Department, Seattle, WA 98195, USA
*
†Email address for correspondence: [email protected]
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Abstract

Many previous studies have shown that the turbulent mixing layer under periodic forcing tends to adopt a lock-on state, where the major portion of the fluctuations in the flow are synchronized at the forcing frequency. The goal of this experimental study is to apply closed-loop control in order to provoke the lock-on state, using information from the flow itself. We aim to determine the range of frequencies for which the closed-loop control can establish the lock-on, and what mechanisms are contributing to the selection of a feedback frequency. In order to expand the solution space for optimal closed-loop control laws, we use the genetic programming control (GPC) framework. The best closed-loop control laws obtained by GPC are analysed along with the associated physical mechanisms in the mixing layer flow. The resulting closed-loop control significantly outperforms open-loop forcing in terms of robustness to changes in the free-stream velocities. In addition, the selection of feedback frequencies is not locked to the most amplified local mode, but rather a range of frequencies around it.

JFM classification

Boundary Layers: Free shear layers Flow Control: Instability control Turbulent Flows: Turbulence control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 797 , 25 June 2016 , pp. 247 - 283
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Copyright
© 2016 Cambridge University Press 

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References

Aström, K. J. & Murray, R. M. 2010 Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press.Google Scholar
Baek, S. J. & Sung, H. J. 2000 Quasi-periodicity in the wake of a rotationally oscillating cylinder. J. Fluid Mech. 408, 275–300.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, 263–298.Google Scholar
Beyer, H.-G. & Sendhoff, B. 2007 Robust optimization – a comprehensive survey. Comput. Meth. Appl. Mech. Engng 196 (33–34), 3190–3218.CrossRefGoogle Scholar
Bradshaw, P. 1971 An Introduction to Turbulence and its Measurement. Pergamon.Google Scholar
Brunton, S. L. & Noack, B. R. 2015 Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67 (5), 050801.Google Scholar
Burl, J. B. 1999 Linear Optimal Control: H 2 and H ∞ Methods. Addison-Wesley Publishing.Google Scholar
Buxton, O. R. H., de Kat, R. & Ganapathisubramani, B. 2013 The convection of large and intermediate scale fluctuations in a turbulent mixing layer. Phys. Fluids 25 (12), 125105.CrossRefGoogle Scholar
Chang, W.-D. 2007 Nonlinear system identification and control using a real-coded genetic algorithm. Appl. Math. Model. 31 (3), 541–550.Google Scholar
Cordier, L., Noack, B. R., Tissot, G., Lehnasch, G., Delville, J., Balajewicz, M., Daviller, G. & Niven, R. K. 2013 Identification strategies for model-based control. Exp. Fluids 54 (8), 1–21.Google Scholar
Delville, J.1995 La décomposition orthogonale aux valeurs propres et l’analyse de l’organisation tridimensionnelle des écoulements turbulents cisaillés libres. PhD thesis, Université de Poitiers.Google Scholar
Duriez, T., Parezanović, V., Laurentie, J.-C., Fourment, C., Delville, J., Bonnet, J.-P., Cordier, L., Noack, B. R., Segond, M., Abel, M. W. et al. 2014 Closed-loop control of experimental shear layers using machine learning (invited). In 7th AIAA Flow Control Conference, Atlanta, Georgia, USA, pp. 1–16. American Institute of Aeronautics and Astronautics (AIAA).Google Scholar
Fiedler, H. E. & Mensing, P. 1985 The plane turbulent shear layer with periodic excitation. J. Fluid Mech. 150 (1), 281–309.Google Scholar
Fleming, P. J. & Purshouse, R. C. 2002 Evolutionary algorithms in control systems engineering: a survey. Control Engng. Pract. 10 (11), 1223–1241.Google Scholar
Gautier, N., Aider, J.-L., Duriez, T., Noack, B. R., Segond, M. & Abel, M. 2015 Closed-loop separation control using machine learning. J. Fluid Mech. 770, 442–457.Google 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.Google Scholar
Ho, C. M. & Huang, L. S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443–473.CrossRefGoogle Scholar
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365–424.Google Scholar
Ho, C. M. & Nosseir, N. S. 1981 Dynamics of an impinging jet. Part 1. The feedback phenomenon. J. Fluid Mech. 105, 119–142.Google Scholar
King, R.(Ed.) 2010 Active Flow Control II, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 108. Springer.Google Scholar
Koza, J. R. 1992 Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press.Google Scholar
Lewis, M. A., Fagg, A. H. & Solidum, A. 1992 Genetic programming approach to the construction of a neural network for control of a walking robot. In IEEE International Conference on Robotics and Automation, vol. 3, pp. 2618–2623. IEEE.Google Scholar
Luke, S., Panait, L., Balan, G., Paus, S., Skolicki, Z., Kicinger, R., Popovici, E., Sullivan, K., Harrison, J., Bassett, J. et al. 1993 A Java-based Evolutionary Computation Research System. https://cs.gmu.edu/∼eclab/projects/ecj/.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.CrossRefGoogle Scholar
Milano, M. & Koumoutsakos, P. 2002 A clustering genetic algorithm for cylinder drag optimization. J. Comput. Phys. 175, 79–107.Google Scholar
Moore, D. W. & Saffman, P. G. 1975 The density of organized vortices in a turbulent mixing layer. J. Fluid. Mech. 69, 465–473.Google Scholar
Morris, S. C. & Foss, J. F. 2003 Turbulent boundary layer to single-stream shear layer: the transition region. J. Fluid Mech. 494, 187–221.Google Scholar
Murphy, K. P. 2012 Machine Learning: A Probabilistic Perspective. MIT Press.Google Scholar
Nordin, P. & Banzhaf, W. 1997 An on-line method to evolve behavior and to control a miniature robot in real time with genetic programming. Adapt. Behav. 5 (2), 107–140.Google Scholar
Oster, D. & Wygnanski, I. 1982 The forced mixing layer between parallel streams. J. Fluid Mech. 123, 91–130.Google Scholar
Parezanović, V., Laurentie, J.-C., Fourment, C., Delville, J., Bonnet, J.-P., Spohn, A., Duriez, T., Cordier, L., Noack, B. R., Abel, M. et al. 2014 Mixing layer manipulation experiment: from open-loop forcing to closed-loop machine learning control. Flow Turbul. Combust. 94 (1), 155–173.CrossRefGoogle Scholar
Pastoor, M., Henning, L., Noack, B. R., King, R. & Tadmor, G. 2008 Feedback shear layer control for bluff body drag reduction. J. Fluid Mech. 608, 161–196.Google Scholar
Pinier, J. T., Ausseur, J. M., Glauser, M. N. & Higuchi, H. 2007 Proportional closed-loop feedback control of flow separation. AIAA J. 45 (1), 181–190.Google Scholar
Rechenberg, I.(1971) Evolutionsstrategie: Optimierung technischer Systeme Nach Prinzipien der Biologischen Evolution. PhD thesis, Technical University of Berlin.Google Scholar
Rowley, C. W., Williams, D. R., Colonius, T., Murray, R. M. & Macmynowski, D. G. 2006 Linear models for control of cavity flow oscillations. J. Fluid Mech. 547, 317–330.Google Scholar
Samimy, M., Debiasi, M., Caraballo, E., Serrani, A., Yuan, X., Little, J. & Myatt, J. H. 2007 Feedback control of subsonic cavity flows using reduced-order models. J. Fluid Mech. 579, 315–346.Google Scholar
Schmidt, M. & Lipson, H. 2009 Distilling free-form natural laws from experimental data. Science 324 (5923), 81–85.CrossRefGoogle ScholarPubMed
Smits, G. & Kotanchek, M. 2005 Pareto-front exploitation in symbolic regression. In Genetic Programming Theory and Practice II, pp. 283–299. Springer.Google Scholar
Wahde, M. 2008 Biologically Inspired Optimization Methods: An Introduction. WIT Press.Google Scholar
Wills, J. A. B. 1964 On convection velocities in turbulent shear flows. J. Fluid Mech. 20 (03), 417–432.Google Scholar
Wiltse, J. M. & Glezer, A. 2011 The effect of closed-loop feedback control on scalar mixing in a plane shear layer. Exp. Fluids 51 (5), 1291–1314.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar