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Cluster-based feedback control of turbulent post-stall separated flows

Published online by Cambridge University Press:  19 July 2019

Aditya G. Nair Open the ORCID record for Aditya G. Nair [Opens in a new window] ,
Chi-An Yeh Open the ORCID record for Chi-An Yeh [Opens in a new window] ,
Eurika Kaiser ,
Bernd R. Noack Open the ORCID record for Bernd R. Noack [Opens in a new window] ,
Steven L. Brunton  and
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]
Aditya G. Nair*
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
Chi-An Yeh
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
Eurika Kaiser
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
Bernd R. Noack
Affiliation:
LIMSI, CNRS, Université Paris-Saclay, Bât 507, rue du Belvédère, Campus Universitaire, F-91403 Orsay, France Institut für Strömungsmechanik, Technische Universität Braunschweig, D-38108 Braunschweig, Germany Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, D-10623 Berlin, Germany Institute for Turbulence-Noise-Vibration Interaction and Control, Harbin Institute of Technology, Shenzhen Graduate School, University Town, Xili, Shenzhen 518058, PR China
Steven L. Brunton
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
Kunihiko Taira
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: agnair@uw.edu
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Abstract

We propose a cluster-based control strategy for feedback control of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law (using blowing/suction actuation) is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in aerodynamic flight. The optimized control laws re-route the flow trajectories to the aerodynamically favourable regions in the feature space in a model-free manner. Utilizing a limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present approach is applied to the control of two- and three-dimensional separated flows over a NACA 0012 airfoil in large-eddy simulations at an angle of attack of $9^{\circ }$, Reynolds number $Re=23\,000$ and free-stream Mach number $M_{\infty }=0.3$. The optimized control laws avoid the intermittent occurrence of long-period shedding associated with high-drag clusters, thus lowering the mean drag. The present work aims to address some of the challenges associated with feedback control design for turbulent separated flows at moderate Reynolds number.

JFM classification

Flow Control: Drag reduction Wakes/Jets: Separated flows Turbulent Flows: Turbulence control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 345 - 375
Copyright
© 2019 Cambridge University Press 

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References

Amitay, M. & Glezer, A. 2002 Role of actuation frequency in controlled flow reattachment over a stalled airfoil. AIAA J. 40 (2), 209–216.10.2514/2.1662Google Scholar
Amitay, M. & Glezer, A. 2006 Aerodynamic flow control using synthetic jet actuators. In Control of Fluid Flow, pp. 45–73. Springer.10.1007/978-3-540-36085-8_2Google Scholar
Anderson, J. D. 1999 Aircraft Performance and Design. McGraw-Hill.Google Scholar
Ariyur, K. B. & Krstic, M. 2003 Real-time Optimization by Extremum-seeking Control. Wiley.10.1002/0471669784Google 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
Bänsch, E., Benner, P., Saak, J. & Weichelt, H. K. 2015 Riccati-based boundary feedback stabilization of incompressible Navier–Stokes flow. SIAM J. Sci. Comput. 37 (2), A832–A858.10.1137/140980016Google 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, 1–50.10.1017/S0022112009991418Google Scholar
Beaudoin, J.-F., Cadot, O., Aider, J.-L. & Wesfreid, J. E. 2006 Bluff-body drag reduction by extremum-seeking control. J. Fluids Struct. 22 (6–7), 973–978.Google Scholar
Benton, S. I. & Visbal, M. R. 2018 High-frequency forcing to mitigate unsteady separation from a bursting separation bubble. Phys. Rev. Fluids 3 (1), 013907.Google Scholar
Bewley, T. R. 2001 Flow control: new challenges for a new renaissance. Prog. Aerosp. Sci. 37 (1), 21–58.10.1016/S0376-0421(00)00016-6Google Scholar
Brès, G. A., Ham, F. E., Nichols, J. W. & Lele, S. K. 2017 Unstructured large-eddy simulations of supersonic jets. AIAA J. 55 (4), 1164–1184.10.2514/1.J055084Google Scholar
Brunton, S. L. & Noack, B. R. 2015 Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67, 050801–48.Google Scholar
Brunton, S. L., Proctor, J. L. & Kutz, J. N. 2016 Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl Acad. Sci. USA, 201517384.Google Scholar
Carini, M., Pralits, J. O. & Luchini, P. 2015 Feedback control of vortex shedding using a full-order optimal compensator. J. Fluids Struct. 53, 15–25.10.1016/j.jfluidstructs.2014.11.011Google Scholar
Chiang, M. M.-T. & Mirkin, B. 2010 Intelligent choice of the number of clusters in k-means clustering: an experimental study with different cluster spreads. J. Classification 27 (1), 3–40.10.1007/s00357-010-9049-5Google Scholar
Colonius, T. & Williams, D. R. 2011 Control of vortex shedding on two-and three-dimensional aerofoils. Phil. Trans. R. Soc. Lond. A 369 (1940), 1525–1539.Google Scholar
Debien, A., von Krbek, K. A. F. F., Mazellier, N., Duriez, T., Cordier, L., Noack, B. R., Abel, M. W. & Kourta, A. 2016 Closed-loop separation control over a sharp edge ramp using genetic programming. Exp. Fluids 57 (3), 40.10.1007/s00348-016-2126-8Google Scholar
Duriez, T., Brunton, S. L. & Noack, B. R. 2016 Machine Learning Control-Taming Nonlinear Dynamics and Turbulence. Springer.Google Scholar
Freund, J. B. 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35 (4), 740–742.Google Scholar
G-Michael, T., Gunzburger, M. & Peterson, J. 2018 Clustering approaches to feature change detection. In Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XXIII, vol. 10628, p. 106281G. International Society for Optics and Photonics.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, 442–457.10.1017/jfm.2015.95Google Scholar
Goutte, C., Toft, P., Rostrup, E., Nielsen, F. Å. & Hansen, L. K. 1999 On clustering fMRI time series. NeuroImage 9 (3), 298–310.10.1006/nimg.1998.0391Google Scholar
Greenblatt, D. & Wygnanski, I. J. 2000 The control of flow separation by periodic excitation. Prog. Aerosp. Sci. 36, 487–545.10.1016/S0376-0421(00)00008-7Google 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
Huang, S.-C. & Kim, J. 2008 Control and system identification of a separated flow. Phys. Fluids 20 (10), 101509.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1998 Eddies, streams, and convergence zones in turbulent flows. In Center for Turbulence Research Report CTR-S88, pp. 193–208.Google Scholar
Illingworth, S. J., Morgans, A. S. & Rowley, C. W. 2012 Feedback control of cavity flow oscillations using simple linear models. J. Fluid Mech. 709, 223–248.10.1017/jfm.2012.330Google Scholar
Kaiser, E., Li, R. & Noack, B. R. 2017a On the control landscape topology. In The Proceedings of the 20th World Congress of the International Federation of Automatic Control (IFAC), pp. 1–5. IFAC.Google Scholar
Kaiser, E., Morzyński, M., Daviller, G., Kutz, J. N., Brunton, B. W. & Brunton, S. L. 2018 Sparsity enabled cluster reduced-order models for control. J. Comput. Phys. 352, 388–409.10.1016/j.jcp.2017.09.057Google Scholar
Kaiser, E., Noack, B. R., Cordier, L., Spohn, A., Segond, M., Abel, M., Daviller, G., Östh, J., Krajnović, S. & Niven, R. K. 2014 Cluster-based reduced-order modelling of a mixing layer. J. Fluid Mech. 754, 365–414.10.1017/jfm.2014.355Google Scholar
Kaiser, E., Noack, B. R., Spohn, A., Cattafesta, L. N. & Morzyński, M. 2017b Cluster-based control of a separating flow over a smoothly contoured ramp. Theor. Comput. Fluid Dyn. 31 (5–6), 579–593.Google Scholar
Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383–417.Google Scholar
Kojima, R., Nonomura, T., Oyama, A. & Fujii, K. 2013 Large eddy simulation of low-Reynolds-number flow over thick and thin NACA airfoils. J. Aircraft 50 (1), 187–196.Google Scholar
Kontovasilis, K. P. & Mitrou, N. M. 1995 Markov-modulated traffic with nearly complete decomposability characteristics and associated fluid queueing models. Adv. Appl. Probability 27 (4), 1144–1185.10.2307/1427937Google Scholar
Lee, D. & Wiswall, M. 2007 A parallel implementation of the simplex function minimization routine. Comput. Economics 30 (2), 17–187.10.1007/s10614-007-9094-2Google Scholar
Leicht, E. A. & Newman, M. E. J. 2008 Community structure in directed networks. Phys. Rev. Lett. 100 (11), 118703.Google Scholar
Lloyd, S. 1982 Least squares quantization in PCM. IEEE Trans. Inf. Theory 28 (2), 129–137.Google Scholar
Loiseau, J.-C., Noack, B. R. & Brunton, S. L. 2018 Sparse reduced-order modelling: sensor-based dynamics to full-state estimation. J. Fluid Mech. 844, 459–490.Google Scholar
Lomax, R. G. & Hahs-Vaughn, D. L. 2013 Statistical Concepts: A Second Course. Routledge.10.4324/9780203137802Google Scholar
Luchtenburg, D. M., Günther, B., Noack, B. R., King, R. & Tadmor, G. 2009 A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration. J. Fluid Mech. 623, 283–316.10.1017/S0022112008004965Google Scholar
Luersen, M. A., Le Riche, R. & Guyon, F. 2004 A constrained, globalized, and bounded Nelder–Mead method for engineering optimization. Struct. Multidiscip. Optim. 27 (1–2), 43–54.10.1007/s00158-003-0320-9Google Scholar
Mao, X., Blackburn, H. M. & Sherwin, S. J. 2015 Nonlinear optimal suppression of vortex shedding from a circular cylinder. J. Fluid Mech. 775, 241–265.Google Scholar
McKay, M. D., Beckman, R. J. & Conover, W. J. 2000 A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42 (1), 55–61.10.1080/00401706.2000.10485979Google Scholar
Munday, P. M. & Taira, K. 2018 Effects of wall-normal and angular momentum injections in airfoil separation control. AIAA J. 56 (5), 1830–1842.Google Scholar
Nair, A. G., Brunton, S. L. & Taira, K. 2018 Networked-oscillator-based modeling and control of unsteady wake flows. Phys. Rev. E 97 (6), 063107.Google Scholar
Nelder, J. A. & Mead, R. 1965 A simplex method for function minimization. Computer J. 7 (4), 308–313.Google Scholar
Newman, M. 2010 Networks: An Introduction. Oxford University Press.Google Scholar
Noack, B., Tadmor, G. & Morzynski, M. 2004 Low-dimensional models for feedback flow control. Part I: Empirical galerkin models. In 2nd AIAA Flow Control Conference, p. 2408.Google Scholar
Noack, B. R. 2019 Closed-loop turbulence control-from human to machine learning (and retour). In Proceedings of the 4th Symposium on Fluid Structure-Sound Interactions and Control (FSSIC) (ed. Zhou, Y., Kimura, M., Peng, G., Lucey, A. D. & Huang, L.), pp. 23–32. Springer.Google Scholar
Noack, B. R., Afanasiev, K., Morzyński, M., Tadmor, G. & Thiele, F. 2003 A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497, 335–363.Google Scholar
Noack, B. R., Morzynski, M. & Tadmor, G. 2011 Reduced-order Modelling for Flow Control. Springer.10.1007/978-3-7091-0758-4Google Scholar
Norris, J. R. 1998 Markov Chains. Cambridge University Press.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
Protas, B. 2004 Linear feedback stabilization of laminar vortex shedding based on a point vortex model. Phys. Fluids 16 (12), 4473–4488.Google Scholar
Rabault, J., Kuchta, M., Jensen, A., Réglade, U. & Cerardi, N. 2019 Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. J. Fluid Mech. 865, 281–302.Google Scholar
Rokach, L. & Maimon, O. 2005 Clustering methods. In Data Mining and Knowledge Discovery Handbook, pp. 321–352. Springer.Google Scholar
Semeraro, O., Bagheri, S., Brandt, L. & Henningson, D. S. 2011 Feedback control of three-dimensional optimal disturbances using reduced-order models. J. Fluid Mech. 677, 63–102.Google Scholar
Taira, K. & Nakao, H. 2018 Phase-response analysis of synchronization for periodic flows. J. Fluid Mech. 846, R2.10.1017/jfm.2018.327Google Scholar
Tibshirani, R., Walther, G. & Hastie, T. 2001 Estimating the number of clusters in a data set via the gap statistic. J. R. Statist. Soc. B 63 (2), 411–423.Google Scholar
Vreman, B. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16 (10), 3670–3681.Google Scholar
Wand, M. P. & Jones, M. C. 1994 Kernel Smoothing. CRC Press.Google Scholar
Yeh, C.-A., Munday, P. & Taira, K.2017 Use of local periodic heating for separation control on a NACA 0012 airfoil. AIAA Paper 2017-1451.Google Scholar
Yeh, C.-A. & Taira, K. 2019 Resolvent-analysis-based design of airfoil separation control. J. Fluid Mech. 867, 572–610.Google Scholar
Young, G. & Householder, A. S. 1938 Discussion of a set of points in terms of their mutual distances. Psychometrika 3 (1), 19–22.Google Scholar