Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-mhx7p Total loading time: 0.36 Render date: 2022-05-24T15:11:46.386Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

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

Published online by Cambridge University Press:  19 July 2019

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

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.

Type
JFM Papers
Copyright
© 2019 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

Amitay, M. & Glezer, A. 2002 Role of actuation frequency in controlled flow reattachment over a stalled airfoil. AIAA J. 40 (2), 209216.10.2514/2.1662CrossRefGoogle Scholar
Amitay, M. & Glezer, A. 2006 Aerodynamic flow control using synthetic jet actuators. In Control of Fluid Flow, pp. 4573. Springer.10.1007/978-3-540-36085-8_2CrossRefGoogle 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.10.1002/0471669784CrossRefGoogle 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, 263298.CrossRefGoogle 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), A832A858.10.1137/140980016CrossRefGoogle 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, 150.10.1017/S0022112009991418CrossRefGoogle 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), 973978.CrossRefGoogle 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.CrossRefGoogle Scholar
Bewley, T. R. 2001 Flow control: new challenges for a new renaissance. Prog. Aerosp. Sci. 37 (1), 2158.10.1016/S0376-0421(00)00016-6CrossRefGoogle 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), 11641184.10.2514/1.J055084CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Carini, M., Pralits, J. O. & Luchini, P. 2015 Feedback control of vortex shedding using a full-order optimal compensator. J. Fluids Struct. 53, 1525.10.1016/j.jfluidstructs.2014.11.011CrossRefGoogle 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), 340.10.1007/s00357-010-9049-5CrossRefGoogle 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), 15251539.Google ScholarPubMed
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/s00348-016-2126-8CrossRefGoogle 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), 740742.CrossRefGoogle 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, 442457.10.1017/jfm.2015.95CrossRefGoogle Scholar
Goutte, C., Toft, P., Rostrup, E., Nielsen, F. Å. & Hansen, L. K. 1999 On clustering fMRI time series. NeuroImage 9 (3), 298310.10.1006/nimg.1998.0391CrossRefGoogle ScholarPubMed
Greenblatt, D. & Wygnanski, I. J. 2000 The control of flow separation by periodic excitation. Prog. Aerosp. Sci. 36, 487545.10.1016/S0376-0421(00)00008-7CrossRefGoogle 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, 2658.CrossRefGoogle Scholar
Huang, S.-C. & Kim, J. 2008 Control and system identification of a separated flow. Phys. Fluids 20 (10), 101509.CrossRefGoogle 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. 193208.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, 223248.10.1017/jfm.2012.330CrossRefGoogle 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. 15. 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, 388409.10.1016/j.jcp.2017.09.057CrossRefGoogle 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, 365414.10.1017/jfm.2014.355CrossRefGoogle 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), 579593.CrossRefGoogle Scholar
Kim, J. & Bewley, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383417.CrossRefGoogle 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), 187196.CrossRefGoogle 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), 11441185.10.2307/1427937CrossRefGoogle Scholar
Lee, D. & Wiswall, M. 2007 A parallel implementation of the simplex function minimization routine. Comput. Economics 30 (2), 17187.10.1007/s10614-007-9094-2CrossRefGoogle Scholar
Leicht, E. A. & Newman, M. E. J. 2008 Community structure in directed networks. Phys. Rev. Lett. 100 (11), 118703.CrossRefGoogle ScholarPubMed
Lloyd, S. 1982 Least squares quantization in PCM. IEEE Trans. Inf. Theory 28 (2), 129137.CrossRefGoogle 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, 459490.CrossRefGoogle Scholar
Lomax, R. G. & Hahs-Vaughn, D. L. 2013 Statistical Concepts: A Second Course. Routledge.10.4324/9780203137802CrossRefGoogle 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, 283316.10.1017/S0022112008004965CrossRefGoogle 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), 4354.10.1007/s00158-003-0320-9CrossRefGoogle Scholar
Mao, X., Blackburn, H. M. & Sherwin, S. J. 2015 Nonlinear optimal suppression of vortex shedding from a circular cylinder. J. Fluid Mech. 775, 241265.CrossRefGoogle 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), 5561.10.1080/00401706.2000.10485979CrossRefGoogle Scholar
Munday, P. M. & Taira, K. 2018 Effects of wall-normal and angular momentum injections in airfoil separation control. AIAA J. 56 (5), 18301842.CrossRefGoogle 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 ScholarPubMed
Nelder, J. A. & Mead, R. 1965 A simplex method for function minimization. Computer J. 7 (4), 308313.CrossRefGoogle Scholar
Newman, M. 2010 Networks: An Introduction. Oxford University Press.CrossRefGoogle 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. 2332. Springer.CrossRefGoogle 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, 335363.CrossRefGoogle Scholar
Noack, B. R., Morzynski, M. & Tadmor, G. 2011 Reduced-order Modelling for Flow Control. Springer.10.1007/978-3-7091-0758-4CrossRefGoogle 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), 181190.CrossRefGoogle Scholar
Protas, B. 2004 Linear feedback stabilization of laminar vortex shedding based on a point vortex model. Phys. Fluids 16 (12), 44734488.CrossRefGoogle 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, 281302.CrossRefGoogle Scholar
Rokach, L. & Maimon, O. 2005 Clustering methods. In Data Mining and Knowledge Discovery Handbook, pp. 321352. Springer.CrossRefGoogle 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, 63102.CrossRefGoogle Scholar
Taira, K. & Nakao, H. 2018 Phase-response analysis of synchronization for periodic flows. J. Fluid Mech. 846, R2.10.1017/jfm.2018.327CrossRefGoogle 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), 411423.CrossRefGoogle Scholar
Vreman, B. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16 (10), 36703681.CrossRefGoogle Scholar
Wand, M. P. & Jones, M. C. 1994 Kernel Smoothing. CRC Press.CrossRefGoogle 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.CrossRefGoogle Scholar
Yeh, C.-A. & Taira, K. 2019 Resolvent-analysis-based design of airfoil separation control. J. Fluid Mech. 867, 572610.CrossRefGoogle Scholar
Young, G. & Householder, A. S. 1938 Discussion of a set of points in terms of their mutual distances. Psychometrika 3 (1), 1922.CrossRefGoogle Scholar
28
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Cluster-based feedback control of turbulent post-stall separated flows
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Cluster-based feedback control of turbulent post-stall separated flows
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Cluster-based feedback control of turbulent post-stall separated flows
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *