Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-23T11:14:27.565Z Has data issue: false hasContentIssue false
  • English
  • Français

Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition

Published online by Cambridge University Press:  23 September 2020

Eric A. Deem ,
Louis N. Cattafesta III Open the ORCID record for Louis N. Cattafesta III [Opens in a new window] ,
Maziar S. Hemati Open the ORCID record for Maziar S. Hemati [Opens in a new window] ,
Hao Zhang ,
Clarence Rowley Open the ORCID record for Clarence Rowley [Opens in a new window]  and
Rajat Mittal Open the ORCID record for Rajat Mittal [Opens in a new window]
Eric A. Deem
Affiliation:
Mechanical Engineering, Florida State University, Tallahassee, FL32310, USA
Louis N. Cattafesta III*
Affiliation:
Mechanical Engineering, Florida State University, Tallahassee, FL32310, USA
Maziar S. Hemati
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN55455, USA
Hao Zhang
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Clarence Rowley
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Rajat Mittal
Affiliation:
Mechanical Engineering, Johns Hopkins University, Baltimore, MD21218, USA
*
†Email address for correspondence: lcattafesta@eng.famu.fsu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Adaptive control of flow separation based on online dynamic mode decomposition (DMD) is formulated and implemented on a canonical separated laminar boundary layer via a pulse-modulated zero-net mass-flux jet actuator located just upstream of separation. Using a linear array of thirteen flush-mounted microphones, dynamical characteristics of the separated flow subjected to forcing are extracted by online DMD. This method provides updates of the modal characteristics of the separated flow while forcing is applied at a rate commensurate with the characteristic time scales of the flow. In particular, online DMD provides a time-varying linear estimate of the nonlinear evolution of the controlled flow without any prior knowledge. Using this adaptive model, feedback control is then implemented in which the linear quadratic regulator gains are computed recursively. This physics-based, autonomous approach results in more efficient flow reattachment compared with commensurate open-loop control. Four Reynolds numbers are tested to assess robustness, $Re_c = 0.9\times 10^5$, $Re_c = 1\times 10^5$, $Re_c = 1.1\times 10^5$ and $Re_c = 1.25\times 10^5$. All controlled cases exhibit a significant reduction in mean separation bubble height, requiring approximately 10 characteristic time periods to establish control.

JFM classification

Boundary Layers: Boundary layer separation Boundary Layers: Boundary layer control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A21
Check for updates
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Akers, J. C. & Bernstein, D. S. 1997 Time-domain identification using ARMARKOV/Toeplitz models. In Proceedings of the American Control Conference, pp. 191–195. IEEE.CrossRefGoogle Scholar
Amitay, M. & Glezer, A. 2006 Flow transients induced on a 2D airfoil by pulse-modulated actuation. Exp. Fluids 40 (2), 329–331.CrossRefGoogle Scholar
Ariyur, K. B. & Krstic, M. 2003 Real-Time Optimization by Extremum-Seeking Control. John Wiley & Sons.CrossRefGoogle Scholar
Becker, R., King, R., Petz, R. & Nitsche, W. 2007 Adaptive closed-loop separation control on a high-lift configuration using extremum seeking. AIAA J. 45 (6), 1382–1392.CrossRefGoogle Scholar
Benard, N., Moreau, E., Griffin, J. & Cattafesta, L. N. III 2010 Slope seeking for autonomous lift improvement by plasma surface discharge. Exp. Fluids 48 (5), 791–808.CrossRefGoogle Scholar
Bendat, J. S. & Piersol, A. G. 2011 Random Data: Analysis and Measurement Procedures. John Wiley & Sons.Google Scholar
Bendat, J. S. & Piersol, A. G. 2013 Engineering Applications of Correlation and Spectral Analysis. Wiley-Interscience.Google Scholar
Brunton, S. L. & Noack, B. R. 2015 Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67 (5), 050801.CrossRefGoogle Scholar
Cattafesta, L. N. & Sheplak, M. 2011 Actuators for active flow control. Annu. Rev. Fluid Mech. 43, 247–272.CrossRefGoogle Scholar
Cattafesta, L., Tian, Y. & Mittal, R. 2009 Adaptive control of post-stall separated flow application to heavy vehicles. In The Aerodynamics of Heavy Vehicles II: Trucks, Buses, and Trains (Lecture Notes in Applied and Computational Mechanics), vol. 41, pp. 151–160. Springer.CrossRefGoogle Scholar
Cossu, C. 2014 An introduction to optimal control lecture notes from the FLOW-NORDITA summer school on advanced instability methods for complex flows, Stockholm, Sweden, 2013. Appl. Mech. Rev. 66 (2), 024801.CrossRefGoogle Scholar
Dawson, S. T. M., Hemati, M. S., Williams, M. O. & Rowley, C. W. 2016 Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition. Exp. Fluids 57 (42).CrossRefGoogle Scholar
Deem, E. 2018 Flow physics and nonlinear dynamics of separated flows subject to ZNMF-based control. PhD thesis, Florida State University, Tallahassee, FL.Google Scholar
Deem, E., Cattafesta, L., Huaijin, Y., Hemati, M., Zhang, H. & Rowley, C. 2018 Experimental implementation of modal approaches for reattachment of separated flows. In 2018 AIAA Aerospace Sciences Meeting. SciTech Forum.CrossRefGoogle Scholar
Deem, E., Cattafesta, L., Zhang, H., Rowley, C., Hemati, M., Cadieux, F. & Mittal, R. 2017 Identifying dynamic modes of separated flow subject to ZNMF-based control from surface pressure measurements. AIAA Paper 2017-3309.CrossRefGoogle Scholar
Dorf, R. C. & Bishop, R. H. 2011 Modern Control Systems. Pearson.Google Scholar
Duriez, T., Brunton, S. L. & Noack, B. R. 2017 Machine Learning Control—Taming Nonlinear Dynamics and Turbulence. Springer.CrossRefGoogle Scholar
Gad-el Hak, M. 2001 Flow control: The future. J. Aircr. 38 (3), 402–418.CrossRefGoogle Scholar
Gaster, M. 1966 The Structure and Behaviour of Laminar Separation Bubbles. AGARD DP-4, pp. 813–854. Aeronautical Research Council.Google Scholar
Glezer, A. & Amitay, M. 2002 Synthetic jets. Annu. Rev. Fluid Mech. 34 (1), 503–529.CrossRefGoogle Scholar
Glezer, A., Amitay, M. & Honohan, A. M. 2005 Aspects of low-and high-frequency actuation for aerodynamic flow control. AIAA J. 43 (7), 1501.CrossRefGoogle Scholar
Greenblatt, D. & Wygnanski, I. J. 2000 The control of flow separation by periodic excitation. Prog. Aerosp. Sci. 36 (7), 487–545.CrossRefGoogle Scholar
Griffin, J. C. 2013 On the control of a canonical separated flow. PhD thesis, University of Florida, Gainesville, FL.Google Scholar
Griffin, J. C., Oyarzun, M., Cattafesta, L. N., Tu, J. H., Rowley, C. W. & Mittal, R. 2013 Control of a canonical separated flow. AIAA Paper 2013-2968.CrossRefGoogle Scholar
Griffin, J. C., Schultz, T., Holman, R., Ukeiley, L. S. & Cattafesta, L. N. 2010 Application of multivariate outlier detection to fluid velocity measurements. Exp. Fluids 49 (1), 305–317.CrossRefGoogle Scholar
Hemati, M. S., Deem, E. A., Williams, M. O., Rowley, C. W. & Cattafesta, L. N. 2016 Improving separation control with noise-robust variants of dynamic mode decomposition. AIAA Paper 2016-1103.CrossRefGoogle Scholar
Hemati, M. S., Rowley, C. W., Deem, E. A. & Cattafesta, L. N. 2017 De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets. Theor. Comput. Fluid Dyn. 31 (4), 349–368.CrossRefGoogle Scholar
Hemati, M. S., Williams, M. O. & Rowley, C. W. 2014 Dynamic mode decomposition for large and streaming datasets. Phys. Fluids 26 (11), 111701.CrossRefGoogle Scholar
Hodson, H. P. & Howell, R. J. 2005 Bladerow interactions, transition, and high-lift aerofoils in low-pressure turbines. Annu. Rev. Fluid Mech. 37 (1), 71–98.CrossRefGoogle Scholar
Joslin, R. D. 1998 Aircraft laminar flow control. Annu. Rev. Fluid Mech. 30 (1), 1–29.CrossRefGoogle Scholar
Jovanović, M. R., Schmid, P. J. & Nichols, J. W. 2014 Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26 (2), 024103–22.CrossRefGoogle 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.CrossRefGoogle Scholar
Kaiser, E., Noack, B. R., Spohn, A., Cattafesta, L. N. & Morzyński, M. 2017 Cluster-based control of a separating flow over a smoothly contoured ramp. Theor. Comput. Fluid Dyn. 31 (5–6), 579–593.CrossRefGoogle Scholar
de Kat, R. & Van Oudheusden, B. W. 2011 Instantaneous planar pressure determination from PIV in turbulent flow. Exp. Fluids 52 (5), 1089–1106.CrossRefGoogle Scholar
Kutz, J. N., Brunton, S. L., Brunton, B. W. & Proctor, J. L. 2016 Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. SIAM.CrossRefGoogle Scholar
Li, R., Noack, B. R., Cordier, L., Boree, J. & Harambat, F. 2017 Drag reduction of a car model by linear genetic programming control. Exp. Fluids 58 (8), 1177.CrossRefGoogle Scholar
Marxen, O. & Henningson, D. S. 2011 The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble. J. Fluid Mech. 671, 1–33.CrossRefGoogle Scholar
Marxen, O., Kotapati, R. B., Mittal, R. & Zaki, T. 2015 Stability analysis of separated flows subject to control by zero-net-mass-flux jet. Phys. Fluids 27 (2), 24107.CrossRefGoogle Scholar
Marxen, O. & Risk, U. 2010 Mean flow deformation in a laminar separation bubble: separation and stability characteristics. J. Fluid Mech. 660, 37–54.CrossRefGoogle Scholar
Melling, A. 1997 Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol. 8 (12), 1406.CrossRefGoogle Scholar
Michelis, T., Yarusevych, S. & Kotsonis, M. 2017 Response of a laminar separation bubble to impulsive forcing. J. Fluid Mech. 820, 633–666.CrossRefGoogle Scholar
Mittal, R. & Kotapati, R. B. 2006 Resonant mode interaction in a canonical separated flow. In IUTAM Symposium on Laminar-Turbulent Transition, pp. 341–348. Springer.CrossRefGoogle Scholar
Mittal, R., Kotapati, R. B. & Cattafesta, L. N. 2005 Numerical study of resonant interactions and flow control in a canonical separated flow. AIAA Paper 2005-1261.CrossRefGoogle 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.CrossRefGoogle Scholar
Mueller, T. J. & DeLaurier, J. D. 2003 Aerodynamics of small vehicles. Annu. Rev. Fluid Mech. 35 (1), 89–111.CrossRefGoogle Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379–405.CrossRefGoogle Scholar
Noack, B. R., Morzynski, M. & Tadmor, G. 2011 Reduced-Order Modelling for Flow Control, CISM Courses and Lectures, vol. 528. Springer.CrossRefGoogle Scholar
van Oudheusden, B. W., Scarano, F., Roosenboom, E. W. M., Casimiri, E. W. F. & Souverein, L. J. 2007 Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp. Fluids 43 (2–3), 153–162.CrossRefGoogle Scholar
de Pando, M. F., Schmid, P. J. & Sipp, D. 2017 On the receptivity of aerofoil tonal noise: an adjoint analysis. J. Fluid Mech. 812, 771–791.CrossRefGoogle Scholar
Platt, J. 1991 A resource-allocating network for function interpolation. Neural Comput. 3 (2), 213–225.CrossRefGoogle ScholarPubMed
Postl, D., Balzer, W. & Fasel, H. F. 2011 Control of laminar separation using pulsed vortex generator jets: direct numerical simulations. J. Fluid Mech. 676, 81–109.CrossRefGoogle Scholar
Proctor, J. L., Brunton, S. L. & Kutz, J. N. 2016 Dynamic mode decomposition with control. SIAM J. Appl. Dyn. Syst. 15 (1), 142–161.CrossRefGoogle Scholar
Raju, R., Mittal, R. & Cattafesta, L. 2008 Dynamics of airfoil separation control using zero-net mass-flux forcing. AIAA J. 46 (12), 3103.CrossRefGoogle Scholar
Reese, B. M., Collins, E. G. Jr., Fernandez, E. & Alvi, F. S. 2016 Nonlinear adaptive approach to microjet-based flow separation control. AIAA J. 54 (10), 3002–3014.CrossRefGoogle Scholar
Rist, U. & Augustin, K. 2006 Control of laminar separation bubbles using instability waves. AIAA J. 44 (10), 2217–2223.CrossRefGoogle Scholar
Rowley, C. W., Mezić, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–127.CrossRefGoogle Scholar
Saini, P., Arndt, C. M. & Steinberg, A. M. 2016 Development and evaluation of gappy-POD as a data reconstruction technique for noisy PIV measurements in gas turbine combustors. Exp. Fluids 57 (7), 122.CrossRefGoogle Scholar
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Schmidt, O. T. & Towne, A. 2019 An efficient streaming algorithm for spectral proper orthogonal decomposition. Comput. Phys. Commun. 237, 98–109.CrossRefGoogle Scholar
Seifert, A., Bachar, T., Koss, D., Shepshelovich, M. & Wygnanski, I. 1993 Oscillatory blowing: a tool to delay boundary-layer separation. AIAA J. 31 (11), 2052–2060.CrossRefGoogle Scholar
Seifert, A., Darabi, A. & Wyganski, I. 1996 Delay of airfoil stall by periodic excitation. J. Aircraft 33, 691–698.CrossRefGoogle Scholar
Seifert, A. & Pack, L. G. 1999 Oscillatory control of separation at high Reynolds numbers. AIAA J. 37, 1062–1071.CrossRefGoogle Scholar
Siauw, W. L., Bonnet, J.-P., Tensi, J., Cordier, L., Noack, B. R. & Cattafesta, L. 2010 Transient dynamics of the flow around a NACA 0015 airfoil using fluidic vortex generators. Intl J. Heat Fluid Flow 31 (3), 450–459.CrossRefGoogle Scholar
Sørensen, J. 2011 Aerodynamic aspects of wind energy conversion. Annu. Rev. Fluid Mech. 43 (1), 427–448.CrossRefGoogle Scholar
Taira, K., Brunton, S. L., Dawson, S. T. M., Rowley, C. W., Colonius, T., McKeon, B. J., Schmidt, O. T., Gordeyev, S., Theofilis, V. & Ukeiley, L. S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 4013–4041.CrossRefGoogle Scholar
Taira, K., Hemati, M. S., Brunton, S. L., Sun, Y., Duraisamy, K., Bagheri, S., Dawson, S. T. M. & Yeh, C.-A. 2019 Modal analysis of fluid flows: applications and outlook. AIAA J. 22 (11), 1–25.Google Scholar
Towne, A., Schmidt, O. T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar
Tu, J. H., Rowley, C. W., Luchtenburg, D. M., Brunton, S. L. & Kutz, J. N. 2014 On dynamic mode decomposition: theory and applications. J. Comput. Dyn. 1 (2), 391–421.CrossRefGoogle Scholar
Wieneke, B. 2015 Piv uncertainty quantification from correlation statistics. Meas. Sci. Technol. 26 (7), 74002.CrossRefGoogle Scholar
Williams, M. O., Kevrekidis, I. G. & Rowley, C. W. 2015 A data-driven approximation of the Koopman operator: extending dynamic mode decomposition. J. Nonlinear Sci. 25 (6), 1307–1346.CrossRefGoogle Scholar
Williams, D. & MacMynowski, D. 2009 Brief history of flow control. In Fundamentals and Applications of Modern Flow Control, vol. 231, pp. 1–20. AIAA.Google Scholar
Wu, Z. 2018 Jet mixing optimization using machine learning control. Exp. Fluids 59 (8), 1–17.CrossRefGoogle Scholar
Yarusevych, S., Kawall, J. G. & Sullivan, P. E. 2006 Airfoil performance at low Reynolds numbers in the presence of periodic disturbances. Trans. ASME: J. Fluids Engng 128 (3), 587–595.Google Scholar
Yarusevych, S. & Kotsonis, M. 2017 Steady and transient response of a laminar separation bubble to controlled disturbances. J. Fluid Mech. 813, 955–990.CrossRefGoogle Scholar
Zhang, H., Rowley, C. W., Deem, E. A. & Cattafesta, L. N. 2019 Online dynamic mode decomposition for time-varying systems. SIAM J. Appl. Dyn. Syst. 18 (3), 1586–1609.CrossRefGoogle Scholar