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Active control of the flow past a circular cylinder using online dynamic mode decomposition

Published online by Cambridge University Press:  10 October 2024

Xin Li  and
Jian Deng Open the ORCID record for Jian Deng [Opens in a new window]
Xin Li
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
Jian Deng*
Affiliation:
State Key Laboratory of Fluid Power and Mechatronic Systems, Department of Mechanics, Zhejiang University, Hangzhou 310027, PR China
*
†Email address for correspondence: [email protected]
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Abstract

This study explores the implementation of an online control strategy based on dynamic mode decomposition in the context of flow control. The investigation is conducted mainly with a fixed Reynolds number of $Re = 100$, focusing on the flow past a circular cylinder constrained between two walls to mitigate vortex shedding. The control approach involves the activation of two synthetic jets on the cylinder through blowing and suction. Velocity fluctuations in the wake, specifically in the $x$-direction, are harnessed to ascertain the mass flow rate of the jets using the linear quadratic regulator and online dynamic mode decomposition. The study systematically assesses the control performance across various configurations, including different values of the input penalty factor ${\boldsymbol {R}}$, varying numbers of probes and distinct probe arrangement methods. The synthetic jets prove effective in stabilising the separation bubble, and their interaction with the unsteady wake leads to a notable reduction in drag force, its fluctuations and the amplitude of the lift force. Specifically, the mean and standard deviation of the drag coefficient witness reductions of $7.44\,\%$ and $96.67\,\%$, respectively, and the standard deviation of the lift coefficient experiences an impressive reduction of $85.18\,\%$. The robustness of the proposed control method has also been tested on two more complicated cases, involving unsteady incoming flows with multiple frequency components. Comparatively, the methodology employed in this paper yields results akin to those obtained through deep reinforcement learning in terms of control effectiveness. However, a noteworthy advantage lies in the substantial reduction of computational resource consumption, highlighting the efficiency of the proposed approach.

JFM classification

Flow Control: Drag reduction Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 997 , 25 October 2024 , A26
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Bai, H.L., Zhou, Y., Zhang, W.G., Xu, S.J., Wang, Y. & Antonia, R.A. 2014 Active control of a turbulent boundary layer based on local surface perturbation. J. Fluid Mech. 750, 316–354.CrossRefGoogle Scholar
Barbagallo, A., Dergham, G., Sipp, D., Schmid, P.J. & Robinet, J.C. 2012 Closed-loop control of unsteadiness over a rounded backward-facing step. J. Fluid Mech. 703, 326–362.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, 1–50.CrossRefGoogle Scholar
Barros, D., Borée, J., Noack, B.R., Spohn, A. & Ruiz, T. 2016 Bluff body drag manipulation using pulsed jets and Coanda effect. J. Fluid Mech. 805, 422–459.CrossRefGoogle Scholar
Cattafesta, L.N. & Sheplak, M. 2011 Actuators for active flow control. Annu. Rev. Fluid Mech. 43, 247–272.CrossRefGoogle Scholar
Chen, J.-H., Pritchard, W.G. & Tavener, S.J. 1995 Bifurcation for flow past a cylinder between parallel planes. J. Fluid Mech. 284, 23–41.CrossRefGoogle Scholar
Chen, W., Li, H. & Hu, H. 2014 An experimental study on a suction flow control method to reduce the unsteadiness of the wind loads acting on a circular cylinder. Exp. Fluids 55 (4), 1707.CrossRefGoogle Scholar
Chen, W.L., Huang, Y., Chen, C., Yu, H. & Gao, D. 2022 Review of active control of circular cylinder flow. Ocean Engng 258, 111840.CrossRefGoogle Scholar
Choi, H., Jeon, W.P. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40, 113–139.CrossRefGoogle Scholar
Chopra, G. & Mittal, S. 2019 Drag coefficient and formation length at the onset of vortex shedding. Phys. Fluids 31 (1), 013601.CrossRefGoogle Scholar
D'Alessandro, V., Clementi, G., Giammichele, L. & Ricci, R. 2019 Assessment of the dimples as passive boundary layer control technique for laminar airfoils operating at wind turbine blades root region typical Reynolds numbers. Energy 170, 102–111.CrossRefGoogle Scholar
Deem, E.A., Cattafesta, L.N., Hemati, M.S., Zhang, H., Rowley, C. & Mittal, R. 2020 Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition. J. Fluid Mech. 903, A21.CrossRefGoogle Scholar
Delaunay, Y. & Kaiktsis, L. 2001 Control of circular cylinder wakes using base mass transpiration. Phys. Fluids 13 (11), 3285–3302.CrossRefGoogle Scholar
Demmel, J., Grigori, L., Hoemmen, M. & Langou, J. 2012 Communication-optimal parallel and sequential QR and LU factorizations. SIAM J. Sci. Comput. 34 (1), A206–A239.CrossRefGoogle Scholar
Deng, J., Xu, J. & Ye, Q. 2022 Experimental investigation of flow around a circular cylinder with attached membranes. J. Fluids Struct. 113, 103628.CrossRefGoogle Scholar
Feng, L.-H., Cui, G.-P. & Liu, L.-Y. 2019 Two-dimensionalization of a three-dimensional bluff body wake. Phys. Fluids 31 (1), 017104.CrossRefGoogle Scholar
Franzini, G.R., Fujarra, A.L.C., Meneghini, J.R., Korkischko, I. & Franciss, R. 2009 Experimental investigation of vortex-induced vibration on rigid, smooth and inclined cylinders. J. Fluids Struct. 25 (4), 742–750.CrossRefGoogle 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.CrossRefGoogle Scholar
Greco, C.S., Paolillo, G., Astarita, T. & Cardone, G. 2020 The von Kármán street behind a circular cylinder: flow control through synthetic jet placed at the rear stagnation point. J. Fluid Mech. 901, A39.CrossRefGoogle Scholar
Greska, B., Krothapalli, A., Seiner, J., Jansen, B. & Ukeiley, L. 2005 The effects of microjet injection on an f404 jet engine. In 11th AIAA/CEAS Aeroacoustics Conference, p. 3047. AIAA.CrossRefGoogle Scholar
Hager, W.W. 1989 Updating the inverse of a matrix. SIAM Rev. 31 (2), 221–239.CrossRefGoogle Scholar
Jang, H.K., Ozdemir, C.E., Liang, J.-H. & Tyagi, M. 2021 Oscillatory flow around a vertical wall-mounted cylinder: dynamic mode decomposition. Phys. Fluids 33 (2), 025113.CrossRefGoogle Scholar
Kibens, V., Dorris, I.J., Smith, D. & Mossman, M. 1999 Active flow control technology transition - the boeing ACE program. In 30th Fluid Dynamics Conference. AIAA.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
Kwon, K. & Choi, H. 1996 Control of laminar vortex shedding behind a circular cylinder using splitter plates. Phys. Fluids 8 (2), 479–486.CrossRefGoogle Scholar
Li, J. & Zhang, M. 2022 Reinforcement-learning-based control of confined cylinder wakes with stability analyses. J. Fluid Mech. 932, 1–35.CrossRefGoogle Scholar
Lorenz, E.N. 1963 Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141.2.0.CO;2>CrossRefGoogle Scholar
Mao, Q., Liu, Y. & Sung, H.J. 2023 Drag reduction by flapping a pair of flexible filaments behind a cylinder. Phys. Fluids 35 (3), 033602.CrossRefGoogle Scholar
Mittal, S. 2003 Effect of a ‘slip’ splitter plate on vortex shedding from a cylinder. Phys. Fluids 15 (3), 817–820.CrossRefGoogle Scholar
Nagib, H.M., Kiedaisch, J.W., Wygnanski, I.J., Stalker, A.D., Wood, T. & McVeigh, M.A. 2004 First-in-flight full-scale application of active flow control: the XV-15 tiltrotor download reduction. Tech. Rep. Illinois Institute of Technology Chicago Mechanical Materials and Aerospace Engineering.Google Scholar
Nair, A.G., Taira, K., Brunton, B.W. & Brunton, S.L. 2021 Phase-based control of periodic flows. J. Fluid Mech. 927, A30.CrossRefGoogle Scholar
Nguyen, D.B., Wu, P., Monico, R.O. & Chen, G. 2023 Dynamic mode decomposition for large-scale coherent structure extraction in shear flows. IEEE Trans. Vis. Comput. Graphics 29 (2), 1531–1544.CrossRefGoogle Scholar
Noack, B.R., Stankiewicz, W., Morzynski, M. & Schmid, P.J. 2016 Recursive dynamic mode decomposition of transient and post-transient wake flows. J. Fluid Mech. 809, 843–872.CrossRefGoogle Scholar
Paris, R., Beneddine, S. & Dandois, J. 2021 Robust flow control and optimal sensor placement using deep reinforcement learning. J. Fluid Mech. 913, 1–34.CrossRefGoogle Scholar
Ping, H., Zhu, H., Zhang, K., Zhou, D., Bao, Y., Xu, Y. & Han, Z. 2021 Dynamic mode decomposition based analysis of flow past a transversely oscillating cylinder. Phys. Fluids 33 (3), 033604.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, 281–302.CrossRefGoogle Scholar
Roache, P.J. 1994 Perspective: a method for uniform reporting of grid refinement studies. Trans. ASME J. Fluids Engng 116 (3), 405–413.CrossRefGoogle Scholar
Roache, P.J. 1997 Quantification of uncertainty in computational fluid dynamics. Annu. Rev. Fluid Mech. 29 (1), 123–160.CrossRefGoogle Scholar
Roache, P.J. 1998 Verification and Validation in Computational Science and Engineering, vol. 895. Hermosa.Google Scholar
Rosenfeld, J.A. & Kamalapurkar, R. 2016 Dynamic mode decomposition with control. SIAM J. Appl. Dyn. Syst. 15 (1), 142–161.Google Scholar
Schäfer, M., Turek, S., Durst, F., Krause, E. & Rannacher, R. 1996 Benchmark Computations of Laminar Flow around a Cylinder. Springer.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2016 Boundary-Layer Theory. Springer.Google Scholar
Schmid, P.J. 2021 Dynamic mode decomposition and its variants. Annu. Rev. Fluid Mech. 54, 225–254.CrossRefGoogle Scholar
Shaw, L., Smith, B. & Saddoughi, S. 2006 Full-scale flight demonstration of active control of a POD wake. In 3rd AIAA Flow Control Conference, p. 3185. AIAA.CrossRefGoogle Scholar
Tezduyar, T., Aliabadi, S., Behr, M., Johnson, A., Kalro, V. & Litke, M. 1996 Flow simulation and high performance computing. Comput. Mech. 18, 397–412.CrossRefGoogle Scholar
Tu, J.H., Rowley, C.W., Kutz, J.N. & Shang, J.K. 2014 Spectral analysis of fluid flows using sub-Nyquist-rate PIV data. Exp. Fluids 55 (9), 1805.CrossRefGoogle Scholar
Walsh, M.J. 1983 Riblets as a viscous drag reduction technique. AIAA J. 21 (4), 485–486.CrossRefGoogle Scholar
Wang, L., Xu, M., Zhao, D. & Huang, G. 2023 a Rapid prediction of flexible deformations of a gust generator vane using data-driven approaches. J. Aerosp. Engng 36 (3), 04023009.Google Scholar
Wang, Q., Yan, L., Hu, G., Chen, W., Rabault, J. & Noack, B.R. 2024 Dynamic feature-based deep reinforcement learning for flow control of circular cylinder with sparse surface pressure sensing. J. Fluid Mech. 988, A4.CrossRefGoogle Scholar
Wang, Q., Yan, L., Hu, G., Li, C., Xiao, Y., Xiong, H., Rabault, J. & Noack, B.R. 2022 DRLinFluids: an open-source Python platform of coupling deep reinforcement learning and OpenFOAM. Phys. Fluids 34 (8), 081801.CrossRefGoogle Scholar
Wang, X., Li, Q., Lu, B. & Li, M. 2023 b Generation of negative peak pressures under a separation bubble. J. Wind Engng Ind. Aerodyn. 236, 105365.Google Scholar
Wang, Z., Fan, D., Jiang, X., Triantafyllou, M.S. & Karniadakis, G.E. 2023 c Deep reinforcement transfer learning of active control for bluff body flows at high Reynolds number. J. Fluid Mech. 973, A32.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
Wu, Y., Tao, R., Yao, Z., Xiao, R. & Wang, F. 2023 Application and comparison of dynamic mode decomposition methods in the tip leakage cavitation of a hydrofoil case. Phys. Fluids 35 (2), 23326.CrossRefGoogle Scholar
Xie, F., Pérez-Muñoz, J.D., Qin, N. & Ricco, P. 2022 Drag reduction in wall-bounded turbulence by synthetic jet sheets. J. Fluid Mech. 941, A63.CrossRefGoogle Scholar
Yang, J., Yan, S., Gong, Y., Guo, Q., Ding, L. & Yu, G. 2023 Application study of dynamic mode decomposition coupled with a high-speed imaging system in jet zone oscillation behavior diagnosis of impinging flames. Control Engng Pract. 135, 105494.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
Zhang, L., Li, K., Shan, X., Zhai, Y., Yan, S. & Xie, T. 2022 Active drag reduction for the wall of microunderwater vehicles by piezoelectric actuated drag reducer. IEEE ASME Trans. Mechatron. 27 (6), 5981–5993.CrossRefGoogle Scholar