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Feedback control of unstable flow and vortex-induced vibration using the eigensystem realization algorithm

Published online by Cambridge University Press:  22 August 2017

W. Yao  and
R. K. Jaiman Open the ORCID record for R. K. Jaiman [Opens in a new window]
W. Yao
Affiliation:
Department of Mechanical Engineering, National University Singapore, 119077, Singapore
R. K. Jaiman*
Affiliation:
Department of Mechanical Engineering, National University Singapore, 119077, Singapore
*
†Email address for correspondence: mperkj@nus.edu.sg
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Abstract

We present an active feedback blowing and suction (AFBS) procedure via model reduction for unsteady wake flow and the vortex-induced vibration (VIV) of circular cylinders. The reduced-order model (ROM) for the AFBS procedure is developed by the eigensystem realization algorithm (ERA), which provides a low-order representation of the unsteady flow dynamics in the neighbourhood of the equilibrium steady state. The actuation is considered via vertical suction and a blowing jet at the porous surface of a circular cylinder with a body-mounted force sensor. While the optimal gain is obtained using a linear quadratic regulator (LQR), Kalman filtering is employed to estimate the approximate state vector. The feedback control system shifts the unstable eigenvalues of the wake flow and the VIV system to the left half-complex-plane, and subsequently results in suppression of the vortex street and the VIV in elastically mounted structures. The resulting controller designed by a linear low-order approximation is able to suppress the nonlinear saturated state of wake vortex shedding from the circular cylinder. A systematic linear ROM-based stability analysis is performed to understand the eigenvalue distribution for the flow past stationary and elastically mounted circular cylinders. The results from the ROM analysis are consistent with those obtained from full nonlinear fluid–structure interaction simulations, thereby confirming the validity of the proposed ROM-based AFBS procedure. A sensitivity study on the number of suction/blowing actuators, the angular arrangement of actuators and the combined versus independent control architectures has been performed for the flow past a stationary circular cylinder. Overall, the proposed control concept based on the ERA-based ROM and the LQR algorithm is found to be effective in suppressing the vortex street and the VIV for a range of reduced velocities and mass ratios.

JFM classification

Flow Control: Flow Control Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 827 , 25 September 2017 , pp. 394 - 414
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Copyright
© 2017 Cambridge University Press 

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References

Ahuja, S. & Rowley, C. W. 2010 Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators. J. Fluid Mech. 645, 447–478.Google Scholar
Baek, H. & Karniadakis, G. E. 2009 Suppressing vortex-induced vibrations via passive means. J. Fluids Struct. 25 (5), 848–866.CrossRefGoogle Scholar
Chakrabarti, S. K. 2005 Handbook of Offshore Engineering. Elsevier.Google Scholar
Chen, W.-L., Gao, D.-L., Yuan, W.-Y., Li, H. & Hu, H. 2015 Passive jet control of flow around a circular cylinder. Exp. Fluids 56 (11), 201.Google Scholar
Chen, W.-L., Xin, D.-B., Xu, F., Li, H., Ou, J.-P. & Hu, H. 2013 Suppression of vortex-induced vibration of a circular cylinder using suction-based flow control. J. Fluids Struct. 42, 25–39.Google Scholar
Choi, H., Jeon, W.-P. & Kim, J. 2008 Control of flow over a bluff body. Annu. Rev. Fluid Mech. 40 (1), 113–139.Google Scholar
Dong, S., Triantafyllou, G. S. & Karniadakis, G. E. 2008 Elimination of vortex streets in bluff-body flows. Phys. Rev. Lett. 100, 204501.Google Scholar
Flinois, T. L. B. & Morgans, A. S. 2016 Feedback control of unstable flows: a direct modelling approach using the eigensystem realisation algorithm. J. Fluid Mech. 793, 41–78.Google Scholar
Flinois, T. L. B., Morgans, A. S. & Schmid, P. J. 2015 Projection-free approximate balanced truncation of large unstable systems. Phys. Rev. E 92 (2), 1–31.Google Scholar
Fransson, J. H. M., Konieczny, P. & Alfredsson, P. H. 2004 Flow around a porous cylinder subject to continuous suction or blowing. J. Fluids Struct. 19 (8), 1031–1048.Google Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.Google Scholar
Jaiman, R. K., Geubelle, P., Loth, E. & Jiao, X. 2011 Transient fluid and structure interaction with non-matching spatial and temporal discretizations. Comput. Fluids 50 (1), 120–135.Google Scholar
Jaiman, R. K., Sen, S. & Gurugubelli, P. S. 2015 A fully implicit combined field scheme for freely vibrating square cylinders with sharp and rounded corners. Comput. Fluids 112, 1–18.Google Scholar
Juang, J.-N. & Pappa, R. S. 1985 An eigensystem realization algorithm for modal parameter identification and model reduction. J. Guid. 8 (5), 620–627.CrossRefGoogle Scholar
Kim, J. & Choi, H. 2005 Distributed forcing of flow over a circular cylinder. Phys. Fluids 17 (3), 033103.Google Scholar
Law, Y. Z. & Jaiman, R. K. 2017 Wake stabilization mechanism of low-drag suppression devices for vortex-induced vibration. J. Fluids Struct. 70, 428–449.Google Scholar
Liu, J., Jaiman, R. K. & Gurugubelli, P. S. 2014 A stable second-order scheme for fluid–structure interaction with strong added-mass effects. J. Comput. Phys. 270, 687–710.Google Scholar
Ma, Z., Ahuja, S. & Rowley, C. W. 2011 Reduced-order models for control of fluids using the eigensystem realization algorithm. Theor. Comput. Fluid Dyn. 25 (1–4), 233–247.CrossRefGoogle 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.CrossRefGoogle Scholar
Owen, J. C. & Bearman, P. W. 2001 Passive control of VIV with drag reduction. J. Fluids Struct. 15 (4), 597–605.Google Scholar
Parkin, D. J., Thompson, M. C. & Sheridan, J. 2014 Numerical analysis of bluff body wakes under periodic open-loop control. J. Fluid Mech. 739, 94–123.Google 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.CrossRefGoogle Scholar
Sumer, B. M. & Fredsoe, J. 1997 Hydrodynamics Around Cylindrical Structures. World Scientific Publishing.Google Scholar
Wang, C., Tang, H., Yu, S. C. M., Duan, F., Wang, C., Tang, H., Yu, S. C. M. & Duan, F. 2016 Active control of vortex-induced vibrations of a circular cylinder using windward-suction- leeward-blowing actuation. Phys. Fluids 28, 053601.Google Scholar
Yao, W. & Jaiman, R. K. 2016 A harmonic balance technique for the reduced-order computation of vortex-induced vibration. J. Fluids Struct. 65, 313–332.CrossRefGoogle Scholar
Yao, W. & Jaiman, R. K. 2017 Model reduction and mechanism for the vortex-induced vibrations of bluff bodies. J. Fluid Mech. 827, 357–393.Google Scholar
Yu, Y., Xie, F., Yan, H., Constantinides, Y., Oakley, O. & Karniadakis, G. E. 2015 Suppression of vortex-induced vibrations by fairings: a numerical study. J. Fluids Struct. 54, 679–700.Google Scholar