Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-19T16:03:07.376Z Has data issue: false hasContentIssue false

Stability analysis of passive suppression for vortex-induced vibration

Published online by Cambridge University Press:  14 January 2020

S. R. Bukka*
Affiliation:
Department of Civil and Environmental Engineering, National University of Singapore, Republic of Singapore
A. R. Magee
Affiliation:
Department of Civil and Environmental Engineering, National University of Singapore, Republic of Singapore
R. K. Jaiman*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Republic of Singapore
*
Email address for correspondence: sandeep@u.nus.edu
Present address: University of British Columbia, Vancouver, BC, V6T 1Z4, Canada

Abstract

In this paper, we present a stability analysis of passive suppression devices for the vortex-induced vibration (VIV) in the laminar flow condition. A data-driven model reduction approach based on the eigensystem realization algorithm is used to construct a reduced-order model in a state-space format. From the stability analysis of the coupled system, two modes are found to be dominant in the phenomenon of self-sustained VIV: namely, the wake mode, with frequency close to that of the wake flow behind a stationary cylinder; and the structure mode, with frequency close to the natural frequency of the elastically mounted cylinder. The present study illustrates that VIV can be suppressed by altering the structure mode via shifting of the eigenvalues from the unstable to the stable region. This finding is realized through the simulations of passive control devices, such as fairings and connected-C devices, wherein the presence of appendages breaks the self-sustenance of the wake–body interaction cycle. A detailed proper orthogonal decomposition analysis is employed to quantify the effect of a fairing on the complex interaction between the wake features. From the assessment of the stability characteristics of appendages, the behaviour of a connected-C device is found to be similar to that of a fairing, and the trajectories of the eigenspectrum are nearly identical, while the eigenspectrum of the cylinder–splitter arrangement indicates a galloping behaviour at higher reduced velocities. Finally, we introduce a stability function to characterize the influence of geometric parameters on VIV suppression.

Type
JFM Papers
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

Allen, D. W., Lee, L., Henning, D. et al. 2008 Fairings versus helical strakes for suppression of vortex-induced vibration: technical comparisons. In Offshore Technology Conference. Offshore Technology Conference.Google Scholar
Baarholm, R., Skaugset, K., Lie, H. & Braaten, H. 2015 Experimental studies of hydrodynamic properties and screening of riser fairing concepts for deep water applications. In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering, p. V002T08A054. American Society of Mechanical Engineers.Google Scholar
Bearman, P. W. 2011 Circular cylinder wakes and vortex-induced vibrations. J. Fluids Struct. 27 (5), 648658.CrossRefGoogle Scholar
Blevins, R. D. & Scanlan, R. H. 1977 Flow-induced vibration. Trans. ASME J. Appl. Mech. 44, 802.CrossRefGoogle Scholar
Chen, M., Liu, X., Liu, F. & Lou, M.2018 Optimal design of two-dimensional riser fairings for vortex-induced vibration suppression based on genetic algorithm. arXiv:1801.03792.Google Scholar
Donea, J. 1983 Arbitrary Lagrangian–Eulerian finite element methods. In Computational Methods for Transient Analysis, pp. 474516. North-Holland.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, 4178.CrossRefGoogle 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), 023012.Google ScholarPubMed
Jaiman, R., Geubelle, P., Loth, E. & Jiao, X. 2011 Transient fluid–structure interaction with non-matching spatial and temporal discretizations. Comput. Fluids 50 (1), 120135.CrossRefGoogle Scholar
Jaiman, R. K., Guan, M. Z. & Miyanawala, T. P. 2016a Partitioned iterative and dynamic subgrid-scale methods for freely vibrating square-section structures at subcritical Reynolds number. Comput. Fluids 133, 6889.CrossRefGoogle Scholar
Jaiman, R. K., Pillalamarri, N. R. & Guan, M. Z. 2016b A stable second-order partitioned iterative scheme for freely vibrating low-mass bluff bodies in a uniform flow. Comput. Meth. Appl. Mech. Engng 301, 187215.CrossRefGoogle Scholar
Juang, J.-N. & Pappa, R. S. 1985 An eigensystem realization algorithm for modal parameter identification and model reduction. J. Guid. 8 (5), 620627.CrossRefGoogle Scholar
Khalak, A. & Williamson, C. H. K. 1999 Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping. J. Fluids Struct. 13 (7–8), 813851.CrossRefGoogle Scholar
Kim, H. & Chang, K. 1995 Numerical study on vortex shedding from a circular cylinder influenced by a nearby control wire. Comput. Fluid Dyn. J. 4, 151164.Google Scholar
Kuhl, E., Askes, H. & Steinmann, P. 2004 An ale formulation based on spatial and material settings of continuum mechanics. Part 1. Generic hyperelastic formulation. Comput. Meth. Appl. Mech. Engng 193 (39), 42074222.CrossRefGoogle Scholar
Law, Y. Z. & Jaiman, R. K. 2017 Wake stabilization mechanism of low-drag suppression devices for vortex-induced vibration. J. Fluids Struct. 70, 428449.CrossRefGoogle Scholar
Liu, B. & Jaiman, R. K. 2016 Interaction dynamics of gap flow with vortex-induced vibration in side-by-side cylinder arrangement. Phys. Fluids 28 (12), 127103.CrossRefGoogle 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, 687710.CrossRefGoogle 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), 233247.CrossRefGoogle Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221252.CrossRefGoogle Scholar
Meliga, P. & Chomaz, J.-M. 2011 An asymptotic expansion for the vortex-induced vibrations of a circular cylinder. J. Fluid Mech. 671, 137167.CrossRefGoogle Scholar
Mittal, S. & Raghuvanshi, A. 2001 Control of vortex shedding behind circular cylinder for flows at low Reynolds numbers. Intl J. Numer. Meth. Fluids 35 (4), 421447.3.0.CO;2-M>CrossRefGoogle Scholar
Miyanawala, T. P. & Jaiman, R. K. 2019 Decomposition of wake dynamics in fluid–structure interaction via low-dimensional models. J. Fluid Mech. 867, 723764.CrossRefGoogle Scholar
Mysa, R. C., Kaboudian, A. & Jaiman, R. K. 2016 On the origin of wake-induced vibration in two tandem circular cylinders at low Reynolds number. J. Fluids Struct. 61, 7698.CrossRefGoogle Scholar
Rowley, C. W. & Dawson, S. T. M. 2017 Model reduction for flow analysis and control. Annu. Rev. Fluid Mech. 49, 387417.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. I. Coherent structures. Q. Appl. Maths 45 (3), 561571.CrossRefGoogle Scholar
Taira, K., Brunton, S. L., Dawson, S., 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), 40134041.CrossRefGoogle Scholar
Yao, W. & Jaiman, R. K. 2017a Feedback control of unstable flow and vortex-induced vibration using the eigensystem realization algorithm. J. Fluid Mech. 827, 394414.CrossRefGoogle Scholar
Yao, W. & Jaiman, R. K. 2017b Model reduction and mechanism for the vortex-induced vibrations of bluff bodies. J. Fluid Mech. 827, 357393.CrossRefGoogle Scholar
Zhang, W., Li, X., Ye, Z. & Jiang, Y. 2015 Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers. J. Fluid Mech. 783, 72102.CrossRefGoogle Scholar