Hostname: page-component-76d6cb85b7-dqfph Total loading time: 0 Render date: 2026-07-11T09:39:32.875Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow-induced vibrations of a pitching and plunging airfoil

Published online by Cambridge University Press:  06 January 2020

Z. Wang Open the ORCID record for Z. Wang [Opens in a new window] ,
L. Du ,
J. Zhao Open the ORCID record for J. Zhao [Opens in a new window] ,
M. C. Thompson Open the ORCID record for M. C. Thompson [Opens in a new window]  and
X. Sun
Z. Wang
Affiliation:
School of Energy and Power Engineering, Beihang University, Beijing100191, PR China
L. Du*
Affiliation:
School of Energy and Power Engineering, Beihang University, Beijing100191, PR China
J. Zhao
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC3800, Australia
M. C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC3800, Australia
X. Sun
Affiliation:
School of Energy and Power Engineering, Beihang University, Beijing100191, PR China
*
†Email address for correspondence: lindu@buaa.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow-induced vibration (FIV) of an airfoil freely undergoing two-degrees-of-freedom (2-DOF) motions of plunging and pitching is numerically investigated as a function of the reduced velocity and pivot location in a two-dimensional free-stream flow. This investigation covers a wide parameter space spanning the flow reduced velocity range of $0<U^{\ast }=U/(\,f_{n}c)\leqslant 10$ and the pivot location range of $0\leqslant x\leqslant 1$, where $U$ is the free-stream velocity, $f_{n}$ is the natural frequency of the system set equal in the plunge and pitch directions, $c$ is the chord length of the foil and $x$ is the normalised distance of the pivot point from the leading edge. The numerical simulations were performed by employing an immersed boundary method at a low Reynolds number ($Re=Uc/\unicode[STIX]{x1D708}=400$, with $\unicode[STIX]{x1D708}$ the kinematic viscosity of the fluid). Through detailed analyses of the dynamics of the 2-DOF vibrations and wake states, a variety of FIV response regimes are identified, including four regions showing synchronisation or near-synchronisation responses (labelled as S‐I, S‐II, S‐III and S‐IV) and four transition regimes (labelled as T‐I, T‐II, T‐III and T‐IV) that show intermittent, switching or chaotic responses, in the $x{-}U^{\ast }$ space.

JFM classification

Vortex Flows: Vortex shedding

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A36
Copyright
© 2020 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.)

Article purchase

Temporarily unavailable

References

Ashraf, M. A., Young, J. & Lai, J. C. S. 2011 Numerical analysis of an oscillating-wing wind and hydropower generator. AIAA J. 49 (7), 1374–1386.CrossRefGoogle Scholar
Baranyi, L. & Lewis, R. I. 2006 Comparison of a grid-based CFD method and vortex dynamics predictions of low Reynolds number cylinder flows. Aeronaut. J. 110 (1103), 63–70.CrossRefGoogle Scholar
Bearman, P. W. 1984 Vortex shedding from oscillating bodies. Annu. Rev. Fluid Mech. 16, 195–222.CrossRefGoogle Scholar
Bearman, P. W., Gartshore, I. S., Maull, D. J. & Parkinson, G. V. 1987 Experiments on flow-induced vibration of a square-section cylinder. J. Fluids Struct. 1, 19–34.CrossRefGoogle Scholar
Blevins, P. W. 1990 Flow-Induced Vibration, 2nd edn. Krieger.Google Scholar
Boudreau, M., Dumas, G., Rahimpour, M. & Oshkai, P. 2018 Experimental investigation of the energy extraction by a fully-passive flapping-foil hydrokinetic turbine prototype. J. Fluids Struct. 82, 446–472.CrossRefGoogle Scholar
Bourguet, R. & Lo Jacono, D. 2014 Flow-induced vibrations of a rotating cylinder. J. Fluid Mech. 740, 342–380.CrossRefGoogle Scholar
Cleaver, D. J., Wang, Z. & Gursul, I. 2012 Bifurcating flows of plunging aerofoils at high Strouhal numbers. J. Fluid Mech. 708, 349–376.CrossRefGoogle Scholar
Corless, R. & Parkinson, G. V. 1988 A model of the combined effects of vortex-induced oscillation and galloping. J. Fluids Struct. 2 (3), 203–220.CrossRefGoogle Scholar
Corless, R. M. & Parkinson, G. V. 1993 Mathematical modelling of the combined effects of vortex-induced vibration and galloping. Part II. J. Fluids Struct. 7, 825–848.CrossRefGoogle Scholar
Crawford, J. D. & Knobloch, E. 1991 Symmetry and symmetry-breaking bifurcations in fluid dynamics. Annu. Rev. Fluid Mech. 23 (1), 341–387.CrossRefGoogle Scholar
Deng, J., Teng, L., Pan, D. & Shao, X. 2015 Inertial effects of the semi-passive flapping foil on its energy extraction efficiency. Phys. Fluids 27 (5), 053103.CrossRefGoogle Scholar
Du, L., Sun, X. & Yang, V. 2016a Generation of vortex lift through reduction of rotor/stator gap in turbomachinery. J. Propul. Power 32 (2), 472–485.CrossRefGoogle Scholar
Du, L., Sun, X. & Yang, V. 2016b Vortex-lift mechanism in axial turbomachinery with periodically pitched stators. J. Propul. Power 32 (2), 1–14.CrossRefGoogle Scholar
Duarte, L., Dellinger, N. & Dellinger, G. 2019 Experimental investigation of the dynamic behaviour of a fully passive flapping foil hydrokinetic turbine. J. Fluids Struct. 88, 1–12.CrossRefGoogle Scholar
Gabbai, R. & Benaroya, H. 2005 An overview of modeling and experiments of vortex-induced vibration of circular cylinders. J. Sound Vib. 282 (3), 575–616.CrossRefGoogle Scholar
Graftieaux, L., Michard, M. & Grosjean, N. 2001 Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows. Meas. Sci. Technol. 12, 1422–1429.CrossRefGoogle Scholar
Griffin, O. M., Skop, R. A. & Koopmann, G. H. 1973 The vortex-excited resonant vibrations of circular cylinders. J. Sound Vib. 31 (2), 235–249.CrossRefGoogle Scholar
Kinsey, T. & Dumas, G. 2008 Parametric study of an oscillating airfoil in a power-extraction regime. AIAA J. 46 (6), 1318–1330.CrossRefGoogle Scholar
Leontini, J. S. & Thompson, M. C. 2013 Vortex-induced vibrations of a diamond cross-section: sensitivity to corner sharpness. J. Fluids Struct. 39, 371–390.CrossRefGoogle Scholar
Lu, L., Qin, J. M., Teng, B. & Li, Y. C. 2011 Numerical investigations of lift suppression by feedback rotary oscillation of circular cylinder at low Reynolds number. Phys. Fluids 23 (3), 1–16.Google Scholar
McKinney, W. & DeLaurier, J. 1981 The wingmill: an oscillating-wing windmill. J. Energy 5 (2), 109–115.CrossRefGoogle Scholar
Morse, T. L. & Williamson, C. H. K. 2009 Prediction of vortex-induced vibration response by employing controlled motion. J. Fluid Mech. 634, 5–39.CrossRefGoogle Scholar
Naudascher, E. & Rockwell, D. 2005 Flow-Induced Vibrations: An Engineering Guide. Dover Publications.Google Scholar
Nemes, A., Zhao, J., Lo Jacono, D. & Sheridan, J. 2012 The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack. J. Fluid Mech. 710, 102–130.CrossRefGoogle Scholar
Paidoussis, M. P., Price, S. J. & De Langre, E. 2010 Fluid Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press.CrossRefGoogle Scholar
Peng, Z. & Zhu, Q. 2009 Energy harvesting through flow-induced oscillations of a foil. Phys. Fluids 21 (12), 123602.CrossRefGoogle Scholar
Peskin, C. S. 1972 Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10 (2), 252–271.CrossRefGoogle Scholar
Peskin, C. S. 1977 Numerical analysis of blood flow in the heart. J. Comput. Phys. 25 (3), 220–252.CrossRefGoogle Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Num. 11, 479–517.CrossRefGoogle Scholar
Platzer, M., Ashraf, M., Young, J. & Lai, J. 2010 Extracting power in jet streams: Pushing the performance of flapping-wing technology. In 27th International Congress on Aeronautical Science, Nice, France. ICAS.Google Scholar
Rosenstein, M. T., Collins, J. J. & Luca, C. J. D. 1993 A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65 (1-2), 117–134.CrossRefGoogle Scholar
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19, 389–447.CrossRefGoogle Scholar
Veilleux, J.-C. & Dumas, G. 2017 Numerical optimization of a fully-passive flapping-airfoil turbine. J. Fluids Struct. 70, 102–130.CrossRefGoogle Scholar
Wang, Z., Du, L., Zhao, J. & Sun, X. 2017 Structural response and energy extraction of a fully passive flapping foil. J. Fluids Struct. 72, 96–113.CrossRefGoogle Scholar
Williamson, C. H. K. 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.CrossRefGoogle Scholar
Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2 (4), 355–381.CrossRefGoogle Scholar
Wong, K. W. L., Zhao, J., Lo Jacono, D., Thompson, M. C. & Sheridan, J. 2017 Experimental investigation of flow-induced vibration of a rotating circular cylinder. J. Fluid Mech. 829, 486–511.CrossRefGoogle Scholar
Wong, K. W. L., Zhao, J., Lo Jacono, D., Thompson, M. C. & Sheridan, J. 2018 Experimental investigation of flow-induced vibration of a sinusoidally rotating circular cylinder. J. Fluid Mech. 848, 430–466.CrossRefGoogle Scholar
Xiao, Q. & Zhu, Q. 2014 A review on flow energy harvesters based on flapping foils. J. Fluids Struct. 46, 174–191.CrossRefGoogle Scholar
Young, J., Lai, J. C. & Platzer, M. F. 2014 A review of progress and challenges in flapping foil power generation. Prog. Aerosp. Sci. 67, 2–28.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, 72–102.CrossRefGoogle Scholar
Zhao, J., Hourigan, K. & Thompson, M. C. 2018a Flow-induced vibration of D-section cylinders: an afterbody is not essential for vortex-induced vibration. J. Fluid Mech. 851, 317–343.CrossRefGoogle Scholar
Zhao, J., Leontini, J. S., Lo Jacono, D. & Sheridan, J. 2014 Fluid–structure interaction of a square cylinder at different angles of attack. J. Fluid Mech. 747, 688–721.CrossRefGoogle Scholar
Zhao, J., Lo Jacono, D., Sheridan, J., Hourigan, K. & Thompson, M. C. 2018b Experimental investigation of in-line flow-induced vibration of a rotating cylinder. J. Fluid Mech. 847, 664–699.CrossRefGoogle Scholar
Zhao, J., Nemes, A., Lo Jacono, D. & Sheridan, J. 2018c Branch/mode competition in the flow-induced vibration of a square cylinder. Phil. Trans. R. Soc. Lond. A 376, 20170243.CrossRefGoogle Scholar
Zhu, Q. 2011 Optimal frequency for flow energy harvesting of a flapping foil. J. Fluid Mech. 675, 495–517.CrossRefGoogle Scholar
Zhu, Q. 2012 Energy harvesting by a purely passive flapping foil from shear flows. J. Fluids Struct. 34, 157–169.CrossRefGoogle Scholar

Wang et al. supplementary movie 1

A 2T wake mode observed at $(x, U^*) = (0.50, 1.32)$ in regime S-I.

Download Wang et al. supplementary movie 1(Video)
Video 646.1 KB

Wang et al. supplementary movie 2

A 2P wake mode observed at $(x, U^*) = (0.50, 1.63)$ in regime S-I.

Download Wang et al. supplementary movie 2(Video)
Video 618.6 KB

Wang et al. supplementary movie 3

A 2T wake mode observed at $(x, U^*) = (0.50, 2.87)$ in regime S-I.

Download Wang et al. supplementary movie 3(Video)
Video 670.5 KB

Wang et al. supplementary movie 4

A multiple P (mP) wake mode observed at $(x, U^*) = (0.50, 3.49)$ in regime S-I.

Download Wang et al. supplementary movie 4(Video)
Video 559.9 KB

Wang et al. supplementary movie 5

A P+S wake mode observed at $(x, U^*) = (0.50, 9.07)$ in regime S-III.

Download Wang et al. supplementary movie 5(Video)
Video 632.5 KB

Wang et al. supplementary movie 6

A P+C wake mode observed at $(x, U^*) = (0.35, 9.07)$ in regime S-II.

Download Wang et al. supplementary movie 6(Video)
Video 704.7 KB

Wang et al. supplementary movie 7

A mP+C wake mode observed at $(x, U^*) = (0.85, 9.07)$ in regime S-IV.

Download Wang et al. supplementary movie 7(Video)
Video 667.2 KB

Wang et al. supplementary movie 8

A stable 2(P+2S) mode observed at $(x, U^*) = (0.65, 1.01)$ in regime S-I.

Download Wang et al. supplementary movie 8(Video)
Video 792.6 KB

Wang et al. supplementary movie 9

An unstable 2(P+2S) mode observed at $(x, U^*) = (0.85, 1.32)$ in regime S-I.

Download Wang et al. supplementary movie 9(Video)
Video 798 KB

Wang et al. supplementary movie 10

A stable 2S mode observed at $(x, U^*) = (0.4, 1.32)$ in regime S-I.

Download Wang et al. supplementary movie 10(Video)
Video 593.3 KB

Wang et al. supplementary movie 11

An unstable 2S mode observed at $(x, U^*) = (0.4, 1.63)$ in regime S-I.

Download Wang et al. supplementary movie 11(Video)
Video 669.7 KB

Wang et al. supplementary movie 12

A mix of wake modes observed at $(x, U^*) = (0.65, 1.63)$ in regime S-I.

Download Wang et al. supplementary movie 12(Video)
Video 1 MB