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Vortex dynamics and vibration modes of a tethered sphere

Published online by Cambridge University Press:  18 December 2019

Methma M. Rajamuni Open the ORCID record for Methma M. Rajamuni [Opens in a new window] ,
Mark C. Thompson  and
Kerry Hourigan
Methma M. Rajamuni*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
Mark C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
Kerry Hourigan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC 3800, Australia
*
†Email address for correspondence: methma.rajamuni@monash.edu
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Abstract

The flow-induced vibration of a tethered sphere was investigated through numerical simulations. A determination of the different modes of sphere vibration was made with simulations conducted at fixed Reynolds numbers (500, 1200 and 2000) with a sphere of mass ratio 0.8 over the reduced velocity range $U^{\ast }\in [3,32]$. The flow was governed by the incompressible Navier–Stokes equations, while the dynamic motion of the sphere was governed by coupled Newtonian mechanics. A new fluid–structure interaction (FSI) solver was implemented to efficiently solve the coupled FSI system. The effect of Reynolds number was found to be significant in the mode I and II regimes. A progressive increase in the response amplitude was observed as the Reynolds number was increased, especially in the mode II regime. The overall sphere response at the highest Reynolds number was relatively close to the observed behaviour of previous higher-$Re$ experimental studies. An aperiodic mode IV response was observed at higher reduced velocities beyond the mode II range in each case, without the intervening mode III regime. However, as the mass ratio increased from 0.8 to 80, the random response of the sphere (mode IV) gradually became more regular, showing a mode III response (characterized by a near-periodic sphere oscillation) at $U^{\ast }=30$. Thus, if the inertia of the system is low, mode IV appears at lower $U^{\ast }$ values, while for high-inertia systems, mode IV appears at high $U^{\ast }$ values beyond a mode III response.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A10
Copyright
© 2019 Cambridge University Press

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References

Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16 (1), 195–222.CrossRefGoogle Scholar
Behara, S., Borazjani, I. & Sotiropoulos, F. 2011 Vortex-induced vibrations of an elastically mounted sphere with three degrees of freedom at Re = 300: hysteresis and vortex shedding modes. J. Fluid Mech. 686, 426–450.CrossRefGoogle Scholar
Behara, S. & Sotiropoulos, F. 2016 Vortex-induced vibrations of an elastically mounted sphere: the effects of Reynolds number and reduced velocity. J. Fluids Struct. 66, 54–68.CrossRefGoogle Scholar
Blackburn, H. & Henderson, R. 1996 Lock-in behavior in simulated vortex-induced vibration. Exp. Therm. Fluid Sci. 12 (2), 184–189.CrossRefGoogle Scholar
Blevins, R. D. 1977 Flow-Induced Vibration. Van Nostrand Reinhold.Google Scholar
Borazjani, I., Ge, L. & Sotiropoulos, F. 2008 Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J. Comput. Phys. 227 (16), 7587–7620.CrossRefGoogle ScholarPubMed
Brücker, C. 2001 Spatio-temporal reconstruction of vortex dynamics in axisymmetric wakes. J. Fluids Struct. 15 (3–4), 543–554.CrossRefGoogle Scholar
Causin, P., Gerbeau, J. & Nobile, F. 2005 Added-mass effect in the design of partitioned algorithms for fluid–structure problems. Comput. Meth. Appl. Mech. Engng 194 (42–44), 4506–4527.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Weber, M. E. 2005 Bubbles, Drops, and Particles. Courier Corporation.Google Scholar
Coulombe-Pontbriand, P. & Nahon, M. 2009 Experimental testing and modeling of a tethered spherical aerostat in an outdoor environment. J. Wind Engng Ind. Aerodyn. 97 (5), 208–218.CrossRefGoogle Scholar
Eshbal, L., Krakovich, A. & Hout, R. V. 2012 Time resolved measurements of vortex-induced vibrations of a positively buoyant tethered sphere in uniform water flow. J. Fluids Struct. 35, 185–199.CrossRefGoogle Scholar
Gottlieb, O. 1997 Bifurcations of a nonlinear small-body ocean-mooring system excited by finite-amplitude waves. Trans. ASME J. Offshore Mech. Arctic Engng 119, 234–238.CrossRefGoogle Scholar
Govardhan, R. & Williamson, C. H. K. 1997 Vortex-induced motions of a tethered sphere. J. Wind Engng Ind. Aerodyn. 69, 375–385.CrossRefGoogle Scholar
Govardhan, R. & Williamson, C. H. K. 2000 Modes of vortex formation and frequency response of a freely vibrating cylinder. J. Fluid Mech. 420, 85–130.CrossRefGoogle Scholar
Govardhan, R. N. & Williamson, C. H. K. 2005 Vortex-induced vibrations of a sphere. J. Fluid Mech. 531, 11–47.CrossRefGoogle Scholar
Harleman, D. R. F. & Shapiro, W. C. 1960 The dynamics of a submerged moored sphere in oscillatory waves. Coast. Engng Proc. 1 (7), 41.CrossRefGoogle Scholar
Hout, R. V., Krakovich, A. & Gottlieb, O. 2010 Time resolved measurements of vortex-induced vibrations of a tethered sphere in uniform flow. Phys. Fluids 22 (8), 087101.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Studying Turbulence Using Numerical Simulation Databases, 2. Stanford University.Google Scholar
Issa, R. I. 1986 Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62 (1), 40–65.CrossRefGoogle Scholar
Jasak, H.1995 Error analysis and estimation in the finite volume method with applications to fluid flows. PhD thesis, Imperial College London.Google Scholar
Jasak, H., Weller, H. G. & Gosman, A. D. 1999 High resolution NVD differencing scheme for arbitrarily unstructured meshes. Intl J. Numer. Meth. Fluids 31, 431–449.3.0.CO;2-T>CrossRefGoogle Scholar
Jauvtis, N., Govardhan, R. & Williamson, C. H. K. 2001 Multiple modes of vortex-induced vibration of a sphere. J. Fluids Struct. 15 (3), 555–563.CrossRefGoogle Scholar
Le Tallec, P. & Mouro, J. 2001 Fluid structure interaction with large structural displacements. Comput. Meth. Appl. Mech. Engng 190 (24–25), 3039–3067.CrossRefGoogle Scholar
Lee, H., Hourigan, K. & Thompson, M. C. 2013 Vortex-induced vibration of a neutrally buoyant tethered sphere. J. Fluid Mech. 719, 97–128.CrossRefGoogle Scholar
Leonard, B. P. 1991 The ultimate conservative difference scheme applied to unsteady one-dimensional advection. Comput. Meth. Appl. Mech. Engng 88, 17–74.CrossRefGoogle Scholar
Leontini, J. S., Thompson, M. C. & Hourigan, K. 2006 The beginning of branching behaviour of vortex-induced vibration during two-dimensional flow. J. Fluids Struct. 22 (6), 857–864.CrossRefGoogle Scholar
Lighthill, J. 1986 Wave loading on offshore structures. J. Fluid Mech. 173, 667–681.CrossRefGoogle Scholar
Mittal, R. 1999 A Fourier–Chebyshev spectral collocation method for simulating flow past spheres and spheroids. Intl J. Numer. Meth. Fluids 30 (7), 921–937.3.0.CO;2-3>CrossRefGoogle Scholar
Morsi, S. A. & Alexander, A. J. 1972 An investigation of particle trajectories in two-phase flow systems. J. Fluid Mech. 55, 193–208.CrossRefGoogle Scholar
Naudascher, E. & Rockwell, D. 2012 Flow-Induced Vibrations: An Engineering Guide. Courier Corporation.Google Scholar
Parkinson, G. 1989 Phenomena and modelling of flow-induced vibrations of bluff bodies. Prog. Aerosp. Sci. 26 (2), 169–224.CrossRefGoogle Scholar
Poon, E., Iaccarino, G., Ooi, A. S. H. & Giacobello, M. 2009 Numerical studies of high Reynolds number flow past a stationary and rotating sphere. In Proceedings of the 7th International Conference on CFD in the Minerals and Process Industries. CSIRO.Google Scholar
Poon, E. K. W., Ooi, A. S. H., Giacobello, M., Iaccarino, G. & Chung, D. 2014 Flow past a transversely rotating sphere at Reynolds numbers above the laminar regime. J. Fluid Mech. 759, 751–781.CrossRefGoogle Scholar
Rajamuni, M. M., Thompson, M. C. & Hourigan, K. 2019 Efficient FSI solvers for multiple-degrees-of-freedom flow-induced vibration of a rigid body. Comput. Fluids. 104340.Google Scholar
Rajamuni, M. M., Thompson, M. C. & Hourigan, K. 2016 Vortex induced vibration of rotating spheres. In 20th Australasian Fluid Mechanics Conference Perth, Australia. The University of Melbourne.Google Scholar
Rajamuni, M. M., Thompson, M. C. & Hourigan, K. 2018a Transverse flow-induced vibrations of a sphere. J. Fluid Mech. 837, 931–966.CrossRefGoogle Scholar
Rajamuni, M. M., Thompson, M. C. & Hourigan, K. 2018b Vortex-induced vibration of a transversely rotating sphere. J. Fluid Mech. 847, 786–820.CrossRefGoogle Scholar
Rao, A., Passaggia, P. Y., Bolnot, H., Thompson, M. C., Leweke, T. & Hourigan, K. 2012 Transition to chaos in the wake of a rolling sphere. J. Fluid Mech. 695, 135–148.CrossRefGoogle Scholar
Roos, F. W. & Willmarth, W. W. 1971 Some experimental results on sphere and disk drag. AIAA J. 9 (2), 285–291.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
Sakamoto, H. & Haniu, H. 1990 A study on votex shedding from sphere in a uniform flow. Trans. ASME 112, 386–392.Google Scholar
Sareen, A., Zhao, J., Lo Jacono, D., Sheridan, J., Hourigan, K. & Thompson, M. C. 2018a Vortex-induced vibration of a rotating sphere. J. Fluid Mech. 837, 258–292.CrossRefGoogle Scholar
Sareen, A., Zhao, J., Lo Jacono, D., Sheridan, J., Hourigan, K. & Thompson, M. C. 2018b Vortex-induced vibrations of a sphere close to a free surface. J. Fluid Mech. 846, 1023–1058.CrossRefGoogle Scholar
Sareen, A., Zhao, J., Sheridan, J., Hourigan, K. & Thompson, M. C. 2018c The effect of imposed rotary oscillation on the flow-induced vibration of a sphere. J. Fluid Mech. 855, 703–735.CrossRefGoogle Scholar
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19 (4), 389–447.CrossRefGoogle Scholar
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Schmid, P. J. 2011 Application of the dynamic mode decomposition to experimental data. Exp. Fluids 50 (4), 1123–1130.CrossRefGoogle Scholar
Schmid, P. J. & Sesterhenn, J. L. 2008 Dynamic mode decomposition of numerical and experimental data. Bull. Am. Phys. Soc. 53, 15.Google Scholar
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2003 From spheres to circular cylinders: the stability and flow structures of bluff ring wakes. J. Fluid Mech. 492, 147–180.CrossRefGoogle Scholar
Sheard, G. J., Thompson, M. C. & Hourigan, K. 2004 From spheres to circular cylinders: non-axisymmetric transitions in the flow past rings. J. Fluid Mech. 506, 45–78.CrossRefGoogle Scholar
Shi-Igai, H. & Kono, T. 1969 Study on vibration of submerged spheres caused by surface waves. Coast. Engng J. 12, 29–40.CrossRefGoogle Scholar
Stewart, B. E., Thompson, M. C., Leweke, T. & Hourigan, K. 2010 Numerical and experimental studies of the rolling sphere wake. J. Fluid Mech. 643, 137–162.CrossRefGoogle Scholar
Thompson, M. C., Hourigan, K., Cheung, A. & Leweke, T. 2006 Hydrodynamics of a particle impact on a wall. Appl. Math. Model. 30 (11), 1356–1369.CrossRefGoogle Scholar
Thompson, M. C., Leweke, T. & Provansal, M. 2001 Kinematics and dynamics of sphere wake transition. J. Fluids Struct. 15 (3/4), 575–585.CrossRefGoogle Scholar
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 45–73.CrossRefGoogle Scholar
White, F. M. 2011 Fluid Mechanics, 7th edn. McGraw Hill.Google Scholar
Williamson, C. H. K. & Govardhan, R. 1997 Dynamics and forcing of a tethered sphere in a fluid flow. J. Fluids Struct. 11 (3), 293–305.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. & Govardhan, R. 2008 A brief review of recent results in vortex-induced vibrations. J. Wind Engng Ind. Aerodyn. 96 (6), 713–735.CrossRefGoogle Scholar
Wu, X., Ge, F. & Hong, Y. 2012 A review of recent studies on vortex-induced vibrations of long slender cylinders. J. Fluids Struct. 28, 292–308.CrossRefGoogle Scholar

Rajamuni et al. supplementary movie 1

Vortex-induced vibration of the sphere at Re = 500 and U* = 6

Download Rajamuni et al. supplementary movie 1(Video)
Video 8.7 MB

Rajamuni et al. supplementary movie 2

Vortex-induced vibration of the sphere at Re = 500 and U* = 9

Download Rajamuni et al. supplementary movie 2(Video)
Video 9 MB

Rajamuni et al. supplementary movie 3

Vortex-induced vibration of the sphere at Re = 1200 and U* = 9

Download Rajamuni et al. supplementary movie 3(Video)
Video 5.9 MB