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Vortex dynamics and associated fluid forcing in the near wake of a light and heavy tethered sphere in uniform flow

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Abstract

Time-resolved particle image velocimetry measurements of vortex-induced vibrations of a negatively (“heavy”) and positively (“light”) buoyant tethered sphere in uniform flow, and its wake characteristics were performed in a closed-loop water channel. Experiments for both spheres were performed at similar bulk velocities, ranging between 0.048 < U < 0.32 m/s, corresponding to reduced velocities, 2.2 < U * < 13.5. Initially stationary, with increasing U, the amplitude response displayed periodic oscillations beyond the Hopf bifurcation as a result of “lock-in” between vortex shedding and the natural structural frequency. However, while the heavy sphere’s amplitude decreased beyond U * = 7.0, the light sphere’s amplitude continuously increased. In the periodic oscillation region, flow field characteristics in the wakes of both spheres (at comparable U *) were similar, characterized by alternately shed hairpin vortices having a horizontal symmetry plane. Primary vortex trajectories in the frame of reference of the sphere collapsed for different U * (but not for different m *) when scaled by f 2,s/U, where f 2,s is the sphere’s transverse oscillation frequency. This allows determination of vortex positions based on sphere dynamics and bulk flow conditions only. Associated vortex convection velocities as a function of downstream position from the sphere also nearly collapsed when normalized by U. In addition, fluid forcing and energy transfer from fluid to sphere were estimated based on an analogy between aircraft trailing vortices and hairpin vortices. Maximum forcing occurred at vortex pinch-off. For the highest comparable U *, despite different amplitudes, total transferred energy during one oscillation period was similar for both spheres. Changes in sphere dynamics must therefore be related to differences in inertia.

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References

  • Achenbach E (1974) Vortex shedding from spheres. J Fluid Mech 62:209–221

    Article  Google Scholar 

  • Adrian RJ, Christensen KT, Liu Z-C (2000) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29:275–290

    Article  Google Scholar 

  • Bernitsas MM, Raghavan K, Ben-Simon Y, Garcia EMH (2008) VIVACE (Vortex Induced Vibration Aquatic Clean Energy): a new concept in generation of clean and renewable energy from fluid flow. J Offshore Mech Arctic Eng 130:041101-1–041101-15

    Article  Google Scholar 

  • Blevins RD (2001) Flow induced vibration. Van Nostrand Reinhold, New York

    Google Scholar 

  • Carberry J, Sheridan J (2007) Wake states of a tethered cylinder. J Fluid Mech 592:1–21

    Article  MATH  Google Scholar 

  • David L, Jardin T, Farcy A (2009) On the non-intrusive evaluation of fluid forces with the momentum equation approach. Meas Sci Technol 20:095401

    Article  Google Scholar 

  • Doh DH, Hwang TG, Saga T (2004) 3D-PTV measurements of the wake of a sphere. Meas Sci Technol 15:1059–1066

    Article  Google Scholar 

  • Dong P, Benaroya H, Wei T (2004) Integrating experiments into an energy-based reduced-order model for vortex-induced-vibrations of a cylinder mounted as an inverted pendulum. J Sound Vib 276:45–63

    Article  Google Scholar 

  • Eshbal L, Krakovich A, van Hout R (2012) Time resolved measurements of vortex-induced vibrations of a positively buoyant tethered sphere in uniform water flow. J Fluids Struct 35:185–199

    Article  Google Scholar 

  • Gabbai RD, Benaroya H (2005) An overview of modeling and experiments of vortex-induced vibration of circular cylinders. J Sound Vib 282:575–616

    Article  Google Scholar 

  • Gottlieb O, Habib G (2011) Nonlinear model-based estimation of quadratic and cubic damping mechanisms governing the dynamics of a chaotic spherical pendulum. J Vib Control 21:1–12

    Google Scholar 

  • Govardhan R, Williamson CHK (1997) Vortex-induced motions of a tethered sphere. J Wind Eng Ind Aerodyn 69–71:375–385

    Article  Google Scholar 

  • Govardhan RN, Williamson CHK (2005) Vortex-induced vibrations of a sphere. J Fluid Mech 531:11–47

    Article  MATH  Google Scholar 

  • Jang Y, Joon Lee S (2008) PIV analysis of near-wake behind a sphere at a subcritical Reynolds number. Exp Fluids 44:905–914

    Article  Google Scholar 

  • Jardin T, Chatellier L, Fracy A, David L (2009) Correlation between vortex structures and unsteady loads for flapping motion in hover. Exp Fluids 47:655–664

    Article  Google Scholar 

  • Jauvtis N, Govardhan R, Williamson CHK (2001) Multiple modes of vortex-induced vibration of a sphere. J Fluids Struct 15:555–563

    Article  Google Scholar 

  • Johnson TA, Patel VC (1999) Flow past a sphere up to a Reynolds number of 300. J Fluid Mech 378:19–70

    Article  Google Scholar 

  • Kim HJ, Durbin PA (1988) Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation. Phys Fluids 31:3260–3265

    Article  Google Scholar 

  • Kurtulus DF, Scarano F, David L (2007) Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp Fluids 42:185–196

    Article  Google Scholar 

  • Lee H, Thompson MC, Hourigan K (2008a) Vortex-induced vibrations of a tethered sphere with neutral buoyancy. XXII ICTAM, 25–29 Augustus, Adelaide, Australia

  • Lee H, Thompson MC, Hourigan K (2008b) Flow-induced vibrations of a non-buoyant sphere. In: Proceedings of the 9th international conference on flow-induced vibration, FIV2008, Prague, Czech Republic

  • Lee H, Hourigan K, Thompson MC (2013) Vortex-induced vibration of a neutrally buoyant tethered sphere. J Fluid Mech 719:97–128

    Article  Google Scholar 

  • Leweke T, Provansal M, Ormières D, Lebescond R (1999) Vortex dynamics in the wake of a sphere. Phys Fluids 11:S12

    Google Scholar 

  • Lin J-C, Rockwell D (1996) Force identification by vorticity fields: techniques based on flow imaging. J Fluids Struct 10:663–668

    Article  Google Scholar 

  • Mittal R (1999) Planar symmetry in the unsteady wake of a sphere. AIAA J 37:388–390

    Article  Google Scholar 

  • Morse DR, Liburdy JA (2009) Vortex dynamics and shedding of a low aspect ratio, flat wing at low Reynolds numbers and high angles of attack. J Fluids Eng 131:051202-1–051202-12

    Article  Google Scholar 

  • Naudascher E, Rockwell D (1994) Flow-induced vibrations: and engineering guide. Dover, New York

    Google Scholar 

  • Noca F, Shiels D, Jeon D (1997) Measuring instantaneous fluid dynamic forces on bodies, using only velocity fields and their derivatives. J. Fluids Struct 11:345–350

    Article  Google Scholar 

  • Noca F, Shiels D, Jeon D (1999) A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives. J Fluids Struct 13:551–578

    Article  Google Scholar 

  • Ouellette NT, Xu H, Bodenschatz E (2006) A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp Fluids 40:301–313

    Article  Google Scholar 

  • Ploumhans P, Winckelmans GS, Salmon JK, Leonard A, Warren MS (2002) Vortex methods for direct numerical simulation of three-dimensional bluff body flows: application to the sphere at Re = 300, 500 and 1000. J Comput Phys 178:427–463

    Article  MathSciNet  MATH  Google Scholar 

  • Raffel M, Willert CE, Wereley S, Kompenhans J (2007) Particle image velocimetry: a practical guide, 2nd edn. Springer, Berlin

    Google Scholar 

  • Saffman PG (1992) Vortex dynamics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Sakamoto H, Haniu H (1990) A study on vortex shedding from spheres in a uniform flow. Trans ASME 112:386–392

    Google Scholar 

  • Sarpkaya T (1979) Vortex-induced oscillations: a selective review. J Appl Mech 46:241–258

    Article  Google Scholar 

  • Schouveiler L, Provansal M (2002) Self-sustained oscillations in the wake of a sphere. Phys Fluids 14:3846–3854

    Article  MathSciNet  Google Scholar 

  • Spedding GR, Hedenström A (2009) PIV-based investigations of animal flight. Exp Fluids 46:749–763

    Article  Google Scholar 

  • Unal MF, Lin J-C, Rockwell D (1997) Force prediction by PIV imaging: a momentum-based approach. J Fluids Struct 11:965–971

    Article  Google Scholar 

  • Van Hout R, Krakovich A, Gottlieb O (2010) Time resolved measurements of vortex-induced vibrations of a tethered sphere in uniform flow. Phys Fluids 22:087101-1–087101-11

    Google Scholar 

  • van Hout R, Katz A, Greenblatt D (2012) Acoustic control of vortex-induced vibrations of a tethered sphere. AIAA J 51:754–757

    Article  Google Scholar 

  • van Hout R, Katz A, Greenblatt D (2013) Time-resolved PIV measurements of vortex and shear layer dynamics in the near wake of a tethered sphere. Phys Fluids 25:077102. doi:10.1063/1.4812181

    Article  Google Scholar 

  • Williamson CHK, Govardhan R (1997) Dynamics and forcing of a tethered sphere in a fluid flow. J Fluids Struct 11:293–305

    Article  Google Scholar 

  • Williamson CHK, Govardhan R (2004) Vortex-induced vibrations. Ann Rev Fluid Mech 36:413–455

    Article  MathSciNet  Google Scholar 

  • Wu Y, Christensen KT (2006) Population trends of spanwise vortices in wall turbulence. J Fluid Mech 568:55–76

    Article  MATH  Google Scholar 

  • Yun G, Kim D, Choi H (2006) Vortical structures behind a sphere at subcritical Reynolds numbers. Phys Fluids 18:015102-1–015102-14

    Google Scholar 

  • Zhou J, Adrian RJ, Balachandar S, Kendall TM (1999) Mechanisms for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech 387:353–396

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the Edmund J. Safra Philanthropic Foundation, the Wolfson Family Charitable Trust, the B. and G. Greenberg (Ottowa) Research Fund, and the Technion Fund for Promotion of Research.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    A. Krakovich, L. Eshbal & R. van Hout

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  1. A. Krakovich
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  2. L. Eshbal
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  3. R. van Hout
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Correspondence to R. van Hout.

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Krakovich, A., Eshbal, L. & van Hout, R. Vortex dynamics and associated fluid forcing in the near wake of a light and heavy tethered sphere in uniform flow. Exp Fluids 54, 1615 (2013). https://doi.org/10.1007/s00348-013-1615-2

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  • DOI: https://doi.org/10.1007/s00348-013-1615-2

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