Abstract
Vortex-induced vibrations of a pivoted cylinder are investigated experimentally at a fixed Reynolds number of 3100, a mass ratio of 10.8, and a range of reduced velocities, \(4.42 \le U^* \le 9.05\). For these conditions, the cylinder traces elliptic trajectories, with the experimental conditions producing three out of four possible combinations of orbiting direction and primary axis alignment relative to the incoming flow. The study focuses on the quantitative analysis of wake topology and its relation to this type of structural response. Velocity fields were measured using time-resolved, two-component particle image velocimetry (TR-PIV). These results show that phase-averaged wake topology generally agrees with the Morse and Williamson (J Fluids Struct 25(4):697–712, 2009) shedding map for one-degree-of-freedom vortex-induced vibrations, with 2S, \(2{\hbox {P}}_{\mathrm{o}}\), and 2P shedding patterns observed within the range of reduced velocities studied here. Vortex tracking and vortex strength quantification are used to analyze the vortex shedding process and how it relates to cylinder response. In the case of 2S vortex shedding, vortices are shed when the cylinder is approaching the maximum transverse displacement and reaches the streamwise equilibrium. 2P vortices are shed approximately half a period earlier in the cylinder’s elliptic trajectory. Leading vortices shed immediately after the peak in transverse oscillation and trailing vortices shed near the equilibrium of transverse oscillation. The orientation and direction of the cylinder’s elliptic trajectory are shown to influence the timing of vortex shedding, inducing changes in the 2P wake topology.
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References
Anagnostopoulos P (2000) Numerical study of the flow past a cylinder excited transversely to the incident stream. Part 2: timing of vortex shedding, aperiodic phenomena and wake parameters. J Fluids Struct 14(6):853–882
Bearman PW (1984) Vortex shedding from oscillating bluff bodies. Annu Rev Fluid Mech 16(1):195–222
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 Arct Eng 130(4):041101
Bilmes JA (1998) A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models. Int Comput Sci Inst 4(510):126
Blevins RD, Coughran CS (2009) Experimental investigation of vortex-induced vibration in one and two dimensions with variable mass, damping, and Reynolds number. J Fluids Eng 131(10):101202
Cagney N, Balabani S (2013) Wake modes of a cylinder undergoing free streamwise vortex-induced vibrations. J Fluids Struct 38:127–145
Cagney N, Balabani S (2014) Streamwise vortex-induced vibrations of cylinders with one and two degrees of freedom. J Fluid Mech 758:702–727
Chong MS, Perry AE, Cantwell BJ (1990) A general classification of threedimensional flow fields. Phys Fluids A 2(5):765–777
Every M, King R, Weaver D (1982) Vortex-excited vibrations of cylinders and cables and their suppression. Ocean Eng 9(2):135–157
Feng CC (1968) The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section cylinders. Masters in applied science thesis, University of British Columbia
Flemming F, Williamson C (2005) Vortex-induced vibrations of a pivoted cylinder. J Fluid Mech 522:215–252
Govardhan R, Williamson CHK (2000) Modes of vortex formation and frequency response of a freely vibrating cylinder. J Fluid Mech 420:85–130
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(9):1422–1429
Green MA, Rowley CW, Haller G (2007) Detection of Lagrangian coherent structures in three-dimensional turbulence. J Fluid Mech 572:111–120
Hsieh SC, Low YM, Chiew YM (2017) Flow characteristics around a circular cylinder undergoing vortex-induced vibration in the initial branch. Ocean Eng 129:265–278
Huang Y, Green MA (2015) Detection and tracking of vortex phenomena using Lagrangian coherent structures. Exp Fluids 56(7):147
Hunt JC, Wray AA, Moin P (1988) Eddies, streams, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88, pp 193–208
Jauvtis N, Williamson CHK (2004) The effect of two degrees of freedom on vortex-induced vibration at low mass and damping. J Fluid Mech 509:23–62
Jeon D, Gharib M (2004) On the relationship between the vortex formation process and cylinder wake vortex patterns. J Fluid Mech 519:161–181
Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94
Khalak A, Williamson C (1999) Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping. J Fluids Struct 13(7–8):813–851
Kheirkhah S, Yarusevych S, Narasimhan S (2012) Orbiting response in vortex-induced vibrations of a two-degree-of-freedom pivoted circular cylinder. J Fluids Struct 28:343–358
Kheirkhah S, Yarusevych S, Narasimhan S (2016) Wake topology of a cylinder undergoing vortex-induced vibrations with elliptic trajectories. J Fluids Eng 138(5):054501
Kim J, Moin P, Moser R (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech 177:133–166
Konstantinidis E, Balabani S, Yianneskis M (2005) The timing of vortex shedding in a cylinder wake imposed by periodic inflow perturbations. J Fluid Mech 543:45–55
Leong C, Wei T (2008) Two-degree-of-freedom vortex-induced vibration of a pivoted cylinder below critical mass ratio. Proc R Soc A Math Phys Eng Sci 464(2099):2907–2927
Moin P, Kim J (1985) The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlations. J Fluid Mech 155:441–464
Morse T, Williamson C (2009) Fluid forcing, wake modes, and transitions for a cylinder undergoing controlled oscillations. J Fluids Struct 25(4):697–712
Morton BR (1984) The generation and decay of vorticity. Geophys Astrophys Fluid Dyn 28(3–4):277–308
Morton C, Yarusevych S (2014) On vortex shedding from low aspect ratio dual step cylinders. J Fluids Struct 44:251–269
Oviedo-Tolentino F, Pérez-Gutiérrez F, Romero-Méndez R, Hernández-Guerrero A (2014) Vortex-induced vibration of a bottom fixed flexible circular beam. Ocean Eng 88:463–471
Perrin R, Braza M, Cid E, Cazin S, Barthet A, Sevrain A, Mockett C, Thiele F (2007) Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD. Exp Fluids 43(2–3):341–355
Perry aE, Chong MS, Lim TT (1982) The vortex-shedding process behind two-dimensional bluff bodies. J Fluid Mech 116:77–90
Rockwood MP, Taira K, Green MA (2017) Detecting vortex formation and shedding in cylinder wakes using Lagrangian coherent structures. AIAA J 55(1):15–23
Sanchis A, Sælevik G, Grue J (2008) Two-degree-of-freedom vortex-induced vibrations of a spring-mounted rigid cylinder with low mass ratio. J Fluids Struct 24(6):907–919
Sarpkaya T (2004) A critical review of the intrinsic nature of vortex-induced vibrations. J Fluids Struct 19(4):389–447
Srinil N, Zanganeh H (2012) Modelling of coupled cross-flow/in-line vortex-induced vibrations using double Duffing and van der Pol oscillators. Ocean Eng 53:83–97
van Oudheusden BW, Scarano F, van Hinsberg NP, Watt DW (2005) Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence. Exp Fluids 39(1):86–98
Wieneke B (2015) PIV uncertainty quantification from correlation statistics. Meas Sci Technol 26(7):074002
Williamson C, Govardhan R (2004) Vortex-induced vibrations. Annu Rev Fluid Mech 36(1):413–455
Williamson C, Roshko A (1988) Vortex formation in the wake of an oscillating cylinder. J Fluids Struct 2(4):355–381
Williamson CHK (1996) Vortex dynamics in the cylinder wake. Annu Rev Fluid Mech 28(1):477–539
Wu Y, Christensen KT (2006) Population trends of spanwise vortices in wall turbulence. J Fluid Mech 568:55–76
Xu L, Jordan MI (1996) On convergence properties of the EM algorithm for Gaussian mixtures. Neural Comput 8(1):129–151
Zdravkovich M (1981) Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding. J Wind Eng Ind Aerodyn 7(2):145–189
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
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The authors gratefully acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) for funding this work.
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Marble, E., Morton, C. & Yarusevych, S. Vortex dynamics in the wake of a pivoted cylinder undergoing vortex-induced vibrations with elliptic trajectories. Exp Fluids 59, 78 (2018). https://doi.org/10.1007/s00348-018-2530-3
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DOI: https://doi.org/10.1007/s00348-018-2530-3