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Vortex-induced vibrations of a circular cylinder at low Reynolds numbers

Published online by Cambridge University Press:  14 December 2007

T. K. PRASANTH  and
S. MITTAL
T. K. PRASANTH
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, UP 208 016, India
S. MITTAL*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, UP 208 016, India
*
†Author to whom correspondence shoud be addressed: smittal@iitk.ac.in
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Abstract

Results are presented for a numerical simulation of vortex-induced vibrations of a circular cylinder of low non-dimensional mass (m* = 10) in the laminar flow regime (60 < Re < 200). The natural structural frequency of the oscillator, fN, matches the vortex shedding frequency for a stationary cylinder at Re = 100. This corresponds to fND2/ν = 16.6, where D is the diameter of the cylinder and ν the coefficient of viscosity of the fluid. A stabilized space–time finite element formulation is utilized to solve the incompressible flow equations in primitive variables form in two dimensions. Unlike at high Re, where the cylinder response is known to be associated with three branches, at low Re only two branches are identified: ‘initial’ and ‘lower’. For a blockage of 2.5% and less the onset of synchronization, in the lower Re range, is accompanied by an intermittent switching between two modes with vortex shedding occurring at different frequencies. With higher blockage the jump from the initial to lower branch is hysteretic. Results from free vibrations are compared to the data from experiments for forced vibrations reported earlier. Excellent agreement is observed for the critical amplitude required for the onset of synchronization. The comparison brings out the possibility of hysteresis in forced vibrations. The phase difference between the lift force and transverse displacement shows a jump of almost 180° at, approximately, the middle of the synchronization region. This jump is not hysteretic and it is not associated with any radical change in the vortex shedding pattern. Instead, it is caused by changes in the location and value of the maximum suction on the lower and upper surface of the cylinder. This is observed clearly by comparing the time-averaged flow for a vibrating cylinder for different Re. While the mean flow for Re beyond the phase jump is similar to that for a stationary cylinder, it is associated with a pair of counter-rotating vortices in the near wake for Re prior to the phase jump. The phase jump appears to be one of the mechanisms of the oscillator to self-limit its vibration amplitude.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 594 , 10 January 2008 , pp. 463 - 491
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Al Jamal, H. & Dalton, C. 2005 The contrast in phase angles between forced and self-excited oscillations of a circular cylinder. J. Fluids Struct. 20, 467–482.CrossRefGoogle Scholar
Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16, 195–222.CrossRefGoogle Scholar
Bishop, R. E. D. & Hassan, A. Y. 1964 The lift and drag forces on a circular cylinder oscillating in a flowing fluid. Proc. R. Soc. Lond. A 277, 51–75.Google Scholar
Blackburn, H. M & Henderson, R. D. 1999 A study of two-dimensional flow past an oscillating cylinder. J. Fluid Mech. 385, 255–286.CrossRefGoogle Scholar
Brika, D. & Laneville, A. 1993 Vortex induced vibrations of long flexible circular cylinder. J. Fluid Mech. 250, 481–508.CrossRefGoogle Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2001 Forces and wake modes of an oscillating cylinder. J. Fluids Struct. 15, 523–532.CrossRefGoogle Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2005 Controlled oscillations of a cylinder: forces and wake modes. J. Fluid Mech. 538, 31–69.CrossRefGoogle Scholar
Feng, C. C. 1968 The measurement of vortex-induced effects in flow past a stationary and oscillating circular cylinder and d-section cylinders. Master's Thesis, University of British Columbia.Google Scholar
Govardhan, R. & Williamson, C. H. K. 2001 Mean and fluctuating velocity fields in the wake of a freely-vibrating cylinder. J. Fluids Struct. 15, 489–501.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, 85–129.CrossRefGoogle Scholar
Gu, W., Chyu, C. & Rockwell, D. 1994 Timing of vortex formation from an oscillating cylinder. Phys. Fluids 6, 3677–3682.CrossRefGoogle Scholar
Henderson, R. D. 1995 Details of the drag curve near the onset of vortex shedding. Phys. Fluids 7, 2102–2104.CrossRefGoogle Scholar
Khalak, A. & Williamson, C. H. K. 1996 Dynamics of a hydroelastic cylinder with very low mass and damping. J. Fluids Struct. 10, 455–472.CrossRefGoogle Scholar
Khalak, A. & Williamson, C. H. K. 1999 Motion, forces and mode transitions in vortex-induced vibrations at low mass damping. J. Fluids Struct. 13, 813–851.CrossRefGoogle Scholar
Koopmann, G. H. 1967 The vortex wakes of vibrating cylinders at low Reynolds numbers. J. Fluid Mech. 28, 501–512.CrossRefGoogle Scholar
Kumar, B. & Mittal, S. 2006 a Effect of blockage on critical parameters for flow past a circular cylinder. Intl J. Numer. Meth. Fluids. 50, 987–1001.CrossRefGoogle Scholar
Kumar, B. & Mittal, S. 2006 b Prediction of the critical Reynolds number for flow past a circular cylinder. Comput. Meth. Appl. Mech. Engng 195, 6046–6058.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, 857–864.CrossRefGoogle Scholar
Lu, X. Y., Dalton, C. 1996 Calculation of the timing of vortex formation from an oscillating cylinder. J. Fluids Struct. 10, 527–541.CrossRefGoogle Scholar
Mittal, S. 1992 Stabilized space-time finite element formulation for unsteady incompressible flows involving fluid-body interaction. PhD thesis, University of Minnesota.CrossRefGoogle Scholar
Mittal, S. & Kumar, V. 1999 Finite element study of vortex- induced cross-flow and in-line oscillations of a circular cylinder at low Reynolds numbers. Intl J. Numer. Meth. Fluids. 31, 1087–1120.3.0.CO;2-C>CrossRefGoogle Scholar
Mittal, S. & Kumar, V. 2001 Flow induced oscillations of two cylinders in tandem and staggered arrangement. J. Fluids Struct. 15, 717–736.CrossRefGoogle Scholar
Mittal, S. & Singh, S. 2005 Vortex-induced vibrations at subcritical Re. J. Fluid Mech. 534, 185–194.CrossRefGoogle Scholar
Mittal, S. & Tezduyar, T. E. 1992 A finite element study of incompressible flows past a oscillating cylinders and airfoils. Intl J. Numer. Meth. Fluids 15, 1073–1118.CrossRefGoogle Scholar
Norberg, C. 2003 Fluctuating lift on a circular cylinder: review and new measurement. J. Fluids Struct. 17, 57–96.CrossRefGoogle Scholar
Ongoren, A. & Rockwell, D. 1988 a Flow structure from an oscillating cylinder Part 1. Mechanisms of phase shift and recovery in the near wake. J. Fluid Mech. 191, 197–223.CrossRefGoogle Scholar
Ongoren, A. & Rockwell, D. 1988 b Flow structure from an oscillating cylinder Part 2. Mode competition in the near wake. J. Fluid Mech. 191, 225–245.CrossRefGoogle Scholar
Parkinson, G. V. 1989 Phenomena and modelling of flow-induced vibrations of bluff bodies. Prog. Aerospace Sci. 26, 169–224.CrossRefGoogle Scholar
Prasanth, T. K., Behara, S., Singh, S. P., Kumar, R. & Mittal, S. 2006 Effect of blockage on vortex-induced vibrations at low Reynolds numbers. J. Fluids Struct. 22, 865–876.CrossRefGoogle Scholar
Sarpkaya, T. 1979 Vortex-induced oscillations – a selective review. J. Appl. Mech. 46, 241–258.CrossRefGoogle Scholar
Sarpkaya, T. 2004 A critical review of the intrinsic nature of vortex-induced vibrations. J. Fluids Struct. 19, 389–447.CrossRefGoogle Scholar
Singh, S. P. & Mittal, S. 2005 Vortex-induced oscillations at low Reynolds numbers: hysteresis and vortex shedding modes. J. Fluids Struct. 20, 1085–1104.CrossRefGoogle Scholar
Stansby, P. K. 1976 The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows. J. Fluid Mech. 74, 641–665.CrossRefGoogle Scholar
Stewart, B. E., Leontini, J. S., Hourigan, K. & Thompson, M. C. 2005 A numerical survey of wake modes and energy transfers for an oscillating cylinder at Re=200. Fourth Symposium on Bluff Body Wakes and Vortex-Induced Vibrations, Greece (ed. Leweke, T. & Williamson, C. H. K.), pp. 239–242.Google Scholar
Tezduyar, T. E., Behr, M. & Liou, J. 1992 a A new strategy for finite element computations involving moving boundaries and interfaces- the deforming-spatial-domain/space–time procedure, I: the concept and the preliminary tests. Comput. Meth. Appl. Mech. Engng 94, 339–351.CrossRefGoogle Scholar
Tezduyar, T. E., Behr, M., Mittal, S. & Liou, J. 1992 b A new strategy for finite element computations involving moving boundaries and interfaces- the deforming-spatial-domain/space–time procedure, II: computations of free-surface flows, two liquid flows and flows with drifting cylinders. Comput. Meth. Appl. Mech. Engng 94, 353–371.CrossRefGoogle Scholar
Tezduyar, T. E., Mittal, S., Ray, S. E. & Shih, R. 1992 c Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity pressure elements. Comput. Meth. Appl. Mech. Engng 95, 221–242.CrossRefGoogle Scholar
Williamson, C. H. K. & Govardhan, R. 2004 Vortex induced vibration. 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, 355–381.CrossRefGoogle Scholar