Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T23:24:04.510Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex synchronization in the cylinder wake due to harmonic and non-harmonic perturbations

Published online by Cambridge University Press:  09 September 2016

Efstathios Konstantinidis  and
Demetri Bouris
Efstathios Konstantinidis*
Affiliation:
Department of Mechanical Engineering, University of Western Macedonia, Kozani 50132, Greece
Demetri Bouris
Affiliation:
School of Mechanical Engineering, National Technical University of Athens, Zografou 15780, Greece
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper reports a numerical study of two-dimensional periodically perturbed flow past a cylinder. Both harmonic and non-harmonic perturbation waveforms of the inflow velocity are considered for a maximum instantaneous Reynolds number of 180. Phase portraits of the lift force are employed to identify the dynamical state of the cylinder wake and determine the range of kinematical parameters for which primary synchronization occurs, that is the regime where vortex formation is phase-locked to the subharmonic of the perturbation frequency. The effect of different perturbation waveforms on the synchronization range and on patterns of vortex formation is examined in detail over the normalized amplitude–frequency space. It is shown that systematic shifts of the synchronization range, towards either higher or lower frequencies, can be attained by imposing different perturbation waveforms. As a consequence, in certain regions of the parameter space it is possible to obtain multiple periodic and/or quasi-periodic wake states for waveforms of exactly the same amplitude and frequency. For the range of parameters where synchronization occurs, different vortex patterns are attained in the wake involving the shedding of solitary and binary vortices, or mixtures thereof, which can be controlled by the perturbation waveform. The phenomenology of these patterns, which result from modification of the basic Kármán mode in the unperturbed wake, is discussed and explained in terms of the generation of circulation that is induced by perturbations in the relative velocity. Vortex patterns from cylinders oscillating either in line with or transverse to a free stream are recast in the framework of the relative velocity.

JFM classification

Aerodynamics: Aerodynamics Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 804 , 10 October 2016 , pp. 248 - 277
Check for updates
Copyright
© 2016 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.)

References

Aissa, M., Bouabdallah, A. & Oualli, H. 2014 Radial deformation frequency effect on the three-dimensional flow in the cylinder wake. Trans. ASME J. Fluids Engng 137 (1), 011104.Google Scholar
Al-Mdallal, Q. M., Lawrence, K. P. & Kocabiyik, S. 2007 Forced streamwise oscillations of a circular cylinder: locked-on modes and resulting fluid forces. J. Fluids Struct. 23 (5), 681–701.Google Scholar
Anagnostopoulos, P. 2000a Numerical study of the flow past a cylinder excited transversely to the incident stream. Part 1: lock-in zone, hydrodynamic forces and wake geometry. J. Fluids Struct. 14 (6), 819–851.Google Scholar
Anagnostopoulos, P. 2000b 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.Google Scholar
Baek, S.-J. & Sung, H. J. 1998 Numerical simulation of the flow behind a rotary oscillating circular cylinder. Phys. Fluids 10 (4), 869–876.Google Scholar
Baek, S.-J. & Sung, H. J. 2000 Quasi-periodicity in the wake of a rotationally oscillating cylinder. J. Fluid Mech. 408, 275–300.Google Scholar
Barbi, C., Favier, D. P., Maresca, C. A. & Telionis, D. P. 1986 Vortex shedding and lock-on of a circular cylinder in oscillatory flow. J. Fluid Mech. 170, 527–544.Google Scholar
Behr, M., Hastreiter, D., Mittal, S. & Tezduyar, T. E. 1995 Incompressible flow past a circular cylinder: dependence of the computed flow field on the location of the lateral boundaries. Comput. Meth. Appl. Mech. Engng 123 (1–4), 309–316.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.Google Scholar
Blevins, R. D. 1985 The effect of sound on vortex shedding from cylinders. J. Fluid Mech. 161, 217–237.Google Scholar
Carberry, J., Sheridan, J. & Rockwell, D. 2005 Controlled oscillations of a cylinder: forces and wake modes. J. Fluid Mech. 538, 31–69.Google Scholar
Detemple-Laake, E. & Eckelmann, H. 1989 Phenomenology of Kármán vortex streets in oscillatory flow. Exp. Fluids 7 (4), 217–227.Google Scholar
Feng, L.-H. & Wang, J.-J. 2014a Modification of a circular cylinder wake with synthetic jet: vortex shedding modes and mechanism. Eur. J. Mech. (B/Fluids) 43, 14–32.Google Scholar
Feng, L.-H. & Wang, J.-J. 2014b The virtual aeroshaping enhancement by synthetic jets with variable suction and blowing cycles. Phys. Fluids 26 (1), 014105.Google Scholar
Feng, L. H., Wang, J. J. & Pan, C. 2010 Effect of novel synthetic jet on wake vortex shedding modes of a circular cylinder. J. Fluids Struct. 26 (6), 900–917.Google Scholar
Gerrard, J. H. 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25, 401–413.Google Scholar
Green, R. B. & Gerrard, J. H. 1993 Vorticity measurements in the near wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 246, 675–691.Google Scholar
Griffin, O. M. 1978 A universal Strouhal number for the locking-on of vortex shedding to the vibrations of bluff cylinders. J. Fluid Mech. 85, 591–606.Google Scholar
Griffin, O. M. 1989 Flow similitude and vortex lock-on in bluff body near wakes. Phys. Fluids A 1 (4), 697–703.Google Scholar
Griffin, O. M. & Hall, M. S. 1991 Vortex shedding lock-on and flow control in bluff body wakes – review. Trans. ASME J. Fluids Engng 113 (4), 526–537.Google Scholar
Griffin, O. M. & Ramberg, S. E. 1974 The vortex-street wakes of vibrating cylinders. J. Fluid Mech. 66, 553–576.CrossRefGoogle Scholar
Griffin, O. M. & Ramberg, S. E. 1976 Vortex shedding from a cylinder vibrating in line with an incident uniform flow. J. Fluid Mech. 75, 257–271.Google Scholar
Gu, W., Chyu, C. & Rockwell, D. 1994 Timing of vortex formation from an oscillating cylinder. Phys. Fluids 6 (11), 3677–3682.Google Scholar
Hall, H. S. & Griffin, O. M. 1993 Vortex shedding and lock-on in a perturbed flow. Trans. ASME J. Fluids Engng 115, 283–291.Google Scholar
Jeon, D. & Gharib, M. 2001 On circular cylinders undergoing two-degree-of-freedom forced motions. J. Fluids Struct. 15 (3–4), 533–541.Google Scholar
Jeon, D. & Gharib, M. 2004 On the relationship between the vortex formation process and cylinder wake vortex patterns. J. Fluid Mech. 519, 161–181.CrossRefGoogle Scholar
Kim, S. H., Park, J. Y., Park, N., Bae, J. H. & Yoo, J. Y. 2009 Direct numerical simulation of vortex synchronization due to small perturbations. J. Fluid Mech. 634, 61–90.Google Scholar
Kim, W., Yoo, J. Y. & Sung, J. 2006 Dynamics of vortex lock-on in a perturbed cylinder wake. Phys. Fluids 18 (7), 074103.Google Scholar
Konstantinidis, E. & Balabani, S. 2007 Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations. J. Fluids Struct. 23 (7), 1047–1063.Google Scholar
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.Google Scholar
Konstantinidis, E., Balabani, S. & Yianneskis, M. 2007 Bimodal vortex shedding in a perturbed cylinder wake. Phys. Fluids 19 (1), 011701.Google Scholar
Konstantinidis, E. & Bouris, D. 2009 Effect of nonharmonic forcing on bluff-body vortex dynamics. Phys. Rev. E 79, 045303.Google Scholar
Konstantinidis, E. & Bouris, D. 2010 The effect of nonharmonic forcing on bluff-body aerodynamics at a low Reynolds number. J. Wind Engng Ind. Aerodyn. 98 (6–7), 245–252.Google Scholar
Konstantinidis, E. & Liang, C. 2011 Dynamic response of a turbulent cylinder wake to sinusoidal inflow perturbations across the vortex lock-on range. Phys. Fluids 23 (7), 075102.Google Scholar
Kumar, S., Lopez, C., Probst, O., Francisco, G., Askari, D. & Yang, Y. 2013 Flow past a rotationally oscillating cylinder. J. Fluid Mech. 735, 307–346.CrossRefGoogle Scholar
Leontini, J. S., Lo Jacono, D. & Thompson, M. C. 2011 A numerical study of an inline oscillating cylinder in a free stream. J. Fluid Mech. 688, 551–568.Google Scholar
Leontini, J. S., Lo Jacono, D. & Thompson, M. C. 2013 Wake states and frequency selection of a streamwise oscillating cylinder. J. Fluid Mech. 730, 162–192.Google Scholar
Leontini, J. S., Stewart, B. E., Thompson, M. C. & Hourigan, K. 2006 Wake state and energy transitions of an oscillating cylinder at low Reynolds number. Phys. Fluids 18 (6), 067101.Google Scholar
Leontini, J. S., Thompson, M. C. & Hourigan, K. 2007 Three-dimensional transition in the wake of a transversely oscillating cylinder. J. Fluid Mech. 577, 79–104.Google Scholar
Liu, Y.-G. & Feng, L.-H. 2015 Suppression of lift fluctuations on a circular cylinder by inducing the symmetric vortex shedding mode. J. Fluids Struct. 54, 743–759.Google Scholar
Lu, X.-Y. & Dalton, C. 1996 Calculation of the timing of vortex formation from an oscillating cylinder. J. Fluids Struct. 10 (5), 527–541.Google Scholar
Marzouk, O. A. & Nayfeh, A. H. 2009 Reduction of the loads on a cylinder undergoing harmonic in-line motion. Phys. Fluids 21 (8), 083103.Google Scholar
Meneghini, J. R. & Bearman, P. W. 1995 Numerical simulation of high amplitude oscillatory flow about a circular cylinder. J. Fluids Struct. 9 (4), 435–455.Google Scholar
Morse, T. L. & Williamson, C. H. K. 2009 Fluid forcing, wake modes, and transitions for a cylinder undergoing controlled oscillations. J. Fluids Struct. 25, 697–712.Google Scholar
Morton, B. R. 1984 The generation and decay of vorticity. Geophys. Astrophys. Fluid Dyn. 28 (3–4), 277–308.Google Scholar
Nazarinia, M., Lo Jacono, D., Thompson, M. C. & Sheridan, J. 2009 Flow behind a cylinder forced by a combination of oscillatory translational and rotational motions. Phys. Fluids 21 (5), 051701.Google Scholar
Ongoren, A. & Rockwell, D. 1988a Flow structure from an oscillating cylinder. Part 1. Mechanisms of phase shift and recovery in the near wake. J. Fluid Mech. 191, 197–223.Google Scholar
Ongoren, A. & Rockwell, D. 1988b Flow structure from an oscillating cylinder. Part 2. Mode competition in the near wake. J. Fluid Mech. 191, 225–245.Google Scholar
Oualli, H., Hanchi, S., Bouabdellah, A., Askovic, R. & Gad-El-Hak, M. 2008 Interaction between the near wake and the cross-section variation of a circular cylinder in uniform flow. Exp. Fluids 44 (5), 807–818.Google Scholar
Papadakis, G. & Bergeles, G. 1995 A locally modified second order upwind scheme for convection terms discretization. Intl J. Numer. Meth. Heat Fluid Flow 5 (1), 49–62.Google Scholar
Patankar, S. V. & Spalding, D. B. 1972 A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Intl J. Heat Mass Transfer 15 (10), 1787–1806.Google Scholar
Perdikaris, P. G., Kaiktsis, L. & Triantafyllou, G. S. 2009 Chaos in a cylinder wake due to forcing at the Strouhal frequency. Phys. Fluids 21 (10), 101705.Google Scholar
Ponta, F. L. & Aref, H. 2005 Vortex synchronization regions in shedding from an oscillating cylinder. Phys. Fluids 17 (1), 011703.Google Scholar
Posdziech, O. & Grundmann, R. 2007 A systematic approach to the numerical calculation of fundamental quantities of the two-dimensional flow over a circular cylinder. J. Fluids Struct. 23 (3), 479–499.Google Scholar
Qu, L., Norberg, C., Davidson, L., Peng, S.-H. & Wang, F. 2013 Quantitative numerical analysis of flow past a circular cylinder at Reynolds number between 50 and 200. J. Fluids Struct. 39, 347–370.Google Scholar
Rhie, C. M. & Chow, W. L. 1983 Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21 (11), 1525–1532.Google Scholar
Roshko, A.1954 On the drag and shedding frequency of two-dimensional bluff bodies. NACA Tech. Note 3169.Google Scholar
Tokumaru, P. T. & Dimotakis, P. E. 1991 Rotary oscillation control of a cylinder wake. J. Fluid Mech. 224, 77–90.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28 (1), 477–539.Google Scholar
Williamson, C. H. K. & Brown, G. L. 1998 A series 1/√Re to respresent the Strouhal–Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12 (8), 1073–1085.Google Scholar
Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355–381.Google Scholar
Xu, S. J., Zhou, Y. & Wang, M. H. 2006 A symmetric binary-vortex street behind a longitudinally oscillating cylinder. J. Fluid Mech. 556, 27–43.Google Scholar
Zdravkovich, M. M. 1996 Different modes of vortex shedding: an overview. J. Fluids Struct. 10 (5), 427–437.Google Scholar
Zdravkovich, M. M. 1982 Modification of vortex shedding in the synchronization range. Trans. ASME J. Fluids Engng 104 (4), 513–517.Google 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.Google Scholar