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Modes of synchronisation in the wake of a streamwise oscillatory cylinder

  • Guoqiang Tang (a1), Liang Cheng (a1) (a2), Feifei Tong (a2), Lin Lu (a1) and Ming Zhao (a3)...


A numerical analysis of flow around a circular cylinder oscillating in-line with a steady flow is carried out over a range of driving frequencies $(f_{d})$ at relatively low amplitudes $(A)$ and a constant Reynolds number of 175 (based on the free-stream velocity). The vortex shedding is investigated, especially when the shedding frequency $(f_{s})$ synchronises with the driving frequency. A series of modes of synchronisation are presented, which are referred to as the $p/q$ modes, where $p$ and $q$ are natural numbers. When a $p/q$ mode occurs, $f_{s}$ is detuned to $(p/q)f_{d}$ , representing the shedding of $p$ pairs of vortices over $q$ cycles of cylinder oscillation. The $p/q$ modes are further characterised by the periodicity of the transverse force over every $q$ cycles of oscillation and a spatial–temporal symmetry possessed by the global wake. The synchronisation modes $(p/q)$ with relatively small natural numbers are less sensitive to the change of external control parameters than those with large natural numbers, while the latter is featured with a narrow space of occurrence. Although the mode of synchronisation can be almost any rational ratio (as shown for $p$ and $q$ smaller than 10), the probability of occurrence of synchronisation modes with $q$ being an even number is much higher than $q$ being an odd number, which is believed to be influenced by the natural even distribution of vortices in the wake of a stationary cylinder.


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Al-Mdallal, Q., Lawrence, K. & Kocabiyik, S. 2007 Forced streamwise oscillations of a circular cylinder: locked-on modes and resulting fluid forces. J. Fluids Struct. 23, 681701.
Anagnostopoulos, P. 2000 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, 819851.
Baek, S.-J. & Sung, H. J. 2000 Quasi-periodicity in the wake of a rotationally oscillating cylinder. J. Fluid Mech. 408, 275300.
Barbi, C., Favier, D., Maresca, C. & Telionis, D. 1986 Vortex shedding and lock-on of a circular cylinder in oscillatory flow. J. Fluid Mech. 170, 527544.
Bishop, R. & Hassan, A. 1964 The lift and drag forces on a circular cylinder oscillating in a flowing fluid. Proc. R. Soc. Lond. A 277, 5175.
Blackburn, H. M. & Henderson, R. D. 1999 A study of two-dimensional flow past an oscillating cylinder. J. Fluid Mech. 385, 255286.
Cantwell, C., Moxey, D., Comerford, A., Bolis, A., Rocco, G., Mengaldo, G., DE GRAZIA, D., Yakovlev, S., Lombard, J.-E. & Ekelschot, D. 2015 Nektar + +: an open-source spectral/hp element framework. Comput. Phys. Commun. 192, 205219.
Carberry, J., Sheridan, J. & Rockwell, D. 2005 Controlled oscillations of a cylinder: forces and wake modes. J. Fluid Mech. 538, 3169.
Cetiner, O. & Rockwell, D. 2001 Streamwise oscillations of a cylinder in a steady current. Part 1. Locked-on states of vortex formation and loading. J. Fluid Mech. 427, 128.
D’Adamo, J., Godoy-Diana, R. & Wesfreid, J. E. 2011 Spatiotemporal spectral analysis of a forced cylinder wake. Phys. Rev. E 84, 056308.
Detemple-Laake, E. & Eckelmann, H. 1989 Phenomenology of Kármán vortex streets in oscillatory flow. Exp. Fluids 7, 217227.
Griffin, O. M. & Hall, M. 1991 Review – vortex shedding lock-on and flow control in bluff body wakes. J. Fluids Engng 113, 526537.
Griffin, O. M. & Ramberg, S. E. 1974 The vortex-street wakes of vibrating cylinders. J. Fluid Mech. 66, 553576.
Griffin, O. M. & Ramberg, S. E. 1976 Vortex shedding from a cylinder vibrating in line with an incident uniform flow. J. Fluid Mech. 75, 257271.
Jiang, H., Cheng, L., Draper, S., An, H. & Tong, F. 2016 Three-dimensional direct numerical simulation of wake transitions of a circular cylinder. J. Fluid Mech. 801, 353391.
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414443.
Karniadakis, G. E. & Triantafyllou, G. S. 1989 Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199, 441469.
Konstantinidis, E. & Balabani, S. 2007 Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations. J. Fluids Struct. 23, 10471063.
Konstantinidis, E. & Bouris, D. 2016 Vortex synchronization in the cylinder wake due to harmonic and non-harmonic perturbations. J. Fluid Mech. 804, 248277.
Koopmann, G. 1967 The vortex wakes of vibrating cylinders at low Reynolds numbers. J. Fluid Mech. 28, 501512.
Leontini, J., Stewart, B., Thompson, M. & Hourigan, K. 2006 Wake state and energy transitions of an oscillating cylinder at low Reynolds number. Phys. Fluids 18, 067101.
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, 551568.
Leontini, J. S., Ll Jacono, D. & Thompson, M. C. 2013 Wake states and frequency selection of a streamwise oscillating cylinder. J. Fluid Mech. 730, 162192.
Lotfy, A. & Rockwell, D. 1993 The near-wake of an oscillating trailing edge: mechanisms of periodic and aperiodic response. J. Fluid Mech. 251, 173201.
Marzouk, O. A. & Nayfeh, A. H. 2009 Reduction of the loads on a cylinder undergoing harmonic in-line motion. Phys. Fluids 21, 083103.
Mittal, S., Ratner, A., Hastreiter, D. & Tezduyar, T. E. 1991 Space-time finite element computation of incompressible flows with emphasis on flows involving oscillating cylinders. Intl Video J. Engng Res. 1, 8396.
Morse, T. & Williamson, C. 2009 Prediction of vortex-induced vibration response by employing controlled motion. J. Fluid Mech. 634, 539.
Nazarinia, M., Lo Jacono, D., Thompson, M. C. & Sheridan, J. 2012 Flow over a cylinder subjected to combined translational and rotational oscillations. J. Fluids Struct. 32, 135145.
Newman, D. J. & Karniadakis, G. E. 1997 A direct numerical simulation study of flow past a freely vibrating cable. J. Fluid Mech. 344, 95136.
Olinger, D. & Sreenivasan, K. 1988 Nonlinear dynamics of the wake of an oscillating cylinder. Phys. Rev. Lett. 60, 797.
Olinger, D. J. 1993 A low-dimensional model for chaos in open fluid flows. Phys. Fluids 5, 19471951.
Olinger, D. J. 1998 A low-order model for vortex shedding patterns behind vibrating flexible cables. Phys. Fluids 10, 19531961.
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, 197223.
Ongoren, A. & Rockwell, D. 1988b Flow structure from an oscillating cylinder. Part 2: mode competition in the near wake. J. Fluid Mech. 191, 225245.
Ott, E. 2002 Chaos in Dynamical Systems. Cambridge University Press.
Rao, A., Leontini, J., Thompson, M. & Hourigan, K. 2013 Three-dimensionality in the wake of a rotating cylinder in a uniform flow. J. Fluid Mech. 717, 129.
Sarpkaya, T., Bakinis, C. & Storm, M. A. 1984 Hydrodynamic forces from combined wave and current flow on smooth and rough circular cylinders at high Reynolds numbers. In Ocean Technology Conference, Houston, TX, October, p. 4830.
Stansby, P. 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, 641665.
Tang, G., Cheng, L., Lu, L., Zhao, M., Tong, F. & Dong, G. 2016 Vortex formation in the wake of a streamwisely oscillating cylinder in steady flow. In Fluid–Structure–Sound Interactions and Control (ed. Zhou, Y., Lucey, A., Liu, Y. & Huang, L.), Springer.
Tanida, Y., Okajima, A. & Watanabe, Y. 1973 Stability of a circular cylinder oscillating in uniform flow or in a wake. J. Fluid Mech. 61, 769784.
Tatsuno, M. 1972 Vortex streets behind a circular cylinder oscillating in the direction of flow. Bull. Res. Inst. Appl. Mech. Kyushu Univ. 36, 2537.
Tatsuno, M. & Bearman, P. 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low Stokes numbers. J. Fluid Mech. 211, 157182.
Tong, F., Cheng, L., Xiong, C., Draper, S., An, H. & Lou, X. 2017 Flow regimes for a square cross-section cylinder in oscillatory flow. J. Fluid Mech. 813, 85109.
Tong, F., Cheng, L., Zhao, M. & An, H. 2015 Oscillatory flow regimes around four cylinders in a square arrangement under small KC and Re conditions. J. Fluid Mech. 769, 298336.
Tudball-Smith, D., Leontini, J. S., Sheridan, J. & Lo Jacono, D. 2012 Streamwise forced oscillations of circular and square cylinders. Phys. Fluids 24, 111703.
Williamson, C. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355381.
Williamson, C. H. K. & Brown, G. L. 1998 A series in 1/√Re to represent the Strouhal–Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12, 10731085.
Woo, H. 1999 A note on phase-locked states at low Reynolds numbers. J. Fluids Struct. 13, 153158.
Wu, J.-Z., Lu, X.-Y., Denny, A. G., Fan, M. & Wu, J.-M. 1998 Post-stall flow control on an airfoil by local unsteady forcing. J. Fluid Mech. 371, 2158.
Xu, S., Zhou, Y. & Wang, M. 2006 A symmetric binary-vortex street behind a longitudinally oscillating cylinder. J. Fluid Mech. 556, 2743.
Zdravkovich, M. 1996 Different modes of vortex shedding: an overview. J. Fluids Struct. 10, 427437.
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