Abstract
Vortex-induced vibration (VIV) of a square cylinder in a cross flow is examined numerically. Both the rigid and elastic cases are simulated at a low Reynolds number of 100. The approach solves the unsteady flow field using a finite element method with a deforming grid to accommodate the moving cylinders. As for the cylinder motions, a two-degree-of-freedom structural dynamics model is invoked. Fluid-structure interactions are resolved through iteration at the same time step. The calculated results for the case of rigid cylinder indicated that the non-dimensional vortex shedding frequency (or the Strouhal frequency) of a square cylinder at rest is 0.13, which is in good agreement with the published results. For the elastic case, with the change of the cylinder’s natural frequency, “lock-in” and “beat” phenomena were successfully captured. The phenomena of resonance and galloping can also be indicated.
Similar content being viewed by others
References
Al-Jamal, H. and Dalton, C., 2004, “Vortex Induced Vibrations using Large Eddy Simulation at a Moderate Reynolds Number,”Journal of Fluids and Structures, Vol. 19, pp. 73–92.
Bernsdorf, J., Zeiser, T., Brenner, G. and Durst, F., 1998, “Simulation of 2D Channel flow Around a Square Obstacle with Lattice-Boltzmann (BGK) Automata,”International Journal of Modern Physics C, Vol. 9 (8), pp. 1129–1141.
Blevins, R. D. 1994, “Flow-Induced Vibration,” 2nd Edition, Krieger, New York.
Blake, W. K., 1986, “Mechanics of Flow-Induced Sound and Vibration,”Academic, New York.
Breuer, M., Bernsdorf, J., Zeiser, T. and Durst, F., 2000, “Accurate Computations of the Laminar flow past a Square Cylinder based on two Different Methods: Lattice-Boltzmann and Finite Volume,”International Journal of heat and fluid flow, Vol. 21, pp. 186–196.
Bristeau, M. O., Glowinski, R. and Periaux, J., 1987, “Numerical Methods for the Navier-Stokes Equations: Applications to the Simulation of Compressible and Incompressible Viscous Flows,”Computer Physics Reports, Vol. 6, pp. 73–187.
Dong, S. and Karniadakis, G. E., 2005, “DNS of flow past a Stationary and Oscillating Cylinder at Re = 10000,”Journal of Fluids and Structures, Vol. 20, pp. 519–531.
Gabbai, R. D. and Benaroya, H., 2005, “An Overview of Modeling and Experiments of Vortex-Induced Vibration of Circular Cylinders,”Journal of Sound and Vibration, Vol. 282, pp. 575–616.
Govardhan, R. and Williamson, C. H. K. 2004, “Critical mass in Vortex-Induced Vibration of a Cylinder,”European Journal of Mechanics B/Fluids, Vol. 23, pp. 17–27.
Guilmineau, E. and Queutey, P., 2004, “Numerical Simulation of Vortex-Induced Vibration of a Circular Cylinder with Low Mass-Damping in a Turbulent flow,”Journal of Fluids and Structures, Vol. 19, pp. 449–466.
Guo, W. B., Shi, B. C. and Wang, N. C, 2003, “Lattice-BGK Simulation of a Two-Dimensional Channel flow Around a Square Cylinder,”Chinese Physics, Vol. 12 (1), pp. 67–74.
Hover, F. S., Davis, J. T. and Triantaryllou, M. S., 2004, “Three-Dimensionality of mode Transition in Vortex-Induced Vibrations of a Circular Cylinder,”European Journal of Mechanics B/Fluids, Vol. 23, pp. 29–40.
Jauvtis, N. and Williamson, C. H. K., 2003, “Vortex-Induced Vibration of a Cylinder with two Degrees of Freedom,”Journal of Fluids and Structures, Vol. 17, pp. 1035–1042
Klamo, J. T., Leonard, A. and Roshko, A., 2005, “On the Maximum Amplitude for a Freely Vibrating Cylinder in Cross-flow,”Journal of Fluids and Structures, Vol. 21, pp. 429–434.
Lam, K., Wang, F. H. J, Li, Y. and So, R. M. C, 2004, “Experimental Investigation of the Mean and Fluctuating Forces of Wavy (varicose) Cylinders in a Cross-flow,”Journal of Fluids and Structures, Vol. 19, pp. 321–334.
Leontini, J. S., Stewart, B. E., Thompson, M. C. and Hourigan, K., 2006, “Predicting Vortex-Induced Vibration from Driven Oscillation Results,”Applied Mathematical Modelling, Vol. 30, pp. 1096–1102.
Liu, Y., So, R. M. C, Lau Y. L. and Zhou, Y., 2003, “Numerical Studies of two Side-by-side Elastic Cylinders in a Cross-flow,”Journal of Fluids and Structures, Vol. 15, pp. 1009–1030.
Marcollo, H. and Hinwood, J. B., 2006, “On Shear Flow Single Mode Lock-in with both Cross-flow and In-line Lock-in Mechanisms,”Journal of Fluids and Structures, Vol. 22, pp. 197–211.
Okajima, A., 1982, “Strouhal Numbers of Rectangular Cylinders,”Journal of Fluid Mechanics Vol. 123, pp. 379–398.
Sarpkaya, T., 2004, “A Critical Review of the Intrinsic Nature of Vortex-Induced Vibrations,”Journal of Fluids and Structures, Vol. 19, pp. 389–447.
Wang, X. Q., So, R. M. C. and Liu, Y, 2003, “Flow-Induced Vibration of an Euler-Bernoulli Beam,”Journal of Sound and Vibration, Vol. 243, pp. 241–268.
Wanderley, J. B. V. and Levi, C. A., 2002, “Validation of a Finite Difference Method for the Simulation of Vortex-Induced Vibrations on a Circular Cylinder,”Ocean Engineering, Vol. 29, pp. 445–460.
Wang, G. C., Shi, B. C. and Deng, B., 2003, “Simulation of flow past Square Cylinders with a Non-Uniform Lattice Boltzmann Method,”Journal of Basic Science and Engineering, Vol. 11 (4), pp. 335–344.
Zhang, H. J., Zhou, Y., So, R. M. C., Mignolet, C. M. P. and Wang, Z. J., 2003, “A note on the Fluid Damping of an Elastic Cylinder in a Cross-flow,”Journal of Fluids and Structures, Vol. 17, pp. 479–483.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Su, Z., Liu, Y., Zhang, H. et al. Numerical simulation of vortex-induced vibration of a square cylinder. J Mech Sci Technol 21, 1415 (2007). https://doi.org/10.1007/BF03177428
Received:
Revised:
Accepted:
DOI: https://doi.org/10.1007/BF03177428