Finite Element study of vortex induced cross-flow and in-line oscillations of a light Circular Cylinder at low Reynolds numbers

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Mittal, S. and Kumar, V. (1999), Finite element study of vortex‐induced cross‐flow and in‐line oscillations of a circular cylinder at low Reynolds numbers. Int. J. Numer. Meth. Fluids, 31: 1087-1120. doi:10.1002/(SICI)1097-0363(19991215)31:7<1087::AID-FLD911>3.0.CO;2-C


Vortex‐induced vibrations of a circular cylinder placed in a uniform flow at Reynolds number 325 are investigated using a stabilized space–time finite element formulation. The Navier–Stokes equations for incompressible fluid flow are solved for a two‐dimensional case along with the equations of motion of the cylinder that is mounted on lightly damped spring supports. The cylinder is allowed to vibrate, both in the in‐line and in the cross‐flow directions. Results of the computations are presented for various values of the structural frequency of the oscillator, including those that are sub and superharmonics of the vortex‐shedding frequency for a stationary cylinder. In most of the cases, the trajectory of the cylinder corresponds to a Lissajoufigure of 8. Lock‐in is observed for a range of values of the structural frequency. Over a certain range of structural frequency (Fs), the vortex‐shedding frequency of the oscillating cylinder does not match Fs exactly; there is a slight detuning. This phenomenon is referred to as soft‐lock‐in. Computations show that this detuning disappears when the mass of the cylinder is significantly larger than the mass of the surrounding fluid it displaces. A self‐limiting nature of the oscillator with respect to cross‐flow vibration amplitude is observed. It is believed that the detuning of the vortex‐shedding frequency from the structural frequency is a mechanism of the oscillator to self‐limit its vibration amplitude. The dependence of the unsteady solution on the spatial resolution of the finite element mesh is also investigated.