Vortex-induced vibrations at subcritical Re

Abstract

Flow past a stationary cylinder becomes unstable at Re$\,{\sim}\,47$. Flow-induced vibrations of an elastically mounted cylinder, of low non-dimensional mass, is investigated at subcritical Reynolds numbers. A stabilized finite-element formulation is used to solve the incompressible flow equations and the cylinder motion in two dimensions. The cylinder is free to vibrate in both the transverse and in-line directions. It is found that, for certain natural frequencies of the spring–mass system, vortex shedding and self-excited vibrations of the cylinder are possible for Re as low as 20. Lock-in is observed in all cases. However, the mass of the oscillator plays a major role in determining the proximity of the vortex-shedding frequency to the natural frequency of the oscillator. A global linear stability analysis (LSA) for the combined flow and oscillator is carried out. The results from the LSA are in good agreement with the two-dimensional direct numerical simulations.

The motion of a 2D pendulum in a channel subjected to an incoming flow

“…They carried out numerical simulations and global stability analysis of the fluid-structure problem and they found that the cylinder starts to oscillate at a Reynolds number beyond Re = 21.7 with a Strouhal number St = 0.12. In order to validate the structural part of the tools for stability analysis, we repeated the same analysis of Mittal & Singh (2005). We found a global mode slightly unstable (λ = 2 × 10 −3 ) at Re = 21.5, with an associated Strouhal number equal to 0.121, showing an excellent agreement with the results of Mittal & Singh (2005).…”

“…In order to validate the structural part of the tools for stability analysis, we repeated the same analysis of Mittal & Singh (2005). We found a global mode slightly unstable (λ = 2 × 10 −3 ) at Re = 21.5, with an associated Strouhal number equal to 0.121, showing an excellent agreement with the results of Mittal & Singh (2005). We first studied the same flow configuration as in Semin et al (2011).…”

“…They found that when the cylinder is light (low values of density ratio α), the critical Reynolds number is less than half of Re 0 c . Mittal & Singh (2005) studied the flow around a cylinder with a low density ratio (α ≈ 5) and with a null structural damping coefficient. The cylinder is allowed to vibrate in the transverse and in-line directions.…”

Instability of the separated shear layer in flow past a cylinder: Forced excitation

“…The values for the same, reported by Fornberg [20], are 0.726 and 20.40D, respectively. For more details on the steady-state flow past a cylinder and for the performance of the present algorithm for unsteady flows, the interested reader is referred to our earlier papers [8,13,14].…”

“…The large-scale coupled non-linear equation systems resulting from the finite element discretization of the governing equations are solved iteratively by employing the GMRES (Generalized Minimal RESidual) procedure in conjunction with diagonal preconditioners. More information on the formulation and its application to computing flows past cylinders can be found in our earlier papers [11][12][13][14].…”