Numerical investigation of the effects of a small fixed sphere in tandem arrangement on VIV of a sphere

Abstract A direct-forcing immersed boundary (DFIB) method with a virtual force is used to investigate the vortex-induced vibration (VIV) of an elastically mounted sphere in uniform flow at a moderate Reynolds number. A novel method is investigated to control VIV of an elastically mounted sphere by placing a small fixed sphere inline in tandem arrangement. The numerical method is validated by comparisons with previously published results for flow past a stationary sphere and for VIV phenomena. The influence of the small sphere diameter and the gap between the spheres on VIV are studied through an analysis of the hydrodynamic force coefficients, sphere responses, vortex shedding modes and energy efficiency. Regression analysis is conducted to propose mathematical relations for estimating the maximum values of hydrodynamic force coefficients and amplitude ratio. This study proves the capability of the DFIB model for investigating VIV of a sphere. It is also found that the small fixed sphere upstream increases the lift coefficient and amplitude ratio of the vibrating sphere while the drag coefficient is reduced. Furthermore, the energy efficiency of VIV of the sphere is found to be increased by up to three times due to the upstream small fixed sphere.