Flow-Induced Vibration of a Sphere in the wake of a upstream stationary sphere.

The presents paper investigates the Flow Induced Vibration of an elastically mounted sphere in the wake of a upstream stationary sphere at Reynolds number Re = 300. The Fluid-multi Structure Interaction problem is numerically solved using in-house code based on Level-set function based Immersed Interface method (LS-IIM). The oscillating sphere has mass ratio m∗ = 10 and damping ratio ζ = 0.1. The Wake Induced Vibration (WIV) is studied at tandem gap ratio of G* = 2.0 and 0.5 for a channel of width L_z=4D and a free-stream case with G* = 2.0 is also considered, with a varying reduced velocity range of U* = 3−10. For G* = 2.0, a significant enhancement of maximum amplitude A* of downstream sphere is observed in a channel as compared to free-stream. The vibration starts at U* = 4 reaching amplitude A* = 1.84 at U* = 10 for channel, whereas vibration commences at U* = 7 with amplitude A* = 0.81 at U* = 10 for free-stream case. For channel case, decreasing the gap to G* = 0.5 results in delayed onset of vibration at U* = 6 as compared to G* = 2.0. However, the amplitude A* increase rapidly with A* = 1.70 at U* = 10. A similar trend of A* may results in vibration enhancement at larger U* for G* = 0.5 as compared to G* = 2.0. The average power extracted in a cycle and efficiency η are quadrupled at U* = 10 for channel as compared to free-stream at G* = 2.0. For channel versus free-stream, we obserevd similar vortical structure in the near wake with a hairpin vortex shed from downstream sphere in both cases. A unique vortex interaction on same side of two sphere is observed during transient period of gap-flow switching. The interaction is observed only for spheres and generates a wake induced negative damping mechanism and in-phase force on downstream sphere. Whereas, during the strong unidirectional gap flow a restoring force is generated for top to mean motion of the sphere. The channel enhances the gap flow and fluctuation of flow field in transverse direction, which enhances the gap-flow induced restoring force and flow induced negative damping resulting in a larger vibration amplitude.