Damping of piston mode resonance between two fixed boxes

Abstract

In this paper, the damping of wave-induced resonant oscillations of water column in the gap between two fixed boxes is investigated through physical model testing. A pair of rectangular fins with different geometries is attached to the sidewalls of the gap to suppress the resonant response. This study is an extension to Tan et al. [“A viscous damping model for piston mode resonance,” J. Fluid Mech. 871, 510–533 (2019)], where the damping of wave resonance in a plain gap without fins was investigated. We found that (1) the resonant wave height in the gap decreased substantially with the increasing fin thickness, but was not very sensitive to the variation of the fin height. This observation suggests that the fin thickness has a more significant influence on the damping of oscillations than the fin height; (2) the resonant frequency decreased as the thickness of the fins was enlarged, which is primarily attributable to the decrease in the natural frequency (due to increasing added mass) and partly ascribed to the increase in viscous damping. The viscous dissipation was found to be approximately 3–10 times larger than the radiation energy and explains the well-known over-estimations of inviscid potential solution in resonant amplitude. A modified potential flow model with a damping mechanism was employed to predict the wave response in the gap, wave reflections, and transmissions. Reasonable agreements were obtained between the experimental results and the modified potential flow solutions with respect to amplitude, whereas a difference of 6%–14% in resonant frequency was observed. This difference is ascribed to the effects of flow separation on the added mass of fins, which cannot be fully captured by modified potential flow models. In addition to the present geometries, the local loss coefficients for other appendage configurations were also calibrated based on the available experimental and computational fluid dynamics data in the literature.