Modelling of multi-bodies in close proximity under water waves—Fluid resonance in narrow gaps

Abstract

Viscous fluid model and potential flow model with and without artificial damping force (f = −µV, µ the damping coefficient and V the local averaging flow velocity) are employed in this work to investigate the phenomenon of fluid resonance in narrow gaps between multi-bodies in close proximity under water waves. The numerical results are compared with experimental data available in the literature. The comparison demonstrates that both the viscous fluid model and the potential flow model are able to predict the resonant frequency reasonably well. However the conventional potential flow model (without artificial damping term) significantly over-predicts the wave height in narrow gaps around the resonant frequency. In order to calibrate the appropriate damping coefficient used for the potential model and make it work as well as the viscous fluid model in predicting the resonant wave height in narrow gaps but with little computational efforts, the dependence of damping coefficient µ on the body geometric dimensions is examined considering the parameters of gap width Bg, body draft D, body breadth ratio Br and body number n (n = 2, 3), where Br = BB/BA for the case of two bodies (Body A and Body B) with different breadths of BA and BB, respectively. It was confirmed that the damping coefficient used for the potential flow model is not sensitive to the geometric dimensions and spatial arrangement. It was found that µ ∈ [0.4, 0.5] may guarantee the variation of Hg/H0 with kh to be generally in good agreement with the experimental data and the results of viscous fluid model, where Hg is the excited wave height in narrow gaps under various dimensionless incident wave frequencies kh, H0 is the incident wave height, k = 2π/L is the wave number and h is the water depth.