Generalized hydrodynamic coefficients of a circular SFT in finite water depth

Abstract

In this work, a numerical model is developed for calculating the generalized hydrodynamic coefficients of a horizontal vibrating cylinder representative of a submerged floating tunnel in finite water depth. In this model, the whole computational domain is divided into three sub-domains and the velocity potential for describing the fluid motion in each sub-domain is solved separately using different approaches. In the inner domain bounding the cylinder, a simple Green function is utilized to form a boundary integral equation, which is solved by the boundary element method (BEM), and the technique of eigenfunction expansion is applied in the outer domains away from the cylinder. The eigenfunctions in the outer domains indicate that there exists a critical vibration frequency below which no propagating wave can be generated and thus the radiation damping is zero. Characteristics of the generalized hydrodynamic coefficient in a wider range of the submergence depth, the vibration frequency and the axial wavenumber are explored. It is found that the generalized hydrodynamic coefficients in the vicinity of the critical vibration frequency experience abrupt changes, characterised by a ‘sharp peak’ profile. Generally, the generalized (horizontal and vertical) added mass increases firstly with the vibration frequency to its maximum value at the critical frequency, and then decreases with the further increase in the vibration frequency. However, behaviours are rather different in terms of the vertical added mass if the cylinder is fully submerged; a discontinuity at the critical frequency is observed, and the value jumps from positive to negative here. Afterwards the vertical added mass starts to increase quickly and becomes positive again with the further increase of the vibration frequency. This phenomenon of discontinuity may be associated with the fact that the radiation force changes its direction suddenly at the critical frequency; from being ‘out-of-phase’ to ‘in-phase’ with the cylinder motion. In addition, semi-analytical solutions are derived for approximating the generalized added mass in a high frequency range, which suggests that the generalized added mass decreases with the axial wavenumber, and with the presence of free surface, especially when the axial wavenumber is small. While for a deeply submerged cylinder, the effect of the free surface is negligible and then further simplified solutions are provided.