The piston and first sloshing modes of two-dimensional moonpools with recess are investigated. Dedicated forced heave experiments are carried out. Different recess lengths are tested from $1/4$ to $1/2$ of the length of the moonpool at the mean waterline. A theoretical model to calculate the natural frequencies is developed based on linearized potential flow theory and eigenfunction expansion. Two numerical methods are implemented: a boundary element method (BEM) and a Navier–Stokes solver (CFD). Both the BEM and CFD have linearized free-surface and body-boundary conditions. As expected, the BEM over-predicts the moonpool response significantly, in particular at the first sloshing mode. The CFD is in general able to predict the maximum moonpool response adequately, both at the piston and first sloshing modes. Both numerical methods fail to predict the Duffing-type behaviour at the first sloshing mode, due to the linearized free-surface conditions. The Duffing behaviour is more pronounced for the largest recess. The main source of damping in the proximity of the first sloshing mode is discussed.

No abstract

Moonpool resonance is investigated in a two-dimensional setting in terms of regular, forced heave motions of a model with moonpool with different rectangular-shaped recess configurations. A recess is a reduced draft zone in the moonpool. Dedicated experiments were carried out. The model consisted of two boxes of 40 cm width each, with a distance of 20 cm between them. Recess configurations varying between 5 cm to 10 cm in length and 5 cm in height were tested. Different drafts were also tested. The free-surface elevation inside the moonpool was measured at eight locations. A large number of forcing periods, and five forcing amplitudes were tested. A time-domain Boundary Element Method (BEM) code based on linear potential flow theory was implemented to investigate the resonance periods, mode shapes as well as the moonpool response as predicted by (linear) potential flow theory. Dominant physical effects were discussed, in particular damping due to flow separation from the sharp corners of the moonpool inlet and recess. The effect of the recess on the piston-mode behavior is discussed. BEM simulations where the effect of flow separation is empirically modelled were also conducted. The non-dimensional moonpool response suggests strong viscous damping at piston-mode resonance. The viscous BEM simulations demonstrate improvement over inviscid BEM, although further improvement of the method is needed. The piston mode shapes are clearly different from the near flat free-surface elevation for a moonpool without recess, consistent with recently published theory.

No abstract

Moonpool resonance is investigated in a two-dimensional setting in terms of regular, forced heave motions of a model with moonpool with different rectangular-shaped recess configurations. A recess is a reduced draft zone in the moonpool. Dedicated experiments were carried out. The model consisted of two boxes of 40 cm width each, with a distance of 20 cm between them. Recess configurations varying between 5 cm and 10 cm in length and 5 cm in height were tested. Different drafts were also tested. A large number of forcing periods and five forcing amplitudes were tested. A time-domain boundary element method (BEM) code based on the linear potential flow theory was implemented to investigate the resonance periods, mode shapes, as well as the moonpool response as predicted by the (linear) potential flow theory. Dominant physical effects were discussed, in particular damping due to flow separation from the sharp corners of the moonpool inlet and recess. The effect of the recess on the piston-mode behavior is discussed. The nondimensional moonpool response suggests strong viscous damping at the piston-mode resonance. The viscous BEM (VBEM) simulations demonstrate improvement over inviscid BEM, although further improvement of the method is needed. The VBEM simulations are, in general, in good agreement with the experiments. For the largest recess case, some discrepancies are observed in the amplitude-dependent response amplitude operators (RAOs). The piston-mode shapes are clearly different from the near flat free-surface elevation for a moonpool without recess, consistent with the recently published theory.