A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green's theorem and linearizing the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalized far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilizing the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape.
Most of the existing drift velocity models have limitations, and sometimes low predictive capabilities, primarily because they are derived from experimental data which scarcely account for the combined effect of viscosity, surface tension and pipe inclination. Published data of drift velocity of elongated bubbles in pipes have been extracted from the open literature, and new data have been generated from Taylor bubble experiments conducted in a low pressure flow loop using nominal oil viscosities of 160cP and 1140cP in 0.099m and 0.057m internal diameter inclined pipes (1.0 to 7.5 degrees from horizontal). These data have been processed and a simplified generalised drift velocity correlation established. The evaluation of some existing elongated bubble rise velocity has also been carried out. The prediction of the drift velocity of a single elongated gas bubble in liquid in pipes can sometimes be overestimated by 20% or more, and sometimes be underestimated by 20% or more. It is shown that the new proposed simplified generalised correlation has an improved predictive capability when used to estimate the drift velocity of a bubble in stagnant liquid in a pipe.
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