Unsteady interactions among multiple ships with free-surface effects

Ships often have to pass each other in proximity inharbor area and waterways in dense shipping trafficenvironment. Hydrodynamic interaction occurs whena ship is overtaking (or being overtaken) orencountering other ships. Such an interactive effectcould be magnified in confined waterways, e.g.shallow and narrow rivers. Since Yeung (1978)published his initial work on ship-interaction inshallow water, progress on unsteady interactionamong multiple ships has been slow though steadyover the following decades. With some exceptions,nearly all the published studies on ship-to-shipproblem neglected free-surface effects, and a rigidwall condition has often been applied on the watersurface as the boundary condition. When the speed ofthe ships is low, this assumption is reasonablyaccurate, as the hydrodynamic interaction is mainlyinduced by near-field disturbances. However, in manymaneuvering operations, the encountering orovertaking speeds are actually moderately high(Froude number Fn>0.2, where ≡ / , U isship speed, g the gravitational acceleration and L theship length), especially when the lateral separationbetween ships is the order of ship length. Here, the farfieldeffects arising from ship waves can be important.The hydrodynamic interaction model must take intoaccount of the surface-wave effects.Classical potential-flow formulation is only ableto deal with the boundary value problem (BVP) whenthere is only one speed involved in the free-surfaceboundary condition. For multiple ships travelling withdifferent speeds, it is not possible to express the freesurfaceboundary condition by a single velocitypotential. Instead, a superposition method can beapplied to account for the velocity field induced byeach vessel with its own and unique speed. The mainobjective of the present paper is to propose a rationalsuperposition method to handle the unsteady freesurfaceboundary condition containing two or morespeed terms, and validate its feasibility in predictingthe hydrodynamic behaviour of the ships duringovertaking or encountering operations. The solutionmethodology used in the present paper is a threedimensionalboundary-element method (BEM) basedon a Rankine-type (infinite-space) source function,initiated introduced in Bai & Yeung (1974). Thenumerical simulations are conducted by using an inhousedeveloped multi-body hydrodynamicinteraction program "MHydro". Waves generated andforces (or moments) are calculated when ships areencountering or passing each other. Published modeltestresults are used to validate our calculations andvery good agreement has been observed. Thenumerical results show that free-surface effects needto be taken into account for Fn > 0.2