Abstract
We use the boundary element method (BEM) to study transient plane strain deformations of water induced by a rigid hull impacting at normal incidence initially stationary water occupying a half space with the goal of finding the hydrodynamic pressure acting on the hull. Water is assumed to be incompressible and inviscid, and its deformations to have zero vorticity. Thus deformations of water are governed by the Laplace equation. Challenging issues addressed are finding the free surface of water whose evolution is governed by a nonlinear partial differential equation, determining the a priori unknown wetted length, and ensuring that water maintains contact with the hull without penetrating into it. The solution of the problem using the commercial software, LSDYNA, resulted in water penetrating into a rigid hull. The developed BEM code has been verified by using the method of manufactured solutions. Computed results for the hydrostatic pressure on straight hulls and ship bow section are found to compare well with the corresponding experimental findings. It is found that the peak pressure acting near the terminus of the wetted length decreases with an increase in the radius of the circular hull.
Highlights
Local water slamming is characterized by large hydrodynamic loads of short duration which can cause significant structural damage, e.g., see Faltinsen [1]
Yettou et al [8] experimentally measured hydrodynamic pressures acting on rigid wedges during their free fall into stationary water and analytically solved the problem
The velocity potential is a solution of the Laplace equation defined on the fluid domain
Summary
Local water slamming is characterized by large hydrodynamic loads of short duration which can cause significant structural damage, e.g., see Faltinsen [1]. Sun [14] and Sun and Faltinsen [15, 16] numerically analyzed water slamming problems for arbitrary geometries using the BEM for studying deformations of water that was modeled as non-viscous and incompressible, and modal analysis for deformations of the cylindrical shell They considered effects of gravity and flow separation from the solid surface. In writing boundary condition (3.a) we have tacitly neglected the surface tension effect These equations imply that the velocity of a point on the free surface equals that of the fluid particle instantaneously occupying it. For an arbitrary shaped hull with deadrise angle at X = 0 equal to zero, we assume that the free surface of water is undisturbed for the first time step. The developed BEM software gives very good solution of the Laplace equation
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