Three-dimensional analysis of slamming

Abstract

Impact between the water and ship, i.e. slamming can cause important global and local effects. A numerical method has been applied to predict water entry loads on three-dimensional bodies. When the local angle between the water surface and the body surface is not small at impact position, local hydroelastic effects are not important for slamming. The problem is solved as an initial value problem using the boundary element method. The Green’s second identity is used to represent the velocity potential as a distribution of Rankine sources and dipoles over the body surface and free surface. The problem is stepped up in time using the information from the boundary conditions. The kinematic free surface condition is used to determine the intersection between the body surface and free surface at each time step. The exact body boundary condition is used, whereas the dynamic free surface condition Φ=0, is approximated on to a horizontal line and not on the exact free surface profile. This generalization of Wagner’s(1932) theory, was presented by Zhao, Faltinsen and Aarsnes (1996) for two-dimensional water entry problems and is hereafter referred to as the ‘simplified method’. In the present work, this ‘simplified method’ is extended to arbitrary three-dimensional bodies, along with the local solution matching techniques and time stepping procedures. Pressure is calculated using complete Bernoulli’s equation, excluding the gravity term, since fluid acceleration is much higher than gravitational acceleration. The numerical method has been compared with experimental results for axisymmetric bodies and the agreement between the results is considered to be good. The numerical method has been extended for general three-dimensional bodies to study bow impact problem of ships, by applying the method to bodies with bow shaped geometry. An idealized shape, which consists of cylindrical mid-body and hemispherical ends, was studied. The wetted body surface is considered to be more important and is calculated with great detail than the free surface elevation away from the body. Drop tests have been carried out to verify and validate the numerical simulation. The effect of the angle between the free surface and the body surface has also been studied. The agreement between theory and experiments is good and the effect of three-dimensionality is accounted. Important non-dimensionalised parameters have been identified in the course of the analyses. The experimental and numerical results have also been compared with strip theory solutions and other published results. Possibilities to extend the numerical simulation in to full-scale application and its full-scale meaning are also looked in to. The presented computational method is found to be robust for engineering use and computationally less demanding. The experimental results for vertical force have a strong oscillatory nature and this has been analyzed using a simplified hydroelastic model. The hydroelastic model gives reasonable representation of the dynamic oscillations found in the vertical force. Reasons for the observed deviations between the numerical and the experimental results are documented. Recommendations for conducting drop tests, with minimal dynamic effects are also presented.