Forced water entry and exit of two-dimensional bodies through a free surface

Abstract

The forced water entry and exit of two-dimensional bodies through a free surface is computed for various 2D bodies (symmetric wedges, asymmetric wedges, truncated wedges and boxes). These bodies enter or exit water with constant velocity or constant acceleration. The calculations are based on the fully non-linear timestepping complex-variable method of Vinje and Brevig. The model was formulated as an initial boundary-value problem with boundary conditions specified on the boundaries (dynamic and kinematic free-surface boundary conditions) and initial conditions at time zero (initial velocity and position of the body and free-surface particles). The formulated problem was solved by means of a boundary-element method using collocation points on the boundary of the domain and solutions at each time were calculated using time stepping (Runge-Kutta and Hamming predictor corrector) methods. Numerical results for the deformed free-surface profile, the speed of the point at the intersection of the body and free surface, the pressure along the wetted region of the bodies and force experienced by the bodies, are given for the entry and exit. To verify the results, various tests such as convergence checks, self-similarity for entry (gravity-free solutions) and Froude number effect for constant velocity entry and exit (half-wedge angles 5 up to 55 degrees) are investigated. The numerical results are compared with Mackie's analytical theory for water entry and exit with constant velocities, and the analytical added mass force computed for water entry and exit of symmetric wedges and boxes with constant acceleration and velocity using conformal mapping. Finally, numerical results showing the effect of finite depth are investigated for entry and exit.