Bow flare slamming and nonlinear free surface-body interaction in the time domain

The hydrodynamic aspects of bow flare impact are discussed and the assumptions implicit in typical flare impact calculations are examined. Calculations based upon a pressure release free surface boundary condition are presented. While this simplified boundary condition eliminates the possibility of important factors such as splash-up and above-surface wetting, it has the significant advantage of being computationally simple. Both three-dimensional and two-dimensional results are compared with experiments. Errors resulting from the approximate free surface condition are examined. Also included in the two-dimensional and three-dimensional analysis are longitudinal distributions of the vertical bending moment and vertical shear force.; The nonlinear interaction problem of a submerged axisymmetric body and the free surface is solved in the time domain using a mixed Eulerian-Lagrangian method. The free surface shape and the forces acting on a submerged sphere oscillating sinusoidally are calculated and compared with published results. The flow in the far field of the body is represented by a three dimensional dipole at the origin of the coordinate system. This is only valid until waves arrive at the truncation boundary in the far field. Waves generated by the numerical error at the truncation boundary are not observed. For the case when the body motion is not prescribed but rather must be determined from the solution of the equations of motion, the time derivative of the potential on the body is required. An integral equation and the boundary conditions for calculating the time derivative of the potential are given. The free surface shape can be calculated simultaneously with the solution of the equations of motion with the aid of a Runge-Kutta 4-th order scheme.; In addition to the nonlinear submerged body calculations, the impact problem for a flared body is attempted. Difficulties with the numerical modeling of the body-free surface intersection for this case are noted and discussed.