Nonlinear Computation of Water Impact of Axisymmetric Bodies

Abstract

A fully nonlinear numerical simulation based on a boundary element method was used to investigate water impact of axisymmetric bodies that strike vertically the horizontal free surface from the air. The main objective was to understand the gravity effect on flow/wave kinematics and dynamics and to quantify the range of validity of existing theories and computations that are based on the infinite Froude number assumption. Two body geometries were considered: inverted cone and sphere. For the inverted cone, we obtained detailed dependencies of free-surface profile and impact pressure and load on the body on the generalized Froude number (Fr(V/gt)1/2, where V is the impact velocity, g is the gravitational acceleration, and t is time) and deadrise angle a. Based on these, we developed an approximate formula for evaluating the contribution of the gravity effect to the total impact force on the body in terms of a similarity parameter Fr/a1/2. For the sphere, we developed and applied a pressure-based criterion to follow the evolution of flow separation on the body and to obtain an appropriate description of the free-surface profile near the body and accurate evaluation of the impact pressure and load on the body during the entire impact process. The numerical result of impact force on the body agreed well with existing experimental measurements. We confirmed that the gravity effect is unimportant in initial impact of the sphere. Significantly, we found that in a later stage of impact, flow separation remains at an almost fixed position at an angle u 62.5 deg to the bottom of the sphere for a wide range of Froude numbers, Fr V/(gR)1/2 1, where R is the radius of the sphere.