The effect of air on solid body impact with water in two dimensions

In this paper we study the motion of wedge and catamaran shaped hulls initially in air, then impacting with water. We consider motion in two dimensions and simulate the impact using SPH in a form suitable for two-phase flow. This SPH algorithm has been tested for a variety of problems involving air and water with very good results. However, we supplement those tests by simulating the dynamics of bubbles, and the motion of piston driven by the pressure of air in a tube. The former confirms that our algorithm simulates the motion of two fluids with a high density ratio (in this case 1000) while the latter is relevant to the impact of a catamaran shaped hull where the trapped air cushions the impact. In both cases the results are in very good agreement with theory. When applied to simulate the dynamics of a wedge falling into a fluid the results are in good agreement with theory and confirm that the effect of the air on the motion is small because the air can escape easily as the wedge enters the water. When applied to simulate a model catamaran hull in two dimensions, where the air is trapped beneath the hull, the effect of air is pronounced. The simulations with the catamaran hull are not in close agreement with experiments because the hull in three dimensions does not trap air effectively as it does in two dimensions.