Water Entry of Freefall Wedges-Wedge Motions and Cavity Dynamics
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- Institutt for marin teknikk 
When a free falling object enters a free surface of water, it may go through four successive phases: impact, flow separation from the body surface, creation and pinch-off of the cavity above the body, and oscillation of cavity after the pinch-off. These phenomena have direct relevance to the effective design of freefall lifeboats. To understand such phenomena, numerical, theoretical and experimental methods are developed/conducted for the water entry of a free-falling wedge, which characterizes the bow section of a lifeboat. The present work focuses on the motion of the wedge and the dynamics of the cavity created on the top of the wedge and the influence of the cavity on the motion of the wedge. Non-linear boundary element methods were developed for simulating the water entry of the freefall wedge with and without the effect of air flow. It was found that the air flow starts to play an important role just before the closure of the cavity and the influence of air flow is limited due to the short duration. Numerical simulations showed that the initial entry speed of the wedge has a negligible influence on the closure period and the size of the cavity, but a significant influence on the submergence depth of the wedge at the closure of the cavity. The mass of the wedge strongly influences the formation and closure of cavities. A cavity will not be formed for light wedges. The cavity size is highly dependent on the mass. A larger mass leads to a larger cavity. The submergence depth at the closure of the cavity increases nearly linearly with mass, but the cavity closure period seems to be independent of the mass of the wedge. The influence of the deadrise angle was also investigated and it was found that the deadrise angle of the wedge has a weak influence on the formation and closure of cavities. Theoretical models were proposed to analyze the motions and cavity dynamics of free falling wedges entering the water surface. The theoretical model successfully predicted the peak acceleration and the evolution of submergence depth and velocity during the water entry of freefall wedges. It was revealed that slamming will significantly reduce the velocity of a light wedge, and there exists a critical initial entry velocity. If the initial velocity of wedge is less than the critical velocity, the velocity of wedge will increase after slamming phase; otherwise it will decrease. The theoretical models explained why the characteristics of the transient cavity, such as the nondimensional pinch-off (closure) time, pinch-off depth and wedge depth at pinch-off, scale roughly linearly as the Froude number (the dimensional pinch-off time is independent of the initial entry speed of the wedge, which is consistent with the finding of numerical simulations). The transient drag coefficients during the collapse phase of the cavity are extensively studied. It was found that for the light wedge the transient drag coefficients have slow variation in the first half stage and rapid variation in the last half stage, which is due to the fact that the hydrostatic force is the dominant component in the drag force at the last half stage for the light wedge. For the heavy wedge the transient drag coefficients vary slowly during the whole stage and can be treated as constant. The cavity closure point was found to move to the deeper water zone with increasing Froude number. This is opposite of the cavity seal mechanism from deep seal to surface seal for circular disks or spheres entering the water. The proposed numerical models and theoretical models were validated by experiments. The experiments also investigated the evolutions of the global hydrodynamic loads, the pressure on the impact side of the wedge, the air-water interface, and the cavity pressure after pinch-off. A typical evolution of the global hydrodynamic loads is found to be: rapid growth during slamming, rapid drop due to flow separation, slow variation during the formation of cavity and oscillation after the closure of cavity. The oscillation of the cavity pressure after pinch-off is a complex phenomenon. The oscillation frequency is related to the shape of the cavity, the mass of the wedge and the shape of the water surface, and the boundary conditions. The air leakage, thermal conductivity, and shear viscosity play important roles during the evolution of the closed cavity and directly affect the damping of the cavity pressure. As a first approximation, it can be assumed that the closed cavity has a uniform pressure field and follows an adiabatic process.