Prediction of the compressible stage slamming force on rigid and elastic systems impacting on the water surface

In this paper some models focusing on hydrodynamic and elastic forces arising during the impact of rigid and elastic systems on the water surface are investigated. In particular, the supersonic compressible stage of the impact is considered by modelling the slamming phenomenon through the Skalk-Feit acoustic approximation. The dynamic equations of the dropping system are coupled to those of the fluid and a nonlinear fluid-solid interaction problem is stated. General relationships between the body's shape, slamming force and body motion are determined. These equations are applied to the wedge water entry cases, and a closed-form expression for the maximum hydrodynamic force is found. Moreover the theoretical correlation between the hydrodynamic force and the body geometry allows us to control the inverse problem and the shape associated to a constant slamming force is determined. Due to some simplifications allowed in the supersonic compressible impact, the results of the hydrodynamic analysis hold in closed form. This permits us to focus on the basic result of the paper addressed to a systematic correlation between hydrodynamic and elastic maximum forces in terms of some characteristic dimensionless quantities involved in fluid-solid interaction. In particular, 'critical conditions' corresponding to those hydorelastic parameters combinations are investigated, leading to severe elastic response of the impacting system.