Numerical Assessment of Similitude Parameters and Dimensional Analysis for Water Entry Problems

The prediction of impulsive loads deriving from the sudden impact of a solid body on the water surface is of fundamental importance for a wide range of engineering applications. The study of hull-slamming phenomena largely relies on laboratory scale experimental investigations and on simplified analytical models. The aim of this paper is to quantitatively assess the interplay between the relevant nondimensional parameters for the water entry of a two-dimensional body, evidencing the similitude conditions that allow the transition from scaled experiments to real size applications. This assessment is performed through the numerical study of the hydrodynamics induced by the water impact of a two-dimensional wedge. The fluid flow is considered incompressible. First of all numerical simulations are validated by comparison with experimental data from the literature and with the Wagner seminal theory. Afterwards, a thorough computational study is performed by systematically varying all the relevant parameters, such as the nondimensional entry velocity and acceleration. We conclude by evidencing some design prescriptions that should be adopted in order to facilitate the transition of laboratory scale experiments to real scale applications.