Formulations of Hydrodynamic Force in the Transition Stage of the Water Entry of Linear Wedges with Constant and Varying Speeds

TL;DR

This paper develops a unified model for hydrodynamic forces during the transition stage of water entry of linear wedges, applicable to constant and varying speeds, aiding in the design of seaplane landings and hull slamming analysis.

Contribution

It introduces a new formulation of hydrodynamic forces in the transition stage based on similitude and added mass effects, extending existing models to varying impact speeds.

Findings

Formulation accurately predicts forces for deadrise angles 5° to 70°.

Hydrodynamic force in transition stage scales with maximum slamming force.

Added mass coefficient increases by 27.13% during acceleration effects.

Abstract

There is an increasing need to develop a two-dimensional (2D) water entry model including the slamming and transition stages for the 2.5-dimensional (2.5D) method being used on the take-off and water landing of seaplanes, and for the strip theory or 2D+t theory being used on the hull slamming. Motivated by that, this paper numerically studies the transition stage of the water entry of a linear wedge with constant and varying speeds, with assumptions that the fluid is incompressible, inviscid and with negligible effects of gravity and surface tension, and the flow is irrotational. For the constant speed impact, the similitude of the declining forces of different deadrise angles in the transition stage are found by scaling the difference between the maximum values in the slamming stage and the results of steady supercavitating flow. The formulation of the hydrodynamic force is conducted based on the similitude of the declining forces in the transition stage together with the linear increasing results in the slamming stage. For the varying speed impact, the hydrodynamic force caused by the acceleration effect in the transition stage is formulated by an added mass coefficient with an averaged increase of 27.13% compared with that of slamming stage. Finally, a general expression of the hydrodynamic forces in both the slamming and transition stages is thus proposed and has good predictions in the ranges of deadrise angles from 5 deg to 70 deg for both the constant and varying speed impacts.