Parametric study on the water impacting of a free-falling symmetric wedge based on the extended von Karman's momentum theory

The present study is concerned with the peak acceleration azmax occurring during the water impact of a symmetric wedge. This aspect can be important for design considerations of safe marine vehicles. The water-entry problem is first studied numerically using the finite-volume discretization of the incompressible Navier–Stokes equations and the volume-of-fluid method to capture the air–water interface. The choice of the mesh size and time-step is validated by comparison with experimental data of a free fall water-entry of a wedge. The key original contribution of the article concerns the derivation of a relationship for azmax (as well as the correlated parameters υz∗, z∗ and t∗ when azmax occurs), the initial velocity υz0, the deadrise angle β and the mass M of the wedge based on the transformation of von Karman's momentum theory which is extended with the inclusion of the pile-up effect. The pile-up coefficient γ, which has been proven dependent on β in the case of water-entry with a constant velocity, is then investigated for the free fall motion and the dependence law derived from Dobrovol'skaya is still valid for β varying from 10° to 45°. Reasonable good theoretical estimates of azmax, υz∗, z∗ and t∗ are provided for a relatively wide range of initial velocity, deadrise angle and mass using the extended von Karman's momentum theory which is the combination of the original von Karman's method and Dobrovol'skaya's solution and this theoretical approach can be extended to predict the kinematic parameters during the whole impacting phase.