Impact of wedge bodies on wedge-shaped water surface with varying speed

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

“…surface with the increasing penetration depth. The result of similarity solution k 1 tan β(−2Φ) [36] in the slamming stage is well consistent with the result h/h 0 = 0.502 in the slamming stage. It can be concluded that the distribution of ∆p/ (0.5ρa w c) remains as k 1 tan β(−2Φ) in the slamming stage and then has a small increase in the transition stage.…”

“…For the slamming stage with h/h 0 = 0.6 in the case of the water entry of a wedge with β = 30 • in a constant speed, Fig. 8 shows the comparisons of the pressure coefficient C p on the wedge surface and the free surface profiles between the predictions of CFD, HBF and similarity solution [36]. The spray root of the jet remains under the knuckle of the wedge, which means the self-similar flow is still satisfied and thereby the similarity solution can be used for a validation.…”

“…3) (a) and the distributions of ∆p/(0.5ρawc), where ∆p is the difference of the pressure between the varying and constant speed impacts in a same penetration depth and with a same instantaneous speed (b). The result of similarity solution k 1 tan β(−2Φ) is also given for comparisons [36]. The result of h/h 0 = 0.502 remains in the slamming stage.…”

“…The most widely used method for the free surface problems, volume of fraction (VOF), was first proposed by Hirt and Nichols [33] based on the framework of finite volume method (FVM). A modified high-resolution interface capturing scheme (Modified HRIC) was developed by Muzaferija et al [34] to solve volume fraction equations and has good applications to the water entry problems [8,35,36]. Compared with the BEM approaches, the CFD methods provide more information about the distributions of pressure and velocities in the whole region which intuitively picture the rapid changes of flow field in the transition stage of the constant speed impact.…”

“…In this paper, the slamming and transition stages of water entry of linear wedges with constant and varying speeds are numerically studied by the FVM with VOF [36] and the HBF of Iafrati and Battistin [24]. To propose a semianalytical solution of a combination of numerical results and theoretical results to address the high speed impact problems, the fluid is considered to be incompressible, non-viscous, weightless and with negligible surface tension effects and the flow is to be irrotational.…”