Numerical and Theoretical Study on the Varying Speed Impact of Wedge Bodies on a Water Surface

Abstract

The varying speed impact of wedge bodies on a water surface is studied numerically and theoretically to provide a fast and accurate prediction of the pressure on the wedge surface and the motion of wedge bodies during the free impact, which can be a 2D model for the strip theory or 2D+t strategy. The fluid is assumed to be incompressible, inviscid, with negligible gravity effect and surface tension effect. The computational fluid dynamics (CFD) method is based on the volume of fluid (VOF) method and global moving mesh (GMM) method. Various cases of a varying speed impact are shown for the CFD method, and a linear relationship between the pressure coefficient Cp and a dimensionless variable K is observed. To clearly explain the linear relationship between Cp and K, we follow the potential theory to derive the Cp expression based on several assumptions on the free surface drawn from the CFD results. The Cp expression and the motion of wedge bodies for a free impact derived from it are considered as an approximate solution for a varying speed impact. The approximate solution is compared with the existing analytical models and the published experimental data. The approximate solution can work well for different deadrise angles, while the existing analytical models can only be used for small deadrise angles. Good agreement is also obtained between the approximate solution and the experimental test results, including the time history of wedge acceleration and the pressure on the wedge surface.

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

“…The agreement between the CFD result and the present model with acceleration effect, e.g., Eq. ( 25), is good in both slamming and transition stages, while the theory of approximate solution without considering the transition stage [21] can only address the slamming stage. The present model without acceleration effect, e.g., Eq.…”

“…From the studies of slamming stage [36,21], the pressure changing caused by the acceleration of wedge can be quantified by the dimensionless velocity potential −2Φ. and Case 3 in Tab.…”

“…Therefore, there is an increasing need to improve the efficiency of the 2.5D methods and the 2D+t theory by proposing an analytical solution as accurate as the numerical methods to predict the hydrodynamic forces in both slamming and transition stages. For the slamming stage, many researchers had contributed to the formulations of hydrodynamic force by added mass methods [4,5,17], asymptotic theories [18,19,20] and approximate solution [21]. Among them, the approximate solution of Wen et al [21] provided the most accurate model for the constant and varying speed cases by a similarity solution of Dobrovol1'skaya [22].…”

“…For the slamming stage, many researchers had contributed to the formulations of hydrodynamic force by added mass methods [4,5,17], asymptotic theories [18,19,20] and approximate solution [21]. Among them, the approximate solution of Wen et al [21] provided the most accurate model for the constant and varying speed cases by a similarity solution of Dobrovol1'skaya [22]. For the transition stage, due to the different hydrodynamic characteristics, the formulation of hydrodynamic force is more difficult and is yet to be fully addressed.…”

“…For the transition stage, due to the different hydrodynamic characteristics, the formulation of hydrodynamic force is more difficult and is yet to be fully addressed. In this paper, by following the formulation work of our previous research [21], the transition stage of the water entry of linear wedges with constant and varying speeds, as shown in Fig. 3, is formulated to complete the 2D water entry model.…”