Numerical simulation of vertical water impact of asymmetric wedges by using a finite volume method combined with a volume-of-fluid technique Rasul Niazmand Bilandi, Saeed Jamei * , Fatemeh Roshan, Mohammad Azizi Faculty of Engineering, Persian Gulf University, Bushehr, Iran ARTICLE INFO Keywords: Symmetry and asymmetry wedges FVM VOF methods Low pressure area ABSTRACT In the present paper, two dimensional (2-D) symmetrical and asymmetrical wedges entering calm water vertically at constant speed are simulated based on the finite volume method (FVM). In order to obtain pressure distribution and free surface profile, volume of fluid (VOF) method coupled with FVM are utilized in Star CCMþ. Pressure distribution and free surface elevation are presented for each different symmetry and asymmetry deadrise angles. Low pressure area of the flow due to asymmetric impact or vertical impact velocity is shown in relation to the present study. Comparison of the obtained results against previously published works shows good agreement. 1. Introduction In the recent years, with the increase in popularity of planing hulls, many studies have been performed to investigate dynamic response and structural behavior of these vessels in waves. Among these researches, prediction of impact load on these vessels is of importance mainly because these boats may go through large motions in waves. Solving the water entry problem, not only provides structural loads for engineers, but also it can be used in solving dynamic motion of planing hulls by extending the 2-D sectional forces in direction of boat's length. From an application point of view, the peak pressure and pressure distribution on the wedge are of utmost concern due to their effect on rigid object integrity during the impact event. Generally, experimental, analytical and computational fluid dynamics (CFD) methods are used to solve water entry problem. Von Karman (1929) was one of the pioneer researcher, who mathe- matically modeled symmetrical planing boat. He reduced 3-D problem to 2-D by simplifying the cross section of landing vessels to a wedge shape. He provided a theoretical model based on momentum variation and the added mass for the force prediction as the V-shaped body penetrates the water surface. Following his work, Wagner (1932) modified the Von Karman solution and proposed an analytical method to calculate pressure distribution on seaplane floats during water landing. Wagner (1932) considered effect of water splash-up on the body during water impact. However, the Wagner method assumes the rigid body has a blunt shape. Mackie (1962) proposed first fully linearized solution for the wedge water entry problem. Later, in 1969, Dobrovol'Skaya (1969) obtained a complete solution for a 2D wedge based on potential theory. This solu- tion is based upon using Wagner's h-function (see Gurevich (1965)) and can be applied to the problems where the flow region is bounded by free surfaces and uniformly moving (or fixed) rectilinear impermeable boundaries. This solution is valid for any deadrise angle, it is implicitly provided in terms of integral equations which must be solved numeri- cally. There are many other publications exploring symmetric and asymmetric water entry problem based on the examined theoretical, numerical and experimental methods. Some of these researches are performed by Greenhow (1987), Chekin (1989), Cointe (1991), Howison et al. (1991), Toyama (1993), Fraenkel and McLeod (1997), Korobkin (1997, 2004), Mei et al. (1999), Scolan et al. (1999), Korobkin and Iafrati (2002), Judge et al. (2004), Wu et al. (2004), Yettou et al. (2007), Moore et al. (2012) and Swidan et al. (2013). As commented earlier, some numerical methods have also been applied by different researchers to simulate the water impact problem. Zhao and Faltinsen (1993) and Zhao et al. (1996) studied water entry problem numerically using a nonlinear boundary element method (BEM) in the time domain, and then they solved potential flow around the body. In their simulations, they removed the thin jet layer from their compu- tations and they assumed that pressure variations in the tip region are small. They calculated the pressure distribution on the wedges and agrees well with previous theoretical works. Afterward, Zhao et al. (1996) proposed two methods for water entry problem with non-linear simula- tion of Laplace equation and analytical solution of Wagner, and then they validated their results against experimental results of a 30  wedge. Moreover, Kihara (2004) also used boundary methods and a mixed Euler * Corresponding author. E-mail address: jaameisa@pgu.ac.ir (S. Jamei). Contents lists available at ScienceDirect Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng https://doi.org/10.1016/j.oceaneng.2018.04.043 Received 1 July 2017; Received in revised form 12 March 2018; Accepted 15 April 2018 0029-8018/© 2018 Elsevier Ltd. All rights reserved. Ocean Engineering 160 (2018) 119–131