RIASSUNTO
Abstract
In the present study, the process of free-falling wedge impacting on water is numerically studied by our in house solver based on Moving Particle Semi-Implicit (MPS) method. Some improved schemes are used in this solver to suppress numerically unphysical pressure oscillation in traditional MPS method. For validation purpose, computational results of wedge with different tilting angles are compared against experimental results from the Wave Induced Loads on Ships Joint Industry Project III (WILS JIP-III). Numerical pressures, free surface elevations and velocities of wedge show agreement with experimental data.
Introduction
During ship sailing at rough sea, slamming occurs when the forefoot of ship hull rises above the water surface and then drops into water with high vertical velocity (Southall et al., 2014). Periodical and short duration impact loads can cause serious damage to ship structure. Hence, the slamming problem is important for ship design and operation.
Over the past decades, the slamming problem was commonly investigated as the similar flow of wedge entry into water (Yang and Qiu, 2012), and firstly studied by von Karman (1929) and Wagner (1932). Among the early established methods, theoretical approaches were much popular to solve this problem. However, these methods are hard to describe the complex nonlinear free surface flow. On the contrary, kinds of numerical methods based on the Navier-Stokes equation are developed and show the capability to solve the water entry problem. Among these approaches, Lagrangian particle methods are more and more popular to free surface flow problems in the near few years. The Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) methods are the representative Lagrangian type mesh-less methods. The SPH method is originally developed for compressible flows by Monaghan (1994). By choosing a sufficiently high speed of sound and a much small size of time step, it can be employed to solve water entry problem (Oger et al., 2006; Shao 2009; Liu et al., 2012; Koukouvinis et al., 2013; Ma and Liu, 2014; Amicarelli et al., 2015). Compared to SPH method, MPS method was originally proposed by Koshizuka and Oka (1996) for incompressible flow. Since the pressure of fluid is computed by a semi-implicit algorithm, a relatively large size of time step can be used in MPS method. Recently, several applications of the water entry problem based on MPS method were published. For example, Lee et al. (2010) employed the MPS method to calculate the impact loads by falling flat plate with incident angles. Yokoyama et al. (2014) numerically studied the water entry of spheres by MPS method and discussed the influence of the surface conditions of the solids falling into the water on the formation of the splashes. Sun et al. (2015) proposed a MPS and modal superposition coupled method to study the 2D flexible symmetric wedge dropping into water problem. Hwang et al. (2015) developed a MPS-FEM coupled method to simulate a wet drop with deformable wedge.