Numerical simulation of flooding of a damaged ship Zhiliang Gao n , Qiuxin Gao,Dracos Vassalos Department of Naval Architecture and Marine Engineering, University of Strathclyde, Glasgow,G4 0LZ,United Kingdom a r t i c l e i n f o Article history: Received 17 March 2011 Accepted 30 July 2011 Editor-in-Chief: A.I.Incecik Keywords: Damaged ship motion Floodwater motion VOF method Dynamic mesh a b s t r a c t A clear understanding of the complex dynamic behaviour of a damaged ship and floodwater remains limited for ship designers and safety authorities.In this paper, a Navier–Stokes (NS) solver,which combines the volume of fluid (VOF) method with dynamic mesh techniques, was developed to simulate the flooding of a damaged ship. The VOF method was used to capture the fluid interface. The dynamic mesh techniques were employed to handle the mesh update following transientship motions. To validate its performance,the solver was applied to the flooding problems ofa damaged barge.The computed results are satisfactory with respect to the experimental data. & 2011 Elsevier Ltd.All rights reserved. 1. Introduction The maritime tragedies that have occurred over the years (e.g., the losses of the Herald of Free Enterprise in 1987,Estonia in 1994, Express Samina in 2000,etc.) have motivated large-scale investigations on the survivability of damaged ships. The study within the European research project SAFEDOR (2005–2009) reveals that the risk to human life from flooding is the dominant issue concerning safety in passenger ships. Thus, a clear under- standing of the dynamic behaviour of damaged ships upon flooding is essential to establish proper life-saving measures and evacuation procedures. During the flooding process,a ship’s motion impacts water flooding and sloshing in its compartment; conversely, the liquid loads acting on the compartment also influence the motion of the ship. Numerical studies on this coupled dynamic problem have been conducted since the 1990s by various researchers (Vassalos and Turan, 1994; Chang and Blume, 1998; Spanos and Papanikolaou,2001; Palazzi and De Kat, 2004; Valanto, 2006; Lee et al.,2007; Santos and Guedes Soares, 2008,2009).In these studies, ship motion equations are modified by introducing additional terms to account for the floodwater effect. The exter- nal-wave-induced loads (Froude–Krylov and diffraction forces) and ship-motion-induced load (radiation force) are calculated using the potential flow method.The viscous effects are treated through different semi-empirical means. Although hydrodynamic loads acting on the external hull surface can be effectively predicted with the aforementioned approaches, addressing floodwater motion is critical and still challenging in numerical simulations.In the above-mentioned mathematical models,the inflow and outflow of water through the damaged opening is determined using a modified empirical Bernoulli’s equation, and thus, the transient dynamics of the flow are ignored. Except for those employing the shallow water equation ( Chang and Blume, 1998 ; Valanto, 2006; Santos and Guedes Soares, 2008), the approaches, which assume the floodwater surface in the compart- ment to be either horizontalor a freely movable plane, lack the ability to model the internal flows with strongly non-linear beha- viours.In addition,all mentioned models cannot fully account for the influence ofthe damaged opening geometry or the complex compartment internal layout on the motion of floodwater. A fundamental,but more sophisticated, method of simulating the intricate flooding phenomenon is based on solving the Navier–Stokes (NS) equations with the free-surface-capturing schemes.The most popular surface-capturing methods include the marker and cell (MAC) method ( Harlow and Welch, 1965), the level set (LS) method (Osher and Sethian, 1988) and the volume of fluid (VOF) method (Hirt and Nichols, 1981).The MAC method is extremely accurate and can account for substantial topology changes in interface.But this method is computationally very expensive due to the requirement of tracing a large number of particles, especially in three-dimensional simulations. The LS method is conceptually simple and relatively easy to implement yielding accurate results when the flow is smooth and evolves with a simple interface. However, the LS method has the principal disadvantage that it suffers from loss of mass in cases where the interface experiences severe stretching ortearing. In the VOF method,a scalar indicator function known as volume fraction is used to represent the interface. An advantage of representing the interface as a volume fraction is the fact that we can write Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2011.07.020 n Corresponding author. Tel.: þ44 0 141 5484914. E-mail address: zlgao@hotmail.com (Z. Gao). Ocean Engineering 38 (2011) 1649–1662