Numerical Study on Impact Pressure due to Violent Sloshing Waves Q.W. Ma 1 , Wen Yang Duan 2 , J. Zhou 1 , Xing Zheng 2 , S. Yan 1 1 School of Engineering and Mathematical Sciences, City University, London, UK 2 College of Shipbuilding Engineering, Harbin Engineering University, China . ABSTRACT Sloshing waves have received numerous studies over the past several decades. Nevertheless, there are still many uncertainties associated with wave breaking and splashing, formation of air pocket and air bubbles, behaviours of impact pressure and dynamic interaction between wave impact and structural response during violent sloshing. This paper will concentrate on impact pressure due to violent sloshing waves. The impact pressure will be investigated by using the MLPG_R (Meshless Local Petrove-Galerkin based on Rankine source solution) method, developed at City University London and the SPH (smoothed partial hydrodynamics) method, developed at Harbin Engineering University and also by using a commercial package – StarCD, which is based on finite volume method. Investigation will be performed for various cases with and without a baffle. Our main interest lies in the behaviours of impact pressure under different conditions, such as the relationship between the maximum pressure and the motion of the waves and effects of baffles. These behaviours are very relevant to analysis of structural responses and so to design of safe structures. KEY WORDS: Meshless method; violent sloshing; impact pressure INTRODUCTION Sloshing waves are those generated in a moving tank, which are associated with various engineering problems, such as liquid oscillations in large storage tanks caused by earthquakes, motions of liquid fuel in aircrafts and spacecrafts, liquid motions in containers and the water flow on decks of ships. This paper will consider the sloshing waves in containers in the application of Offshore Engineering and Naval Architecture. There has been a considerable amount of work on sloshing waves. For the case of small motions, Abramson (1996) used a linear theory and Solaas and Faltinsen (1997) adopted a perturbation theory. For relatively large motions, Jones and Hulme (1987), Faltinsen (1978), Okamoto and Kawahara (1990), Chen et al. (1996) and Armenio and La Rocca (1996) used various numerical methods for the two dimensional problem. For the three dimensional problem, Huang and Hsiung (1996) used the shallow water equation for the flow on the ship deck and Wu et al (1998) employed the full nonlinear potential formulation to study sloshing waves in a tank. More detailed review on sloshing waves can be found in (Ibrahim 2005). This body of work has significantly advanced our knowledge about sloshing waves. Nevertheless, there are still many uncertainties, particularly associated with violent sloshing waves, such as features of breaking and splashing, formation of air pocket and air bubbles, behaviours of impact pressure and dynamic interaction between wave impact and structural response during violent sloshing (Kim, 2007, Lee et al 2007). This paper will concentrate on impact pressure due to violent sloshing waves. In the cases where violent sloshing waves are involved, numerical modelling is very challenging. This is because the free surface can not be determined any more by assuming that the fluid particles on the free surface will always remain on the free surface. Actually, the particles initially within the fluid can emerge on the free surface and the particles initially on the free surface can immerge into the water. This clearly increases the difficulty to identify the free surface and also indicates that the viscosity can play an important role. The motion of water inside tanks can become very sensitive to boundary and initial conditions. In addition, the challenge of modelling violent waves may come from the fact that the gradient of pressure and velocity in violent waves can be very large and therefore the large number of particles or nodes as well as extremely small time step is required. This does not only increase the computational cost but may also lead to instability. A method, which may yield good and stabile solutions for problems without violent waves, may suffer from instability when it is used to simulate violent waves and result in the pressure with spurious fluctuations. To understand phenomenon associated with violent sloshing waves, a great effort has been made and various models have been developed, such as those given by Lee at al (2007), Kishev, et al (2006), Colagrossi, et al (2004) and so on. Nevertheless, the research on them is far from complete and there is no conclusion about which method or model is the best. In this paper, three different numerical models will be used to investigate the impact pressure under different conditions. They are the MLPG_R (Meshless Local Petrove-Galerkin based on Rankine source Proceedings of the Nineteenth (2009) International Offshore and Polar Engineering Conference Osaka, Japan, June 21-26, 2009 Copyright © 2009 by The International Society of Offshore and Polar Engineers (ISOPE) ISBN 978-1-880653-53-1 (Set); ISSN 1098-618 71