Numerical Simulation Of Sloshing In Two Dimensional Rectangular Tanks With SPH

Liquid sloshing are encountered in a wide variety of hydraulic engineering situations and significant in theory. It is one kind of representative free surface flows and will experience violent fluid motion which is confined inside the tanks. SPH (Smoothed Particle Hydrodynamics), as a meshfree, Lagrangian, particle method, is a recently developed method. It has been widely applied in astrophysics, hydrodynamics and other relative subjects. Compared with other grid-based numerical methods, the most advantage of SPH is that it can naturally handle hydrodynamic problems with extremely large deformation of the free surface and wave break. In this thesis, the application of SPH in sloshing problems is discussed.The SPH formulation of the Navier-Stokes equations is derived. The formulations for the Navier-Stokes equations in a coordinate system moving with the tank motions are derived. Some basic conditions and treatment for using SPH method are introduced, such as artificial viscosity, density re-initialization, boundary treatment and so on.The main work in this thesis is numerical simulation of sloshing processes in two dimensional rectangular tanks which are under surge and pitch excitation by SPH method. The results are close agreement with the researches available. The computational results show that when the excitation frequency is closed to the highest natural frequency, the impulse pressure on the tops of the tank and wave breaking appears. The velocity and pressure fields are also given. The simulation of pitch shows short-lived circulations occur when the surface profile at the wall is a relative peak. Coupled surge-pitch motions show that the wave elevations are smallest when the phase difference is equal to zero and highest when the phase difference is 180 degree.