NUMERICAL SIMULATION OF LIQUID SLOSHING IN RECTANGULAR TANKS USING CONSISTENT PARTICLE METHOD AND EXPERIMENTAL VERIFICATION

Abstract

The use of numerical simulation has made an enormous impact on the study of free surface motion of incompressible liquid such as liquid sloshing. Simulating this complex problem has many important applications, ranging from coastal protection and offshore structure design to LNG/oil sloshing on vessels. Furthermore, animated wave motion has great potential in modern movies and computer games where violent liquid motion is featured. In this context, conventional mesh-based numerical methods have met difficulties in simulating waves involving discontinuity of liquid motion (e.g. wave breaking). Even with some free-surface capturing techniques incorporated, such as marker-and-cell and volume of fluid, mesh-based methods suffer from the problem of numerical diffusion. This is mainly due to the discretization of advection terms in the Navier-Stokes equation in Eulerian formulation. In addition, tracking of free surface requires complex and time consuming algorithm to update the time varying nonlinear boundary. In recent years, a new generation of computational methods known as meshless (mesh-free) methods has been shown to outperform conventional mesh-based method in dealing with discontinuous fluid motion. Lagrangian meshless methods called particle methods have shown very good potential in dealing with large-amplitude free surface flows, moving interfaces and deformable boundaries. The problem of numerical diffusion does not arise in particle methods. Nevertheless, in many of the existing particle methods such as Smoothed Particle Hydrodynamics (SPH) method and Moving Particle Semi-Implicit (MPS) method, the approximation of partial differential operators requires a pre-defined kernel function. Accuracy is not necessarily satisfactory when the particle distribution is irregular. In particular, these particle methods tend to give severe and spurious pressure fluctuation. In this thesis, a new particle method addressing the above-mentioned problems is proposed for 2D large amplitude free-surface motion. Called the Consistent Particle Method (CPM), it eliminates the use of kernel function which is somewhat arbitrarily defined. The required partial differential operators are approximated in a way consistent with Taylor series expansion. A boundary particle recognition method is applied to help define the changing liquid domain. The incompressibility condition of free surface particles is enforced by an adjustment scheme. With these improvements, the CPM is shown to be robust and accurate in long time simulation of free surface flow particularly for the smooth pressure solution without spurious fluctuation. The CPM is applied to study different 2D free surface flows, i.e. free oscillation of water in static tank, dam break in tank with different water depth-to-height ratios, dam break with obstacle. In the simulation of both gentle and violent free surface motion, the CPM outperforms the original MPS method in both particle distribution and pressure solution. An important free surface problem, 2D liquid sloshing in rectangular tanks is then studied experimentally and numerically by CPM. A series of sloshing experiments are carried out making use of a hydraulic-actuated shake table. Standing waves in high filling tanks, traveling waves in low filling tanks and breaking waves in a closed tank are well simulated by CPM in terms of free surface profiles and pressure fields. The CPM solution of pressure history shows tremendous improvement compared with MPS results. In all cases considered, the CPM solutions of free surface elevation and pressure are in very good agreement with the experimental results.