Numerical Analysis For Metal Foaming Process With Lattice Boltzmann Method

In the recent years, the Lattice Boltzmann Method (LBM) has become popular for many applications in the field of computational fluid dynamics. Its simplicity allows comfortable implementation and optimization in parallel programming and blocking, which are greatly appreciated in high performance computing.The LBM has been used to metallic foam simulation for multi-dimensional problems. This thesis will present gas bubbles expansion within a liquid matrix by numerical simulation in order to better understand the physics of the complex underlying foaming process. The interest in metal foams has grown rapidly bringing to excellent results in innovative parts where, for example, high energy absorption, high stiffness, low weight and strict design parameters. The metal foaming process is up to now not completely understood, many physical phenomena are not well known and some information are still lacking. Hence, this thesis's aim is to use numerical simulations to achieve better understanding and optimize the necessary physical parameters of the foaming process like viscosity, bubbles'size, temperature, density, gas fraction, liquid fraction.The numerical solver is based on the lattice Boltzmann method. The LBM is capable to simulate the metal foaming process by developing an approach based on solving the discrete Boltzmann equation with a treatment of free boundary flow and the gas diffusion phenomenon. Using the lattice Boltzmann method to simulate fluid flows (gas/melt) means to not solve the Navier-Stokes equation (N-S) directly, instead one uses the aspect that from the Boltzmann equation the N-S equations can be recovered.The simulation is built up by a regular grid that consists of fluid, interfaces and bubble cells. The LBM is used on the cells occupied the fluid. Appropriate boundary conditions are settled at the interface cells. The simulations are constructed based on Chapman-Enskog expansion with macroscopic boundary conditions of the physical model and take into account the coefficients of expansion. The gas-liquid interfaces are determined by using an interface capturing method similar to volume of fluid approaches. Additionally, the LBM treats well the influence of material and the physical parameters such as density, viscosity, gas fraction, surface tension, stability and their inter-dependence. The influence of the processing parameters like temperature, ambient pressure, geometry of crucible is systematically investigated by numerical simulations and finally compared to experimental results. The numerical implementation of our model is based on lattice Boltzmann scheme. The lattice Boltzmann scheme is used for the aluminium foaming process by elaborating a study of free boundary flow and gas diffusive transport. The formation of oxides films on the surface of the cells is shown thermodynamically to be a necessary step in the production of low-density aluminium foams with a titanium hydride (TiH2). A temperature-dependent is only observed upper limit on porosity. It establishes that this the consequence of inhibition of the titanium hydride decomposition reaction by its products as the thickness of the surface oxide film increases. The variation of bubbles size, porosity of the material and chemical decomposition on the thicknessof the surface oxide film is derived. Thus, the LBM is applied on whole the fluids. Appropriate boundary conditions for the treatment of interface cells are developed and constructed according to a first order Chapman-Enskog expansion, whereas the macroscopic boundary conditions of the physical model of foaming process enter in the coefficients of the expansion providing a consistent approacj of the first order.The description of gas-liquid interfaces are used by an interface method similar to volume of fluid approaches. A strong and accurate algorithm for the foam expansion is used in order to integrate bubbles interaction, temperature evolution and surface tension effects. Furthermore, the algorithm easily integrates the incorporation of additional foaming specific features as for instance management of the bubbles size variation, disjoining pressure in cell films. The results of the simulation of foam structures compare very well with the experimental foam structures. The simulations demonstrate for the first time the two-dimensional and three-dimensional models of metallic foams. The impact of materials parameters used such as viscosity, density,surface tension, gas diffusion in the aluminium melt are investigated numerically.