Year: 2005
Type: dissertation
Abstract: The evolution of cell structures in metal foams is investigated in detail by numerical simulations in order to improve the understanding of the complex underlying processes. The development of the simulation tool, which is based on the lattice Boltzmann method (LBM), is comprehensively presented. The work focuses on the powder metallurgical manufacturing route of metal foams. Here, in-situ gas generation produces gas bubbles in the liquid metal, which eventually form up to a foam structure. The formation of these metal foams is described and analyzed in detail. From this, a physical model of the foaming process is drawn. The model is relatively general. In such a way numerous foaming aspects are integrated into the model. As the present work is a first step to a comprehensive and complete simulation tool, some simplifications are included in the model as for instance the restriction to two dimensions. Essentially, the model consists of the diffusion equation for the description of the diffusion of the dissolved propellant into the bubbles and the Navier-Stokes equation to describe the flow of the liquid metal. The two partial differential equations are coupled by the free surface and Sieverts' boundary conditions at the interface of the gas bubbles. The ideal gas law is assumed in the gas bubbles. Additionally, foam specific phenomena as the disjoining pressure in the cell films enter into the model. In summary, melt flow, bubble growth, gravitational and capillary drainage, surface tension effects, foam stabilization, bubble coalescence, foam coarsening, foam rheology and collapse are comprised by the model. The numerical implementation is based on the lattice Boltzmann model. The LBM is adapted for the foaming process by developing a treatment of free boundary flow and diffusive transport. The simulation area is built up by a regular grid that consists of fluid, interface and bubble cells. The LBM is solely applied on the cells occupied by fluid. Appropriate boundary conditions are developed for the interface cells. Here, a priory unknown distribution functions exist. These are constructed according to a first-order Chapman-Enskog expansion, where the macroscopic boundary conditions of the physical model enter exactly in the coefficients of the expansion. This provides a self-consistent approach of first order. An interface capturing method similar to volume of fluid approaches is used to describe the movement of gas-liquid interfaces. A new robust and accurate algorithm for the curvature calculation is developed in order to integrate surface tension effects. Furthermore, the LBM allows easily for the incorporation of additional foaming specific features as for instance management of the bubble variables, disjoining pressure in cell films and film rupture criteria. The simulated foam structures compare very well with real foam structures. The influence of material parameters such as melt viscosity, surface tension, cell film stabilization, diffusion coefficient of the propellant in the melt and the influence of process parameters like ambient pressure, heating rate, amount of blowing agent, geometry of the mold, on the formation of the foam structure are systematically investigated by numerical simulations. The simulations demonstrate for the first time the pronounced impact of the disjoining pressure in the cell films on the foam stabilization.
Author: Michael Thies
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3212908343