A Volume of Fluid (VOF) Method for the Simulation of Metallurgical Flows

Abstract

A finite difference numerical method, based on the VOF approach for tracking interface distortions, is presented. It is capable of accurately simulating the fluid flow of multiple immiscible fluids for metallurgical applications. This volume tracking method is based on piecewise linear reconstructions of interfaces, density distributions based on a shifted grid approach, and a fully kernel-based CSF method for surface force modelling. Second order temporal and spatial accuracy are achieved using improved Euler time-stepping enhancement of a two-step projection algorithm, supported by a multigrid-preconditioned GMRES solver that enabled large density ratios (1 : 30000) between the fluids and fine scale flow phenomena to be resolved. The code was used to simulate the rise of an air bubble in water and in liquid pig iron and was able to capture the time dependent oscillation of the bubble. The bubble velocity varied with the instantaneous shape of the bubble. The averaged terminal velocity of the gas bubble in water was in good agreement with published experimental data. Splash formation from a top submerged gas injection lance was simulated to illustrate the capability of the code in resolving the break up and fragmentation of liquid drops for possible use in the study of bath smelting processes.