A comprehensive approach for CFD modeling of slag foaming with population balance modeling

A comprehensive approach for simulating the formation of slag foam is proposed. Foam is considered as a separate phase which is comprised of a mixture of air and liquid. A computational fluid dynamic (CFD) model has been developed for the simulation of slag foaming on bath smelting slag (CaO-SiO-Al2O3-FeO). The model accounts for the formation of foam due to transformation of both gas and liquid into foam and it's destruction due to liquid drainage and bursting of bubble. The bubble break up model of Luo and Svendsen 1) and the coalescence model of Prince and Blanch 2) are used in the present study. The bubble coalescence model based on film rupture by Tong et al. 3)has been used in the foam layer of the present study. Population balance modeling was used to track the number density of different bubble class. The advent of high speed computing machine facilitates the use of computational fluid dynamic model in many engineering fields. Numerous CFD model of multiphase flow have been developed, and numerical data has been validated through comparison with experimental data. It has been successfully used in metal processing involving gas-liquid flow 4, 5, 6, 7, 8). The CFD solver employed uses the finite volume discretization method which rests on integral conservation statements applied to a general control volume. The Eulerian multiphase flow model solves the conservation of mass, momentum, and energy of each phase in each cell. The exchange of mass, momentum, and energy are dealt with the interphase exchange term in the conservation equation. The governing equations in this approach can be derived by ensemble averaging the fundamental conservation equations for each phase to describe the motion of liquid and gas in a bubble column. Both the continuous and the dispersed phases are modelled in the Eulerian frame of reference as interpenetrating continua. The momentum equations of the phases interact with each other through inter-phase momentum exchange terms. The numerical simulation was performed by a commercial CFD solver in AVL FIRE 2009.2 9), but the full foaming model comprising of equation of bubble break up, coalescence and foam formation and destruction were incorporated into AVL FIRE 2009.2 as subroutine written by the author in FORTRAN. The foaming index as a function of percentage of FeO in slag is presented in Figure 1. The predicted results from the present study are validated against the experimental data 10, 11) and was found to be in reasonable agreement with the available experimental data. Dimensionless analysis was performed based on the model available in the literature to correlate the foaming index with the physical properties of the slag and the coefficient of the foaming index was found to be 109 and 127 when the dimensionless group of Jiang and Fruehan 10) and Ito and Fruehan 11) was used respectively. The predicted results from the present study are in reasonable agreement with the experimental data. The CFD model predicted the foaming height and the number density of different bubble class. The influences of different parameters on the foaming index and bubble number density are discussed in the presentation.