Modeling Study of Metallurgical Slag Foaming via Dimensional Analysis

A procedural model is urgently required for optimization of slag foaming in metallurgical processes. Through physical modeling following the similarity criterion of the Morton number (Mo), this paper investigates the effects of superficial gas velocity, dynamic viscosity, and surface tension on the foaming height. From the physical modeling results, several dimensionless numbers relevant to the slag foaming were identified, and this includes the Reynolds number (Re), Weber number (We), Froude number (Fr), and Mo. In addition, the relationships between Mo and Re for the various types of slag foaming were derived via dimensional analysis. Furthermore, assuming that these dimensionless numbers follow a power law, correlations of foaming height as a function of the slag physical properties and the superficial gas velocity were obtained based on the physical modeling results. Consequently, this study proposes a dynamic mathematical model for predicting the liquid height variation with time during slag foaming according to the gas balance.