A mathematical model to predict the growth and elimination of inclusions in liquid steel stirred by natural convection

Abstract

A model is developed to predict the rate of removal and the change in the size distribution of inclusions in a melt stirred by natural convection. Difficulties in obtaining an exact solution to the problem due to lack of adequate knowledge for the velocity fields in the melts are discussed. The model is based on Smoluchowski’s Theory of Gradient Collision to obtain the probability of collision between two inclusions under an arbitrarily chosen velocity gradient. Initial size distributions obtained in experimental heats are used as the input to the model. Various conditions are proposed by which inclusions are removed from the melt. The rates of removal are compared with the experimentally obtained rate of removal of oxides. It is observed that a boundary layer effect and the presence of a thin liquid metal film prevent rapid removal of inclusions from the stirred melts. Inclusion size distribution predicted by the model agrees qualitatively with the experimentally observed size distribution. It is postulated that the surface forces play a significant role in coalescence and assimilation of inclusions. Finally, the application of similar models to understand the removal of inclusions in such processes as argon sparging, solidification, degassing and electroslag remelting are advocated.