Mathematical Model for Nucleation, Ostwald Ripening and Growth of Inclusion in Molten Steel

Numerical simulation is a powerful tool to investigate inclusion behavior in the molten steel Although many mathematical models have been developed to predict inclusion collision growth behavior in different metallurgical reactors the inclusion size distribution had to be obtained by experiment or assumption Thus a general nucleation-growth model which involves in chemical reaction homogeneous nucleation and growth kinetics is developed to investigate the inclusion nucleation Ostwald ripening Brownian collision-growth Stokes collision growth and turbulent collision-growth In order to speed up the calculation the deoxidation products are divided into two parts The first part only consists of embryos and directly numerical simulation is used to solve the differential equations The second part only consists of inclusion particles and particle size-grouping method is introduced to solve the related equations Numerical results showed that the predicted inclusion size distributions are consistent with previous experimental data With the increasing diffusion coefficient the peak value diameter keeps unchanged and the maximum number density decreases With the increasing turbulent energy dissipation rate the peak-value diameter and the maximum number density decrease under the assumption on floating-out of larger inclusions