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

Abstract

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 collisiongrowth, 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.

Modeling Inclusion Formation during Solidification of Steel: A Review

“…At the same time, a numerical method was introduced to reduce the load of the enormous computation. In the following work, a similar mathematical model was proposed by Lei et al [71]. In their model, the deoxidation products were divided into embryos and inclusion particles.…”

Modeling of manganese sulfide formation during the solidification of steel

“…Brownian motion, Stokes collisions, and turbulent collisions are normally considered when studying the inclusion coalescence in steelmaking vessels, such as an RH degasser and a casting tundish [32,33]. However, during the solidification process at the dendritic scale, it is difficult to calculate the collision frequencies in the same way as in metallurgical vessels due to the lack of corresponding parameters.…”

“…2, the collision frequencies of Brownian motion and Stokes collision are calculated using Eqs. (15) and (16) [32,33]. It is assumed that the average radius of MnS is 0.3 lm and the size ranges from 0 to 1.0 lm in the targeted system.…”

Evolution of Non-Metallic Inclusions in Secondary Steelmaking: Learning from Inclusion Size Distributions

“…Among the mathematical models, population balance equations have been used by Zhang and Pluschkell, 6) Zhang and Lee, 5) Kwon et al 40) and Lei et al 41) to build a general nucleation-growth model that can predict time-dependent particle size distribution of inclusions. The predicted number density of inclusions as function of inclusion size, as mentioned in section 2.1, is qualitatively very similar to experimental size distributions.…”

“…Numerical simulations 5,6,11,[35][36][37][38][39][40][41] have been extensively used to simulate inclusion size distributions in molten steel in order to understand the inclusions behavior in the melt and control their size distribution. Among the mathematical models, population balance equations have been used by Zhang and Pluschkell, 6) Zhang and Lee, 5) Kwon et al 40) and Lei et al 41) to build a general nucleation-growth model that can predict time-dependent particle size distribution of inclusions.…”