Mathematical modelling of mass transfer rates between solid and liquid in high-temperature gas-stirred melts

Abstract

A mathematical model for the prediction of mass transfer rates between solid additions and liquid metals in high-temperature gas-stirred metallurgical reactors has been developed. Isothermal dissolution of steel rods in gas-stirred Fe-C melts has been mathematically simulated, and the distribution of flow variables and turbulence parameters has been estimated through numerical solution of turbulent Navier-Stokes equations in conjunction with the k-∈ turbulence model.On the basis of these results, relevant dimensionless groups have been estimated, embodied in a transport correlation proposed recently by Mazumdar and coworkers, and the corresponding mass transfer coefficients (for steel rod dissolving isothermally in a Fe-C melt) have been estimated as a junction of gas flow rates. Sensitivity of computations to various numerical and process parameters (grid configurations, plume dimensions, vessel geometry, thermophysical properties, etc.) has been rigorously assessed, and results independent of these have been established first. Numerically predicted mass transfer coefficients for a wide range of operating conditions have been compared directly with equivalent experimental measurements reported in the literature, and excellent agreement between theory and experiments has been achieved. Finally, in the absence of any detailed computational results, a simple yeteffective macroscopic approach has been suggested for ready calculation of mass transfer rates (e.g., of class II ferroalloys such as FeNb and FeW) in industrial gas-stirred ladle systems.