Mathematical Modelling of Transport Phenomena in Continuous Casting of Steel.

Abstract

A steady state, two dimensional mathematical for continuous casting of steel has been developed. Towards this, governing partial differential equations of fluid flow and thermal energy transport together with the appropriate set of boundary conditions were derived and a procedure for their non-dimensional representation outlined. The modelling of (1) turbulence, (2) flows and energy transport within the mushy region, and (3) bulk motion of the descending strand on liquid steel flow and heat transfer phenomena were also discussed. The governing p.d.e's and the associated boundary conditions were solved numerically via a control volume based finite difference procedure. To this end, incorporating the SIMPLE algorithm, a computational procedure was developed in double precision, FORTRAN 77. Finally, three different industrial billet casting operations reported in the literature were mathematically modelled and direct comparison were made between predicted and experimental solidified shell thickness. Such comparisons demonstrated reasonable to excellent agreement between the two. Present estimates were also compared with our earlier predictions derived via an effective thermal conductivity based model. This indicated that for mathematical modelling of transport phenomena in continuous casting of steel, a conjugate heat and fluid flow model is the most appropriate.