Fluid flow is very important to quality in the continuous casting of steel. With the high cost of empirical investigation and the increasing power of computer hardware and software, mathematical modeling is becoming an important tool to understand fluid flow phenomena. This paper reviews recent developments in modeling phenomena related to fluid flow in the continuous casting mold region, and the resulting implications for improving the process. These phenomena include turbulent flow in the nozzle and mold, the transport of bubbles and inclusion particles, multi-phase flow phenomena, the effect of electromagnetic forces, heat transfer, interfacial phenomena and interactions between the steel surface and the slag layers, the transport of solute elements and segregation. The work summarized in this paper can help to provide direction for further modeling investigation of the continuous casting mold, and to improve understanding of this important process.KEY WORDS: mathematical modeling; computational simulation; review; continuous casting; nozzles; molds; multiphase; turbulent; fluid flow; electromagnetic; coupled solidification; inclusion entrapment; segregation.steel. This paper will review recent developments in modeling each of the phenomena above, which are related to fluid flow in the continuous casting mold, and the resulting implications for improving the continuous casting process.
Fluid Flow ModelingA typical three dimensional fluid flow model solves the continuity equation and Navier Stokes equations for incompressible Newtonian fluids, which are based on conserving mass (one equation) and momentum (three equations) at every point in a computational domain. 17,18) The solution of these equations, given elsewhere in this issue, 19) yields the pressure and velocity components at every point in the domain. At the high flow rates involved in this process, these models must incorporate turbulent fluid flow. Many different turbulence models have been employed by different researchers for fluid flow in continuous casting, such as effective viscosity models 20,21) (for the cylindrical mold and straight nozzle), one equation turbulence models (turbulent energy plus a given length-scale), 22) two-equation turbulence models such as the K-e Model, 19,23) LES (Large Eddy Simulation), [24][25][26][27][28] possibly with a SGS (sub-grid scale) model, 29,30) and DNS (Direction Numerical Simulation).
19)Among these models, direct numerical simulation is the simplest yet most computationally-demanding method. DNS uses a fine enough grid (mesh), to capture all of the turbulent eddies and their motion with time. To achieve more computationally-efficient results, turbulence is usually modeled on a courser grid using a time-averaged approximation, such as the popular K-e model, 23) which averages out the effect of turbulence using an increased effective viscosity field, m eff . This approach requires solving two additional partial differential equations for the transport of turbulent kinetic energy and its dissipation rate.19...