Mathematical Modeling of Iron and Steel Making Processes. Mathematical Modeling of Fluid Flow in Continuous Casting.

Abstract

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...

Effect of Double Ruler Magnetic Field in Controlling Meniscus Flow and Turbulence Intensity Distribution in Continuous Slab Casting Mold

“…The global flow characteristic is the function of mold thickness, mold width, argon injection rate, casting speed, and geometrical configuration of submergence entry nozzle (SEN). 1) Furthermore, abrupt enhancement in mold surface velocity variation brings asymmetry on the surface directed flow and its later effect passes to the formation of localized vortex and therefore occurrences of instability between the molten steel and slag layer interface. As a result, intermittent slag layer further entrained into the molten pool to form internal and surface defects in the final cast products.…”

Computational and experimental study of turbulent flow in a 0.4-scale water model of a continuous steel caster

“…[5] However, due to the nearly equal kinematic viscosities of molten steel and water, water models have been extensively used to investigate the flow in steel casters. [6][7][8][9][10][11] The dimensions and operating conditions of a water model are usually chosen to have geometry and Froude number (or sometimes Reynolds number) similarities [12] with the actual steel caster. Figure 1(a) shows an example of a scaled water model.…”

Transport Phenomena in a Beam-Blank Continuous Casting Mold with Two Types of Submerged Entry Nozzle

“…A number of studies have shed light on the important aspects of top free surface characteristics in slab, billet and bloom continuous casting molds, 1) but few studies are related to the beam-blank continuous casting. Figure 4 shows the predicted level fluctuation, maximum velocity magnitude and temperature distribution on the top free surface.…”