Study of Computational Issues in Simulation of Transient Flow in Continuous Casting

The attachment probability of inclusions on a bubble surface is investigated based on fundamental fluid flow simulations, incorporating the inclusion trajectory and sliding time of each individual inclusion along the bubble surface as a function of particle and bubble size. Then, the turbulent fluid flow in a typical continuous casting mold, trajectories of bubbles and their path length in the mold are calculated. The inclusion removal by bubble transport in the mold is calculated based on the obtained attachment probability of inclusion on bubble and the computed path length of the bubbles. The results are important to estimate the significance of different inclusion removal mechanisms. This work is part of a comprehensive effort to optimize steelmaking and casting operations to lower defects. Introduction Computational fluid dynamics (CFD) is becoming a powerful tool to study turbulent fluid flow in complex metallurgical processes, such as the continuous casting of steel slabs. These fundamentally-based mathematical models have advantages over other tools, such as water models and plant experiments, owing to their ability to quickly and accurately visualize and quantify flow patterns and related phenomena such as free surface motion, multiphase particle transport and entrapment, and heat transfer. Furthermore, their use is rapidly accelerating, due to the tremendous increases in computer hardware and software, which doubles in power about every 1.5 years. [1] Although CFD models are growing in power and complexity, accurate results are often difficult to achieve. This can be due to modeling assumptions in the turbulence model, inappropriate assumption of flow symmetry, insufficient domain size, oversimplified inlet conditions, inadequate mesh refinement, convergence problems, poor choice of boundary conditions such as wall laws and outlet conditions, and many others. Many different modelling choices are available, and the best choice is often problem dependent. Thus, the present work was undertaken to investigate some of the issues affecting the numerical accuracy of CFD models in the context of turbulent flow in the nozzle and mold during the continuous casting of steel slabs. Based on the results of many simulations of the same system with different models, guidelines are offered for choosing the simulation domain, symmetry assumption, inlet conditions, mesh refinement, and turbulence model. This work should be useful for developing future models of continuous casting, or similar flow systems, and in evaluating the accuracy of the results. Previous Work In spite of the widespread application of CFD models to continuous casting, and the many different modeling options that are available, relatively few studies have systematically investigated the numerical accuracy of CFD models of this system. The accuracy of CFD models has been investigated systematically in other systems [2-4]. Najjar et al [5, 6] studied the effects of inlet conditions and wall laws on velocity distribution in a continuous slab casting mold fed from a bifurcated nozzle using a 2-D finite-element Kmodel. They developed guidelines for achieving efficient convergence, consisting of larger relaxation factors for early iterations to accelerate reduction of the initial error, followed by smaller relaxation factors to maintain stable convergence. A new wall law was found to produce better accuracy than the standard wall law for this flow problem involving jet impingement and recirculation. Inlet conditions, including those for turbulence parameters, had a huge influence on the flow pattern. Hershey et al [7] found that uncoupling the nozzle and mold simulations was reasonable, as it produced only small differences in the flow pattern near the recirculation region near the upper ports. MS&T 2004 Conference Proceedings, (New Orleans, LA), AIST, Warrendale, PA 333 Thomas et al [8] compared 4 different methods for studying fluid flow in slab casting. Two different modelling approaches both matched well with measurements in a water model and in an actual steel caster. The standard Kmodel was able to simulate the time averaged 3-D flow pattern with almost equal accuracy to a fully-transient, large eddy simulation with a fine mesh, as compared with Particle Image Velocimetry measurements and measurements in an operating steel slab casting mold. However, the Kmodel was less accurate for time-related phenomena, such as the turbulent kinetic energy distribution and flow oscillations. These and other related phenomena, such as the distribution of superheat, the transport and removal of inclusion particles, and the multiphase interactions between the top surface of the steel and the flux layers above are much more important than the fluid flow itself. The accuracy of CFD predictions of these phenomena has not been compared quantitatively. This work focuses on single-phase fluid flow and heat transfer in a continuous caster of stainless thin slabs [9] pictured in Fig. 1 for the conditions given in Table 1. Previous work [10, 11] has demonstrated that predictions of an LES model of transient flow in this caster matches well with measurements in a water model, including the flow velocities, [10] top surface contour, and particle flotation rates.[11] The present work investigates computational issues involved in obtaining accurate predictions of this system, including the time averaged flow pattern, transient behaviour, and heat transfer in the molten pool. Pressure Boundary Condition at Bottom 984mm 1 2 0 0 m m 132mm No-Slip Boundary Free-Slip Bounary Casting Speed = 25.4mm/s z y x SEN Stopper Rod Tundish Region Figure 1. Schematic of the nozzle and mold domains. Table I. Parameters and properties for steel caster simulation. Mold (domain) thickness 132 mm Mold width 984 mm Model domain width 492 mm Nozzle domain length (to port top) 687 mm Strand domain length 1.2 m Model domain length (total) 1.76 m Nozzle bore diameter 70 mm Side Nozzle port height 75 mm Side Nozzle port width 32 mm Bottom Nozzle port diameter 32 mm SEN submergence depth 127 mm Casting speed 25.4 mm·s Casting temperature 1832 K Steel composition Stainless Steel liquidus temperature 1775 K Reference temperature, T