Simulation of bubbles behavior in steel continuous casting mold using an Euler-Lagrange framework with modified bubble coalescence and breakup models

Simulation of Spatial Distribution of Multi-Size Bubbles in a Slab Continuous-Casting Mold Water Model

In this paper, a fully coupled large eddy simulation model, including the volume of fluid model, the discrete phase model, the bubble-collision model, and the bubble-breakup model was used to simulate the spatial distribution of multi-size bubbles and its impact on the instantaneous two-phase flow in a slab continuous-casting mold. The influence of the bubble-interaction model on the bubbles' three-dimensional spatial distribution and size distribution, as well as on two-phase flow was discussed. By comparison with the velocity on the meniscus and the average bubble diameter inside a continuous-casting slab water model, the appropriate numerical model was recommended to accurately simulate the two-phase flow and characteristics of discrete bubbles. The submerged entry nozzle and the area around it saw bubble coalescence and breakage more frequently than other areas. The key interaction between the bubbles was their bouncing in the deep region of the mold. In the mold, the average bubble diameter was 0.741 mm, and 44.5% of the total number of bubbles had an approximately average diameter.

Numerical Modeling of Transient Two-Phase Flow and the Coalescence and Breakup of Bubbles in a Continuous Casting Mold

The multiphase flow and spatial distribution of bubbles inside a continuous casting (CC) mold is a popular research issue due to its direct impact on the quality of the CC slab. The behavior of bubbles in the mold, and how they coalesce and break apart, have an important influence on the flow pattern and entrapment of bubbles. However, due to the limitations of experiments and measurement methods, it is impossible to directly observe the multiphase flow and bubble distribution during the CC process. Thus, a three-dimensional mathematical model which combined the large eddy simulation (LES) turbulent model, VOF multiphase model, and discrete phase model (DPM) was developed to study the transient two-phase flow and spatial distribution of bubbles in a continuous casting mold. The interaction between the liquid and bubbles and the coalescence, bounce, and breakup of bubbles were considered. The measured meniscus speed and bubble diameter were in good agreement with the measured results. The meniscus speed increased first and then decreased from the nozzle to the narrow face, with a maximum value of 0.07 m/s, and appeared at 1/4 the width of the mold. The current mathematical model successfully predicted the transient asymmetric two-phase flow and completely reproduced the coalescence, bounce, and breakup of bubbles in the mold. The breakup mainly occurred near the bottom of the submerged entry nozzle (SEN) due to the strong turbulent motion of the molten steel after hitting the bottom of the SEN. The average bubble diameter was about 0.6 mm near the nozzle and gradually decreased to 0.05 mm from the nozzle to the narrow face. The larger bubbles floated up near the SEN due to the effect of their greater buoyancy, while the small bubbles were distributed discretely in the entire mold with the action of the molten steel jet. Overall, the bubbles were distributed in a fan shape. The largest concentration of bubbles was in the lower part of the SEN and the upper edge of the SEN outlet.

Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

In this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problems.

Influence of the Submerged Entry Nozzle’s Bottom Well on the Characteristics of Its Exit Jets

In vertical continuous casting machines the liquid steel from the tundish is poured into the mold through the Submerged Entry Nozzle (SEN). The shape and direction of the SEN exit jets affect the liquid steel dynamics inside the mold. This work quantifies the effect of the SEN pool on the principal characteristics of the jets emerging from it, precisely, the shape, the spread angles, and the mold impact point. Experimental and numerical simulations were carried out using a SEN simplified model, a square-shaped bore nozzle with square-shaped outlet ports whose length is minimal. These experiments showed two well-defined behaviors. When a single vortex dominates the hydrodynamics inside the simplified SEN, the exit jets spread out and are misaligned about the mold’s central plane. On the contrary, when the inner flow pattern shows two vortexes, the exit jets are compact and parallel to the mold wide walls. The measured difference on the jet’s falling angles is 5°, approximately, which implies that in an actual casting machine, the impingement point at the narrow mold wall would have a variation of 0.150 m. This hydrodynamic analysis would help design new SENs for continuous casting machines that improve steel quality.

Numerical Analysis of Effect of Initial Bubble Size on Captured Bubble Distribution in Steel Continuous Casting Using Euler-Lagrange Approach Considering Bubble Coalescence and Breakup

A mathematic model considering the bubble coalescence and breakup using the Euler-Lagrange approach has been developed to study the effect of the initial bubble size on the distribution of bubbles captured by the solidification shell. A hard sphere model was applied for dealing with the bubble collision. Advanced bubble coalescence and breakup models suitable for the continuous casting system and an advanced bubble captured criteria have been identified established with the help of user-defined functions of FLUENT. The predictions of bubble behavior and captured bubble distribution agree with the water model and plant measurements well respectively. The results show that the number of small bubbles captured by solidification shell is much higher than that of large bubbles. What is more, the number of captured bubbles at the sidewalls decreases with the distance from the meniscus. For the case of large gas flow rate (gas flow fraction of 8.2%), the initial size of bubbles has little effect on bubble captured distribution under various casting speeds. When the gas flow rate is small (gas flow fraction of 4.1%), the number density of captured bubbles increases as the initial bubble size increases, and the effect of initial bubbles size on captured bubble number density is amplified when the casting speed decreases. The average captured bubble diameter is about 0.12–0.14 mm. Additionally, for all cases, the initial bubble size hardly affects the average size of captured bubbles.