Numerical simulation on molten steel flow in the mold under the effect of vertical traveling wave magnetic field and horizontal steady magnetic field

The brake effect of the freestanding adjustable combination electromagnetic brake (FAC-EMBr) and EMBr ruler on the behavior of molten steel flow and the level fluctuation were investigated with the numerical method. The effects of the horizontal magnetic pole position (EMBr ruler), magnetic induction intensity, and casting speed on two types of electromagnetic brakes were studied. The numerical simulation results show that the magnetic field caused by the EMBr ruler is mainly distributed under the submerged entry nozzle (SEN), and it is very weak nearby the meniscus area. After the FAC-EMBr is applied, the magnetic field is mainly distributed in the area below the submerged entry nozzle, the upper roll region, and in the meniscus region. The application of the electromagnetic brake can effectively suppress the impact of the jet and decrease the molten steel velocity in the meniscus area. The brake effect of the EMBr ruler on the behavior of the molten steel flow and the level fluctuation is significantly influenced by the horizontal magnetic pole position. The increasing of the magnetic flux density can significantly increase the velocity of molten steel in the upper roll region and lead to an intense fluctuation in the steel/slag interface, as the horizontal magnetic field cannot cover the three key regions. The brake effect of the FAC-EMBr is less influenced by the variation of the process parameters due to the addition of vertical magnetic poles. Additionally, the “secondary braking effect” of the vertical magnetic poles can help to lower the increase of velocity in the upper roll region caused by the excessive magnetic induction intensity and the high casting speed. Therefore, even under the high casting speed conditions, the application of a new type of FAC-EMBr is also an efficient way to suppress the molten steel flow and level fluctuation at the meniscus area and decrease the possibility of slag entrapment.

In steel continuous casting, flow in the mold region is related to many quality problems such as surface defects and slag entrainment. An electromagnetic braking (EMBr) system is a method to control the steel flow field to minimize defects and capture inclusions. The position of the port of the Submerged Entry Nozzle (SEN) and the peak magnetic field both affect the performance of the EMBr. In the present work, an efficient multi-GPU based code, CUFLOW, is used to perform Large Eddy Simulations of the turbulent flow by solving the time-dependent Navier-Stokes equations in a domain that includes the slide gate, SEN and mold region. The computations were first validated by comparing the predicted surface velocity with plant measurements. Subsequently, eight LES simulations were conducted to study the effects of different EMBr values and SEN depths. The flow patterns in various regions are presented. The results show that applying EMBr greatly lowers top surface velocities and turbulent fluctuations.

Vertical magnetic fields have been known for decades to exist in the internetwork region of the Sun, while the properties of horizontal magnetic fields have only recently been extensively investigated with Hinode. Vertical and horizontal magnetic fields in the internetwork region are considered to be separate entities and have thus far not been investigated in a unified way. We discover a clear positional association between the vertical and horizontal magnetic fields in the internetwork region with Hinode. Essentially, all of the horizontal magnetic patches are associated with the vertical magnetic patches. Alternatively, half of the vertical magnetic patches accommodate the horizontal magnetic patches. These horizontal patches are located around the borders of the vertical patches. The intrinsic magnetic field strength as obtained with the Stokes V line ratio inside the horizontal patches is weak, and is in the subequipartition field regime (B < 700 G), while the field strength outside the horizontal patches ranges from weak to strong (kG) fields. Vertical magnetic patches are known to be concentrated on mesogranular and supergranular boundaries, while the horizontal magnetic patches are found only on mesogranular boundaries. These observations provide us with new information on the origin of the vertical and horizontal internetwork magnetic fields, in a unified way. We conjecture that internetwork magnetic fields are formed by the emergence of small-scale flux tubes with bipolar footpoints, and the vertical magnetic fields of the footpoints are intensified to kG fields due to convective collapse. Resultant strong vertical fields are advected by the supergranular flow, and eventually form the network fields.

A 3-D mathematical model has been developed to study the multiphase phenomena of magnetic field, flow field and temperature distribution of molten steel and inclusion behaviour, considering the coupled effects of electromagnetic brake (EMBR) and argon gas injection in the slab continuous casting mold with high casting speed. The effects of EMBR and argon gas injection on the flow and temperature of molten steel and inclusion removal rate have been investigated. Simulation results indicate that EMBR can slow down the flow velocity of molten steel effectively, especially near the meniscus; the areas of upper and lower re-circulation zones are reduced and temperature distribution of molten steel is more uniform and the temperature gradient is reduced; but it has no helpful for the removal of small inclusions. The argon gas injection can increase the molten steel flow up tendency in the upper re-circulation area duo to the buoyancy effect of ascending argon gas bubbles near the submerged entry nozzle (SEN) and be in favour of the floating up of inclusion particles, and temperature in the upper re-circulation zone increases. The increasing of argon gas flow rate results in a stronger vortex flow zone near the free surface, especially near the SEN and easily forms a secondary eddy flow with EMBR, which impacts the fluctuation of free surface and the slag entrapment. The double action of EMBR and argon gas injection can further increase the temperature in the upper re-circulation zone, especially near the meniscus, and the floating up rate of inclusions are also improved and the inclusions to be trapped into solidified shell is reduced.

Effects of vertical, horizontal and rotational magnetic fields on convection in an electromagnetically levitated droplet

To optimize the submerged entry nozzle (SEN) for an ultra-thick slab mold, a mathematical model has been established. The molten steel flow and solidification, inclusion transports, and meniscus fluctuation have been investigated through the model. Compared with the concave-bottom SEN cases, the convex-bottom SEN decreases the imping depth of the jet flow and increases the horizontal velocity and temperature on the meniscus. However, the remelting of the solidified shell is dramatic for the convex-bottom case. The well depth of the concave-bottom SEN and the SEN’s submerged depth have little influence on molten steel flow and solidification. The effects of SEN port shape and port angle on the molten steel flow are significant. As the port shape changes from rectangle to square or the port downward angle decreases, the imping depth of jet flow decreases, the horizontal velocity and the temperature on the mold free surface increase. For the ultra-thick mold, a square-shaped-port SEN with a −10° downward angle is more beneficial by comprehensive consideration of molten steel flow and solidification, inclusion removal, and mold powder melting. The optimized SEN has been applied to the actual caster and its performance has been assessed, indicating that the SEN optimization is efficient.

Electromagnetic braking (EMBr) technology, as one of the most effective technologies in the continuous casting process, provides an effective tool for improving the internal and external defects of steel products. Specifically, the EMBr technology takes the benefit of the generation of Lorentz force to decrease flow instability, mold powder entrapment, and surface defects, if applied properly. For this purpose, to gain a clear understanding of the effect of EMBr technology on the continuous casting process, a commonly used EMBr technology, namely ruler EMBr technology, is applied in the current work to investigate the dynamic behaviors of molten steel flow and steel–slag interface fluctuation inside a slab mold. Furthermore, to obtain a desirable braking effect of the ruler EMBr technology, operational parameters including the magnetic flux density, submerged entry nozzle (SEN) depth, and magnetic pole location are numerically investigated. The results demonstrate that the braking effect exerted by the ruler EMBr device is favorable for suppressing the impact of upward stream on the steel–slag interface with the magnetic flux density exceeding 0.3 T. For the influence of the SEN depth and magnetic pole location on the effect of ruler EMBr mold, the results show that a steady jet flow pattern can be obtained through the adjustment of a location between the ruler EMBr device and the SEN depth. For instance, when the ruler EMBr device installation position of 225 mm corresponds to the SEN depth of 150 mm, the upward deflection of jet stream is suppressed and a stable interface fluctuation profile is formed. With this adjustment, the possibility of mold flux entrapment is decreased.

Analyzed in this paper is the induced current density in the homogeneous prolate spheroid model of a biological object exposed to concurrent 60‐Hz vertical electrical field (1 kV/m), and horizontal and vertical magnetic fields (1 to 5 μT) with different phase angle. The analysis has been carried out separately considering the presence of electric and magnetic fields. The current density induced by the electric field is calculated using the finite element method, whereas the current density induced by the magnetic fields is calculated with exact solution for the prolate spheriod model. The total induced current density is the vector sum of the current density components induced by the electric and magnetic fields. It is found that the density of the total current is determined by the vertical electric field and horizontal magnetic field. The horizontal magnetic field has an important effect on the total induced current density distribution. The distribution of the density of the total current varies with the phase difference between the vertical electric and horizontal magnetic fields. As the model gets close to the ground, however, the contribution of the horizontal magnetic field to the total induced current density is found to decrease. © 2001 Scripta Technica, Electr Eng Jpn, 135(3): 8–15, 2001

The steel/slag interface behavior under a new type of electromagnetic brake (EMBr), vertical electromagnetic brake (V-EMBr), was investigated. The influence of the magnetic induction intensity, the submerged entry nozzle (SEN) immersion depth, and the port angle of the SEN are investigated numerically. The effect of magnetic induction intensity on the meniscus fluctuation of molten alloy is further studied by the experiments. The results show that the meniscus fluctuation is depressed as the magnetic induction intensity is increased, especially for the region in the vicinity of the narrow face of the slab mold. This result is validated by the following experiments. For the influence of the SEN immersion depth and the port angle, the results show that the meniscus fluctuation is suppressed as the values of the immersion depth and the port angle are increased (absolute values for the port angle). However, the influence of the immersion depth and the port angle are not as sensitive as those in the other type of EMBr, e.g., EMBr Ruler. The industrial application of V-EMBr could benefit from this result.

Analyzed in this paper is the induced current density in the homogeneous prolate spheroid model of a biological object exposed to concurrent 60-Hz vertical electric field (1kV/m), and horizontal and vertical magnetic fields (1-5μT) with different phase angle. The analysis has been carried out separately considering the presence of electric and magnetic fields. The current density induced by electric field is calculated using finite element method (FEM). Whereas the current density induced by magnetic fields is calculated with exact solution for prolate spheroid model. Total induced current density is the vector sum of the current density components induced by electric and magnetic fields. It is found that the density of total current is determined by vertical electric field and horizontal magnetic field. The horizontal magnetic field has an important effect on the total induced current density distribution. The distribution of the density of total current varies with the phase difference between vertical electric and horizontal magnetic fields. As the model gets close to the ground, however, the contribution of the horizontal magnetic field to the total induced current density is liable to decrease.

PurposeTo effectively control the molten steel flow and the stability of free surface in continuous casting mould, this paper aims to propose a new type electromagnetic brake technique, namely, vertical electromagnetic brake (V-EMBr). Its brake effect under special processing parameters such as submerged entry nozzle (SEN) depth and port angle is evaluated by the numerical simulation methods.Design/methodology/approachA couple three-dimensional mathematical model of fluid flow and static magnetic field was developed to investigate the behaviour of molten steel flow and steel/slag interface in the continuous casting mould, and a volume of fluid model is used to track the interfacial behaviour of molten steel and liquid slag by solving the continuity equation of the phase volume fraction.FindingsThe simulation results showed that the application of V-EMBr can significantly reduce the flow intensity in upper recirculation zone and decrease the meniscus height and the flow velocity of molten steel in the vicinity of narrow side of mould, which is beneficial to reduce the possibility of mould flux entrapment. Especially, the brake effect of V-EMBr has a little affected by the SEN depth and port angle, which is helpful for V-EMBr to better adapt the actual continuous casting process.Originality/valueCompared to the conventional-level EMBr, the new proposed V-EMBr has the advantage to effectively control the molten steel flow and steel/slag interfacial fluctuation in the vicinity of narrow side of mould with a pair of magnetic fields, and its brake effect is less affected by the changes in continuous casting processing parameters.

In a continuous casting process, magnetic coil has been applied to the molten steel flow control in a mold. Some of the magnetic coils are applied to stabilize the molten steel flow and the meniscus fluctuation to prevent powder entrapments. Others are applied to activate the molten steel flow to keep proper temperature at the meniscus or wash inclusions off near the solidification front. The Electromagnetic Level Accelerator (EMLA) has been developed to accelerate the molten steel flow from the nozzle in order to carry the molten steel to the narrow side of the mold when the casting speed is low or the mold width is wide. It applies low frequency alternating magnetic field moving from the nozzle to the narrow side of the mold just below the nozzle exits, because the electromagnetic force acts on the molten steel in the same direction as the magnetic field moving. In this study, the effect of the EMLA on the molten steel flow is investigated. Numerical simulation of the molten steel flow was carried out. The molten steel flow velocity measurement was also conducted in operation.Applying the EMLA, the molten steel flow is accelerated proportional to the imposed magnetic field. The molten steel flow from the nozzle can be controlled to reach the narrow side of the mold. Therefore, the risk of the extraordinary temperature drop at the mold corner of the meniscus decreases and the capture of the inclusions into the solidification shell that causes the surface defects is avoidable.

A kind of composite magnetic field for flow control in slab mold is proposed, in which an electromagnetic stirring (EMS) is carried out near the meniscus and an electromagnetic braking (EMBr) is carried out near the outlet of the submerged entry nozzle (SEN), simultaneously. The yoke for the EMS and the EMBr is made independent from each other, with a ruler type for the EMBr. A three-dimensional model of the magnetic field calculation is established. The simulation results show that the magnetic induction intensity generated with the EMS mainly concentrates in the EMS area. The magnetic induction intensity generated with the EMBr has a large component in the EMS results, which has little effect on the flow of this area. Based on the composite magnetic field calculation results, the three-dimensional numerical simulation of the flow field is carried out, and the flow field obtained is compared to that without the magnetic field but with the EMS and the EMBr only, respectively. The results show that under the composite magnetic field, EMBr and EMS can play their respective roles well under certain conditions, the impact of the jet flow on the narrow face is reduced, and the stirring beneath the meniscus is intensified.

Observations of narrow radio-emitting filaments near the Galactic center have been interpreted in previous studies as evidence of pervasive vertical (i.e. perpendicular to the Galactic plane) milliGauss magnetic field in the central 150 pc of the Galaxy. A simple cylindrically symmetric model for the equilibrium in this central region is proposed in which horizontal (i.e. parallel to the Galactic plane) magnetic fields embedded in an annular band of partially ionized molecular material of radius 150 pc are wrapped around vertical magnetic fields threading low-density hot plasma. The central vertical magnetic field, which has pressure that significantly exceeds the thermal pressure of the medium, is confined by the weight of the molecular material. The stability of this equilibrium is studied indirectly by analyzing uniformly rotating cylinder of infinite extent along the z axis in cylindrical coordinates (r,theta,z), with low-density plasma and an axial magnetic field at r 150 pc, and gravitational acceleration g* proportional to r directed in the negative-r-hat direction. The density profile and gravity tend to destabilize the plasma, but the plasma tends to be stabilized by rotation and magnetic tension--since the interface between the high and low-density plasmas can not be perturbed without bending either the horizontal or vertical field. It is shown analytically that when beta= 8(pi)p/B^2 is small and the dense plasma is supported against gravity primarily by rotation, the necessary and sufficient condition for stability to k_z=0 modes is |g| < (2|Omega| a), where g = g* - Omega^2 r is the effective gravity, Omega is the uniform angular velocity, and a is the sound speed in the dense plasma.

Complex multi-phase phenomena, including turbulent flow, solidification, and magnetohydrodynamics (MHD) forces, occur during the continuous casting (CC) under the applied electromagnetic brake (EMBr). The results of the small-scale experiment of the liquid metal model for continuous casting (mini-LIMMCAST) at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), investigating MHD flow with a deep immersion depth of 100 mm, are supplemented by newly presented numerical studies with the shallow position of the submerged entry nozzle (SEN) at 50 mm below the meniscus. Herein, the focus is on the MHD effects at the meniscus level considering (i) a fully insulating domain boundary, (ii) a perfectly conductive mold, or (iii) the presence of the solid shell. The volume-of-fluid (VOF) approach is utilized to model a Galinstan flow, including free surface behavior. A multiphase solver is developed using conservative MHD formulations in the framework of the open-source computational fluid dynamics (CFD) package OpenFOAM®. The wall-adapting local eddy-viscosity (WALE) subgrid-scale (SGS) model is employed to model the turbulent effects on the free surface flow. We found that, for the deep immersion depth, the meniscus remains calm under the EMBr for the conductive and semi-conductive domain. For the insulated mold disregarding the SEN position, the self-inducing MHD vortices, aligned with the magnetic field, cause strong waving of the meniscus and air bubble entrapment for shallow immersion depth. Secondary MHD structures can form close to the meniscus under specific conditions. The influence of the EMBr and immersion depth on the flow energy characteristics is analyzed using power spectral density (PSD).