numerical simulation of the effects of horizontal and ...€¦ · in the continuous casting...

Numerical Simulation of the Effects of Horizontaland Vertical EMBr on Jet Flow and Mold LevelFluctuation in Continuous Casting

LIN XU, ENGANG WANG, CHRISTIAN KARCHER, ANYUAN DENG,and XIUJIE XU

In this article, a new type of electromagnetic braking (EMBr), named vertical EMBr (V-EMBr)was introduced in the continuous casting process. In order to investigate its capability andapplicability, the impacts of horizontal and vertical EMBrs on the flow pattern in a continuouscasting mold were simulated by means of an implemented Reynolds-averaged Navier–Stokes(RANS) SST k–x turbulence model. The characteristics of electromagnetic field and flow fieldinside a 1450 mm 9 230 mm mold with Ruler-EMBr and V-EMBr have been compared. Thenumerical simulation results indicate that the static magnetic field generated by Ruler-EMBrcan cover the main part of the discharging jet flow, which has a better control of the flow patternin lower part of the mold. The static magnetic field generated by V-EMBr can cover both thevicinity of the mold narrow faces and the impingement region of the jet flow, which caneffectively control the liquid steel flow in the upper recirculation zone. The parametric study alsoshows that the large vortices beneath the jet flow can be almost completely eliminated at anoptimized magnetic flux density with Ruler-EMBr. In addition, the surface velocity and steel/slag interface fluctuation can be suppressed with the application of V-EMBr toacceptable values even with a wide variation of SEN port angles. It is estimated that to reachthe same level of braking effect on the upper recirculation flow, a magnetic flux density of 0.1 Tis sufficient for V-EMBr, while 0.2 T is needed for Ruler-EMBr. Based on the results, asecond-generation V-EMBr has been developed, which combines both of the merits ofRuler-EMBr and V-EMBr.

https://doi.org/10.1007/s11663-018-1342-4� The Minerals, Metals & Materials Society and ASM International 2018

I. INTRODUCTION

IN the continuous casting process, especially underthe condition of high casting speed, increased flow rateof the liquid steel at the outlet of submerged entry nozzle(SEN) can easily cause disturbances at the steel/slaginterface at the top of the mold. This phenomenon maycause mold flux entrapment and result in entrainment ofinclusions and bubbles into the liquid steel, which areentrapped in the newly formed steel shell, thus affectingthe slab quality.[1,2] Therefore, effectively controlling

level fluctuations in the mold is key to producing highquality steel slabs. Equipment which controls fluid flowin the mold through the application of static magneticfields is referred to as an electromagnetic brake (EMBr).The design of EMBrs is continuously being improved,and they have been demonstrated to be effective inreducing the potential for liquid steel breakouts from thestrand shell, and decreasing slab and final productsurface defects.[3–6]

Up to now it has been developed into three typicaltypes: Local EMBr,[3,4] Ruler-EMBr[5–9] and flow con-trol mold (FC-Mold) EMBr.[10] Local EMBr has acharacteristic that two separate magnets are locatednear the SEN ports, which is mainly used to suppressmolten steel velocity from the nozzle and prevent moldflux entrapment. Ruler-EMBr utilizes one pair ofmagnets, which covers the entire wide faces of the mold,with the aim to stabilize the meniscus velocity andprevent mold flux entrapment. To better control menis-cus fluctuations and molten steel flow behavior in themold, a third-generation electromagnetic brake(FC-Mold EMBr) was proposed. FC-Mold EMBr

LIN XU, ENGANG WANG, ANYUAN DEN, and XIUJIE XUare with the Key Laboratory of Electromagnetic Processing ofMaterials (Ministry of Education), Northeastern University, No. 3-11,Wenhua Road, Shenyang 110004, P.R. China and also with the Schoolof Metallurgy, Northeastern University, Shenyang 110004, P.R. China.Contact e-mail: [email protected] CHRISTIAN KARCHER iswith the Institute of Thermodynamics and Fluid Mechanics, TechnischeUniversitat Ilmenau, P.O. Box 100565, Ilmenau 98684, Germany.

Manuscript submitted December 15, 2017.

METALLURGICAL AND MATERIALS TRANSACTIONS B

http://crossmark.crossref.org/dialog/?doi=10.1007/s11663-018-1342-4&domain=pdf

http://crossmark.crossref.org/dialog/?doi=10.1007/s11663-018-1342-4&domain=pdf

consists of two pairs of magnets across each wide face.One is located on the meniscus of the mold, and theother is located below the SEN port.

Currently, there are two widely used EMBr devices:Ruler-EMBr and FC-Mold EMBr.[11,12] It was foundthat, in the slab continuous casting process, the brakingeffects of Ruler-EMBr on the surface velocity and levelfluctuation are not significant and usually Ruler-EMBrwas u nable to suppress mold flux entrapment effec-tively.[6] Compared to Ruler-EMBr, FC-mold is good atcontrolling meniscus velocity and level fluctuation.However, it’s not applicable for the continuous castingof thin slabs due to large volume, heavy weight andcomplicated structure. Therefore, on the basis of under-standing the characteristics of the existing EMBr, a newtype of EMBr, named vertical electromagnetic brake(V-EMBr) was proposed by our research group inprevious publications.[13–16] Two pairs of magnetic polesare installed vertically on the mold wide sides close tothe narrow faces for V-EMBr while a pair of magneticpoles is mounted on the mold wide sides horizontally forthe Ruler-EMBr as shown in Figure 1. The specialcharacteristic of V-EMBr device lies in the fact that thestatic magnetic field covers both the vicinity area of thenarrow faces of the mold and the impingement region ofliquidmetal jet from the SEN. Hence, it shows thepotential to suppress the upper recirculation flow andcontrol the fluctuation of meniscus.

From the perspective of investigating the fluctuationbehavior of the surface flow, most previous researchfocused on the numerical simulation in which thedeformed interface was simplified as a plane.[17] Forexample, Hwang et al.[18] utilized a finite volume methodto analyze the influence of EMBr on the flow of liquidsteel in the mold with different operation parameters,

and the shape of liquid surface was calculated by thepressure distribution on the free surface. Harada et al.[19]

simplified the deformed interface to a flat surface, andcompared the damping effect of the local magnetic fieldwith the level magnetic field. In recent years, theresearchers improved the simulation method of thedeformed interface, and the simulation results showedthat the fluctuation behavior of the surface flow weremore practical. For instance, Anagnostopoulos et al.[20]

showed a volume tracking method to simulate thebehavior of three-dimensional (3D) water–oil interfacefluctuation in continuous casting mold. Yu et al.[21]

utilized a volume of fluid (VOF) model to investigate theeffects of the casting speed and the shape of nozzle onthe fluctuation behavior of steel/slag in the mold underthe condition of argon blowing. In comparison, theVOF method is more applicable to the numericalsimulation of two-phase turbulent flows.[22–25]

Another aspect addressed in the present study is theturbulence modeling. Until now, three approaches havebeen commonly employed to predict the effects of turbu-lence, i.e., direct numerical simulation (DNS), large eddysimulation (LES), and Reynolds-averaged Navier–Stokes(RANS). DNS is a direct approach of solving theNavier–Stokes equations for turbulent flows which is apowerful research tool for investigating simple turbulentflows atmoderateReynolds numbers.Nevertheless, due tothe high computational cost, it is inapplicable to practicalengineering systems with complex geometry or flowconfigurations.[26] In the LES approach, larger-scale vor-tices are separated from smaller-scale ones using low-passfiltered Navier–Stokes equations. Subsequently, the largerunsteady turbulent motions are directly represented,whereas the smaller-scalemotions aremodeled.Obviously,it can capture the instantaneous turbulence characteristics,

Fig. 1—Schematics of (a) Ruler-EMBr and (b) V-EMBr.


e.g. the coherent structure within the turbulent boundarylayer.[27,28] However, the computational cost of LES is stillhigh which hinders its extensive use in turbulent flowmodeling. The approach of RANS is widely utilized invarious turbulence flows, in which Spalart-Allmarasmodel, k–e model, and k–x model are developed to closethe RANS equations.

The k–e model is the most widely used completeturbulence model.[26] Many efforts have been made to usethe k–e model to reveal the influence of a static directcurrent (DC) magnetic field on the mean flow and theturbulent fluctuation in the mold. For example, Tianet al.[29] utilized a low-Reynolds-numbered k–e model tostudy the influence of EMBr on the liquid steel flow in afunnelmold.Basedon the realizablek–emodel,Liu et al.[30]

described the behavior of liquid steel flow and heat transferin the compact strip production (CSP) andflexible thin slabcasting (FTSC) funnel molds under a static magnetic field,respectively.However, the k–emodel is quite inaccurate forcomplexflowsdue to inaccuracies in the turbulent-viscosityhypothesis. Another commonly used two-equation modelis the k–x model which has a distinct advantage in thetreatment of the viscous near-wall region.[26] In order topredict the Reynolds stress, Menter[31] proposed the SSTk–xmodel on the basis of k–xmodel which combines themerits of the k–e model and the k–x model. Asad et al.[32]

utilized the SST k–x model to simulate the transient-freesurfacebehavior ina continuous castingmold.Miao etal.[7]

performed numerical calculations on the fluid flow in thecontinuous castingprocessunderaDCmagnetic fieldusingthe SST k–x model, which displayed a good agreementwith the measurement results of turbulent flow in a facilitytermed as Liquid Metal Model for Continuous Casting(LIMMCAST).[33] The previous studies demonstrated thatthe SST k–x model can successfully describe the liquidmetal flow exposed to a DC magnetic field.

In this study, the SST k–x model was utilized todescribe the transient flow in a continuous casting slabmold, and the VOF model was applied for the treatmentof the two-phase surface flow. A grid independence testwas first performed to determine an appropriate griddensity to ensure computational efficiency and accuracy.On this basis, the numerical simulations were carried outto examine the braking effect of V-EMBr in comparisonwith the Ruler-EMBr. The current study focuses on theeffect of a static magnetic field on the fluctuation ofsteel/slag interface and the flow pattern in the mold,without considering the impacts of solidification andheat transfer on the liquid metal flow. In addition, theinfluences of the magnetic flux density and the nozzleport angle on the braking effect were analyzed.

II. DESCRIPTION OF HORIZONTAL ANDVERTICAL EMBR

In the continuous casting process, the electromagneticbrake device is installed on the mold, which can affectfluid flow and consequently temperature distribution inthe mold. Reasonable electromagnetic parameters andthe installation position of electromagnetic brake device

have an important influence on the effectiveness ofEMBr on the slab quality improvement in industrialproduction. Schematics of two types of electromagneticbrake (Ruler-EMBr and V-EMBr) are illustrated inFigure 1. The cross section of the mold is 1450mm 9 230 mm, with a height of 800 mm. TheRuler-EMBr device consists of two sets of electrifiedcoils, which covers the entire wide faces of the mold, asshown in Figure 1(a). For Ruler-EMBr device, thedistance between the upper surface of the magnetic poleand the free surface is 290 mm, and the height of themagnetic pole is 200 mm. Different from the Ruler-EMBr device, the V-EMBr device has two pairs ofmagnetic poles with a height of 600 mm which arearranged vertically near the mold narrow face, as shownin Figure 1(b).[13,14] It could cover the impact region ofthe metal jet out from the SEN and could control thefree surface of liquid steel flow.

III. MATHEMATICAL MODEL ANDNUMERICAL METHOD

A. Mathematical Formulation

In order to better describe liquid steel flow in the slabcontinuous casting mold under the influence of EMBr,and on the premise of making the simulation resultsreasonable, the following assumptions were made.The flow of liquid steel and mold flux in the mold was

assumed to be unsteady, and their physical propertiesconstant. The liquid steel and mold flux were consideredto be homogeneous, viscous, and Newtonian incom-pressible fluids. The influence of oscillation and negativetaper of the mold was not taken into account. Heattransfer in the mold and the presence of the solidifiedshell were ignored. In the process of continuous casting,mold flux was assumed to infiltrate into the mold fluxchannel between the mold wall and solidified shell toreduce withdrawal force. Therefore, for the calculationof the electromagnetic field, the mold wall was assumedto be electrically insulated. Finally, the electromagneticcharacteristics of liquid steel were homogeneous andisotropic.Under these assumptions the time-averaged governing

equations read as follows:

@ðq/Þ@t

þr � ðqU/Þ ¼ r � ðC/ � r/Þ þ S/; ½1�

where / stands for various time-averaged variables,i.e., turbulence kinetic energy and turbulence dissipa-tion rate; C/ and S/ represent the diffusion coefficientof the variable / and the source term for varioustransport equations, respectively. More details for thetime-averaged governing equations are given inAppendix.

1. Turbulence modelIn this paper, the Reynolds-averaged Navier–Stokes

(RANS) SST k–x model was utilized to simulate themean flow characteristics of liquid steel and the steel/


slag interface behavior in the mold. Different from theother two-equation eddy-viscosity turbulence models,the SST k–x model computes the anisotropic turbulentflow field and considers the effect of Reynolds stress.Moreover, in the near wall region, where the SST k–xmodel is superior to the other two-equation models, anautomatic wall function is utilized.[31]

2. Electromagnetic force equationsThe magnetic induction method[34] was utilized to

calculate the induced current and electromagnetic force,which is derived from Ohm’s law and Maxwell’sequations. The induced current density can be deducedfrom the following equation:

J ¼ 1

lr� B; ½2�

where the magnetic flux density B consists of theapplied DC magnetic field B0 and the secondary field binduced by the mold flow. Hence, we have B = B0+b. The induced field b can be calculated from the mag-netic equation, i.e.

@b

@tþ U � rð Þ � b ¼ 1

lrr2bþ B � rð Þ �U� U � rð Þ � B0

½3�Finally, the Lorentz force is given by

Fmag ¼ J� B ½4�

3. VOF model equationThe method of volume of fluid (VOF) was utilized to

build two-phase turbulent transient flow model, whichcould track the shape of fluctuating steel/slag interfacein the slab continuous casting mold. A characteristic ofVOF model is that it utilizes a moving steel/slaginterface to define the fraction of fluid volume in aspace lattice. For an incompressible fluid, assuming thatthe densities of liquid steel and mold flux are constant,so the volume fraction of liquid steel should satisfy thefollowing equation.[35]

@ust

@tþr � ustUstð Þ ¼ 0; ½5�

where ust = 1 represents the liquid steel, ust = 0stands for the mold flux, and 0 < ust < 1 representsthe steel/slag interface.

4. Boundary conditionsThe inlet velocity was positioned at the exit of the side

aperture of the nozzle, which was calculated from thespecific casting speed to maintain flow equilibrium. Thetop surface of the mold was set as a free surface, and itsboundary condition was the same as symmetry bound-ary condition, where the velocity components perpen-dicular to the free surface and normal gradients of othervariables were set to zero. For the mold wall, anautomatic near wall treatment was adopted by the SSTk–x model. Normal component of the induced currentand normal gradients of other variables were set to zero.

At the exit of computational domain, fully developedflow was assumed, and normal gradients of all variableswere set to zero.At the boundary, the induced magnetic field b can be

represented by[36]:

b ¼ bn bt1 bt2f gT; ½6�

where bn represents normal component, bt1 and bt2 aretangential components. In this paper, an electricallyinsulating boundary condition was assumed (jn = 0).Therefore, according to Ampere’s law, bt1 and bt2 atthe boundary should satisfy the following condition.

bt1 ¼ bt2 ¼ 0 ½7�

5. Computational domainIn this study, we mainly discuss the influence of the

Ruler-EMBr and V-EMBr on the behavior of the liquidmetal jet from the submerged entry nozzle (SEN) portsand steel/slag interface fluctuation in the mold. In orderto better observe the flow distribution and expansion ofthe liquid metal jet, we define a mid-plane at the nozzleport as a-plane, whose angle relative to the horizontalplane equals to the nozzle port angle a as shown inFigure 2(a).The geometry of the computational domainis shown in Figure 2(b).Due to the fact that the model is symmetrical, in order

to reduce the calculation time and improve the compu-tational efficiency, one half of the mold geometry wasconsidered. Hexahedral unstructured meshing wasadopted in which a local mesh refinement method wasused in the region near the mold wall and the steel/slaginterface. The operating parameters and physical prop-erties of the mold are shown in Table I.

B. Numerical Method

For the first stage of the numerical calculation, the 3Dexternal magnetic field B0 in the mold was solved by thecommercial software ANSYS (version 16.2.0), whichwas then imported into the FLUENT software as thecalculated load of 3D flow field. More specifically, themagnetic field data was imported to the activatedmagnetohydrodynamic (MHD) module in order tocouple the flow field. Afterwards, the FLUENT flowmodeling software package was utilized to simulate theinterfacial fluctuation behavior of steel/slag and fluidflow patterns of the liquid metal jet from the SEN portunder a static direct current (DC) magnetic field. Inaddition, the computation of the effect of the DCmagnetic field on the flow field was based on a 3Dfinite-volume method. Finally, the governing equationswere discretized in the FLUENT software using thepressure implicit with splitting of operators (PISO)algorithm for pressure–velocity coupling. The compu-tations were performed on an AMD OPTERON 6134CPU with a frequency of 2.3 GHz.A grid independence test was performed to minimize

the effect of grid density on the computational results.The operating parameters are as follows: a casting speedof 1.6 m/min, a SEN port angle of downward 15 deg,


and a magnetic flux density of 0 T. Calculations werecarried out for three grid sizes as listed in Table II. Therelative errors dp and dt correspond to the calculatedresults at the peak and trough of the steel/slag interface,respectively. The results showed that even the nodenumber was increased to 1.5 times of the node numberin the meshM1, the relative errors of the height were lessthan 5 pct. Therefore, considering the balance betweencomputational cost and accuracy, M1 was selected forthe present computations.

IV. RESULTS AND DISCUSSION

A. Magnetic Field

Figure 3 shows distributions of magnetic flux densityof two types of EMBr in one half volume of the moldunder a magnetomotive force (MMF) of 31500 amper-e-turns (A�t).[37] Irrespective of the EMBr type (Ruler-EMBr or V-EMBr), the distribution of magnetic fluxdensity within the coverage area of the magnetic pole isuniform. At the central cross section of the mold, themaximum magnetic flux density (Bmax) is 0.2 T. Thestatic magnetic field generated by the Ruler-EMBr cancover the entire wide faces of the mold. In contrast, forV-EMBr, the magnetic field can not only cover the freesurface, but also the impact region of the liquid metal jet

from the SEN. In order to show the details about thedifferences in the magnetic flux density between theRuler-EMBr and V-EMBr, the distributions of magneticflux density along three lines (the lines AB, CD, and EFin Figures 3(a) and (b)) were extracted at the moldcentral cross section along the direction of width, height,and thickness of the mold, respectively.Figure 4 represents the magnetic flux density distri-

bution with two types of magnets along three typicallines (the lines AB, CD and EF). With the Ruler-EMBr,the curvature of the magnetic flux density forms aplateau along the width direction, and it descendsslightly near the narrow face of the mold due tomagnetic flux leakage as shown in Figure 4(a1). On thecontrary, when the V-EMBr is applied, the magneticflux density along the width direction is considerablystronger in the vicinity of mold narrow face while it isdistinctly smaller within the central zone, which forms asaddle shape as shown in Figure 4(b1). Figures 4(a2) and(b2) indicate that the magnetic flux density along themold height direction is higher within the magnet zone,and gradually decreases along both sides of the mold forthe case of Ruler-EMBr and V-EMBr. As shown inFigures 4(a3) and (b3), the magnitude of magnetic fluxdensity along the mold thickness direction with theRuler-EMBr is almost the same as that with theV-EMBr under the same magnetomotive force (MMF).

Fig. 2—Schematic and mesh to be based on the geometry of the mold: (a) schematic of the mold and (b) geometry of the mold.


B. Electromagnetic Field

Using the same operating parameters described ear-lier, Figures 5 and 6 show the contour of magnetic fluxdensity, vectors of current density and Lorentz force athalf thickness in the mold with Ruler-EMBr andV-EMBr, respectively. The black dashed lines in theplots indicate the EMBr position.

Figure 5(a) shows that the distribution of magneticfield with Ruler-EMBr is almost uniformly focused onthe mold wide face, which can cover the main part of thedischarging jet flow. Figure 5(b) shows that the path ofthe induced current is concentrated in the vicinity of thenozzle exit. The vortices of induced current are formedat the region where the jet flow splits into an upwardflow and a downward flow. Figure 5(c) shows that the

Lorentz force acts to the direction of the nozzle port,which produces a braking effect directly on the initialsegment of the jet.Figure 6(a) shows that the magnetic field with

V-EMBr is concentrated in the region which is close tothe narrow face of the mold, and it decays significantlymoving toward the SEN. Figure 6(b) shows that theinduced current flows clockwise from the region wherethe front of the jet flow interacts with the highermagnetic field. As a consequence, the Lorentz forceproduces a braking effect on the upward flow anddownward flow as shown in Figure 6(c).

C. The Effect of EMBr on the Flow Pattern and MoldLevel Fluctuation

Figure 7 presents the velocity distribution in themid-plane at the mold wide face with two types ofmagnets under different magnetic flux densities. In casewhen no EMBr is applied, a typical double-roll flowpattern is predicted as shown in Figure 7(a). Note that theliquid metal jet discharged from the SEN shows thetendency of tilting upward at the main body section. Itsplits into an upward and a downward flow pattern afterimpacting on the narrow face of themold. The liquid steelflows upward along the mold narrow face, approaches tothe steel/slag interface and then flows back to the center ofthe mold to form an anticlockwise vortex. The downwardliquid steel flow penetrates deeply into the molten pooland generates a big clockwise vortex.Figures 7(b) and (c) show that the jet impingement

upon the narrow face of the mold is suppressed byRuler-EMBr. In the lower recirculation zone, the core ofthe vortex is shifted downward by the magnetic fieldwhich is in agreement with the results of Reference 7. Inaddition, extra small vortices are generated below the jetstream when the magnetic flux density reaches to 0.2 T.However, in the upper recirculation zone, the brakingeffect is not significant. Figures 7(d) and (e) show thatthe tendency of tilting of the jet flow is weakened byV-EMBr, which is beneficial for the stabilization of themold level. In addition, the lower recirculation zone ispushed away by the Lorentz force from the narrow faceof mold, which could promote the uniformity of theinitial solidified shell on the narrow side of the mold.However, at a higher magnetic field, an extra vortex isformed below the jet flow which may have an adverseeffect on the flotation of bubbles and nonmetallicinclusions.Figure 8 shows the streamlines and velocity distribu-

tion of jet stream in a-plane with different magnets. Thejet stream from the SEN has an obvious expansioncharacteristic. In case when the EMBr is absent, the jetstream in a-plane is irregular and divergent. Figures 8(b)through (c) illustrate that in the case of Ruler-EMBr, theextent of expansion of the jet stream increases with theincrease of magnetic flux density. The vortex in thevicinity of the nozzle disappears when magnetic fluxdensity is increased to 0.2 T. Figures 8(d) through (e)show that in the case of V-EMBr, the discharging jetflow is stretched by the gradient of the magnetic field.This stretching effect is enhanced by the increase of

Table I. Geometrical Parameters and Physical Properties

Parameter Value

Mold Size (mm) 1450 9 230Mold Length (mm) 800Computational Domain (mm) 1450 9 230 9 4000Casting Speed (m min�1) 1.6The Height of Liquid Mold Flux (mm) 35Angle of Nozzle Port (deg) � 10, � 15, � 20Depth of SEN (mm) 225Total Height of SEN Outlet (mm) 80Magnetomotive Force (A t) 0, 15750, 31500Liquid Steel Density (kg m�3) 7020Mold Flux Density (kg m�3) 3500Steel Viscosity (kg m�1 s�1) 0.0062Mold Flux Viscosity (kg m�1 s�1) 0.2664Interface Tension Coefficient (N m�1) 1.2Steel Electric Conductivity (S m�1) 7.14 9 105

Magnetic Permeability (H m�1) 1.257 9 10�6

Ruler-EMBr V-EMBr

Reynolds Number (Re ¼ qUd=l;Based On Nozzle Diameter)

69500 69500

Reynolds Number (Re ¼ qUL=l;Based on Magnetic Pole Width)

702000 232000

Hartmann Number(Ha ¼ B0L

ffiffiffiffiffiffiffiffi

r=lp

; Based on Mag-netic Pole Width)

1550 515

Stuart Number (N ¼ B20Lr=qU;

Based on Magnetic Pole Width)3.4 1.14

Depth of SEN is the distance from the top of port to the mold level.The Hartmann number can be obtained by imposing the magnetic

flux density of 0.2 T.

Table II. Statistic Results of the Error with Different GridNode Numbers

Mesh M1 M2 M3

Total Node Number 291365 360062 437985dp ¼ HMi

�HM1j j=HM1

0 0.642 pct 1.519 pctdt ¼ hMi

� hM1j j=hM1

0 1.648 pct 3.942 pct

H: distance from the level of steel/slag interface (z = � 0.035 m) tothe peak of the fluctuating interface.

h: distance from the level of static steel/slag interface (z = � 0.035m) to the trough of the fluctuating interface.


magnetic flux density, in which the velocity of liquidsteel close to the mold wall is further decreased.Moreover, the jet stream flows regularly towards thenarrow face of the mold which presents a fan-shape. As

a consequence, the impingement of the jet stream on themold wall should be controlled by V-EMBr whichreduces the potential for breakout of liquid steel fromthe solidified shell.

Fig. 3—Contour plot of magnetic flux density in the mold with (a) Ruler-EMBr and (b) V-EMBr.

Fig. 4—Distribution of magnetic flux density in different directions with (a) Ruler-EMBr and (b) V-EMBr.


Figure 9 illustrates the 3D steel/slag interface profileswith different EMBrs. The results show that the defor-mation of the steel/slag interface with V-EMBr is muchsmaller than that with Ruler-EMBr. Furthermore, thisphenomenon is more apparent under a higher magneticfield.

The quantitative analysis of the steel/slag interfacefluctuation is shown in Figure 10. On the condition ofno EMBr, the fluctuation height is up to 16.2 mm. In thecase of Ruler-EMBr, the fluctuation height is reduced to15.0 and 11.9 mm with a magnetic flux density of 0.1and 0.2 T, respectively. With the application of

V-EMBr, the fluctuation height is remarkably reducedfrom 11.2 to 6.0 mm when the magnetic flux density isincreased from 0.1 to 0.2 T.Figure 11 shows the velocity distribution along the

centerline in x-y cross section (z = � 35 mm) withdifferent magnetic flux densities under Ruler-EMBr andV-EMBr. With the absence of EMBr, the maximumsurface velocity is � 0.24 m/s. When the Ruler-EMBr isapplied, the surface velocity is reduced to � 0.23 and� 0.22 m/s with a magnetic flux density of 0.1 and 0.2 T,respectively. In the case of V-EMBr, when the magneticflux density is increased from 0.1 to 0.2 T, the maximum

Fig. 5—Distribution of magnetic flux density, induced current density, and Lorentz force in the central plane with Ruler-EMBr: (a) B0 = 0.2 T,(b) induced current density, and (c) Lorentz force.

Fig. 6—Distribution of magnetic flux density, induced current density, and Lorentz force in the central plane with V-EMBr: (a) B0 = 0.2 T, (b)induced current density, and (c) Lorentz force.


Fig. 7—Velocity distribution under two types of magnets in the central plane: (a) B = 0 T, no EMBr; (b) B = 0.1 T, and (c) B = 0.2 T, withRuler-EMBr; (d) B = 0.1 T, and (e) B = 0.2 T, with V-EMBr.

Fig. 8—Streamlines and velocity distribution under Ruler-EMBr and V-EMBr in the a-plane: (a) B = 0 T, no EMBr; (b) B = 0.1 T, and (c) B= 0.2 T, with Ruler-EMBr; (d) B = 0.1 T, and (e) B = 0.2 T, with V-EMBr.


surface velocity is significantly reduced from � 0.20 to� 0.15 m/s. It can be summarized from above that toreach the same level of braking effect on the surface flowand steel/slag interface fluctuation, a magnetic fluxdensity of 0.1 T is sufficient for V-EMBr, while 0.2 T isneeded for Ruler-EMBr.

D. The Effect of Nozzle Port Angle on the BrakingEffect

Figure 12 describes the velocity distribution in themid-plane of the mold wide face with different nozzleport angles. It can be seen from Figures 12(a) through(c), when the Ruler-EMBr is applied, the penetrationdepth in the lower part of the mold and the range of the

upper recirculation zone are increased with increasedport angles. Furthermore, extra vortices below the jetstream are restrained especially when the port angle isincreased to downward 20 deg. Obviously, the flowpattern in the lower recirculation zone is more stronglyinfluenced by the nozzle port angle than that in theupper recirculation zone with the fixed location ofRuler-EMBr. With the application of V-EMBr,Figure 12(d) shows that the front jet stream is rejectedby the magnetic field and extra small vortices are formedbelow the jet stream. When the downward port angleincreases, the front jet stream is deflected rather thanrejected by the magnetic field as show in Figures 12(e)and (f). Additionally, the vortex core in the upper

Fig. 9—Steel/slag interface profiles under two types of magnets with different magnetic flux densities: (a) B = 0 T, no EMBr; (b) B = 0.1 T,and (c) B = 0.2 T, with Ruler-EMBr; (d) B = 0.1 T, and (e) B = 0.2 T, with V-EMBr.

Fig. 10—Profile of fluctuating steel/slag interface with variousmagnetic flux densities.

Fig. 11—Distribution of horizontal component of velocity on thecenterline in the mold width direction 35 mm deep from the freesurface.


Fig. 12—Velocity vectors in the central plane under two types of magnets with different SEN port angles: (a) � 10, (b) � 15, and (c) � 20 deg,with Ruler-EMBr; (d) � 10, (e) � 15, and (f) � 20 deg, with V-EMBr.


recirculation zone is shifted downward with the increaseof SEN port angle, which results in a more stable steel/slag interface.

Figure 13 shows the streamlines and velocity distri-bution of jet stream in the a-plane with various nozzleport angles. From Figures 13(a) through (c), it can beseen that when the Ruler-EMBr is applied, the expan-sion of the jet stream is slightly restrained with theincrease of SEN port angles. However, the impingementvelocity of the jet stream on the mold narrow face isobviously weakened. In contrast, a fan-shaped jetstream is produced by V-EMBr, regardless of thevariations of the nozzle port angle as shown inFigures 13(d) through (f). Note that both the expansionand the impingement of the jet stream on the moldnarrow face are significantly restrained, which decreasesthe impact strength against the mold faces.

Figure 14 shows the fluctuation of steel/slag interfacewith various port angles under Ruler-EMBr andV-EMBr. With Ruler-EMBr, the fluctuation height isreduced to 12.6, 11.9 and 11.3 mm when the port angleis � 10, � 15 and � 20 deg, respectively. In addition,with V-EMBr, the fluctuation height is remarkablyreduced to 8.7, 6.0 and 3.8 mm, when the correspondingto the downward port angle is � 10, � 15 and � 20 deg,respectively.

The velocity distribution along the centerline in x-ycross section (z = � 35 mm) with different port anglesunder Ruler-EMBr and V-EMBr is illustrated inFigure 15. The velocity of the backflow under the freesurface is decreased with the increase of port angle forboth Ruler-EMBr and V-EMBr. When the Ruler-EMBris applied, the braking effect on the upper recirculation

is not obvious. The maximum velocity is reduced to� 0.22, � 0.22 and � 0.21 m/s in turn when thedownward port angle is � 10, � 15 and � 20 deg,respectively. In comparison, the surface velocity issignificantly reduced by V-EMBr. The maximum veloc-ity is reduced to � 0.19, � 0.16 and � 0.13 m/s, whenthe corresponding to the downward port angle is � 10,� 15 and � 20 deg.From Figures 12 through 15, it can be seen that

Ruler-EMBr and V-EMBr have their own characteris-tics in terms of the braking effect. Ruler-EMBr has abetter control of the flow pattern in the lower part of themold, while V-EMBr has a better suppression on thesurface flow. Moreover, with V-EMBr the surface

Fig. 13—Streamlines and velocity distribution contour under Ruler-EMBr and V-EMBr in the a-plane with different SEN port angles: (a) � 10,(b) � 15, and (c) � 20 deg, with Ruler-EMBr; (d) � 10, (e) � 15, and (f) � 20 deg, with V-EMBr.

Fig. 14—Profile of fluctuating steel/slag interface with different portangles.


velocity and fluctuation can be suppressed to a desirableextent even with a wide variation of nozzle port angles,which can be influenced by inclusion buildup in the SENport during casting. Last but not least, it’s necessary tomention that these findings are based on computationsthat experimental data are needed to verify thesepredictions.

V. CONCLUSIONS

In this study, the Reynolds-averaged Navier–Stokes(RANS) SST k–x model was utilized to investigate theinfluence of EMBr on the steel/slag interface fluctuationand liquid metal jet flow. A horizontal EMBr (Ruler-EMBr) and a vertical EMBr (V-EMBr) were consideredand compared in the present study. Two importantparameters including magnetic flux density and nozzleport angle were taken into account to analyze thebraking effects of Ruler-EMBr and V-EMBr, with thefollowing findings.

1. The characteristics of electromagnetic field inside a1450 mm 9 230 mm mold with Ruler-EMBr andV-EMBr have been compared. In the model simula-tions with Ruler-EMBr configuration, the effectivearea of influence can cover the mold wide face, which

produces a braking effect directly on the main part ofdischarging jet flow. However, the effective area thatthe V-EMBr influences can not only cover the frontjet stream, but also the free surface, which produces abraking effect to maintain a favorable double-rollflow pattern in the mold and stabilize the mold levelsurface.

2. When the Ruler-EMBr is applied, the lower recircu-lation flow can be effectively controlled with an in-crease of magnetic flux density. However, theinfluence of the Ruler-EMBr is insufficient to controlthe upper recirculation flow due to the significantmagnetic field decay in the upper part of the mold.When the magnetic field from a V-EMBr is imposed,both the expansion and the velocity of jet flow aresignificantly restrained, which suppresses theimpingement of the liquid steel on the mold narrowface. In addition, the upward deflection of jet flownear the mold narrow face is further suppressed asthe magnetic field is strengthened, and the brakingeffect on the surface flow and steel/slag interfacefluctuation are more effective. To reach the same levelof braking effect on the upper recirculation flow, amagnetic flux density of 0.1 T is sufficient forV-EMBr, while 0.2 T is needed for Ruler-EMBr.

3. An increase of the nozzle port angle results in adownward movement of the liquid metal jet stream.When the nozzle port angle is increased to match theinstallation position of the Ruler-EMBr, the largevortices beneath the jet flow is almost completelyeliminated. On the condition with V-EMBr, the frontjet stream is deflected rather than rejected by themagnetic field with the increasing port angles. How-ever, the surface velocity and steel/slag interfacefluctuation can be suppressed to acceptable valueseven with a wide variation of nozzle port angles.

In the current study, the focus is mainly on theinfluence of Ruler-EMBr and V-EMBr on the behaviorof steel/slag interface fluctuation and metal jet flow inthe continuous casting mold. The effects of the sec-ond-generation V-EMBr device, which combines themerits of the Ruler-EMBr and V-EMBr on the flow ofliquid steel, solidification. and heat transfer in thecontinuous casting mold will be the subject of ongoingstudies.

Fig. 15—Distribution of horizontal component of velocity on thecenterline in the mold width direction 35 mm deep from the freesurface.


ACKNOWLEDGMENTS

This study was financially supported by the Na-tional Nature Science Foundation of China (GrantNo. 51574083, Grant No. 51474065 and Grant No.U1760206), the Program of Introducing Talents ofDiscipline to Universities (The 111 Project of China,Grant No. B07015), and the Fundamental ResearchFunds for the Central Universities (Grant No.N160904004). Computer resources were provided bythe computing center at the Technische UniversitatIlmenau, Germany. The authors are also grateful toDeutsche Forschungsgemeinschaft (DFG) for thefinancial support in the framework of Research Train-ing Group Lorentz Force Velocimetry and LorentzForce Eddy Current Testing (GRK 1567).

APPENDIX: GOVERNING EQUATIONSFOR FLUID FLOW

Continuity Equation:

r � qUð Þ ¼ 0; ½A1�

where

q ¼ qstust þ qsl 1� ustð ÞMomentum Equation:

@ qUð Þ@t

þr � q U�Uð Þ½ � ¼ �rpþr� leff rUþrUT

� ��

þ qgþ fþ Fmag

½A2�Turbulence Equations:

@ qkð Þ@t

þUj@ qkð Þ@xj

¼ @

@xjlþ lt

rk

� �

@k

@xj

þ Gk; ½A3�

@ qxð Þ@t

þUj@ qxð Þ@xj

¼ @

@xjlþ lt

rx

� �

@x@xj

þ a3qlt

Gk

þ 2 1� F1ð Þq 1

xrx;2

@k

@xj

@x@xj

;

½A4�

where rk, rx are the turbulent Prandtl numbers

rk ¼1

F1

�

rk;1þ 1� F1ð Þ�

rk;2

rx ¼ 1

F1

�

rx;1þ 1� F1ð Þ�

rx;2;

where F1: a function of the wall distance;y: the distance to the nearest wall

F1 ¼ tanh arg41� �

arg1 ¼ min max

ffiffiffi

kp

0:09xy;500lqy2x

!

;4qk

rx;2CDkxy2

" #

:

where CDkx: the positive portion of the cross-diffusionterm

CDkx ¼ max 2q1

rx;2

1

x@k

@xj

@x@xj

; 10�10

� �

;

where leff: effective viscosity

leff ¼ lþ lt

l ¼ lstust þ lsl 1� ustð Þ;

where lt: turbulent viscosity

lt ¼qa1k

max a1x;SF2ð Þ ;

where S: strain rate magnitude

S ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi

2SijSij

p

;Sij ¼1

2

@Ui

@xjþ @Uj

@xi

� �

;

where F2: a blending function is similar to F1

F2 ¼ tanh arg22� �

arg2 ¼ max 2

ffiffiffi

kp

0:09xy;500lqy2x

!

;

where a3: a linear combination of the correspondingcoefficients

a3 ¼ a1F1 þ a2 1� F1ð Þ;

where Gk: generation of turbulence kinetic energy

Gk ¼ lt 2@u

@x

� �2

þ @v

@y

� �2

þ @w

@z

� �2" #(

þ @u

@yþ @v

@x

� �2

þ @u

@zþ @w

@x

� �2

þ @v

@zþ @w

@y

� �2)

Turbulence model constants:a1 = 0.56, a2 = 0.44, rk,1 = 1.176, rx,1 = 2, rk,2 = 1,

rx,2 = 1.168.

NOMENCLATURE

t Time (s)d Nozzle diameter (m)p Pressure (Pa)U Average mixture velocity vector (m/s)Ust Velocity vector of the steel (m/s)Uin Normal velocity of inlet (m/s)


g Gravitational acceleration (m/s2)f Interaction force (N/m3)J Eddy current density (A/m2)B0 External magnetic field (T)Fmag Lorentz force (N/m3)

GREEK SYMBOLS

r Electrical conductivity of the fluid (S/m)q Average density of the fluid (kg/m3)leff Effective viscosity of the fluid (kg/(m s))l Average dynamic viscosity of the fluid (kg/(m s))k Turbulent kinetic energy (m2/s2)x Turbulent dissipation rate (1/s)u Volume fraction of the fluid

SUBSCRIPTS

in Inletmag Magneticsl Slagst Steelp Peakt Trough

REFERENCES1. T. Honeyands and J. Herbertson: Steel Res., 1995, vol. 66,

pp. 287–93.2. L. Zhang, S. Yang, K. Cai, J. Li, X. Wan, and B.G. Thomas:

Metall. Mater. Trans. B, 2007, vol. 38B, pp. 63–83.3. B. Li, T. Okane, and T. Umeda: Metall. Mater. Trans. B, 2000,

vol. 31B, pp. 1491–503.4. S. Kim, W.S. Kim, and K.H. Cho: ISIJ Int., 2000, vol. 40,

pp. 670–76.5. H. Yamamura, T. Toh, H. Harada, E. Takeuchi, and T. Ishii: ISIJ

Int., 2001, vol. 41, pp. 1229–35.6. R. Chaudhary, B.G. Thomas, and S.P. Vanka: Metall. Mater.

Trans. B, 2012, vol. 43B, pp. 532–53.7. X.C. Miao, K. Timmel, D. Lucas, Z.M. Ren, S. Eckert, and G.

Gerbeth: Metall. Mater. Trans. B, 2012, vol. 43B, pp. 954–72.8. R. Singh, B.G. Thomas, and S.P. Vanka: Metall. Mater. Trans. B,

2013, vol. 44B, pp. 1201–21.9. L.S. Zhang, X.F. Zhang, B. Wang, Q. Liu, and Z.G. Hu: Metall.

Mater. Trans. B, 2014, vol. 45B, pp. 295–306.

10. A. Idogawa, M. Sugizawa, S. Takeuchi, K. Sorimachi, and T.Fujii: Mater. Sci. Eng. A, 1993, vol. 173A, pp. 293–97.

11. Y. Miki and S. Takeuchi: ISIJ Int., 2003, vol. 43, pp. 1548–55.12. S.M. Cho, S.H. Kim, and B.G. Thomas: ISIJ Int., 2014, vol. 54,

pp. 845–54.13. E.G. Wang, J.C. He, L. Kang, Z.H. Chen, and A.Y. Deng: China

Patent, ZL 2008 10011104.7.14. E.G. Wang, L. Kang, F. Li, and J.C. He: Proceedings of 6th

International Conference on Electromagnetic Processing of Mate-rials, Forschungszentrum Dresden-Rossendorf, Dresden, 2009,pp. 583–86.

15. F. Li, E.G. Wang, M.J. Feng, and Z. Li: ISIJ Int., 2015, vol. 55,pp. 814–20.

16. Z. Li, E.G. Wang, L.T. Zhang, Y. Xu, and A.Y. Deng: Metall.Mater. Trans. B, 2017, vol. 48B, pp. 389–402.

17. F.M. Najjar, B.G. Thomas, and D.E. Hersey: Metall. Mater.Trans. B, 1995, vol. 26B, pp. 749–66.

18. Y.S. Hwang, P.R. Cha, H.S. Nam, K.H. Moon, and J.K. Yoon:ISIJ Int., 1997, vol. 37, pp. 659–67.

19. H. Harada, T. Toh, T. Ishii, K. Kaneko, and E. Takeuchi: ISIJInt., 2001, vol. 41, pp. 1236–44.

20. J. Anagnostopoulos and G. Bergeles: Metall. Mater. Trans. B,1999, vol. 30B, pp. 1095–1105.

21. H.Q. Yu, M.Y. Zhu, and J. Wang: ISIJ Int., 2010, vol. 17, pp. 05–11.

22. C.W. Hirt and B.D. Nichols: J. Comput. Phys., 1981, vol. 39,pp. 201–25.

23. T. Menard, S. Tanguy, and A. Berlemont: Int. J. Multiph. Flow,2007, vol. 33, pp. 510–24.

24. S. Galera, P.H. Maire, and J. Breil: J. Comput. Phys., 2010,vol. 229, pp. 5755–87.

25. S.S. Rabha and V.V. Buwa: Chem. Eng. Sci., 2010, vol. 65,pp. 527–37.

26. S.B. Pope: Turbulent Flows, 1st ed., Cambridge University Press,United Kingdom of Great Britain and Northern Ireland, UK,2000, pp. 558–58.

27. Z.Q. Liu, L.M. Li, B.K. Li, and M.F. Jiang: JOM, 2014, vol. 66,pp. 1184–96.

28. P. Zhao, Q. Li, S.B. Kuang, and Z.S. Zou: Metall. Mater. Trans.B, 2017, vol. 48B, pp. 456–70.

29. X.Y. Tian, B.W. Li, and J.C. He: Metall. Mater. Trans. B, 2009,vol. 40B, pp. 596–604.

30. H.P. Liu, C.Z. Yang, H. Zhang, Q.J. Zhai, and Y. Gan: ISIJ Int.,2011, vol. 51, pp. 392–401.

31. F.R. Menter: AIAA J., 1994, vol. 32, pp. 1598–1605.32. A. Asad, C. Kratzsch, and R. Schwarze: Steel Res., 2016, vol. 87,

pp. 181–90.33. K. Timmel, S. Eckert, G. Gerbeth, F. Stefani, and T. Wondrak:

ISIJ Int., 2010, vol. 50, pp. 1134–41.34. S. Garciahernandez, R.D. Morales, and E. Torresalonso: Ironmak.

Steelmak., 2010, vol. 37, pp. 360–68.35. H.Q. Yu and M.Y. Zhu: Acta Metall. Sin., 2008, vol. 44, pp. 1141–

48.36. ANSYS FLUENT User’s Guide: ANSYS Inc., ver. 16.2.0 edition,

2016.37. T. Mautner: The Penguin Dictionary of Philosophy, 1st ed., Pen-

guin Books, New York, NY, 1996, pp. 28–28.


numerical simulation of the effects of horizontal and ...€¦ · in the continuous casting...

Documents