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Two indexes to evaluate the flow field in slab continuouscasting mold with electromagnetic stirring

Zuosheng Lei, Bin Li, Rujun Wei, Yueming Zhou, Yunbo Zhong, ZhongmingRen

To cite this version:Zuosheng Lei, Bin Li, Rujun Wei, Yueming Zhou, Yunbo Zhong, et al.. Two indexes to evaluate theflow field in slab continuous casting mold with electromagnetic stirring. 8th International Conferenceon Electromagnetic Processing of Materials, Oct 2015, Cannes, France. �hal-01334086�

Two indexes to evaluate the flow field in slab continuous casting mold

with electromagnetic stirring

ZuoSheng Lei1, Bin Li

1, RuJun Wei

1, Yueming Zhou

2, Yunbo Zhong

1, Zhongming Ren

1

1 State Key Laboratory of Advanced Special Steel, Shanghai University, 200072, Shanghai, China.

2 Baosteel Central Research Institute, 201900, Shanghai, China.

Corresponding author : lei_zsh@staff.shu.edu.cn

Abstract:

Electromagnetic technologies, such as electromagnetic brake and electromagnetic stirring, are two efficient technologies

to control the flow field in slab continuous casting mould. However, up to now there is still an important open problem

to be answered firstly. It is that what kind of flow structure is our best choice to get good casting products when we use

electromagnetic technologies ? We establish an physical model and an numerical model to study the flow field in slab

continuous casting mold with electromagnetic stirring. During our physical experiments, we use liquid mercury as the

analogue of liquid steel. In this study, we study the flow field under different casting parameters and stirring currents,

respectively. At last, in order to evaluate the flow field in the mold, we propose two parameters. They are Mould Flux

Entrapment Index and Velocity Uniform Index.

Two parameters, named , are proposed in order to . Based on these two indexes, some optimized stirring parameters are

proposed under different casting situations. These kinds of parameters are some reasonable criterions in order to find the

optimized casting parameters when we use Electromagnetic flow control technologies.

Key words:

Slab Continuous Casting, Flow Control, Electromagnetic Stirring.

Introduction

Fluid flow in the mold is very important to product quality in the slab continuous casting of steel[1]

. There are two kinds

of technologies to control the flow field in the CC mold. One is the submerged entry nozzle technology in that the

submerge depth or the mechanical structure of SEN can be changed in order to modify the jet flow throughout the SEN

exit port. The other one is electromagnetic technology in that Lorentz force can be generated in the up zone of liquid

steel to realize the aim of controlling the flow field in the mold. Electromagnetic brake and electromagnetic stirring[2]

are two typical electromagnetic technologies widely applied in the industrial process.

Due to the high cost of empirical investigation by test-error type study on the relationship between the flow field in the

mold and the CC slab quality, recently, mathematical modeling[1, 3]

and physical modeling using low melt point metal[4,5]

have been developed to understand the fluid flow phenomena with electromagnetic field and we have achieve many

valuable quantitative results. But up to now, most of the work about the flow field in mold can only tell us what it is

rather than what should be. There is still an important open problem to be answered firstly.It is what kind of flow

structure is our best choice to get the best casting products when we use electromagnetic technologies? As the

complication of the multi-physical transport phenomena in the CC mold, it is indeed very difficult to answer the

question. How to evaluate the flow field with the addition of electromagnetic field in the mold is a key problem when

the standing position is improving the initial solidifying slab quality in the up part of the mold.

In this study, two parameters, named Mold Flux Entrapment Index and Velocity Uniform Index, are proposed in order

to evaluate the flow field in the mold. Based on these two indexes,some optimized stirring parameters are proposed for

different casting situations. These kinds of parameters are some reasonable criterion in order to find the optimized

casting parameters when we use Electromagnetic flow control technologies.

Physical modeling and mathematical modeling

A physical model using mercury is set up[6]

, whose photo and dimension of main parts are showed in Fig. 1(a) and (b).

In this system, mercury is circulated by a electromagnetic pump from the mold bottom to the tundish and then flowing

back to the up zone of the mold via the SEN. The vertical and horizontal velocity in the mold is measured by means of

the ultrasonic Doppler velocimetry (UDV) in the measurement area showed in Fig. 1(b). The 1/5 scale mold with

section size of 430mm×46mm and 1000mm height is designed. And it is based on the same governing non-

dimensional Reynolds number and magnetic interaction parameter. The EMS Stirrer is a 6 poles linear induction

motors with iron core height 80mm and width 450mm, and the maximum magnetic flux density is about 120 mT when

the current is 60A.

According to the same dimension of the physical model, a mathematical model using commercial packages Ansys® is

built(Fig.1 (c)). Fig.1 (d) and (e) show the electromagnetic field in the mold on the center level of EMS Stirrer iron core.

The governing Maxwell equations, N-S equations and boundary conditions will not be given here because these are not

the critical points of this paper. Compared with the physical measurement flow field, the mathematical model is

considered reasonable. The relevant results with or without EMS are showed in Fig.2.

Valuation of the flow field in the mold

Then the validated mathematical model is used to simulate the flow field in the industrial mold under different EMS

parameters and continuous casting conditions. Fig. 3 show some calculated results when the casting speed, the section

Fig.1 Physical modeling and mathematical modeling System

(a) Experimental system. (b) Schematic of experimental system. (c) mathematical modeling.

(d) Calculate result of electromagnetic field when phase angle=0. (e) Current density in the mold.

(c) (d)

(e)

(a) (b)

x/mm

y/m

m

-200 -150 -100 -50 0 50 100 150 200

0

20

40

60

80

100

120

140

160

180

0

0.1

0.2

0.3

0.4

0.5

x/mm

y/m

m

-200 -150 -100 -50 0 50 100 150 200

0

20

40

60

80

100

120

140

160

180

0

0.1

0.2

0.3

0.4

0.5

Fig.2 Validation of the mathematical model by comparing with the

measurement flow field with EMS (left) and without EMS (right)

of the mold the SEN submerge depth, and the exit port angle are 1.4m/min, 2150mm×230mm, 170mm, and 15°downward, respectively.

It only can be seen from Fig.3 that: the flow field without EMS is a typical double-roll structure, and a horizontal

circulation in the upper part of mold appears with EMS, and the velocity increases with the EMS current. But the

problem is: Which EMS current is the best one in order to improve the slab quality? So, it needs further research.

In slab continuous casting process, the free surface is very important to control the velocity of the liquid metal flow

under the mold flux. If the velocity of this area is too high, the possibility of mold flux entrapment might increase. In

order to valuate this effect quantitatively, a new index, named Mold Flux Entrapment Index (MFEI), is introduced and it

is defined as the surface c

v vS

in free surface in the mold where the steel velocity is greater than the critical mold flux

entrapment velocityc

v to the total surface of free surface to ta l

S . The MFEI can be calculated as

1 0 0 %c

v v

to ta l

SM F E I

S

（1）

Where c

v can be obtained by eq.

1 / 22 1 2

1 2

1 2

2

cv

（2）

Where ρ1 and ρ2 are the density of liquid steel and mold flux, and

is the surface tension between liquid steel and

mold flux. Eq.(2) is the Kelvin- Helmholtz instability criterion between two immiscible flow liquid. It suggests that

once the velocity difference of liquid steel and mold flux is greater than the critical velocity, the possibility of mold flux

(a) (b) (c) (d) (e) (f)

Fig.3 Calculate flow field in the mold with different EMS current

(a) 0A, (b) 300A, (c) 400A, (d) 500A, (e) 600A, (f) 700A

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Width,m

Thic

kness,m

Flow Field of Free Surface,2150-600A-14mmin

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Width,m

Thic

kness,m

Flow Field of Free Surface,2150-600A-14mmin

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Width,m

Thic

kness,m

Flow Field of Free Surface,2150-600A-14mmin

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Width,m

Thic

kness,m

Flow Field of Free Surface,2150-600A-14mmin

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Width,m

Thic

kness,m

Flow Field of Free Surface,2150-600A-14mmin

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Width,m

Thic

kness,m

Flow Field of Free Surface,2150-600A-14mmin

400A

0A

600A 700A

500A

300A

0.0

2

0.0

20.0

2

0.0

40.0

40.0

4

0.0

60.0

60.0

6

0.0

80.0

80.0

8

0.1

0.1

0.1

0.1

20.1

2

0.1

2

0.1

4

0.1

40.1

60.1

8

EMS Current, A

Casting S

peed,m

/min

EMS Core Position: 0mm, SEN Depth:170mm, SEN Angle: 15 degree

0 300 400 500 600 7001.2

1.3

1.4

1.5

1.6

0

0.05

0.1

0.15

0.2

0.25

0.3

Fig.4 Free surface flow

field under different

EMS currents and

contour map of mold flux

entrapment index

entrapment will increase. Although mathematic modeling describe above the flow field of mold flux is not calculated,

an reasonable hypothesis is that the critical velocity should be 0.8m/s (Which can be determined by experiments in

facts).

Fig.4 shows the free surface flow field and contour map of mold flux entrapment index under different EMS

currents and casting speed. From the map, the region right to the red line is relatively dangerous for

the viewpoint of mold flux entrapment. So the maximum EMS current should be selected under

different casting speed. As we know that the growth speed of initial solidifying shell is decided by two aspects. One is the cooling density from

the water-cooled copper mold, and the other is the impact of the hot liquid steel flow in front of the initial shell. In order

to prevent the crack formation caused by thermal stress, it is very important to keep the shell growing uniformly. It is

the flow velocity in front of the initial solidifying shell that determine the convection heat transfer between the interface

of the shell and liquid steel, so the uniform of the velocity in front of this interface is applied to valuate the impact of

flow field on initial shell growth.

Due to the help of EMS Lorentz force, a horizontal circulation will form in the stirring zone, and it will affect the flow

structure of the low part in the mold. A index named, Velocity Uniform Index (VUI), is introduced followed ref.[7]

to

give a quantitative valuation of the effect of flow field on solidification on every level, which is defined as:

1 0 0 %

m a x

V x d x

V U I

V x d x

（3）

Where Γ is a closed curve 20 mm away from the inner mold wall, see in the Fig.5, and x

V is the absolute velocity of

every point on Γ . It is obvious that VUI has a value between 0 and 1. This value is greater, better the flow field.Fig.5

shows the VUI of different levels in the mold when the EMS currents are different. It can be seen that the VUI

increases with the EMS current, but decreases a little in the deep part of the mold. Through the comprehensive index of

two effects, an optimized EMS current can be achieved under a given Continuous casting condition.

Conclusions

In this study, the flow field in slab continuous casting mold with EMS is measured by physical modeling and calculated

by numerical simulation under different casting parameters and stirring currents. Two parameters, named Mold Flux

Entrapment Index and Velocity Uniform Index, are proposed in order to evaluate the flow field in the mold. Based on

these two indexes, some optimized stirring parameters are proposed under different casting situation.

Acknowledgment

This project financially supported by National Science Foundation of China (NO. 50874133 and NO. 51274137).

References

[1] Thomas, B. G., & Zhang, L. (2001). ISIJ international, 41(10), 1181-1193.

[2] Toh, T., Hasegawa, H., & Harada, H. (2001). ISIJ international, 41(10), 1245-1251.

[3] Miao, X., Timmel, K., Lucas, D., Ren, Z., Eckert, S., & Gerbeth, G. (2012). Metall. Mat. Trans.B, 43(4),

954-972.

[4] Timmel, K., Eckert, S., & Gerbeth, G. (2011). Metall. Mat. Trans.B, 42(1), 68-80.

[5] Timmel, K., Eckert, S., Gerbeth, G., Stefani, F., & Wondrak, T. (2010). ISIJ international, 50(8), 1134-1141.

[6] Yueming Zhou, ZuoSheng Lei, Bin Li, RuJun Wei, Yunbo Zhong, Zhongming REN. (2015), EPM2015,

in this book

[7] Okazawa, K., Toh, T., Fukuda, J., Kawase, T., & Toki, M. (2001). ISIJ international, 41(8), 851-858.

0 50 100 150 200 250 300 350 400 450 5000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Uniform Index atdifferent EMS current,1.4/min,EMS Core Position: 0mm, SEN Depth:170mm, SEN Angle: 15 degree

Depth,mm

Uniform

Index

0A

300A

400A

500A

600A

700A

Fig.5 VUI under different EMS currents