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A New Model to Calculate Different

Regions’ Volume Fraction in Tundish

Reporter ： Pan Hongwei PH.D. candidate( 潘宏伟 博士 )

PH.D. tutor: Cheng Shusen professor ( 程树森 教授 )

School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, China

（北京科技大学 冶金与生态工程学院）

Cheng Shusen, E-mail: chengsusen@metall.ustb.edu.cnPan Hongwei ,E-mail: pan5025@163.com

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Tracer ( 加入示踪剂 )

Measure tracer’s concentration( 监测示踪剂浓度 )Tundish ( 中间包 )

Inlet

Outlet

questions:

For tundish reactor, how to calculate each region’s volume fraction through

RTD curve?

In tundish, each region’s volume fraction is key point

for tundish metallurgy !

Obtain tracer’s concentration

changing with time, )( jtc

How could we deal with this result into standard

residual time distribution (RTD) curve?

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mold

Ladle furnace

tundish

Inclusions floating-up

Componentuniform

Temperatureuniform

Tundish is important for clean steel technology!

夹杂物上浮

温度均匀化

成分均匀化

1. Plug flow region

2. Backmix flow region

3. Dead region

4. Bypass flow region

in tundish flow field it contains:

结晶器

钢包

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1. Temperature and component in plug flow region is uniform because of its piston-movement.

2. Inclusions in plug flow is easily to be absorbed by slag layer at top.3. With the help of flow control device, plug flow can be controlled to pass

a longer distance before it flowing out of tundish, and this is good for increasing residual time, and this also good for inclusions floating-up .

Plug flow (活塞流 )

So, plug flow is what we need in tundish flow field!

Fig.1 RTD curve for plug flow

If there is only plug flow

plug flow

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1. In some local region of tundish, backmix region may be good for temperature uniform and component uniform, but it can’t make that in the whole tundish volume.

2. Backmix region isolates itself from other regions because of its circle-movement in some local region.

3. Liquid in backmix region has different residual time, this will do harm to temperature uniform, and make the flow pattern uncontrollable.

This is the main feature of backmix regionBackmix flow (返混流 )

Generally speaking, backmix flow is not what we need in tundish flow field!

Attention: backmix flow is completely different from mix flow ( well-mix flow, liquid in this region can be uniform instantly ), so it’s not proper for some metallurgist to call the backmix region as the mix region! Mix region doesn’t exit in the tundish practical application.

Backmix flow region

If there is only mix flow

Fig.2 RTD curve for bypass flow

backmix flow

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1. Liquid in bypass flow region doesn’t mix or react with other liquid, it just directly flows to outlet from inlet, so this is not good for temperature uniform, component uniform and inclusions floating up.

2. Generally speaking, bypass flow makes tundish of no use.

So, bypass flow is what we try to avoid in tundish flow field!

Bypass flow (短路流 )

bypass flow Fig.3 RTD curve for bypass flow

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1. Dead region reduces production rate, and reduces the usage co-efficiency of tundish volume.

2. It’s not good for temperature uniform and component uniform, because liquid in this region spend much longer residual time than other liquid and then this region is isolated by other liquid.

So, dead region is also what we try to avoid in tundish

Dead region (死区 )

If there is dead region

Fig.4 RTD curve for dead region

Dead region

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modified mixed model （ In 198

6 ） :)(

2

1maxmin

V

V p

avd

V

V1

V

V

V

V

V

V dpm 1

0

0

)(

)(

dE

dE

av

minV

V p

aad

Q

Q

V

V1

V

V

V

V

V

V dpm 1

2

0

2

0

)(

)()/()(

dE

dE

Q

V

Qa

Vaa

combined model （ in 1996

） : is the same for thes

e two case ！

each peak value appearsat the same time

two models to calculate different region’s volume fraction!

V

Vplug

1.The sharper the curve is, the la

rger the plug flow region is;

2. The longer the time to reach pe

ak value ， the larger the plug fl

ow region is.

Large plug flow region

Intermediate plug flow region

Small plug flow region

Fig.6 RTD curves for different flow pattern

Feature of plug flow

These two models are widely used in

the world!

attention !

contradict

Based on chemical reaction

engineering

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1.it contradicts with the conclusion that “The sharper the curve is, the larger the plug

flow region is”!

2. It is impossible to explain the minus value

3. It is impossible to explain the value over 100%

1.These two models have limitation!

2.A new model is needed to evaluate and improve the tundish designing and tundish metallurgy. 4. It is impossible to explain dead region’s

volume fraction is over than 30% for in a practical tundish

J.J.Wang, S.H.Peng, Z.Q.Xiao. Flow Model for Analysis on Flow Pattern in Multi-Strand Tundish, steelmaking, No.5(1998), p.27~29[in Chinese].

Result:

Obtaining minus value for dead region’s volume fraction when modified mixed model is applied.

Case 1:

Case 2:

Case 3:

S.G.Zheng and Zhu Miaoyong. Optimization of Baffles in Six Strand Round Bloom Continuous Casting: A Physical Modeling Study, Ironmaking and Steelmaking, Vol.33(2006), No.5, p.398-406.Result:dead region’s volume fraction is high up to about 30% when combined mixed model is applied.

Liangcai ZHONG, Baokuan Li, Yingxiong ZHU, etc. Fluid Flow in A Four-strand Bloom Continuous Casting Tundish with Different Flow Modifiers. ISIJ International, Vol. 47 (2007), No. 1, p. 88–94.Result:For multi-strand tundish, the sum of backmix region’s volume fraction is over than 100% when modified mixed model and combined mixed model are used together.

5. It doesn’t consider the bypass flow

Limitation of modified mix model and

combined model

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1.Tracer is injected at the inlet of tundish in the way of approximate pulse-function, and the injection amount of tracer is:

'0 tQcM

Here, M is the amount of tracer injected to tundish, and is the tracer’s injection concentration, and is the injection time, and Q is the liquid’s volumetric flow flux at the inlet.

0c't

2.And the amount of trace flowing out of tundish outlet is:

3.According to mass conservation principle, the output amount is equal to the input amount:

And dimensionless form of normalization is as follows:

1)(0

dE

/jj t /t

Q/V

Compensate the inaccuracy of measurement or calculation inaccuracy, and follow close to the line of mass conservation principle!

suitable for single-strand and multi-

strand tundish

n

i jjiE

1 0

1)( ）（

)(1

'

)()/1()(

0

jiji

ji cntQc

tQcnE

＝

n

i jji ttc

ntc

1 00 )(

1/' ）（

n

1 0 ii )( dttcQM j

'0

n

1 0ii )( tQcdttcQ j

）（ n1,2,i For single-strand:

n=1“i” is sequence number for each strand

Problems would present if it is not

calculated correctly

Key parameter for RTDcurve

Propose standard to obtain key parameter of RTD curve, According to mass conservation principle)(E

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1)(0

dE

n

i jjiE

1 0

1)( ）（

)(1)()/1(

)(0

jiji

ji cntQc

tQcnE

‘＝

n

i jji ttc

ntc

1 0

'0 )(

1/ ）（

1.New model considers all different regions in tundish flow field.2. New model definitely reflects connection between each region.3.New model describes the dead region and backmix region.

Advantage:

2 i

idead, )( dEV

V

n

1i

idead,dead

V

V

V

V

dEV

V

0 iibypass, )(

n

1i

ibypass,bypass

V

V

V

V

）（V

V

V

V

V

V deadbypass2backmix -

）（V

V

V

V

V

V

V

Vdeadbackmixbypassplug -1

dE )()1(i ji0

2j

2

）（

A new model

If it is not satisfied the mass conservation principle, minus value of dead region’s volume fraction could be obtained, and

the over 100% value of backmix region’s volume fraction could be obtained!

ATTENTION !

Here, the lower limit of integral can be adjusted according to actual demand.

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Vdead/V Vbackmix/V Vplug/V Vbypass/V

Volume fraction

-2% 80% 22% Can’t be

calculated

Vdead/V Vbackmix/V Vplug/V Vbypass/V

Volume fraction

10% 50% 40% 0%

Practical application of new model

This single-strand tundish is from a certain steel plant.

The result of modified mixed model:

The result of new model:

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Fig.8 RTD curves for 3rd and 4th strand in each tundish

NO.2 tundishNO.1 tundish

It’s impossible!

Calculated by modified mixed model

Calculated by new model

These are multi-strand tundishes

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1. The modified mixed model and combined model have limitation, and it is not reliable to evaluate the tundish designing and tundish metallurgy.

2. New model completely obey the mass conservation principle. And it proposes the standard to obtain the residual time distribution curve (RTD-curve).

3. It can better describe the deviation of real flow from plug flow.

4. The feature of dead region is carefully studied and proposes a new method to calculate its volume fraction, and calculation formula can be adjustable according the actual demand.

5. new model considers the bypass flow and proposes the method to calculate its volume fraction.

6. New model is suitable for single-strand tundish and multi-strand tundish at the same time.

Conclusions:

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Thanks for your listening!