A New Model to Calculate Different Regions’ Volume Fraction in Tundish

1. 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.cn Pan Hongwei ,E-mail: pan5025@163.com

2. questions: Tracer (加入示踪剂) In tundish, each region’s volume fraction is key point for tundish metallurgy ! Inlet Outlet Measure tracer’s concentration (监测示踪剂浓度) Tundish (中间包) Obtain tracer’s concentration changing with time, For tundish reactor, how to calculate each region’s volume fraction through RTD curve? How could we deal with this result into standard residual time distribution (RTD) curve?

3. Tundish is important for clean steel technology! Inclusions floating-up Ladle furnace 钢包 夹杂物上浮 tundish Temperature uniform Component uniform 温度均匀化 结晶器 mold 成分均匀化 • Plug flow region • Backmix flow region • Dead region • Bypass flow region in tundish flow field it contains:

4. Plug flow (活塞流) Temperature and component in plug flow region is uniform because of its piston-movement. Inclusions in plug flow is easily to be absorbed by slag layer at top. 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 . So, plug flow is what we need in tundish flow field! Fig.1 RTD curve for plug flow plug flow If there is only plug flow

5. Backmix flow (返混流) This is the main feature of backmix region 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. Backmix region isolates itself from other regions because of its circle-movement in some local region. Liquid in backmix region has different residual time, this will do harm to temperature uniform, and make the flow pattern uncontrollable. 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 Fig.2 RTD curve for bypass flow backmix flow If there is only mix flow

6. Bypass flow (短路流) 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. Generally speaking, bypass flow makes tundish of no use. So, bypass flow is what we try to avoid in tundish flow field! bypass flow Fig.3 RTD curve for bypass flow

7. Dead region (死区) Dead region reduces production rate, and reduces the usage co-efficiency of tundish volume. 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 Fig.4 RTD curve for dead region If there is dead region

8. two models to calculate different region’s volume fraction! modified mixed model（ In 1986）: combined model（ in 1996 ）: attention ! is the same for these two case ！ These two models are widely used in the world! each peak value appears at the same time contradict Fig.6 RTD curves for different flow pattern The sharper the curve is, the larger the plug flow region is; The longer the time to reach peak value ，the larger the plug flow region is. Large plug flow region Intermediate plugflow region Small plug flow region Feature of plug flow Based on chemical reaction engineering

9. 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 deadregion’s volume fraction when modified mixedmodel is applied. Case 1: 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 mixedmodelis applied. Case 2: Case 3: 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 mixedmodel and combined mixedmodel are used together. it contradicts with the conclusion that “The sharper the curve is, the larger the plug flow region is”! 1.These two models have limitation! 2.A new model is needed to evaluate and improve the tundish designing and tundish metallurgy. 2. It is impossible to explain the minus value Limitation of modified mix model and combined model 3. It is impossible to explain the value over 100% 4. It is impossible to explain dead region’s volume fraction is over than 30% for in a practical tundish 5. It doesn’t consider the bypass flow

10. For single-strand: n=1 Propose standard to obtain key parameter of RTD curve, According to mass conservation principle Tracer is injected at the inlet of tundish in the way of approximate pulse-function, and the injection amount of tracer is: 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. And the amount of trace flowing out of tundish outlet is: “i” is sequence number for each strand According to mass conservation principle, the output amount is equal to the input amount: Key parameter for RTD curve Problems would present if it is not calculated correctly And dimensionless form of normalization is as follows: suitable for single-strand and multi-strand tundish Compensate the inaccuracy of measurement or calculation inaccuracy, and follow close to the line of mass conservation principle!

11. Advantage: A new model New model considers all different regions in tundish flow field. New model definitely reflects connection between each region. New model describes the dead region and backmix region. ATTENTION ! 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! Here, the lower limit of integral can be adjusted according to actual demand.

12. 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:

13. These are multi-strand tundishes NO.1 tundish NO.2 tundish Fig.8 RTD curves for 3rd and 4th strand in each tundish Calculated by modified mixed model Calculated by new model It’s impossible!

14. Conclusions: The modified mixed model and combined model have limitation, and it is not reliable to evaluate the tundish designing and tundish metallurgy. New model completely obey the mass conservation principle. And it proposes the standard to obtain the residual time distribution curve (RTD-curve). It can better describe the deviation of real flow from plug flow. 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. new model considers the bypass flow and proposes the method to calculate its volume fraction. New model is suitable for single-strand tundish and multi-strand tundish at the same time.

15. Thanks for your listening!