A New Method Based on the F-Curve for Characterizing Fluid Flow in Continuous Casting Tundishes
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tundish in a continuous casting operation is an important link between the ladle and the casting mold. The melt flow within the tundish has a significant influence on the metallurgical effect. However, the flow field of the high-temperature reaction vessel is not easy to approach directly. The small-scale water model was widely used by most researchers.[1] In such studies, the nonreactive tracer is injected in the incoming water stream in different ways, such as, the pulse input, the step input, the periodic input, and the random input,[2] which is listed in Figure 1. One of the methods which has been extensively used for analyzing the melt flow is the pulse experiment, which is known as the ‘‘pulse stimulus–response technique’’. The plot of the exit concentration against time is the residence time distribution (RTD) curve, its normalized form is called the E-Curve. The E-Curve is usually analyzed to characterize the fluid flow inside the tundishes.[3–9] The model which is frequently used is called the ‘‘Combined Model’’, revised by SAHAI and EMI. Meanwhile, another available method is the step experiment. The plot of the exit concentration against time is the accumulated residence time distribution curve and its normalized form is called the F-Curve. Both of those methods and its application will be discussed in later paragraphs.
II.
THE COMBINED MODEL
The ‘‘Combined Model’’ indicates that the fluid flow characterization in tundishes is assumed to be the following three kinds of flow regions: plug flow region, mixed region, and the dead region. And the fluid, which stays in the vessel for a period longer than twice the mean residence time, is considered as the dead volume.[3] The total volume of the tundish is considered to be divided into an active volume of Va and a dead volume of Vd, as shown in Figure 2 then tc Va =Qa : ¼ V=Q t Thus, the dead volume fraction Vd Va Qa tc ¼1 ¼1 : V V Q t
METALLURGICAL AND MATERIALS TRANSACTIONS B
½2
Then, a totally well-mixed tundish is considered by the ‘‘Combined Model’’. Obviously, the mixed volume fraction of this well-mixed tundish is 1, and its E-Curve conforms to the exponential equation:[10] EðhÞ ¼ eh , as shown in Figure 3. According to the ‘‘Combined Model’’, the dead volume fraction Vd Qa tc ¼1 ¼1 V Q t
Z2 0
DONGXIA LI, YANG LIU, and ENHUA TIAN, Graduate Students, and HENG CUI, Associate Professor, are with the Engineering Research Institute, University of Science and Technology Beijing, Beijing 100083, P.R. China. Contact e-mail: cuiheng@ustb. edu.cn JIANXIN DU, formerly Lecturer with Beijing Keda Hengxing Hi-Tech Co. Ltd., Beijing 100083, P.R. China, is now with the Design Research Institute, University of Science and Technology Beijing Co. Ltd., Beijing 100083, China. Manuscript submitted August 3, 2014. Article published online January 25, 2016.
½1
R2
h eh dh e dh 0R 2 h 0 e dh h
½3
¼ 1 ð1 3e2 Þ 40:6 pct: As we know, the dead volume of a well-mixed tundish should be 0 pct ideally, which have a large deviation against the results we just
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