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ISIJ International. Vol. 36 (1996), No. 6, pp. 667-672

Melt Flow Characterization in Continuous Casting Tundishes

YogeshwarSAHAIand Toshihiko EM11)

Departmentof Materials Science and Engineering, TheOhio State University, 2041 College Rd.. Columbus,OH,4321OUSA.
1)Base Metal Research Station, Institute for AdvancedMaterials Processing, TohokuUniversity. Katahira. Aoba-ku, Sendai,
980-77 Japan.

(Received on December5, l995, accepted in final form on January 18. 1996)

Melt flow in continuous casting tundishes is normal[y characterized by a combinedmodel. The model is
used to analyze the residence time disttibution of fluid in a tundish, In this model, the fluid volume in tundish
is considered to be consisting of the plug flow, well-mixed flow, and dead volumes. Although this model
was proposed over 20 years ago, most researchers have either used it incorrectly or madean assumption
in analyzing melt flow in tundishes. Both approaches may lead to incorrect and misleading calculations
of the dead volume. In this paper, the combinedmodel has been discussed and its correct application to
tundish melt flow has been outlined,

KEYWORDS:continuous casting; tundish; modeling; combinedmodel; plug flow; mixedflow, deadvolume;
clean steel; inclusions.

1. Introduction

The tundish in a continuous casting operation is an
important link between the ladle, a batch vessel, and
the casting mold with a continuous operation. It has
traditionally served as a reservoir and distributor of
molten steel but now, its role has considerably expanded
to deliver metal of desired cleanness and composition.
With the increasing emphasis on the stringent quality
control and reduced cost of production, in future, it may
be required to take up on someadditional responsibilities,
such as refining andprocessing. Thus, the inclusion flota-
tion and separation, and the composition adjustment
have nowbecomeimportant functions of a tundish. The
efficiency and optimization of these processes require a
close control of the molten steel flow characteristics
within the tundish. If the flow of metal in the tundish
is not properly controlled, it mayeven deteriorate the
'quality' of steel produced in the ladle. Thus, tundishes,
in terms of their shapeand use of the flow control devices
(dams, weirs, baffles, pour pads, etc.), are designed to
provide optimumflow characteristics.

To assess the effectiveness of a given tundish design,
researchers have simulated the metal flow either mathe-
matically or physically, before actually using the design
in actual industrial production. Mathematical modeling
has been used by manyresearchers for fiow predictions.
There are several commercial software packages which
can be used for predicting melt flow and residence time
distribution in tundishes. In spite of all claims for their
user friendliness, these codes are not very simple to use,
and can only be used by highly trained professionals.
The results obtained by these computer programs, Iike
any other computer program, are dependent on the as-


surnptions and the boundary conditions used in solving
them. Thus, any inappropriate boundary condition may
lead to erroneous and misleading results. Evennow, the
use of these codes to treat free surface or multi-phase
flow which mayexist in a tundish is relatively difficult
and cumbersometask. It is therefore recommendedthat
the results of a mathematical model must be verified by
actual experiments, such as water modeling.

Watermodeling, on the other hand, is relatively straight
forward experimentation and can be madeby relatively
less experienced personnel. A carefully planned experi-
mentmaygive very useful results, and the correct inter-
pretation of these results mayprovide an insight into the
tundish design. Water modeling in full or reduced scale
model of a tundish has been a very popular meansof
physical simulation of melt flow in tundishes. It is a rel-
atively quick and less expensive method of qualitative
and semi-quantitative study of the melt flow and hence,
the design assessment of a tundish. In such studies, a
tracer (e.g, dye, acid, or salt) is injected in the incoming
water stream and its concentration at the exit is record-
ed as a function of time. The plot of the exit concen-
tration against time is knownas the Residence Time
Distribution (RTD) curve. The RTDof the fluid in
a tundish is analyzed to characterize the flow which,
normally, includes the determination of the extent of
mixing (plug and mixed volumes) and dead volume in
the tundish. Thechoice of dye as a tracer also provides
fiow visualization which mayput the results obtained by
the RTDanalysis in proper perspective,

Oneof the models which has been extensively used
for the analysis of the RTDcurve is a combined or
mixed model for the calculation of the plug fiow, mixed
flow, and dead volumes in a tundish. In the plug fiow

@1996 ISIJ

ISIJ International. Vol.

region, the longitudinal mixing is non-existent, however,
there maybe transverse mixing to any extent. In the
plug flow, all fluid elements have equa] residence times
in the tundish. The mixed flow is the other extreme
where the mixing in a tundish is maximumpossible.
The dead volumel) is the fluid that movesslowly in the
tundish and stays for longer than two times the mean
residence time (see definition* below). A review of the
tundish modeling literature shows that the combined
mode]has beenmisinterpreted and used incorrectly. The
assumption used in the calculation of the dead volume
maylead to a significant error in the dead volume. The
authors are not aware of any publication in the open
literature where this model has been correctly applied
(without the assumption) to the tundish flow. The pur-
pose of this paper is to discuss the combinedmodel and
outline its application to the tundish melt flow character-
ization. Basedon the authors' experience of dealing with
the researchers in steel and related (ceramic flow control
device manufactures) industries, especially in the North
America, the purpose is clearly worthwhile. Most of the
theoretical framework and definitions presented in this
paper are taken from Levenspiel's book.1)

2. CombinedModel
The simplest type of a combinedmodel and the one

most frequently used for the flow characterization in
tundishes assumesthat the following three kinds of flow
regions are present in the total volume of the fluid in a

Plug fiow region,
Mixed region, and

36 (1996), No. 6


3 Actrve Volume
Anycombination of the plug flow and well-mixed flow

volumes maybe termed as an active volume. Consider
that fluid fiowing in a vessel maybe represented by a
combination of the plug flow and well mixed regions as
shownin Figs. l(a) and 1(b). Theorder of the two regions
is reversed in the two models. The two models give anidentical tracer response to a pulse or any other type of
input for a linear system. A Iinear system is one in which
any change in the input or stimulus signal results in
a corresponding proportional change in the output or
response signal. The residence time distribution curve is
shownin Fig. 2. As shownin this figure, the minimum
residence time (O*i.) corresponds to the plug volume
fraction (Vp/V), and maximumconcentration (C~..) is
equal to the inverse of the well mixed volume fraction
(V/V*). WhereVp, V*, and Vare the plug, mixed, and
total volumes, respectively. The equation of the expo-
nential decay curve is given in the figure.

4. DeadRegion
For the simplicity of discussion, the deadvolumemaybe divided into two types. In the first type, the liquid in

the dead region is considered to be completely stagnant
such that the incoming fluid does not even enter this
region. Figure 3schematically represents a system with
this type of dead volume. In the second type, the fiuid
in this region movevery slowly, and as a result sorne
fluid stays muchlonger in the vessel. In fact, the fluid
in the dead region continually exchangeswith the fluid




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