Flow Optimization in Multi-Strand Billet Caster Tundish using

Computational Fluid Dynamics

Antariksh Gupta, Rajeev Kumar Singh, Nirmal Pradhan

Research and Development Center for Iron and Steel, SAIL, Ranchi, India

E-mail: antariksh@sail-rdcis.com, singhrajeev@sail-rdcis.com, npradhan@sail-rdcis.com

Tundish is the last metallurgical reactor whose aim is to provide stable feed of liquid metal

for casting with good and thermal homogeneity. Aim of this work was to develop a

mathematical model to optimize the tundish geometry for improving chemical and thermal

homogeneity using computational fluid dynamics. The velocity vector fields and the flow

characteristics for the tundishwith different positions of flow modification device “dam” are

mathematically simulated. Options for different positions of dam are available in a billet

caster tundish due to large number of strands being operated from same tundish. The 3D

model, meshing and fluid flow simulation is carried out using Design Modeler, Meshing and

Fluent respectively from ANSYS 17.0 package. The tundish designed is of 4.954 m3 capacity

for IISCO Steel Plant (ISP), Steel Authority of India, Ltd. The results from the velocity

vector fields and the flow pattern for different position of dam are utilized to study ways for

prevention of flow short circuiting and temperature homogenization across the tundish at

different strand outlets.

INTRODUCTION

With increasing demands of quality steel products, the importance of continuous casting of

steel as manufacturing step is increasing exponentially. Unlike past, in latent yearstundishis

being viewed as continuous metallurgical reactor instead of a buffer or a simple distribution

vessel [1]. Tundish metallurgy is now widely researched domain andunder tundish

metallurgy, a modern day steel making tundish is designed to provide maximum opportunity

for carrying out various metallurgical operations such as inclusion separation, inclusion

floatation, alloy trimming of steel, and thermal and chemical homogenization.Optimizing

ABSTRACT

the efficiency of these processes involves close control of flow characteristics of molten

steel inside the tundish. If the flow is not properly controlled it might have negative effects

on quality of steel i.e. quality may even deteriorate from the quality of incoming steel

ladle.Heat and mass transfer governs majority of metallurgical operations, consequently, the

nature of the fluid flow (viz., spatial velocity distribution, turbulent kinetic energy etc.)

influences tundish performance considerably.

Generally, two research methods, physical modelling and mathematical simulation [2–5],

are used for the tundish configurations optimization and flow control devices, such as weirs,

dams, baffles with inclined holes, and turbulence inhibitors (TI), have been widely used to

increase residence times, plug and mixed flow volume of liquid steel [6–8].

Since detailed knowledge of the molten steel flow is a prerequisite to any effective flow-

control optimization, significant efforts have been made by researchers to investigate fluid

flow phenomena in tundish systems. Estimation of the various residence time distribution

(RTD) parameters via the pulse tracer addition technique has been widely used to study the

fluid flow patterns in tundish system [9–11]. In such studies, a tracer is injected through the

incoming stream and its concentration at the exit is recorded as a function of time. The plot

of the exit concentration against time is known as the RTD curve. The RTD of 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 the dead volume in the tundish. And it

has been generally considered that the mathematical model is able to simulate RTD

phenomena realistically [12–14].

In the present work, fluid flow in a 35 T billet caster tundish having six strands with

different positions of dam is investigated by mathematical models. In each case of study,

flow characteristics, velocity patterns and RTD curves are obtained. The objective of this

work is to study the effects of the flow control devices on the fluid flow pattern and RTD

curves in present tundish of billet caster.

PHYSICAL DESCRIPTION OF PROBLEM

The modelled geometry of six strand billet caster along with pouring shroud and outlet

nozzlesprepared using ANSYS Design Modeller 17.0 is as shown in Fig.1(a) and 1(b)

Fig: 1(a)

Fig: 1(b)

Metal height in the tundish during operation is around 750 mm equivalent to operational

steel volume of about 4.954 m3. Fluid inlet to tundish is by a 110 mm diameter shroud.

During operation shroud is immersed in liquid steel upto a depth of around 385 mm. Six

outlets (one per strand) are present in tundish as shown in Fig. 1a & 1b. Outlet nozzles

attached to tundish outlets are designed such as to converge the outgoing flow to cylindrical

shaped outlet ports each of length 150 mm. Flow modelling is carried along with these

nozzles to minimize the disturbing effect of sudden expansion on the flow inside tundish.

Top view showing position of inlet shroud and tundish outlet ports in half tundish (owing to

symmetrical shape) is as in Fig.2 below

Outlet Nozzles

Ladle to Tundish Shroud

Tundish

* All dimensions are in mm

Fig 2.0: Schematic of half Tundish top view

Mathematical Formulation

The flow field in the tundish is computed by solving the mass and momentum conservation

equations in a boundary fitted coordinate system along with a set of realistic boundary

conditions. The species continuity equation is solved in a temporal manner to capture the

local variation of the concentration of the tracer in the tundish. The free surface of the liquid

in the tundish was considered to be flat and the slag depth was considered to be

insignificant. With these two assumptions the flow field was solved with the help of the

following equations with a built in k–ε turbulence model because the flow field is normally

turbulent in the tundish.

Governing Equations:

Continuity Equation

𝜕

𝜕𝑥𝑖 𝜌𝑈𝑖 = 0 ..................(1)

Momentum

𝐷(𝜌𝑈𝑖)

𝐷𝑡= −

𝜕𝑝

𝜕𝑥𝑖+

𝜕

𝜕𝑥𝑗 𝜇

𝜕𝑈𝑖

𝜕𝑥𝑗+

𝜕𝑈𝑗

𝜕𝑥𝑖 − 𝜌𝑢𝑖𝑢𝑗 ..................(2)

Turbulent Kinetic Energy

𝐷(𝜌𝑘 )

𝐷𝑡= 𝐷𝑘 + 𝜌𝑃 − 𝜌𝜖 .......................(3)

Rate of dissipation of k

𝐷(𝜌휀 )

𝐷𝑡= 𝐷휀 + 𝐶1𝜌𝑃

휀

𝑘− 𝐶2

𝜌휀2

𝑘 ......................(4)

Concentration

𝜕

𝜕𝑡 𝜌𝐶 +

𝜕

𝜕𝑥𝑖 𝜌𝑢𝑖𝐶 =

𝜕

𝜕𝑥𝑖

𝜇

𝜎𝑐

𝜕𝐶

𝜕𝑥𝑖 ......................(5)

Where,

𝑢𝑖𝑢𝑗 =2

3𝑘𝛿𝑖𝑗 − 𝑣𝑡

𝜕𝑈𝑖

𝜕𝑥𝑗+

𝜕𝑈𝑗

𝜕𝑥𝑖

𝑣𝑡 = 0.09𝑘2

휀

𝐷∅ =𝜕

𝜕𝑥𝑗 𝜇 +

𝜇𝑡

𝜎∅

𝜕∅

𝜕𝑥𝑗

𝑃 = −𝑢𝑖𝑢𝑗 𝜕𝑈𝑖

𝜕𝑥𝑗

Constants: C1=1.44, C2=1.92, σc=1.0, σk=1.0, σε=1.3

Computation of Active and Dead Volume

The procedure adopted for computation of these tundish parameters are adopted from

previous works discussed by Sahai and Emi[15]. The simplest type of a combined model

and the one most frequently used for the flow characterization in tundishes assumes that the

following three kinds of flow regions are present in the total volume of the fluid in a

tundish.

Plug flow region,

Mixed region, and

Dead Region

Any combination of the plug flow and well-mixed flow volumes maybe termed as an active

volume. The residence time distribution curve is shown in Fig. 3. As shownin this figure,

the minimum residence time (Ɵmin) corresponds to the plug volume fraction (Vp/V), and

maximum concentration (Cmax) is equal to the inverse of the well mixed volume

fraction(V/Vm). WhereVp,Vm, and Vare the plug, mixed, and total volumes, respectively.

For the simplicity of discussion, the dead volume may be 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. In the second type, the fluid in this region

move very slowly, and as a result some fluid stays much longer in the vessel. In fact, the

fluid in the dead region continually exchanges with the fluid in the active region. Thus, the

fluid which stays in the vessel for a period longer than two times the mean residence time is

considered as the dead volume. The dead volume in most of the normally operating

tundishes falls in the second type, and is characterized by a long tail extending beyond the

two times the mean residence time.

The average residence time of the fluid for any given tundish at a constant volumetric flow

rate remains constant. Thus, the slower moving fluid or dead volume stays longer in the

tundish at the expense of other fluid. In other words, if some fluid assumes much longer

residence time in the tundish, an equivalent amount of other fluid has, accordingly, a shorter

residence time in the tundish. This faster moving melt may not spend sufficient time to

separate and float out the non-metallic inclusions. Also, molten metal in the dead (slow

moving) regions may lose sufficient heat, and may start to solidify metal. Thus, tundishes

are designed to have dead volume as small as possible.

Consider a combined model consisting of an active (plug flow and well-mixed flow) and a

dead region. Let the total volumetric flow rate through the system be Q which is also

divided in Qa through the active region and Qd through the dead region. For completely

stagnant dead volume Qd will be zero and Q will be equal to Qa.

For a dead region with slowly movingfluid, a typicalexperimentally obtained RTDis

shownin Fig. 3. ARTDcurve corresponding to a pulse input is knownas theC-curve. Let the

dimensionless meantime of the C-curveupto the cut-off point of dimensionless time,

Ɵ=2beӪc,then

Ӫc=𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑎𝑛𝑡𝑖𝑚𝑒𝑢𝑝𝑡𝑜𝜃 =2

𝑚𝑒𝑎𝑛𝑟𝑒𝑠𝑖𝑑𝑒𝑛𝑐𝑒𝑡𝑖𝑚𝑒 .......................(6)

Fig 3.0: Typical Residence Time Distribution (RTD) curve for flow in tundish

Ӫc=𝑉𝑎 𝑄𝑎

𝑉 𝑄 =

𝑉𝑎

𝑉×

𝑄

𝑄𝑎 ...................(7)

𝑉𝑎

𝑉=

𝑄𝑎

𝑄× Ӫc ...................(8)

Thus, the dead volume fraction

𝑉𝑑

𝑉= 1 −

𝑄𝑎

𝑄× Ӫc ....................(9)

The term Qa/Q is the area under the C-curve from Ɵ=0 to 2, and represents the fractional

volumetric flow rate through the active region. With the presence of dead region(s), the

measured average dimensionless residence time, Ӫc< 1

If the dead region is completely stagnant so that the flowing fluid does not enter or leave the

region, the volume of the system through which the fluid flows in the system is effectively

reduced to Va. Thus, the deadvolumefraction will be

𝑉𝑑

𝑉= 1 − Ӫc ..................(10)

The dead volume fraction with stagnant volume is given by Eq. (10), which is a special case

of Eq. (8). The dead volume with the slowly moving fluid is given by Eq. (9).

Boundary Conditions and Solution Methodology

Boundary conditions can be well visualized with referenceto Fig. 1a& 1b. The walls areset

to a no slip condition. At the inlet the velocity ofthe incoming jet was set to a prescribed

value of 0.521 m/s(2.079 ton/min of liquid steel) with a turbulent intensity of5 % and

hydraulic diameter equivalent to diameter of inlet shroud i.e. 0.11 m. The top surface of the

tundish is taken to be a freesurface where zero shear stress condition is applied accordingto

references. The bottom of the tundish istreated as a wall where no slip conditions are used

for thevelocity. At the outlets a pressure outlet boundary condition is applied.At the outlet

and at the free surfacealso zero gradient conditions for the tracer is used. Atthe inlet the

concentration of the tracer is kept to one (1) till five secondsafter which the concentration is

changed to zero (0). Fiveseconds is normally very small compared to the mean

residencetime of the tundish so the influx of the tracer during itstravel is not likely to change

the local velocity field becausethe mass influx of the tracer is also very small.

Solution of the model has been carried out using meshing and fluent components of ANSYS

17.0 package. Inbuilt models in ANSYS FLUENT 17.0 are used for solving above discussed

equations for obtaining the solution.

RESULTSANDDISCUSSIONS

Velocity Profile

Figure 4, 5, 6 are velocity vector profile from the front plane just above outlet nozzle. For

the sake of clarity the advantage of symmetry is used and only one half of the tundish is

shown. Inlet stream coming from the shroud flow towards the bottom of the tundish. After

striking the bottom it spreads radially outward in all directions. A part of the stream flows

along the bottom which on encountering with dams at different locations changes direction

and rises to the top. The other part of stream rises along the wall and flow outwards towards

the extreme end of the tundish. A part of the bottom stream appears out of the outlets if it

does not encounter any dam before it reaches the outlet. One thing which clearly stands out

is that the dam forces the incoming steel to rise towards the top which is beneficial. The

liquid steel rising to the top can help in promoting inclusion floatation. Moreover, liquid

steel rising to the top helps in improving the mixing in the vessel thereby promoting

chemical and thermal homogeneity.

Fig 4.0: Velocity vector profile over tundish outlet plane for Configuration 3,4

The flow before dam is very strong compared to other regions of the tundish. This is

because most of the flow passes out from the tundish from outlet 4 causing very weak flow

near outlet 5 and 6.

Fig 5.0: Velocity vector profile over tundish outlet plane for Configuration 1,6

For the configuration when dam is before outlet 6 the flow profile shows some improvement

over previous configuration. However, the flow is stronger above outlet 6 with weaker flows

over outlet 4 and 5.

Fig 6.0: Velocity vector profile over tundish outlet plane for Configuration 2, 5

In this configuration we find that the flow is more uniform over all the three outletswhen the

dam is placed just before outlet 5. In this case majority of the vectors are directed

downwards from the top. This reveals that a major portion of the flow must have risen to the

top which is now being directed downwards. This helps in increasing the mixing in the

tundish which can be quantitatively evaluated using the Residence Time Distribution

Analysis of the vessel

Residence Time Distribution

Table 1 shows the distribution of active volume in the tundish for the three cases. Active

volume has been calculated for all the six strands. For the purpose of calculating active

volume, the total volume of tundish was divided into six equal parts and it was assumed that

in ideal situation equal amount of liquid steel should flow out from each strand outlet. From

the table, it is very much clear that when dams are placed before 2 and 5, the spread of

active volume across all strands is more uniform than other two cases. The spread is

calculated as the difference between the maximum and the minimum active volume. The

configuration also has minimum variance for all the strands (outlets) indicating uniform

flow for this configuration.

Table 1.0: Active volume of tundish for different configurations

Table 2.0: Peak residence time of tundish for different configurations

Table 2 shows the distribution of peak residence time for the three configurations studied. It

can be seen that peak residence time (which is a measure of time taken by new incoming

metal to reach the outlets) is high for outlets 1 and 6 in case of configurations 1,6 and 3,4.

This suggests that the time taken by stream coming out from the outlets is more that the

mean residence time which can lead to cooling of these streams. The peak residence time for

the configuration 2, 5is around 0.5 even for the outer streams which suggests that hotter

metal will be coming to outlets. Also the spread and variance in case of 2,5 is lower as

compared to other configurations suggesting more uniformity in flow.

Configuration Strand

1

Strand

2

Strand

3

Strand

4

Strand

5

Strand

6

Spread Variance

1,6 0.92 0.83 0.35 0.44 0.84 0.83 0.57 0.058

2,5 0.68 0.67 0.54 0.54 0.68 0.67 0.14 0.005

3,4 0.83 0.71 0.35 0.30 0.71 0.83 0.53 0.055

Configuration Strand

1

Strand

2

Strand

3

Strand

4

Strand

5

Strand

6

Spread Variance

1,6 1.28 0.53 0.1 0.2 0.56 1.44 1.340 0.308

2,5 0.51 0.15 0.015 0.015 0.145 0.5 0.495 0.051

3,4 1.13 0.43 0.11 0.031 0.426 1.12 1.099 0.231

CONCLUSIONS

From current study of flow characteristics of various configurations importance of “Dam” as

a tundish furniture is well understood. Dams have a great role in improving the flow

uniformity in multi strand tundish. The advantages of dam can be even maximized with its

proper positioning, which is very necessary to avoid short circuiting and optimize flow. For

the current tundish geometry studied, it has been found that placement of dam (almost

halfway) just before the outlet 2 and 5 provides most optimum flow characteristics.

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