The Effect of Electromagnetic Stirring and Flow Control ...

DEGREE PROJECT IN MATERIALS SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2018

The Effect of Electromagnetic

Stirring and Flow Control Devices

on Eight-Strand Tundish

Performance

BINTANG BERGAS CENDEKIA

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

i

ABSTRACT The strand similarity and inclusion removal capability are two critical parameters to

measure the performance of multi-strand tundish in clean steel production. In this work, the

effect of two flow regulators, i.e., Flow Control Devices (FCD) and Electromagnetic Stirring

(EMS) on eight-strand tundish performance have been investigated by establishing a water

model and conducting numerical simulations of water model. The water model was focused on

revealing the effect of stirring while the simulation was employed to investigate the effect of

two FCDs, namely baffle wall and turbo-stopper. The analysis of strand similarity and inclusion

removal were conducted by analyzing flow characteristics derived from Combined Model of

Residence Time Distribution (RTD) curve and observing the flow movement in the tundish

model. In addition, the tundish capability to remove inclusions was also studied by injecting

inclusion particles using Discrete Phase Model (DPM) in ANSYS Fluent. Experiment results

cause the Combined Model needs to be modified. This modification was employed when

analyzing tundish configuration involving stirring. By using the modified Combined Model,

the stirring can significantly increase the well-mix volume to almost 100% as it annihilates

dead zone. The stirring also increases the similarity between strands and makes the RTD curve

more similar to ideal mixing curve. However, the problem of short-circuiting flow need to be

solved and care should be taken into consideration regarding the selection of stirring direction

as well as bath surface condition when implementing EMS in reality. The simulation results

show that the addition of baffle wall and turbo-stopper are beneficial to improve mixing as well

as to avoid the short-circuiting flow. Furthermore, compared to individual FCD, the

combination of baffle wall and turbo-stopper results in the best performance to remove

inclusions by providing surface-directed flow and generating a higher plug flow.

Keywords: multi-strand tundish, strand similarity, flow characteristic, EMS, flow control

device

ii

PREFACE

I would like to express my gratitude to my supervisor at KTH, Mikael Ersson for all his

help and guidance throughout this project. I also want to thank Lidong Teng and Hongliang

Yang as my supervisor in ABB Metallurgy for all their support and advice during my time in

ABB Metallurgy. Finally, I want to thank LPDP (Indonesia Endowment Fund for Education)

for giving me scholarship during my master degree education in KTH.

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TABLE OF CONTENT

1 INTRODUCTION ................................................................................................................... 1

2 TUNDISH METALLURGY AND PHYSICAL MODELLING .......................................................... 3

2.1 Tundish Role in Clean Steel Production ..................................................................... 3

2.2 Non-Metallic Inclusion Removal in the tundish ......................................................... 4

2.3 Current Strategies on Inclusion Removal in the tundish ............................................. 4

2.4 Tundish Flow............................................................................................................... 5

2.4.1 Tundish Flow Characterization ............................................................................ 5

2.4.2 Tundish Flow Problem ......................................................................................... 6

2.5 Tundish Performance Measurement............................................................................ 6

2.6 Residence Time Distribution Experiment ................................................................... 7

2.6.1 Tracer Injection Method ...................................................................................... 7

2.6.2 Dimensionless C-Curve ....................................................................................... 8

2.7 Flow Characterization Calculation .............................................................................. 9

2.7.1 RTD curve of Plug flow ....................................................................................... 9

2.7.2 RTD curve of Well-Mixed Volume ................................................................... 10

2.7.3 Combined Model ............................................................................................... 10

2.7.4 Plug Volume Fraction ........................................................................................ 11

2.7.5 Dead Volume Definition .................................................................................... 11

2.7.6 Dead Volume Fraction ....................................................................................... 12

2.7.7 Well-Mixed Volume Fraction ............................................................................ 13

2.7.8 Multi-strand Tundish Model .............................................................................. 13

2.7.9 Strand Similarity ................................................................................................ 14

2.8 Tundish Water Model Criteria .................................................................................. 14

2.8.1 Geometric Similarity .......................................................................................... 14

2.8.2 Dynamic Similarity Consideration .................................................................... 15

2.9 Multi-strand tundish problem .................................................................................... 16

2.10 Electromagnetic Stirring Technology .................................................................... 17

3 BASIC THEORY OF NUMERICAL MODELLING .................................................................... 18

3.1 Governing Equations ................................................................................................. 18

3.1.1 Conservation of Mass ........................................................................................ 18

3.1.2 Conservation of Momentum .............................................................................. 18

3.1.3 Species Transport Conservation ........................................................................ 18

3.1.4 Discrete Phase Model (DPM) ............................................................................ 19

3.2 Turbulence Model ..................................................................................................... 19

3.2.1 The Reynold Average Navier Stokes (RANS) model ....................................... 19

3.2.2 The realizable 𝒌−∈ method ............................................................................... 20

3.2.3 Law of the wall and Near Wall-Treatment ........................................................ 20

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4 EXPERIMENT SETUP .......................................................................................................... 21

4.1 Model selection ......................................................................................................... 21

4.2 Similarity Consideration ........................................................................................... 22

4.3 Experimental Tools design ........................................................................................ 22

4.3.1 General Setup : Material and – Scale consideration .......................................... 22

4.3.2 Water Tank Requirement ................................................................................... 23

4.3.3 Inlet and Outlet Configuration ........................................................................... 23

4.3.4 Turbo-stopper and Baffle wall attachment ........................................................ 23

4.4 Water Pump for Stirring Position .............................................................................. 26

4.4.1 Pump Location-1 ................................................................................................ 26

4.4.2 Pump Location-2 ................................................................................................ 27

4.4.3 Pump Location-3 ................................................................................................ 27

4.5 Experimental Method and Setup ............................................................................... 28

4.5.1 Velocity Mapping .............................................................................................. 28

4.5.2 Flow Behavior Observation ............................................................................... 29

4.5.3 RTD Experiment ................................................................................................ 29

4.5.4 Dye-Color Injection ........................................................................................... 30

4.6 Data Processing Steps of RTD Experiment .............................................................. 30

4.7 Experiment variables ................................................................................................. 31

5 NUMERICAL SIMULATION SETUP ...................................................................................... 33

5.1 Computer specifications ............................................................................................ 33

5.2 Geometry Domain ..................................................................................................... 33

5.3 Simulation Steps ........................................................................................................ 33

5.3.1 Tracer Injection Simulation ............................................................................... 34

5.3.2 Inclusion Injection Simulation ........................................................................... 34

5.4 Simulation List .......................................................................................................... 35

5.5 Assumption and Model Setup ................................................................................... 36

5.6 Meshing ..................................................................................................................... 36

5.7 Convergence Criteria................................................................................................. 37

5.8 Mesh Sensitivity Study ............................................................................................. 38

6 EXPERIMENT RESULTS ...................................................................................................... 40

6.1 Velocity Mapping ...................................................................................................... 40

6.2 Flow Behavior Observation ...................................................................................... 40

6.3 RTD Experiment ....................................................................................................... 42

6.3.1 Repeatability ...................................................................................................... 42

6.3.2 RTD Curve ......................................................................................................... 43

6.3.3 Flow Characteristics........................................................................................... 46

6.4 Dye-Color Injection................................................................................................... 46

7 NUMERICAL SIMULATION RESULT .................................................................................... 50

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7.1 RTD Curve ................................................................................................................ 50

7.2 Flow Characteristics Calculation .............................................................................. 51

7.3 Flow-related variable Comparison ............................................................................ 51

7.4 Results of Inclusion Injection Simulation ................................................................. 52

8 EXPERIMENT ANALYSIS ............................................................................................ 53

8.1 Velocity Mapping ...................................................................................................... 53

8.2 Analysis of individual strand..................................................................................... 54

8.3 Analysis of Overall Performance of tundish ............................................................. 54

8.3.1 Plug Flow ........................................................................................................... 55

8.3.2 Dead and Well-Mixed Volume .......................................................................... 56

8.3.3 Plug to Dead Zone ratio ..................................................................................... 56

8.4 New Approach of Dead Zone calculation in Stirring Case ....................................... 58

8.4.1 Reason 1: Fast Moving Fluid ............................................................................. 58

8.4.2 Reason 2: Quick Mixing time ............................................................................ 58

8.4.3 Reason 3: Similarity with RTD Curve of Ideal Mix Flow................................. 59

8.4.4 Modified Combined Model................................................................................ 60

8.5 Type of RTD curve in Stirring Case ......................................................................... 61

8.6 Analysis of Overall Performance Using the New Approach .................................... 63

8.7 Strand Similarity ....................................................................................................... 64

8.8 The Similarity with Ideal Mix Curve ........................................................................ 64

8.8.1 Derivation formula ............................................................................................. 67

8.8.2 Analysis of deviation from ideal mix................................................................. 68

8.9 Plug to Well-Mix Volume ratio ................................................................................ 69

8.10 Particle Collision ................................................................................................... 70

8.11 Surface Condition .................................................................................................. 71

8.12 Ethical and Social Aspect Consideration............................................................... 72

9 NUMERICAL SIMULATION ANALYSIS ................................................................................ 73

9.1 Wall Y+ Problem ...................................................................................................... 73

9.2 Validation of CFD Simulation .................................................................................. 73

9.2.1 Validation of Color Tracer Injection .................................................................. 73

9.2.2 Validation of Prediction Regarding Dead Zone Location ................................. 74

9.2.3 Validation of RTD Curve and Flow Characteristics .......................................... 75

9.3 Effect of Baffle wall .................................................................................................. 77

9.4 Effect of Turbo-stopper ............................................................................................. 79

9.5 Dead Zone Comparison ............................................................................................. 81

9.6 Inclusion Injection Simulation .................................................................................. 81

10 CONCLUSION ..................................................................................................................... 83

11 FURTHER STUDY ............................................................................................................... 84

12 REFERENCES ................................................................................................................ 85

1

1 INTRODUCTION

Tundish has become a fundamental component in clean steel production because it acts as

a metallurgical reactor to remove non-metallic inclusions by allowing floatation of non-

metallic inclusion towards the slag on the surface. Besides, tundish can also homogenize the

steel composition and temperature in such a way by providing a proper flow that promotes

floatation of inclusion and sufficient residence time so that the heat and concentration can be

distributed homogeneously to the whole tundish. Thus, the melt flow has become an interesting

parameter for researchers as it is an influencing factor to improve tundish performance [1].

Currently, several tools to adjust the melt flow within the tundish has been developed as

standard practices in casting foundries such as baffles, weird, dam, or turbo-stopper. Those

techniques, which commonly known as flow control devices (FCD), aim to optimize the melt

flow by creating optimum turbulence and mixing within the melt. However, the consideration

of FCD installation becomes more complicated in a multi-strand tundish. The vast amount of

strands lead to increase the tendency of non-homogeneous melt [2]. The melt flowed to the

strand closer to the ladle shroud only needs a shorter time to reach the strand so that it tends to

have a higher temperature and contains more inclusions compared to the melt which flows to

the further strand [3]. The uneven temperature of each strand can also lead to the different cast

steel microstructure [4].

The particular combination of FCD could still be used to overcome the similarity

problem in the multi-strand tundish. Several studies related to the use of FCD in multi-strand

tundish have been conducted by researchers. Zheng and Zhu conducted an experimental study

using a physical model of the ten-strand tundish and they stated that the combination of the

specific design of turbulence inhibitor and baffles could reduce the inclusion as 42% and lead

an evener distribution of inclusion among the strands [5]. This result has a good agreement

with Tomasz and Marek who did the similar study for six-strand tundish by numerical

modelling and industrial measurements. It is concluded that specific design of baffle could

reduce the transient zone in the tundish [6].

Nevertheless, there are some limitations when using FCD in the multi-strand tundish.

Firstly, the multi-strand tundish usually has insufficient working spaces which make

challenging to install several FCD. In addition, the shape and design of FCD are also very case

sensitive [2, 5, 7, 8] which means the selection of flow control devices must involve both of

tundish design and casting parameters. Moreover, the FCD refractory material is also

susceptible to wear during the long practice so that it affects the productivity, quality as well

as the total cost of its implementation. The last, FCD cannot provide the adjustment of flow for

the whole process time.

One of the solutions that could overcome those problems is to use electromagnetic stirring

(EMS) installed on the tundish to control the melt flow. This technology has been developed

by ABB Metallurgy in Västerås, Sweden. One or two EMS which is installed on the side wall

of tundish can provide stirring during the whole casting process thus there is a possibility to

replace or simplify the FCDs using EMS technology. Theoretically, a horizontal stirring

generated in the melt will mix the melt and adjust the melt flow so that the composition and

temperature could be homogenized. From the flexibility point of view, it can be adjusted easily

2

based on the tundish design and the casting process. Furthermore, although the EMS equipment

is more expensive than FCD, the longer lifetime and lower running cost will make the total

cost becomes comparable. All those advantages make this technology seems to be promising

in the future.

However, a comprehensive analysis of the melt flow generated from EMS has not well-

understood due to the lack of studies related to the application of this technology in the tundish

application. Hence, the focus of this work is to investigate the possibility to replace FCD with

EMS in multi-strand tundish application by comparing the flow pattern generated in the tundish

for both cases. The investigation was conducted via physical modelling of eight strand tundish

and numerical modelling of the experiment. The water model experiment was focused on

revealing the effect of stirring while the numerical modelling was employed to investigate the

effect of such FCD. The analysis of flow movement, Residence Time Distribution (RTD)

curve and dye-color injection were employed to measure two parameters of tundish

performance, i.e., flow characteristics and strand similarity in different tundish configurations.

In addition, a simulation of inclusion injection was also conducted to get more understanding

regarding the effect of baffle wall and turbo-stopper on inclusion removal.

3

2 TUNDISH METALLURGY AND PHYSICAL MODELLING

2.1 Tundish Role in Clean Steel Production

In a high-quality steel production route, the removal of non-metallic inclusion becomes a

necessary step to gain high cleanliness of steel. It can be accomplished in several stages before

casting process such as in hot metal treatment and ladle treatment as shown in Figure 1.

However, in the recent years the removal of inclusion is also conducted in the tundish and even

in the mold of continuous casting.

Figure 1 Steelmaking stages and important stage to reduce inclusion [9]

The tundish is an intermediate vessel between casting ladle and the mold. In continuous

casting, the molten steel from ladle will flow down into a tundish as can been in Figure 2. The

steel melt then continues to flow through a copper mold, where the solidification occurs.

Furthermore, the further cooling applied to ensure the strands are fully solidified before the

solidified steel is shaped by roller and cut into a certain dimension.

Figure 2 Schematic illustration of continuous casting process [10]

Tundish has several functions in continuous casting. The primary role is to be a vessel

where the steel melt is distributed to different strands. In addition, tundish is necessary to

provide a constant casting rate by controlling the melt level. Tundish can also serve

homogenization of steel composition and temperature if the melt has proper flow and sufficient

time to stay in the tundish so that the heat and concentration can be distributed homogeneously

to the whole tundish. However, over the last decades, the tundish has a new important role

4

which influences the quality of steel. Since it is the last vessel before mold in continuous

casting, the inclusion removal in the tundish is essential for clean steel production.

2.2 Non-Metallic Inclusion Removal in the tundish

The existence of non-metallic inclusion in steel leads to a detrimental effect on the

mechanical properties of steel. Besides, non-metallic inclusion can also cause clogging

problems in the nozzle of continuous casting. Furthermore, the non-metallic inclusion in

clogging may also be carried by the stream during the process, which results in non-

homogeneous mechanical properties in steel product. Therefore, the amount and size of non-

metallic inclusion are necessary to be limited.

One of the fundamental mechanism of inclusion removal in the tundish is by promoting

the floatation of non-metallic inclusion to the tundish slag. The inclusion then can be trapped

on the surface so that it can be removed together with the slag. The floatation of inclusion

spontaneously happens, since the density of inclusion is lighter than hot liquid steel. However,

it is more problematic for small inclusions as the buoyancy force is highly dependent on the

diameter of inclusion as can be seen in Equation 1.

𝑉𝑟 =2𝑅𝑖𝑛𝑐

2 𝑔 (𝜌𝑓−𝜌𝑖𝑛𝑐)

9𝜇𝑓 Equation 11

𝑉𝑟 is the Stoke rise velocity, 𝑅𝑖𝑛𝑐 is the radius of inclusion, g is the gravity, 𝜇 is the laminar

viscosity of the steel, 𝜌𝑓, and 𝜌𝑖𝑛𝑐 are the density of steel and inclusion respectively. Thus, it

is evident that inclusions with the larger size could float to the surface more quickly than the

smaller inclusions.

2.3 Current Strategies on Inclusion Removal in the tundish

There are different mechanisms of inclusion removal in the tundish and one of the

dominant mechanism is by the Stokes floatation [11]. Therefore, the inclusion removal in the

tundish is highly dependent on how long the melt can stay in the tundish so that the inclusion

has enough time to float towards the slag at the surface before it goes to the outlet of tundish

[12]. The time, which is called as residence time, could be affected by different parameters of

the tundish, whether it is related with the tundish design or the process parameter [11]. One of

the parameters related to the design is the size of the tundish. A larger tundish results in a longer

residence time since the melt has to travel with a longer distance to the outlet [11]. However,

this option is not preferable due to the limitation of cost and space in reality.

There is, however another way to promote the flotation of inclusion by adjusting the melt

flow in the tundish using a flow control devices (FCD) as illustrated in Figure 3. The addition

of this FCD could change the melt pathway towards the surface as well as prevent any short-

circuiting flow. However, it should be mentioned that the low turbulence at the wall and the

surface should be maintained otherwise the exogenous inclusion due to refractory wear or slag

entrainment appears.

5

Figure 3 Different type of flow control devices (FCD) in the tundish [13]

Nevertheless, the addition of FCD is limited by the available space inside the tundish.

In addition, it is also highly dependent on tundish design. The parameter, such as the location

or the height of turbo-stopper, influences the mixing phenomena significantly [8]. The different

design of baffles can also create different phenomena which are very specific for every tundish

[5, 7]. Moreover, the position of strand and casting parameter such as shroud immersion depth

can also affect the performance of FCD [2, 8]. Therefore the consideration when selecting a

type and design of FCD must involve both tundish and casting parameters. Another

disadvantage is the FCD is susceptible to wear for long time usage. This can affect the

productivity, quality and as well as the total cost of its implementation. The last, the FCD

cannot provide the adjustment of flow for the whole process time.

The other method to adjust the melt flow inside tundish is by performing a stirring by

argon gas or electromagnetic stirring (EMS). Theoretically, the stirring enhances the

probability of collision and agglomeration between inclusions resulting in a larger size and

floatation velocity [11]. In addition, it also helps the temperature and composition

homogenization due to increasing of mixing intensity. However, the gas stirring is limited by

injection rate due to a possibility of slag entrainment may occur. The limitation of using FCD

and argon stirring could be partly solved by using EMS, which is investigated in this project.

2.4 Tundish Flow

The main objective when designing a tundish is to provide a melt flow that promotes

floatation of inclusions and a homogeneous composition in the whole tundish [14]. On the other

hand, the flow should be carefully controlled to prevent over-stirring that may induce an

exogenous inclusion in the melt. In this chapter, the model of flow characteristic in the tundish

was discussed and the preferable flow was also elaborated.

2.4.1 Tundish Flow Characterization

Since the melt flow affects the performance of tundish, a Combined Models of flow

characterization has been developed by Sahai and Emi [11]. In this model, the flow inside

tundish consists of three types: Plug flow, well-mixed, and dead volumes.

Figure 4 illustrates the difference between those flows in the tundish. The plug volumes

6

represent a ‘direct channel flow’ where the longitudinal mixing has no effect on this flow, but

the transverse mixing may be present to some extent. It means the residence time for every

volume element in the plug flow region is identical. The well-mixed volume is the volume

where the optimum turbulence create the perfect mixing so that the homogeneous concentration

achieved at any location. The combination of plug flow and well-mixed flow in the tundish is

termed as an active region. Meanwhile, in the dead volumes, the fluid movement is very slow

and even tend to be stagnant. Due to this definition, the dead volume is calculated as a portion

of the fluid which stays more than two times of theoretical residence time in the tundish [15].

Figure 4 Illustration of different type of flow in the tundish: (a) Plug Flow, (b) Well-Mixed Flow, (c) Dead Volume [11, 16]

This model is developed to analyze the behavior of melt flow in the tundish by

analyzing the fraction of each flow-type from a Residence Time Distribution (RTD) curve

obtained from tracer injection experiment. The details of the tracer experiment and the formula

to calculate each flow-types is explained in section 2.7.

2.4.2 Tundish Flow Problem

Besides the flow should be adjusted to promote floatation of inclusion, problems related

to the flow also have to be avoided during the continuous casting process, namely surface

turbulence, short-circuiting flow, dead zone and vortexing [14]. High surface turbulence

exposed the melt to the air which leads to the re-oxidation reaction as well as entrains the slag

to the melt. Meanwhile, the short-circuiting flow is undesired as it contains more inclusions

due to insufficient time for floatation of inclusion. The dead zone has a colder temperature

which can lead to different steel temperature of different strands. Thus the dead zone could

greatly affect the steel quality due to the different microstructure of each strand [17].

Meanwhile, vortexing can entrain the slag to the melt when the melt level is too shallow.

2.5 Tundish Performance Measurement

The investigation of tundish performance is necessary before implementing tundish and

FCD design to the real process. In multi-strand tundish, the tundish performance is measured

by determining the inclusion removal capability and strand similarity. The tundish capability

to remove inclusion can be observed from flow characteristics generated. In this project, the

eight-strand tundish performance was measured using a physical model and numerical model.

The physical model or water model is utilized to perform the experiment on a reduced

scale of the real industrial tundish. It can be a reliable approach if the geometry and dynamic

similarity between the model and real tundish are maintained. By performing a tracer injection

experiment in this model, an RTD curve can be obtained. In the end, the inclusion removal

7

capability can be determined by calculating the fraction of flow-type from the RTD curve.

Meanwhile, the numerical model is carried out by simulating the fluid flow in CFD

software. Besides analyzing the RTD Curve, the numerical model is also useful to predict the

behavior of melt flow in the tundish. The relevant variables in fluid flow such as turbulence

energy in any location of tundish can also be observed. Another advantage is the quick result

may be obtained for every configuration change in the tundish. However, the appropriate

assumption and correct input of boundary condition is necessary to obtain a reliable result.

For both methods, following variables are determined in order to quantify the

performance of tundish as a metallurgical reactor to remove inclusions:

1. Minimum dead volume;

2. High Mixing Volume;

3. The melt flow with less turbulence near the wall and slag-metal interface;

4. High Plug Volume or no short-circuiting melt flow from inlet to the outlet of

tundish;

5. The Long residence time of melt in the tundish;

6. Large Plug to dead or mixing ratio [11].

2.6 Residence Time Distribution Experiment

The residence time distribution (RTD) curve has been obtained by performing the

experiment in water model. A certain amount of soluble and non-reactive chemical is injected

through the inlet so that the tracer flows together with the water stream. The tracer should be

detectable so that the important phenomena such as short-circuiting stream could be easily

observed. Commonly, the tracer used in such experiment is a dye, acid or salt. The time in

which the tracer injected is defined as t =0 and then the concentration of tracer will be measured

at the outlet of the model. The results are plotted as an RTD curve where the dimensionless

time and the dimensionless concentration becomes x- and y-axes respectively.

2.6.1 Tracer Injection Method

Two methods commonly used to inject the tracer during the RTD experiment, i.e., the

step input and the pulse input. The difference between the injection method and the RTD curve

result is summarized in Figure 5. In the pulse input, a certain amount of tracer is suddenly

injected into the water stream in a short time. It is indicated as a peak Figure 5 and the result is

named as a C-Curve. The concentration gradually increases up to the maximum peak before it

gradually decreases to the initial level. This method is employed to model the continuous

casting during steady condition.

In the step input, a certain amount of tracer is injected at the beginning of the experiment

until reach a certain level of concentration. Then the concentration is maintained during the

duration of the experiment. Thus, the concentration at the outlet increases until reaching the

same level of concentration at the inlet. The result of this method is called as F-Curve. This

method is more useful when investigating the transient state such as in grade changing during

casting. In this work, a salt solution of 20%NaCl was used as a tracer and the pulse method

was chosen since the steady state in casting process is the interesting condition.

8

Figure 5 the schematic RTD curve of pulse and step injection method [18]

2.6.2 Dimensionless C-Curve

The response of tracer injection by pulse method is plotted as dimensionless C-curve

as can be seen in Figure 6. This curve shows a changing of tracer concentration detected at the

outlet with the increasing of flow time. In order to obtain the dimensionless time (𝜃), the flow

time is divided by the theoretical average residence time (𝑡𝑎𝑣𝑒𝑟𝑎𝑔𝑒) which can be calculated

using Equation 2. The theoretical average residence time is defined as the volume of tundish

(V) per volumetric flow rate of water input (Q) as expressed in Equation 3.

𝜃 = 𝑡

𝑡𝑎𝑣𝑒𝑟𝑎𝑔𝑒 Equation 2

𝑡𝑎𝑣𝑒𝑟𝑎𝑔𝑒 =𝑉

𝑄 Equation 3

Figure 6 A typical dimensionless C-Curve or Residence Time Distribution (RTD) curve

The area under C-Curve should be equal to unity. Therefore, the dimensionless

concentration (C), can be determined by the concentration observed at the outlets (c) divided

by the total area under c vs. 𝜃 curve as expressed in Equation 4.

𝐶 =𝑐

∫ 𝑐 𝑑𝜃∞

0

Equation 4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0

0.2

0.4

0.5

0.7

0.9

1.1

1.3

1.4

1.6

1.8

2.0

2.1

2.3

2.5

2.7

2.9

3.0

3.2

3.4

3.6

3.8

3.9

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time

9

When investigating the similarity between strands, the mean of dimensionless residence

time (𝜃𝑚) is necessary to describe the difference of RTD curve and to calculate the dead volume

fraction. The mean residence time can be determined by Equation 5.

𝜃𝑚 =∑ 𝜃𝑖𝑐𝑖 ∞

𝑖=0

∑ 𝑐𝑖 ∞𝑖=0

Equation 5

2.7 Flow Characterization Calculation

The dimensionless C-Curve was used to study the similarity between strands in the model

as well as the tundish performance by determining the flow characteristics. The explanation of

each flow characteristics and its formula is explained in this section.

2.7.1 RTD curve of Plug flow

Due to the absence of longitudinal mixing in the ideal plug flow, the liquid melt will

have the same residence time in the tundish. This will produce a maximum peak at the

theoretical residence time (𝜃 = 1 ) as shown in Figure 7. However, in the actual process, a

horizontal mixing always presence due to the turbulence or the molecular diffusion [11]. This

lead to a dispersed plug flow which has a broader peak than the ideal condition as illustrated in

Figure 8.

Figure 7 RTD curve of ideal plug flow

Figure 8 RTD curves of Non-ideal plug flow with various dispersion number constants [16]

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time

10

2.7.2 RTD curve of Well-Mixed Volume

In an ideal well-mixed flow, the extreme mixing causes an identical tracer concentration

at the outlet and at any position in the tundish. The residence curve of this flow is derived from

the mass balance equation of tracer injection as written in Equation 6 to Equation 9 [11].

𝑅𝑎𝑡𝑒 𝑜𝑓 𝑡𝑟𝑎𝑐𝑒𝑟 𝑖𝑛𝑝𝑢𝑡 − 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑇𝑟𝑎𝑐𝑒 𝑂𝑢𝑡𝑝𝑢𝑡 = 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑎𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 Equation 6

𝑄(0) − 𝑄(𝑐) = 𝑑

𝑑𝑡𝑉𝑐 Equation 7

𝑑𝑐

𝐶= −

𝑄

𝑉 𝑑𝑡 Equation 8

The integration of Equation 8 leads to the solution as stated in Equation 9. From this equation,

the RTD curve is plotted and presented in Figure 9.

𝑐 = 𝑒−𝜃 Equation 9

In an ideal mix curve, the dimensionless concentration at 𝜃 = 0 equals the average

concentration of tracer injected (𝐶 = 1). Then the concentration at any point of tundish

decreases exponentially with the increasing of time.

Figure 9 RTD curve of ideal mix volume

2.7.3 Combined Model

Sahai and Emi proposed a new model for analyzing flow in the tundish based on an

assumption that the tundish contains three different type of flow: plug flow volume, well-mix

flow volume and the dead volume [11]. The model is derived based on a configuration where

the plug flow and well-mixed flow presence in a series reactor. The result of RTD curve of this

configuration is presented in Figure 10. In this model, the minimum residence time is

considered as the plug volume fraction. Meanwhile, the dead zone is defined as a melt that

moves very slowly or tends to be stagnant so that it has a long residence time in the tundish.

The further explanation regarding the calculation of those three flow-type fractions are

discussed in the next chapter.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.0

0.2

0.3

0.5

0.6

0.8

0.9

1.1

1.3

1.4

1.6

1.7

1.9

2.0

2.2

2.4

2.5

2.7

2.8

3.0

3.1

3.3

3.5

3.6

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time

11

Figure 10 RTD curves of reactor containing ideal plug flow and ideal well-mixed flow in series [11]

2.7.4 Plug Volume Fraction

There are two different approaches used by researchers to calculate the fraction of plug

flow. The first way is mentioned in Equation 10, where it is derived from an RTD curve as

shown in Figure 10. The plug volume fraction is considered the first appearance of tracer at the

outlet indicated by a vertical peak line. 𝑉𝑝

𝑉= 𝜃𝑚𝑖𝑛 Equation 10

However, the different approaches should be used if there is a deviation of C-Curve

from the ideal Combined Model curve due to the presence of longitudinal mixing in the system.

Typically the peak of C-curve becomes wider as illustrated previously in Figure 8 where there

is a discrepancy between 𝜃𝑚𝑖𝑛 and 𝜃𝑚𝑎𝑥 [19, 20]. This phenomenon typically happened in the

tundish. This second approach, which is named as a dispersed plug flow, was used in this work.

This approach was formulated by Ahuja and Sahai [21] and was used in several studies [20, 22,

23]. By using this method, the plug flow volume is determined by the average of minimum

dimensionless time and the time when the peak is observed as expressed in Equation 11.

𝑉𝑝

𝑉=

𝜃𝑚𝑖𝑛+ 𝜃𝑝𝑒𝑎𝑘

2 Equation 11

2.7.5 Dead Volume Definition

According to the Combined Model, the dead volume is defined either as stagnant fluid

or slowly moving fluid. From the first definition, it can be concluded that the flow does not

flow through the dead regions so that the total flow rate (Q) is always the same as the flow rate

through active regions (𝑄𝑎), as illustrated in Figure 11(a).

Meanwhile, from the second definition, the dead volume is determined by calculating

the portion of the fluid which stays more than two times of theoretical residence time in the

tundish as it moves very slowly [19]. Therefore there is a possibility where the fluid can enter

the dead zones or even continually exchange to the active region as illustrated in Figure 11(b).

The second definition was used in this work since it suits the reality in the configuration of bare

tundish with and without FCD where the fluid with a long residence time is characterized by

the long tail in the RTD curve.

12

Figure 11 Schematic Model of Dead Volume as a stagnant fluid [19]

2.7.6 Dead Volume Fraction

According to the two definitions of dead volume, there are two different formula to

calculate this flow in the tundish. First, the fraction of the dead volume can be calculated based

on the difference of theoretical residence time and the mean residence time as expressed in

Equation 12.

𝑉𝑑

𝑉= 1 − 𝜃𝑐𝑢𝑡−𝑜𝑓𝑓 Equation 12

It should be stated that the 𝜃𝑐𝑢𝑡−𝑜𝑓𝑓 used in calculating the fraction of dead volume applies

within the range from 𝜃 = 0 to 𝜃 = 2 and this formula is shown in Equation 13.

𝜃cut−off =∑ 𝜃𝑖

2𝑖=0 𝑐𝑖

∑ 𝑐𝑖2𝑖=0

𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 13

However, according to the second definition, some portion of fluid moves very slowly

so that the flow rate through the active region must be considered in the calculation. Therefore

Equation 12 is modified into Equation 14.

𝑉𝑑

𝑉= 1 −

𝑄𝑎

𝑄 𝑥 𝜃𝑐𝑢𝑡−𝑜𝑓𝑓 Equation 14

The term 𝑄𝑎

𝑄 is the flow rate through the active region and it represents the area under

the RTD curve up to 𝜃 = 2 as shown in Figure 12. Meanwhile, the flow rate through the dead

region ( 𝑄𝑑

𝑄 ) is defined as the area under the curve after 𝜃 = 2. Thus, if the fluid in dead zones

is completely stagnant, the fraction of 𝑄𝑑

𝑄 becomes 0 so that the formula in Equation 12 is valid.

The formula also indicates that the smaller flow rate through the dead region is preferable

because it can reduce the fraction of dead zone in the tundish.

The total fraction of tracer stays in the tundish from t=0 to ∞ should be equal to 1. This

represents the total area under the curve which is always unity [11, 18] and this relationship is

expressed in Equation 15.

∫ 𝐶(𝑡)𝑑𝑡∞

0= 1 Equation 15

13

Therefore, the term 𝑄𝑎

𝑄 can be determined based on Equation 16.

𝑄𝑎

𝑄= 𝑡𝑜𝑡𝑎𝑙 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑐𝑢𝑟𝑣𝑒 𝑢𝑝 𝑡𝑜 (𝜃 = 2)

𝑄𝑎

𝑄=

∑ 𝑐𝑖∆𝜃2𝑖=0

∑ 𝑐𝑖∆𝜃∞𝑖=0

Equation 16

Figure 12 Representation of flow rate through active and dead region in RTD curve [19]

2.7.7 Well-Mixed Volume Fraction

From the Combined Model theory, the well-mixed volume can be determined using

Equation 17.

𝑉𝑚

𝑉=

1

𝐶𝑚𝑎𝑥 Equation 17

However, this formula cannot be used directly in the current case as the actual C-curve is not

ideal as in the Combined Model. It is indicated by the presence of the dead volume and a

broader peak which represents a dispersed plug flow in the tundish. Therefore the fraction of

well-mixed volume is simply defined as the remaining fluid beside the dead and dispersed plug

flow as shown in Equation 18.

𝑉𝑚

𝑉= 1 −

𝑉𝑝

𝑉−

𝑉𝑑

𝑉 Equation 18

2.7.8 Multi-strand Tundish Model

All equations of flow characteristic mentioned previously were developed for analyzing

the performance of single strand tundish. Hence, another approach must be employed to

calculate the flow characteristics in a multi-strand tundish. The formula proposed by Zheng

and Zhu [3] was used in this work. In this approach, the flow fraction of each strand initially

was calculated using Combined Model formula and then its value was combined with other

strands as summarized in Equation 19 to Equation 21. This value is called the overall flow

characteristics and the tundish performance between different configurations is evaluated by

these variables.

𝑉𝑝

𝑉=

1

𝑁[(

𝜃1𝑚𝑖𝑛+ 𝜃1𝑝𝑒𝑎𝑘

2) + (


2) + ⋯ . + (

𝜃𝑁𝑚𝑖𝑛+ 𝜃𝑁𝑝𝑒𝑎𝑘

2)] Equation 19

14

𝑉𝑑

𝑉= 1 −

1

𝑁(

𝑄1𝑎

𝑄1 𝑥 𝜃1𝑐𝑢𝑡−𝑜𝑓𝑓 +

𝑄2𝑎

𝑄2 𝑥 𝜃2𝑐𝑢𝑡−𝑜𝑓𝑓 + ⋯ +

𝑄𝑁𝑎

𝑄𝑁 𝑥 𝜃𝑁𝑐𝑢𝑡−𝑜𝑓𝑓 ) Equation 20

𝑉𝑚

𝑉= 1 −

𝑉𝑝

𝑉−

𝑉𝑑

𝑉 Equation 21

2.7.9 Strand Similarity

Besides the flow characteristics which become a reference to measure tundish

capability to remove inclusion, a similarity among strands also become an essential parameter

to measure the performance of multi-strands tundish. It is because the excellent similarity

among strands is essential to guarantee an uniform temperature and steel cleanliness.

Unfortunately, researchers have a different way to measure this parameter, such as by

comparing the maximum concentration of the inner and outer strand tundish [24] or by

calculating the standard deviation of some important variables, i.e., the first time tracer appears

at the outlets [25, 26]. However, an approach developed by Zheng and Zhu was used in this

work and the formula is presented by Equation 22 [5]. The N in the equation represents the

number of strands, z is the number of instantaneous time 𝑡𝑗 and ��(𝑡𝑗) is the average of

dimensionless concentration at time 𝑡𝑗.

𝑆𝑁 =

1

𝑍∑ {

[∑ (𝐶𝑖(𝑡𝑗)−��(𝑡𝑗))2𝑁𝑗=1 ]

𝑁−1}

1/2

𝑍𝑗=1 Equation 22

In the other word, 𝑆𝑁 is the strand similarity from strand 1 to N which defined as the

average of total standard deviation of the dimensionless concentration from time j=1 to t=z.

Therefore, the lower this value means the deviation of concentration in all strands at every time

is small so that it leads to the better strand similarity. This approach is better than others since

it considers all of the concentration of every strand in every recorded time in the experiment

[5].

2.8 Tundish Water Model Criteria

The utilization of water model to perform RTD experiment is useful due to its reliability

to represent the actual industrial tundish. However, it is obvious that several parameters are

different and it is impossible to create similar condition as the reality. Hence, the model has to

fulfill a number of similarity criteria, i.e., geometric, dynamic, kinetic, thermal, and chemical

similarity. Since the steel melt is assumed as non-reactive in isothermal condition, the thermal

and chemical similarity consideration is excluded in this study.

2.8.1 Geometric Similarity

The tundish size has a great effect on the capability of tundish to remove inclusions

since the melt can stay longer in a bigger tundish [1]. Besides, the design parameter such as

FCD location in the tundish also influences the tundish performance [27]. Thus, the changing

of geometry may lead to a different result in the physical modelling. In order to minimize this

effect, each linear dimensions in the tundish have to be reduced by the same scale factor 𝜆 as

shown in Equation 23. Lm is the dimension of model and Lp is the prototype or real industrial

15

tundish dimension, so that λ may vary from 0 to 1. A reduced scale model has a benefit

concerning space and for experiment setting. Nevertheless, a reduced scale model has the

drawback as it is impossible to achieve a similar Froude and Reynold number in dynamic

similarity consideration [15]. The more detail explanation of the problem to achieve a similar

Froude and Reynold Number in dynamic similarity is explained in section 2.8.2.

𝜆 =𝐿𝑚

𝐿𝑝 Equation 23

2.8.2 Dynamic Similarity Consideration

The dynamic similarity between industrial tundish and water model entails that the

presence of all forces act on steel melt must be changed by a certain scale in the water model.

In the tundish, the considered forces are the forces related to fluid flow behavior such as the

gravity, the viscosity and the inertial forces. In fluid mechanics, the flow behavior could be

expressed in the form of a ratio between the two forces which is known as the Reynold and

Froude number. The Reynold number is a ratio between the inertial to the viscous forces

whereas the Froude number represents the ratio of viscous to the gravitational forces. Formulas

of those two similarity considerations were shown in Equation 24 and Equation 25 where the

Re and Fr is the symbol of Reynold and Froude number respectively, 𝜐 is the velocity of the

fluid, 𝜌 is the density of the fluid, 𝐿 is the characteristic length and 𝜇 is the dynamic viscosity

of the melt.

𝑅𝑒 =𝜐𝜌𝐿

𝜇 Equation 24

𝐹𝑟 =𝜐2

𝑔𝐿 Equation 25

In dynamic similarity consideration, the Reynold and Froude numbers are desired to be

similar between model and the industrial tundish. For Reynold number similarity, this leads to

Equation 26.

(𝜐𝜌𝐿

𝜇)

𝑚𝑜𝑑𝑒𝑙= (

𝜐𝜌𝐿

𝜇)

𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑖𝑎𝑙 𝑡𝑢𝑛𝑑𝑖𝑠ℎ Equation 26

Since the difference between the kinematic viscosity of steel at 1600℃ and water at room

temperature as shown in Table 1 is insignificant, the Equation 26 can be simplified into

Equation 27. By using a similar step in Froude number similarity consideration, the relationship

between model and industrial tundish is expressed in Equation 28. Table 1 Comparison of kinematic viscosity of steel and water [28]

𝜐𝑚𝑜𝑑𝑒𝑙 ≈1

𝜆 𝜐𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑖𝑎𝑙 𝑡𝑢𝑛𝑑𝑖𝑠ℎ Equation 27

𝜐𝑚𝑜𝑑𝑒𝑙 ≈ √𝜆 𝜐𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑖𝑎𝑙 𝑡𝑢𝑛𝑑𝑖𝑠ℎ Equation 28

Based on Equation 27 and Equation 28, it is clear that the similarity of Froude and

Reynold number can only be achieved in a full-scale model as 𝜆 = 1. It is impossible to satisfy

Property Steel at 1600 ℃ Water at 20 ℃

Dynamic Viscosity, 𝜇 (kg m-1 s-1) 0.0064 0.001

Density,𝜌 (kg m-3) 7014 1000

Kinematic Viscosity, 𝜇

𝜌 (m2 s-1) 1. 10-6 0.913. 10-6

16

both number in a reduced scale model, because when the Reynold number similarity is

achieved, the velocity becomes higher in the model and the opposite result occurs if the Froude

number similarity becomes the reference. That is the reason why researchers have a different

opinion regarding which number should be used when developing a water model.

In relation with this problem, a comparison study of the importance of Reynold and

Froude number on fluid flow behavior in the tundish has been carried out by Sahai and Emi.

They stated that actually neither of the Reynold number nor Froude number similarity is

necessary to predict the fluid flow behavior in water model experiment. However, the Froude

number similarity is useful for the prediction of the inclusion removal in the tundish [15].

The reason of why Reynold number similarity is not important in water model

experiment is because the turbulent flow becomes the dominant fluid flow in the tundish. In

turbulent flow, a combination of molecular and turbulent viscosity is used to describe the

diffusive momentum transfer capability. The turbulent viscosity is much important due to the

exchange happened by eddies length are much dominant than by the molecular exchange.

Therefore, a Reynold number similarity is not so important to be fulfilled as in turbulent flow

the inertia flow is much higher than the viscous forces. The Reynold number similarity is only

important to be considered in a laminar flow where the viscous layer becomes the only

mechanism of diffusive momentum transfer [15].

The Froude number similarity criteria are also not important for modelling fluid flow

since the isothermal condition in water model causes the gravity forces do not affect the melt

flow. Thus it is unnecessary to achieve a Froude number similarity for modelling fluid flow.

However, the Froude number similarity can provide the similarity of important aspect related

with inclusion removal, such as the inclusion size and inclusion density as can be seen in Figure

13 [15]. Hence, the water model with Froude Number similarity can describe the similar

behavior of floatation of inclusion or agglomeration. This is the reason of why the Froude

number was chosen as the dynamic similarity consideration in this study.

Figure 13 Relationship between inclusion size (left) and density (right) in industrial tundish and water model [15]

2.9 Multi-strand tundish problem

The multi-strand tundish is commonly used in a billet steel production, where the number

of strands varies from three to ten. This high number of strands may lead to a significant quality

dissimilarity among strands. Since the inclusion removal depends on the residence times, the

further strand from the ladle shroud tend to has more inclusions and lower temperature than the

strand near to the ladle shroud. Thus, the inclusion removal capability as well as the strand

similarity are essential to be investigated.

To overcome the problem, the melt flow inside tundish is usually be adjusted by installing

17

several flow control devices (FCD) such as dams, weirds, or baffle wall. However, the proper

FCD varies for different tundish geometry and design. This means the solution of optimum

FCD design and its position in the tundish is very specific for each case. In addition, the multi-

strand tundish typically has a limited working space and the refractory material may

contaminate the steel. Another weakness of FCD is it is vulnerable to wear for long-term usage.

It affects the productivity, quality and also the total cost of its implementation. The last, the

FCD cannot provide the adjustment of melt flow for the whole process time.

One solution that could overcome those problems is using electromagnetic stirring

(EMS) for stirring the melt. This technology has been developed by ABB Metallurgy in

Västerås, Sweden. The horizontal stirring created by EMS will mix and adjust the melt flow

then it homogenize the composition and temperature. Thus, there is a possibility to replace

FCD with EMS. In addition, EMS is also more flexible to be controlled based on the tundish

design and the casting process. Despite being more expensive than FCD, EMS has a much

longer lifetime that the total cost becomes comparable. However, the comprehensive behavior

of the flow generated by EMS has not been understood due to the lack of studies related with

EMS in the tundish.

2.10 Electromagnetic Stirring Technology

EMS is a set of tools which can provide mixing in the melt with the help of

electromagnetic force generated by coil induction. This technology can be used as a method to

adjust flow behavior inside the tundish so that better steel cleanliness can be obtained. The

EMS unit consists of four components namely an electromagnetic coil, frequency converter,

transformer and a water station as can be seen in Figure 14.

Figure 14 Typical Electromagnetic Stirring System and Components [29]

The basic principle is the current from the converter will flow into the coil. This current

then will produce a strengthened electromagnetic field which penetrates into the steel melt.

Furthermore, the electromagnetic field induces a current in the steel melt. As a result, the

Lorentz Force will be generated in the steel melt and this becomes the source of stirring force.

Meanwhile, the water station act as a cooling unit for reducing the temperature of iron ore

inside the coil. In this work, the EMS will be replaced by the water pumps in the water model

experiment. This method has not been used previously in the tundish stirring. Even though it

is definitely not similar, however, it can be the good way to model the EMS in water.

18

3 BASIC THEORY OF NUMERICAL MODELLING

A Computational Fluid Dynamics (CFD) can be a method to predict the fluid behavior in

the tundish model by solving governing equations related to fluid flow. It can also complement

the result of physical experiments since it is allowed us to observe more variables related to

fluid flow. However, correct settings such as meshing or turbulence model are required in order

to have reliable results,. In this project, a CFD Software ANSYS Fluent 18.2 was used.

Theories behind some setup in this software are elaborated in this section.

3.1 Governing Equations

ANSYS Fluent simulates the fluid flow behavior based on the conservation of mass and

momentum equation. Since the tracer as a chemical species is injected during the water model

experiment, the conservation of species equation was activated. For simulating particle trap

during particle injection, a Discrete Phase Model (DPM) was selected. Meanwhile, the equation

of heat transfer was turned due to isothermal assumption. Those equations are solved together

during simulation in this work. Firstly, the mass and momentum are iterated until reach a steady

state condition. The conservation of species and discrete phase model equation are solved after

the tracer or inclusion particle injection in a transient simulation.

3.1.1 Conservation of Mass

The conservation of mass is expressed in Equation 29: 𝜕𝜌

𝜕𝑡+ 𝛻 ∙ 𝜌�� = 𝑆𝑚 Equation 29

The 𝐯 represents the fluid velocity, ρ is the density and Sm is the mass added to the system

from a dispersed phase, which equals to 0 in this work.

3.1.2 Conservation of Momentum

The equation of momentum conservation is expressed in Equation 30.

𝜕

𝜕𝑡(𝜌��) + 𝛻 ∙ (𝜌��) = −𝛻𝑝 + 𝜌�� + 𝛻 ∙ 𝜏 + �� Equation 30

This equation is derived from the Newton’s second law where p represents the static pressure,

g is the gravity and 𝜏 is the stress tensor acts on fluid and �� is the external force. The left side

in the equation is the initial force and the right side represents pressure forces, viscous forces

and external forces respectively. This equation, together with the mass continuity equation is

known as Navier-Stokes equation [30].

3.1.3 Species Transport Conservation

Fluent predicts the mass fraction changing of the species Yi, by solving the equation of

convection-diffusion of the solution as shown in Equation 31. 𝜕

𝜕𝑡(𝜌𝑌𝑖) + 𝛻 ∙ (𝜌��𝑌𝑖) = −𝛻 ∙ 𝐽𝑖

+ 𝑅𝑖 + 𝑆𝑖 Equation 31

𝑅𝑖 and 𝑆𝑖 represent the net rate of production of species i by chemical reaction and by addition

from any other sources respectively. Meanwhile, 𝑱𝒊 represents the diffusive flux which occurs

19

due to the difference between temperature and concentration in the system.

3.1.4 Discrete Phase Model (DPM)

The Discrete Phase Model (DPM) was used to study the particle trajectory from an

injection. In this work, the particle injected represents the alumina inclusion which is dispersed

due to turbulent flow. The particle trajectory is calculated by solving the particle force balance

equation as expressed in Equation 32.

𝑑𝑈𝑖𝑃

𝑑𝑡= 𝐹𝐷(𝑢𝑖 − 𝑢𝑖

𝑜) + 𝑔𝑖 (𝜌𝑝−𝜌

𝜌𝑝) +

𝐹𝑖

𝜌𝑝 Equation 32

The first part in the right side of Equation 32 represents the drag force, while the second and

the last are the gravity and external forces [31]. The DPM also consider the particle-wall

interactions such as escape, reflect or trap as shown in Figure 15.

Figure 15 Particle Interaction in DPM [31]

3.2 Turbulence Model

The turbulence flow is characterized by a high Reynold number, high degree of instability

as well as irregular movements where the mass, momentum and species transport is always

changing every time [32]. Because the flow inside tundish always involves the turbulence flow,

it needs to be modelled aiming to get more accurate results as in reality.

Figure 16 Turbulence flow structure [32]

There are small and large structures in a turbulence flow as shown in Figure 16. In order

to describe the behavior of turbulence in those structures, several mathematical models which

solves the energy and dissipation rate in those structures has been developed. In CFD, three

approaches can be used to solve the turbulence flow: Reynold Average Navier Stokes (RANS),

Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS). The illustration of those

approaches is shown in Figure 17. The RANS method, specifically a Realizable 𝑘−∈ model

was chosen due to its simplicity.

3.2.1 The Reynold Average Navier Stokes (RANS) model

The basic principle of RANs model is expressed in Equation 34.

𝑈𝑖 = �� + 𝑈′ Equation 33

20

Figure 17 Three difference method of turbulence model [33]

Where the velocity at certain time (𝑼𝒊) is a sum of the average velocity (��) and a fluctuating

component (𝑼′). The RANS Equation then can be obtained by substituting Equation 34 into

mass and continuity equation in Navier-Stokes Equation. The results are basically similar as

Navier-Stokes equation, but the velocity contains the ensemble time averaging of velocity and

the fluctuating component.

3.2.2 The realizable 𝒌−∈ method

The realizable 𝑘−∈ method is an improvement from the standard 𝑘−∈ method, where it

satisfies certain mathematical constraint on the Reynold stress tensor. This model was used in

this simulation since it is more suitable and more accurate for predicting the flow behavior

which involves rotation and recirculation and spreading from inlet jets as occur in this problem

[34].

3.2.3 Law of the wall and Near Wall-Treatment

´ The flow near wall experiences differences behavior depending on the distance from

the wall. The behavior of fluid flow near wall can be explained by the law of the wall. This law

divided fluid near wall into three regions: viscous sublayer, a buffer layer and fully turbulent

region. The viscous sublayer is the region closest to the wall where the fluid flow is almost

laminar as the viscosity plays an important role in momentum transfer. Meanwhile, the fully

turbulent region is the region where the turbulent plays a dominant role in momentum transfer.

The buffer layer is the layer between a viscous and turbulent layer where the fluid flow as a

mix between laminar and turbulent flow. Due to this phenomena, a grid setup near the wall

needs to be setup properly so that the accurate results are obtained.

There are two ways to setup the mesh around the wall. The first way is by resolving the

viscous sublayer and the second is by using a logarithmic-based wall function. The first method

required a high mesh resolution near the wall whereas the second method used a wall function

which relates the flow variables near the wall to the cell at the wall. In this work, the wall

inflation used for generating a thin mesh near the wall. In addition, the enhanced wall treatment

was used in the turbulence model setting window. This treatment was chosen because it is a

preferred method for predicting the mixing phenomenon [32].

21

4 EXPERIMENT SETUP

4.1 Model selection

An eight-strand industrial tundish was selected as the prototype in this project. Due to

the symmetrical consideration, only a half of tundish was manufactured. The model was

completed with flow control devices namely baffle walls and turbo-stopper. The tundish model

and baffle wall were respectively made from Plexiglas 20 mm and 10 mm of thickness while

the turbo-stopper was made from polypropylene. In order to have a flexible experiment setting,

the baffle wall and turbo-stopper have a detachable design. The dimension of tundish model

and flow control devices are shown in Figure 18 and Figure 19. The water was used to replace

1600℃ of hot steel melt due to a comparable kinematic viscosity as discussed section 2.8.2.

Figure 18 Drawing of tundish water model

Figure 19 drawing of turbo-stopper (left) and baffle wall (right)

22

4.2 Similarity Consideration

The Froude number similarity was employed as a similarity criterion with a scale factor

of 40%. Comparison between important properties and parameters in industrial tundish and

water model was summarized in Table 2. Table 2. Comparison of properties and process parameter in industrial tundish and water model

4.3 Experimental Tools design

All experiment tools were designed considering the process parameter mentioned in

Table 2. The schematic layout and photo of the whole experiment tools are shown in Figure 20

while the actual photo is presented in Figure 21. The lower water tank and big water tank are

put on the floor, while the tundish water model as well as upper water tank are held by tables

as the supporting structures.

In order to circulate the water during experiments, all water tanks and tundish model are

connected by pipes. The upper and big water tank as well as tundish model are connected to

the water tap source by P-11, P-12 and P-13 for a faster water filling. Meanwhile, the water

sink route is provided by P-9 and P-10. All crucial connections between tundish and tanks are

completed with valve and flow meter so that the net balance of flow rate can be adjusted. The

four outlets which represent SEN outlet in industrial tundish completed with conductivity

meters. The data transmission system is provided by connecting conductivity meter to the

laptop. The water conductivity as the transmitted data is converted into the salt concentration.

Details of some important configurations are discussed in next section.

4.3.1 General Setup : Material and – Scale consideration

The Plexiglas was selected as the material of tundish model because of its transparent

property which is useful for the observation of the flow behavior during experiments. The same

material also used for the upper water tank as the water level during experiment needs to be

controlled at a constant level in order to provide a constant velocity at the inlet. Meanwhile,

the other water tanks are made from stainless steel to prevent corrosion. The 40% scale was

used because this is the maximum scale that fits in the available room space. The model

geometry was kept same as the real industrial tundish to obtain an accurate result.

Parameter Unit Industrial Tundish Water Model Scale Factor 1 0.4

Density kg/m3 7038 998

Kinematic Viscosity m2/s 9.13 E-7 1.006 E-06

Length at base mm 6062.4 2438.8

Bath level mm 850 340

Volume of steel/water at max bath level m3 5.94 0.3734

Volumetric Flow rate at the inlet l/h 13648 1380

Mass Flow Rate kg/min 1592.3 23

Theoretical Mean residence time min 26.12 16.23

Froude Number 3.285 E-05 3.29 E-05

23

4.3.2 Water Tank Requirement

The three water tanks used in this work act as a temporary vessel as well as a water

storage for providing water during experiments. All tanks and water were filled by water and

the water is circulated from tundish model to the tanks until reach steady state as continuous

casting in the real process. Because of this, the total volume of all water tanks must be big

enough to supply the water up to four times of theoretical residence times with the desired flow

rate. The dimension of each water tank is listed in Table 3.

The smaller volume of upper and lower water tank compared to the big tank indicates

that the main role of these two tanks is not for providing water. The upper tank was built for

inlet installation and for providing tracer injection point location whereas the lower water tank

was fabricated to preserve the water from the four outlets. Table 3 Water tank dimension

4.3.3 Inlet and Outlet Configuration

The upper water tanks is a representation of a ladle in the industrial process whereas

the inlet acts a ladle shroud. In addition, the inlet is required since this is the location where the

tracer solution injected. The inlet was constructed from a 22 mm diameter of Plexiglas pipe

connected to the upper water tank as depicted in Figure 22. The inlet was completed with a

small pipe of 4 mm diameter for the tracer injection. The check valve was used as a connection

between the small pipe and the inlet so that the flow can only flow out to the inlet.

The outlets were fabricated from a small 12 mm diameter of Plexiglas pipe as displayed

in Figure 22. In this work, the outlet pipe furthest to the nearest from the inlet is called as strand

1 to strand 4. At the end of the outlets, a set of conductivity meter equipment was installed to

detect the changing of salt concentration during the experiment.

4.3.4 Turbo-stopper and Baffle wall attachment

Effects of two different flow control devices, turbo-stopper and a baffle wall, were

investigated in this experiment. The installation location of these two things can be seen in

Figure 23. The baffle wall covers the area around the inlet and the turbo-stopper is located

exactly below the inlet.

The baffle wall and turbo-stopper need to be fixed during the experiment. Therefore,

four steel bars tightened by bolt were utilized to hold the four corner of the turbo-stopper.

Meanwhile, the baffle wall was designed as a ‘box’ which is assembled by bolts to the bottom

surface of water model. Those two constructions are displayed in Figure 24.

Water Tank Dimension in mm (l x w x h) Volume (l)

Upper Water Tank 1420 x 480 x 420 208

Big Water Tank 1500 x 800 x 1535 1170

Lower Water Tank 2120 x 280 x 320 120

24

Figure 20 Schematic Layout of Tundish Water Model

Figure 21 Actual photo of experiment setup

25

Figure 22 Tracer injection system and conductivity meter arrangement

Figure 23 Location of baffle wall and turbo-stopper in experiment

Figure 24 Installation of turbo-stopper and baffle wall

26

4.4 Water Pump for Stirring Position

The aquarium water pump of Turbelle Stream 6105 was used as a stirring source as a

representation of electromagnetic stirring (EMS) in the reality. The product specification is

summarized in Table 4. The stirring power can be adjusted from 20 to 100% of its capacity

while the direction can also be altered freely. The pumps were installed at the tilt side of tundish

model because this is the only possible side to install EMS in the real industrial process due to

space limitation. The water pump was held by a magnetic clamp acts on steel bars as can be

seen in Figure 25. Table 4 Water pump specification

Three pumps were located along the tilt side of tundish model as displayed in Figure

25. The specific pump location and stirring direction are different for several tundish

configurations investigated in this work. This difference arises due to the consideration to avoid

high surface turbulence as well as high backflow from the wall. The pumps were located in

such a way to obtain more homogeneous stirring force distribution along the tilt side of the

model. From 13 different tundish configurations, there are three different pump location used

and the details of each pump location are discussed in the next section.

Figure 25 Water pump installation

4.4.1 Pump Location-1

In this configuration, three pumps were located 120 mm above the bottom at the tilt

side. The pumping force was directed to the left side so that the counterclockwise stirring was

generated. The distance between each pump is 510 mm and the right pump was located 250

mm from the right side wall as illustrated in Figure 26. This setup was employed for experiment

case number 2, 3,4,6,7 and 8. The details of each case number are listed in Table 5.

No Specification Information Picture

1 Brand Turbelle Stream 6105

2 Flow rate 3000 – 13000 l/h

3 Outlet diameter 63 mm

27

Figure 26 Schematic illustration of pump location-1


The three pumps were directed to the right side and the clockwise stirring was generated

in pump location-2 configuration as illustrated in Figure 27. The pump height level is same as

the pump location-1, but the distance between right pump to the right side was longer in order

to minimize the backflow and surface turbulence around this area. This configuration was used

in the experiment case number 9 as explained in Table 5.

Figure 27 Schematic Illustration of Pump Location-2


This pump configuration was applied for experiments involving baffle wall and pump

stirring. Since the hole from baffle wall directs the flow to the right side, the clockwise stirring

was chosen for this configuration. The details distance and setup is explained in Figure 28.

28

Figure 28 Schematic Illustration of Pump Location-3.

4.5 Experimental Method and Setup

Four types of experiments were conducted in this work. Firstly, a velocity mapping was

investigated in order to know the extent of stirring force by water pumps in 30 different

locations within the tundish model. By conducting this measurement, the degree of similarity

between the water pump and EMS can be imagined. Even though it is clear that the pump

stirring is not similar to EMS, at least this measurement can be a foundation to understand the

extent of stirring force that applied in different pump capacity. In addition, it can be a reference

to setup the EMS force in the reality. The second experiment is a flow behavior observation.

The objective is to understand the tendency of flow movement within the tundish. The third

experiment is a salt injection experiment aiming to obtain an RTD Curve for different tundish

configurations. Due to this goal, the RTD experiment term was used to mention this kind of

experiment. The last experiment type is dye color injection, where the flow behavior as well as

the changing of concentration distribution can be observed. In addition, a comparison of mixing

time of each case can also be investigated qualitatively.

4.5.1 Velocity Mapping

The velocity measurement was carried out by a low-velocity meter Nixon flowmeter

430. The measurement tools are displayed in Figure 29. It comprises of a sensing probe of five-

bladed PVC rotor connected to the meter. At the center of the rotor, an insulated gold wire is

installed within a slim tube. The principle of the measurement is when the rotor is moved by a

conductive liquid, the flow passes the gold wire and changes the impedances. This detection is

converted into velocity measurement. The velocity mapping was conducted by measuring 30

different locations. The illustration of measurement points is presented in Figure 30. In this

work, the longitudinal velocity or velocity in x-axes direction was measured for four different

configurations: bare tundish without any stirring and bare tundish with 20%, 30%, and 40% of

water pump capacity.

29

Figure 29 Low velocity meter used in the experiment

Figure 30 Schematic Illustration of measurement point in velocity measurement

4.5.2 Flow Behavior Observation

The flow behavior observation was conducted using a plastic particle which has a

similar density to water. The specific movement in every location was difficult to be observed,

but the general tendency can still be analyzed. The movement of particles at the top surface

from the top view and the right side of tundish model were observed and recorded. This

experiment was conducted for five different configurations, as summarized in Table 5.

4.5.3 RTD Experiment

The RTD experiment procedures are simplified in Figure 31. It was begun by filling the

tundish model and all water tanks with the water from a water tap using pipe P-11, P-12 and

P-13. Then all valves were adjusted to reach the desired volumetric flow rate except V-9 and

V-10 which is kept closed to prevent the water flow to the sink. The circulation of water was

maintained until the desired bath level in the tundish model was reached. Furthermore, the V-

11, V-12 and V-13 were turned off that the water circulation only relies on the water from the

tank. The water flow route is from V-1 to the tundish model, four outlets and then it is circulated

back to the tundish model. This continuous circulation was maintained for 20 minutes to make

30

sure the steady condition and flow pattern is fully generated. Furthermore, a 30 mL of 20%

NaCl as a tracer solution was injected through a syringe connected to the pipe P-2 and valve

V-2. At this time the conductivity meter was turned to record the conductivity data at each

outlet up to 4000 s which is similar around four times of theoretical residence times. Then the

data was transmitted to the computer and the RTD curve was plotted. In total, 13 different

configurations of experiments were conducted by this kind of experiment as summarized in

Table 5.

Figure 31 RTD Experiment Steps

4.5.4 Dye-Color Injection

In this experiment, a 30mL of Dr.Oetker liquid food color was injected at the same location

as salt injection point through a syringe. At the same time, a video was recorded to observe the

changing of concentration gradient inside tundish model. The video was documented until an

approximately homogeneous concentration for the whole tundish achieved. The mixing time

as well as the flow behavior then can be compared qualitatively between different

configurations of the tundish.

4.6 Data Processing Steps of RTD Experiment

In order to analyze the flow behavior at different strands, several flow characteristics such

as: 𝜃𝑚𝑖𝑛, 𝜃𝑝𝑒𝑎𝑘 , 𝐶𝑚𝑎𝑥 , 𝜃𝑚𝑒𝑎𝑛,, fraction of plug flow(𝑽𝒑

𝑽), fraction of dead volume(

𝑽𝒅

𝑽), fraction

of well-mixed volume (𝑽𝒎

𝑽) were calculated from RTD curve. Those flow characteristics can

be obtained using following steps:

1. Run the RTD Experiment up to four times of theoretical residence time and record the

conductivity at each strand.

2. Convert the conductivity value into the concentration (c) based on the relationship as

shown in Figure 32.

3. Determine 𝜃 using Equation 2 and Equation 3.

4. Plot the curve of concentration (c) vs 𝜃 and then determine the area under the curve.

5. Change the concentration (c) into a dimensionless concentration (C) using Equation 4.

6. Plot the C-curve (C vs 𝜃) for each strand and compare each flow characteristics of each

individual strands that have been calculated.

7. 𝜃𝑚𝑖𝑛 and 𝜃𝑝𝑒𝑎𝑘 can be determined from the data of dimensionless time where the tracer

appears for the first time and at the highest concentration value respectively. Meanwhile,

𝜃𝑚𝑒𝑎𝑛 can be calculated based on Equation 5.

8. Determine the plug flow fraction based on Equation 11 using the value obtained from step

(5).

9. In order to obtain the dead volume fraction (𝑉d

𝑉), calculate the cut-off time (𝜃𝑐𝑢𝑡−𝑜𝑓𝑓) then

flow rate through active region (𝑄𝑎

𝑄) using Equation 13 and 16 respectively.

31

10. Using the value obtained from steps (8), the fraction of dead volume can be determined

from Equation 14. The well-mixed volume is then calculated using Equation 18.

11. Calculate and compare the overall tundish performance as well as strand similarity of each

experiment configurations by Equation 19, Equation 20, Equation 21 and Equation 22.

Figure 32 Conductivity vs concentration relationship for a solution of NaCl and water tap at 25℃

4.7 Experiment variables

Four variables were investigated aiming to know the effect of its presence on the tundish

performance. The experiment variables are the existence of flow control devices, namely baffle

wall and turbo-stopper, the three different magnitudes of stirring force by water pump (20%,

30% and 40% of pump capacity) and the stirring direction (clockwise and counterclockwise).

In total, there are13 experiment case number with different configurations and the detail is

explained in Table 5.

y = -3828.7x2 + 1874.1x + 0.2703

0

50

100

150

200

250

0% 3% 5% 8% 10% 13% 15% 18% 20% 23%

Co

nd

uct

ivit

y (m

S/cm

)

NaCl Concentration (wt%)

32

Table 5Experiment Configuration List

Remark:

NS : No Stirring

CC : Counter Clockwise

CW : Clockwise

Case

No

Configuration Experiment Type/ Simulation

Tundish Model Construction Stirring

direction

Pump

Location CFD

Velocity

Mapping

RTD

Experiment

Particle

Movement

Dye

Injection

1 Bare Tundish NS -

2 Bare Tundish + 20% pump capacity CC 1 -

3 Bare Tundish + 30% pump capacity CC 1 - - -

4 Bare Tundish + 40% pump capacity CC 1 - -

5 Tundish + Turbo-stopper NS - - - -

6 Tundish + Turbo-stopper + 20%

pump capacity CC 1 - - - -





9 Bare Tundish + 20% pump capacity CW 2 - -

10 Tundish + Baffle wall NS 3 -

11 Tundish + Baffle wall + 20% pump

capacity CW 3 - -

12 Tundish + Baffle wall + Turbulence

pad CW - - -

13 Tundish + Baffle wall + Turbulence

pad + 20% pump capacity CW 3 - - - -

33

5 NUMERICAL SIMULATION SETUP

The main advantage of numerical simulation is the prediction of the tundish flow behavior

and the characteristics in the real process can be gained in a shorter time and a cheaper cost if

the setup is accurate. In addition, the numerical simulation is used to get a more comprehensive

understanding of flow behavior in the tundish. However, it is necessary to compare and validate

the experiment results in water model before developing a simulation of steel melt flow in the

real tundish. Because of this reason, the simulation of RTD experiment in water model was

developed in this work. Therefore, it can be a comparison as well as the prediction for the future

studies if the result has a comparable similarity with the result from water model experiment.

In this chapter, the details setup of the simulation conducted is elaborated.

5.1 Computer specifications

The CFD analysis was conducted using software of ANSYS Fluent version 18.2 on a

Windows 7 64-bit operating system with an Intel Core Xeon (R) CPU E5-2660 @ 2.60 GHz

processor and 64GB of RAM.

5.2 Geometry Domain

Four 3D models of different experimental configurations were developed by CAD

software: Solid Edge. The geometry and dimension refer to the same drawing used for

manufacturing the water model. The inlet which represents a ladle shroud was included in the

model as it is the location of tracer injection in the experiment. Due to the limitation of time,

the simulation only conducted for configurations of a bare tundish and tundish with flow

control devices as shown in Figure 33.

Figure 33 3D Model in Simulation: (a) bare tundish; (b) Tundish with baffle wall; (c) tundish with turbo-stopper; (d)

Tundish with baffle wall and turbo-stopper

5.3 Simulation Steps

There are three kinds of simulation conducted in this work. Initially, a fluid flow

34

simulation was run in order to simulate the fluid flow until reach the steady condition. Then,

the simulation was continued in the transient mode for simulating salt injection experiment.

The last is a simulation of floatation of inclusion by observing particle trajectory from an

injection of inclusion particle. This simulation was also conducted in the transient mode using

the convergence result of fluid flow simulation as the initial condition. The flow work, as well

as the boundary condition of tracer and inclusion injection simulation was elaborated in the

next section.

5.3.1 Tracer Injection Simulation

The summary of tracer injection simulation and its boundary condition was presented in

Figure 34 and Figure 35. The simulation was begun with a fluid flow simulation until reaching

a steady state. Then, the flow and turbulence equation was turned off while the species equation

was activated. Furthermore, the simulation was changed into the transient mode and the tracer

which is a mixture of water and NaCl was injected for a short period of 5s. The simulation

then was run until four times of theoretical residence time. During this period, the concentration

of tracer at each outlet was monitored and extracted in order to obtain an RTD curve.

Figure 34 Steps of salt injection experiment

Figure 35 Boundary condition in tracer injection simulation

5.3.2 Inclusion Injection Simulation

In this simulation, inclusion particles are injected from the inlet and then the amount of

inclusion that trapped on the surface is calculated. As described in Figure 36, the simulation

was started with a simulation of fluid flow until reaching a convergence condition before the

transient mode was activated. The inclusion particles are injected during 2s and the transient

simulation was run until 200s.

Simulation of fluid flow until steady state

Injection of tracer (5s)Transient Simulation up to 4 times of theretical

residence timePlot the results

35

Figure 36 Steps of inclusion injection simulation

Since the water was used as the fluid phase in the simulation instead of hot steel melt

as in the real process, an adjustment of inclusion particle density is necessary to maintain the

similar buoyancy force of inclusion. As a simple approach, the density of inclusion particle

was decided as 560 kg/m3 so that the ratio of inclusion to water density is similar as alumina

inclusion and steel melt in the real process as shown in Table 6.

For boundary condition, a specific interaction between particle and wall was defined.

The surface of the domain was defined as ‘trapped’ while outlets and wall were defined as

‘escaped’ and ‘reflect’ respectively. Thus, a ‘trapped’ surface represent a slag which can react

with inclusion as it is reached the surface. For a details analysis, the surface identity was divided

into two different regions of the surface inside baffle wall (surface 1) and surface outside the

wall (surface 2) for configuration involving baffle wall, as shown in Figure 37.

Table 6 Comparison of fluid-inclusion density in simulation and real industrial tundish

Figure 37 Surface defined as trapped in the configuration: (a) without a baffle wall; (b) and (c) with a baffle wall.

5.4 Simulation List

In this work, a total of eight simulations were run for different objectives as summarized

in Table 7. There are five simulations of bare tundish configurations with different mesh setup

in order to investigate the mesh independence. The rest of simulations were conducted using a

final mesh for simulating the fluid flow, RTD experiment and floatation of inclusion in the

tundish configuration involving flow control devices. As already mentioned previously, the

simulation of pump stirring has not been conducted due to the limitation of time in this work.

Therefore, the analysis from simulation result focuses on the effect of flow control devices.

Simulation of fluid flow until steady state

Injection of inclusion particles (2s)

Transient Simulation for 200s

Observe the results

Material Density (kg/m3) Representation

Steel Melt 7020 Real Industrial Process

Alumina Inclusion 3950

Water 998 CFD Simulation

Inclusion Particle 560

36

Table 7 Simulation List

5.5 Assumption and Model Setup

In order to simplify the simulation, the isothermal assumption was employed. This means

there is no influence from the convection on fluid flow inside the domain. The top surface is

assumed as a flat surface during simulation. The ANSYS Fluent was run in double precision

mode aiming to reduce the truncation error during numerical calculation. For solving the

behavior of turbulence flow, the realizable 𝑘−∈ model with standard wall treatment was

chosen. The simulation was initialized by standard initialization method and several solution

schemes were employed. Most of the fluid flow simulation can reach convergence using the

setup: SIMPLEC, Second order of Pressure, Second-order upwind for Momentum, turbulence

kinetic energy and dissipation rate.

The species transport was turned on when simulating salt injection in transient simulation

whereas the Discrete Phase Model (DPM) was activated when injecting inclusions in

simulation. The third-order MUSCLE scheme was utilized to solve species equation during

transient simulation of tracer injection. Under-relaxation factors were changed from the default

value due to high fluctuation of residual for some variables. The complete list of every

numerical scheme and solver setup in every simulation are summarized in Appendix A.

5.6 Meshing

The polyhedral mesh was developed in order to minimize the cell number and reduce the

computational time. Therefore there are two steps in creating the mesh in this work. Firstly the

tetrahedral mesh generation was developed in Meshing window. Secondly, the generated

tetrahedral mesh was converted into the polyhedral mesh in the Fluent Setup window.

The first setup was accomplished by adjusting the maximum face size of the tetrahedral

mesh. The inflation was used for setting the mesh close to the wall. Then the polyhedral mesh

generation was conducted by converting the whole domain of previous tetrahedral mesh. The

orthogonal quality and aspect ratio were observed to ensure the mesh quality above the

Simulation Number

Experiment Case Number (refer to

Table 5) Configuration Total Mesh Cells

Objective / Simulation conducted

S1 1 Bare tundish 154109 Mesh Sensitivity study

S2 1 Bare tundish 158724


Mesh Sensitivity study,

Fluid Flow, Salt Injection

(RTD experiment), Inclusion

injection

S4 1 Bare tundish 185191 Mesh Sensitivity study


S6 5 Tundish + Turbo-stopper 313313 Fluid Flow, salt injection

(RTD experiment), inclusion

injection

S7 10 Tundish + baffle wall 197889

S8 12 Tundish + baffle wall +

Turbo-stopper 399086

37

minimum requirement of a good mesh. However, for some simulations, several meshes have

orthogonal quality less than 0.1 when generating the tetrahedral mesh. However, those bad

meshess were neglected as the amount is small and the location exist at the unimportant area,

i.e., around the sharp corner of tundish model. The amount, complete setting and mesh quality

used in this work after were summarized in Appendix B.

5.7 Convergence Criteria

The standard criteria for convergence condition of residual for all variables related to

the flow and turbulence equation are less than 10-3 [35]. In this project, convergence criteria of

10-6 were employed to get more accurate steady state results. Meanwhile, the convergence level

10-5 was used for species equation during transient simulation as suggested in ANSYS Fluent

solver setting [36]. Figure 38 shows the simulation that has reached convergence based on this

residual criteria.

Figure 38 Convergence condition of simulation S3

In addition to this observation, several variables were also monitored to ensure a

convergence status has been reached. The volume-average of velocity magnitude, turbulence

related variables, vertex average of velocity at the end of strand 4 and the mass flow rate were

observed. The example of monitoring results is shown in Figure 39 and Figure 40. Based on

those monitoring, it is clear that the simulations have reached convergence as all monitored

variables already have a constant magnitude. Table 8 also shows that the net mass balance is

less than 1% of the smallest flow rate through the domain which also means a convergence

condition has been reached. All those observations were used for all simulations in this work.

Figure 39 Monitor of the average velocity of simulation S3

38

Figure 40 Monitor of velocity at outlet strand 4 of simulations S3

Table 8 Summary of Mass Flow Rate Observation of simulation S1 to S5

Simulation

Number

Mass Flow rate (kg/s)

Inlet Strand 4 Strand 3 Strand 2 Strand 1 Balance

S1 0.3641 -0.09045 -0.09094 -0.09129 -0.09142 -3.51E-08

S2 0.3641 -0.09039 -0.09088 -0.09148 -0.09135 -7.76E-08

S3 0.3641 -0.09009 -0.09094 -0.09155 -0.09152 -8.43E-08

S4 0.3641 -0.09033 -0.09089 -0.09152 -0.09135 -1.17E-07

S5 0.3641 -0.09031 -0.09083 -0.09155 -0.09141 4.94E-09

5.8 Mesh Sensitivity Study

Before analyzing the result of CFD simulation, the mesh sensitivity study was carried

out in order to ensure the grid size independence. This investigation was carried in bare tundish

model. Five different mesh setups were used to compare the volume-average of velocity in

steady state condition. The summary of mesh sensitivity study results was shown in Table 9

and Figure 41. The significant difference between the volume-average of velocity was clearly

observed in simulation number 1, 2 and 3 and the difference decreases gradually from

simulation 3 to simulation 5. Since the relative difference between simulations 3 to 4 is less

than 5%, the grid independence can be concluded has been achieved in simulation 3. Therefore,

the meshing setup of simulation 3 was decided to be used for all simulations in this work. The

final mesh of this setup is displayed in Figure 42.

39

Table 9 Summary of Mesh Sensitivity Study

Simulation number

Configuration

Max Face Size (mm) in

Tetrahedral Mesh Generation

Total Polyhedral

Mesh

Volume-Average of Velocity Magnitude

(m/s)

Relative Difference (%)

1 Bare tundish 45 154109 0.01556159 0

2 Bare tundish 37 158724 0.017263088 10.93

3 Bare tundish 29 169851 0.020424319 18.31

4 Bare tundish 24 185191 0.0208207 1.94

5 Bare tundish 21 199209 0.020871245 0.24

Figure 41 Mesh sensitivity study result

Figure 42 Final Mesh after mesh sensitivity study (mesh of simulation S3)

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

0.0155

0.0165

0.0175

0.0185

0.0195

0.0205

0.0215

0 50 100 150 200 250

Vo

lum

e-A

vera

ge V

elo

city

(m

/s)

Number of Polyhedral cells (thousands)

Average Velocity after steady state

40

6 EXPERIMENT RESULTS

6.1 Velocity Mapping

The velocity cannot be detected in all measurement points in a bare tundish

configuration (case 1) due to the very low velocity. Therefore it can be concluded that in

bare tundish configuration without stirring, the fluid is moving very slowly. When the

stirring of 20% pump capacity with counterclockwise direction was introduced (case 2), a

velocity distribution along measurement points appears as shown in Figure 43. The similar

curve of 30% and 40% pump capacity (case 3 and case 4) are provided in Appendix C.

Generally, the area in the center of tundish model specifically at point D to G is the most

affected area since this is the location where pumps installed. The velocity from point A to

J varies from 0.08 to 17.96 cm/s, 0.42 to 20 cm/s and 3.24 to 25.6 cm/s for case 2, 3, and 4

respectively. The average of velocity from the whole measurement points is 7.04, 9.07 and

13.3 cm/s for those case numbers.

Figure 43 Velocity mapping in case 2: bare tundish with stirring (20% capacity and CW direction)

6.2 Flow Behavior Observation

The examples of results from this experiment are presented in Figure 44 to Figure 47.

The plastic particle movement which represents the flow movement is illustrated by the

arrow. Nevertheless, the thickness and length of the arrow do not represent the velocity

magnitude. The top view illustration describes the fluid movement at the top surface while

the Section A-A demonstrates the fluid movement from the right side view of the tundish

model. In Figure 44 a strong inlet jet generates a counterclockwise movement. However,

the fluid moves very slowly from strand 4 to strand 1 so that the stagnant particles were

observed on the right side of tundish model. Meanwhile, examples of the fluid movement

in tundish configuration involving stirring are shown in Figure 45 to Figure 47. In those

cases, there is a strong movement of fluid in the whole tundish even as it creates a strong

backflow on the right side of the tundish. The results of flow behavior are discussed more

comprehensively in section 8 and section 9. Meanwhile, another result of flow illustration

41

in configuration of tundish with baffle wall is provided in Appendix D.

Figure 44 Flow illustration of case no.1: bare tundish

Figure 45 Flow illustration of case no.2: bare tundish + stirring (20% pump capacity, CC direction)

Figure 46 Flow illustration of case no.9: bare tundish + stirring (20% pump capacity and CW direction)

42

Figure 47 Flow illustration of case no.11: tundish + baffle wall +stirring (20% pump capacity and CW direction

6.3 RTD Experiment

This experiment aims to analyze the tundish performance to remove inclusion and to

investigate strand similarity using flow characteristics obtained from the RTD curve. In this

section, the analysis of experiment repeatability and RTD curve of several interesting

configurations are presented. In the end, the overall flow characteristics are summarized.

6.3.1 Repeatability

The experiments were repeated three times for each configuration to acquire a proper

statistical evaluation in the limited time available in this work. There is always occur a

discrepancy for different runs such as in RTD curves of strand 2 in bare tundish configuration

(case 1), as shown in Figure 48. This lead to the different result of 𝜃𝑚𝑖𝑛, 𝜃𝑝𝑒𝑎𝑘 and other RTD

curve characteristics. As a summary, the variability of overall tundish performance and strand

similarity are written in the form of standard deviation as listed in Table 10.

Figure 48 Reproducible test of RTD curve of strand 2 in case 1 for different runs

0

0.2

0.4

0.6

0.8

1

1.2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.4

1.5

1.6

1.7

1.8

1.9

2.0

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2.2

2.3

2.4

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nce

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atio

n

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Run 1 Run 2 Run 3

43

Table 10 Standard Deviation of Overall Performance of Tundish

Case Number

Standard Deviation

𝑉𝑝

𝑉

𝑉𝑑

𝑉

𝑉𝑚

𝑉 𝑆4

1 10.6% 5.7% 8.9% 18.8%

2 19.0% 10.0% 6.1% 8.2%

3 4.0% 2.4% 1.7% 15.3%

4 14.0% 5.4% 3.3% 0.0%

5 13.8% 6.0% 3.2% 22.8%

6 5.7% 1.7% 1.4% 20.5%

7 9.5% 10.4% 5.6% 24.6%

8 13.6% 2.2% 2.3% 12.4%

9 19.7% 7.7% 7.9% 4.5%

10 3.7% 7.6% 2.9% 3.7%

11 3.0% 2.6% 2.5% 10.4%

12 3.4% 0.4% 1.9% 14.2%

13 4.3% 9.9% 4.9% 15.5%

Most of the important flow characteristics demonstrate a relatively small standard

deviation, namely below 10%. However, there is a high degree of variability for some variables

in certain case number which varies from 10 to 24.6%. This large variation probably occurs

due to many factors such as difference of tracer amount and concentration injected, fluctuation

of the flow rate at inlet and outlets, unstable water tap conductivity, or natural variability of a

transient condition. However, a significant difference of specific variable can still be observed

in two or more cases despite the considerable variability. Therefore a reliable analysis can still

be executed by conducting a proper comparison.

6.3.2 RTD Curve

Several interesting RTD curves of different experiment configuration are presented in this

section. For a configuration without stirring, only a bare tundish configuration (case 1) is

displayed in this section. Figure 49 and Figure 50 displays the RTD curve in case 1 and case

10 while the other configurations involving flow control devices are shown in Appendix E.

Meanwhile Figure 51 to Figure 53 displays the RTD curve in the configuration involving

stirring. Since the RTD curve generated for stirring with different pump capacity have a similar

shape, the only configuration with 20% pump capacity stirring is presented.

44

Figure 49 RTD curve of case 1: bare tundish

Figure 50 RTD curve of case 10: tundish + baffle wall

0.0

0.5

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Strand 4 Strand 3 Strand 2 Strand 1

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45

Figure 51 RTD curve of case 2: bare tundish + stirring (20% pump capacity + CC direction)

Figure 52 RTD Curve of case 9: bare tundish +stirring (20% pump capacity, CW Direction)

0.0

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atio

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46

Figure 53 RTD curve of case 13: tundish + baffle wall + turbo-stopper + stirring (20% pump capacity, CW direction)

6.3.3 Flow Characteristics

Before determining the overall performance of tundish, the flow characteristics of each

strand was calculated and the results are presented in Appendix F. Furthermore, the overall

flow characteristics were calculated using Equation 19, Equation 20 and Equation 21.

Meanwhile, the strand similarity was determined from Equation 22. The summary of overall

tundish performance of all configurations are summarized is in Table 11.

6.4 Dye-Color Injection

The results of color injection experiment for some configurations are presented in Figure

54 to Figure 59. In those figures, the sequence of color concentration changing from the

beginning to the estimated homogeneous concentration reached are displayed. The sequence

displayed in every case is unique depending on the interesting phenomenon observed.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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0.7

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1.2

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2.2

2.3

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47

Table 11 Overall Flow Characteristics for different tundish configuration

Case

Number

Flow Characteristics

Configuration 𝑉𝑑𝑝

𝑉(%)

𝑉𝑑

𝑉(%)

𝑉𝑚

𝑉(%)

𝑉𝑝

𝑉𝑑

𝑆4

1 20.5 ± 2.2 40.9 ± 2.3 38.6 ± 3.4 0.50 ± 0.055 0.087 ± 0.0164 Bare Tundish

2 3.3 ± 0.6 37.9 ± 3.8 58.8 ± 3.6 0.09 ± 0.001 0.007 ± 0.0006 Bare Tundish + Pump Stirring (CC, 20% capacity)



5 17.2 ± 2.4 54.3 ± 3.2 28.4 ± 0.9 0.32 ± 0.062 0.089 ± 0.0204 Tundish + Turbulence Impact Pad

6 3.3 ± 0.2 37.0 ± 0.6 59.7 ± 0.8 0.09 ± 0.004 0.015 ± 0.0031 Tundish + Turbulence Impact Pad + Pump Stirring (CC, 20% capacity)



9 8.2 ± 1.6 36.0 ± 2.8 55.8 ± 4.4 0.23 ± 0.029 0.020 ± 0.0009 Bare tundish + Pump Stirring (CW,20% capacity)

10 25.7 ± 1.0 28.5 ± 2.2 45.8 ± 1.3 0.91 ± 0.097 0.025 ± 0.0009 Tundish + baffle wall

11 22.1 ± 0.7 28.2 ± 0.7 49.7 ± 1.2 0.78 ± 0.021 0.020 ± 0.0021 Tundish + baffle wall + Pump Stirring (CW, 20% capacity)

12 28.9 ± 1.0 24.6 ± 0.1 46.5 ± 0.9 1.17 ± 0.044 0.023 ± 0.0033 Tundish + baffle wall + Turbulence Impact Pad

13 24.6 ± 1.0 28.0 ± 2.8 47.3 ± 2.3 0.89 ± 0.124 0.021 ± 0.0033 Tundish + baffle wall + Turbulence Impact Pad + Pump Stirring (CW, 20%

capacity)

48

Figure 54 Sequence of the changing of color concentration in case 1: bare tundish

Figure 55 Sequence of the changing of color concentration in case 2: bare Tundish + stirring (20% pump capacity, CC

Direction)

Figure 56 Sequence of the changing of color concentration in case 9: bare tundish + stirring (20% pump capacity, CW

Direction)

49

Figure 57 Sequence of the changing of color concentration in case 10: Tundish + Baffle Wall

Figure 58 Sequence of the changing of color concentration in case 12: Tundish + Baffle Wall + Turbo-stopper

Figure 59 Sequence of the changing of color concentration in Case 13: tundish + baffle wall + turbo-stopper + stirring (20%

pump capacity, CW Direction

50

7 NUMERICAL SIMULATION RESULT

7.1 RTD Curve

Figure 60 and Figure 61 displays the RTD curve generated from the simulation of

experiment case 1 and case 10. The other results are provided in Appendix G. The shape and

size of RTD curves is comparable to the curve generated from the water model experiment.

The simulations result in a smooth curvature of the RTD curve because the changing of

concentration at the outlets were detected by a very small convergence criterion of species

equation residual: 1e-05. This criterion is small enough to increase the sensitivity of

concentration detection.

Figure 60 RTD Curve of case 1: bare tundish

Figure 61 RTD Curve of case 10: tundish + baffle wall + turbo-stopper

0.0

0.5

1.0

1.5

2.0

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4.5

5.0

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on

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ntr

atio

n

Dimensionless time


51

7.2 Flow Characteristics Calculation

The steps to obtain the overall performance, as well as strand similarity of all

configuration, are similar as in the experiment. Initially, the flow characteristics of each strand

were obtained from RTD curve and the summary is provided in Appendix G. From these

results, the overall flow characteristics of tundish were determined and the results are displayed

in Table 12. Table 12 Overall Flow Characteristics from CFD Simulation

7.3 Flow-related variable Comparison

Initially, the simulation was run to obtain a steady state of fluid flow before it was

continued with salt injection or inclusion particles injection in transient mode. Thus, a fluid

flow simulation becomes an initial condition which influences the result of the latter

experiment. Several interesting contours, as well as the velocity vector, were captured and the

comparison of them between different configurations is discussed in section 9 in order to reveal

the effect of turbo-stopper and baffle wall. In addition, a volume-average of velocity and

turbulent variables were calculated and it is displayed in Table 13.

Table 13 Volume-average of velocity and turbulence related variables in the steady-state condition

Simulation number

Configuration

Variable

Average Velocity (m/s)

Average turbulent Kinetic Energy (m2/s2)

Average turbulent Dissipation Rate (m2/s3)

3 bare tundish 2.04E-02 1.21E-04 3.91E-04

6 Baffle wall only 1.73E-02 3.97E-05 3.09E-04

7 Turbo-stopper only 9.22E-03 1.34E-05 2.74E-04

8 Turbo-stopper + baffle

wall 1.38E-02 1.56E-05 3.04E-04

Case Number 𝑉𝑑𝑝

𝑉(%)

𝑉𝑑

𝑉(%)

𝑉𝑚

𝑉(%)

𝑉𝑝

𝑉𝑑

Configuration

1 19.4 36.1 44.5 0.54 0.151 Bare Tundish

5 18.3 34.2 47.6 0.53 0.114 Tundish + Turbulence Impact Pad

10 23.5 24.0 52.5 0.98 0.028 Tundish + baffle wall

12 19.9 25.5 54.6 0.78 0.025 Tundish + baffle wall + Turbulence Impact Pad

��𝟒

52

7.4 Results of Inclusion Injection Simulation

In the simulation of inclusion injection, the trajectory of inclusion particles injected was

monitored and the number of particles trapped at the surface was observed. For the simulation

involving baffle wall in the domain, the number of particles trapped is separated for two

different surface definition as already explained in section 5.3.2. In addition, the simulation can

also show the number of inclusion particles escaped to each outlet and the residence time of

each different fate of particles as shown in Table 14.

Table 14 Summary of inclusion injection results

Configuration Fate of Particle

Position No. of

particles Percentage of Particle

Residence time in the tundish

Min Max Average

Bare Tundish

Trapped Surface 1861 84.4% 3.9 198.7 52.8

Escaped Strand 4 126 5.7% 9.1 198.2 75.2

Escaped Strand 3 135 6.1% 4.2 197.4 98.9

Escaped Strand 2 82 3.7% 7.8 196.5 119.3

Escaped Strand 1 0 0.0% 0.0 0.0 0.0

Tundish + Turbo-stopper

Trapped Surface 1876 83.4% 6.1 29.6 29.6

Escaped Strand 4 235 10.4% 47.7 199.1 126.2

Escaped Strand 3 113 5.0% 59.7 192.1 114.3

Escaped Strand 2 25 1.1% 166.5 196.9 184.8

Escaped Strand 1 0 0.0% 0.0 0.0 0.0

Tundish + Baffle Wall

Trapped Surface 1895 90.4% 6.1 198.2 6.3

Escaped Strand 4 56 2.7% 7.1 197.8 138.0

Escaped Strand 3 16 0.8% 110.2 188.7 140.0

Escaped Strand 2 20 1.0% 138.3 198.0 163.5

Escaped Strand 1 110 5.2% 147.6 198.2 172.2

Tundish + Baffle Wall +

Turbo-stopper

Trapped Surface1 68 3.1% 33.9 196.2 99.1

Trapped Surface2 2025 93.3% 6.1 198.6 39.9

Escaped Strand 4 42 1.9% 143.6 196.2 180.0

Escaped Strand 3 5 0.2% 153.8 190.5 175.5

Escaped Strand 2 2 0.1% 131.6 146.0 138.8

Escaped Strand 1 29 1.3% 96.7 198.5 135.1

53

8 EXPERIMENT ANALYSIS

8.1 Velocity Mapping

Figure 62 and Figure 63 displays a combination of several velocity measurement curves at

the different stirring force and different bath level. Two interesting phenomena can be

interpreted from those figures. Firstly, an extremely slow-moving fluid exists in a bare tundish

configuration without any stirring. It is indicated by undetected velocity, or in the other word

the velocity is very close to zero, which reflects a large dead fraction exist in the tundish.

Secondly, the addition of stirring drives the water to move faster. Moreover, a relatively higher

velocity was detected at the area furthest from the inlet. The fluid velocity was also observed

to increase with the increase of pump capacity. Nevertheless, pumps create a local high stirring

force, as shown in Figure 62 by a velocity distribution along the measurement points. The

middle area of the model (between E to G) tend to become the most affected area while the

area near strand 1 (the furthest strand from inlet) becomes the most unaffected area. This means

the velocity at every point is highly dependent on pump location. Therefore, probably the

velocity distribution generated is not precisely similar to EMS. However, the water pump can

still be considered as a good way to model EMS in water model because it generates a similar

macro-stirring as EMS.

The different stirring force was also detected in the vertical direction of the model as

depicted in Figure 63. Velocity detected near the bottom surface (bath level 2) is generally

higher than near the surface (bath level 1) because the pump was located closer to the bottom

than to the surface.

Figure 62 Velocity mapping for different pump stirring force at top side and bath level 2

54

Figure 63 Velocity mapping with stirring of 20% pump capacity at the top side with different level

8.2 Analysis of individual strand

The analysis of individual strands was conducted by observing and comparing the first

time when tracer detected at the outlets (𝜃𝑚𝑖𝑛) between the strands as presented in Figure 64.

Generally, the 𝜃𝑚𝑖𝑛, which is also called as the breakthrough time, decline from the furthest

strand (strand 1) to the closest strand (strand 4) in any experiment configuration. As results,

two important phenomena can be detected. First, the short time required to reach a strand can

be an indication of a short-circuiting flow tendency. Second, strands similarity can also be

measured qualitatively by observing the similarity of 𝜃𝑚𝑖𝑛 at each individual strands.

In a bare tundish configuration (case 1), the strands are heterogeneous as specified by a

substantially different of 𝜃𝑚𝑖𝑛 at each strand. The addition of turbo-stopper alone unable to

remove this strand similarity problem effectively despite the short-circuiting flow can be

negated. The installation of baffle wall can be a solution to improve the strand similarity. In

addition, it leads to the higher 𝜃𝑚𝑖𝑛 of strand 4 and 3 as shown in configurations involving a

baffle wall (case 10 and case 12).

The effect of pump stirring can be observed in case no 2, 6 and 9. It can be seen

qualitatively that the most similar strand can be achieved by the implementation of stirring in

the tundish. However, a pump stirring without any flow control devices results in a very short

breakthrough time in all strands. The very low magnitude of breakthrough time means a small

plug flow volume remains to exist beside a large fraction of well-mix volume generated by

stirring. This phenomenon is discussed further in section 8.4.

8.3 Analysis of Overall Performance of tundish

Every strand in each experiment configuration possess a different RTD curve and flow

characteristics. A comparison of overall calculation of flow characteristics is necessary to

investigate the best configuration of the tundish. The comparison was carried out by calculating

the fraction of plug flow, well-mix and dead volume in the tundish model using Equation 19 to

Equation 22 of a Combined Model theory for multi-strand tundish. Nonetheless, a new

approach was developed for calculating flow characteristics in the experimental case involving

stirring as a response to the discrepancy between the actual condition in the experiment and the

55

results from Combined Model theory. In this section, the analysis was conducted using

Combined Model was elaborated while the explanation regarding the new approach of

Combined Model was discussed later in section 8.4.

Figure 64 Effect of experiment configuration on minimum dimensionless time at each strand

8.3.1 Plug Flow

A higher plug flow implies a capability of tundish to give more chances for inclusion

to float towards the surface. As the opposite, a lower plug flow means the flow tends to escape

directly to the outlet without any proper floatation of inclusion. Figure 65 displays the variation

of the fraction of plug flow in different experiment configurations. The highest plug fraction

exhibited by tundish configurations involving baffle wall without any stirring (case 10 and case

12), which means the presence of baffle wall can increase the plug flow fraction significantly.

In the other side, the stirring causes a much smaller plug flow fraction as shown in experiment

case 2-4 and 6-8. The effect of stirring on lowering the plug flow was also observed in the

tundish completed with baffle wall as can be seen in case 9 and 11. This effect occurs due to

the impossibility to gain a tundish with 100% of well-mix volume in stirring cases since the

existence of plug flow cannot be avoided. This phenomenon is discussed deeper in 8.4.

Meanwhile, note case 9 case 2-4 and 6-8 are significantly different, which suggest that the

stirring direction may affect the extent of mixing in the tundish.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 1 2 3 4 5

Min

imu

m D

imen

sio

nle

ss T

ime

Strand

Case 1 (bare tundish)

Case 2 (Bare Tundish + 20% Pump Stirring CC)

Case 5 (Tundish +Turbostopper)

Case 6 (Tundish + Turbostopper + 20%pump stirring CC)

Case 9 (Bare Tundish + 20% Pump Stirring CW)

Case 10 (Tundish + Baffle Wall)

Case 12 (Tundish + Baffle wall + Turbostopper)

56

Figure 65 Fraction of plug flow obtained from Combined Model theory

8.3.2 Dead and Well-Mixed Volume

Figure 66 and Figure 67 present results of the well-mix and the dead volume fraction

determined by Combined Model theory. The well-mix volume increases quite significantly

from the bare tundish configuration (case 1) to the configuration involving baffle wall or

stirring. However, the well-mix and dead volume are unaffected by the addition of turbo-

stopper alone as shown in case 5. On the other hand, the pump stirring, as well as the baffle

wall, reduce the fraction of dead volume.

Unexpectedly, the configuration involving stirring exhibit similar results to configuration

of tundish with baffle wall even though both configurations behave differently during the

experiment. Contrast to baffle wall configuration, the stirring mix the water vigorously and

even create a high fluid circulation. In other words, stirring cases is expected to possess no

slow-moving fluid. Hence, by defining a dead zone in Combined Model as a slowly moving or

stagnant fluid, it can be concluded that Combined Model formula causes an inaccurate flow

fraction in stirring cases. For this argument, the fraction of dead volume in stirring cases

depicted in Figure 67 is still relatively high because the formula considers the fluid flow which

stays over than two times of theoretical residence time as a dead zone. Therefore, a new

approach was developed by the present author to calculate the dead and well-mix volume in

stirring cases. This approach was carried out by modifying the equations in Combined Model

theory and the explanation has been provided in section 8.4.4.

8.3.3 Plug to Dead Zone ratio

One of the purposes of tundish design is to reduce the fraction of dead volume and

increase the fraction of plug flow. A low dead volume is preferred to increase the strand

similarity and avoid the extreme difference of temperature between strands. Meanwhile, a

substantial plug flow indicates a good capability to avoid the short-circuiting flow as well as to

promote a channeling flow for floatation of inclusion. Thus, the plug to dead zone ratio was

used as an indicator for measuring the tundish performance by some researchers [21]. The

results of this ratio for all configurations are presented in Figure 68. The case 10 and case 12

of tundish with the baffle wall seems to be much better than the others. However, the incorrect

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Plu

g FL

ow

Fra

ctio

n (

%)

Case Number

57

calculation for the dead and well-mix zone in stirring cases, as mentioned previously, causes

the unreliable value in stirring cases.

Figure 66 Fraction of well-mix volume for different configurations obtained from Combined Model theory

Figure 67 Fraction of dead volume for different configurations obtained from Combined Model theory

Figure 68 Plug to dead zone ratio for different configurations obtained from Combined Model theory

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14% F

ract

ion

of

Wel

l-M

ix V

olu

me

Case Number

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Frac

tio

n o

f D

ead

Vo

lum

e (%

)

Case Number

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Plu

g to

Dea

d Z

on

e R

atio

Case number

58

8.4 New Approach of Dead Zone calculation in Stirring Case

As mentioned in the previous chapter, the formula developed by Sahai and Emi of

Combined Model result in the inaccurate fraction of dead and well mix volume for experiment

configuration involving stirring. In this section, the reasons which support that statement are

elaborated and a new approach for calculating the dead and well-mix volume in stirring cases

was proposed.

8.4.1 Reason 1: Fast Moving Fluid

When the stirring applied, the pump generates powerful forces that mix the whole water

in the tundish model. Even high turbulence and backflow observed in some areas in the model.

Thus, it can be concluded that the stirring significantly increases velocity and eliminate the

slow-moving fluid, i.e., dead zone. This conclusion also suggested by the velocity measurement

results which shows a substantial increase in velocity for three different pump capacity as

presented in Figure 55. In addition, the increasing of turbulence also increases the mixing

volume significantly which is undetected by the current formula of Combined Model. Details

explanation regarding the turbulence condition in the model is discussed in section 8.11.

8.4.2 Reason 2: Quick Mixing time

In a color tracer injection experiment, a qualitative comparison of mixing time between

different configurations can be estimated approximately. The mixing time of each

configuration was estimated at the condition where the color tracer has been distributed

homogeneously in the whole tundish as presented in chapter 6.4. On the other hand, the dead

volume existence can also be estimated from the area where the color changed slowly.

Therefore, if the color injected can be mixed very quickly and the homogeneous color

concentration quickly achieved, it can be concluded that there is no dead volume anymore in

the tundish. That is the case that happens in pump stirring configuration as written in Table 15

where the stirring configuration in case 2 only needs 29 s to mix the color homogeneously. It

is much faster compared to the configuration of bare tundish or tundish with a baffle wall which

requires 567 and 377 s respectively to reach a similar condition. The consistent result also

showed in the other cases involving stirring as the faster mixing time than case 1, 10 or 12 can

still be obtained. Based on this observation, it is clear that the velocity of water is much faster

in stirring cases. Therefore, there should be a very high fraction of well-mix volume as the dead

zone does not exist anymore.

Table 15 Summary of estimated mixing time obtained from color injection experiment in different tundish configurations

Case no

Estimated mixing time (s)

Configuration

1 567 Bare tundish

2 29 Tundish with stirring (20% pump capacity, CC direction)

9 115 Tundish with stirring (20% pump capacity, CCW direction)

10 377 Tundish + baffle wall

12 409 Tundish + baffle wall + turbo-stopper

13 280 Tundish + baffle wall + turbo-stopper + stirring (20% pump capacity, CW

direction)

59

8.4.3 Reason 3: Similarity with RTD Curve of Ideal Mix Flow

The argument regarding the influence of pump stirring on the significant increase of

well-mix volume can be understood more clearly from the comparison between two curves of

ideal mix flow and RTD curve involving stirring obtained from the experiment as shown in

Figure 69. In that figure, the ideal mixed flow was determined using equation 9 as explained

in the theory of well-mix flow in chapter 2. Meanwhile, the RTD curve of bare tundish with

20% pump capacity in case 2 was chosen to be compared since the other stirring case also

generates a similar curve.

Unlike the comparison with a bare tundish configuration displayed in Figure 70, it is

apparent that the curvature of ideal mix flow almost fits with the RTD curve from the

experiment involving stirring. It is considered a great similarity which means the pump stirring

results in an almost perfect mixing. However, there is a significant peak observed in the RTD

curve from the experiment which indicates the existence of a very small fraction of plug flow.

Therefore it is impossible to have tundish with 100% of well-mix volume.

Figure 69 Comparison between ideal mix flow and RTD curve from experiment case 2 (type I): tundish + stirring (20%

capacity and CC direction)

It can also be observed that a portion of the fluid which stays more than two times of

theoretical residence times still exist in the ideal mix curve. This dead portion exists not because

of a slow movement, but because there is some portion of the fluid which has a longer traveling

distance covered due to the stirring.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.1

0.3

0.4

0.5

0.7

0.8

0.9

1.1

1.2

1.3

1.5

1.6

1.7

1.9

2.0

2.1

2.3

2.4

2.5

2.7

2.8

2.9

3.1

3.2

3.3

3.5

3.6

3.7

3.9

4.0

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless timeStrand 4 Strand 3 Strand 2 Strand 1 Ideal Mix Flow

60

Figure 70 Comparison between ideal mix flow and RTD curve from experiment case no.1: bare tundish

8.4.4 Modified Combined Model

Based on the discussion above, the stirring from pumps increase the mixing volume

significantly and annihilate the dead zone. However, the calculation for case no. 2 using

formula developed in Combined Model still results in a contradictive outcome of 58.8% well-

mixed volume and 37.8% dead volume as mentioned in Table 11. Thus, a new approach should

be developed in order to calculate these two flows in all stirring cases more accurately. For this

purpose, a modified combine model was developed and the equations used were shown in

Equation 19, 33 and 34. In this approach, a dead volume is directly determined as 0 because

the slow-moving fluid does not exist anymore. Since the plug flow formula still identical to the

Combined Model theory, then a mixing volume is determined by equation 34. The summary

of the modification in this new approach is illustrated in Figure 71.

𝑉𝑝

𝑉=

1

𝑁(


2) + (


2) + ⋯ . + (

𝜃𝑁𝑚𝑖𝑛+ 𝜃𝑁𝑝𝑒𝑎𝑘

2) Equation 19

𝑉𝑑

𝑉= 0 Equation 34

𝑉𝑚

𝑉= 1 −

𝑉𝑝

𝑉 Equation 35

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0

0.1

0.3

0.4

0.5

0.7

0.8

0.9

1.1

1.2

1.3

1.5

1.6

1.7

1.9

2.0

2.1

2.3

2.4

2.5

2.7

2.8

2.9

3.1

3.2

3.3

3.5

3.6

3.7

3.9

4.0

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time

Strand 4 Strand 3 Strand 2 Strand 1 Ideal Mix Flow

61

Figure 71 A modified combined model used for calculating flow characteristics in stirring cases

8.5 Type of RTD curve in Stirring Case

The new approach of modified Combined Model was employed in all configurations

involving stirring despite there are three different types of RTD curve generated in stirring

cases. Each type indicates a different phenomenon occurred in the experiment. The first type,

or type I, is the RTD curve that demonstrates a very good similarity among the strands and the

curvature almost fits perfectly with the ideal mix curve as already shown in Figure 69. RTD

curve type I occurs in the case number 2, 3, 4, 6, 7 and 8. In this type, the counterclockwise

stirring was successfully distributed the stirring forces homogeneously to all strands as

illustrated in flow behavior in Figure 45.

The second type, which is called type II in this work, is displayed in Figure 72. It is

characterized by one strand, namely the closest strand from the inlet (strand 4), which

experiences a remarkably different behavior compared to the other strands at the beginning of

tracer injection. Even though the difference in strand 4 gradually decreases with the increasing

of time, a slight discrepancy from other strands can still be observed. Figure 72 visualizes the

phenomenon occurred in case 9 where the CW stirring direction is applied on tundish model.

A very tall peak of strand 4 corresponds to the existence of a relatively larger plug flow fraction

compared to the other strands. Meanwhile, a slightly different curvature of strand 4 among the

other strands indicates a different intensity of pump stirring. As depicted in Figure 46, the

stirring forces in the area around strand 4 is a relatively weaker than the other strands because

of the clockwise direction of stirring direct the flow to the right side of tundish model.

Therefore, the velocity of fluid was getting slower when it reaches the area near inlet at the left

side of tundish model.

62

Figure 72 Comparison between ideal mix flow and RTD curve from experiment case 9 (type II): tundish + stirring (20%

capacity and CW direction

The last type or type III is the RTD curve generated in cases where the stirring is

combined with the baffle wall such as in case 11 and case 13. In this type, there is a large

discrepancy between RTD curves of all strands and the ideal mix flow curve because the peak

is more dispersed than the peak in type I and II. In addition, the peak shifts to the right side as

displayed in Figure 73. The peaks indicate that these configurations possess the largest fraction

of plug flow compared to the other stirring cases. The slight difference of strand 4 can still be

observed in this type. The reason for this phenomenon is the same as in Type II where it appears

due to the effect of clockwise stirring direction. In addition, the existence of baffle wall also

adds more restrictions for stirring force to reach the area near strand 4 as depicted in flow

behavior observation in Figure 47.

Figure 73 Comparison between ideal mix flow and RTD curve from experiment case 13 (type III): tundish + baffle wall +

turbo-stopper + stirring (20% capacity and CW direction)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.0

0.1

0.3

0.4

0.5

0.7

0.8

1.0

1.1

1.2

1.4

1.5

1.6

1.8

1.9

2.0

2.2

2.3

2.5

2.6

2.7

2.9

3.0

3.1

3.3

3.4

3.6

3.7

3.8

4.0

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time

Strand 4 Strand 3 Strand 2 Strand 1 Ideal Mix flow

0

0.2

0.4

0.6

0.8

1

1.2

0.0

0.1

0.3

0.4

0.6

0.7

0.8

1.0

1.1

1.2

1.4

1.5

1.7

1.8

1.9

2.1

2.2

2.3

2.5

2.6

2.8

2.9

3.0

3.2

3.3

3.4

3.6

3.7

3.9

4.0

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time

Strand 4 Strand 3 Strand 2 Strand 1 Ideal Mix Flow

63

In conclusion, the stirring influences the curvature of RTD curve in all stirring cases so

that it becomes more similar to the ideal mix curve. The only difference in those three types of

RTD Curve types is the amount of plug flow as well as the different stirring intensity at each

strand. Nevertheless, the velocity of the fluid is still considered as fast enough that all strands

contain zero dead zones despite the different of stirring intensity that may happen at a strand.

Therefore, in all stirring cases, the tundish contains a relatively small plug flow and a high

fraction of well-mixed volume as explained in the new approach of Combined Model.

In the other hand, although the strand 4 in Type II and Type III had different mixing

intensity, the formula of well-mix volume in the new approach of Combined Model is assumed

to be valid in both types. It is because in this new approach, the well-mix volume is defined as

a portion of the fluid which has some extent of stirring which means it is independent of the

stirring intensity. As a consequence, the phenomenon of different behavior of strand 4 in type

II and type III cannot be detected by observing the fraction of a well-mix value since it is

possible that a big portion of the well-mixed volume contains some portion of volume with a

weaker stirring intensity. Therefore, a method to detect this ‘non-homogeneous stirring force’

as well as to measure the degree of similarity with ideal mix curve needs to be developed. For

the first mentioned, the strand similarity value (𝑆4) as mentioned in Equation 22 can be used

while for the latter problem, a measure of deviation to the ideal mix curve needs to be

developed. The analysis of these two variables is discussed in section 8.7 and section 8.8

8.6 Analysis of Overall Performance Using the New Approach

Two approaches may be utilized to calculate the overall flow characteristics in the tundish.

The first way is using an old approach or a Combined Model theory where the results are

displayed in Figure 74. In this approach, the Combined Model formula was employed in all

tundish configurations. The second way is the new approach or a modified Combined Model.

This method was developed to improve the accuracy when calculating the fraction of dead and

well-mix volume in configurations involving stirring. As a consequence of this new approach,

a new result of overall flow characteristics in all cases was obtained and it is presented in Figure

75. In this new results, both methods were used: an old approach or a Combined Model was

utilized to calculate the cases without stirring and the modified Combined Model for cases

involving stirring.

Based on the comparison between Figure 69 and Figure 70, it is obvious that there is a big

difference between the dead and well-mix volume fraction in stirring cases. By using the

definition of the dead zone as a slow-moving fluid as proposed by Sahai and Emi [11], it can

be concluded that the results in Figure 69 are inaccurate.

In Figure 75, it is shown that the stirring can exhibit almost 100% of well-mix volume.

However, as mentioned in the previous discussion, the quality of well-mix volume probably

not identical for every strand due to the different extent of stirring intensity reached every

strands. This phenomenon cannot be detected from this result summary, but it is possible to

observe it by analyzing the strand similarity value (𝑆4). Despite good effect to significantly

increase well-mix volume, noticed that the direction of stirring plays a fundamental role in

influencing the results. A change from CC to CW direction in case 9 slightly reduces the well-

mix volume because it affects the amount of plug flow generated inside tundish.

Another interesting fact is it is difficult to create a dominant or full mixing volume since

64

the existence of plug flow cannot be avoided. Therefore it becomes a challenge in stirring cases

to generate fluid flow which allows a bigger fraction of plug flow in order to avoid a short-

circuiting. For this purpose, a new parameter of the plug to well-mix ratio should be calculated

to measure the mixing capability as well as to measure the tendency of short-circuiting flow in

the tundish. This is also useful since the previous parameter used i.e., plug to dead volume ratio

cannot be used anymore due to the zero definition of the dead zone in the new approach for

stirring cases.

8.7 Strand Similarity

Figure 76 presents the similarity among the strands using a strand similarity value (𝑆4)

explained in equation 22. The blue bar represents the value of 𝑆4 in the tundish configuration

with and without flow control devices (baffle wall and turbo-stopper) while the yellow and

brown represent the same parameter in stirring cases but with different stirring direction. A

smaller strand similarity suggests a more homogeneous stirring that the strands quality

becomes more similar to each other.

From the result in Figure 76, it is obvious that the addition of baffle wall increases the

strand similarity significantly as displayed in case 10 and 12. However, an improvement was

presented by the implementation of stirring where the strand similarity is 84% better than in

are tundish configuration (case 1) and 12% better than the configuration involving baffle wall

(case 10 and 12). This result is consistent with the growing of well-mix volume in stirring cases

as presented in Figure 70. Hence, it is proved that a higher mixing is preferred for achieving a

better similarity among strands.

Nevertheless, the stirring direction has a fundamental role which affects the strand

similarity as the 𝑆4 value in CC direction is slightly lower than CW direction. This difference

becomes an indication of the phenomenon happen in RTD curve type II and type II regarding

the strand 4 behavior. Thus, the parameter of 𝑆4 can be used to predict the different intensity

of pump stirring in stirring cases. A lower 𝑆4 value, i.e., 𝑆4 < 0.017, guarantee a better similarity

of strand, and in the other hand, a higher𝑆4, i.e., 𝑆4 >0.017 can be an indication of a different

quality of one or more strands due to different stirring intensity. In addition, this phenomenon

means that careful consideration must be employed to decide the stirring direction as an

appropriate direction can exhibit a very high similarity between strands. The correct stirring

direction depends on the geometry of tundish, steel volume, as well as the EMS location.

8.8 The Similarity with Ideal Mix Curve

The similarity between RTD curves and the ideal mix curve was determined by

calculating the deviation of the area under the RTD curve. In this section, the explanation of

the deviation was presented and the results of all configurations were discussed.

65

Figure 74 Overall flow characteristics using Combined Model theory proposed by Sahai and Emi [19]

20.533.32 2.54 2.49

17.233.35 3.38

2.82 8.23

25.7122.05

28.8824.64

38.62

58.80 59.01 59.28 28.4259.69 62.09

55.08

55.76

45.7849.71

46.52

47.33

40.8537.89 38.45 38.24

54.35

36.96 34.52

42.1036.01

28.50 28.2324.60

28.03

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13

Frac

tio

n o

f Fl

ow

Ch

arac

teri

stic

(%

)

Case Number

Plug Volume Well-Mixed Volume Dead Volume

66

Figure 75 Revision of overall flow characteristics after using modified Combined Model in stirring cases

20.533.32

2.54 2.49

17.233.35 3.38 2.82

8.23

25.7122.05

28.8824.64

38.62

96.68 97.46 97.51

28.42

96.65 96.62 97.1891.80

45.78

77.95

46.52

75.36

40.85

54.35

28.5024.60

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13

Frac

tio

n o

f Fl

ow

Ch

arac

teri

stic

(%

)

Case Number

Plug Volume Well-Mixed Volume Dead Volume

67

Figure 76 Strand similarity of all configurations

8.8.1 Derivation formula

Four different area, i.e., A, B, C, and D, were defined under the actual RTD curve from

experiment and the ideal mix curve as depicted in Figure 77. Since the total area under the

curve equal to 1, then the Equation 37 and Equation 38 can be derived.

𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑎𝑐𝑡𝑢𝑎𝑙 𝑐𝑢𝑟𝑣𝑒 = 𝐴 + 𝐵 Equation 36

𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑖𝑑𝑒𝑎𝑙 𝑚𝑖𝑥 𝑐𝑢𝑟𝑣𝑒 = 𝐵 + 𝐶 + 𝐷 Equation 37

Area D can be assumed as a very small area due to the similarity of the long tail from

both curves. This assumption led to the similarity between area A and C, and this relationship

was shown in Equation 39.

𝑇ℎ𝑒 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑎𝑐𝑡𝑢𝑎𝑙 𝑐𝑢𝑟𝑣𝑒 = 𝑇ℎ𝑒 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑖𝑑𝑒𝑎𝑙 𝑐𝑢𝑟𝑣𝑒, 𝑡ℎ𝑒𝑛:

A ≈ C Equation 38

Furthermore, the deviation was defined as the difference between the areas under both curves,

as expressed by Equation 40.

𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝛿) =|𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑎𝑐𝑡𝑢𝑎𝑙 𝑐𝑢𝑟𝑣𝑒 − 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑖𝑑𝑒𝑎𝑙 𝑐𝑢𝑟𝑣𝑒|

𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑖𝑑𝑒𝑎𝑙 𝑡ℎ𝑒 𝑐𝑢𝑟𝑣𝑒

𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝛿) =𝐴+𝐶

𝐵+𝐶+𝐷=

2𝐴

𝐵+𝐶+𝐷 Equation 39

The final formula of deviation was decided as 𝛿

2 and the equation was shown in Equation 41.

68

𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝛿

2) =

𝐴

𝐵+𝐶+𝐷=

∑ |𝐶𝑎𝑐𝑡,𝑖−𝐶𝑖𝑑𝑒𝑎𝑙,𝑖|𝑥 𝑑𝜃𝑁𝑖=1

𝐶𝑖𝑑𝑒𝑎𝑙,𝑖 𝑥 𝑑𝜃=

∑ |𝐶𝑎𝑐𝑡,𝑖−𝐶𝑖𝑑𝑒𝑎𝑙,𝑖|𝑁𝑖=1

𝐶𝑖𝑑𝑒𝑎𝑙,𝑖 Equation 40

By this definition, the closer 𝛿

2 value to 0, the more similar the RTD curve to the ideal mix

curve.

Figure 77 Deviation of area under the actual RTD curve and the ideal mix curve

8.8.2 Analysis of deviation from ideal mix

The deviation to the ideal mix ( 𝛿

2 ) of all strands for all configurations is summarized in

Table 16. The stirring not only causes the strands becomes more similar each other, but also it

become more similar to the ideal mix curve as a low 𝛿

2 found in all configurations of bare

tundish with stirring or in combination with a turbo-stopper (case 2-4 and case 6-8). However,

the similar result cannot be achieved by the addition of baffle wall as a higher 𝛿

2 observed in

case 11 and 13. This result is consistent with the RTD curve obtained from the experiment, i.e.,

RTD curve type III. In such RTD curve, the ideal mix curve is clearly not identical to the RTD

curve of all strands because of a relatively high fraction of plug flow results in a broader and

right-shifted peak. Meanwhile, noticed that the 𝛿

2 in stirring cases with a baffle wall (case 11

and case 13) and in baffle wall configuration (case 10 and case 12) are insignificantly different

to the bare tundish (case 1). It is strange considering the RTD in bare tundish should exhibit a

great difference with the ideal mix curve as already shown in Figure 65. Therefore, the 𝛿

2 value

cannot successfully describe the deviation to ideal mix in any configurations without stirring

as this approach cannot detect the difference of curvature in RTD curve.

69

Table 16 Deviation from ideal mix for all configurations

8.9 Plug to Well-Mix Volume ratio

The plug to well-mix ratio, which is also suggested to measure the performance of

tundish by Ahuja and Sahai [21], is a replacement for the similar parameter of the plug to dead

zone ratio. This replacement is necessary since after the revision from Combine Model to the

new approach, the previous ratio becomes invalid due to zero dead zone in all stirring cases. A

careful analysis should be considered when observing this ratio because in one side a higher

plug flow is preferred to promote floatation of inclusion, and in the other side a higher mixing

volume is also worthy for strand similarity.

Figure 78 shows the summary of this variable for all configurations. It can be seen that all

stirring cases in bare tundish with and without a turbo-stopper (case 2-4 and case 6-9) have the

lowest ratio since the tundish consists of very low plug flow and an extremely high well-mix

volume. Interestingly, the insignificant difference was observed between the unstirred

configuration of bare tundish with (case 10 and case 12) and without a baffle wall (case 1 and

case 5). Such insignificant difference happens because both of plug flow and well-mix volume

increases if the baffle wall is installed. Such result exposes a difficulty in determining an ideal

value of this ratio. Therefore, ranges of the optimal plug to the well-mix ratio for ideal tundish

need to be investigated further.

Case

no.

Deviation ( 𝛿

2 )

Configuration Strand

4

Strand

3

Strand

2

Strand

1 Average

1 20.1% 16.8% 16.5% 30.2% 20.9% Bare Tundish

2 6.7% 7.5% 7.6% 7.2% 7.3% Bare Tundish + Stirring (20% pump capacity

and CC direction)


and CC direction)


and CC direction)

5 24.5% 29.0% 20.4% 24.5% 24.6% Tundish + Turbo-stopper

6 6.1% 9.8% 7.3% 7.4% 7.6% Tundish + Turbo-stopper + Stirring (20%

pump capacity and CC Direction)






and CW direction)

10 19.1% 21.8% 14.7% 15.6% 17.8% Tundish + Baffle Wall

11 19.0% 15.0% 16.1% 14.9% 16.2% Tundish + Baffle Wall + Stirring (20% pump

capacity and CW Direction)

12 21.4% 23.3% 19.3% 18.7% 20.7% Tundish + Baffle Wall + Turbo-stopper

13 21.0% 16.7% 18.9% 16.7% 18.3%

Tundish + Baffle Wall + Turbo-stopper

Stirring (20% pump capacity and CW

Direction)

70

In this work, a simple suggestion of ideal ratio was proposed by combining the result from

tundish configuration with baffle wall (case 10) and stirring cases. Specifically, the ideal

fraction of plug flow in the tundish was assumed to be acquired if the baffle wall installed,

while the rest tundish volume contains a well-mix flow as there is no dead zone in stirring

configuration. Therefore, the ideal plug to well-mix volume ratio was determined equals 0.34

as explained in Equation 42. The closer the ratio to this value, the better the tundish

performance.

Hence by using this suggestion, it can be concluded that the ratio of all stirring cases is still

too low to be classified as the ideal solution for improving tundish performance. Despite a

proper mixing achieved by stirring, care should be taken into consideration to negate the short-

circuiting flow. Consequently, the plug to volume ratio becomes higher. Above all, it is

definitely fair that the simple suggestion of ideal plug flow fraction as mentioned in Equation

42 still need to be investigated deeper in further study.

𝑖𝑑𝑒𝑎𝑙 𝑝𝑙𝑢𝑔 𝑡𝑜 𝑤𝑒𝑙𝑙 − 𝑚𝑖𝑥 𝑟𝑎𝑡𝑖𝑜 =

𝑉𝑝

𝑉 (𝑓𝑟𝑜𝑚 𝑐𝑎𝑠𝑒 𝑛𝑜.10)

1−𝑉𝑚

𝑉(𝑛𝑜 𝑑𝑒𝑎𝑑 𝑣𝑜𝑙𝑢𝑚𝑒)

=25.71

74.29= 0.34 Equation 41

Figure 78 Ratio of plug to well-mix volume for all configurations

8.10 Particle Collision

Besides the analysis of flow characterization, there is another interesting observation

related to flow behavior inside the tundish. As already mentioned, the stirring enhances the

mixing volume and the mixing intensity in the tundish. The increasing of mixing intensity was

proved by a quick and random particle movement as observed from the right side of tundish

model as displayed in Figure 79. Even though the inclusion is not well represented as its density

is similar to water, this fact can be an indication that the stirring may enhance the particle

collision. If this is happening in reality, it would be a great benefit for floatation of inclusion

because the inclusion becomes bigger and consequently the Stokes rise velocity become higher.

In addition, there is also a possibility that the stirring exhibit surface-directed flow. As a result,

the criteria for higher plug flow to promote floatation of inclusion is not necessary anymore in

the stirring application. Nevertheless, a further study needs to be conducted to prove this

argument.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Plu

g to

Wel

l-M

ix R

atio

Case Number

71

Figure 79 Illustration and actual photo of particle collision from the right view of tundish in stirring application

8.11 Surface Condition

Despite the positive effect of pump stirring on increasing mixing volume, attention should

be taken into consideration regarding surface turbulence condition. Relatively low surface

turbulence observed at the surface of tundish with stirring of 20% pump capacity (Figure 80-

a) and stronger surface turbulence was observed when the stirring force changed into 30%

pump capacity (Figure 80-b). Although the pump stirring is not exactly similar to EMS in

reality and the pump position in different bath level highly affects the surface condition, a

careful setup should be measured when implementing stirring in the tundish as a relatively calm

surface is preferred to negate the slag entrainment.

In addition, the consideration of stirring direction selection is also vital because it may

affect the surface condition. Since the tundish shape in this work is asymmetrical, i.e., the

volume in the right side is smaller than in the left side, a high backflow was observed when

implementing a clockwise stirring direction as presented in Figure 80-c and Figure 80-d. Such

unstable surface condition around the corner is vulnerable to the slag entrainment in the real

industrial process.

72

Figure 80 Surface condition observed in stirring configuration: (a) with 20% pump capacity; (b) with 30% pump capacity;

(c) and (d) high backflow in the right side of tundish.

8.12 Ethical and Social Aspect Consideration

Based on the previous discussion it is clear that the stirring has many positive advantages

for increasing tundish performance although attention regarding the surface condition should

be taken into consideration. Concerning to the ethical and social aspect, the work conducted in

this project does not violate any ethical issues as it does not harm any person or any company

which relates to this technology. Even the EMS technology may give benefit to the society

since it helps the steelmaking company to improve their product quality and work efficiency.

This means the EMS technology, which is modelled in this work, is feasible to be implemented

in the real industrial casting process.

73

9 NUMERICAL SIMULATION ANALYSIS

The CFD simulation conducted in this work can be used for predicting the results in the

real industrial tundish if reliable results obtained. Therefore, some comparison between the

experiment and simulation results were presented in this chapter to validate the simulation

results. Furthermore, the effect of baffle wall and turbo-stopper were also investigated by

analyzing some variables that are difficult to be observed in the water model experiment. In

addition, a simulation of inclusion injection was also elaborated to give more comprehensive

analysis regarding the role of those two flow control devices.

9.1 Wall Y+ Problem

Before analyzing the result, the wall Y+ were checked to acquire the idea regarding the

validity of simulation around the wall. Since a Standard Wall Treatment used in the simulation

setup, the valid wall Y+ value should range from 30 to 300. The simulation results show that

there are some invalid wall Y+ as shown in Figure 81. However, since the mixing in the tundish

is the interest phenomena rather than the forces acting around the wall, the effect of invalid

wall Y+ was neglected. In addition, in such a big volume of the multi-strand tundish, the mixing

phenomena is independent of forces around the wall.

Figure 81 Wall Y value of Simulation number 1: Bare Tundish

9.2 Validation of CFD Simulation

Several comparisons between the experiment and simulation result were discussed in this

section as a way to validate the simulation result. The validation was examined in three

different experiment: color injection experiment, particle movement and RTD experiment. The

first two validation give a qualitative comparison while the last validation gives a quantitative

judgement.

9.2.1 Validation of Color Tracer Injection

Figure 82 and Figure 83 show a comparison of the concentration gradient of tracer

during color injection for a different flow time. In bare tundish simulation, the tracer moves

very slowly without any help from external force except inlet jet. Thus the tracer can only reach

the first-two strand after 37s. At this time, the contour of concentration gradient is slightly

different with experiment. Then the tracer travels to the right side of tundish with a higher

74

velocity around the bottom surface as also observed in the experiment.

A more similar comparison was observed in case 10 of tundish with the baffle wall. In

this case, a little amount of color appears from the inclined holes of the baffle wall at 14s before

a much higher concentration flow through these holes as detected at 35s. Both experiment and

simulation show the homogeneous condition is approximately reached at 377s. Based on these

two comparisons, it can be concluded that the simulation was successfully described the

tendency of concentration distribution during color injection the experiment. Therefore, a valid

and reliable result can be obtained.

Figure 82 Comparison between color injection experiment and simulation result in case no.1: bare tundish configuration

Figure 83 Comparison between color injection experiment and simulation result in simulation no.3: Tundish + baffle wall

9.2.2 Validation of Prediction Regarding Dead Zone Location

Even though the fraction of dead volume can be determined by calculating a portion of

fluid stays over than two times of theoretical residence time as explained in Combined Model,

the location is still unknown. The problem to determine the dead zone location can be solved

75

by numerical simulation. As the dead zone is defined as a slow-moving or stagnant fluid [19],

the prediction of dead zone location was determined by showing the area where the slow

velocity fluid exists.

As mentioned in Table 13, the simulation of bare tundish configuration specified that

average of velocity in the whole tundish in steady condition was 0.02 m/s. Hence, in this work,

a very slow-moving fluid is defined as the fluid which has the velocity less than 10% of the

average which displayed as the green area in Figure 84. The results show that most dead zones

exist at the area located around the two-furthest strand, i.e., strand 2 and 1 and it suits the result

from particle movement observation in the water model experiment, where the stagnant particle

exists at the right side of the tundish. Based on this validation, it can be concluded that the

result of velocity contour was also reliable to be analyzed.

Figure 84 Comparison of slow-moving fluid in the particle movement observation (top) and simulation (bottom)

9.2.3 Validation of RTD Curve and Flow Characteristics

The discrepancy between the experiment and simulation result was also observed in RTD

curve, as occurred in a bare tundish configuration shown in Figure 85 and tundish with the

baffle wall shown in Figure 86. In the first case, the clear difference was found at several

variables such as the maximum concentration, area under the curve, and minimum nor peak

dimensionless time (𝜃min and 𝜃𝑝𝑒𝑎𝑘) of each strand. However, a general tendency of RTD

curve between each strand seemed similar, as the closer strand from the inlet always appears

earlier before the further strand. In addition, a short-circuiting flow phenomenon clearly can be

detected in both experiment and simulation.

In the baffle wall configuration, even though there is a slight difference in term of the

sequence of tracer appearance among strands, the curves from experiment and simulation have

a relatively great similarity in total area under the curve, strand similarity as well as maximum

76

peak. In conclusion, some degree of similarity can be found between the RTD curve from

experiment and simulation. However, the discrepancy of the RTD curve generated in

experiment and simulation still leads to the difference of flow characteristics as quantified in

Table 17.

Figure 85 Comparison of RTD curves obtained from experiment and simulation in bare tundish configuration (case 1)

Figure 86 Comparison of RTD curves obtained from experiment and simulation in the tundish with baffle wall (case 10)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.0

0.1

0.1

0.2

0.3

0.3

0.4

0.4

0.5

0.6

0.6

0.7

0.8

0.8

0.9

0.9

1.0

1.1

1.1

1.2

1.3

1.3

1.4

1.4

1.5

1.6

1.6

1.7

1.8

1.8

1.9

1.9

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time

Strand 4 (Exp) Strand 3 (Exp) Strand 2 (Exp) Strand 1 (Exp)

ST 4 (Sim) ST 3 (Sim) ST 2 (Sim) ST 1 (Sim)

0

0.2

0.4

0.6

0.8

1

1.2

0.0

0.1

0.1

0.2

0.3

0.3

0.4

0.4

0.5

0.6

0.6

0.7

0.8

0.8

0.9

0.9

1.0

1.1

1.1

1.2

1.3

1.3

1.4

1.4

1.5

1.6

1.6

1.7

1.8

1.8

1.9

1.9

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time

Strand 4 (Exp) Strand 3 (Exp) Strand 2 (Exp) Strand 1 (Exp)

ST 4 (Sim) ST 3 (Sim) ST 2 (Sim) ST 1 (Sim)

77

Table 17 the difference of flow characteristics from experiment and simulation

Based on the comparison in Table 17, it was observed that the result of flow

characteristics vary from a relatively small difference of 5.27% to a huge difference of 67.43%.

The difference which is less than 10% are believed as a reliable result while the rest means the

simulation cannot describe the reality in the experiment accurately.

However, despite the large discrepancies observed, the general effect of the addition of

flow control devices addition on certain flow characteristics can still be predicted by

simulation. The examples are the growing of the well-mix volume, the improvement of strand

similarity, and the decreasing of the dead zone which can be observed after the addition of

baffle wall. However, a contradictive result from experiment and simulation was found in the

configuration involving turbo-stopper. The discrepancy between experiment and simulation

may be caused by the simplification of the radius inside the turbo-stopper when developing the

3D model in simulation. The other factor is probably caused by inappropriate turbulence model

and wall Y+ value inside the turbo-stopper because of the strong turbulence and circulation.

9.3 Effect of Baffle wall

One of the main advantages of the baffle wall used in this work is the inclined holes

which direct the flow towards the surface. This effect was clearly shown in Figure 87, where

the tracer only needs 14s to reach the surface. The other benefit is the baffle wall has three

holes which serve to distribute the flow to different strands properly. This outcome was

displayed in Figure 88, where one hole direct the flow towards the strands 2 and 1 on the right

side of the tundish and the other two holes distribute the melt to the two-closer strand from the

inlet. Lastly, the baffle wall plays an important role to avoid the fluid flow directly to the strand

4 without any proper mixing inside the baffle wall as displayed in Figure 89.

Case Number Flow Characteristics Result

%Difference Experiment CFD Simulation

1

Plug flow fraction (%) 20.5 19.4 5.27%

Dead volume fraction (%) 40.9 36.1 11.66%

Well-mix volume fraction (%) 38.6 44.5 -15.13%

Plug to Dead Zone Ratio 0.50 0.53 -7.06%

Strand similarity 0.087 0.150 -73.24%

5

Plug flow fraction (%) 17.2 18.3 -6.01%



Plug to Dead Ratio 0.32 0.53 -67.39%


10




Plug to Dead Zone Ratio 0.91 0.98 -8.28%


12


Dead volume fraction (%) 24.6 25.4 -3.51%


Plug to Dead Zone Ratio 1.17 0.78 33.34%


78

Figure 87 effect of baffle wall: surface-directed flow

Figure 88 Effect of the baffle holes on the flow distribution among strands

79

Figure 89 Comparison of tracer concentration contour at 60 s between bare tundish and tundish with baffle wall

configuration

9.4 Effect of Turbo-stopper

In the real process, a turbo-stopper was utilized when producing a very clean steel

grade. Therefore, it must have an important role in improving steel cleanliness. In this chapter,

the function of this flow control device was analyzed based on the result of the CFD simulation.

One of the main function was displayed in Figure 90 where the addition of turbo-stopper can

inhibit the fluid flow more than the baffle wall. Whereas the tracer has flown through the

inclined holes in the tundish without a turbo-stopper at 14 s, the tracer remains inside the baffle

wall if the turbo-stopper used. Such result indicates a higher 𝜃𝑚𝑖𝑛 and a higher fraction of plug

flow for the strand far from the inlet. Consequently, the configuration involving turbo-stopper

achieved better prevention from a short-circuiting flow and a better circumstance for promoting

floatation of inclusion. This effect was clearly observed in both of experiment and simulation

especially at the two-furthest strand namely strand 2 and 1. result as shown in Table 18.

However, the effect of inhibiting the flow cannot be found for the strand closer to the inlet as

there is no increase in 𝜃𝑚𝑖𝑛 in strand 4 and 3.

Figure 90 Comparison of tracer concentration contour in configuration with and without Turbo-stopper at 14 s

Another advantage of using a turbo-stopper is its capability to change the fluid pathway

so that the inlet jet is reflected towards the surface as observed in the color injection experiment

80

as well as the concertation contour from simulation in Figure 91. Moreover, a strong circulation

formed inside the turbo-stopper enhances a proper mixing and inclusion collision before the

melt moves through the hole of baffle wall as shown by strong circulation vector below inlet

jet in Figure 92.

Table 18 Comparison of minimum dimensionless time from experiment and simulation between case 10 and case 12

Strands

Minimum Dimensionless time

Tundish + baffle wall (case 10) Tundish + baffle wall + Turbo-stopper (case 12)

Experiment Simulation Experiment Simulation

1 0.0897 0.0185 0.1324 0.0277

2 0.0975 0.0164 0.1287 0.0164

3 0.1047 0.0144 0.1376 0.0133

4 0.0852 0.0123 0.0122 0.0123

Figure 91 Effect of turbo-stopper on creating surface-directed flow

Figure 92 Velocity vector below inlet jet

81

9.5 Dead Zone Comparison

Using the same approach when estimating the dead zone location in chapter 9.2.2, a

qualitative comparison between dead zone fractions can be investigated by observing the slow-

moving fluid of green area in Figure 93. It is clear that the addition of baffle wall and in

combination with turbo-stopper can reduce the dead zone. This result has a good agreement

with the experimental result, which means the simulation is successfully predicting this

phenomenon.

Figure 93 Qualitative comparison of location and fraction of dead zone in three different configurations

9.6 Inclusion Injection Simulation

In this section, a result of particle trajectory from an injection of inclusion particle with

the density around half of the water was presented. It can be seen in Figure 94 that the

percentage of particles trapped on the surface increase with the addition of baffle wall and it

even more with the addition of turbo-stopper. Such result probably occurs due to the surface

directed flow generated by both flow control devices. Besides, a baffle wall also adds more

‘restriction’ as has been discussed previously so that the inclusion stays longer in the tundish.

A comparison between the number of trapped particles at the surface 1 (surface inside the baffle

wall) and surface 2 (surface outside the baffle wall) was conducted to reveal the tendency of

particles to be trapped inside or outside of the baffle wall and the result was displayed in Figure

95. Based on the result, more inclusion particles tend to be trapped at the surface inside the

wall as the percentage of trapped inclusion is significantly higher on the surface 1. This result

means that the main function of baffle wall in inclusion removal aspect is to stop the flow and

avoid a short-circuiting flow. Therefore, it gives more chances for inclusion to float towards

the surface inside of the baffle wall.

Meanwhile, another interesting fact was displayed in Figure 96 where the number of

inclusion escaped to the outlet decreasing from strand 4 to strand 1. Even there is no inclusion

82

escaped to the strand 1 in the tundish configuration without baffle wall. This result shows a

challenge to improve the steel cleanliness in strand closer to the inlet in a multi-strand tundish.

The strand further from inlet has more plug flow which allows the floatation of inclusion

towards the surface. The result also shows that the combination of two FCDs: baffle wall and

turbo-stopper results in the best cleanliness and strand similarity among the individual FCD

installation.

Figure 94 Percentage of trapped particles at the surface

Figure 95 Percentage of trapped particles at the surface inside and outside baffle wall

75.0%

80.0%

85.0%

90.0%

95.0%

100.0%

bare tundish tundish + turbo-stopper

tundish + baffle wall tundish + baffle wall +turbo-stopper

% t

rap

ped

par

ticl

e at

th

e su

rfac

e

82.2%

93.3%

7.3%

3.1%

50.0% 55.0% 60.0% 65.0% 70.0% 75.0% 80.0% 85.0% 90.0% 95.0% 100.0%

tundish + baffle wall

tundish + baffle wall + turbo-stopper

% trapped particle

Surface 1

Surface 2

83

Figure 96 Percentage of escaped particles at all strands in different tundish configurations

10 CONCLUSION

Based on the analysis of simulation and experiment results, following conclusions can be

summarized:

1. Baffle wall has a great role in increasing the mixing volume and plug flow and reduce the

dead zone. It also acts as a ‘brake system’ to prevent the short-circuiting flow as well as

enhances mixing and inclusion removal inside the wall. In addition, the holes design are

crucial to distribute the flow and to promote surface-directed flow.

2. The addition of turbo-stopper creates the circulation and mixing within the device as well

as promotes a surface-directed flow. The combination of this device with baffle wall results

in a better configuration for inclusion removal compared to the configuration with a single

FCD. On the other side, the addition of turbo-stopper without baffle wall results in similar

tundish performance to the bare tundish configuration.

3. A modified Combined Model was developed to analyze the flow characteristics in the

tundish configurations involving stirring. By using the definition of the dead zone as slow-

moving fluid, a utilization of stirring results in almost 100% of well-mix volume in the

tundish as it has zero dead zones. In addition, the stirring reduces the mixing time

significantly. However, a short-circuiting flow becomes a challenge to be solved before

implementing the EMS technology in the tundish.

4. The application of stirring in the tundish can be a good solution for increasing strand

similarity as well as make strands to be more similar to ideal mix curve.

5. Stirring direction affects the flow characteristics generated in the tundish. An appropriate

direction needs to be considered depending on the tundish geometry and dimension as well

as stirring source position.

6. The stirring enhances the probability of particle collisions. This result can be a good

indication for promoting the inclusion removal. If the collision of particles represents the

real interaction of inclusions in the tundish, a tundish with stirring does not need a higher

plug flow to promote the inclusion flotation.

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

Strand 4 strand 3 strand 2 strand 1

% e

scap

ed p

arti

cle

bare tundish

tundish + turbo-stopper

tundish + baffle wall

tundish + baffle wall +turbo-stopper

84

7. Care should be taken into consideration regarding the surface turbulence condition when

implement stirring in the tundish. Excessive stirring and inappropriate stirring direction may

generate high surface turbulence and a high backflow.

11 FURTHER STUDY

Considering some limitations in the results and analysis, following suggestion should be

conducted for further research:

1. A numerical simulation of pump stirring should be conducted to have more comprehensive

comparison regarding the effect of EMS and FCD on tundish performance.

2. A combination of stirring with other baffle wall design is necessary to find the best solution

to avoid short-circuiting flow in stirring configuration.

3. The ideal plug to well mix ratio in the tundish need to be investigated as this parameter can

be a reference to determine the best tundish configuration to solve problems in the multi-

strand tundish.

4. Modelling of inclusion removal in water model would be a beneficial experiment to have a

better understanding of inclusion removal from a physical model.

85

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APPENDIX A

Numerical Scheme and Solver Setting in simulation

Simulation number

Experiment Configuration

(Case Number)

Solution Methods : Pressure-Velocity Coupling Under Relaxation Factors

Scheme Gradient Pressure Momentum Turbulence

Kinetic Energy

Turbulent Dissipation

Rate Pressure Density

Body Forces

Momentum

Turbulent Kinetic Energy

Turbulent Dissipatio

n Rate

Turbulent Viscosity

1 bare tundish(1) SIMPLEC Least

Squares Cell Based

Second Order

Second Order

Upwind

Second Order

Upwind

Second Order

Upwind 0.3 1 1 0.7 0.2 0.2 0.5


Squares Cell Based

Second Order

Second Order

Upwind

Second Order

Upwind

Second Order

Upwind 0.3 1 1 0.7 0.2 0.2 0.5


Squares Cell Based

Second Order

Second Order

Upwind

Second Order

Upwind

Second Order

Upwind 0.3 1 1 0.7 0.2 0.2 0.5


Squares Cell Based

Second Order

Second Order

Upwind

Second Order

Upwind

Second Order

Upwind 0.3 1 1 0.7 0.2 0.2 0.5


Squares Cell Based

Second Order

Second Order

Upwind

Second Order

Upwind

Second Order

Upwind 0.3 1 1 0.7 0.2 0.2 0.5

6 Tundish +

Turbo-stopper (5)

SIMPLEC Least

Squares Cell Based

Standard First Order

Upwind First Order

Upwind First Order

Upwind 0.3 1 1 0.1 0.2 0.2 0.5

7 Tundish +

Baffle wall (10) SIMPLEC

Least Squares

Cell Based Standard

First Order Upwind

First Order Upwind

First Order Upwind

0.3 1 1 0.7 0.2 0.2 0.5

8


+ baffle wall (12)

SIMPLEC Least

Squares Cell Based

Standard First Order

Upwind First Order

Upwind First Order

Upwind 0.3 1 1 0.1 0.2 0.2 0.5

88

APPENDIX B

Mesh Setup and Mesh Quality in simulation

Simulation Number

Experiment Configuration

(Case Number) Objective

Tetrahedral Mesh Generation Setup Polyhedral Mesh Conversion

Maximum face size

(mm) Wall Inflation Total Cells

Orthogonal Quality Total Cells

Min Orthogonal Quality

Max Aspect ratio

Min Max Averag

e

1 bare tundish(1) Mesh Study 45 First aspect ratio 4.9 ; 4 layers,

growth rate 1.0 393386 0.1096 0.994 0.753 154109 1.50E-02 8.68


growth rate 1.0 407872 0.1167 0.995 0.754 158724 1.27E-02 1.06E+02


growth rate 1.0 442722 0.1164 0.994 0.755 169851 1.87E-02 7.2


growth rate 1.0 491182 0.1188 0.998 0.757 185191 2.38E-02 5.37


growth rate 1.0 541091 0.1204 0.997 0.760 199209 8.59E-03 1.64

6 Tundish +

Turbo-stopper (5)

RTD Curve analysis

29 First aspect ratio 4.9 ; 4 layers,

growth rate 1.0 657712 0.054 0.993 0.738 313313 2.25E-02 5.29E+02

6 Tundish +

Baffle wall (10) RTD Curve

analysis 29

First aspect ratio 4.9 ; 4 layers, growth rate 1.0

508911 0.1005 0.994 0.751 197889 7.01E-02 5.67

7


+ baffle wall (12)

RTD Curve analysis

29 First aspect ratio 4.9 ; 4 layers,

growth rate 1.0 832423 0.05 0.997 0.736 399086 1.11E-02 1.35E+02

APPENDIX C

• Velocity Mapping with stirring (30% pump capacity)

• Velocity Mapping with stirring (40% pump capacity)

90

APPENDIX D

Flow Behavior Observation

• Case 10: Tundish with baffle wall

91

APPENDIX E

Residence Time Distribution Curve from Experiment

• Case 5: Tundish + turbo-stopper

• Case 12: Tundish + baffle wall + turbo-stopper

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.2

0.4

0.5

0.7

0.9

1.1

1.3

1.4

1.6

1.8

2.0

2.2

2.3

2.5

2.7

2.9

3.1

3.2

3.4

3.6

3.8

4.0

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0

0.2

0.3

0.5

0.6

0.8

1.0

1.1

1.3

1.4

1.6

1.8

1.9

2.1

2.2

2.4

2.5

2.7

2.9

3.0

3.2

3.3

3.5

3.7

3.8

4.0

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time


APPENDIX F

Experiment data of flow characteristics of each strand using a combined model

Case

Number

Strand


𝜃𝑚𝑖𝑛 𝜃𝑎𝑣𝑒𝑟𝑎𝑔𝑒 (𝑢𝑝 𝑡𝑜 𝜃

= 2)

𝑉𝑝

𝑉(%)

𝑉𝑑

𝑉(%)

𝑉𝑚

𝑉(%) 𝜃𝑎𝑣𝑒𝑟𝑎𝑔𝑒 Configuration

1

1 0.3402 ± 0.0533 0.9685 ± 0.0178 42.51 ± 4.79 24.20 ± 10.71 33.30 ± 12.47 1.411 ± 0.023

Bare Tundish 2 0.1691 ± 0.0201 0.8023 ± 0.0423 26.25 ± 5.04 42.08 ± 2.61 31.68 ± 5.23 1.229 ± 0.102

3 0.0780 ± 0.0057 0.6934 ± 0.0159 11.94 ± 0.80 42.92 ± 3.94 45.14 ± 3.44 1.129 ± 0.094

4 0.0110 ± 0.0021 0.5049 ± 0.0298 1.40 ± 0.30 54.22 ± 1.55 44.38 ± 1.27 0.781 ± 0.154

2

1 0.0376 ± 0.0086 0.7812 ± 0.0184 5.80 ± 0.94 38.26 ± 2.28 55.94 ± 2.56 1.151 ± 0.182

Bare Tundish + Pump Stirring

(CCW, 20% capacity)

2 0.0240 ± 0.0073 0.7677 ± 0.0088 3.30 ± 0.74 38.19 ± 4.52 58.50 ± 4.15 1.140 ± 0.142

3 0.0181 ± 0.0052 0.7617 ± 0.0176 2.45 ± 0.52 36.14 ± 5.52 61.41 ± 5.45 1.158 ± 0.149

4 0.0137 ± 0.0036 0.7445 ± 0.0199 1.73 ± 0.47 38.94 ± 3.34 59.33 ± 3.14 1.099 ± 0.177

3

1 0.0274 ± 0.0021 0.7485 ± 0.0148 4.06 ± 0.67 40.40 ± 1.69 55.54 ± 1.05 1.065 ± 0.075


(CCW, 30% capacity)

2 0.0178 ± 0.0033 0.7473 ± 0.0212 2.36 ± 0.42 38.21 ± 0.65 59.43 ± 0.74 1.107 ± 0.091

3 0.0140 ± 0.0021 0.7437 ± 0.0264 1.85 ± 0.32 37.43 ± 1.98 60.72 ± 2.04 1.121 ± 0.127

4 0.0147 ± 0.0030 0.7471 ± 0.0174 1.90 ± 0.26 37.76 ± 2.11 60.34 ± 2.32 1.128 ± 0.081

4

1 0.0233 ± 0.0031 0.7657 ± 0.0164 3.92 ± 0.58 38.56 ± 1.89 57.52 ± 1.95 1.128 ± 0.098


(CCW, 40% capacity)

2 0.0175 ± 0.0021 0.7574 ± 0.0141 2.72 ± 0.59 37.52 ± 2.00 59.76 ± 1.93 1.145 ± 0.082

3 0.0127 ± 0.0016 0.7508 ± 0.0183 1.68 ± 0.26 37.55 ± 3.16 60.77 ± 3.10 1.135 ± 0.104

4 0.0116 ± 0.0006 0.7417 ± 0.0073 1.63 ± 0.08 39.31 ± 2.02 59.06 ± 2.08 1.092 ± 0.081

5

1 0.2830 ± 0.0809 0.8411 ± 0.1194 30.70 ± 7.52 41.95 ± 10.70 27.35 ± 17.99 1.379 ± 0.015

Tundish + Turbulence Impact Pad 2 0.1759 ± 0.0342 0.6710 ± 0.0960 21.18 ± 2.65 52.76 ± 11.30 26.05 ± 10.04 1.262 ± 0.165

3 0.0859 ± 0.0080 0.5440 ± 0.0262 11.26 ± 0.50 55.90 ± 12.06 32.84 ± 12.30 1.167 ± 0.269

4 0.0469 ± 0.0033 0.5384 ± 0.0682 5.77 ± 0.40 66.80 ± 2.20 27.44 ± 1.84 1.245 ± 0.359

93

APPENDIX F


Case

Number Strand



= 2)

𝑉𝑑𝑝

𝑉(%)

𝑉𝑑

𝑉(%)

𝑉𝑚


6

1 0.0353 ± 0.0039 0.7621 ± 0.0258 4.66 ± 0.98 37.89 ± 1.32 57.45 ± 1.99 1.018 ± 0.147

Tundish + Turbulence Impact Pad

+ Pump Stirring (CCW, 20%

capacity)

2 0.0257 ± 0.0011 0.7538 ± 0.0314 3.87 ± 0.25 37.47 ± 2.47 58.66 ± 2.46 1.024 ± 0.170

3 0.0192 ± 0.0016 0.7563 ± 0.0208 2.91 ± 0.19 34.86 ± 1.21 62.23 ± 1.40 1.055 ± 0.158

4 0.0147 ± 0.0032 0.7443 ± 0.0202 1.95 ± 0.23 37.63 ± 1.57 60.41 ± 1.39 0.999 ± 0.126

7

1 0.0301 ± 0.0012 0.7843 ± 0.0220 4.19 ± 0.70 32.37 ± 4.43 63.44 ± 4.24 1.067 ± 0.167



capacity)

2 0.0236 ± 0.0010 0.7746 ± 0.0303 3.95 ± 0.09 34.78 ± 2.93 61.27 ± 2.98 1.049 ± 0.192

3 0.0198 ± 0.0006 0.7699 ± 0.0221 3.18 ± 0.14 34.68 ± 4.40 62.13 ± 4.36 1.046 ± 0.158

4 0.0151 ± 0.0033 0.7571 ± 0.0209 2.21 ± 0.54 36.27 ± 3.56 61.53 ± 3.33 1.020 ± 0.162

8

1 0.0226 ± 0.0010 0.7684 ± 0.0059 4.11 ± 0.64 41.15 ± 0.97 54.74 ± 0.72 1.279 ± 0.048



capacity)

2 0.0175 ± 0.0027 0.7578 ± 0.0175 3.20 ± 0.85 42.79 ± 0.78 54.01 ± 1.06 1.247 ± 0.070

3 0.0151 ± 0.0016 0.7520 ± 0.0075 2.34 ± 0.26 42.11 ± 1.52 55.55 ± 1.70 1.257 ± 0.035

4 0.0113 ± 0.0010 0.7462 ± 0.0030 1.64 ± 0.22 42.33 ± 1.76 56.03 ± 1.79 1.246 ± 0.032

9

1 0.0332 ± 0.0016 0.7932 ± 0.0279 11.36 ± 1.5412 33.53 ± 5.3711 55.11 ± 6.6905 1.144 ± 0.186

Bare tundish + Pump Stirring

(CW,20% capacity)

2 0.0352 ± 0.0036 0.8000 ± 0.0271 11.21 ± 1.3672 33.65 ± 2.8581 55.15 ± 4.2032 1.185 ± 0.166

3 0.0298 ± 0.0027 0.7879 ± 0.0255 7.51 ± 3.8676 34.68 ± 0.7022 57.81 ± 3.4188 1.172 ± 0.195

4 0.0128 ± 0.0007 0.6909 ± 0.0466 2.70 ± 1.0142 42.18 ± 3.2236 55.12 ± 4.1494 1.040 ± 0.195

94

APPENDIX F


Case

Number Strand



= 2)

𝑉𝑑𝑝

𝑉(%)

𝑉𝑑

𝑉(%)

𝑉𝑚


10

1 0.0897 ± 0.0113 0.8163 ± 0.0054 22.0910 ± 1.3191 30.1388 ± 2.7903 47.7702 ± 2.0800 1.131 ± 0.076

Tundish + baffle wall 2 0.0975 ± 0.0081 0.8265 ± 0.0072 25.4620 ± 0.9994 32.3484 ± 1.6733 42.1896 ± 1.8045 1.107 ± 0.072

3 0.1047 ± 0.0080 0.8871 ± 0.0049 30.1335 ± 0.8727 25.0164 ± 2.1141 44.8501 ± 1.4519 1.214 ± 0.063

4 0.0852 ± 0.0058 0.8811 ± 0.0090 25.1711 ± 1.7044 26.4991 ± 2.2003 48.3297 ± 0.5120 1.227 ± 0.074

11

1 0.0339 ± 0.0041 0.8218 ± 0.0190 18.8056 ± 1.3191 30.8424 ± 1.2272 47.7702 ± 0.9401 1.063 ± 0.047

Tundish + baffle wall +

Pump Stirring (CW, 20%

capacity

2 0.0342 ± 0.0039 0.8323 ± 0.0221 19.9863 ± 0.9994 27.7516 ± 0.2522 42.1896 ± 1.2763 1.134 ± 0.057

3 0.0438 ± 0.0046 0.8244 ± 0.0243 21.9028 ± 0.8727 29.1920 ± 0.6455 44.8501 ± 4.0963 1.104 ± 0.071

4 0.0575 ± 0.0131 0.8850 ± 0.0221 27.5154 ± 1.7044 25.1498 ± 0.9761 48.3297 ± 0.5395 1.172 ± 0.068

12

1 0.1324 ± 0.0054 0.8428 ± 0.0165 26.2834 ± 2.3963 26.5707 ± 1.7992 47.1460 ± 1.4928 1.077 ± 0.042


Turbulence Impact Pad

2 0.1287 ± 0.0132 0.8530 ± 0.0126 27.7036 ± 1.9442 25.8917 ± 0.9783 46.4046 ± 2.8988 1.077 ± 0.052

3 0.1376 ± 0.0168 0.9056 ± 0.0173 32.9055 ± 1.7849 21.4545 ± 2.0283 45.6399 ± 3.0151 1.150 ± 0.007

4 0.1022 ± 0.0327 0.8761 ± 0.0076 28.6277 ± 2.0056 24.4883 ± 2.3620 46.8840 ± 3.7077 1.143 ± 0.016

13

1 0.0732 ± 0.0041 0.8379 ± 0.0096 23.5113 ± 0.3593 29.6039 ± 1.8883 46.8848 ± 1.9219 1.130 ± 0.125


Turbulence Impact Pad +

Pump Stirring (CW, 20%

capacity)

2 0.0746 ± 0.0062 0.8430 ± 0.0065 24.1444 ± 1.9791 29.0258 ± 4.4523 46.8298 ± 3.1480 1.144 ± 0.081

3 0.0667 ± 0.0165 0.8339 ± 0.0047 23.2546 ± 3.3908 29.6761 ± 2.0348 47.0693 ± 3.4409 1.128 ± 0.118

4 0.0785 ± 0.0094 0.9040 ± 0.0079 27.6352 ± 0.9636 23.8233 ± 4.3596 48.5415 ± 3.5330 1.235 ± 0.090

APPENDIX G

Residence Time Distribution Curve from Simulation

• Case 5: Tundish + turbo-stopper

• Tundish + baffle wall + turbo-stopper

0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.2

0.3

0.5

0.6

0.8

1.0

1.1

1.3

1.4

1.6

1.8

1.9

2.1

2.2

2.4

2.5

2.7

2.9

3.0

3.2

3.3

3.5

3.7

3.8

4.0

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time


0

0.2

0.4

0.6

0.8

1

1.2

0.0

0.2

0.3

0.5

0.6

0.8

0.9

1.1

1.2

1.4

1.5

1.7

1.8

2.0

2.1

2.3

2.4

2.6

2.8

2.9

3.1

3.2

3.4

3.5

3.7

3.8

4.0

Dim

ensi

on

less

Co

nce

ntr

atio

n

Dimensionless time


APPENDIX H

Simulation data of flow characteristics of each strand using a combined model

Case Number Strand

𝜃𝑚𝑖𝑛 𝜃𝑎𝑣𝑒𝑟𝑎𝑔𝑒 (𝑢𝑝 𝑡𝑜 𝜃 = 2) 𝑉𝑑𝑝

𝑉(%)

𝑉𝑑

𝑉(%)

𝑉𝑚

𝑉(%)

𝑉𝑝

𝑉𝑑

Configuration

1

1 0.1324 1.2564 63.76 15.19 21.05 4.197

Bare Tundish 2 0.0257 0.7603 7.91 31.97 60.13 0.247

3 0.0113 0.5682 4.11 46.53 49.36 0.088

4 0.0092 0.5203 2.00 50.67 47.33 0.040

5

1 0.0893 1.1199 43.58 17.08 39.33 2.551

Tundish + Turbulence Impact Pad 2 0.0298 0.8223 15.25 27.32 57.44 0.558

3 0.0133 0.5947 6.11 44.59 49.30 0.137

4 0.0103 0.5548 8.11 47.63 44.26 0.170

10

1 0.0185 0.8590 23.9733 22.4977 53.5290 1.0656

Tundish + baffle wall 2 0.0164 0.8689 24.7433 21.7624 53.4943 1.1370

3 0.0144 0.8824 28.6961 21.1501 50.1538 1.3568

4 0.0123 0.7510 16.7351 30.4412 52.8237 0.5498

12

1 0.0277 0.8194 15.8111 25.1050 59.0839 0.6298

Tundish + baffle wall + Turbulence Impact Pad 2 0.0164 0.8401 19.4045 23.4817 57.1138 0.8264

3 0.0133 0.8542 25.7700 22.6310 51.5990 1.1387

4 0.0123 0.7417 18.7372 30.6461 50.6167 0.6114

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