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Institut für Eisenhüttenkunde

Xiaohuan Zhang

Investigation of Mould Filling and Solidification during Ingot Casting

Process with Experiments and OpenFOAM Numerical Modelling

Von der Fakul tät für Georessourcen und Materialtechnik der

Rheinisch -Westfälischen Technischen Hochschule Aachen

zur Erlangung des akademischen Grades einer

Doktorin der Ingenieurwissenschaften

genehmigte Dissertation

vorgelegt von Master of Science

Xiaohuan Zhang

aus Shanxi, China

Berichter:

Univ.-Prof. Professor h.c. (CN) Dr.-Ing. Dr. h.c. (CZ) Dieter George Senk

Univ.-Prof. Dr.-Ing. Bernhard Peters

Univ.-Prof. Dr.-Ing. Yanping Bao

Tag der mündlichen Prüfung: 27. Januar 2016

Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar

Acknowledgement

The research work reported in this thesis was carried out under the

supervision of Univ.-Prof. Dr.-Ing. Dieter Senk at the Department of Ferrous

Metallurgy (IEHK), RWTH Aachen University.

I gratefully acknowledge the encouragement and guidance of Prof. Senk.

My special thanks are given to Prof. Peters and Prof. Bao for their in-depth

discussions and valuable suggestions.

I would like to thank Zhiye Chen, Xiaoxue Liu and Shahid Maqbool for the

help in water model experiments. I would also like to express my sincere

thanks to Min Wang for reviewing the manuscript.

I am grateful to Prof. Peters and Florian Hoffmann for technical advice on

OpenFOAM. I also thank the OpenFOAM development team for sharing of

this excellent software.

I would also like to thank my husband who helped me a lot in finishing this

project.

Contents

i

Contents

Nomenclature .................................................................................................................................................. iii

Abstract ............................................................................................................................................................... v

Kurzfassung ...................................................................................................................................................... vi

1. Introduction .............................................................................................................................................. 1

2. Literature review .................................................................................................................................... 3

2.1. Filling of ingot moulds ........................................................................................................................................... 3

2.1.1. Bottom teeming process ............................................................................................................................ 3

2.1.2. Influencing parameters of the flow conditions ................................................................................ 6

2.2. Solidification of cast ingots .................................................................................................................................. 6

2.2.1. Structure of steel ingots ............................................................................................................................. 6

2.2.2. Mathematical modelling of the solidification process ................................................................ 10

2.3. Introduction of the OpenFOAM software .................................................................................................... 16

2.4. Objective and methods of the study ............................................................................................................... 18

3. Water model experiments of the mould filling process ......................................................... 20

3.1. Design of experiments ......................................................................................................................................... 20

3.1.1. Water model set-up ................................................................................................................................... 20

3.1.2. Model parameters ...................................................................................................................................... 22

3.1.3. Experimental procedure ......................................................................................................................... 24

3.2. Results about the models with one bottom nozzle .................................................................................. 26

3.2.1. Water-air two-phase flow without oil addition ............................................................................. 26

3.2.2. Water-air-oil three-phase flow with oil addition .......................................................................... 28

3.3. Results about the models with four bottom nozzles ............................................................................... 32

3.3.1. Features of the flow fields ...................................................................................................................... 33

3.3.2. Influence of the filling rate ..................................................................................................................... 35

3.3.3. Influence of the bottom nozzles ........................................................................................................... 42

3.3.4. ............................................................................................................ 47

3.4. Optimization of filling conditions ................................................................................................................... 50

3.4.1. Influence of experimental parameters on the open surface..................................................... 51

3.4.2. ....... 52

3.4.3. Optimal filling conditions ....................................................................................................................... 53

3.5. Conclusions .............................................................................................................................................................. 54

4. Numerical simulation of filling process with OpenFOAM software .................................... 55

4.1. Model description .................................................................................................................................................. 55

4.2. Results of the calculated flow fields ............................................................................................................... 57

4.2.1. Flow patterns in the early stage of teeming .................................................................................... 57

Contents

ii

4.2.2. Velocity fields of the flow ....................................................................................................................... 59

4.2.3. Comparison with the water model experiments .......................................................................... 62

4.3. Conclusions .............................................................................................................................................................. 63

5. Simulation of solidification process with OpenFOAM software .......................................... 65

5.1. Liquid-solid 2-phase model with phase change ....................................................................................... 65

5.1.1. Model assumptions ................................................................................................................................... 65

5.1.2. Governing equations ................................................................................................................................ 67

5.1.3. Solution algorithm ..................................................................................................................................... 73

5.2. Application to a steel ingot ................................................................................................................................ 76

5.2.1. Model setup .................................................................................................................................................. 76

5.2.2. Results ............................................................................................................................................................ 79

5.3. Attempt on the coupling of mould filling and solidification process ............................................... 88

5.4. Conclusions .............................................................................................................................................................. 90

6. Overall discussion ................................................................................................................................ 91

7. Summary .................................................................................................................................................. 96

8. Reference ................................................................................................................................................. 99

Nomenclature

iii

Nomenclature

cp: Specific heat capacity, J·kg-1·K -1;

C: Concentration of carbon, wt%;

Cls: Solute transfer rate from liquid to solid phase, kg·m-3·s -1;

Csl: Solute transfer rate from solid to liquid phase, kg ·m-3·s -1;

ds: Grain diameter, m;

D: Diffusion coefficient, m2·s -1;

f: Mass fraction;

: Grain packing limit;

: Fraction of the open surface;

g: Volume fraction;

g: Gravity vector, m·s-2;

h: Enthalpy, J ·kg-1;

kp: Partition ratio;

Kls: Drag force coefficient, kg·m-3·s -1;

L: Latent heat, J·kg-1;

m: Liquidus slope, K·wt %-1;

Mls: Mass transfer rate from liquid to solid phase, kg·m-3·s -1;

Ns: Nucleation rate, m-3·s -1;

n: Grain density, m-3;

nmax: Maximum grain density, m-3;

p: Pressure, N ·m-2;

Re: Reynolds number;

Sv: Interfacial area concentration, m-1;

t: Time, s;

T: Temperature, K;

Nomenclature

iv

TL: Liquidus temperature, K;

Tm: Melting point of pure iron, K;

T: Undercooling, K;

U: Velocity, m·s-1.

Uls: Momentum transfer rate from liquid to solid phase, kg ·m-2·s -2;

Greek Symbols

: Thermal conductivity, W·m-1·K -1;

C: Solutal expansion coefficient, wt %-1;

T: Thermal expansion coefficient, K-1;

: Solute diffusion length, m;

: Dynamic viscosity, kg ·m-1·s -1;

: Density, kg·m-3;

: Stress tensor, kg·m-1·s -1.

: Wetting angle, rad.

Subscripts and Superscripts

0: Initial value;

l: Liquid phase;

s: Solid phase;

*: Equilibrium at the solid-liquid interface;

ref: Reference;

eff: Effective value.

Abstract

v

Abstract

The fluid flow and solidification of ingot casting was studied. In this study,

the fluid flow during the bottom teeming process was investigated with

water model experiments and numerical simulation. A user-defined liquid-

solid two-phase solidification solver was developed based on the software

platform of OpenFOAM, using Euler-Euler two-phase approach. The

solidification solver was performed on a 3-dimensional model of steel ingot

to simulate the solidification and macrosegregation distribution.

In water model experiments, water and vegetable oil were used to simulate

the molten steel and slag phase, respectively. The influence of model

parameters, such as the filling rate, nozzle dimensions and oil film thickness,

on the filling conditions was investigated, concerning two aspects: one is

the slag entrapment, and the other is reoxidation of molten steel. Both of

the two situations should be avoid to provide a better filling condition. The

numerical simulation on water-air two-phase flow with the interFoam

solver of OpenFOAM was performed. The obtained predictions were in

good agreement with the water model experiments.

The simulation of solidification can obtain the evolution of the solid fraction,

velocity, temperature, concentration and grain density fields. The

macrosegregation was indicated by the concentration of the only solute

carbon. The cone-shaped negative segregation at the bottom, positive

segregation at the top, V-segregation at the upper center of the ingot, and

the channel-shaped A-segregation were predicted. The simulation results

of macrosegregation ratio on certain lines were generally in agreement

with the experimental measurements from the literature, except for some

deviations at the bottom and the near-wall regions, where the predicted

degree of negative segregation was much stronger than the measured one.

Kurzfassung

vi

Kurzfassung

Der Fluidstrom und die Erstarrung des Blockguss wurden untersucht. In dieser Studie wurde der Fluidstrom während des Unterseite wimmelt Prozess mit Hilfe von den Wasser Modellexperimenten und numerischen Simulation untersucht. Eine benutzerdefinierte Flüssig-Fest-Zwei-Phasen-Erstarrungslöser wurde auf Basis der Softwareplattform von OpenFOAM mit Euler-Euler-Zwei-Phasen-Ansatz entwickelt. Der Erstarrungslöser wurde auf eine 3-dimensionale Modell des Stahlblocks ausgeführt, um die Erstarrung und die Verteilung der Makroseigerung zu simulieren. In Wasser Modellversuchen wurden Wasser und Pflanzenöl verwendet, um den geschmolzenen Stahl und die Schlacke zu simulieren. Der Einfluss von Modellparametern, wie die Füllungsrate, Düsenabmessungen und Ölfilmdicke wurde bei den Füllungsbedingungen unter Berücksichtigung von zwei Aspekten untersucht. Das sind die Schlackeneinschlüsse und die Reoxidation des geschmolzenen Stahl. Beide Situationen sollten vermieden werden, um einen besseren Füllungszustand bereitzustellen. Die numerische Simulation von Wasser-Luft-Zweiphasenströmung wurde mit der Interfoam Löser OpenFOAM durchgeführt. Die erhaltenen Voraussagen waren in guter Übereinstimmung mit den Ergebnissen von Wassermodell-versuchen. Die Evolution des Feststoffanteils, Geschwindigkeit, Temperatur, Konzentration und Korndichte können mit Hilfe von der Simulation der Erstarrung erhalten werden. Die Makroseigerung wurde durch die Konzentration des einzigen gelösten Stoffes (Kohlenstoff) angezeigt. Der kegelförmige negativer Seigerung am Boden, positive Seigerung an der Spitze, V-Seigerung an der oberen Mitte des Gussblock und die kanalförmigen A-Seigerung wurden vorhergesagt. Die Simulation-sergebnisse bezüglich des Verhältnisses bei der Makroseigerung auf bestimmten Linien stimmen im allgemeinen mit den experimentellen Untersuchungen aus der Literatur überein, mit Ausnahme einiger Abweichungen an der Unterseite und den wandnahen Bereichen, in denen der vorausgesagte Grad der negativen Seigerung viel stärker als gemessene Werte war.

1. Introduction

1

1. Introduction

The process of pouring molten steel from a ladle into an ingot mould until

the melt solidifies to an ingot is called ingot casting. The flow field during

the pouring process is of great importance for the development of

solidification structures and the removal of inclusions. Therefore, huge

efforts to improve the flow conditions and thereby the quality of cast ingots

and final steel products have been made.

Besides the inclusions, the chemical heterogeneities should also be

reduced as a way to minimize defects of products. The chemical

heterogeneities develop mainly during the solidification stage, which result

from the rejection of solutes from the solid phase back into the liquid phase.

This phenomenon is called segregation. It can be classified into

microsegregation and macrosegregation depending on the length scale.

The microsegregation takes place in the scale of dendrites, due to the

different solubility of chemical species in the solid and liquid phases. The

macrosegregation takes place at a larger scale ranging from 1 mm to 1 m.

The formation of macrosegregation is related to the relative motion

between the liquid and solid phases, and therefore the phenomenon of

melt convection and grain sedimentation are helping to understand the

macrosegregation. Macrosegregations are serious defects that should be

suppressed to improve the quality of as-cast products.

The objective of this thesis is to study the filling conditions as well as the

solidification phenomena during ingot casting process. The fluid flow of

filling stage was investigated by water modeling and numerical simulations.

Computational Fluid Dynamics (CFD) has become a widely used numerical

method to solve and analyze problems that involve fluid flows. There are

some famous commercial CFD software packages such as ANSYS CFX,

ANSYS Fluent, Star-CCM+ and others. These softwares are not only

expensive but also have low scalability for certain problems. In this study,

1. Introduction

2

an open-source CFD software, OpenFOAM, was employed to solve both the

fluid flow and solidification problems, synchronously.

This thesis includes the following chapters: After the general introduction,

literature reviews about the filling problems, solidification structure of a

typical steel ingot, previous simulation methods, and the features of

OpenFOAM software are described in chapter 2. Chapter 3 is about the

water model experiments of the mould filling process, aiming to optimize

the filling conditions of large ingot casting. Mathematical modelling of

mould filling process based on the OpenFOAM software was carried out

and the predicted results were compared with water models experiments,

as described in chapter 4. Further on, in chapter 5 a liquid-solid 2-phase

solidification model was developed and applied to a small steel ingot to

study the solidification process. The computational simulation work of this

thesis was done with OpenFOAM-2.1.1.

2. Literature review

3


2.1. Filling of ingot moulds

During the steelmaking process, after the ladle metallurgical treatment and

secondary refining, the molten steel is poured into ingot moulds, where the

metal then solidified to form ingots.

There are two principal methods of pouring molten metal to ingot moulds:

top pouring and bottom teeming.

Top pouring is easy to carry out but has several disadvantages, such as the

considerable turbulence and splashing. As a result of the turbulent flow,

there is a tendency for non-metallic inclusions to become entrapped into

the melt and further more deteriorate the solidification structure.

Additionally, the accompanying splash is detrimental to the mould walls

and the ingot surface, which is subjected to highly erosive forces and the

life tends to be reduced.

A prevailing pouring method in steel industry is bottom teeming, which can

get better flow conditions than top pouring method, due to much less

turbulence and splashing [1, 2], and several moulds can be filled

synchronously from one feeder in a network of runners. In this thesis, the

bottom teeming method is concerned.

2.1.1. Bottom teeming process

The increasing demand for quality steels has led to the evolution of bottom

pouring technology for casting of steel ingots. This process constitutes of a

set up involving pouring sprue and runner system to deliver liquid steel into

one or more cast iron moulds through the bottom nozzles. Bottom teeming

is very common for small ingots, as shown in Fig.2.1. For small ingots, two

or more ingot moulds are filled at the same time, and typically, each small

ingot mould has only one bottom nozzle. While for the bottom teeming of

large ingots, the optimal method is to pour only one ingot mould, with

multiple nozzles at the mould bottom.


4

Fig. 2.1 Bottom teeming process of small steel ingots

In the traditional bottom teeming process, a bag of casting powder is

placed on the bottom or hung about 30 cm above the bottom of the mould

before pouring [2]. After the teeming started, when the liquid steel enters

the mould, the contacted powder receives maximum heat from the

meniscus and produces a fused or molten slag layer. The functions of this

liquid/fused slag layer in bottom teeming process are: (a) Protection from

the atmosphere; (b) Thermal insulation of the meniscus; (c) Absorption of

the non-metallic inclusions [3]. However, this slag layer may cause

undesirable problems meanwhile, such as slag entrapment, which leads to

formation of defects in the final products. It has been proved that during

gas stirred ladle metallurgy, due to the rising gas bubbles from a bottom

gas jet, a plume zone and an (slag less area) at the top of the

plume can be formed [4-6]. For the bottom teeming process, the liquid jet

from bottom nozzle has a similar effect on the surface behavior as the

submerged gas jet. For example, the mathematical modeling work by Z. Tan

et al. shows a hump on the surface above the bottom nozzle [7]. H.F.

Marston observed an ace as well as slag entrapment

at the early stage of teeming [2].

Fig.2.2 shows typical features of the molten steel-slag interface in bottom

teeming process. As shown in Fig.2.2(a), the slag layer is thin and the

downward back driving force on the hump is relatively small, so the hump

can break the slag layer and is exposed to air, which leads to the reoxidation

of molten steel. If the slag layer is thick enough, as shown in Fig.2.2(b), the


5

movement of the hump was damped by the heavy layer and the metal is

totally covered by the slag layer, in which case the risk of reoxidation is

largely reduced [8, 9].

(a) (b)

Fig. 2.2 Steel-slag interface in bottom teeming process

Slag droplets tend to form at the rim of the hump bottom, and then they

are entrapped into molten steel due to the downwards liquid flow. There

are three different kinds of droplets formation mechanisms [6], as shown

in Fig.2.3, also using a water-model slag-system: (a) detaching of single

droplets; (b) detaching of tube-shaped slag volumes which, in turn, break

up into single droplets of different sizes; (c) detaching of plate shaped slag

volumes dissociating into tubes and single droplets.

Fig. 2.3 Observed mechanisms of droplet formation [6]

model slag

water bath


6

2.1.2. Influencing parameters of the flow conditions

Since the flow conditions, especially the surface behavior, have a significant

influence on slag entrapment and reoxidation of molten steel, theoretical

and experimental studies have been made on the influencing parameters.

By some studies of a liquid-submerged jet impinging on free surface [10-

12], it has been proved that the surface hump depends on both, the velocity

of jet and the distance from bottom nozzle to top surface. Large jet velocity

and small distance lead to large hump and instability of the surface. The

shape of the humps therefore decide the degree of slag entrapment and

reoxidation of molten steel.

2.2. Solidification of cast ingots

Solidification takes place when the heat is removed from the molten steel

through the ingot mould to the surrounding atmosphere. In the traditional

ingot casting process, the cooling methods are mainly natural cooling,

which gives lower cooling rate and can help to reduce the thermal stress

and structural stress defects of ingot. The solidification process is

associated with the phenomenon of heat transfer, solute redistribution,

fluid flow, nucleation, grain growth, and transport of solid fragments. All of

these phenomena dominate the structure of the cast ingots, especially the

morphology of the grains and macrosegregation level. The mathematical

modelling of solidification and macrosegregation during ingot casting

process has long received much attention.

2.2.1. Structure of steel ingots

Fig. 2.4 Sketch of the grain structure of steel ingots [13]

Chill zone

Equiaxed zone Columnar zone


7

Fig.2.4 shows the grain structure of the solidified steel ingots, including the

chill zone, columnar dendritic zone and equiaxed zone, which were

described as follows [13, 14].

The chill zone: This zone is a thin layer of fine equiaxed grains which forms

rapidly as the hot melt contacts with the cold mould wall. The mould walls

provide lots of nucleation sites. This zone develops before the appearance

of an air gap which forms between the solidified shell and the mould wall

because of solidification shrinkage.

The columnar dendritic zone: As the thermal gradient drops ahead of the

chill zone, the structure quickly changes to columnar dendritic grains. The

growth direction of the columnar grains is in counter direction of heat flow.

The driving force of the columnar zone is the constitutional undercooling

which involves the solute redistribution in front of the liquid-solid interface.

As the solidification progresses, the temperature of the melt, which is

adjacent to the solidification front, increases due to the liberation of the

latent heat. Then the thermal gradient decreases and the driving force for

the growth of columnar grains disappears. The dendrite arms (primary and

secondary dendrite arm spacing, den 1 2, respectively) control

the microstructure of ingot, also the size and distribution of porosity. The

relationship between primary and secondary dendrite arm spacing was

1 2 [15-17]. The secondary

dendrite arm spacing is essentially determined by the local solidification

rate and the carbon content [18]. Increasing the solidification rate can

result in smaller secondary dendrite arm spacing. An empirical relationship

was put forward by Y. Won and B.G. Thomas [18], as follows:

4935.0

2 9.7201.169 RCm , for 0<C<0.15

CpctCRm

996.15501.03616.0

2 9.143 , for C>0.15

where R is the cooling rate ( /s) and C is the carbon content (wt pct C).


8

2 predicted by

the above equation were compared with measured ones, as shown in

Fig.2.5.

Fig. 2.5 Comparison of the predicted and measured secondary dendrite arm spacing as a function of carbon content at various cooling rates [18]

The equiaxed zone: In the center, due to the low temperature gradient, the

equiaxed grains are formed with large size. During the solidification, if the

liquid in the center of the mould is undercooled sufficiently, grains may

nucleate and grow without contact with any surface. Such grains are also

equiaxed which grow to approximately equal dimensions in all 3

perpendicular directions. The grains in the center can also originate from

the fragment of the columnar dendrites, which may be broken or remelted

by the flow.

During the solidification of molten steel, due to the different solubility of

chemical elements in solid and liquid phase, the solute redistribution takes

place, which leads to regions either enriched in solute or depleted in solute.

Macrosegregation refers to the chemical heterogeneities at length scales

of the order of millimeters or meters, which is a very common defect and

undesirable for casting manufacturers due to the degraded quality and

mechanical properties of steel ingots [19, 20]. Fig.2.6 shows some typical


9

macrosegregation pattern of steel ingots. In the figure, positive segregation

clearly from the figure that the macrosegregation generally includes the

following zones: positive segregations at the hot-top, cone-shaped

negative segregations at the bottom of ingots, channel-shaped A-

segregations and V-segregations at the center of ingots, also the banding

and inverse segregation region near the cold walls of ingot mould.

Fig. 2.6 Typical macrosegregation pattern of steel ingots [20]

Generally, there are two reasons for the formation of macrosegregation.

One reason is the flow of segregated liquid, including the solidification

shrinkage driven flow, and buoyancy driven flow. The buoyancy driven flow

is caused by the thermal gradient or solutal gradient in the liquid. Another

reason for macrosegregation is the sedimentation of free equiaxed grains

or solid fragments.

The positive segregation appears near the centerline, particularly at the top

of the ingot. It is caused by the buoyancy and shrinkage driven

interdendritic fluid flow during the final stage of solidification, where the

flow is enriched in solute, and therefore the segregation is positive. The

cone-shaped bottom negative segregation is a result of the sedimentation

of equiaxed dendrites, which formed in the early stage of solidification and


10

poor in solute. The A-segregation is channel shaped and occurs at the end

of columnar zone [21]. It is also related with the buoyancy-driven flow.

Liquid with light element enriched can rise upwards and tend to dissolve

coarse dendrites in its path. As the stream progresses, channels are formed

in this path until the enriched melt freezes. The V-segregation in the center

is associated with large equiaxed grains settling down to the V-shaped

solidification front. The liquid surrounding the solidification front is solute-

rich. Near the end of solidification, due to the lower density of solid phase

than liquid phase and not enough liquid to compensate for solidification

shrinkage, the local pressure drops. Pores are nucleated when the pressure

drop exceeds a critical value [20]. The formation of porosity leads to

decrease in the mechanical properties of ingots. To diminish the shrinkage

porosity by feeding liquid steel as long as possible, the ingot moulds are

always designed with a hot-top, which is wider in upper level and thermally

isolated.

As shown in Fig.2.6, a region of inverse segregation arises near the cold wall

of ingot mould, which is positive segregation and forms due to the motion

of enriched interdendritic fluid towards the wall to feed solidification

shrinkage in the early stage of solidification [20, 22].

Adjacent to the inverse segregation region, several solute-rich or solute-

poor bands have been found. The banding segregation is considered

resulting from the abrupt changes in heat transfer rate. The solute-rich

bands can be formed due to reheating, which may be caused by the

formation of air gap at the mould-ingot interface. The reheating can also

expand the mushy zone, where the solid dendrites and liquid phase coexist

during solidification. The solute-poor bands result from reduction in cross

section through which fluid flow feed shrinkage takes place [20, 23].

2.2.2. Mathematical modelling of the solidification process

The mathematical modelling of solidification process has aroused great

interest. According the coupling method of the fluid flow in the bulk liquid


12

equations for each phase. Therefore it cannot be simulated by the one-

domain continuum model.

Fig.2.7(b) and Fig.2.7(c) of solid and

liquid. For the assumption of mushy fluid, the solid is fully dispersed in the

liquid phase and the velocities of solid and liquid are equal, so we have

U=Us =Ul. For the assumption of columnar zone, the solid matrix is distinct

from the liquid. The velocity of the mixture system can be calculated based

on the volume fraction with U = fl Ul + fs Us. For the ingot casting, the solid

velocity Us is 0 and then U = fl Ul ; while for the continuous casting, the

solid moves with a pre-described velocity.

To simulate the solidification of ingot casting process, the one-domain

model can be developed based on the assumptions of both mushy fluid and

columnar zone for mushy region. By this approach, only one single set of

governing equations is needed, which is valid not only in the mushy region

but also in the bulk liquid and solid regions.

The previous models are usually under the assumption of constant density

with sl . Then according to the mass fraction relationship of 1sl ff ,

it can be deduced that the liquid and solid volume fractions have the

relationship of 1sl gg .

The mass conservation equation takes the form:

0)( Ut

With constant density, it can be simplified to: 0)(U

The momentum conservation equation depends on the assumed nature of

the mushy region. With the assumption of mushy fluid, the momentum

equation has the form:

gPUUUt

Ueffmix


13

In the momentum equation, the source due to buoyancy driven flow is

added based on the Boussinesq approximation with [34, 35]:

)]()([ refcrefTeff CCTT

The mixture viscosity mix is defined by llssmix gg . By this way, the

solid viscosity s is set as a very large value.

With the assumption of fixed columnar zone, the momentum equation has

the form:

momeffl SgPUUUt

U

In this equation, the source term Smom due to drag force is concerned, which

can be defined after the Carman-Kozeny equation as follows:

Ug

gKS

l

l

mom 3

2

0 )1(

The energy equation can be expressed by the conservation of enthalpy [24,

28, 36, 37], with the form:

hShc

ht

hU

Where h a function of temperature:

T

Tref

ref

dTchh

The source due to the latent heat of solidification is taken into account by

the use of an additional source term Sh in the energy equation, which also

depends on the assumed nature of the mushy region. With the assumption

of mushy fluid,

)()( ULfLft

S llh

While with the assumption of columnar zone,


14

)()( ULLft

S lh

The solute transport equation in the case of mushy fluid can be written as:

11

11

)()()(p

sl

p

sls

p

lll

sssssk

UCfk

Cft

Ck

DgDgUCC

t

In the case of columnar zone, the solute transport equation has the form:

slpllllllll ft

CkfCt

CDgUCCt

)1()()()(

At the solid-liquid interface, the concentration of solute in the liquid and

solid phases can be related via lps CkC . Hence the solute transport can be

expressed in terms of the solute concentration in solid phase sC or in liquid

phase lC , resulting in different source terms on the right side of the above

two solute transport equations.

To solve the above equations, an auxiliary relationship needs to be defined

for coupling the enthalpy (temperature) and concentration fields [28, 35,

38]. The temperature-concentration coupling relationship can be obtained

by the lever rule of phase change diagram or by a linear equation. In the

case of mushy fluid, the lever rule relationship is recommend, while in the

case of columnar zone, the linear relationship of temperature and

concentration is used.

Fig. 2.8 Phase diagram of a binary system [30]


16

56] developed a solidification model using Eulerian-Eulerian multiphase

approach and verified it by NH4Cl-H2O solidification experiment.

2.3. Introduction of the OpenFOAM software

To study the flow fields, Computational Fluid Dynamics (CFD) methodology

has been widely used. OpenFOAM is a kind of CFD software, and its name

comes from Open Source Field Operation and Manipulation. The greatest

strengths of OpenFOAM is that it is a free and open source software. The

highly capable free CFD codes can be applied to a wide variety of flow types,

and even to non-fluids applications, which make it possible to simulate

phase change such as solidification. The programming language of

OpenFOAM is C++ and it runs on Linux system.

Fig. 2.9 Overview of OpenFOAM structure [57]

Fig.2.9 shows an overall structure of OpenFOAM software. Like other CFD

softwares, OpenFOAM is supplied with pre-processing tools, solvers, and

post-processing tools. Each solver is designed to solve a specific problem in

computational continuum mechanics. To perform the pre- and post-

processing tasks, lots of utilities are designed that ensure consistent data

manipulation and algebraic calculations. For example, the blockMesh utility

is a meshing tool for generating simple meshes of blocks of hexahedral cells,

and the snappyHexMesh utility is a meshing tool for generating complex

meshes of hexahedral and split-hexahedral cells automatically from

triangulated surface geometries. Moreover, the users are capable to


17

convert a mesh that has been generated by a third-party software into a

format that OpenFOAM can read. After the calculation, the results are

obtained and listed in a set of time files. The post-processing utilities are

used to present the results. One of the post-processing utility is paraFoam

that uses ParaView, which is an open source third-party software. Also

other utilities are offered, including EnSight, Fieldview and the post-

processing supplied with Fluent.

The capability of a solver is mainly depend on the involved partial

differential equations (PDEs). Another strength of OpenFOAM is that the

programming language is C++ and it has object-oriented features, which

makes it easy to add PDEs into the solver. For example, the momentum

equation for a flow

PUUt

U

is represented by the code:

solve ( fvm::ddt(rho, U) + fvm::div(phi, U) - fvm::laplacian(mu, U) == - fvc::grad(p)

);

OpenFOAM uses finite volume method to discretize and solve PDEs for

complex fluid dynamics problems. All the information about the geometry,

physical properties, and discretization schemes have to be set before

calculation. Generally, an OpenFOAM simulation model is performed by

the following steps. Firstly, the model geometry is created and divided into

small volumes or cells, obtaining the so-called mesh. Secondly, the initial

and boundary conditions for solving the PDEs are defined and applied to


18

the geometry. Thirdly, the discretization schemes, time steps, data output

parameters are specified. Then the OpenFOAM solver is applied to the

model case, and the calculation results are presented using a post-

processing tool. More details about OpenFOAM can be found in the

OpenFOAM User Guide [57] [58].

OpenFOAM is supplied with several standard solvers which are used mainly

for CFD, for example, multiphase flow, incompressible and compressible

flow. So far, no standard solver has been released to simulate solidification

phenomenon. Even so, some projects on the simulation of solidification

with OpenFOAM software is already in progress, which refers to the

coupling of fluid flow with solidification, heat transfer, nucleation and

segregation.

OpenFOAM software is an excellent tool to tackle multi-physics problems,

which is also capable of simulating certain metallurgical process, such as

tundish filling, slag coverage of steel surface, mixing after ladle change. In

addition, B. Peters and his coworkers [59, 60] dedicated to the Extended

Discrete Element Method (XDEM), coupling to OpenFOAM to handle multi-

phase flow with granular materials or particles, by which method the

packed bed is modeled as a flow through a porous medium. The dripping

zone and cohesive zone of blast furnace have also been simulated, with

multi-phase flow, heat transfer and chemical reactions involved.

2.4. Objective and methods of the study

The flow conditions during the filling process has a crucial influence on the

quality of the solidified steel ingot. In this study the bottom teeming

process was concerned as the filling method. From the previous physical

and mathematical modeling of bottom teeming process, most of these

studies deal with small ingots, which have only one nozzle at the bottom of

the ingot mould. Few studies on large ingot with multiple bottom nozzles

have been reported in literatures. In this study, the initial filling conditions


19

for the mould of a 60-tonne large steel ingot with 4 bottom nozzles were

investigated, by both water modelling and numerical simulation.

In the water model experiments, a layer of oil was added to the water

phase to study the behavior of the steel-slag interface. The water-air-oil

three-phase flow was investigated to describe how the flow conditions are

influenced by the model parameters such as filling rate, nozzle dimension,

thickness. Finally, the model parameters were optimized to

obtain better filling conditions.

The numerical simulation of filling process was performed with OpenFOAM

software to get more quantitative information about the flow field,

especially the velocity field which is directly related to the phenomenon of

surface turbulence and slag entrapment.

To study the solidification process, a solidification model was developed.

Since the one-domain continuum model, which has only one set of

governing equations, cannot correctly simulate the nucleation of solid

particles and the movement of solid dendrites, therefore it gives

unsatisfactory prediction of macrosegregation. In this study, an Euler-Euler

two-phase approach was used to develop a solidification model based on

OpenFOAM software. Then the solidification model was performed on a

reported steel ingot and the results was compared with experimental

measurements from literature.

3. Water model experiments of the mould filling process

20


To study the fluid flow conditions during the mould filling process, water

model experiments were carried out on water-air two-phase flow and

water-air-oil three-phase flow, where water was used to simulate the

molten steel as they have a similar kinematic viscosity, and vegetable oil

was used to study the fused slag. The density and viscosity of water,

vegetable oil and molten steel were listed in Tab.3.1. The influence of the

investigated.

Tab. 3.1 Density and viscosity data

Densi

kg·m-3 Dynamic viscosity ,

kg·s-1·m -1

m2·s -1 Water 1000 0.001 1.00×10-6 Molten steel 7000 0.006 8.57×10-7 Vegetable oil 913.5 0.056 6.13×10-5 Liquid slag 2600 0.140 5.38×10-5

3.1. Design of experiments

The experimental model was designed based on a 60-tonne large steel

ingot, with the consideration of geometry and dynamic similarity. The steel

ingot was 3.84m in height and 0.868m thick. A water model of 1:4 scale was

developed, with 0.96m in height and 0.217m thick.

3.1.1. Water model set-up

Fig.3.1 shows a photograph and Fig.3.2 shows the schematic diagram of the

water model set-up. As shown in the figure, the inflow path was established

by connecting the water tank and the sprue via a bypass hose, using a pump

and flowmeter. Water was introduced by the pump and the flowmeter was

used to adjust the filling rate. A 3-way valve was installed to change the

flow direction: one way is connecting the flowmeter and the sprue to fill


21

the mould; the other way is making a water loop between the flowmeter

and the water tank, and then adjusting the flowmeter to obtain a constant

filling rate. The sprue, runner and mould were made of plexiglass due to its

good mechanical properties and transmittance. In order to study the

influence of nozzle dimensions on flow conditions, the nozzles on the

bottom plate of the mould were changeable.

Fig. 3.1 A photograph of the experimental set-up

Fig. 3.2 Schematic diagram of the water model set-up

In the real ingot casting process, casting powder melts into liquid slag after

getting contact with molten steel. However, the melting process cannot be

investigated by water modeling. Due to limited heat transfer, the melting

velocity decreases with increasing thickness of slag layer. Turbulence at the

steel-slag interface promotes the melting of mould powder. According to


22

the measurement of Kromhout [61] and Görnerup et al. [62], the melting

rate of mould powder is about 0.1mm/s irrespective of the slag layer

thickness. Therefore, the melting time of mould powder can be neglected.

To get a preliminary understanding of the steel-slag interface behavior by

water modeling, vegetable oil was used to simulate the liquid slag, without

consideration of the melting time. During the teeming process, a layer of

oil with dissolved pigment was added on the top surface of water and then

more water flowed into the mould through the bottom nozzles. Two video

cameras were used to record the flow characteristics from the front view

and top view respectively. The filling rate, nozzle dimensions and oil

thickness were studied concerning the flow conditions and surface

behaviors.

3.1.2. Model parameters

(a) Filling of the mould (b) Symmetry plane

(c) Bottom plate of the mould Fig. 3.3 Scale of the water model (unit: mm)


23

The prototype of the ingot mould came from a steel plant. It was used to

produce 60-tonne large steel ingots, and the mould was big-end-up, with 4

nozzles at the bottom plate of the mould. Based on the real ingot mould

and the gating system, a physical water model was designed in reduced

scale 1:4. Fig.3.3 shows a schematic diagram of the scale of the water

model. As shown in Fig.3.3(a), water is directed into the mould cavity

through four bottom nozzles. In order to distinguish the four nozzles, we

call them nozzle A, B, C, D respectively, as marked in Fig.3.3(c).

Besides the geometry similarity, the dynamic similarity between the

prototype and model is also important, which can be achieved by the

similarity in Reynolds number, Froude number and Weber number.

However, it is not possible to satisfy all of the three similarities

simultaneously for a reduced-scale model. The filling rate of molten steel is

about 1.0~1.8t/min for the ingot bottom teeming process, and the

corresponding Reynolds number can reach up to 6×104, which represents

a fully developed turbulent flow. It was suggested that Reynolds similarity

is insignificant for such a fully developed turbulent flow [63, 64]. Weber

number is useful in analyzing fluid flow with interface between two fluids.

The present work aims to study the behavior of the steel-slag interface, and

therefore Weber similarity is the best choice. Weber number represents

the ratio between inertial force and surface tension force, which is defined

as:

LuWe

2

Where u is velocity; L is characteristic length; is density; is surface

tension. For molten steel, = 7000kg/m3 and = 1.6N/m; for water, =

1000kg/m3 and = 0.073N/m. Based on the Weber similarity and the filling

rate of 1.0~1.8t/min in real ingot bottom teeming process, the filling rate

of water is about 10.1~18.2L/min. In order to investigate the influence of

filling rate on the flow conditions, the filling rates of 10L/min, 15L/min and

19L/min were studied in water model experiments.


24

Besides the filling rate, the design of bottom nozzles is also important for

the flow field. In this model, the bottom nozzles are changeable and

different sizes of nozzles were used.

3.1.3. Experimental procedure

In the experiment, the control variable method was used to investigate the

influence of operation parameters on the flow conditions (filling rate,

number of nozzles, nozzle dimensions and oil thickness). Two types of

models were conducted, one with only one nozzle at the bottom plate of

the mould and the other with four bottom nozzles. Appropriate filling rates

were chosen: 10L/min, 15L/min, 19L/min for four-nozzle model; 6L/min,

8L/min, 12L/min for one-nozzle model. The initial water level in the mould

was about 10cm. The thickness of added oil layer changed from 1cm to 3cm.

Besides these filling variables, the design of bottom nozzles is also

important for the flow field. In this experiment, eight groups of nozzle

dimensions were studied, as listed in Tab.3.2.

Tab. 3.2 Diameters of the nozzles used in the experiments (unit: mm) Nozzle A Nozzle B Nozzle C Nozzle D Group 1 blocked 22.5 blocked blocked Group 2 15.0 15.0 15.0 15.0 Group 3 22.5 22.5 22.5 22.5 Group 4 25.0 25.0 25.0 25.0 Group 5 12.5 15.0 22.5 25.0 Group 6 25.0 22.5 15.0 12.5 Group 7 25.0 25.0 12.5 12.5 Group 8 12.5 12.5 25.0 25.0

In Group 1, besides Nozzle B the other three nozzles were blocked. The

diameters of the four nozzles were the same in Group 2-4. In Group 5, the

diameters of the four nozzles were arranged in ascending order from nozzle

A to D, however that were arranged in descending order in Group 6. Fig.3.4


25

shows four unequal nozzles with the diameter of 25-22.5-15-12.5 mm from

A to D.

Fig. 3.4 Four unequal nozzles with diameter of A25-B22.5-C15-D12.5 mm

The specific experimental procedures are listed as follows:

(1) Preparation: The mould was filled with certain amount of water (initial

water level) and vegetable oil was added on the water surface. A ruler was

pasted on the front wall of the mould to record the position of the changing

liquid level. A video camera was set in front of the model and another

camera was set right above the water model to record the behavior of the

top surface.

(2) Connect the flowmeter to the water tank with a bypass hose. Turn on

the pump and then adjust the filling rate by the flowmeter to obtain a

steady filling rate before filling the mould.

(3) Turn on the two cameras at the same time, and then switch the flow

pass to connect the flowmeter with the sprue. Therefore, water from the

water tank can flow into the mould through bottom nozzles. During bottom

teeming, the video camera was moved upwards continuously to keep the

camera lens at the same height as the rising liquid level.

(4) Each group of nozzles was conducted with different filling rates, initial

water levels and oil thicknesses. After one group of nozzles was conducted,

the water was sucked out of mould and the mould must be cleaned by

water and detergent. Then a new group of nozzles were installed for the

following experiments.


26

(5) The videos were imported to a computer and analyzed with GIMP, Excel

and Origin software.

3.2. Results about the models with one bottom nozzle

With the nozzle of Group 1 (the diameter of Nozzle B was 22.5mm and the

other three nozzles were blocked), different tests were carried out to study

the influence of filling rate and oil thickness on the filling conditions.

3.2.1. Water-air two-phase flow without oil addition

When water flows into the mould, the incoming flow through the bottom

nozzle with high speed will generate a water jet to spread out to the mould.

As the liquid level rises in the mould, the impact force of the jet on the

surface will lead to a hump right above the nozzle, also turbulent surface.

It was observed in water model experiments that the variation of

turbulence degree with liquid level was consistent with the variation of

hump size. Strong surface turbulence and large humps were observed at

low liquid level. For quantitative description, hump height ( H) is

introduced as a parameter to evaluate the surface behavior. The hump

height is defined as the difference of the maximum height above nozzle

(Hm) and the liquid level (H), i.e. H= Hm-H (see Fig.3.5).

With the fixed nozzles, the hump height H is related with the filling rate.

Fig.3.6 shows the influence of filling rate on the hump height with rising

liquid level. As shown in the figure, the hump height decreases with the

decrease of filling rate, and with the increase of liquid level. In Fig.3.6(a),

regression analysis based on the water model experimental data describes

the relationship between the hump height, liquid level, and filling rate. The

regression lines satisfy the equation:

VHdVcHbaH

Where H represents the hump height with unit mm; H represents the

liquid level with unit m; V represents the filling rate with unit L/min. The


28

The influence of filling rate and liquid level on the hump height is easy to

understand, since the hump height depends on the impact force of the jet

on the top surface. A larger filling rate brings more energy to impact the

surface thus results in larger hump. The impact force of the jet is reduced

with the increasing distance between the bottom nozzle and the top water

level. As the water level rises, the hump height gradually declines to 0.

3.2.2. Water-air-oil three-phase flow with oil addition

In the real ingot casting process, normally the casting powder is hung about

30cm above the bottom plate of the mould before pouring. As the molten

steel flows into the mould and reaches to the level, the powder is fused to

form a slag layer. The melting of casting flux cannot be simulated by cold

water model, as mentioned before. The purpose of the water model

experiments was to investigate the behavior of the interface between

molten steel and slag during teeming process, so we added the oil layer to

the top surface of water at a certain initial water level, then more water

was filled in through the runner and the flow fields were observed. In the

experiments, special pigments were used: the red pigment was soluble in

oil but insoluble in water, while the blue pigment was soluble in water but

insoluble in oil. The selective solubility of the pigments make it clear to

observe the interface between oil and water.

(a) Open surface at the top

(b) The interface, side view

Fig. 3.7 Typical surface features of the one-nozzle model

Oil

Water

Air

Oil

Water

Hump


29

Fig.3.7 shows the typical surface features of the one-nozzle model. As

shown in Fig.3.7(a), the oil layer was open during teeming, developing an

open eye of eye

nozzle, and it was formed due to the upward water jet from the bottom

nozzle eye

indicates that the molten steel may be exposed to air without the

protection of slag. Therefore, the fraction of the open surface , defined

as the ratio between the area of water exposed to air Aopen and the total

area of liquid surface Abath, i.e. bathopenos AAf / , is an important parameter to

evaluate the risk of reoxidation. Fig.3.7(a) was obtained from the top view,

while Fig.3.7(b) from the front view. As observed in Fig.3.7(b), the water

hump was exposed to air, and some oil droplets were entrapped in the

water phase, which was related to the phenomenon of slag entrapment in

ingot casting process.

For a model with fixed bottom nozzles, the filling rate and oil thickness are

two important parameters to decide the surface behaviors. To study the

influence of filling rate, the one-bottom-nozzle model was tested on

different filling rates: 6L/min, 8L/min, 10L/min and 12L/min, with the same

initial liquid level of 0.08m and 1cm-thick oil. As illustrated in Fig.3.8(a), at

the same liquid level, the fraction of open surface increases with increasing

filling rate, which shows a consistent trend with the hump height. For the

filling rate of 6L/min, it shows that the fraction of open surface has no

significant change with rising liquid level. For the filling rate of 8L/min, the

fraction of open surface maintains steady firstly and then shows an

ascending trend during the mould filling at high liquid level. For the filling

rate of 10L/min and 12L/min, the fraction of open surface increases at the

beginning and then reaches a steady state with rising liquid level. The open

surface fraction for 12L/min filling rate is the largest, which indicates that

it has the greatest risk of reoxidation with a high filling rate.


30

0.1 0.2 0.3 0.4 0.50.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40F

ractio

n o

f th

e o

pe

n s

urf

ace

fo

s

Liquid level H, m

6L/min

8L/min

10L/min

12L/min

Nozzle dimension: 1 22.5mm

Oil thickness: 1cm

Filling rate:

5 6 7 8 9 10 11 12 13

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.21766

0.12807

0.10291

Average value in the range of fos

Fitting curve

0.04185

Filling rate V, L/min

Fra

ction o

f th

e o

pen

surf

ace

fo

s

(a) (b)

Fig. 3.8 Fraction of open surface variation with filling rate for one-nozzle model

With the rising liquid level, the fraction of open surface fos changes in a

certain range. From Fig.3.8(b), the range of the open surface fraction under

each filling rate can be clearly seen. For the filling rate of 6L/min, the range

of fos is narrow and average value is small; while for the filling rate of

12L/min, the range is wide and average value is large.

understand that the area of the is related with the impact energy

of liquid jet on the top surface, and further on, the impact energy is

determined by the filling rate. From the view of kinetic energy ( 221 vmE

), the fraction of open surface fos may be a function of the square of filling

rate. Therefore, as shown in Fig.3.8(b), a fitting curve was made based on

the average values of fos, with the equation:

2

VcVbafos

Where fos represents the fraction of open surface; represents the filling

rate with unit L/min. The parameters a, b and c in the regression equation

are 0.00949, -0.00447min/L and 0.00178min2/L2, respectively.

To study the influence of oil thickness on the flow conditions, the one-

bottom-nozzle model was tested on different thickness of oil addition:

0.5cm, 1cm, 2cm and 3cm, with the same initial liquid level of 0.08m and

filling rate of 10L/min. As shown in Fig.3.9(a), for a thicker oil layer, such as

2cm and 3cm in thickness, the fraction of open surface generally decreases


31

thicker oil layer. For a thinner oil layer, such as 0.5cm and 1cm in thickness,

no closure trend of open can be observed during the experiments. For

oil thickness of 1cm, the open surface fraction keeps nearly stable with the

rising liquid level. For oil thickness of 0.5cm, the open surface fraction

increases considerably and even reaches 47% at the water level of 0.5m.

From Fig.3.9(b), the open surface fraction shows a negative correlation

with the oil thickness.

0.1 0.2 0.3 0.4 0.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fra

ctio

n o

f th

e o

pe

n s

urf

ace

fo

s

Water level H, m

Oil thickness Experimental data Fitting curve

0.5cm

1cm

2cm

3cm

Nozzle dimension: 1 22.5mm Filling rate: 10L/min

0 1 2 3

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.1m

0.2m

0.3m

0.4m

0.5m

Nozzle dimension: 1 22.5mm

Filling rate: 10L/min

Water level:

Oil thickness , m

Fra

ction o

f th

e o

pen s

urf

ace

fo

s

(a) (b)

Fig. 3.9 Fraction of open surface variation with oil thickness for one-nozzle model

According to the experimental data, a regression equation was put

forward:

22

2 11 HfeHdcHbafos

Where osf represents the fraction of open surface; H represents the liquid

level with unit m; represents the oil thickness with unit mm. The

parameters a, b, c, d, e and f in the regression equation are -0.03, 0.13m-1,

0.17mm, -0.53m-2, -0.04mm2 and 0.19mm respectively. The regression

curves in Fig.3.9(a) appear to fit the experimental data well.

As the oil phase covers on the water bath, the mechanism of

related with the dynamic equilibrium between the gravity force of oil and

the impact force of water stream due to bottom teeming. The oil phase can


32

be treated as some parallel layers of fluid with high viscosity. The upward

water stream tends to break the oil layers from the bottom up to form

, while the top oil layers tends to make up the lower breaking

area due to gravity force. Therefore, a thicker oil film has more capacity to

counteract the impact force of water stream, which in turn causes a small

as consistent with Fig.3.9. Moreover, since the impace force of

water jet on top surface is reduced with the rising water level, the water

phase may be totally covered with the oil phase after reaching to a certain

level, which takes places only under the condition of enough oil thickness.

If the oil film is too thin, the inward flowing of oil due to gravity will be

weaker than the outward extension of which is caused by the

enlarging outward component force of water stream with rising water

level. As shown in Fig.3.9(a), the open surface fraction increases

considerably with rising water level when oil thickness is 0.5cm. In addition,

even at a high water level where the influence of water jet can be ignored,

water-oil interface, in particular under the condition of less oil addition.

3.3. Results about the models with four bottom nozzles

With a constant filling rate, the total volumetric flow rate streaming into

the mould is also constant. For a model with more bottom nozzles, the total

flow will be distributed to all the bottom nozzles. Therefore, for a model

with four bottom nozzles, the jet velocities through each nozzle become

smaller than that for a one-bottom-nozzle model. In this section, the flow

fields for the model with four bottom nozzles were studied. The dimensions

and arrangement of the nozzles were expected to influence the flow

conditions. Similarly to the one-bottom-nozzle model, the filling rate and

oil thickness also have influence on the filling conditions for the four-

bottom-nozzle models.


33

3.3.1. Features of the flow fields

For four-bottom-nozzle models, there are four humps at water-oil interface

and each hump corresponds to one bottom nozzle. The hump height is

related to the position of bottom nozzles. As observed in water models with

four equal bottom nozzles (see Tab.3.2, nozzles of Group 2, 3, 4), the hump

height above nozzle A is the smallest and that above nozzle D is the largest

at the same liquid level. The degree of turbulence and slag entrapment has

a positive correlation with the hump height, therefore, only the maximum

hump height was concerned in this work. As shown in Fig.3.10, the

maximum hump height H was defined again as the difference of the

maximum height above nozzle D (Hm) and the liquid level (H), i.e. H=Hm-H.

Fig. 3.10 Schematic of the humps in four-equal-bottom-nozzle models

For the model with four bottom nozzles, the water jet from each nozzle

may break through the oil layer to form an

various forms of the open surface, such as a continuous region or four

separated

rising liquid level. Tab.3.3 lists the shape of the

of four-bottom-nozzle models, at the same water level of 0.15m, with the

same filling rate of 15L/min and oil thickness of 1cm or 2cm. In the figures,

the grey regions represent regions denote

that the surface is covered with oil phase. The vertical mapping points of

the centers of the four bottom nozzles A, B, C and D were marked in the

figures. As a supplement, Tab.3.4 gives the nozzle diameters used in the

seven groups of models. Four equal bottom nozzles were used in Group 2,

Incoming flow


37

similar to the influence on the hump height, as shown in Fig.3.11. Filling

rate affects the development of the open surface as liquid level rises. With

1cm-thick oil layer, as shown in Fig.3.12(a), for the filling rate of 10L/min,

the fraction of open surface slowly reduces during teeming and the water

surface is totally covered by oil at the liquid level of 0.48m. For the filling

rate of 15L/min, the open surface fraction has no obvious change with

rising liquid level. For the filling rate of 19L/min, the fraction of open

surface first increases until the liquid level of 0.4m and then shows a

downward trend with rising liquid level. The initial increase of open surface

is related with the entrapment of oil droplets which is encouraged by the

powerful water jets under a large filling rate. With the rising liquid level,

the entrapped oil droplets may rise up to reduce the open surface. With

2cm-thick oil layer, as shown in Fig.3.12(b), the open surface is smaller and

gradually closes at early stage of the teeming process when the filling rate

is small enough, such as 10L/min and 15L/min. However, for the filling rate

of 19L/min, the open surface is much larger and cannot close at the liquid

level of 0.5m, even though it shows a declining trend during the filling

process. From Fig.3.12 it can be concluded that with the same oil thickness

and at the same liquid level, the open surface is smaller for a smaller filling

rate and it is more likely to be closed in the end.

0.1 0.2 0.3 0.4 0.50.00

0.05

0.10

0.15

0.20

Fra

ctio

n o

f th

e o

pen

su

rfa

ce

fos

Liquid level H, m

15L/min, experimental data


15L/min, fitting line


Nozzle dimension: 4 25mm

Oil thickness: 1cm

Filling rate:

0.1 0.2 0.3 0.4 0.5

0.00

0.05

0.10

0.15

0.20

Fra

ction o

f th

e o

pen

surf

ace f

os

Liquid level H, m





Nozzle dimension: 4 25mm

Oil thickness: 2cm

Filling rate:

(a) (b)

Fig. 3.13 Fraction of the open surface variation with filling rate, for the model with four 25mm-diameter equal nozzles: (a) 1cm-thick oil layer; (b)

2cm-thick oil layer


44

diameter nozzles. Even though the jet velocity is the largest for the model

with four 15mm-diameter equal nozzles, the total area of bottom nozzles

are the smallest. However, for the model with four 22.5mm-diameter equal

nozzles, both the jet velocity and the total area of bottom nozzles are

relatively large, which leads to the largest open surface.

0.1 0.2 0.3 0.4 0.50.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Fra

ctio

n o

f th

e o

pe

n s

urf

ace

fo

s

Liquid level H, m

12.5-15-22.5-25

25-22.5-15-12.5

25-25-12.5-12.5

12.5-12.5-25-25


Oil thickness: 1cm

Nozzle dimension:

0.1 0.2 0.3 0.4 0.50.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

12.5-15-22.5-25

25-22.5-15-12.5

25-25-12.5-12.5

12.5-12.5-25-25


Oil thickness: 1cm

Nozzle dimension:Fra

ctio

n o

f t

he

op

en

su

rfa

ce

fo

s

Liquid level H, m

(a) (b)

0.1 0.2 0.3 0.4 0.50.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Liquid level H, m

Fra

ction o

f th

e o

pen s

urf

ace

fo

s

12.5-15-22.5-25

25-22.5-15-12.5

25-25-12.5-12.5

12.5-12.5-25-25


Oil thickness: 2cm

Nozzle dimension:

0.1 0.2 0.3 0.4 0.5

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

12.5-15-22.5-25

25-22.5-15-12.5

25-25-12.5-12.5

12.5-12.5-25-25


Oil thickness: 2cm

Nozzle dimension:

Fra

ctio

n o

f th

e o

pe

n s

urf

ace

fo

s

Liquid level H, m (c) (d)

Fig. 3.19 Fraction of the open surface variation with the nozzle dimensions, for the models with four unequal bottom nozzles and: (a) 15L/min filling rate, 1cm oil thickness; (b) 19L/min filling rate, 1cm oil

thickness;(c) 15L/min filling rate, 2cm oil thickness; (d) 19L/min filling rate, 2cm oil thickness.

Fig.3.19 compares the models with four different groups of nozzle

dimensions, which are 12.5-15-22.5-25mm, 25-22.5-15-12.5mm, 25-25-

12.5-12.5mm, 12.5-12.5-25-25mm from nozzle A to D respectively.

Fig.3.19(a) is under the same filling rate of 15L/min and same oil thickness

of 1cm. It can be seen that at the same liquid level, the open surface for the


45

model with 12.5-15-22.5-25mm nozzles is smaller than that for the model

with 25-22.5-15-12.5mm nozzles, and the open surface for the model with

12.5-12.5-25-25mm nozzles is smaller than that for the model with 25-25-

12.5-12.5mm nozzles. Therefore, it can be concluded that under this filling

condition, the nozzle dimensions of ascending order from nozzle A to D is

better to reduce the risk of reoxidation. With higher filling rate of 19L/min,

as shown in Fig.3.19(b), even though the open surface fraction for the

model with 25-22.5-15-12.5mm nozzles and 12.5-12.5-25-25mm nozzles is

approximately the same, the open surface fraction for the model with 12.5-

15-22.5-25mm nozzles is the smallest, which reveals that the model with

ascending nozzle diameters from nozzle A to D is better as well. From

Fig.3.19(c) and 3.19(d), it is found that the nozzle dimensions have no

significant influence on the fraction of open surface for the model with

2cm-thick oil.

In general, with 1cm-thick oil layer, the development of the open surface

shows a growth tendency and it cannot close even at the liquid level of

0.5m. Moreover, the nozzle dimensions of ascending order from nozzle A

to D is better to reduce the risk of reoxidation. While with oil thickness of

2cm, the open surfaces are all closed in the end and the nozzle dimensions

have little effect on the fraction of the open surface.

2 3 4 5 6 7 80.00

0.05

0.10

0.15

0.20

0.25


Oil thickness: 1cm

Water level: 0.3m

Group Number

Fra

ction o

f th

e o

pen s

urf

ace f

os

Nozzle parameters (unit: mm)

Nozzle

A Nozzle

B Nozzle

C Nozzle

D Group 2 15.0 15.0 15.0 15.0

Group 3 22.5 22.5 22.5 22.5

Group 4 25.0 25.0 25.0 25.0

Group 5 12.5 15.0 22.5 25.0

Group 6 25.0 22.5 15.0 12.5

Group 7 25.0 25.0 12.5 12.5

Group 8 12.5 12.5 25.0 25.0

Fig. 3.20 Comparison of the open surface fraction for the models with different nozzles, but same filling rate of 15L/min and oil thickness of 1cm,

at the water level of 0.3m


46

In Fig.3.20, the fraction of open surface at the same water level of 0.3m for

different groups of nozzles was compared. It can be clearly seen that the

model with nozzles of group 4 (four equal 25mm nozzles) has the smallest

, while the model with nozzles of group 6 (25-22.5-15-12.5mm

For the model with nozzles of group 4,

the total area of nozzle cross section is the largest, which reduces the

average velocity through each nozzle, thus the impact force on top surface

is reduced. For the model with nozzles of group 6, the total area of nozzle

cross section is relatively small, and the nozzles are arranged in descending

order, in which case, the velocities through the last nozzles can be larger,

and therefore increase the impact force on top surface.

0.1 0.2 0.3 0.4 0.50.0

0.1

0.2

0.3

0.4


Oil thickness: 1cm

Nozzle dimension:

4 × 15mm

4 × 25mm

12.5-15-22.5-25mm

25-22.5-15-12.5mm

Liquid level H, m

Fra

ction o

f th

e o

pen s

urf

ace

fos

Fig. 3.21 Fraction of the open surface variation with nozzle dimensions, for the models with 1cm-thick oil layer and filling rate of 15L/min

Based on the previous comparison of models with equal bottom nozzles

and unequal bottom nozzles respectively, a comparison of models with

both types of bottom nozzles is made, as shown in Fig.3.21, with the same

filling rate of 15L/min and the same oil thickness of 1cm. The models with

unequal nozzle diameter of 12.5-15-22.5-25mm and 25-22.5-15-12.5mm

are chosen, which correspondingly represent the model with ascending

nozzle diameters and the model with descending nozzle diameters from

nozzle A to D. From Fig.3.21, it can be seen that the fraction of open surface

for the model with 25mm-diameter equal nozzles is much smaller than the

other three cases, and it gradually decreases to 0 at the liquid level of


50

addition. One possible reason of this phenomenon may be that when the

liquid jet breaks through the oil layer, thin oil layer can be easily pushed

aside and keeps far away from the center of the liquid jet. The oil droplets

generated at the lower boundary of the hump are caused by the downward

force of reflux flow acting on the oil layer. Therefore, less oil droplets are

generated for thin oil layer. For a relatively thick oil layer, the lower

boundary of the hump is surrounded by oil, so oil droplets can easily form

and are entrapped into the downward flow. However, if the oil layer is too

thick, for example 3cm, only a few oil droplets were observed, and the

depth of oil inclusions reduced, perhaps due to the suppression of the

above heavy oil layer on the interface flow.

3.4. Optimization of filling conditions

Exogenous inclusions in ingots originate mainly from reoxidation of the

molten steel, slag entrapment, and lining erosion [1]. In general, the degree

of reoxidation is determined by the contact area between the molten steel

and air, which can be evaluated by the fraction of the open surface. From

the water model experiments, we can know that a thicker slag layer

contributes to smaller open surface so as less reoxidation. However, thicker

slag layer usually leads to more slag entrapment, which could become

inclusions in the final products. Also more slag addition means increased

cost of production. Therefore, the expected optimal filling conditions

should balance the risk of reoxidation and slag entrapment, which is also

the major objective of the experiments.

The risk of reoxidation can be evaluated by the fraction of the open surface,

while the degree of slag entrapment is related with the surface turbulence,

which can be evaluated by the hump height. The influence of experimental

parameters on the open surface and the hump height was summarized as

follows.


51

3.4.1. Influence of experimental parameters on the open surface

As has been demonstrated that the oil layer may be broken by the

submerged water jets. As the water level increases, the jet impinging force

on the oil layer is reduced. There must be a critical jet impinging force on

the oil layer, below which a complete coverage of the water-oil interface

can be achieved. Tab.3.5 lists the liquid level when the open surface is

closed under different conditions.

Tab. 3.5 The liquid level when the open surface is closed (unit: m)

Nozzle dimension 1cm oil 2cm oil 3cm oil

10L/min 15L/min 19L/min 10L/min 15L/min 19L/min 10L/min 15L/min 19L/min

mm 0.47 open open 0.2 0.27 open 0.16 0.24 0.37

mm open open open 0.18 0.41 0.52

mm 0.36 open 0.29 0.4

12.5-15-22.5-25mm

open open 0.32 0.52

25-22.5-15-12.5mm

open open 0.29 0.42

25-25-12.5-12.5m open open 0.3 0.46

12.5-12.5-25-25mm

open open 0.42 0.44

From the experimental results, it was found that for the model with the

same nozzles, the open surface is closed much earlier under a smaller filling

rate, which is totally covered by the oil layer even at low liquid level.

Also the nozzle dimensions have influence on the open surface. According

to the following formula:

uAV

Where is the volume flow rate through the area; A is the area of the cross

section; u is the velocity of the liquid flow. We can know that when water

flows through larger nozzles, the induced velocity of water jet is smaller.

Therefore, under the same filling rate, the jet impinging force on the oil

layer is related to both the jet velocity and the area of the nozzle. Normally,


52

the open surface is easy to close finally for the model with larger nozzle

diameters and lower filling rates.

As can be seen from Tab.3.5, the thickness of oil layer plays an important

role on the open surface. With the increase of oil thickness, the open

surface tends to be closed at lower liquid level. It is also revealed that 3cm-

thick oil layer can generate a smaller open surface than that of 1cm- and

2cm-thick oil layer. Therefore, in the real ingot casting process, the molten

steel can be well protected by more slag from reoxidation.

The open surface consists of open eyes . For the model with four equal

nozzles, open eye D has the largest average radius, while open eye A has

the smallest average radius and is the most concentrated, which is due to

the velocity distribution through the corresponding nozzles. The surface

behavior for models with different nozzle diameters is quite different under

specific filling conditions. In general, the smallest open surface was

observed in the model with four 25mm-diameter equal nozzles.

3.4.2. Influence of experimental parameters on the hump height and

entrapment

The hump height reduces with rising liquid level, decreasing filling rate and

increasing oil layer. The influence of nozzle dimensions on the hump height

is more complicated. Normally, the model with four 25mm-diameter equal

nozzles has relatively small humps, and the hump upon nozzle D is the

largest.

Generally, the larger the hump is, the stronger the downward flow at the

edge of the hump is, and therefore the larger degree of slag entrapment it

gives rise to. The water model experiments reveal

entrapment is also layer. For example,

it was found that the entrapped depth of oil inclusions was the largest for

the model with 2cm-thick oil layer, which was larger than both of the two

cases with more or less oil addition.


53

3.4.3. Optimal filling conditions

As mentioned above, the expected optimal filling conditions should

balance both the risk of reoxidation and slag entrapment. The production

cost should also be taken into account.

On one hand, in order to reduce the surface turbulence and slag

entrapment, the filling rate should be small. At a low liquid level, the hump

is large and the surface turbulence is strong due to the larger jet impinging

force on the top surface. Therefore, it is required to reduce the filling rate

to avoid On the other hand, too small filling rate

would cause undesirable problems, such as low productivity and strong

reoxidation of the molten steel, which results from the low rising velocity

of liquid surface and therefore the delayed contact between mould powder

and molten steel. Based on the above two aspects, it is recommended that

during the first several minutes of water modeling, the filling rate is kept at

a low value (10-13 L/min), and then after some time when the water level

reaches a certain height, the filling rate can be increased gradually (15-18

L/min). The hump height is expected to retain below 5mm to minimize the

oil entrapment in water modelling. Correspondingly, the filling rate of

molten steel for the real ingot casting process is about 1.0-1.3 t/min at the

beginning, and then gradually increases to about 1.5-1.8 t/min. Because the

water model was developed in reduced scale of 1:4, the maximum hump

height of molten steel is expected to below 20mm.

To reduce the reoxidation of molten steel, the open surface fraction should

be reduced, which can be realized by addition of more slag. However, more

slag addition can increase the production cost, and may lead to more slag

entrapment. It is expected to optimize the slag layer thickness to reduce

the risk of slag entrapment and reoxidation of melt at the same time.

From the experiments, the smallest open surface and humps were

observed in the model with four 25mm-diameter equal nozzles. It becomes


54

the best choice for the nozzle design in terms of minimizing the risk of

reoxidation and slag entrapment.

3.5. Conclusions

The water model experiments were carried out to simulate the molten

steel-slag interface during large steel ingot bottom teeming process. The

experimental results reveal the influence of model parameters, such as the

filling rate, nozzle dimensions and oil thickness on the filling conditions,

which can evaluate the risk of slag entrapment as well as reoxidation of

molten steel. The following conclusions can be drawn from the study:

(1) At a certain liquid level, with the reduction of filling rate, on one hand,

the hump height decrease, thus the risk of slag entrapment is reduced; on

the other hand, the fraction of open surface decreases, thus the risk of

reoxidation is reduced.

(2) The hump height is reduced with rising liquid level, so the slag

entrapment and surface turbulence at low liquid level is stronger. In order

to reduce slag entrapment and surface turbulence at low liquid level while

improve the productivity at high liquid level, it is recommended that during

the first several minutes, the filling rate of molten steel should be kept at a

low value (1.0-1.3 t/min), and then after the level of molten steel reaches

to a certain height where the hump is small enough, the filling rate can be

increased gradually (1.5-1.8 t/min). The hump height is expected to retain

below 20mm to minimize the slag entrapment.

(3) For a large steel ingot mould, it is better to design multiple bottom

nozzles to reduce the jet velocity through each nozzle. In the experiment

models, the model with four 25mm-diameter equal nozzles shows better

performance from the view of both slag entrapment and reoxidation.

(4) With the increase of slag thickness, the open surface decreases and

therefore the risk of reoxidation is reduced. However, more slag addition

may lead to more slag entrapment and increase the production cost as well.

4. Numerical simulation of filling process with OpenFOAM software

55


The computational fluid dynamic simulations were performed with

OpenFOAM software to get more quantitative information about the flow

field during the filling process, especially the velocity field which is directly

related to the phenomenon of surface turbulence and slag entrapment.

4.1. Model description

OpenFOAM is supplied with a large set of standard solvers, in which

interFoam is designed to solve two incompressible, isothermal immiscible

fluids, using a VOF (volume of fluid) phase-fraction based interface

capturing approach [57]. In this study, the standard solver interFoam of

OpenFOAM 1.7.1 was used to calculate the water-air two-phase flow. The

geometry of the simulation model was the same as the water model, with

four nozzles at the mould bottom. As illustrated in Fig.3.3, the model has a

symmetry plane, therefore, only half of the total geometry was calculated

as the three dimensional computational domain to save computational

time.

The following assumptions were made to simplify the mathematical model:

(i) only the flow in the early stage of filling were concerned in this paper,

without the consideration of solidification as well as heat transfer; (ii)

room-temperature water was used to simulate molten steel; (iii) both

water and air are incompressible Newtonian fluids, and the physical

properties of the two fluids are constant. Then the flow is governed by the

following equations [65]:

The mass continuity equation: 0Ut

The momentum equation: FgTUUU

t

Where t is time; is density; U is velocity vector; T is total stress tensor; F

is the force due to surface tension . For a Newtonian fluid in local

thermodynamic equilibrium, T is defined as:


56

T)(3

2UUIUT P

Where P is pressure; I is the unit tensor; µ is dynamic viscosity. At the

interface between water and air, VOF method is adopted to simulate the

evolution of free surface. The volume fraction of water, , is equal to 1 for

the cells completely occupied by water, and equal to 0 for the cells

completely occupied by air. Hence, the interface is located within the cells

where 0< <1. is governed by the phase conservation equation:

0Ut

Based on the VOF method, the physical properties of fluids in the above

governing equations, such as density and viscosity, are computed as follows:

airwater )1(

airwater )1(

For this incompressible Newtonian flow, Ubbink [65] reformulated the

momentum equation:

FUUgUUU

Pt

F

These transport equations were employed in the solver interFoam, also the

standard - model was adopted to simulate the turbulent behavior of the

flow. Therefore, the viscosity µ in the governing equations was replaced by

the effective viscosity µeff, which was defined as:

2

Cwith tteff

The initial and boundary conditions must be defined to complete the

mathematical model. For this transient flow, the system was initially filled

with air, and then water flowed into the mould from the inlet boundary


57

with a constant uniform velocity. At the outlet boundary, atmosphere

boundary conditions were specified, where the pressure could be

calculated from the specified total pressure and local velocity. The

boundary conditions of symmetry plane were set to be symmetryPlane,

which is a standard boundary type in OpenFOAM. Moreover, no-slip

conditions were assumed on the walls of the model. Based on the finite

volume method, the governing equations described above were discretized

on meshes which were generated by a mesh-generation utility in

OpenFOAM called snappyHexMesh. The PISO (Pressure-Implicit Split-

Operator) algorithm was applied to solve the pressure-velocity coupling.

4.2. Results of the calculated flow fields

The numerical simulations were carried out on different parameters of

filling rate and nozzle dimensions. In chapter 3, the filling rates of 10L/min,

15L/min and 19L/min were studied with water model, which had a circular

entrance 26mm in diameter, so the corresponding inlet velocities for the

numerical model were 0.31m/s, 0.47m/s and 0.60m/s, respectively.

Furthermore, the calculated flow fields were compared with the

measurements of water modeling.

4.2.1. Flow patterns in the early stage of teeming

Fig.4.1 shows the calculated flow patterns on the symmetry plane after 4s

and 20s of bottom teeming start-up. In the early stage of teeming, when

water flows into the sprue, air is pushed out through the bottom nozzles.

As Fig.4.1(a) clearly shows, air bubbles are entrapped into the water flow

during mould filling. The air bubbles tend to rise due to low density. Once

the bubbles move to the first nozzle, they rise to the mould and spout out

at the liquid surface, which results in strong surface turbulence. After all

the air spouts out, the liquid level tends to be stable, as illustrated in

Fig.4.1(b), from which we can see clearly the interface between water and

air phases. The surface turbulence at the beginning can increase the risk of

slag entrapment, thus it is better to add casting powder after all the air


58

bubbles spout out. Moreover, because of the submerged liquid jets from

bottom nozzles, four humps form at the impinging zone of the surface and

they generally decrease with rising liquid level, which are consistent with

the water model experimental observation.

(a) t=4s (b) t=20s

Fig. 4.1 Predicted flow patterns on the symmetry plane, for the model with equal nozzle diameter of 15mm and inlet velocity of 0.6m/s

Tab. 4.1 Influence of model parameters on the rising of air bubbles Nozzle diameters from A to D(mm)

Filling rate (m/s)

Rising of air bubbles Time (s) Liquid level (m)

4 × Ø15 0.60 8 0.010 0.47 10.5 0.010 0.31 52 0.056

4 × Ø25 0.47 10 0.008 12.5-15-22.5-25 0.47 12 0.014 25-22.5-15-12.5 0.47 10 0.009

Tab.4.1 lists the influence of filling rate and nozzle dimensions on the time

needed for rising of air bubbles and on the liquid level immediately after all

air bubbles spout out. It is found that the filling rate has a significant

influence on the rising of air bubbles. It takes more time for a smaller filling

rate and the corresponding liquid level is higher. While at a certain filling

rate, the nozzle dimensions have little influence on the rising of air bubbles.

Interface

Air

Empty space (air)

Sprue, filled

with water

Mixture

Water


59

In the real ingot bottom teeming process, the mould powder should be

added at an appropriate level. On one hand, because the rising air bubbles

can result in strong surface turbulence, to avoid slag entrapment, the

mould powder should be added at a relatively high level where all the air

bubbles had spouted out. On the other hand, to protect the molten steel

from reoxidation, the mould powder should be added as early as possible,

which means adding the mould powder at a relatively low level or using a

larger filling rate. In conclusion, the level to add the mould powder should

take both the filling rate and rising of air bubbles into account.

4.2.2. Velocity fields of the flow

(a) Velocity field at t=60s

(b) Velocity vector field at t=20s

Fig. 4.2 Predicted velocity profile on the symmetry plane, for the model with 15mm-diameter equal nozzles and 0.6m/s inlet velocity

water Interface

Velocity, m/s

Interface

air


60

Fig.4.2 shows the predicted velocity profile on the symmetry plane for the

model with four 15mm-diameter nozzles and 0.6m/s inlet velocity. It can

be seen that the liquid flow from bottom nozzles acts as powerful

submerged jets directed upward, and impinges on the water-air interface,

then results in humps on the surface. The velocities of the liquid jets are

considerably larger than that in the zone which is far away from the jets.

The velocities at each nozzle are directed upward and have different values.

As observed in the water model experiments, the shapes of the hump

above each nozzle were different, which were supposed to depend on the

energy flux of the water jets though the bottom nozzles. Hence, the velocity

and energy flux at each nozzle were studied.

0 5 10 15 20-0.3

0.0

0.3

0.6

0.9

1.2

1.5

Nozzle A

Nozzle B

Nozzle C

Nozzle D

Time, s

Ve

rtic

al velo

city c

om

po

ne

nt, m

/s

Fig. 4.3 Time variations of the vertical velocity component at the center point of each nozzle, for the model with 15mm-diameter equal nozzles

and 0.6m/s inlet velocity

Fig.4.3 shows the time variations of the vertical velocity component at the

center point of each nozzle, for the model with 15mm-diameter equal

nozzles and 0.6m/s inlet velocity. At the beginning of teeming, it is air or

mixture of air and water that flows through the nozzles, and therefore

causes strong velocity fluctuation. The velocity fluctuation of nozzle A is the

largest because most of the air flows out through nozzle A. After 8s of

teeming, it is totally water that flows through each nozzle and then the

velocity achieves stability. The velocity values are related to the position of

the nozzles. In this case, nozzle A has the smallest velocity of 0.417m/s, and


61

the velocity increases with the increasing distance from the nozzle to the

vertical sprue.

Tab. 4.2 Influence of model parameters on the vertical velocity component and energy flux of each nozzle

Nozzle diameters from A to D (mm)

Filling rate

(m/s)

Vertical velocity (m/s) Kinetic energy flux ( ×10-3 J/s)

Nozzle A

Nozzle B

Nozzle C

Nozzle D

Nozzle A

Nozzle B

Nozzle C

Nozzle D

Sum

4 × Ø15 0.60 0.417 0.496 0.568 0.590 4.59 7.38 11.2 12.7 35.87 0.47 0.327 0.389 0.445 0.463 2.21 3.58 5.43 6.13 17.35 0.31 0.217 0.258 0.294 0.305 0.64 1.03 1.54 1.75 4.96

4 × Ø25 0.47 0.050 0.045 0.165 0.266 0.02 0.017 1.05 4.53 5.62 12.5-15-22.5-25

0.47 0.144 0.111 0.207 0.288 0.14 0.09 1.37 5.68 7.28

25-22.5-15-12.5

0.47 0.128 0.266 0.344 0.341 0.44 3.06 2.54 1.90 7.94

Moreover, the influence of filling rate and nozzle dimensions on the vertical

velocity and kinetic energy flux through each nozzle was investigated and

listed in Tab.4.2. The kinetic energy flux is related to the velocity of the fluid

passing through the cross section of the nozzle and given by the following

equation:

Az dAuE3

2

1

Where is density of the fluid; A is cross sectional area of the nozzle; uz is

the velocity component perpendicular to the cross section of the nozzle.

The vertical velocity and kinetic energy flux indicate the stirring force of the

flow through each nozzle. Both of the velocity and energy flux significantly

reduce with the decrease of filling rate. Generally, the velocity and energy

flux of nozzle D are larger than that of the other three nozzles, except for

the model with 25-22.5-15-12.5 mm nozzles, in which case the velocity of

nozzle C is larger than that of nozzle D and the energy flux of nozzle B is the

largest due to a larger nozzle diameter.


62

4.2.3. Comparison with the water model experiments

Both of the computational and water modelling found that there were four

humps at the top surface because of the submerged water jets. The hump

heights were measured by water model experiments, as described in

Chapter 3. In this section, the numerical simulation results are compared

with the corresponding experimental results.

0.00 0.05 0.10 0.15 0.20 0.25 0.300.000

0.003

0.006

0.009

0.012

0.015

Nozzle dimension: 4 × 15mm


OpenFOAM Water model

Nozzle A

Nozzle B

Nozzle C

Nozzle D

Liquid level, m

Hu

mp

he

igh

t, m

Fig. 4.4 Comparison of the hump height above each nozzle for the model

with 15mm-diameter equal nozzles and 19L/min filling rate

Fig.4.4 compares the predicted and measured results of the hump height

above each nozzle for the model with four 15mm-diameter equal nozzles

and 19L/min filling rate. They are in good agreement and reveal that the

hump height above nozzle D is the largest while that above nozzle A is the

smallest. This is consistent with the variation of vertical velocities at the

bottom nozzles, as listed in Tab.4.2. Moreover, the hump height shows a

decreased tendency with rising liquid level, as a result of reduced liquid-jet

impinging force on the surface, which is because that the input kinetic

energy at the bottom nozzles is transferred to gravitational potential

energy.

At a certain liquid level, up to four humps form at the top surface. A larger

hump height indicates stronger surface turbulence and therefore increases

the risk of slag entrapment. Hence, more attention should be paid to the

maximum hump heights. Generally, for a model with four equal nozzles,

the maximum hump heights were found above nozzle D, whereas for a


63

model with unequal nozzles that may be found above other nozzles. For

example, the maximum hump heights were found above nozzle C for the

model with 25-22.5-15-12.5 mm nozzles.

0.00 0.05 0.10 0.15 0.20 0.25 0.300.000

0.003

0.006

0.009

0.012

0.015

Nozzle dimension: 4 × 15mm

OpenFOAM Water model Filling rate

19L/min

15L/min

10L/min

Liquid level, m

Maxim

um

hum

p h

eig

ht,

m

0.00 0.05 0.10 0.15 0.20 0.25 0.300.000

0.003

0.006

0.009

0.012

0.015


OpenFOAM Water model Nozzle dimension

4 × 15mm

4 × 25mm

12.5-15-22.5-25mm

25-22.5-15-12.5mm

Liquid level, m

Maxim

um

hum

p h

eig

ht,

m

(a) (b) Fig. 4.5 Comparison of the hump height variation with: (a) filling rate; (b)

nozzle dimensions

Fig.4.5 shows the influence of model parameters on the maximum hump

heights, investigated by both OpenFOAM simulation and water model

experiments. From Fig.4.5(a), both of the predicted and measured results

show reduced maximum hump heights with decreasing filling rate.

Comparison of the maximum hump heights for four groups of nozzle

dimensions in Fig.4.5(b) reveals that: at low liquid level, the model with

15mm-diameter equal nozzles has the largest hump height, however, it

rapidly reduces with rising liquid level; at high liquid level, the concerned

nozzle dimensions have little influence on the hump height.

4.3. Conclusions

The fluid flow during bottom teeming process of large steel ingot was

investigated by OpenFOAM simulation. The predictions obtained from the

numerical simulation were in good agreement with the water model

experiments. Moreover, the numerical simulation can give more

quantitative information about the flow fields, especially about the velocity

field.


64

At the beginning of teeming, the incoming water flow pushes the air out

through bottom nozzles, especially through the first nozzle (Nozzle A). The

rising air bubbles can lead to surface turbulence and further increase the

risk of slag entrapment. Therefore, it is not recommended to add the mould

powder at a low liquid level with air bubbles. It takes more time for a

smaller filling rate to spout out all air bubbles. However, the contact

between the mould powder and molten steel cannot be too late, otherwise

it will increase the risk of reoxidation. So, the level to add the mould

powder should take both the filling rate and rising of air bubbles into

account.

After all air spouts out from the bottom nozzles, the jet velocity and kinetic

energy flux of each nozzle are stable. With rising liquid level, the input

kinetic energy at the bottom nozzles is transferred to gravitational

potential energy, and then the hump height decreases.

5. Simulation of solidification process with OpenFOAM software

65


A liquid-solid 2-phase solidification model based on OpenFOAM software

was developed to predicate the macrosegregation of steel ingots. Then the

solidification model was performed on a steel ingot and the results were

compared with the experimental measurements from literature.

5.1. Liquid-solid 2-phase model with phase change

In this model, the mass transfer, melt convection, heat transfer as well as

solute transport were described using Euler-Euler two-phase approach. The

nucleation, grain growth and grain movement were also involved in the

model, which makes it possible to calculate the mass and solute transfer

between the liquid and solid phases.

Indeed, the present model was developed based on the previous

multiphase solidification models of M. .Combeau [66, 67],

M.Wu and A.Ludwig [46, 47, 68-70], C.Beckermann [71], W.Li [72] and W.Tu

[73].

5.1.1. Model assumptions

The solidification model was developed based on the following

assumptions:

The mould filling process is not considered and the solidification starts

from the total liquid phase as the temperature decreases. Two phases

are defined: the liquid phase (l) and solid phase (s). The corresponding

mass fractions have the relationship of .

The liquid phase is Newtonian and incompressible. The liquid flow is

laminar with a constant dynamic viscosity .

The solid phase consists of equiaxed grains, and the grains are globular.

The viscosity for the mixture of liquid and solid grains is calculated by

, where and represent the viscosity of the liquid

phase and solid phase, respectively. In mushy region, the mixture of

liquid and solid grains still retain some fluidity, like slurry. The viscosity


66

of the mixture can be described as relative to the viscosity of the liquid

phase: , where is the relative viscosity (dimensionless).

Therefore, in the mushy region the viscosity for the solid phase can be

expressed as: )1(/ srsls ff . Depending on the concentration of

the solid grains, several models for describing the relative viscosity

were proposed. In this study, the model c

sfc

ssr ff5.2

)/1( was used,

where is the fraction of solid phase and is the packing limit [71].

Once the solid fraction reaches to the packing limit, the viscosity of solid

phase is assumed as an infinitely large value. With this method, nearly

zero velocity will be obtained in the packed bed region. Overall, the

viscosity of solid phase can be defined as [71]:

when , )1()/1(5.2

s

fc

ss

s

l

s ffff

cs ;

when , is infinitely large.

The densities of the liquid and solid phases are equal and constant,

. In the momentum equation, the Boussinesq approximation for

buoyancy-driven flow is used to take into account the influence of

temperature and solute concentration on the liquid density [34, 35].

)]()(1[, reflCrefTrefleff CCTT

Where: p

TT

1 is the thermal expansion coefficient;

pl

CC

1 is the solute expansion coefficient.

The shrinkage porosity is not taken into accounted, and the control

volume of the mixture is saturated, i.e., , where denotes

the volume fraction of the solid phase and denotes that of the liquid

phase.

The temperatures of the liquid and solid phases are equal, i.e.,

.


68

)]()(1[ ,refllCrefTleff CCTT

The momentum exchange rate from liquid to solid phase, Uls, consists of

two parts: d

ls

p

lsls UUU . p

lsU is the part due to phase change, and it can be

calculated by: *UU ls

p

ls M , with lUU* for solidification and sUU* for

remelting [46, 68]. d

lsU is the part due to drag force, which can be calculated

by )( slls

d

ls K UUU . There are two methods to obtain the drag force

coefficient lsK :

(1) One-region method (valid for ) [68, 74]:

2

2

2 4

p

l

llsd

fK

with: 2/1

65

5 1

2332

3/42

2

9

p

s

C

f

3/1

sf

17.0

7.00

163.0lg26.1

2

l

l

e

e

pf

fC

The shape coefficient can be simplified to 1 for globular equiaxed grains.

(2) Two-region method [67]:

At the region with low solid fraction (valid for )

The flow regime in this region like free particles, and the drag force can be

modeled using the well-known Stokes law. For the free particle regime, the

drag coefficient for a single sphere is modeled as:

sl

p

ds

lsd

CfK UU

4

3

with: ie

kes

d CCf

CRe

48


72

of the heterogeneous nucleation sites is limited. Once a nucleation site is

occupied, the available nucleation sites will lose one. Therefore, the

instantaneous nucleation rate depends not only on the maximum density

of the potential nucleation sites np, but also on the grain density at that

time n(t). The heterogeneous nucleation rate Ns is expressed as [75]:

TkTs

fptnn

dt

tdnN

Bf

sl

cps 2

3

0)(

)(

3

16exp))((

)(

where: np is the maximum density of the potential nucleation site, and in

this study we assume np=2.5 1011 m-3. n(t) is the grain density at time t,

which can be obtained from the grain transport equation. 0 is the atomic

vibration frequency being about 1013s-1. pc is the probability of capturing an

atom at the surface of nucleus. We assume that there is no difficulty in

attaching an atom to the surface, so pc 1. sl is the interfacial energy, and

sf is the entropy of fusion. For the molten steel, sl =0.204 J m-2 and

sf=1.07 10-6 J m-3K-1. B is the Boltzmann s constant with the value of

1.38 10-23 J K-1. is the wetting angle ranging from 0 to , which indicates

the possibility to form a solid nucleus on the surface of the foreign

substrate, as illustrated in Fig.5.1.

Fig. 5.1 The nucleation of a spherical solid cap at a liquid-substrate

interface [75]

)(f is a geometric factor given by the ratio of the volumes of the spherical

solid cap and a full sphere of the identical radius, calculated by:

4

)cos1)(cos2()(

2

f


73

Fig. 5.2 The function of )(f for heterogeneous nucleation [75]

The nature of the heterogeneous nucleation is determined by the function

)(f . As can be seen from Fig.5.2, for , we have 1)(f , in which case

the nucleation is similar to homogeneous nucleation. For 0 , we have

0)(f , in which case the nucleation is similar to start on the fragment of

the solid. Above all, the value of is of crucial importance for the

heterogeneous nucleation rate.

is the undercooling, which serves as the driving force for nucleation,

defined as:

TmCTT lm

5.1.3. Solution algorithm

The above equations were edited into a solidification solver based on

OpenFOAM software, and discretized using the finite volume method.

There are 9 unknown fields to be solved: fl, fs, Ul, Us, P, T, Cl, Cs and n. The

liquid and solid phases share a single pressure field p, and also the

temperature field T.

Fig.5.3 shows the flowchart of the solution scheme. To start, the initial

conditions of the fields are read. At each time step, firstly, the mass

conservation equations are solved to get the fields of fl and fs. Secondly, the


74

momentum equations are solved to get intermediate velocity fields,

without the consideration of the pressure and buoyancy terms in the right

side of the momentum equations. The coupling of velocity and pressure is

handled by PISO algorithm (Pressure implicit with splitting of operator). The

intermediate velocities do not satisfy the mass conservation equations. To

ensure mass conservation of each phase, a pressure equation is

constructed using the velocity flux by considering the mass conservation

equations. After solving the pressure equation, the flux and velocity are

corrected. Next, solve the energy equation to get the temperature field.

After that, the concentration equations are solved to obtain the Cl and Cs

fields. Then calculate the undercooling T and nucleation rate Ns to solve

the grain transport equation and get n field. Finally, other parameters are

updated for the next time step, such as the transfer rate Mls, the main

grain diameter ds, the interfacial area concentration Sv, and the momentum

exchange coefficient Kls. The iterative procedure stops as the stopping time

is reached.


75

Fig. 5.3 Flowchart of the solution scheme


78

transfer in the walls is heat conduction which obeys Fourier's law. For the

side walls, the contact resistance between the outer wall and ambient is

evaluated by the radiation heat transfer. For the bottom wall, it contacts

with ground, so the heat transfer coefficient was assumed to be a relatively

small value. The top side was set as insulating boundary.

For the numerical implementation of the solidification, a user-defined

thermal boundary condition type was developed in OpenFOAM. In the

boundary condition, no heat accumulation through the mould wall was

assumed, meaning that the heat flux should balance at the boundary.

According to the Fourier's law, we have:

hB

TT

Rl

TTq

mould

w

cmix

w

/1//

11

Therefore the variable Tw1 can be solved as the temperature field at the

boundary of mould walls. The thermal boundary conditions used in the

simulation are summarized in Tab.5.1, similar with that of A. Kumar [76].

The employed thermo-physical properties and other parameters are listed

in Tab.5.2.

Tab. 5.1 Thermal boundary conditions used in the simulation Top side with powder Temperature of zero gradient (insulation) The contact resistance Rc for air gap

Rc = 0.0035 fs W-1m2K

Interface between the mould and ambient air

W/(m2K), =0.9, =293K

Interface between the hot-top refractory material and ambient air

W/(m2K), =0.5, =373K

Interface between the bottom wall and ground

= 100 W/(m2K), =373K

Thermal conductivity of the mould

= 26.3 Wm-1K-1

Thermal conductivity of the hot-top refractory

= 1.4 Wm-1K-1


79

Tab. 5.2 Thermo-physical properties and model parameters Property Values in liquid or solid phase

when , )1()/1(5.2

s

fc

ss

s

l

s ffff

cs ;

when , is infinitely large.

As listed in Tab.5.2, the densities of the liquid phase and the solid phase are

assumed to be equal.

5.2.2. Results

The solidification model was a 3-dimensional model with the shape of cube.

The transverse section of the model was a square, and the longitudinal

sections through the median line A- , diagonal line B- , and the boundary

line C- , as shown in Fig.5.6. The solidification fields on

the longitudinal sections through these 3 lines were investigated. After a


81

(a) Velocity vector field (b)Temperature field (c) Concentration field Fig. 5.8 The solidification fields on the A-

Fig.5.8 shows the velocity vector, temperature, and concentration fields on

the A- Without the

consideration of filling process, the flow in the mould is driven by the

thermal and solutal buoyancy force, and the movement of the solid grains

can also cause a drag force on the surrounding melt. Near the mould walls,

because of the strong heat transfer, the thermal buoyancy force dominates

a downward flow. The downward flow changes direction as contacts with

the mould bottom, that moves inwards and then upwards in the middle

region of the ingot, as can be seen in Fig.5.8(a). The melt flow transports

the grains from the bottom center to the upper region, and then the grains

sink down forming a vortex-like contour line (see Fig.5.7). In this stage, at

the near-wall region and bottom, where the temperature is lower and the

solid phase firstly appears, the solute is precipitated from the mushy region

simultaneously, forming solute-poor solid phase. At the hot-top, because

of the lower heat transfer rate through refractory material, the

temperature keeps higher.


82

t=300s t=800s t=1600s

t=2400s t=3200s t=4100s

Fig. 5.9 The sequence of solid fraction field fs on the A-section


83

The progress of solidification can be presented by the time evolution of

solid fraction fs, as shown in Fig.5.9. The contour lines of solid fraction were

also plotted. The solid fraction of 0.637 was assumed as the packing limit,

so the solid phase in the mushy zone would be blocked when the local solid

fraction is larger than 0.637. The solid fraction of 0.99 represents that the

solidification in the local control volume is nearly completed. It can be seen

that, initially the contour lines of the solid fraction are U-shaped. Because

of the intensive heat transfer from the side walls, the temperature near the

side walls is much lower and the solid phase is formed much earlier. While

at the bottom, the heat transfer is relatively slow, and it stays in the mushy

region for a longer time. At the top region, the phase transfer rate is very

slow, due to the hot-top refractory material and insulating powder,

therefore, the contour lines of solid fraction becomes trumpet-shaped and

it takes a long time to finish the solidification. When the ingot is already

almost completely solidified, the near-top region is still mostly liquid. After

4100s, the liquid is completely solidified.

The distribution of carbon concentration reveals the degree of

macrosegregation. A variable, macrosegregation ratio R, was employed to

denote the macrosegregation, defined as:

0

0

C

CCR

where C0 is the initial carbon concentration. In this model, C0=1.01 wt%. For

the region where C>C0, we have R>0, then the segregation is positive; and

conversely that is negative segregation.

Fig.5.10 shows the sequence of the carbon concentration field at the A-

longitudinal section, plotted with three contour lines of macrosegregation

ratio: R=-0.1, 0, and 0.1. The white points in the figure were numerical

errors. From the contour lines of R=-0.1, we can see clearly the

development of the cone-shaped negative segregation, which expands

from the bottom of the ingot to the upper center. From the contour lines


84

of R=0 and 0.1, the curves in the upper center region changes from A shape

to M shape, which indicate the V-shaped positive segregation in the center.

The formations of V-segregation is related to the sedimentation of

equiaxed grains, that generated from the solute-rich melt, at the V-shaped

solidification front (see Fig.5.9). Strong positive segregation was predicted

at the top of the ingot.

t=800s t=1600s t=4100s

Fig. 5.10 The sequence of concentration field at the A-section

The solidification is completed at time 4100s. Therefore, the corresponding

concentration field represents the final segregation distribution. To

observe the region near the cone-shaped negative segregation clearly, a

partial enlarged plot was made to display the segregation field in detail, as

shown in Fig.5.11. Fig.5.11(a) shows the segregation pattern at the A-

longitudinal section from the height of 0.1m to 2m, colored by a narrow

range of value. From this figure, some channels can be observed, as the so-


86

measurements come from A. Kumar [76]. Both of the predicted and

measured results show positive segregation at the hot top, and negative

segregation at the bottom region of the ingot, up to the height of about 2

meter. However, the degree of the predicted segregations is stronger than

the measured segregations.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

Experiment by A. Kumar [65]

Predicted by X. Zhang, this work

Distance from center, m

(C-C

0)/

C0

(a) Along the median line A- of the transverse section

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

Experiment by A. Kumar [65]

Predicted by X. Zhang, this work

Distance from center, m

(C-C

0)/

C0

(b) Along the diagonal line B- of the transverse section

Fig. 5.13 Comparison of the predicted and measured segregation ratio in the transverse section (Z=1.8m)

Fig.5.13 shows a comparison of the predicted and measured segregation

ratio in the transverse section, which is at the height of 1.8m. Both of the

segregations along the median line and along the diagonal line of the


88

transfer and solidification. The grain morphology at the hot top is more

complicate, with fine grain structure in the center which is surrounded by

coarse grains. Also the fields at the transverse section of Z=1.8m were

plotted. As can be seen that, the 4 corners have higher grain density and

smaller grain diameter, which is considered to be resulted from the strong

cooling at the corners.

5.3. Attempt on the coupling of mould filling and solidification process

In the solidification model developed above, only solid and liquid phases

were considered and the mould filling process cannot be simulated. In the

real ingot casting process, before the molten steel flows into the ingot

mould, it is totally air phase in the mould. As molten steel flows in, the air

will be pushed out from the top side of the mould. During the filling process,

with the decrease of temperature, the solidification may take place before

the finish of filling. Moreover, molten steel through the bottom nozzle can

induce a liquid jet. This stirring flow jet has a strong influence on the melt

convection in the mould, and therefore, it may impact on the growth of the

solid dendrites.

So far, most of the commercial solidification softwares divide the casting

process into two steps. The first step is mould filling, and the second step

is solidification, which assumes that the solidification starts after the mould

is fully filled. It is the same situation with my solidification mode developed

above. In this case, the initial solidification during the mould filling stage

cannot be well simulated. To combine the mould filling and solidification

process, it should be a liquid-solid-gas 3-phase model with phase change.

An advantage of my solidification model is that, it was developed based on

OpenFOAM software, which is an open-source software with well compiled

code structure. It is possible to extend the function of my solidification

model by the addition of more equations in the solver. So far, much effort

has been made to do this work but not yet succeed.


90

grain interfacial area concentration Sv, mass transfer rate Mls, and finally

cause a fatal error on the liquid-solid phase change at the interface.

Although some assumed conditions of solidification at the interface had

been given, the calculation error occurred after some steps, which makes

the attempt on the coupling of mould filling and solidification process to

stop.

5.4. Conclusions

A solidification solver was developed based on OpenFOAM software using

the Euler-Euler two-phase approach. In the solver, the mass transfer, melt

convection, heat transfer as well as solute transport equations were

included. The nucleation, grain growth and grain movement were also

described, which makes it possible to calculate the mass and solute transfer

rate between the liquid and solid phases.

The solver was applied to simulate the solidification of a 3-dimensional

steel ingot. The evolution of the concerned fields was obtained, such as the

solid fraction field, velocity field, temperature field, concentration field and

grain density field. The predicted final macrosegregation pattern shows

strong positive segregation of carbon at the top of the ingot. While at the

bottom of the ingot, the segregation is negative with cone-shaped, and it

develops to the upper center of the ingot. The V-segregation at the upper

center and the channel-shaped A-segregation were also observed.

The predicted values of macrosegregation ratio were compared with the

experimental measurements from a literature. The comparison shows that

they generally were in good agreement, except that the degree of the

predicted macrosegregation ratio is much stronger than the measured one,

especially in the near-wall regions.

Extension of the liquid-solid 2-phase solidification model to a liquid-solid-

air 3-phase filling and solidification model was attempted. Due to the

numerical characteristic of the liquid-air interface, so far the attempt has

not succeeded yet.

6. Overall discussion

91


In this study, the bottom teeming process as well as the solidification

process of ingot casting was investigated.

Water model experiments were carried out to study the flow conditions

during bottom teeming process of a large steel ingot. From the water

model experiments, it was observed that water jets from bottom nozzles

impacted on the top surface, which can form humps on the surface and the

size of humps reduced with the rising liquid level. The experimental results

have proven that the filling rate and also the bottom nozzle dimensions

have a significant influence on the humps. Comparing the hump height

under different filling rates at the same liquid level, it was found that the

hump height increases with the increase of filling rate. We can attribute it

to the powerful impact force of a submerged water jet under a larger filling

rate. The hump is formed mainly due to this impact force on top surface.

The influence of bottom nozzles on hump height is not only related to the

size of the nozzles, but also related to the arrangement of different nozzles,

in particular of multi-nozzles. According to the following formula:

uAV

where is the total volume flow rate; A is the area of the nozzle cross

section; u is the velocity of the flow through nozzle. Under the same filling

rate , a larger nozzle area will result in a smaller velocity of flow through

the nozzle, which in turn leads to a weaker impact force on the top surface

and thus the resulting hump height is smaller. In case of multi-nozzles, not

only the size of each nozzle, but also the arrangement of nozzles can affect

the velocity through each nozzle. Water model experiments with four equal

bottom nozzles were conducted, and it was found that the hump above the

last nozzle, which is the farthest away from the vertical sprue, is the largest.

This means that the velocity through the last nozzle is the largest, as has

been proved with OpenFOAM numerical simulation. Comparing the water

model experiments with four unequal bottom nozzles arranged in


92

increasing size and in reverse order, little influence on the maximum hump

height was observed.

The numerical simulation of filling process with OpenFOAM software gave

more quantitative information about the flow field, and the predictions

were in good agreement with the water model measurements. From both

the water model experiments and OpenFOAM simulation, it was observed

that at the beginning of teeming, the incoming water flow pushes the

original air out mostly through the first nozzle which is the closest to the

vertical sprue. The air phase was pushed out as small bubbles. The rising air

bubbles cause strong turbulence. After all the air has been pushed out from

the runner, the water bath tends to be stable, only humps left on the top

surface. It was clear that for a small filling rate, more time is needed to push

out all the air bubbles. With the rising water level, the hump is reduced and

disappears when reaches to a certain water level, that was thought to be

related with the reduced impact force of water jet on top surface.

To study the molten steel-slag interface behavior, water model

experiments with oil addition were conducted. Vegetable oil was chosen as

an analogue of the fused slag phase, because that oil can float on water and

doesn't mix with water, like the behavior between molten steel and fused

slag phases. However, the density ratio of oil to water is not the same with

that of slag to molten steel. This may cause some uncertain difference

between the real molten steel-slag interface and simulated water-oil

interface behaviors. A better analogue of slag phase than oil may be found

in the future to give more accurate simulation.

As the oil film covers on water bath, during teeming the water jets from

bottom nozzles flow upwards and impinge on the oil phase, then the oil

film in the area above the jets may be open The

similar open between molten steel and slag phases in the real steel

ingot mould filling process indicates that the molten steel is exposed to air

and the risk of reoxidation increases, which is important to the quality of


93

steel ingots. It was proved that the filling rate, nozzle dimensions and oil

At a certain liquid

level, with the reduction of filling rate, the fraction of open surface

decreases, which is also resulted from the reduced impact force of liquid

jet on top surface. Covering on the water bath, the gravity force of oil phase

can suppress the breaking of open surface. So with the increase of oil

thickness, the fraction of open surface decreases. 7 groups of nozzle

dimensions were used in the water model experiments. Comparing the

open surface at the same water level of 0.3m, it was fund that the model

with 25-22.5-15-

In the real ingot filling process, the hump height is related with the surface

the degree of reoxidation of molten steel. To optimize the filling conditions,

the risk of both reoxidation and slag entrapment should be reduced, by

adjusting the related parameters, such as the filling rate, nozzle dimensions

and slag thickness.

Obviously, water model experiments can simulate the mould filling process,

which is only the initial stage of ingot casting. The following solidification

stage was not simulated by water models in this study. However, in our

research group, a small water model with NH4Cl solution was carried out to

simulate the solidification[77]. The temperature of some special points was

measured during solidification. Various solidification phenomena, such as

columnar and equiaxed growth, CET (Columnar to Equiaxed Transition),

sedimentation of the equiaxed grains were observed and quantitatively

analyzed. A disadvantage of the solidification water model was that the

dimension of the model was too small (130mm width x 210mm height x

18mm depth) and the model was filled from the top side. A large water

model with NH4Cl solution is expect to simulate not only the bottom

teeming but also the solidification process, after solving the control

problems of cooling condition. In addition, the solidification of NH4Cl


94

solution cannot simulate the macrosegregation phenomena which occurs

during the solidification of molten steel.

In this study, the solidification process was investigated with OpenFOAM

numerical simulation. The solidification solver was self-defined based on

several standard OpenFOAM multiphase flow solvers, by implanting the

governing equations of solidification. With the transport equations of mass,

momentum, heat, solute and grains, the concerned fields was solved,

including the solid fraction field, velocity field, temperature field,

concentration field and grain density field. After all the liquid was solidified,

the concentration field can indicate the degree of macrosegregation. As

agreed with the description in literatures, a cone-shaped negative

segregation at the bottom, positive segregation at the top, V-segregation

at the upper center of ingot, and channel-shaped A-segregation were

predicted. Regarding to the mechanism, the cone-shaped bottom negative

segregation is a result of the sedimentation of equiaxed grains, which are

mainly formed in the early stage of solidification and poor in solute. The

positive segregation at the top is caused by the buoyancy and shrinkage

driven interdendritic fluid flow during the final stage of solidification, where

the flow is enriched in solute. The V-segregation in the top center is

associated with large equiaxed grains settling down to the V-shaped

solidification front. The channel-shaped A-segregation is caused by the fact

that the liquid phase is enriched in solute with low melting points among

the dendrite due to the concentration and density difference. Near the cold

wall of ingot mould, it should be a region of inverse segregation, which is

positive and forms due to the motion of enriched interdendritic fluid

towards the wall to feed solidification shrinkage in the early stage of

solidification. However, in this study the near wall inverse segregation was

not successful predicted by the solidification model, which has some

deviations with the experimental measurements from literature.

The solidification model in this research was developed based on Euler-

Euler two-phase approach. The solidification process was simulated


95

starting from the uniform field which was completely filled with liquid melt.

In other words, the initial filling process was not simulated. Actually, the

solidification may takes place early before the finish of mould filling. The

flow field during filling has influence on the solidification structure, also the

formation of solid phase can change the flow direction. To couple the filling

and solidification process, the air, liquid and solid phases are all involved.

Therefore the present liquid-solid 2-phase solidification model does not

have capability to couple the filling process. To solve this problem, a set of

governing equations for the air phase should be added in the solver.

Simultaneously, the liquid-air interface variables should be carefully

defined in case of phase change. This is a numerical difficulty on the VOF

method. In addition, the introduction of the third-phase equations makes

it possible to simulate the pore formation. Further studies on the coupling

of filling and solidification process should be tried.

7. Summary

96

7. Summary

The flow conditions during the filling process are of great importance on

the quality of the solidified steel ingots. In this study, the fluid flow during

the bottom teeming process was investigated with water model

experiments and OpenFOAM simulation.

In water model experiments, water was used to simulate the molten steel

and vegetable oil was used to simulate the slag phase. The water-oil

interface during the bottom teeming process was observed to study the

molten steel-slag interface at the initial stage of mould filling. The influence

of model parameters, such as the filling rate, nozzle dimensions and oil

thickness, on the filling conditions was investigated, concerning two

aspects: one is the slag entrapment, and the other is reoxidation of molten

steel. Both of the two situations should be avoid to provide a better filling

condition. Moreover, the computational simulation on water-air two-

phase flow with the interFoam solver of OpenFOAM software was

performed. The obtained predictions were in good agreement with the

water model experiments.

The main conclusions about the study of filling process are summarized as

follows:

(1) At the beginning of teeming, the incoming water flow pushes the air out

through bottom nozzles, especially through the first nozzle which is near

the vertical sprue. The rising air bubbles can lead to surface turbulence and

further increase the risk of slag entrapment. Therefore, it is not

recommended to add the mould powder at a low liquid level with air

bubbles.

(2) The hump height, which can indicate the surface turbulence, is gradually

reduced with rising liquid level. To reduce the slag entrapment caused by

surface turbulence, the filling rate at low liquid level should be smaller.

7. Summary

97

(3) However, the initial filling rate could not be too small, in which case the

time for rising of air bubbles will be extended, and before the formation of

slag layer the contact time between the melt and ambient air will also be

extended, which will further increase the risk of reoxidation of molten steel.

(4) After the level of molten steel reaches to a certain height where the

hump is small enough, the filling rate can be increased gradually to increase

productivity.

(5) It should be noted that even at high liquid level, the filling rate cannot

be too large. Because at a certain liquid level, with the reduce of filling rate,

on one hand, the hump height decrease, thus the risk of slag entrapment is

reduced; on the other hand, the fraction of open surface decreases, thus

the risk of reoxidation is reduced.

(6) For a large steel ingot mould, it is better to design multiple bottom

nozzles to reduce the jet velocity through each nozzle. For a mould with

multiple nozzles of equal size, the velocity of the flow through the last

nozzle, which is the farthest away from the vertical sprue, is the largest. In

the experiment models, the model with four 25mm-diameter equal nozzles

shows better performance of filling conditions from the view of both slag

entrapment and reoxidation.

(7) With the increase of slag thickness, the open surface decreases and

therefore the risk of reoxidation is reduced. However, more slag addition

may lead to more slag entrapment and increase the production cost as

well.

Besides the filling process, the solidification process was also investigated

with numerical simulation. A user-defined liquid-solid two-phase

solidification solver was developed based on the software platform of

OpenFOAM, using Euler-Euler two-phase approach. The globular equiaxed

grains was assumed as the solid morphology. In the solver, governing

equations about the mass transfer, melt convection, heat transfer, solute

7. Summary

98

transport, nucleation and grain transport were included, so that the

solidification as well as macrosegregation formation can be simulated.

The solidification solver was performed on a 3-dimensional model of a

reported steel ingot. The solid fraction, velocity, pressure, temperature,

concentration and grain density fields were calculated. The

macrosegregation was indicated by the carbon concentration. From the

predicted macrosegregation pattern, the cone-shaped negative

segregation at the bottom, positive segregation at the top, V-segregation

at the upper center of the ingot, and the channel-shaped A-segregation

were obtained. The simulation results of macrosegregation ratio on certain

lines were generally in agreement with the experimental measurements

from the literature, except for same deviations at the bottom and the near-

wall regions, where the predicted degree of negative segregation was much

stronger than the measured one.

In the present liquid-solid 2-phase solidification model, it was assumed that

the solidification occurs after the mould has been filled with liquid melt,

which means that the mould filling process was not coupled with the

solidification process. Extension of the liquid-solid 2-phase solidification

model to a liquid-solid-air 3-phase filling and solidification model was

attempted. Due to the numerical characteristic of the liquid-air interface,

so far the attempt has not succeeded yet. Further studies on this topic

would be conducted in the future.

8. Reference

99

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