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1990

Fluid dynamics and droplet generation in the BOFsteelmaking processHe QinglinUniversity of Wollongong

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Recommended CitationQinglin, He, Fluid dynamics and droplet generation in the BOF steelmaking process, Doctor of Philosophy thesis, Department ofMaterials Engineering, University of Wollongong, 1990. http://ro.uow.edu.au/theses/1497

FLUID DYNAMICS AND DROPLET GENERATION IN THE BOF STEELMAKING PROCESS

A thesis submitted in fulfilment of the requirements for the award of the degree

Doctor of Philosophy

from

THE UNIVERSITY OF WOLLONGONG

by

H E Qinglin, B.Sci., M.Sci.

Department of Materials Engineering 1990

Candidate's Certificate

This is to certify that the work presented in this thesis was carried out in

the laboratories of the Department of Materials Engineering in the

University of Wollongong and has not been submitted to any other

university or institution for a higher degree.

ABSTRACT

The present project was conceived as a fundamental study of the interaction between

oxygen jet and liquid metal bath and the effect of bottom blowing on the interaction in the

combined blowing B O F steelmaking processes with respect to droplet generation due to

the jet impingement, the droplet size distribution and the droplet residence time.

Mechanisms of droplet generation and mechanisms of the effect of bottom blowing on the

droplet generation were investigated in a 2-D water model, using high speed

cinephotography. T w o mechanisms of the droplet generation, "dropping" and

"swanning", were found, corresponding to low and high jet gas flow rates respectively.

Ejection of individual droplets and liquid fragments are characteristics of the "dropping"

and the "swarming" regions respectively. It was found that the significant increase in the

droplet production due to bottom blowing is principally caused by the interaction between

the top and bottom blowing in the impingement zone, and not by the bottom blowing as

such.

The droplet production, droplet size distribution and droplet residence time were

experimentally studied in a wide range of blowing parameters such as gas flow rates

through top lance and bottom tuyeres, lance height and bottom tuyere location etc., using

2-D and 3-D water modelling and 3-D mercury/glycerine modelling. The relationship

between those three phenomena and the blowing conditions were established. The

evidence obtained from this study suggests that there is a strong indication to take the

momentum number as a link between the model and the prototype in terms of droplet

generation due to an impinging gas jet

All findings from this study can be explained based on the "ripple theory" of the droplet

generation recommended from this work.

ACKNOWLEDGEMENTS

I wish to express m y gratitude to m y supervisor Professor N. Standish for his expert

guidance and willing assistance throughout this project.

I am also grateful to Dr. G. R. Belton, who acted as my co-supervisor, for his invaluable

suggestions during the period of m y study.

Thanks are due to Dr. C. Dobson for his helpful discussion, and to Mr. C. Carey for his

continual assistance.

Thanks are also extended to Ms. Ann Webb for her excellent typing.

Financial support by BFIP Steel International Group is gratefully acknowledged.

Finally, I wish to thank my dear wife Li for her encouragement and understanding

throughout this project.

P U B L I C A T I O N S

1. "Drop generation due to an Impinging Jet and the Effect of Bottom Blowing in the

Steelmaking Vessel", ISU International, Vol.29 (1989), No.6 (June), pp.455-461.

2. "A Model Study of Droplet Generation in the BOF Steelmaking", ISIJ International,

Vol.30 (1990), No.4 (April), pp.305-309.

3. "A Model Study of Residence Time of Metal Droplets in the Slag in the BOF

Steelmaking", ISU International, Vol.30 (1990), No.5 (May), pp.356-361.

LIST OF SYMBOLS

A

c

cwp

Fc

Fg

Fu Fug

Fs

g h

m

mi

mg

M;

Mm

nG P Po r

r0 R d

t

tR

tv

U

wp

: cross-sectional area of jet.

: carbon content.

: cumulative weight percentage of droplets, %.

centripetal force.

gravitational force.

viscous force in liquid phase.

viscous force in gas phase.

: surface force.

: gravitational acceleration, cm/s2.

: lance height, cm.

: weight of droplets, g.

droplet production, g/s or %.

top gas flow rate, 1/min.

jet momentum flux.

• jet momentum number.

jet penetration depth, cm.

phosphorus content of metal droplets.

phosphorus content of metal bath.

radius of droplet to be generated.

radius of lance nozzle, cm.

radius of curvature of crater surface.

droplet diameter, m m .

time.

reaction time of metal droplets in slag.

residence time of metal droplets in slag.

velocity.

weight percentage of droplet, %.

Greek letters

b : angle between tangent of crater surface and horizontal line. s : surface tension. r : density. \i : viscosity. d : thickness of boundary layer. t : residence time of droplet. tg : shear force at gas phase side. ti : shear force at liquid phase side.

Subscript

g

j 1

m

o

s oo

: gas phase.

: jet.

: liquid phase.

: centre-line of jet.

: outlet of lance nozzle.

: surface liquid of crater.

: bulk.

CONTENTS

Chapter I INTRODUCTION

Chapter H THEORETICAL ASPECTS AND PREVIOUS WORK

2.1 Refining Mechanism in B O F Steelmaking

2.1.1 "Hot spot" Theory

2.1.2 Metal/slag Emulsion

2.2 Analysis of Droplet Generation

2.3 Jet Characteristics

2.4 Behaviours of Impingement Zone

2.4.1 Flow Patterns in the Impingement Zone

2.4.2 Depth of the Cavity

2.5 Droplet Product of an Impinging Gas Jet

2.5.1 Droplet Production

2.5.2 Drop Size and Drop Size Distribution

2.6 Dimensional Analysis

Page

1

3

4

5

9

14

15

15

17

18

18

18

21

Chapter HI APPARATUS A N D P R O C E D U R E

3.1 Introductory Remarks

3.2 Apparatus

3.3 Procedure

25

25

26

27

Chapter IV RESULTS A N D DISCUSSION 30

4.1 Droplet Generation 30

4.1.1 Mechanisms of Droplet Generation 30

a. Under the condition of top blowing only 30

b. Under the condition of combined blowing 34

4.1.2 Effect of Blowing Conditions on Droplet Generation 36

a. Effect of top gas flow rate 36

b. Effect of lance height 38

c. Effect of bottom gas flow rate 41

d. Effect of position of bottom tuyere 42

e. Effect of other factors 44

(i) multi-hole nozzle lance 44

(ii) thickness of upper phase layer 45

4.1.3 Remarks on Similarity Criteria 46

4.2 Drop Size Distribution 47

4.3 Residence Time of Droplets 50

4.3.1 Definition of Mean Residence Time 50

4.3.2 Effect of Blowing Condition on the Residence Time 53

4.3.3 Discussion 55

Chapter V CONCLUSIONS 59

REFERENCES 62

APPENDLX 68

1

Chapter I. INTRODUCTION

In a basic oxygen steelmaking converter, an oxygen jet of high velocity impinges on the

surface of the molten bath and ejects a great number of metal droplets, having the bath

composition, into the slag. The individual droplets are refined down to lower contents of

impurities due to the reactions between the droplets and the slag and also between the

droplets and the oxidizing gas. After a certain residence time the refined droplets fall

back into the bath again so that they cause the bath refinement due to mixing. The

refining rate due to the reaction of the dispersed droplets should depend on three factors:

(i) the total amount of droplets in the metal/slag emulsion,

(ii) drop size distribution, and

(iii) residence time of the droplets.

The former two provide the total interfacial area for reaction and the latter allows time for

the droplets to react with slag or oxidizing gas. Therefore, an understanding of those

phenomena is needed to establish a dynamic control model of the BOF steelmaking

process.

Since the emulsion mechanism of the refining in the BOF steelmaking was realized the

metal droplet generation due to an oxygen jet has been the subject of investigation by a

number of metallurgists [15,17,26,27,30,33]. However, the mechanism of drop

generation is not well understood because of the complexity of the phenomenon, and a

lack of systematic investigations into the effect of various blowing conditions on the drop

generation, especially under the condition of combined blowing.

Meanwhile, many investigations [4-10,20-24,56-60] on the metal drop size and its

variation with blowing parameters have been also carried out under the condition of top

blowing only. Unfortunately, effect of blowing conditions on the droplet size in the

combined blowing process has not been investigated.

2

Very few experimental studies [34] on the residence time of the droplets have been

performed because of the difficulty in experiments. So far, available information on the

residence time is limited.

The purpose of the present work, therefore, is as follows.

(1) To understand the mechanism of the droplet generation due to an impinging gas jet

- this being fundamental to gaining an insight into the three factors mentioned above.

(2) To systematically investigate the variations of the droplet production with blowing

parameters, especially under the condition of combined blowing - this should help

understand the total effect of how the blowing conditions influence the droplet

production.

(3) To study the effect of bottom blowing on the drop size and size distribution in order

to obtain the information of total interfacial area for reactions under various blowing

conditions in combination with the data of the droplet production.

(4) To investigate the residence time of the droplets in the upper phase, with emphasis

on the effect of the blowing parameters on the residence time rather than its absolute

values, this being necessary information for calculating the degree of dephosphorization

and decarburization.

3

Chapter II. T H E O R E T I C A L A S P E C T S A N D P R E V I O U S W O R K

2.1 REFINING M E C H A N I S M S IN B O F STEELMAKING

Since the advent on a commercial scale at Linz, Austria, in 1952, the Basic Oxygen

Furnace (BOF) Steelmaking has grown rapidly and widely in the world steelmaking

industry. The raw steel production by B O F steelmaking surpassed Bessemer and electric

furnace outputs as much as twice and 1.5 times respectively by 1960, and drew even

with the rapidly declining open hearth by 1970. The world B O F capacity was 466 M

tons in 1978, which is equivalent to 5 3 % of the world total [1]. The reason for the

growth of the B O F steelmaking is based on the following advantages [2]:

(1

(2

(3

(4

(5

(6

(7

(8

extremely high speed of refining,

economy of labour,

modest capital requirement

low refractory usage,

comparative ease of fume control,

high quality of its products,

promise of full automation, and

regularity of its production cycle.

Among those advantages a primary reason for creating this forward position of the B O F

steelmaking process in comparison with other commercial methods of steel production is

due to its extremely high refining rate [4].

In association with the massive increase in output of the BOF steelmaking there has been

considerable research activity into the refining mechanism of the process.

The refining of liquid iron can take place by following five basic reaction mechanisms

[15] as schematically indicated by Fig.2.1. The reactions occur:

1. in the bulk of the bath,

metal/slag emulsion

droplets

slag

Figure 2.1 Potential BOF sleeimaking

reaction zones in the

4

2. between oxygen jet and liquid iron in the cavity,

3. between 'in flight' iron droplets and the gas phase above the bath,

4. between emulsified iron droplets and oxidizing slag,

5. between oxidizing slag and iron bath at the interface away from the cavity.

An equation for the refining rate in the converter, taking carbon as an example, may be

given as follows [34].

dc dc dc dc -rr (total) = -rr (impact zone) + -rr (emulsion) + -rr (in flight droplets)

dc dc + -rr (bath) + -rr (slag-bath interface) (2.1)

Usually, it is very difficult to differentiate between two bath type reactions - slag/bath

interface and bath itself, and between two droplet type reactions - emulsion and 'in-flight'

droplets. So those five basic reaction mechanisms are classified into three as follows:

JT (total) = -JT (impact zone) + -rr (droplets) + -r: (bath) (2.2)

The refining rate due to the bath-type reaction is very low in comparison with the other

two [34,37]. Thus, the refining reactions principally take place between the oxygen jet

and the iron bath in the impact zone and between the dispersed droplets and slag or

oxidizing gas, i.e.

dc dc dc -r- (total) = -j- (impact zone) + -^ (droplets) (2.3)

Each of the two mechanisms has been reported principally to predominate the overall

refining rate in the BOF steelmaking process in the literature [3-10,31,32,80-82,85].

2.1.1 "Hot spot" Theory

Early explanations of the high refining rate were based on the supposed existence of the

high temperature in the impingement zone [2,31,32,80-85], in which most of the

reactions were claimed to occur.

5

The temperature in the impingement zone was measured at 2200-2500°C with the aid of

an optical pyrometer [31, 32], 1950-2800°C with a type TsEP-3 photoelectric colour

pyrometer [80], and about 2200°C with a compact long-focus radiation pyrometer [81].

The temperature was also judged, but not measured, according to the brightness of the

impingement zone, to be in excess of 2200°C [2]. The experimental difficulties have led

to theoretical calculations [82-85] which gave divergent results, e.g. 2400°C [85] and

4150°C [82].

The temperature differences between the impingement zone and the metal bath were

reported to remain a constant, about 850°C [80] for varying oxygen flow rates, and to

vary between 480 and 630°C [81], depending on heat and mass transfer conditions.

However, although the temperatures are about 700-900°C higher in the impact zone than

in the bulk of the bath the idea of such a small reaction area and high reaction rate was

unacceptable in the face of a large body of chemical engineering experience. As a result,

doubts arose regarding the validity of the "hot spot" theory.

2.1.2 Metal/slag Emulsion

Since the early 1960s, people started to show interest in metal-slag emulsions which

contained a large number of metal droplets, and realized their importance to the BOF

steelmaking process. Initially, these droplets were quantitatively described by

Kozakevitch et al. [3] in connection with the foaming of basic phosphate slag in the

LDAC/OLP process. The nature of these processes when refining high phosphorus iron

is such that a foamy slag is a natural occurrence. Intuitively one would expect such a slag

terentrain a certain quantity of metal droplets. Kozakevitch found that this-was-indeed-the

case and reported discovering metal globules and large fragments of metal in the slag

samples. It was not possible for these workers to relate the chemistry of the metal

globules in the slag, exactly, to that existing in the bulk metallic bath at the same moment,

but they were able to conclude that decarburization of the metal occurred within the slag

6

emulsion. At one point, Kozakevitch made an extremely important and prophetic

statement, "One might even ask oneself whether in the swelling up of the slag the part

played by the release of C O inside the foam may not be more important than the direct

effect of the oxygen jet".

The rejection of the "hot spot" theory became complete when experimental evidence from

the U S A [4] and France [5] showed that the primary reason for the high rates of the

refining reactions was not to be found in the existence of a zone of high temperature but

in the fact that though the apparent surface area of the slag/metal interface was fairly small

compared to the total mass of the metal to be refined. In reality the high-velocity oxygen

jet atomized the metal into many tiny droplets which create an extremely large interfacial

area between metal and slag. It has been proved experimentally [33] that the creation of a

large number of metal droplets is an inherent feature of L D steelmaking because the

momentum of a normal L D jet is at least an order of magnitude higher than that required

theoretically to break up the metal surface [33].

The proportion of dispersed metal in slag is often surprisingly high, but varying with

location, with blowing time and from one blow to another. A result of analysis of

samples taken 3 min after stopping the blow showed that over 2 0 % of metallic iron can

be found in phosphate slags in the low-temperature range (of the order of 1580°C). Also

in-blow samples taken from overflown slags off the shell of the converter indicated that

more than 5 0 % of iron beads exist in the total sample. This means that the emulsion

contains more metallic iron than slag by weight [5].

A work by Meyer et al. [4,6] on the metal/slag emulsion, the samples of the emulsion

obtained by placing: a shallow steefpan~approximately 2x2 feet on the operating floor in

line with the tap hole to collect the material ejected out of the furnace through the hole,

showed that the formation of the metal/slag emulsion begins almost as soon as refining

itself. The emulsion contained 45-80% metal droplets by weight after 6-7 min in a 20-22

min blowing period; 40-70% at 10-12 min; and 30-60% at 15-17 min. The specific area

7

for reactions between the dispersed metal and the slag was of the order of 43-57cm2/kg

of hot metal charged. It should be pointed out that the above conclusions were based on

the samples taken from the upper portion of the converter. It could therefore be argued

that the lower portion of the emulsion might contain even larger fractions of metal.

The size of droplets ejected has been reported [4-10,20-24,46-60] to vary in the range

0.05-5.0mm. Separation and analysis of those droplets showed interesting results, as the

droplets were always found to be more decarburized, dephosphorizedand demanganized

than the metallic bath [4-7,10], about one-tenth those of the bath itself [3,72], sampled at

the same time. Fig. 2.2 [10] shows a typical result which indicates the difference in

phosphorus content between the droplets and the bath. In addition, the smaller the

droplets, the lower the carbon, phosphorus and manganese contents were.

Another evidence of the importance of the droplets for the decarburization was given by

Chatterjee et al. [8]. Some heats blown with a single-hole nozzle lance of 6 4 m m dia.

were compared with those blown with a 1 6 m m dia. single-hole lance in an identical

manner. Since under otherwise identical conditions the impulse of a gas jet is inversely

proportional to the cross-sectional area of the nozzle, the impulse of the oxygen jet

issuing from the 6 4 m m dia. nozzle was one-sixteenth that of the jet from the 1 6 m m dia.

nozzle. In the second period of decarburization (when the decarburization rate is a

maximum), the average rate of carbon oxidation was found to be 5-6kg/min in the 6 4 m m

dia. nozzles heats compared to 12-13kg/min in the other heats. This was because more

metal droplets were generated in the latter case than in the former one.

Further evidence to prove the emulsion mechanism of the refining reaction is the variation

of slag temperature during blowing. The slag temperaturexlimbs very rapidly,-as-shown-

typically by the data of Bardenhauer et al. [12]. Much of the heat released by silicon

oxidation is, therefore, not produced in the metal bath or at the point of impact of the

oxygen jet on the bath, but is produced within the slag itself. After 3-4 mins of blowing,

Blowing time , min

Figure 2.2 Variation of average phosphorus content of bath and metal droplets with blowing time

8

the liquid slag temperature can reach 2850°F or more, while the metal bath remains at

2300-2350°F.

On the basis of the results of the investigations into the emulsified droplets [3-15] a

refining mechanism model of the BOF steelmaking was constructed [10] as follows.

During the blowing process a stream of metal droplets with an initial composition, i.e.

that of the bath, is ejected out of the bath into the slag. The individual droplets are refined

down to lower contents of impurity elements due to the reactions between the droplets

and the slag and also between the droplets and the oxidizing gas. After the period when

the droplets are out of the bath, they fall back into the bath again so that they cause the

bath refinement due to mixing. The metal bath is turned over many times by the stream

of the metal droplets during the blow. This is usually called emulsion mechanism of the

refining in the BOF steelmaking. The emulsion mechanism is schematically shown in

Fig.2.3, taking phosphoms removal as an example.

Since the late 1970s the combined blowing BOF steelmaking has been developed and

widely applied in the world steelmaking industry, because of its potential of obtaining the

best characteristics of both top and bottom blowing processes. In a recent study by

Jahanshahi and Belton [18], on the kinetics of dephosphorization, it was found that the

rate of phosphorus removal from the metal bath is in broad accord with the proposed

emulsion mechanism. An interesting and practically important result was obtained from

analysis of plant data [18]. As shown in Fig.2.4 there is marked reduction in the degree

of disequilibrium when bottom bubbling is introduced into medium-soft blown heats.

Conversely, bottom bubbling has no statistically significant effect for hard blown heats.

In view-of the likelyemirisioirineehanriremfor^ephosphorization, several exploratory

cold model experiments were carried out in their work to determine if bottom bubbling

can significantly affect the ejection of droplets into a slag layer and if the above

observations can be accounted for by such phenomena. It was found from their model

experiment [18] that the interaction between the rising bubbles and the impinging jet can

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9

increase the relative weight of metal in the emulsion. Consistent with some of these

observations, the marked effect of bubbling on the phosphorus distribution for medium-

soft blown heats may be reasonably attributed to an increase in the droplet generation.

The lack of any effect on hard blown heats suggests that these may be in the regime

where any enhanced droplet formation is negligible. This explanation is supported by the

findings of the present study (see Section 4.1.2). The evidence from their work indicated

that the refining rate in the combined blowing process is also dominated by the emulsion

mechanism.

2.2 ANALYSIS OF DROPLET GENERATION

As with the movement of any other substance, the phenomenon that the droplets are

ejected by a gas jet impinging on a liquid surface must obey the laws of mechanics. A

theoretical explanation of the drop generation, based on a force balance, was

recommended by Kleppe and Oeters [16] (see Fig.2.5).

A depression forms, due to impact of the gas jet, in the liquid surface. The deflected gas

flowing along the surface of the crater exerts a shear force on the surface and drives the

surface liquid flow and subsequent circulation in the bulk of the bath [42,53]. Centripetal

force caused by gravity and surface force, Fgcosp+Fa, the surface liquid flowing at a

certain velocity tends to curvilinear motion. Drop ejection from the crater depends on the

balance of forces exerted on it. It is known that there are no droplets produced at the

edge of the crater until jet momentum at the liquid surface reaches a critical value,

although a depression forms in the liquid surface due to action of the jet. The reason for

this is that dense phase has a tendency of self-adjustment by changing the shape of the

depression to keep the force balance on the surfaceliquid, that is, the centripetal force

required for the surface liquid to tend to curvilinear motion is always equal to that being

exerted on the surface liquid by changing the radius of curvature of the depression

surface in this region. The force balance is as follows.

0) Q.

O imm

CO

c o CJ)

c o 03 CO CD U

CD

JZ

o •*-• CD mX.

in

oi CD >_

3

L

10

Fc = Fs + Fgcosp (2.4)

where

4 * us2

F c = ? n r3p. -j|-, centripetal force

F c = 7t r2 -TJ- , surface force

4 F g = o 7C r

3 p.g, gravity force

where r = radius of droplet to be generated

R = radius of curvature of depression surface

p. = density of dense phase

us = velocity of surface liquid

o = surface tension

The term on the left hand side of equation (2.4) is the centripetal force required for

surface liquid flowing at tangential velocity of us. S u m of the terms on the right hand of

eqn. (2.4) is the exerted centripetal force. Once the required centripetal force becomes

larger than that being exerted, due to further increase in gas jet momentum which leads to

increase in velocity of surface liquid, droplets will be ejected at the edge of the

depression. According to the above analysis, it can be concluded that, for a certain

system, any factor which is able to increase the shear force exerted on the crater surface

and/or the velocity of the surface liquid, can increase the rate of droplet generation.

From the above analysis it is seen that the gravity and surface force, FgeosP + FCT, which

cause the centripetal force, have a tendency to force the surface liquid to tend towards

curvilinear motion and thus restrict the departure of droplets from the crater. Therefore,

the higher the gravity and surface tension of the dense phase, the fewer droplets are

produced.

11

Shear forces from both gas and liquid phase side act on the surface of the crater. The

shear force from gas phase tends to accelerate the surface liquid and, conversely, the

other force tends to resist the movement of the surface liquid. According to Newton's

L a w of viscosity, for a given velocity gradient, the shear force is proportional to the

viscosity of the fluid. Therefore, surface velocity (i.e. drop production) increases with

increasing the viscosity of gas phase and decreasing that of dense phase. This conclusion

can be also obtained from the following derivation.

The shear force on the surface at gas side is,

H'Hfe) as) v 7x=o

With the known definition of Prandtrs boundary layer [73,74], we have

t dug\ _ Uoog - us

'g 9x k=o 5c

(2-6)

Considering that us « Uoo,g and substituting eqn. (2.6) in eqn. (2.5) w e obtain

H = ^ (2-7) 5g

O n the liquid side, the shear force is

x , = w(^L (28)

again with Prandtl's boundary layer, w e have

because of Uoo/« us

x/ = n / ^ (2.10)

12

The shear force on both sides of the surface must be equal, that is,

x/ = xg (2.11)

and, M g T « = W ^ <2-12> 5 g o/

Rearrange eqn.(2.12), we have

us = | - , (2.13)

generally,

Uoog^uj (2.14)

thus

» , « £ * , (2.15)

where us = velocity of surface liquid

Uoojg = bulk velocity of reflected flow

Uooj = bulk velocity of dense phase

8g, 8; = thickness of boundary layers of gas and liquid

p.g, p./ = viscosities of gas and liquid

UJ = jet velocity at undisturbed surface of the bath.

From eqn. (2.15) it can be seen that the surface velocity is proportional to the viscosity of

gas phase, and inversely proportional to the viscosity of dense phase for a given jet

velocity.

To sum up, it is concluded that increases in dense phase density, viscosity and surface

tension tend to reduce the amount of droplets generated by an impinging jet. This

conclusion is identical to the results of recent experimental work by Tanaka [30]. In

addition, the result of Tanaka [30] suggested that splashing directions of droplets varied

with blowing conditions. The splashing angle against the bath surface increases with

w \ \

\ \

\ \

\ \

Figure 2.6 Variation of R and p along the crater surface

13

increasing jet momentum or decreasing lance height. This can be explained from above

force balance analysis by rewriting eqn. (2.4) in detail,

4 ^ us2 4 c, Q 2m:2G

^rcr^p -g- = n r3 p gcosp + R (2.16)

thus

^f- = | —+ cosf3R (2.17) 8 ^rp^g

From eqn. (2.17) it can be seen that the centripetal force exerted on the surface liquid

depends on the value of cosfiR, if r is assumed to be constant. A droplet will depart from

the cavity surface at the location where maximum value of cosfiR required for satisfying

the following inequality

u2 3 CF

— >§• + cosf3R (2.18) g ^rp^g

is obtained.

From Fig.2.6 it is seen that (3 and R increase along the surface in the direction towards

the bottom of the cavity. The calculation, assuming the profile of the crater surface to be

represented by sine-curve shows that the product, cosfiR also increases in this direction.

When the jet momentum is increased, or lance height is decreased the velocity of the

surface liquid is increased. This results in increasing the maximum value of cosfJR,

which means the position where a droplet departs moves towards the bottom of the

cavity. Because of the fact that a droplet is ejected along tangential direction and (3 is

larger at the lower position of cavity surface, the splashing angle increases with increase

in the jet momentum or decrease in the lance height.

CD

CD CD

CO

CO

o w v-CD O 03 i_

03 JC

O CN

CD i-m

3 cp LL

14

2.3 JET C H A R A C T E R I S T I C S

As discussed in Section 2.2, the jet momentum at the undisturbed surface of the bath,

which is affected by characteristics of the jet, is one of the main factors influencing the

droplet generation. The characteristics of a gas jet have been extensively studied both

theoretically and experimentally [61-68]. The jet structure is schematically shown in

Fig.2.7. Close to the nozzle a region of intense shear exists between the jet fluid and its

surroundings. This results in an acceleration of the surrounding fluid and a deceleration

of the jet. In most practical cases the flow is turbulent and eddies are produced which

diffuse towards the centre. The length of the potential core which is unaffected by the

diffusion of eddies has been reported to be between 3 and 7 times the exit diameter of the

nozzle [62,63]. The jet becomes wider downstream in the axial direction due to the

entrainnment of the surrounding fluid. There is a linear relationship between the distance

downstream from the nozzle and the corresponding width of the jet [69], i.e.

yb = cx (2.19)

where y. is half jet width, and x is the distance downstream from the nozzle, c is a

constant, usually c = 0.238 [69].

It has been proved theoretically and experimentally that the component of jet velocity in

the transverse direction is negligible, compared with that in the axial direction, so that the

axial component of the jet velocity is referred to as the velocity of the jet. The pressure in

the jet is uniform and equal to that of the surroundings. In these circumstances Newton's

Second Law of Motion shows that the momentum of the jet must be conserved, that is

jAPUj2dA =7tr02puo2 (2.20)

where A = cross-section area at a distance from the nozzle

rQ = radius of the nozzle

Uo = jet velocity at the outlet of the nozzle

uj = jet velocity at a distance from the nozzle.

15

The velocity profiles of the jet at different distances from the jet origin are similar. In

other words

^ = f ( n ) (2.2i)

The function f(T|) can be approximated by the following empirical formula [69],

^=(1-T]1- 5) 2 (2.22)

where r\ = y/y . y is the distance from the centre-line of the jet, UJ, um are velocity

profile and the centre-line velocity of a jet at a distance from the jet origin, corresponding

to y and y,. b

The centre-line velocity of a jet decreases downstream along the axis of the jet due to

momentum transfer between the jet and the surroundings. The centre-line velocity at a

distance from lance nozzle can be calculated by the following formula [69].

u m 0.97 00 (—+0.29)

ro

(2.23)

where a is a constant, determined experimentally: usually a = 0.07.

2.4 BEHAVIOUR OF IMPINGEMENT ZONE

2.4.1 Flow Patterns in the Impingement Zone

Jets impinging vertically on liquid surfaces give rise to oscillatory flows in the

impingement zone. The flow pattern influences the droplet generation in the cavity.

Molloy [26] suggested that there existed three main modes of flow, as described below:

(i) with a low jet velocity and/or a large nozzle height, a classical wall jet pattern

is formed with a slight surface depression (Fig.2.8a);

(a)Dimpling

(b)Splashing

/

V \ (c) Penetrating

it s A\ I'll

Figure 2.8 Comparative geometry of the flow modes

16

(ii) with increased jet velocity and/or reduced nozzle height, a shallow depression

forms in the liquid surface (Fig.2.8b); entrainment of the dense phase takes

place in the indent. The resulting production of large quantities of outwardly

directed droplets characterizes this pattern which is referred to as the splash

mode;

(iii) with further increased velocity and/or reduced nozzle height, much deeper

penetration of the bath takes place accompanied by an apparent reduction in

the amount of outwardly directed splash; this is referred to as the penetration

(Fig.2.8c).

The shallow indent of the splash mode tends to appear stable and axisymmetric with the

splash originating from the edge of the crater. The smooth indent does move about the

vertical axis of the jet, but the excursions are relatively limited [26]. In the penetration

mode the flow pattern becomes very complex. The flow develops non-symmetrical

patterns. Periodic horizontal and vertical movements of the impingement zone take place.

The crater oscillates in size, shape and position about the vertical jet axis [15,26,27,29]

due to the oscillation of the jet

Molloy [26] found that two-phase jet is formed due to entrainment of ejected liquid phase

into the jet in the penetration mode. This was also identified by Koria et al. [27] and

Sharma et al. [2] in their hot model experiments, from the observation of a bright flame in

the jet. It was suggested [26] that the vertical oscillation of the crater was caused by the

behaviour of the two-phase jet which tends to be intermittent in character. A deep cavity

is produced by the presence of a second phase in the impinging jet because the particles

of the dense phase tend to continue into the bath surface instead of following the less

dense phase around the curvature of the crater surface [28,29].

17

2.4.2 Depth of the Cavity

A number of studies [30,33,38-45,50,54] relating to the depth of the cavity formed in a

liquid surface due to the action of an impinging gas jet has been canied out. From the

results of a variety of gases with widely differing densities [33], it was found that the jet

momentum rather than the jet velocity is the variable determining the depression depth.

The depth increases with increase in the jet momentum at the liquid surface (by increasing

jet velocity or reducing lance height). It was found that the influence of the surface

tension and viscosity is small and the depth of the depression can be predicted by the

following equation derived from stagnation pressure analysis [43,50].

where the constant 115 was determined from experiments on free jet. The prediction of

this equation and the results from room temperature investigation agree satisfactorily in

splashing and non-splashing regions [30,34,50] so that this equation is valid both before

and after the onset of the splashing. The depth of the depression was found to be related

to the commencement of the splashing [32,38-42]. Investigations [38-40] at room

temperature using single liquids showed that splashing started at a definite or critical

depth of depression for each system. The results of Chatterjee [33], Mathieu [41] and

Wakelin [42] indicated that this depth decreased slightly with an increase inlance height

The above results suggest that in a particular system the critical depth of depression

depends primarily on the stagnation pressure. However, the small variation with lance

height indicates that the area over which the shearing forces act may be important As the

lance height is increased the area of the depression also increases and this probably

lowers the minimum stagnation pressure required for the break-up of the liquid surface.

1500

1000

500

Mj=1.89

8.75

10

d=0.42 cm

Lance height , cm

Figure 2.9 Relation between lance height and the amount of liquid splashed per unit time

18

2.5 D R O P L E T P R O D U C T O F A N IMPINGING G A S JET

2.5.1 Droplet Production

Many investigations [15,17,30,33,46,55] have been performed in terms of the effect of

blowing conditions on the amount of splash due to a gas jet impinging on a liquid

surface. From those studies it was generally concluded that the amount of droplets

ejected from the cavity increased with increase in the jet momentum at the bath surface

(by increasing jet momentum at nozzle or by reducing lance height) up to a maximum

value. Any further increase in the jet momentum [33,49] or decrease in the lance height

[30,33,47,48] beyond this caused the amount of splash to be reduced. Figure 2.9 shows

a typical result of Tanaka et al. [30] which illustrates the relationship between the amount

of splash and lance height at a given jet momentum. Maximum amount of liquid ejected

was obtained at a certain lance height in each case.

Under the condition of combined blowing, apart from the jet momentum and lance

height bottom flow rate and position of bottom tuyere are also factors influencing the

droplet generation. Turner et al. [17] studied the effect of bottom blowing on the

dispersed metal in the slag using mercury and glycerine to simulate molten steel and slag

phases respectively. It was found that the concentration of mercury droplets in the upper

phase was markedly increased by the introduction of bottom blowing, and the mercury

content increased with an increase in the bottom gas flow rate. Much higher

concentration of mercury was obtained when the tuyeres were located underneath the

impingement zone (due to interaction between the rising bubbles and the impinging jet)

than when they were outside the zone.

2.5.2 Drop Size and Drop Size Distribution

A considerable amount of work on the drop size due to an oxygen jet in the BOF

steelmaking process has been carried out by many investigators by collecting the droplet

samples from either an L D converter [4-6,8,10] or a hot model [9,20] and either inside

19

[8,21,24] or outside [4-6] the converter. The droplet size was found to vary with the

position where the samples were taken and the time of blow [10]. Table 2.1 summarizes

the position of sample collection by various investigators and the droplet size. It can be

seen from this table that, with one exception [20], the reported droplet size lies in

between 0.05 and 5mm, irrespective of the scale of the experiment

The reason for the very large droplet size observed by Koria et al. [20] is probably that

large metal pieces which were produced at the wall of the vessel (due to oscillation of the

bath), because the vessel height was kept equal to the bath height and the diameter of die

impingement zone approached the vessel diameter, as well as agglomerates of drops or

small metal pieces formed on the platform, were involved. The size of the metal pieces

was characterised by the equivalent spherical diameter.

The drop size distribution was also studied by a few investigators [20,59,60]. The

results of an investigation [60], where droplets resulted from the disintegration of a

falling Fe-5%C drop in a high velocity oxygen jet, showed that the drop size distribution

could be approximated to a normal distribution. But Koria et al. [20] found from then-

hot model study using a crucible in which an oxygen jet impinged on a molten iron, that

the drop size distribution obeyed the Rosin-Rammler-Sperling (RRS) distribution.

The RRS distribution function is expressed as follows [88,89].

R = 100 exp [-(d/d')n] % (2.25)

where R is cumulative weight of droplets remaining on the sieve with diameter d. d'

represents the size of droplets and n is a measure of the homogeneity of the particle size

distribution.

Koria et al. [20,59] found from their investigations that d' decreased as the lance height

increased, or as the supply pressure decreased. This indicates that hardening the jet by

either decreasing lance height or increasing oxygen supply pressure increases weight

20

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percentage of large droplets. The exponent, n, was found [20] to be independent of the

blowing intensity and the way of sample collection.

The drop size depends, in addition to the oxygen supply pressure and the lance height, on

the number of nozzle holes and the inclination angle of the nozzle relative to the axis of

the lance. The mean drop size decreases remarkably as the inclination angle increases,

and the mean drop size also decreases as the number of the nozzle holes increases [59].

Schoop [10] studied the size distribution of droplets dispersed in the emulsion in relation

to blowing time in a full scale (200t) L D converter. It was found that the drop size

distribution varied with the blowing time. This is probably because of the combination

effect of various factors: top gas flowrate, lance height and properties of slag - all of

which are variable during the course of oxygen blow.

2.6 DIMENSIONAL ANALYSIS

Modelling is a popular research method to investigate the phenomena occurring in real

systems. However, because of the complexity of the systems, it is very difficult, or even

impossible to fully model them in most cases. Nevertheless, in a recent paper [20] it was

claimed that full geometric and dynamic similarity had been maintained in that particular

work. This claim is, however, unsustainable. Approximate modelling that maintains

similarity between model and the prototype in the principal aspects which dominate the

process is the usual method employed by research workers.

Based on the discussion in Section 2.2, the phenomenon of droplet generation by a jet

impinging on a liquid surface should be mainly dominated by two factors. One is the

momentum flux of the gas jet at the undisturbed surface of the bath, which is an external

factor. The second factor involves the properties of the liquid from which droplets are

ejected, such as density, viscosity and surface tension. This factor is an internal factor.

U p to a certain limit, the greater the jet momentum, the more droplets are produced, and

the higher the density, viscosity and surface tension, the less droplets are generated.

22

Therefore, the factors influencing the droplet production, m , are the behaviour of the jet

(gas flow rate, mg, lance height, h, and jet momentum flux, Mj) and the properties of the

jet phase (pg, iig) and the bath phase (p/s \a., s^). The relationship between those

variables governing the splashing phenomenon can be expressed by

m; = f (mg, Mj, h, pg, |ig, P/, \i., a, g) (2.26)

If the droplet production is expressed as the amount of splash per unit top gas flow rate,

then we have

m/ /mg = f (Mj> h> Pg' lig. P , M-, cr, g) (2.27)

From the results given by Chatterjee et al. [33], using jets of various gases with widely

different properties impinging on water bath, it was found that the critical depths of

depression, at which splash commences at corresponding lance heights were virtually

identical. Thus it can be concluded that the influence of the gas properties on the

commencement of splashing, and hence on the quantity of splash, is minimal, so that the

variables in eqn. (2.26) relating to the properties of gas can be ignored. Thus, we have,

m /mg = f (Mj, h, p , \it. a, g) (2.28) 1 I

Dimensional analysis for the variables on the right hand side of eqn. (2.28) is taken as

determining the dimensionless numbers governing the amount of splash. The

corresponding dimensional matrix is as follows.

M

L

T

Mj

1

-1

-2

h

0

1

0

P/

1

-3

0

»l

1

-1

-1

a

1

0 -2

g

0 1 -2

From the matrix it is seen that there are 6 independent variables and 3 basic dimensions

so that from the modelling laws [69] there are 6-3 = 3 independent dimensionless

23

numbers. The dimensional analysis results in the following three dimensionless

numbers.

Jtl = Mj/pgh3 = M m (2.29)

K2 = g\i4/po = C (2.30)

7C3 = p gh2 / G = We/Mm (2.31)

where Mm expresses a ratio of the jet momentum flux to the gravitational force of the

bath liquid. It is referred to as the jet momentum number. C is the liquid constant which

describes a kind of combination of the physical properties of the liquid. 7C3 (We/Mm)

represents a ratio of the gravitational force to the surface tension of the liquid. So, we

obtain,

m / m g = f(Mj/pgh3,gii4/pa,pgh2/o) (2.32)

The results of the experimental work of Tanaka et al. [30] have shown that since the

influence of the viscosity of liquid is small in the range 0.01 < p < 1.3p, an error of

1 5 % was made within 2.5xl0-n < C < 5.5xl0'3. Also, it was found from their

experiments that 713 caused an error of 8 % in the range 2.6xl03 < W e / M m < 6.6X104.

Therefore, it is reasonable to eliminate the dimensionless numbers, 112 and 713 from

eqn. (2.32). Then,

m/mg=f(Mj/pgh3) (2.33)

where

Mj=Aopgu02 (2-34)

Since the lance nozzle used in the present work is straight type, maximum jet velocity at

the nozzle is the sonic velocity. Nominal jet velocity at the outlet of the nozzle is

considered and defined by

Uo = Qo/Ao (2-35)

24

where, QQ is gas flow from top lance, and Ao is cross-sectional area of the nozzle.

The jet momentum number calculated from the nominal jet velocity is called the nominal

jet momentum number.

25

Chapter III. APPARATUS AND PROCEDURE

3.1 INTRODUCTORY REMARKS

Though the phenomenon of metal droplets generation due to an oxygen jet impinging

onto the bath surface has been studied by a number of investigators [4-10] in industrial

scale LD converter, systematic investigation of the phenomenon is very difficult or even

impossible under such conditions because of the high temperature and the complexity of

the system. This is why many studies of this subject have been carried out at room

temperature [15,17,27,30,33] where water, glycerine-water solutions, mercury, oil etc.

were employed as modelling liquids.

In the present study the drop generation is investigated in a single-phase (water) model

and a two-phase (mercury/glycerine) model. Apart from the obvious advantages of cost

and the ease of operation the use of water as the modelling liquid makes it possible to

obtain the size distribution of the droplets in addition to the total quantity of the droplets

ejected. Main reason for the use of mercury is simply because it is a metallic liquid at

room temperature, rather than non-metallic liquid. Glycerine is chosen as the modelling

slag phase because of its high viscosity, about 1500 times that of water, which is able to

hold more droplets of dense phase than a low viscosity liquid.

In the water model experiments the slag phase was ignored. The reasons for this, apart

from experimental simplicity and convenience, are as follows. From observation of high

speed film taken in two-phase (water/paraffin oil) model, it was found that when a jet

impinges on the slag (oil) surface the jet pushes the slag outwards and interacts with the

bath directiy at the impingement zone where the droplets are generated. The bath is

exposed to the jet all the time during blowing if the jet momentum is high enough. Based

on this observation, the same mechanism of metal drop generation due to an impinging jet

would be expected in single and two phase cases. Additionally, preliminary experiments

with a two-phase (mercury/glycerine) system in which mercury content of the

26

mercury/glycerine emulsion was explored, showed the same pattern in the results as in

the single-phase experiments.

3.2 APPARATUS

The single phase experiments on the drop generation rate were carried out in a 3-

dimensional water model with a diameter of 2 0 0 m m using a set-up shown in Fig.3.1.

Line diagram of this experimental apparatus is shown in Fig.3.2. The bath depth was

80mm. The ratio of bath height/model height was about 0.8 to allow the ejected droplets

to fall outside the model. Nitrogen, metered by rotameters in the usual way, was blown

through the top lance with one hole (2mm ID) or through both the top lance and bottom

tuyeres with diameter of 3 m m , at various controlled gas flow rates. 41 tuyeres were

distributed on the bottom of the model, which allows gas to be introduced into the bath at

a different position in the bottom. As a large amount of water is ejected out of the bath

during blowing, the water level was maintained at a constant height by connecting the

model with a flexible tube to a large water reservoir placed on an electronic balance.

In order to understand the mechanism of the drop generation due to an impinging jet and

the effect of bottom blowing on the drop generation, high speed film (5000 frames/s) was

taken using a 2-dimensional water model of dimension of 300x200x20mm (height x

width x thickness). A lance with a rectangular hole of 11.5x0.16mm was used in these

experiments. The apparatus is shown in Fig.3.3.

The experiments on the drop size and drop size distribution were performed in both a 2-

dimensional water model of dimension of 300x150x15mm (height x width x thickness)

and a 3-D water model of diameter of 2 0 0 m m and height of 300mm. Figure 3.4 shows

the apparatus of the 3-D water model experiments, and Fig.3.5 shows schematically the

experimental apparatus of both the 2-D and the 3-D water model. As seen in Figs.3.4

and 3.5, a liquid nitrogen bath was placed beside the models to collect the droplets blown

out of the models. One of the side walls of the 2-D model on the liquid nitrogen bath

side, 2 m m above the water bath, was open, which allowed the ejected droplets to fall out

Figure 3.1 Apparatus of water model experiments of the drop generation rate

: i ' i .

O > OJ CO CD

CD LJ

c cs

JZ

ft

MI^-VE-

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co i_

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=5.2 •4-»

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Figure 3.3 2-D water model apparatus for high speed film

Figure 3.4 Apparatus of 3-D model experiments of drop size distribution

CO

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27

of the model. The same idea was applied to the 3-D model. The 3-D model had an open

side with opening angle of 20° on its wall 2 m m above the bath. The bath depth in the two

cases was 80mm. As mentioned earlier, a large amount of water was ejected out of the

bath during blowing, especially in the case of the 2-D model experiments. To maintain

the water level constant, a large water reservoir was connected to the model.

In the two-phase experiments on the drop production and the droplet residence time,

mercury and glycerine were used to simulate molten steel and slag in the B O F

steelmaking process, respectively. The experimental apparatus and technique were

designed based upon those used by Poggi et al. [77] and Turner et al [17]. The apparatus

employed in these experiments is shown in Fig.3.6, and also schematically in Fig.3.7.

The model was made of perspex with internal dimensions of (|)195mm x 2 7 0 m m and

divided into two parts by a slide gate at the interface between mercury and glycerine.

Depth of mercury bath was 7 5 m m and thickness of glycerine layer was 25mm. There

were eight movable tuyeres with diameter of 1.5mm on the bottom of the model and a top

lance with one hole of 2 m m ID.

3.3 PROCEDURE

In the water model experiments on the drop generation rate, only the total amount of

splash ejected to the outside of the model was considered. The balance on which the

large water reservoir rested was set to zero before each m n started. After the end of

blowing, water was poured into the reservoir until the reading of the balance returned to

zero. The weight of the water poured into the reservoir was recorded as the total amount

of droplets ejected. The amount of the splash was divided by blowing time to obtain the

rate of drop generation. In these experiments each m n was repeated until relative error of

the results was less than 5%. Average values of the results were used in subsequent

analysis and calculations.

In the experiments of drop size distribution, nitrogen gas was used as jet gas phase. The

droplets ejected due to an impinging gas jet fell into the liquid nitrogen bath and turned

Figure 3.6 Apparatus of two-phase model experiment

cu o c CO

<D a-A

<D

E CO

o

<3> a~>

CO

CO

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0)

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28

into solid ice particles. These ice particles of various size were collected after blowing

and then classified into several size groups for the analysis of drop size distribution. The

drop size distribution was obtained from the following calculation [88-90].

Drop Size

(mm)

do<d<di

di<d<d2

dn-l<d<dn

Weight of Droplets

(g)

mi

m2

mn

Weight Fraction

(%)

wpi = mi/m

wp2 = mi/m

w p n = mn/m

Cumulative Weight Fraction (%)

cwpi = wpi

cwp2 = wpi+wp2

n cwpn = Z wpi

i=l

Total weight of the sample: m

In the two-phase experiments, nitrogen gas was blown into the system at predetermined

flowrates. At the required time the gas supply was cut off and the slide gate was quickly

closed to separate the mercury/glycerine emulsion from the mercury metal in the lower

portion of the model. Shutting off the bottom bubbling gas was controlled by solenoid

valve, which ensured that the bottom gas supply was turned off at the same time for each

run. The mercury content of the emulsion was determined from the measured density of

the emulsion by standard density bottle technique.

Based on the preliminary results of the effect of blowing time on the mercury

concentration, shown in Fig.3.8, 8 min was chosen as the blowing time in the present

experiments, for reaching steady state of the mercury content. 6-8 min and 10 min were

used in references [77] and [17] respectively.

-

—

-

—

—

1 1

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% uojsiniua eiu jo jueiuoo B H

29

Because of absorption of water vapour from the atmosphere the viscosity of glycerine

decreases with time which affects mercury content in glycerine as shown in Fig.3.9. To

overcome any possible influence on the mercury concentration of the emulsion the

glycerine was renewed after every 20 runs.

30

Chapter IV. RESULTS AND DISCUSSION

4.1 DROPLET GENERATION

4.1.1 Mechanisms of Droplet Generation

a. Under the condition of top blowing only. Fig. 4.1 shows the variation of the rate of

droplet generation with top gas flow rate. It is evident that the drop generation rate

gready increases with increasing the top flow rate. Two regions of the top gas flow rate,

according to the droplet generation, have been found from the results. The rate of drop

generation increases with the gas flow rate slower at low flow rate (AB), than at high

flow rate (BD). Similar result from the two phase model (mercury/glycerine)

experiments, in which mercury contents of the mercury/glycerine emulsion, rather than

the drop generation rate, were considered, is shown in Fig.4.2.

To gain an insight into the mechanism behind those phenomena, high speed films were

taken under varying top gas flow rates from a 2-dimensional water model. Two

mechanisms of the droplet generation, corresponding to the two regions in Figs. 4.1 and

4.2, were identified from the observation of the high speed films. Fig.4.3 shows a set of

photos which demonstrates the sequence of the formation of the droplet at low top gas

flow rate. From these photographs, it can be seen that when the top gas flow rate is low

a shallow depression with small ripples in the surface forms. In this case, a single

droplet as a crest of the small ripple gradually forms along the surface of the crater and

finally departs at the edge of the crater.

This observation is similar to that of the third type of surface breakdown due to an

impinging jet given by Molloy [26]. He described the phenomenon as follows. "The

passage of the jet at high velocity parallel to the crater surface produces wind-induced

waves which is sharp crested. Shearing of the crests gives rise to the entrained material

that appears as splash from the crater edge."

60

50

ra

40 -

30

20

10

10

top blowing only lance height: 80 m m

20 30 40 50 60

Top gas flow rate (i/min)

70

N \

80 90

Figure 4.1 Variation of drop generation rate with top flow rate(water model)

OU

40

30

20

10

0

I I

top blowing only lance height: 25mm

cr B

l A I

I

I

C

I /

/ r

it* Y/

I

I

Y °

i

—

—

10 20 40 60 80

Top gas flow rate , //min

100 120

Figure 4.2 Variation of Hg content in glycerine with top flow rate

t=0.0 s t=0.02 s

t=0.035 s t=0.06 s

Figure 4.3 Sequence of single droplet formation at a low gas flow rate in top blowing process

t=0.0 s t=0.02 s

t=0.05 s t=0.06 s

t=0.08 s t=0.095 s

Figure 4.4 Sequence of droplet formation at high gas flowrate in top blowing process

31

The generation of individual droplets is a characteristic of this range of top flow rate,

which corresponds to the line AB in Figs.4.1 and 4.2 called "dropping" region in this

work.

Futher increase of the top flow rate leads to the change of the mechanism of drop

generation. Figure 4.4 shows the sequence of formation of droplets at high gas flow

rate. In this region, not only single droplets but also fragments of liquid are produced at

the edge of the crater during blowing. Increase of the top flow rate results in the growth

of the ripples in the crater surface. Each of the ripples might cause the ejection of liquid

tears at the edge of the crater. From observation of the high speed films, it has been

found that formation of a tear of liquid starts with a ripple which becomes bigger and

bigger as it moves up along the crater surface. Finally, a necking-off forms due to the

ripple, and the liquid tear is cut off at the edge of the crater. The liquid tear is impacted by

the deflected gas flow to become several small drops. Meanwhile, a number of individual

drops are directly generated from the crater. The generation of liquid tear is a

characteristic of this range of top flow rate, which corresponds to the line BD in Figs.4.1

and 4.2, called "swarming" region in this work. The reason why there is different

increasing rates of drop generation in "dropping" region and in the "swarming" region is

that different mechanisms of drop generation exist in different regions. The two

mechanisms of drop generation are schematically shown in Fig. 4.5(a) and (b)

respectively.

On the other hand, increase in the flow rate results in an increase in the ripple size, and

the existence of the ripples leads to an increase in shear force being exerted on the crater

surface. Theiarger the ripple, the larger is the shear force. As discussed in Section 2.2,

more splashing is expected at high flow rate than at low flow rate, simply due to the

dimension of the ripples.

The generation of individual droplets and liquid fragments were also observed by Koria et

al. [27] from their hot model study on production of drops at the initial stages of BOF

II (a)--dropping

\ \

\ \

\ \

\

\

u

\\ \ /

v-

(b)--swarming

/ /

/ /

K7

\

1 / y ) ^s I

\

V / \ /

Figure 4.5 The two region of drop generation

32

steelmaking. From their study it was suggested that there existed two stages for a

preselected pressure - build-up stage and steady stage. The characteristic features of the

build-up stage are formation of a stable cavity the depth of which increases with time, and

splashing of metal drops from the edge of the cavity. The period for the build-up stage is

very short, less than 1.0 seconds. In the steady stage, large fragments of liquid metal are

ejected from the impingement zone.

On closer examination of their results, it will be found that the build-up stage defined by

Koria et al. [27] is actually the same as the dropping region defined in this work although

they are defined in different ways. This is because no matter what the preselected

pressure is, the build-up stage is a regime in which gas flow rate increases from zero up

to the predetermined value. The ejection of droplets at the build-up stage takes place

under the condition of low gas flow rate which is in the dropping region. On the other

hand, at high preselected pressure or flow rate, the steady stage is the same as the

swarming region because the regions are defined at steady stage in the present work.

Unfortunately, the mechanism of the droplet generation was not well understood from

their work. Also, Koria et al. [27] did not distinguish the difference between low and

high predetermined pressure for the steady stage. Obviously, the conclusion that metal

fragments are generated in the steady stage is not applicable when the preselected flow

rate is low enough to be in the dropping region in which no fragments of liquid metal are

produced.

The mechanism of the drop generation has been explained to be due to periodic vertical

and horizontal oscillations of the impingement zone [15,26,27]. It was described by

Urquhart et al. [15] that each oscillation of the crater was accompanied by ejection of

droplets. However, on the basis of the analysis of the factors influencing the droplet

formation in Section 2.2, it is hard to believe that the oscillation is able to cause the

ejection of droplets. From the present investigation, it is found that the mechanism of the

droplet generation due to an impinging gas jet is more in line with the "ripple theory"

described above, rather than with the oscillation of the cavity.

33

In fact, from the observation of the high speed film, it is found that the ejection of liquid

fragments makes a contribution to the movement of the impingement zone. For a high jet

momentum or small lance height, a deep penetration with a small opening on the top

forms in the bath surface, as shown in Fig. 4.5b. The jet gas is deflected in a direction

with a small angle against the jet axis. Once the ejection of the fragment occurs, the

deflection angle increases, as shown in Fig. 4.6, and the velocity of deflected flow

decreases because of larger cross-section area for the deflected flow created. This results

in a decrease in impact of the jet at the crater bottom and a subsequent shorter penetration.

This can be explained as follows.

The jet impact acting on the bottom of depression is (see Fig.4.6),

Im = m ui - m (- U2cosoc)

= m (ui + U2cosoc) (4.1)

From eqn. (4.1) it is seen that decrease in U2 and cosoc, due to the occurrence of the

ejection of the fragment, leads to a decrease in the jet impact. In addition, part of the

splash is entrained into the jet to form a two-phase flow which causes a deeper

penetration than a single-phase (gas) jet [26]. Thus, intermittent ejection of liquid

fragments causes a vertical oscillation of the crater. On the other hand, the ejection of the

fragment can also result in a horizontal movement of the impingement zone. The jet will

switch to the side where the ejection occurs because there is larger cross-sectional area

and lower resistance for the deflected flow at this side.

It should be pointed out that the two modes, viz. splashing and penetrating, mentioned in

Section 2.1.4-, whieh^was^ defined ^s based- on the flow pattern of a gas jet in the

impingement zone, are different from the two regions defined in this thesis on the basis

of the mechanisms of the drop generation.

Comparing definitions of the two modes and those of the two regions, it is found that the

criterion for the transition from "splashing" to "penetrating" should be point C or even

3 cr

c o o ci> •+-•

—> o a> ca

a.

o E

4—

LU c

o CD * c CO g

ra ra

O) co LL £

34

further where splashing quantity reached a maximum value, and that for transition from

"dropping" to "swarming" shouldbe point B in Fig.4.1 and 4.2 respectively.

From Figs.4.1 and 4.2 it can be seen that the increase in the droplet production with

increasing top flow rate tends to be slower when gas flow rate is over a certain value

(point C in Figs.4.1 and 4.2). This phenomenon may be explained as follows: a

proportin of the splash ejected from the bath is entrained by the gas jet and then returned

to the bath with the jet, when top flow rate is over a certain value, as has been found in

the present investigation, and also referred to by Molloy [27]. The data which were used

in the present experiments to obtain the droplet generation rate and the mercury content

were the mass of the dense phase which was ejected and fell outside of the model vessel,

and which remain in the upper phase respectively. A s the proportion of dense phase

entrained increases with increasing top flow rate, the slope of the tangent of curve C D

decreases as the top flow rate increases.

b. Under the condition of combined blowing. In a recent paper by G. Turner et al. [8]

on emulsification of metal droplets in B O F steelmaking, it was found that the drop

production was greatly increased by introduction of bottom blowing into the system.

This is also identified in the present work from 3-D water model and mercury/glycerine

model experiments (see Figs. 4.7 and 4.8). Initially, droplet production is proportional

to bottom gas flow rate. A plateau is reached after the bottom flow rate is increased to a

certain value. N o increase in the drop production was obtained with further increasing

the bottom flow rate. However, the mechanism of the effect of bottom bubbling on the

drop generation is not understood.

— The bottom blowing^irrast influence the dorplet generation in two ways, viz. by a direct

effect and by an indirect effect The direct effect means the direct interaction between the

bottom gas bubbles and the impingement zone when the bubbles rise up and pass the

impingement zone. O n the other hand, during ascent the bubbles apply the energy due to

buoyancy into the bath and accelerate it. The change of flow pattern due to the bottom

uo

30

LD

<

cr

o i— <

cr

LD

g>20 CD

two tuyeres located symmetrically, 30mm from the centre top gas flow rate: 46.67 1/min

lance height: 80 m m

TOP BLOWING ONLY

TT

0 1 2 3 4 5 6 BOTTOM GAS FLOWRATE ( L / MIN )

7 -8

Figure 4.7 Variation of drop generation rate with bottom gas flow rate

c E

CO

CO i-

o

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35

blowing must influence the fluid flow at the surface of the crater, which affects the

droplet generation as discussed in Section 2.2. This is the indirect effect referred to in

this work.

To gain an insight into the mechanism, high speed films were also taken under the

conditions of combined blowing with one bottom tuyere at the centre. Figures 4.9 and

4.10 show two set of photographs taken at different top gas flow rates, which

demonstrate the mechanism of the effect of bottom blowing on the drop generation.

From these figures it is clearly seen that a bubble floats up and turns near the bottom of

the crater and then travels up along the crater surface. The bubble then bursts near the

free surface of the bath, which causes a large ripple in the surface. The extra ripples,

relative to the intrinsic ones caused by top blowing only, result in increased splash from

the bath. From these figures it is also clearly seen that the ripple due to the bursting of

the bubble becomes a necking-off that causes a liquid tear and a few drops to be

produced. This phenomenon can not occur in the case of bottom blowing only. This is

the direct effect of bottom blowing.

Additionally to the above, there are also some open bubbles at the bottom of the crater

when the introduction of bottom blowing is central. W h e n the bubble is opened up, it

becomes a part of the crater surface, which increases the surface area of the crater, but the

bubble does not cause a large ripple (see Fig.4.11). In this case, the influence of the

bottom blowing on the droplet generation is by the indirect effect, the efficiency of which

is much smaller than that of the direct effect. Therefore, the effect of the bottom blowing

on the drop generation depends, to a great extent, on the proportion of the bubbles which

float up along the side of the crater to the total number of the bubbles which are blown

into the bath through the bottom tuyeres. The higher this proportion is, the greater is the

effect of the bottom blowing on the drop generation. From the observation of high speed

films, for low top gas flowrate, most of the bubbles turn near the bottom of the crater,

and then rise up along the side. For high top flow rate, most of the bubbles are opened

up at the bottom of the crater because of the impact of a high velocity jet. These

t=0.0 s t=0.04 s

t=0.055 s t=0.07 s

t=0.085 s t=0.11 s

Figure 4.9 Mechanism of the effet of bottom blowing on the drop generation at low top flow rate

t=0.0 s t=0.015 s

t=0.03 s t=0.05 s

t=0.06 s t=0.08 s

Figure 4.10 Mechanism of the effect of bottom blowing on the drop generation at high top flow rate

t=0.0 s t=0.02 s

t=0.04 s t=0.05 s

Figure 4.11 Open-up of a bubble at the bottom of the crater

36

phenomena indicate that the effect of the bottom blowing on the droplet generation,

relative to top blowing only, is greater for lower top gas flow rate than for higher top

flow rate. This is identified by the results of the present model investigation shown in

Section 4.1.2.

From the results described above, it can be concluded that the droplet production can be

gready increased by the introduction of bottom blowing into the system, and the

significant increase in the droplet generation is mainly caused by interaction between

bottom blowing and top blowing in the impingement zone, but not by bottom blowing

itself.

4.1.2 Effect of Blowing Conditions on Droplet Generation

a. Effect of top gas flow rate. Figure 4.12 shows the results of variation of droplet

generation rate with top gas flow rate at different bottom gas flow rate, obtained from

water model experiments. It is evident that the drop generation rates increase with

increasing the top gas. It is clearly seen that there is a transition criterion at which the

region changes from "dropping" to "swarming" in each case, that is each curve in Figure

4.12 can be approximated by two straight lines with different slopes. The drop

generation rates increase faster in "sewarming" than in "dropping" regions with increase

in the top gas flow rates.

Results of the effect of top gas flow rates on the mercury content of the emulsion from

the two-phase experiments are shown in Fig.4.13. Compared with Fig.4.12 it is clear

that the same conslusions as those from the single phase modelling can be drawn from

the results of the two-phase model experiments. The similarity indicates that the

existence of slag layer does not change the mechanism of the droplet generation, but it

could change the criterion for the transition because it reduces the jet momentum at bath

surface. From Figs. 4.12 and 4.13 it is clearly seen that the transition takes place at

different top gas flow rates for different models, about 35 1/min for water model and

T

O top blowing only

25 30 40 50 60

Top gas flow rate i min

Figure 4.12 Variation of drop generation rate with top gas flow rate

40 60 80

Top gas flow rate (1/min) 120

Figure 4.13 Variation of Hg content in glycerine with top gas flow rate

37

about 60 1/min for mercury/glycerine model. The reason for this is most probably

associated with the different properties of the two liquids, mercury and water.

According to the definition of "swarming" region and the mechanism of the effect of

bottom blowing on droplet generation, described in Section 4.1.1, it can be deduced that

introduction of bottom blowing into the system must result in a change of the criterion for

transition from "dropping" to "swarming". From elementary considerations it was

expected that relative to that in top blowing only, the transition should occur at lower top

flow rate in the case of combined blowing, because the rising bubbles cause the ripples in

the crater surface which result in the ejection of liquid fragments. This has been

confirmed in this investigation. Figure 4.14 shows the effect of bottom blowing on the

critical top gas flow rate at which the transition from the "dropping" to the "swarming"

occurs. The criterion for the transition decreases with increase in the bottom gas flow

rate.

It is interesting to compare the present results with those of Herbertson [70], on mass

transfer from a jet to liquid phase, in which an oxygen jet impinged on a molten silver

bath. His results are shown in Fig, 4.15 in the form of a plot of liquid phase mass

transfer coefficient, K/, versus jet momentum. The dependence of K/ on jet momentum

suggests three separate mass transfer regimes, marked on Fig. 4.15 as I, II, III. On

comparison of Figs. 4.12, 4.13 and 4.15, it is found that the result of the mass transfer

and those of the drop generation follow the same pattern although they represent different

physical variables. This is probably because they are both associated with the

impingement of a jet on a liquid surface. The three regimes were explained by

Herbertson as follows:

In regime I, the impact of the jet induces insufficient forced convection to

significandy increase the total mass transfer at the free surface. The predominant

transport mechanism within this regime would be some form of natural convection.

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inui// ' uojiisuBLii em JOI OJBJ M O U do; leoilMO

0 8 16 24 32 40 48 56

Jet momentum , dyn x 103

Figure 4.15 Variation of K/with ]et momentum

38

In regime II, K/ increases linearly with jet momentum. The predominant liquid

phase transport mechanism would be the forced convection induced by the jet

action.

In regime III, K/ increased linearly with jet momentum at higher rates. The

enhancement in mass transfer with further increase in jet momentum is possibly due

to dispersion of silver droplets into the gas phase and agitation of the surface.

On the basis of the results from the present investigation, the following explanation for

the three regimes may be suggested. From Fig. 4.15 it is clearly seen that K/ suddenly

increases at the criterion of the jet momentum for the transition from regime I to regime n.

This is most likely due to the commencement of droplet ejection which greatly increases

the interfacial area between oxygen and silver metal (it should be pointed out that K/

plotted in Fig. 4.15 is a function of the interfacial area between dispersed metal and

oxygen). A n increase in droplet production by increasing the jet momentum resulted in

an increase in the value of K/ as the jet momentum increased in regime II. In regime I,

the jet momentum was not high enough to produce droplets. The result of this linear

increase in the value of K/ at a higher rate in regime HI than in regime II can probably be

explained by the occurrence of the transition of the mechanisms of the drop generation

from "dropping" to "swarming". The more droplets thus produced led to a faster mass

transfer in regime HI.

This comparison strongly suggests that regimes II and III correspond to the "dropping"

and "swarming" regions defined in this work (see Section 4.1.1).

b. Effect of lance height: L,anee-height is a main operational parameter in practice.

Intensity of oxygen blow (soft, medium-soft and hard blow) in the B O F steelmaking is

principally controlled by adjusting the level of lance height. The effect of the lance height

on droplet production was studied in the present work, using both water modelling and

mercury/glycerine modelling for a wide range of lance heights.

40

30 -

20 -

10 -combined blowing top flow rate: 48.5 l/min bottom gas flow rate: 2.68 l/min two tuyeres located symmetrically, 30mm from thecentre

40 80 120

Lance height (mm)

160 200

Fiqure 4.16 Variation of drop generation rate with lance height

c o \n

E CD CU SZ

c o c o u I

50

40

30

20

10

I

o/

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I

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top blowing only

gas flow rate: 80.4 l/min

i l l i

I

-

-

i 10 20 30 40 50 60

Lance height (mm) 70 80

Figure 4.17 Variation of Hg content in glycerine with lance height

c '— E ""5

CO

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ro u-t-o »*— > c o

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tn Oi m.

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E£

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s/6 ' ejej uouBjeueB doja

70

60

50

# top blowing only,flowrate:80.4 //min O combined blowing,one tuyere at centre

flowrate:80.4(top) 2.9(bottom) //min (j) combined blowing.two tuyeres,

symmetrically,30mm from centre flowrate:80.4(top) 3.18(bottom) //min

40

30 -

20

10

10 20 30 40 50 60

Lance height , m m

Figure 4.19 Effect of blowing conditions on the critical lance height(mercury/giycerine model)

39

In a recent paper by Turner et al. [17], on emulsification of metal droplets in the B O F

steelmaking, it was reported that mercury concentration monotonously increased with

decreasing lance height This was explained by them as being due to the combination of

an increase in the rate of droplet ejection and a decrease in the settling rate of the droplets

as the lance height decreased. However, from the present study, as the lance height

increases, this explanation has been found not to be the case. The results obtained from

the present single-phase model and the two-phase model are shown in Figs. 4.16 and

4.17 respectively. In both cases, the droplet production at first increases and then

decreases as the lance height increases. Maximum droplet production is obtained at a

certain lance height.

The critical lance height for the maximum splashing quantity could be of importance to the

operation of the BOF steelmaking. In practice, lance height should be controlled not to be

in the region where the splashing quantity is proportional to the lance height

The effects of blowing conditions on the value of the critical lance height were also

investigated in this work. The results from the water and the mercury/glycerine models

are shown in Figs. 4.18 and 4.19 respectively. The results in these figures indicate that

(i) the critical lance height increases with the increase in the top gas flow rate, i.e. the jet

momentum - about 50mm for top flow rate of 48.5 1/min and 60mm for 57.161/min (see

Fig.4.18), and (ii) despite the introduction of bottom blowing which significantly

increases the droplet production the value of the critical lance height is not changed (see

Fig.4.18 and Fig.4.19).

Some of the findings of this study are in broad accord with the results of Tanaka et al.

[30], where maximum amounts of the splashing were obtained at different lance heights

for different jet impacts, and the critical lance height increased as the jet impact increased

(see Section 2.5.1). Similar phenomena were also observed in other studies [33,47,48].

However, the values of the critical lance height from the present investigation are different

from those obtained by Tanaka et al., both of which were carried out in a water model,

40

about 50-60mm in the former (see Fig.4.18), and 110-200mm in the latter [30] (also see

Fig.2.9). This disparity is most likely due to different jet momenta employed in the two

cases. The results in ref.[30] are replotted in Fig.4.20 in the form of the variation of the

critical values with the jet momentum flux. The present results are also plotted in this

figure. It can be seen from the figure that the present results fit well the results of Tanaka

et al. if the latter are extended to the low values of the jet momentum.

It is easy to understand that the droplet production increases with decreasing lance height

when the lance height is greater than the criterion value because the jet momentum

intensity at the bath surface is increased. The decline of the splashing quantity after

reaching a maximum value was explained by Tanaka et al. as follows:

(1) separation of gas/liquid becomes less efficient part of the jet intrudes into the

bath generating air bubbles;

(2) because the splashing angle against the bath surface increases, the liquid

droplets receive a higher drag from the jet.

The interpretation of Chatterjee et al. [33] for the phenomenon is that as the lance height is

decreased or the momentum increased, the depression changes from a parabolic or

semicircular shape to 'IT shape with almost vertical sides. When this occurs, the jet itself

is affected in two ways. Firstly, a major portion of the jet striking the depression surface

is reflected back into the incoming jet. Secondly, the portion of the reflected jet not

entrained in the incoming jet has further to travel before reaching the Up of the depression.

It is thought that both these features contribute to the decrease in the volume of liquid

splashed when the momentum or lance height are altered beyond the values which give

the maximum.

Molloy [27] describes this behaviour as a change from the "splashing mode" to the

"penetration mode".

E o 4-a

JO

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c CO 75 o *-• mm

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20

16

12

8

4

-

I I

£ present work O previous work(30)

I I

I

I

I

I

CJ^

-

—

0 0.4 0.8 1.2 1.6

Jet momentum , dyn x105

Figure 4.20 Comparison with previous work in terms of the critical lance height

Lance height , cm

Figure 4.21 The effect of lance height on liquid phase mass transfer

41

In addition to the above explanation, from observation of the present water model

experiments, it was found that when the lance height is lower than the criterion value a

very deep depression formed in the bath. Big bubbles form around the nozzle and then

escape from the bath. This phenomenon is similar, to a certain extent, to that caused by

submerged injection which produces much less splash than an impinging jet. In this

case, the phenomenon of the drop generation can not be explained by the "ripple theory",

described in Section 4.1.1.

The present results can probably be used to explain the results of Herbertson [70] on

mass transfer between an impinging oxygen jet and the silver metal bath, where a

maximum value of the liquid phase mass transfer coefficient was obtained at a critical

lance height as shown in Fig.4.21. Comparing the result in Figs. 4.16 and 4.17 with that

in Fig.4.21 a conclusion may be drawn that the dependence of the mass transfer

coefficient on the lance height is caused by the influence of the lance height on the amount

of liquid splashed.

c. Effect of bottom gas flow rate. Figure 4.22 shows the results of the variation of drop

production with bottom gas flow rate at different top gas flow rate obtained from water

modelling. The results from the mercury/glycerine model experiment are shown in

Fig.4.23. In both cases, initially, drop generation is proportional to the bottom gas flow

rate. A plateau is then reached after the bottom flow rate has increased to a certain value.

This finding is identical to that obtained from 2-D mercury/glycerine model [17].

From Figs. 4.22 and 4.23 it is seen that critical bottom flow rate at which the plateau is

reached is different for different top gas flow rates, and it decreases with increasing top

flow rate. This can probably be explained as follows. According to the mechanism of

droplet generation described in Section 4.1.1, the ripples caused by top blowing or by

interaction between top blowing and bottom blowing play a very important part in droplet

generation in the "swarming" region. The frequency of the formation of the ripples in the

crater surface increases with increasing top flow rate and bottom flow rate. It may be

Bottom gas flow rate i min

Figure 4.22 Variation of drop generation rate with bottom flow rate(water model)

~i 1 r i 1 1 1 r

1 2 - one bottom tuyere at the centre lance height: 50mm

4 -

-O

top blowing only Q=80.4 l/min

top blowing only Q=39.84 l/min

J I L 2 4 6 8

Bottom gas flow rate i min

Figure 4.23 Variation of Hg content in glycerine with bottom flow rate

42

reasonable to assume that there is a constant upper limit of the frequency for a given

system because the area of the crater surface is finite. For a certain top flow rate, the

number of ripples increases with increasing bottom flow rate up to the upper limit Once

the limit is reached the bottom blowing no longer greatly influences the droplet

generation. So, the higher the top gas flowrate, the less the difference between the

limiting frequency and that caused by top blowing. This means that less bottom flow is

needed to obtain the upper limit frequency. This also indicates that the effect of bottom

blowing on the droplet generation weakens with increasing top flow rate, which is indeed

one of the conclusions from Figs.422 and 4.23. The figures show that droplet

production is increased by the introduction of bottom blowing, relative to that of top

blowing only, by 80% for top flow rate of 39.841/min, by 55% for top flow rate of 48.5

1/min, and by 35% for top flow rate of 53.261/min in the water model experiment, and by

more than 1000% for top flow rate of 39.84 1/min and 70% for top flow rate of 80.4

1/min in mercury/glycerine modelling in the plateau region. The evidence in those figures

suggests that there should be a critical top gas flow rate at which the effect of bottom

bubbling on the drop production is small enough to be ignored. This is identical to the

result obtained from analysis of plant data [18] which showed that bottom bubbling had

statistically significant effect on the degree of disequilibrium for medium-soft blown

heats, but not for hard blown heats.

d. Effect of position of bottom tuyere. Effect of the position of bottom tuyeres on

droplet generation was also investigated in the present work. The results are shown in

Fig.4.24. Two tuyeres are symmetrically located on the bottom of the model at a distance

away from the centre. By inspection of the figures, maximum droplet production was

achieved-at-a^itieal-positien of bottom tuyeres, about 25-30mm away from the centre in

both cases. Further increase of the distance beyond the maximum point lowers the

droplet production because of the smaller influence of the bottom blowing on the

impingement zone. A similar result was also reported in the 2-D mercury system referred

to earlier [17].

T""

C O

u I 0 -

O mercury model lance height: 50mm top gas (low rate: 80.4 l/min bottom gas flow rate: 3.2 I min

A water model lance height: 80mm

: 46.67 l/min rate: 2.68 I min

U 25 mm

40mm

top blowing only(mercury)

top blowing only(water) JCL

20 40 60

Distance from the centre (mm) 80

•30

-25

-20

Figure 4.24 Effect of tuyere position on the drop production

combined blowing lance height: 50 mm 0 two tuyeres,symmetrically

30mm from centre O one tuyere at centre

0 2 4 6 8

Total bottom gas flowrate through tuyere(s) , //min

Figure 4.25 Effect of bottom gas distribution on Hg content of the emulsion

43

This behaviour can be explained by the "ripple theory" described in Section 4.1.1. In the

case when bottom tuyeres are symmetrically placed underneath the impingement zone, all

of the bubbles will rise up along the side of the crater because they do not contact the

bottom of thecrater. In this case, the bottom blowing mainly affects the droplet

generation by the direct effect. Compared with the case of one tuyere at centre where

some of the rising bubbles open up at the bottom of the crater, more droplets are expected

to be produced. This, indeed, is the finding of this study (see Figs. 4.24 and 4.25).

From Fig.4.25 it can be seen that for bottom flow rate of about 4% of the total, the

mercury content in the glycerine is increased by 2.5 times when the two tuyeres are

symmetrically located 30mm away from the centre, and by 1.5 times when one tuyere is

positioned at the centre. When the tuyeres are positioned outside the impingement zone

the bottom blowing only influences the droplet generation at the impingement zone by the

indirect effect in which case the rate of droplet generation is lower than in all cases when

tuyeres are located underneath the impingement zone, as shown in Fig.4.24.

In addition to the above, another mechanism of the effect of bottom bubbling on the drop

production in the two-phase case should be taken into account. In the case when there is

an upper liquid phase, then as a rising bubble passes the interface it would carry a dense

phase film around it into the upper phase where it subsequently sheds the film or it

ruptures, thus scattering droplets of the liquid phase into the upper phase [11,71]. In the

present study the amount of entrapped mercury was found to increase with increasing the

flow rate of bottom bubbling, as shown in Fig. 4.26, because the increase in the flow rate

results in an increase in the rate at which droplets are scattered into the upper phase [11].

This-tnechanism should contribute to the increasein the droplet production due to the

introduction of bottom blowing when the tuyeres are positioned outside the impingement

zone. For this mechanism to be solely responsible, there should be almost no difference

in drop production between top blowing only and combined blowing when the upper

liquid phase is absent, because the mechanism is not applicable in this case. Since the

c E

co

o

tn ca D)

E o *-A *-A

o m

E o •A-.

o mm.

tn

C Q)

c o O D)

I

O a c

c o E =5 2 . _ • « — •

CO.E CM

-* 2> CO

3 5 Bo u-

% uojsinuie eiu io lueiuoo 6 H

Figure 4.27 Apparent tuyere position

44

results obtained are to the contrary (see Fig.4.24), it is reasonable to conclude that this

mechanism could only be partially responsible for the behaviour observed.

It should be noted that the position of tuyeres at which maximum droplet generation was

achieved is at the outside of the impingement zone, which seems to be contradictory to the

above explanation. The observation from water modelling indicates that when two

tuyeres are symmetrically located, the two rising bubble columns tend to be closer to each

other (see Fig.4.27). The positions of the tuyeres are not the location where the bubble

columns are. The droplet generation depends on the latter position called "apparent tuyere

position" in this work. So, the results in Fig.4.24 are not surprising.

e. Effect of other factors, (i) multi-hole nozzle lance. Effect of the number of nozzle

holes was examined in the two phase model, using single-hole and multi-hole lances.

Total area of the nozzle outlet was kept constant in the cases of single hole and multi-hole

lances. The results are shown in Fig. 4.28. Although jet velocities at the outlets are the

same in all cases, the droplet production is found to decrease with increase in the number

of nozzle holes. This finding is in accord with the result of Koria et al. [55] where, for a

given supply pressure, total drop generation rate decreased when single-hole nozzle was

replaced by multi-hole lance at all dimensionless lance distances. This is probably

because of a combination of the following factors.

(1) Mercury content increases with increase in unit jet momentum by a factor of more

than two, as is seen in Fig. 4.29 in which the result with single-hole lance is

replotted as a function of jet momentum, so that splash quantity due to a two-hole

lance, which should be twice that of a single-hole lance with half of total jet

momentum is lesirthairthat ofsingle-hole lance with the total jet momentum.

(2) With the same lance distance, there are larger distances between multi-hole nozzle

and undisturbed bath surface than in the case of single-hole lance, because of the

existence of nozzle inclination angle of 12°. For a given supply pressure this

results in lower jet momentum at the bath surface.

40 60 80

Top gas flow rate , //min

120

Figure 4.28 Effect of multi-hole nozzle lance on the drop production

r i i i i I 0 2 4 6 8 10

Jet momentum flux , dyn x104

Figure 4.29 Variation of Hg content in glycerine with jet momentum flux

45

This result confirms, from a different viewpoint that the jet momentum rather than the jet

velocity is the variable determining the amount of liquid splashed [33].

From Fig.4.28 it is clearly seen that the transition from "dropping" to "swarming" occurs

in all cases, but the transition value increases with increasing the number of lance holes.

(ii) Thickness of upper phase layer. The thickness of the upper phase layer is

another factor influencing the production of metal droplets in the slag. The influence of

the slag phase thickness was examined in this study in two-phase (mercury/glycerine)

model. The results are shown in Fig.4.30. From this figure it is seen that mercury

content of the emulsion decreases with increase in the thickness of the glycerine layer, but

the total amount of the dispersed mercury droplets in glycerine at first decreases and then

increases with the increase in the slag phase layer thickness.

From elementary considerations the effect of the glycerine layer thickness on the mercury

content is related to the following three factors.

(i) For a given lance distance from lance nozzle to the surface of the lower phase

bath, the existence of the upper phase layer reduces the jet momentum at the bath

surface.

(ii) For the same mercury content, larger volume of the upper phase due to increase

in its thickness can hold up more droplets.

(iii) Flow pattern in the upper phase layer is another factor. The slag phase easily

circulates in a thick layer than in a thin layer. Also, turbulence in slag increases

wrthairincrease in the thickness of slag layer, because the distance between the

lance nozzle and the slag surface becomes shorter.

It is clear that the results shown in Fig. 4.30 are caused by a combination of these three

factors.

o

o CO

o CN

E E "

i—

CD >» CO

Q)

1_

CD O

CD c 1_

CO O >» D) »•—

O CO CO CD C

c o o u £5

o D)

CO CO 0

c z<

o « x: I-

O CL

O rt CD

LU

O CO r*

CD »_ 3 Ui LL

1_

-a CD sz a-A

c o l_

CD >. CO

% ' uoisintue ei\\ jo lueiuoo 6 H

46

4.1.3 Remarks on Similarity Criteria

As is noted, in the present work water and mercury were used in the model experiments

to simulate the bath phase of BOF steelmaking. As we know, there are large differences

in properties between modelling liquid and liquid steel (pH20 = 1000 kg/m3, OH2O =

0.0728 w/m, pHg = 13600 kg/m3, oHg = 0.47, psteei = 7000 kg/m

3, asteei = 1.7 w/m),

which could make the application of the present results to real systems questionable.

However, from the present results (see Section 4.1.1 and 4.1.2) it can be seen that

despite different properties of mercury and water, the same pattern of results with

different criterion values were obtained from both model experiments. This indicates that

the similarities between modelling and prototype may exist, at least qualitatively.

Although different variables, drop generation rate and mercury content appear in Fig.4.12

and 4.13 respectively, it is reasonable to expect the same mechanism to dominate the

phenomena in those figures, i.e. the changes in slope of the curves are due to the

occurrence of the transition from "dropping" to "swarming".

The results of top blowing only in Figs. 4.12 and 4.13 are replotted in Fig. 4.31 as a

function of the nominal momentum number defined in Section 2.6. As shown in this

figure, the transition from the "dropping" to the "swarming" in both model systems

occurs at about the same critical value of the momentum number. Also, the results in

Figs. 4.16 and 4.17 are replotted in Fig. 4.32 in relation to the nominal momentum

number. The maximum droplet productions are obtained at some the same critical value

of the momentum number.

The evidence in Figs. 4.31 and 4.32 suggests that there is a strong indication that the

nominal momentum number may be a link between the model and the prototype in terms

of droplet generation due to a jet impinging on a liquid surface. However, it has been

found from the present study that the amount of droplets ejected is determined by not only

the jet momentum number, but also the top gas flow rate. This means the different top

gas flow rate results in different splash quantity even if the values of the momentum

c o 'tn

zz E CD CD SZ O D _

c C D *-<

c o o Ui X

0.02 0.04 0.06 0.08

Nominal momentum number , Mm

Figure 4.31 Comparison between water model and mercury model in terms of the transition from 'dropping' to 'swarming'

50

40

30

20 -

10

"rnr O mercury-glycerine model • water model

50

40

30

20

10

0 0.001 0.01 0.1 1 10

Nominal momentum number , Mm

Figure 4.32 Comparison of water model and Hg-glycerine model in terms of the critical lance height for maximum drop production

50

- 40 c o w

CD 30 CD

- 20 c CD mS-m

c o o D) 10

- /

- L

i

•/^S /• y

i

i i

g / §

O varying top flow rate only • varying lance height only

i i 0.0 0.2 0.4 0.6 0.8

Nominal momentum number , %

Figure 4.33 Comparison of the two group results

0.5

— •

O varying top flow rate only • varying lance height only

0.2 0.4 0.6

Nominal momentum number , Mm

0.8

Figure 4.34 Relation between drop production per unit top flow rate and nominal momentum number

47

number are the same. T w o groups of data are plotted in Fig. 4.33 as a function of the

momentum numbers. The variations of the momentum number values in the two cases

are result from the change in the top gas flow rate and the change in the lance height

respectively. From Fig.4.33 it is clearly seen that there exists a large discrepancy

between the results of the two groups of data. This is because the same value of the

momentum number in the two groups corresponds to different top gas flow rate and lance

height, respectively. But, the discrepancy almost disappears if the mercury concentration

of the emulsion per unit top flow rate is plotted in relation to the jet momentum number,

as shown in Fig. 4.34. An excellent correlation between these two quantities is obtained

in this figure. This result is identical to the expression of eqn. (2.33), which was also

confirmed by Tanaka et al. [30] in their study on the interaction between a gas jet and a

liquid bath, where the data obtained from four different liquids can be arranged in terms

of m//mg and Mm.

4.2 DROP SIZE DISTRIBUTION

According to the emulsion mechanism, the high refining rate of BOF process is due to

extremely large reaction interfacial area between metal droplets and slag. The interfacial

area depends on two factors, viz. the number of metal droplets and the drop size

distribution. So one is more interested in knowing both factors than only one of them.

The former was studied in Section 4.1 of this work, by considering the drop generation

rates in the single-phase (water) model and the concentration of dense phase in the upper

phase in the two-phase (mercury/glycerine) model. The results of the drop size

distribution are given in this section.

~ ~ Both 2-D~and 3-D water models were used and a liquid nitrogen bath was placed beside

the model to collect the droplets blown out of the model. The frozen droplets were

analysed by using a set of sieves, as described in Chapter in. A typical sample of the

frozen droplets collected from the liquid nitrogen bath is shown in Fig. 4.35. It is

48

interesting to note that the shape and the size range of the ice particles are similar to those

of the droplets collected from the LD converters [4,6].

The results of drop size distribution from the present work are shown in Figs. 4.36 to

4.40, in which cumulative weight percent remaining on the sieve against the lower limit

of class diameter is plotted on a normal probability scale. Results in Figs. 4.36 and 4.38

were obtained from the 2-D model and results in Figs. 4.39 and 4.40 were obtained from

the 3-D model. From these figures it is evident that an approximate linear relationship

exists, which means that the drop size distributions are reasonably normal. The present

results are identical to those of an earlier work [60] where drops were generated by the

breakup of a vertically falling single drop of Fe-5%C due to the action of a horizontal gas

jet of high velocity. But another study [20] of the drop size distribution, resulting from

drops ejected from a molten bath and falling onto a platform outside the crucible,

concluded that the Rosin-Rammler-Sperling distribution is obeyed. It should be pointed

out that in the latter work [20], metal pieces which were ejected from the bath and

agglomerates of drops or small metal pieces formed on the platform were involved.

Additionally, as a very small crucible was used in that work, the flow pattern in the bath

would be quite different and consequently affect the drop generation. These combined

factors would almost certainly be expected to result in a different drop size distribution.

By comparison of the results from Koria et al. with those from the present study, it is

found that the main difference between those two distributions is the proportion of large

droplets. The proportion of droplets of size larger than 8mm is about 50-95% of the total

amount of droplets collected under their experimental conditions, and only less than 10%

in the present work.

Figures 4.36 and 4.39 show the effect of lance height on the drop size distribution, and

Figs. 4.37 and 4.40 give the results of the drop size distributions at different top gas flow

rates. With the exception of the results in Fig. 4.36 it can be seen that the proportion of

large droplets increases with increasing top gas flow rate and with decreasing lance

. 5mm .

Figure 4.35 Frozen droplets collected from liquid nitrogen bath

99.98

99.8 -

99 -

95 -

9 w 90 --s—>

sz Ui 80

'53 S 60 •*->

03 D 40

E 5 20

10 -

2

0.5

—

—

—

—

—

]

I

I

I

I I I

top blowing only

gas flow rate: 46.67 l/min

lance height:

, -C] 140 m m ^^^^ j*7 100 m m

\x\^^^^ y^am\ 80 m m

^v\ ^y^\y7* 60 m m

i A V / / O 40 mm

I I I

—

—

—

—

1 2 3 4 5

Lower limit of class diameter (mm)

Figure 4.36 Drop size distribution at different lance height(2-D)

99.8

98

90

U) 0) <:

Q> > •>-> CO 13

E 3

o

80

60

40

20

10 -

2 -

0.1

-

—

—

—

—

—

I

I

!

I

I

l

1 1

top blowing only lance height: 60 m m

gas flow rate: ____- D 60.81 l/min ~~

- — - — ' ^^ ^53.74 l/min ^ ^ ^ ^ ~ " V46.67 l/min vT^ ^ ^ - ^ • 3 9 . 6 0 l/min _ s > > < ^ / ^ O 32.03 l/min

v/\ w ^v^N.

\ ^v >^ —

0\ Nv \

\^ —

I I 1 2 3 4 5

Lower limit of class diameter (mm)

Figure 4.37 Drop size distribution at different top flow rate(2-D)

99.98

99.8

99

95 ^ fV- 90 -

Ui 80 "<1>

§> 60

E 3

o

40

20 -

10

5 top flow rate: 46.67 l/min

— lance height: 60 m m

2

1 r-

0.5

O A D

V

I

bottom flowrate: 0.99 l/min.

one tuyere at centre

1.98 l/min

2.79 l/min J

1.98 l/min,two tuyeres, 25 m m from centre top blowing only

in all cases

1 1 _L 1 2 3 4 5

Lower limit of class diameter (mm)

Figure 4.38 Effect of bottom blowing on the drop size distribution(2-D)

99.9 -

99

95

~ 90

_ 80

G> 60

> +--

03 D

E D

o

40

20

10

2

1

0.2

005

top blowing only gas flow rate: 46.67 l/min lance height:

O 40 mm V 60 mm A 70 mm D 80 mm

i. _L _L _L X 2 3 4 5 6 7

Lower limit of class diameter (mm)

-I

8

Figure 4.39 Drop size distribution at different lance height(3-D)

99.9 -lance height: 80 m m top blowing only gas flow rate: V 65.80 l/min • 53.74 l/min A 46.67 l/min O 32.60 l/min

2 3 4 5 6 7

Lower limit of class diameter (mm)

Figure 4.40 Drop size distribution at different top flow rate(3-D)

49

height, in other words with increasing jet momentum at the bath surface. This

dependence of drop size on blowing conditions implies that the refining rate via metal

droplets reaction could be of less importance with flow patterns that favour the production

of larger size droplets which provide a smaller surface area per unit mass.

The exception in Fig. 4.36 can be explained if the data are replotted in terms of the drop

generation rate as a function of lance height as shown in Fig. 4.41. From Fig. 4.41 it can

be seen that the drop generation rate increases with decreasing lance height when the lance

height is large. The maximum rate is reached at the lance height of about 100mm and

then the drop generation decreases with further decrease of the lance height. Visual

observations of the bath surface showed that when lance height is reduced down to near

100mm, very deep penetration forms in the bath surface and a large proportion of large

size droplets is entrained by the jet and returned to the bath, and the more so the lower the

lance height. This phenomenon results in the decrease in the amount of the splash and the

proportion of large droplets. That is why the mean drop size decreases with decreasing

lance height in Fig. 4.36.

From Fig.4.38 it can be seen that the introduction of bottom blowing leads to the increase

in the mean size of the droplets. This result may be explained by the "ripple theory"

discussed in Section 4.1.1. The ripples in the surface of the crater caused by bottom

blowing might result in liquid tears at the edge of the crater and therefore also large

droplets. The increased proportion of large droplets due to the bottom blowing would

decrease the effect of the bottom blowing on steelmaking refining rate than may be

expected on the basis of the amount of droplet alone because for the same amount of

splash larger droplets give a smaller surface area which affects the refining rate.

0.90

0.75

0.60

0.45

0.30

0.15

—

l l i l

top blowing only gas flow rate: 46.67 l/min

I l l I

I

I

I

I

I

I

I

I

—

-

—

-

—

i

20 40 60 80 100 120 140

Lance height (mm)

160 180

Figure 4.41 Variation of drop generation rate with lance height(2-D)

50

4.3 R E S I D E N C E T I M E O F D R O P L E T S

The residence time or settling time of the metal droplets in the slag influences the refining

rate of the BOF steelmaking process [10,34]. The residence time provides a chance for

the droplets to react with the slag and consequendy to be refined. It can be imagined that

if the metal droplets stayed in the slag for zero time, they would fall back into the bath

with the initial composition so that they would not cause the bath refinement due to

mixing. For droplets to reside in the slag for too long is not a desirable case either.

Thus, any information on the residence time of the droplets in the slag should provide a

better understanding of the BOF process, in terms of the refining rate. However, due to

the difficulty in obtaining the residence time experimentally, either from an industrial scale

converter or from a model, very few experimental studies [34] on the residence time have

been carried out

As far as is known, the only measurement of the residence time in a BOF vessel was

performed by Price [4], who employed a radioactive gold isotope tracer technique. The

average residence time obtained from this investigation was 2.0 ± 0.5 min. However, the

assumptions made in this study may have resulted in this estimated value of the mean

residence time being larger than it should have been. This will be discussed later.

The purpose of this part of the present investigation is to study the residence time of the

droplets dispersed in the slag, with emphasis on the effect of blowing parameters on the

residence time, rather than their absolute values in the BOF steelmaking process, by use

of a two-phase (mercury/glycerine) model.

4.3.1 Definition of Mean Residence Time

During the blow, metal droplets are ejected out of the bath into slag due to impingement

of gas jet on the bath surface. The droplets fall back into the bath after spending a certain

residence time in slag. The results of preliminary experiments in which mercury and

glycerine were used to simulate liquid steel and slag, respectively, show that the amount

51

of mercury in glycerine accumulates in the initial stage of the blow and then reaches

steady state after a certain length of blowing time (see Fig. 3.8). This indicates that the

rate of generation of the droplets is initially higher than the rate at which the droplets

return to the bath from the slag layer, and these two rates tend to become equal as the

blowing time increases.

Droplets of different size have different residence time in the slag, due to different settling

velocities. It is assumed that the droplets have a residence time distribution as shown in

Fig.4.42.

After a blowing period of o-t, the droplets which are generated at time ti between o-t, and

whose residence time is less than t-ti have returned to the bath. If the drop generation

rate is assumed to be constant throughout the blow, the total amount of droplets produced

and the total amount of droplets returned within this period can be expressed by the

following equations.

Q l = qi-t

03 = rt qi

t-ti (t>(t) dx dti = qi

o o

t-ti <))(T) dx dti

(4.2)

(4.3)

where qi - drop generation rate, constant throughout blow

Ql - the total amount of droplets produced

Q3 - the total amount of droplets returned to the bath

t - blowing time

<|)(x) - residence time distribution density

x - residence time

From material balance the amount of droplets in slag layer (Q2) is

02 =Ql-Q3

= qi-t - qi o

t-ti <J>(x) dx dti (4.4)

c o -*-t

D JQ s_ *-• CO

0)

E

CD O

c CD

•o Ui CD

cr CN

CD J_

ZJ

L

e

A

3>R(T)

•mm XR

Figure 4.43 Residence time distribution of plug flow

52

If it is assumed that all droplets have the same residence time, XR, in the slag, then the

corresponding residence time distribution is shown in Fig.4.43.

Mathematically,

<1>R C O = | oo X = X R

[o X^XR (4.5)

N o droplets return to the bath during the period of blowing time O-XR, that is,

Q 3 = qi TR TR-ti

4>R (t) dxdti = 0

o

(4.6)

and, steady state is reached at time XR. S O , w e have,

Q 2 =qi.ts-qi Jo

ts-ti <j)(x) dx dti

o

= qi-tR - qi TR

O

TR-tl <)>R(X) dx dti

o

= qi-XR (4.7)

where ts - time needed for attaining steady state.

From eqn.(4.7) the mean residence time is then simply

XR = 02/qi (4.8)

53

4.3.2 Effect of Blowing Condition on the Residence Time

In these experiments, two parameters needed to be determined from the experiments, the

total amount of mercury in the emulsion at steady state, and the drop generation rate, i.e.

Q2 and qi in eqn. (4.8). The former was obtained after the blow of 8 min. The blowing

time for obtaining steady state was selected on the basis of the preliminary results shown

in Fig. 3.8. Total amount of mercury in glycerine layer after nitrogen blow of 1.0s into

the bath was divided by the blowing time to give the value of qi, assuming that no

droplets fell back into the bath during this time. The droplet generation rate is assumed to

be constant throughout the period of blowing time for a given blowing condition. The

details of apparatus and procedure employed in these experiments were described in

Chapter HI.

Figures 4.44-4.46 show the effect of top gas flow rate, bottom gas flow rate of combined

blowing and top lance height on the mean residence time, respectively. From these

results it is evident that:

(i) the mean residence time significantly increases with increasing top gas flow rate

(Fig. 4.44),

(ii) the mean residence time decreases with increasing bottom gas flow rate in combined

blowing process (Fig. 4.45),

(iii) the mean residence time increases at first, and then decreases as the top lance height

increases. A maximum residence time is obtained at a certain lance height (Fig.

4.46).

The residence time of droplets in slag mainly depends on the following factors.

(a) Physical properties of slag, e.g. viscosity and density. The higher the viscosity and

density are, the longer is the residence time.

20

16

co

CD 12

E

CD

o c CD

!E CO CD c CO CD

8

50

top blowing only lance height: 50mm

1 1 60 70 80

Top gas flow rate , //min

90

Figure 4.44 Effect of top flow rate on the residence time

16

combined blowing top flowrate:80.4 //min lance height:50 m m O one tuyere at centre 0 two tuyeres,symmetrically

30 m m from centre

2 4

Bottom gas flow rate , //min

Figure 4.45 Effect of bottom flow rate on the residence time

o

o CO

o m

o

o CO

o CN

O T—

E F

mC

O) CD SZ

o o c CO -1

CD

E *m<

CD O

c CD TJ CO <D

a> sz a--

c o *-• x: O) CD SZ

CD O c ca

•a—

o *-•

o CD H—

LU CD

CD

i l

S ' 9LUIJ 90Uep!S9J UB9I/\J

54

(b) Turbulence of slag layer, which results in longer residence time.

(c) Degree of slag foaming which leads to an increase in thickness of slag layer and a

decrease in bulk density of slag. The decrease in the slag bulk density results in

higher setding velocity of the droplets. The increase in the thickness increases the

distance for the droplets to travel in the slag.

(d) Drop size distribution. The smaller the droplets, the longer is the residence time.

(e) Height to which the droplets are ejected. Obviously, the larger the height, the

longer is the time period during which the droplets are out of the bath.

(f) Decarburization rate. The dispersed droplets are decarburized during their stay in

the slag to form CO bubbles, which may attach themselves to the droplets. The CO

bubbles significantly affect the residence time of the droplets in the slag [78,79].

The existence of the bubbles results in a decrease in the settling velocity of the

droplets, or even a change in direction of movement of small droplets [78,79].

Therefore, the occurrence of decarburization of the droplets in the slag leads to an

increase in their residence time in the slag. Unfortunately, this phenomenon could

not be simulated in the present cold model experiments.

The results shown in Figs. 4.44-4.46 can be explained from the viewpoint of the factors

described above. Figure 4.44 shows the effect of top gas flow rate on the mean residence

time. Increase in top gas flowrate increases (i) degree of slag foaming, as it is shown in

Fig. 4.47, where bulk density of glycerine decreases with increases in top gas flow rate

(ii) turbulence of slag phase, (iii) height to which the droplets are ejected and, (iv) size of

the droplets (see Section 4.2). As discussed above, these parameters, except the drop

size and degree of slag foaming, all result in longer residence time of the droplets in the

slag. The reason for the increase in the average residence time with top gas flowrate, as

shown in Fig.4.44, is probably due to (ii) and (iii) above. The effects of drop size and

>» c o

E f= o in . a

a-* ass: c 5 o XI

Q. O

D) CD £

<D o c CO

i

o CO

CO

o

c

E CQ

o CD

c 1—

CD

u >.

o co

o <*

o CM

c ._ E *—

CD CQ i_

it O 5= CO CO

D. O 1-

o CD CD i_

CD •a

CD SZ +-<

c o CD

ca 5 o H—

CO ca

CL

o

;LU0/6 ' 9UU90A|6 BUJIUBO^ 3,0 Ai!SU9Q

o CD »*-UJ

•

CD i-

3 U)

55

degree of slag foaming are relatively small compared with the combined influence of the

other two factors.

The result in Fig.4.45 shows that the residence time decreases with increase in bottom

gas flowrate of combined blowing. A m o n g the factors influencing the residence time

discussed earlier, the drop size is the only factor significantly influenced by bottom

blowing. The increase in droplet size accompanying bottom blowing (see Section 4.2)

results in a decrease in the mean residence time.

As shown in Fig.4.46, the average residence time at first increases and then decreases as

the lance height is increased. A maximum value is obtained at a critical lance height. This

result is very similar to that of an increase in the top gas flow rate, because they both lead

to an increase in the jet momentum at the bath surface. As discussed in connection with

the effect of top gas flow rate, decrease in the lance height results in an increase in the

mean residence time in this region. Further decrease in the lance height causes the

formation of a deep depression in the bath surface. Under these conditions big bubbles

form around the nozzle (see Section 4.1.2) and, on escaping from the bath, they carry

large fragments of the lower phase into the upper phase with them. Being large in size,

these fragments fall back into the bath very soon after generation, and this explains the

observed decrease in the residence time as shown in Fig.4.46.

4.3.3 Discussion

Although the conditions in the model and in the real system can not be identical, and

therefore the absolute values of the residence times may be different, the influence of the

factors relating to blowing conditions on the residence time are considered to be not too

different in the two cases. Therefore, it is reasonable to expect similarity of the variation

of the residence time with the blowing parameters between the model and the converter.

Hence, the results of the present work may be used, at least qualitatively, to explain the

phenomena occurring in the real system, and gain better understanding of the process.

56

In Section 4.1.2 the effect of bottom blowing on the refining rate of the B O F steelmaking

was discussed. It was pointed out that the increased proportion of large droplets due to

the bottom blowing would decrease the effect of the bottom blowing on the steelmaking

refining rates that may be expected on the basis of the droplet generation rate (ejected

weight per unit time) or the total amount of metal emulsified in the slag layer alone. This

is because larger droplets create smaller surface area per unit mass. In making this

conclusion, however, the residence time was not taken into account. Whether and how

the residence time influences the effect of the bottom blowing on the steelmaking refining

rates depends on the relative value of the residence time and the reaction time needed for

obtaining the chemical equilibrium between the droplets and the slag. The refining rate

will be increased by the bottom blowing if the residence time is equal or greater than the

required reaction time.

Although the introduction of bottom blowing results in a decrease of droplet residence

time (Fig.4.45), the refining rate may, or may not, be decreased, as this depends on the

reaction time, metal emulsification rate and droplet size distribution. Oeters [75] has

shown that for reasonable values of the mean droplet size and average residence time, the

droplets will essentially reach equilibrium with the slag, even with the relatively low mass

transfer coefficient expected [76] for fine droplets suspended in a slag. This suggests that

the residence time is longer than the reaction time required for equilibrium, and the

decrease in the residence time due to the introduction of bottom blowing may actually

increase the refining rate of the B O F steelmaking.

As is known, the residence time of the droplets in the slag is of importance to the refining

rate due to the reaction occurring in the emnlsion. But its absolute value is, at present,

still uncertain. The average residence times of a wide range viz., 0.25s - 2.5min, have

been evaluated by experiment [34], or obtained from experience [7,15,18,74].

Price [34] measured the mean residence time in an industrial scale converter using a

radioactive gold isotope tracer technique. In this work, the period from the instant at

57

which the isotope was added into the bath to the time at which the two radioactivity

levels, viz. those of bath and droplets, became similar was taken as a half of the average

residence time. A value of 2.0±0.5min was obtained. However, this value may be larger

than it should have been, because: (i) the isotope needed a certain time to dissolve in the

bath so that some of the ejected droplets were radioactive and some of them were not.

This gave an impression of lower droplet replacement rate than it was in reality and

consequendy longer residence times were obtained than they should have been; (ii) the

time taken for the two activity levels (bath and droplets) to become similar was taken as

one half of total residence time. This value also represented the time taken for non­

radioactive droplets to return to the bath. Because smaller droplets stay in the slag longer

under otherwise identical conditions, the residence time estimated in this way was actually

that of the smallest droplets among those which had returned to the bath and,

consequently, the residence time was greater than the average value; (iii) the assumption

that the time for radioactive droplets to be ejected from the bath to the emulsion were

equal to that for non-radioactive droplets to return to the bath from the emulsion also

resulted in residence time overestimates because the former is much smaller than the

latter.

In the work of Urquhart et al [15] a mean residence time of 0.25s was assumed, based

upon the observation of room temperature experiments, for their mass transfer calculation

of hot model experiments.

Kozakevitch [7], following his investigation into the metal/slag emulsion, pointed out that

the mean residence time may be of the order of l~2min, perhaps much less, but certainly

not more.

In the work by Oeters [74], on kinetic treatment of chemical reactions in emulsion

metallurgy, an average residence time of l.Omin was suggested. This suggested value

was used by Jahanshahi and Belton [18] in their dephosphorization calculation in which

the reactions occurring in the emulsion were considered to dominate the overall refining

58

rate of the BOF steelmaking process. It was found that the observed rate was broadly in

accord with expected rate for the emulsion mechanism.

From the above discussion it appears that a value of l.Omin, or so, for the mean

residence time of metal droplets is reasonable.

59

Chapter V. C O N C L U S I O N S

The refining rate of the BOF steelmaking due to the reaction of the dispersed droplets is

determined by the total amount of metal droplets in the metal/slag emulsion, the droplet

size distribution and the residence time of the droplets. The former two parameters

provide the total interfacial area for the reaction, and the latter allows the droplet to have

the chance to react with slag.

The present investigation was originally conceived as a fundamental study of the

interaction between oxygen jet and liquid metal bath and the effect of bottom blowing on

the interaction in the combined blowing B O F steelmaking process in the respect of the

three parameters mentioned above. It is believed that the present study is a positive

contribution to an understanding of the fundamentals of the B O F steelmaking process in

terms of the refining rate.

On the basis of this investigation, the following conclusions can be drawn.

1. From the observation of the high speed films it has been found that the drop

generation due to a gas jet impinging on a liquid surface is caused by the "ripple

mechanism", but not the periodic vertical and horizontal oscillations of the

impingement zone [15,26,27].

2. The results of this study indicate that there are different mechanisms of the drop

generation in the "dropping" and the "swarming regions. Ejections of individual

droplets and liquid fragments at the edge of the crater are characteristics of the

"dropping" and the "swarming" regions respectively. The criterion of top gas flow

rate for the transition from the "dropping" to the "swarming" can be changed by the

introduction of bottom blowing. The value of the criterion decreases with

increasing bottom flow rate.

60

3. The results of the present study have shown that bottom blowing significandy

increases the amount of droplets ejected, and that this increase is principally caused

by the interaction of the bottom blowing and top blowing in the impingement zone,

and not by the bottom blowing as such. The effect of bottom blowing on the

droplet production weakens with increase in top flow rates.

4. Droplet production is not a monotonous function of lance height. The amount of

dispersed droplets increases up to a maximum value with decreasing the lance

height. Any further decrease in the lance height beyond this causes the volume of

splashing to be reduced.

5. The direct and indirect effects of bottom blowing on the droplet generation are

defined in this work. The amount of droplets ejected is more increased due to the

introduction of bottom blowing by the former than the latter.

6. It has been found from this investigation that the effect of bottom blowing can be

intensified or weakened by changing the positions of the bottom tuyeres. For

combined blowing, more droplets are produced when the tuyeres are located

underneath the impingement zone than if they are positioned outside the zone.

Additionally, the "apparent tuyere position" should be taken into account in terms

of the effect of the tuyere position on the droplet generation.

7. The results of the present investigation indicate that the size distribution of the

droplets produced by an impinging gas jet obeys the normal distribution function.

The proportion of large droplets increases with increase in the jet momentum at the

undisturbed bath surface {by increase in the top gas flow rate or decrease in the

lance height). It has been also found that the introduction of bottom blowing leads

to an increase in the mean droplet size. The increased proportion of large droplets

due to the introduction of bottom blowing and the increase in the jet momentum at

the bath surface would result in less effect of those blowing parameters on the BOF

61

steelmaking refining rate than may be expected on the basis of the total amount of

the droplets alone.

From the experiments on the residence time, it has been found that the mean

residence time defined in Section 4.3.1 increases with increase in top gas flow rate

and decreases with increasing bottom flow rate of combined blowing. A s the

droplet production, the mean residence time at first increases and then decreases as

the lance height is increased. A maximum value of the residence time is obtained at

a certain lance height The decrease in the residence time due to the introduction of

bottom blowing would increase or decrease the steelmaking refining rate,

depending on relative value of the residence time to the reaction time required for

obtaining equilibrium with the slag.

As is known, there are large differences of properties between modelling liquids

and molten steel, which could make the application of the present results to the real

system questionable. However, from the results of this investigation it is found

that the similarities between model and prototype may exist, at least qualitatively.

The evidence obtained from the present study suggests that there is a strong

indication to take the jet m o m e n t u m number defined in Section 2.6 as a link

between the model and the prototype in terms of droplet generation due to an

impinging gas jet.

62

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65

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67

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68

A P P E N D I X

EXPERIMENTAL DATA

Table 1 Build-up of H g content with blowing time

Blowing conditions

Combined blowing

Top flow rate:

57.161/min

Bottom flow rate:

1.86 1/min

Lance height: 50 m m

One tuyere at centre

Blowing time (min)

0.5

1.0

1.0

2.0

4.0

6.0

8.0

10.0

12.0

15.0

15.0

Hg content (%)

4.83

5.11

5.09

5.65

5.71

6.44

6.46

6.69

6.31

7.15

6.33

Table 2 Effect of viscosity on H g content of the emulsion

Blowing conditions

combined blowing

gas flow rate:

57.161/min (top)

1.86 1/min (bottom)

lance height: 50 m m

one tuyere at the centre

Percentage of glycerine (%)

56

68

88

92

96

100

Viscosity (N.s/m2)

10.0

27.5

105.5

385.0

770.0

1487.0

Hg content (%)

1.33

1.66

1.59

2.40

3.01

4.90

3 Variation of drop generation rate with top flow rate(water model)

Table 3.1

Blowing conditions

top blowing only

lance height:

80 m m

Top flow rate (1/min) !

23.23

27.28

31.61

35.94

39.84

44.17

48.50

53.26

57.16

61.64

Drop generation rate (g/s)

0.031

0.250

1.198

2.690

6.200

14.090

21.280

26.980

34.530

38.400

,

0.038

0.250

1.199

2.820

6.070

14.160

20.410

26.030

34.190

38.860

Table 3.2

Blowing conditions

combined blowing

one tuyere at the centre

bottom flow rate:

1.081/min

lance height: 80 m m

Top flow rate (1/min)

27.28

31.61

35.94

39.84

44.17

48.50

53.26

57.16

61.64

Drop generation rate (g/s)

0.26

1.09

2.85

8.95

16.02

23.80

28.50

34.64

39.22

0.29

1.12

2.88

9.01

15.93

23.5

29.00

35.47

39.99

Table 3.3

Blowing conditions

combined blowing

two tuyeres located

symmetrically 30 m m

from centre

bottom flow rate:

2.68 1/min

lance height: 80 m m

Top flow rate (1/min)

27.28

31.61

35.94

44.17

48.50

53.26

57.16

61.64

Drop generation rate (g/s)

1.20

3.06

5.49

20.16

26.70

32.83

40.82

44.37

1.15

2.99

5.34

20.04

27.27

33.15

40.13

44.11

Table 3.4

Blowing conditions

combined blowing

one tuyere at centre

bottom flow rate:

2.681/min

lance height:

80 mm

Top flow rate (1/min)

27.28

31.61

35.94

39.84

44.17

48.50

53.26

57.16

61.64

Drop generation rate (g/s)

2.18

6.74

13.20

20.51

23.12

32.34

35.31

40.06

43.38

2.38

6.91

10.69

20.45

25.51

30.58

35.07

40.68

44.64

Table 3.5

Blowing conditions

combined blowing

one tuyere at centre

bottom flow rate:

6.67 1/min

lance height:

80 mm

Top flow rate (1/min)

27.28

31.61

35.94

39.84

44.17

48.50

53.26

57.16

61.64

Drop generation rate (g/s)

6.83

12.63

15.32

24.91

26.69

31.69

35.27

40.79

43.53

6.67

12.97

15.34

21.93

27.16

31.91

34.56

40.57

44.10

Table 4 Variation of H g content in glycerine with top flow rate

Table 4.1

Blowing conditions

top blowing only

lance height:

25 mm

one - hole nozzle

Gas flow rate (1/min)

23.23

31.61

39.86

48.50

57.16

66.25

72.03

80.40

80.40

86.00

86.00

94.00

94.00

102.00

H g content (%)

3.52

4.54

7.02

10.73

18.69

26.60

30.66

37.47

36.48

38.17

37.70

43.98

42.09

44.54

Table 4.2

Blowing conditions

combined blowing

one tuyere at centre

bottom flow rate:

1.47 1/min

lance height: 50 m m

Top flow rate (1/min)

31.61

39.86

48.50

57.16

66.25

76.70

86.00

Hg content (%)

1.34

1.59

1.75

2.81

3.57

7.54

10.82

Table 4.3

Blowing conditions

top blowing only

lance height: 50 m m

Top flow rate (1/min)

31.61

39.86

48.50

48.50

57.16

66.25

66.25

71.00

76.70

80.40

80.40

86.00

Hg content

0.58

0.73

0.79

0.79

1.41

2.61

2.95

3.52

6.02

6.17

8.32

9.55

Table 4.4

Blowing conditions

combined blowing

one tuyere at centre

bottom flow rate:

3.2 1/min

lance height: 50 m m

Top flow rate (1/min)

31.61

39.86

48.50

48.50

57.16

66.25

71.00

71.00

80.40

86.00

Hg content

2.44

2.74

3.34

3.66

4.13

6.44

6.91

6.78

11.54

13.41

Table 5 Variation of drop generation rate with bottom flow rate (water model)

Table 5.1

Blowing conditions

combined blowing

two tuyeres located

symmetrically 30 m m

from centre

top gas flow rate:

48.5 1/min

lance height: 80 m m

Bottom flow rate (1/min)

0.00

1.08

1.47

1.86

2.29

3.07

3.46

3.85

4.24

4.68

5.07

5.89

6.28

6.67

7.27

Drop generation rate (%)

21.28 |

24.20

24.85

25.47

26.50

28.15

29.94

29.96

29.04

30.47

31.58

31.50

32.22

33.00

32.48

20.41

24.17

24.93

24.95

26.34

28.72

29.20

29.23

28.94

30.31

31.72

31.10

32.48

33.27

32.66

Table 5.2

Blowing conditions

combined blowing

one tuyere at centre

top flow rate:

38.841/min

Bottom flow rate (1/min)

0.00

1.08

1.86

2.68

3.46

4.24

5.07

5.89

6.67

7.49

Drop generation rate (%)

6.20

8.61

10.74

12.39

16.76

20.28

21.96

23.89

24.85

24.87

6.07

8.76

10.31

12,68

16.62

20.79

21.93

23.52

24.13

24.46

Table 5.3

Blowing conditions

combined blowing

one tuyere at centre

top flow rate:

53.261/min

-

Bottom flow rate (1/min)

0.00

1.08

1.86

2.68

3.46

4.24

5.07

5.89

6.67

7.49

Drop generation rate (%)

25.96

28.50

29.85

30.18

32.71

32.93

33.43

34.01

34.66

33.87

26.03

28.72

29.43

30.71

32.84

33.43

33.84

34.27

34.42

33.85

Table 6 Variation of Hg content in glycerine with bottom flow rate

Table 6.1

Blowing conditions

top blowing only

flow rate: 80.41/min

lance height: 5 0 m m

Bottom flowrate (1/min)

0.0

1.17

2.01

2.89

3.74

4.58

4.58

5.48

5.48

5.48

6.36

Hg content

5.55

6.96

8.38

9.08

9.76

9.97

10.12

10.10

10.85

10.53

10.51

Table 6.2

Blowing conditions

combined blowing

one tuyere at centre

top flow rate:

39.84 l/min

lance height:

50 mm

Bottom flow rate (1/min)

0.0

1.08

1.86

2.86

3.46

4.24

5.07

5.89

6.67

7.49

Hg content (%)

0.11

1.93

2.19

2.47

3.13

5.15

4.14

4.66

4.89

4.89

Table 6.3

Blowing conditions

combined blowing,

two tuyere located

symmetrically

30 m m from centre,

top flow rate:

80.4 1/min

lance height:

50 mm

Bottom flow rate (1/min)

0.0

2.34

2.34

3.18

3.18

4.96

4.96

4.96

5.78

5.78

Hg content (%)

6.17

13.09

13.21

15.15

15.4

16.5

18.36

17.34

17.94

17.76

Table 6.4

Blowing conditions

bottom blowing only

one tuyere at centre

Bottom flow rate 0/min)

1.86

3.46

5.07

6.67

7.49

8.2

Hg content

0.58

0.86

1.1

1.3

1.36

1.66

Table 7 Variation of drop generation rate with top flow rate(water model)

Table 7.1

Blowing conditions

combined blowing

two tuyere located

symmetrically

30 m m from centre

bottom flow rate:

2.681/min

top flow rate:

48.51/min

Lance height (mm)

20

30

40 |

50

60

70

80

90

100

110

120

130

140

150

160

180

200

Drop generation rate (g/s)

24.16

29.53

30.97

30.94

30.22

29.69

27.26

26.36

25.50

23.92

22.40

20.01

18.84

15.96

14.46

12.45

8.86

23.78

28.73

31.16

30.92

30.47

29.94

27.27

26.58

25.03

23.56

22.72

19.92

18.76

15.94

14.39

12.35

8.89

Table 7.2

Blowing conditions

top blowing only

flow rate:

57.161/min

Lance height (mm)

10

20

40

60

80

100

120

140

160

Drop generation rate (g/s)

22.95

25.96

33.03

34.50

34.27

32.10

26.96

24.69

19.24

22.33

26.29

33.05

35.46

33.83

31.76

27.98

23.88

18.93

Table 7.3

Blowing conditions

top blowing only

flow rate:

48.51/min

Lance height (mm)

10

20

40

60

80

100

120

140

Drop generation rate (g/s)

16.08

19.27

22.52

21.82

20.08

16.62

14.04

9.19

16.2

19.41

22.25

22.33

20.44

16.42

13.88

9.13

Table 8 Variation of H g content in glycerine with lance height

Table 8.1

Blowing conditions

top blowing only

flow rate:

80.41/min

Lance height (mm)

10

10

20

20

25

25

30

30

30

35

40

50

60

70

80

Hg content (g/s)

18.01

14.07

28.02

28.28

33.29

33.79

31.69

31.08

27.75

24.76

16.89

9.57

6.92

5.43

3.01

Table 8.2

Blowing conditions

combined blowing

one tuyere at centre

top flow rate:

80.41/min

bottom flow rate;

2.91/min

Lance height (mm)

10

10

20

20

30

30

40

40

40

50

50

Hg content (g/s)

19.02

16.15

34.05

28.90

33.75

37.44

18.93

19.34

23.09

15.00

11.17

Table 8.3

Blowing conditions

combined blowing

two tuyeres located

symmetrically

30 m m from centre

top flow rate:

80.41/min

bottom flow rate:

3.181/min

Lance height (mm)

10

10

20

20

20

30

30

40

40

50

50

Hg content (g/s)

21.6

22.76

39.14

39.63

40.28

38.18

39.33

28.21

28.24

14.99

18.23

Table 9 Variation of H g content with tuyere position

Blowing conditions

combined blowing

two tuyeres located

symmetrically

top flow rate:

80.41/min

bottom flow rate:

3.21/min

lance height:

50 mm

-

Distance from centre (mm)

0

0

10

10

20

20

30

30

40

50

60

70

80

90

Hg content (%)

12.56

11.54

17.0

16.78

18.64

19.97

18.91

18.62

12.98

12.37

10.44

11.43

9.23

10.68

Table 10 Variation of drop generation rate with tuyere position

Blowing conditions

combined blowing

two tuyeres located

symmetrically,

flow rate:

46.67 l/min(top)

2.68 l/min(bottom)

lance height: 8 0 m m

Distance from centre (mm)

0

15

30

45

60

75

Drop generation rate ^ (%)

25.14

26.45

26.46

24.54

24.34

24.45

25.52

25.99

27.14

25.03

24.92

24.60

Table 11 Effect of multi-hole lance on H g content in glycerine (also see Table 4.1)

Table 11.1

Blowing conditions

top blowing only

two-hole nozzle

lance height

25 mm

Top flowrate (1/min)

31.61

39.86

48.50

57.16

66.70

72.03

77.00

86.00

Hg content

1.3

1.8

2.1

2.7

5.4

9.9

16.1

27.4

Table 11.2

Blowing conditions

top blowing only

three-hole nozzle

lance height:

25 mm

Top flowrate (1/min)

39.84

48.50

57.16

66.70

72.03

80.40

86.00

92.00

•

Hg content (%)

1.87

1.92

2.13

3.67

6.79

11.64

14.56

23.10

Table 11.3

Blowing conditions

top blowing only

4-hole nozzle

lance height:

25 mm

Top flowrate (1/min)

48.50

57.16

66.70

72.03

77.00

86.00

H g content (%)

0.63

0.64

0.99

2.14

5.06

5.06

Table 12 Effect of glycerine layer thickness on H g content

Blowing conditions

top blowing only

lance height:

50 mm

Tickness of gly. layer (mm)

15

15

25

35

35

Hg content ~ (%)

15.02

13.98

7.01

5.85

5.48

Total H g in g]

(g)

99.30

95.99

82.22

92.47

88.06

Table 13 Effect of top flowrate on residence time

Blowing conditions

top blowing only

lance height:

50 mm

Top flowrate (1/min)

57.16

71.00

80.4

86.00

Mean residence time (s)

4.85

7.61

12.24

14.27

Table 14 Effect of bottom flowrate on residence time

Table 14.1

Blowing conditions

combined blowing

top flowrate:

80.41/min

lance height: 5 0 m m

one tuyere at centre

Bottom flowrate (1/min)

0.00

2.00

2.89

4.58

5.48

Mean residence time (s)

12.24

4.40

3.04

1.77

1.56

Table 14.2

Blowing conditions

combined blowing

top flowrate:

80.4 l/min

lance height: 5 0 m m

two tuyeres, symme­

trically 3 0 m m from

centre ._ . . .

Bottom flowrate (1/min)

0.00

2.00

2.89

4.58

5.48

Mean residence time (s)

12.24

7.41

6.64

4.54

3.39

Table 15 Effect of lance height on residence time

Blowing conditions

top blowing only

gas flowrate:

80.4I/min

Lance height (mm)

10

25

40

50

Mean residence time (s)

6.55

37.31

24.5

12.24

Table 16 Effect of top flowrate on density of foaming glycerine

Blowing conditions

top blowing only

blow nitrogen into

glycerine bath for

8 min.

lance height:

50 mm

Top flowrate (1/min)

27.28

31.61

35.94

35.94

39.98

44.17

44.17

48.50

57.16

66.25

Foaming gly. density g/cm3

1.230

1.173

1.110

1.105

1.073

1.060

1.040

1.028

1.025

1.025

Table 17 Drop size attribution

Table 17.1

Blowing conditions

top blowing only

top flowrate:

46.671/m in

lance height:

50 mm

3-D model

d (mm)

d>8.0

8.00>d>6.30

6.30>d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

32.78

34.70

41.14

45.65

38.38

23.12

10.46

11.44

6.15

6.81

3.41

wp (%)

12.90

13.66

16.19

17.97

15.11

9.10

4.12

4.50

2.42

2.68

1.34

cwp (%)

12.90

25.56

42.76

60.73

75.83

84.93

89.05

93.55

95.97

98.65

100.00

Table 17.2

Blowing conditions

top blowing only

top flowrate:

46.67 1/min

lance height:

60 m m

3-D model

d (mm)

d>8.00

8.00>d>6.30

6.30>d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

13.41

38.61

57.29

51.19

45.60

31.81

15.51

15.93

9.13

9.82

3.19

wp (%)

4.60

13.25

19.65

17.55

16.64

10.92

5.32

5.46

3.13

3.37

1.09

cwp (%)

4.60

17.85

37.50

55.05

70.69

81.61

86.93

92.39

95.52

98.89

100.00

Table 17.3

Blowing conditions

top blowing only

top flowrate:

46.67 1/min

lance height:

70 m m

3-D model

d (mm)

d>8.00

8.00>d>6.30

6.30>d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

1.90

17.31

35.77

41.68

37.23

25.27

15.54

13.28

8.32

7.57

1.52

wp (%)

0.90

8.43

17.42

20.29

18.13

12.30

7.57

6.47

4.05

3.69

0.74

cwp (%)

0.90

9.35

26.77

47.06

65.19

77.49

86.06

91.52

95.57

99.26

100.00

Table 17.4

Blowing conditions

top blowing only

top flowrate:

46.67 1/min

lance height:

80 m m

3-D model

d (mm)

d>8.00

8.00>d>6.30

6.30>d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

0.26

11.26

25.00

46.98

43.19

28.08

16.35

14.66

8.63

8.47

3.31

wp (%)

0.13

5.46

12.12

22.77

20.94

13.66

7.93

7.11

4.18

4.11

1.60

cwp (%)

0.13

5.58

17.70

40.48

61.41

75.07

83.00

90.11

94.29

98.40

100.00

Table 17.5

Blowing conditions

top blowing only

top flowrate:

32.53 1/min

lance height:

80 m m

3-D model

d (mm)

d>8.00

8.00>d>6.30

6.30>d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m

(g)

0.00

2.24

11.01

20.06

25.55

23.71

13.79

12.63

7.34

7.23

1.98

wp (%)

0.00

1.78

8.77

15.98

20.35

18.89

10.89

10.06

5.85

5.76

1.58

cwp (%)

0.00

1.78

10.55

26.53

46.88

65.77

76.75

86.81

92.66

98.42

100.00

Table 17.6

Blowing conditions

top blowing only

top flowrate:

53.741/min

lance height:

80 m m

3-D model

d (mm)

d>8.00

8.00>d>6.30

6.30>d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

3.71

18.10

42.43

49.88

42.01

29.88

16.92

14.81

9.67

9.72

3.27

wp

1.54

7.53

17,65

20.75

17.47

12.43

7.04

6.16

4.02

4.04

1.36

cwp (%)

1.54

9.07

26.72

47.47

64.95

77.38

84.41

90.57

94.60

98.64

100.00

Table 17.7

Blowing conditions

top blowing only

top flowrate:

65.8 1/min

lance height:

80 m m

3-D model

d (mm)

d>8.00

8.00>d>6.30

6.30>d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

14.32

35.14

70.96

71.29

52.77

30.65

16.28

16.47

9.46

10.19

3.81

wp (%)

4.32

10.61

21.14

21.52

15.93

9.29

4.91

4.97

2.86

3.08

1.15

cwp (%)

4.32

14.93

36.29

57.81

73.73

83.03

87.95

92.92

95.77

98.85

100.00

Table 17.8

Blowing conditions

top blowing only

flowrate:

32.531/min

lance height:

60 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

0.21

1.09

4.27

5.11

2.83

2.72

1.38

1.38

0.39

wp (%)

1.10

5.64

22.04

26.36

14.60

14.03

7.12

7.12

2.01

cwp (%)

1.10

6.74

28.77

55.13

69.73

83.75

90.87

97.99

100.00

Table 17.9

Blowing conditions

top blowing only

flowrate:

39.601/min

lance height:

60 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

1.48

4.71

9.97

8.41

6.38

5.66

3.20

2.88

0.66

wp (%)

3.40

10.87

23.00

19.40

14.72

13.06

7.38

6.64

1.52

cwp (%)

3.40

14.27

37.27

56.67

71.39

84.44

91.82

98.47

100.00

Table 17.10

Blowing conditions

top blowing only

flowrate:

53.741/min

lance height

60 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

26.64

15.72

15.59

13.21

9.00

10.08

5.89

6.41

1.44

wp (%)

25.60

15.11

14.99

12.70

8.66

9.69

5.66

6.16

1.38

cwp (%)

25.60

40.73

55.73

68.44

77.09

86.79

92.45

98.62

100.00

Table 17.11

Blowing conditions

top blowing only

flowrate:

60.811/min

lance height:

60 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

51.95

25.99

24.75

20.73

13.34

16.03

8.82

7.98

3.29

wp (%)

30.05

15.03

14.32

11.99

7.72

9.27

5.10

4.62

1.90

cwp (%)

30.05

45.08

59.40

71.39

79.11

88.38

93.48

98.10

100.00

Table 17.12

Blowing conditions

top blowing only

flowrate:

46.471/min

lance height:

40 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

7.33

7.15

10.09

9.47

6.82

7.55

4.81

4.81

2.08

wp

12.20

11.90

16.79

15.76

11.35

12.56

8.00

8.00

3.46

cwp (%)

12.20

24.10

40.89

56.65

68.00

80.56

88.57

96.57

100.00

Table 17.13

Blowing conditions

top blowing only

flowrate:

46.671/min

lance height:

60 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

8.82

10.57

20.23

15.98

11.00

11.51

6.66

7.37

0.58

wp (%)

9.51

11.40

21.82

17.23

11.86

12.41

7.18

7.95

0.63

cwp

9.51

20.91

42.73

60.00

71.83

84.24

91.43

99.37

100.00

Table 17,14

Blowing conditions

top blowing only

flowrate:

46.67 1/min

lance height:

80 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m

(g)

10.63

14.22

18.37

16.75

11.18

11.56

6.51

6.15

1.86

wp (%)

10.93

14.63

18.89

17.23

11.50

11.89

6.70

6.33

1.92

cwp (%)

10.93

25.56

44.45

61.68

73.18

85.07

91.76

98.09

100.00

Table 17.15

Blowing conditions

top blowing only

flowrate:

46.671/min

lance height

100 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

17.80

22.16

26.48

19.08

13.36

14.23

7.15

7.01

1.49

wp (%)

13.82

17.21

20.57

14.82

10.38

11.05

5.55

5.44

1.16

cwp (%)

13.82

31.03

51.16

66.42

76.80

87.85

93.40

98.84

100.00

Table 17.16

Blowing conditions

top blowing only

flowrate:

46.67 1/min

lance height:

140 m m

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m

(g)

18.20

19.35

19.03

15.56

9.10

8.35

3.83

3.11

1.11

wp

18.64

19.82

19.49

15.94

9.32

8.55

3.92

9.19

1.14

cwp (%)

18.64

38.46

57.95

73.88

83.20

91.76

95.68

98.87

100.00

Table 17.17

Blowing conditions

combinedblowing

flowrate:

46.67 l/min(top)

1.98 l/min(bottom)

lance height 60mm

two tuyeres, 3 0 m m

from centre, located

symmetrically

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m

(g)

82.80

21.85

22.65

14.40

9.53

9.29

5.62

5.13

1.77

wp (%)

47.85

12.63

13.09

8.32

5.51

5.37

3.25

2.96

1.02

cwp (%)

47.85

60.48

73.57

81.89

87.40

92.76

96.01

98.98

100.00

Table 17.18

Blowing conditions

combined blowing

flowrate:

46.671/min (top)

.991/min (bottom)

lance height:

60 mm

one tuyere at centre

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m

(g)

22.57

13.03

20.34

17.32

13.45

13.91

8.15

7.53

0.92

wp

19.28

11.13

17.38

14.80

11.49

11.88

6.96

6.28

0.79

cwp (%)

19.28

30.41

47.79

62.59

74.41

85.96

92.93

99.21

100.00

Table 17.19

Blowing conditions

combined blowing

flowrate:

46.67 Vmin(top)

1.98 l/min(bottom)

lance height:60 m m

one tuyere at centre

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m

(g)

25.25

16.77

16.91

13.79

10.15

10.27

6.41

6.28

2.27

wp (%)

23.36

15.51

15.64

12.76

9.39

9.50

5.93

5.81

2.10

cwp

23.36

38.87

54.52

67.27

76.66

86.16

92.01

97.90

100.00

Table 17.20

Blowing conditions

combined blowing

flowrate:

46.67 1/min (top)

2.97 1/min (bottom)

lance height: 60 m m

one tuyere at centre

2-D model

d (mm)

d>5.00

5.00>d>4.00

4.00>d>3.15

3.15>d>2.50

2.50>d>2.00

2.00>d>1.40

1.40>d>1.00

1.00>d>0.50

0.50>d>0.00

m (g)

26.22

12.39

15.07

13.65

10.82

11.31

6.20

5.57

1.69

wp (%)

25.48

13.01

14.64

13.26

10.51

10.99

6.02

5.41

1.64

cwp (%)

25.48

38.49

53.13

66.39

76.90

87.89

93.92

99.33

100.00