SOLIDIFICATION ANALYSIS OF CRYSTAL GROWTH IN OHNO CONTINUOUS CASTING PROCESS

SOLIDIFICATION ANALYSIS OF CRYSTAL GROWTH IN OHNO CONTINUOUS CASTING PROCESS

Computer Aided Innovation of New Materials M. Doyama, T. Suzuki, J. Kihara and R. Yamamoto © Elsevier Science Publishers B.V. (North-Holland), 591 (...

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Computer Aided Innovation of New Materials M. Doyama, T. Suzuki, J. Kihara and R. Yamamoto © Elsevier Science Publishers B.V. (North-Holland),

591

(Editors) 1991

SOLIDIFICATION ANALYSIS OF CRYSTAL GROWTH IN OHNO CONTINUOUS CASTING PROCESS

J. C. Liu, J. D. Hwang and K. C. Su Materials Research Laboratories, Industrial Technology Research Institute, 195 Chung-hsing Rd., Sec.4, Chutung, Hsinchu, 31015, Taiwan, C h i n a

The Ohno continuous casting process(O.C.C.process) has recently been developed by using a heated mold instead of a conventional cooling mold. This process can produce high quality and smooth surface of directionally solidified or single crystal bars. In this study, a solidification analysis system based on heat transfer equations and solidification theory was developed for the O . C C . process. From our calculation, the temperature distribution and solidification behaviors such as thermal gradient(G), growth rate(R) and the crystal/melt interface were obtained. The effects of process variables including withdrawal speed, heated mold temperature, and cooling conditions were studied. The results of the analysis were compared with the experimental data, which exhibit in good agreement with our simulation. The crystal/melt interface and G/R values have been successfully used to predict whether the casting bars of pure tin or aluminum will result in necking or not during the process.

behaviors over the process. From the numerical

1. INTRODUCTION The Ohno continuous casting process(

O.CC

calculation, the temperature variation, the

process ) has been recently developed by using

configuration of crystal/melt interface and the

heated mold instead of the conventional

temperature gradient(G) were obtained. The calc­

cooling

1 9

mold

. The mold is heated slightly above the

melting temperature of the metal being casted, to prevent nucleation of solid grains from the mold wall. This process can produce near net sh­ ape castings with smooth surface and u n i d i r e g i ­ onally solidified, or even single-crystal struc­ tures. Several factories in Japan have employed this new process to produce pure copper/aluminum wires which have been widely applied for audio, video c a b l e s .

ulated results may provide us a good understand­ ing on the process control and optimize the casting design.

2.

MATHEMATICAL MODEL 2.1. Description of the physical phenomena Figure 1. is a schematic diagram of the vert­

ically upward O . C C . apparatus. The apparatus consists of a stainless steel crucible, a graph­ ite heated mold, cooling system, a dummy bar and

0

The main parameters that dominate the

O.CC

process are withdrawal speed, heated-mold tempe­ rature and cooling conditions. It is very tough to optimize and well control the operating cond­ itions. In past years, there have been some exp­ erimental study in investigating the effects of process variables^, and Wang etal. have employed a enthalpy method to numerically solve the stea­ dy heat flow equation coupled with thermal meas­ urement . However, the aim of this study was to 5

develop a mathematical model with the Finite Difference Method to simulate the solidification

the level control rod. To start up the casting, the dummy bar is set at the mold exit and the level control rod is lowered into the melt to raise the melt surface level to the desired height. As soon as the melt contacts with the dummy bar, coolant is introdu­ ced into cooling system and the dummy bar is pu­ lled by rotating pinch rolls to initiate casting . The cooling system drives the heat flow along axial bar, causing the crystal/melt interface to move in axial direction.

592

I

q:internal

Pinch rolls

a

source

T:temperature

.Dummy bar

t:time

^ Metal bar CJooling system

Level control Muroi rod

heat

p:density

r.zithe

r—

coordinate

in

radial

and

axial

di r e c t i o n 2.4. (1)At

Boundary

the

Conditions

centerline aT

-

7

of t h e metal

0

bar,

r-0

for

ar (2)0n

Heater

Melting metal

the

metal

surface above

of the dummmy

the mold

bar and

the

exit.

aT K 1:

Figure

A schematic upward

OCC

diagram

of

a

= h(T-T
for

r-R

= h(T-T»)

for

z=0

ar

vertically

apparatus

aT K az

2.2.

Assumptions

Although process make

the

are not very

some

follows

it

of the

is n e c e s s a r y

establishing

assumptions

to

the

were made

the

as

is

of the

constant.

natural

convection

in

of the dummmy

or

ambient

(3)At

the

(4)0n

the mold

the

bottom

Tr

bar

or

cooling

system

air

of the

= Tq

of the

melt

Tq:the melt

temperature

Tw:the mold

temperature

wall

= Tw

negligible.

physical linear

properties

to

the O.C.C.

process

solidification

governing

1

a T

ar

as

a

2

method

heat

merical

can

be

follows^:

2

] + q az

a

METHOD the

heat

technique

transfer

equation

by e x p l i c t

finite

was employed. m o d e l , the

number

of

Before

system

regular

discretization re c o m p o n e n t

2

+ r

solve

in

a T

2

+ r

transient

equation

coordinate

aT

+ 2

3. N U M E R I C A L To

is e s s e n t i a l l y The

1

2

metal

numerical

the

in c y l i n d r i c a l e

casting

Equations

earlier,

problem.

aT T p C p — = K[ at ar

of the

temperature.

2.3. Governing As described

expressed

is

surface

metal

T<»:the t e m p e r a t u r e

m-

Tz temperature

effect

transfer

:on t h e

O.C.C.

:

melt

are

before

model. The

(1)The mold

(3)The

phenomena

complex,

assumptions

athematical

(2)The

T

physical

was

was

located

in

difference

establishing first

cells. The mesh

is s h o w n

(2), a

Fig.2.

the

nu­

divided

into

system

The

after

temperatu­

at every

corner

30

45

of

the

cell.

2

M

]

a T 2

For a x i s y m m e t r i c

heat

flow

= 0, and

a

equati-

2

on[1]

can

be e x p r e s s e d

aT

a T

PCp—

= K [ —

at

2

ar

1

aT

r

ar

as:

+

2

aT

2

3 + q

+ — az

[2]

2

0

5

10

15 20

25

35

40

50

55

60

DISTANCE FROM MOLD EXIT CMM3

where K:thermal Cp:specific

conductivity heat

Figure

2: Mesh the

diagram system

of discretization

of

593

Next, the explicit tion

for the conductive

within

T

finite difference

n

the casting

+

1

= T i . i

( T . M . 2*Ti.

T i .

At Ar

K

( T i - i . ;

i

n

equation

The withdrawal

8

of t h e m a i n

as follows

- T i . i

- T i . i

n

n

+

)

)

n

(pCp

s=

r/Ar ( s='1,2,..

•[3]

where

At:time

speed

from

20 mm/min

to 50 mm/min. The mold and the cooling

20 m m a b o v e t h e m o l d

exit with

Fig.3

of various withdrawal

50 mm/min

respectively).

speed

t o 5 0 m m / m i n . T h e full Sn

direction

bar will

get small

exit.

RESULTS AND DISCUSSIONS Based

on the mathematical

above, a solidification

analysis

O . C C process was developed. withdrawal cooling

speed, the mold

system

for the

from

and t h e

physical

properties

investigated. The

and t h e o p e r a t i n g

in t h i s c a l c u l a t i o n

phenom­

a r e listed

conditions

in T a b l e

1.

of different

in F i g . 4 .

It c a n b e s e e n

The

higher

properties of casting

(metal)

Specific (metal) Thermal (metal)

(g/cm ) 3

heat

pure tin bar

Density

(cal/g.deg) 0.054-0.056

heat (dummy

bar)

Specific heat (dummy b a r )

(°c)

232

(cal/g)

12

(g/cm )

8.9

3

(cal/g.deg)

Thermal conductivity (dummy b a r ) (cal/cm.°C.s) Mold

temperature

Cooling water Ambient

7.21-7.17

conductivity (cal/cm. ° C s ) 0.143-0.136

Tm Latent

un d i r e c t i o n a l

temperature

Withdrawal

(°C)

temperature(°C)

velocity

(°C) (mm/min)

0.092

rolled

Fig.5 erent min

236 - 256 25 25 20 - 50

speed

and 55 m m / m i n .

necking

speed

as t h e speed

the crystal/melt exit

interface

ller when

the speed

the calculated

good

casting bar be c o n t ­

case. results of diff­ 25 m m / m i n , 4 0 m m / -

r e s u l t s in

This

is b e c a u s e

is f u r t h e r

a n d t h e G/R v a l u e is a b o v e

away

from

becomes too sma­

30 mm/min

as predi­

r e s u l t s . It t h e r e f o r e

semi-quantitative

the experimental

is f o r

should

and finally increased.

cted

from

30 mm/min.

It d i s c l o s e s that t h e ingot

gets smaller

the mold

about

is

increases and

above

and uniform

in t h i s

with

speed

t h a t t h e G/R v a l ­

i s , the better

withdrawal

30 mm/min

should

solidification.

speed

shows the experimental

casting

diameter

shows 0.94

below

interface

casting

as t h e speed

t h e G/R v a l u e

. Therefore,the values

Density

as the casting

abruptly

from the mold

in f r o n t o f c r y s t a l

interface

producing Table 1 The physical

G/R v a l u e

shown

it d r o p s

pure

in n e c k i n g

e x i t a s p o s s i b l e in

/melt

ue d e c r e a s e s

exit

20 mm/min

diameter of casting er and result

unidirectional

The calculated

that the

out of the mold

increased

the crystal/melt

order to obtain

The effects of the

temperature

Ideally,

rate o f

speed(20,30,40,

It w a s found

keep as close t o t h e mold

described

conditions on the solidification

ena of pure Sn bar were then

used

model

temperatu­

shows the crystal/melt

interface

the withdrawal

speed

system w a s

flowing

as t h e i n t e r f a c e m o v e d m o r e o u t w a r d 4.

beha­

withdrawal

re w a s k e p t a t 2 3 6 ° C

as

values

in t h e radial

is o n e

on the solidification

by increasing

interface w a s progressively

values

step

Ar:mesh s i z e

of casting metal

in t h e O . C C p r o c e s s . It

to the process. The effect of

viors w a s studied

water of 2m/sec.

n= t / A t ( n = 0 , 1 , 2 .

time

sensitive

speed

r

2

nrprevious time

speed

parameters

the withdrawal

W ( T i . i - i

J")

W=

n+1:latest

4.1. T h e effects of t h e withdrawal

is v e r y

+ W(l-l/2s)

n

V(l+l/2s)

+

heat transfer

can be expressed

formula­

agreement

and calculated

between

results.

594

4.2. The effect of the mold exit temperature

MATER RATE HY=2 M/SEC MOLD T=236°C

A heated mold temperature was employed to av­ oid grain nucleation at the inside surface of

R=50 MM/MIN

the mold in this process. Thus the mold exit te­ mperature has a significant effect on the crystal

R=40 MM/MIN

growth. Fig.6 shows the effect of the mold exit temp­ erature on the crystal/melt interface. The mold

R=30 MM/MIN

temperature are 236°C, 246°C and 256°C respecti­ vely, comparing to the melting temperature of

R=20 MM/MIN

pure Sn of 232°C. The withdrawal speed is 30 mm/ min and the cooling system is 20 mm above the

IHEATED MOLD HATER COOLING AREA 0 10 20 30 40 50 60 70 80 90 DISTANCE FROM MOLD BOTTOM CMMD

mold exit. It can be seen that the interface is getting out of the mold exit as the mold temper­ ature increases. Because the higher mold exit

Figure 3: The effect of various withdrawal speed (20,30,40,50mm/min) on the crystal/m­ elt interface 3000

temperature is the more superheat it provides, the high mold exit temperature obliges the crystal/melt interface to move away from the mold exit. It seems that the mold exit temperat­ ure at 236°C will be suitable in this operating

2500

condition. £

2000 H

PULLING RATE R=30 MM/MIN w w Cu H

z w

1500 H 1000

MOLD T=256°C

500 - i

5

MOLD T=246 °C DISTANCE F R O M C E N T E R O F B A R

(mm)

Figure 4: The calculated G/R value of various withdrawal speed.

MOLD T=236 C HEATED MOLD COOLING HATER AREA 0 10 20 30 40 50 60 70 80 90 DISTANCE FROM MOLD BOTTOM CMM) Figure 6: The effect of mold exit temperature on crystal/melt interfacejthe temperature is varied from 236°C to 256°C 4.3. The effect of cooling conditions Most of the heat was extracted from the cool­

Figure 5: The experimental results of various withdrawal speed on crystal growth: (a) 25 mm/min, (b) 40 mm/min,and (c) 55 mm/min.

ing system in the O.C.C.process. The cooling conditions such as the cooling method and the position of cooling system will have a obvious effect on the process.

595

4.3.1. The

the effect

of cooling

natural

was examined

air cooling, forced

cooling during

and t h e m o l d

Since the natural

air cooling extracted

cooling, the crystal/melt of the mold as shown

and

in F i g s . 7 ( b ) and

results are

air cooling

less heat than

7 ( c ) . As a

well

be f o u n d

that the calculated

with the experimental

out

ied

by c h a n g i n g

exit

Fig.9, the crystal/melt

was

the

from

stud­

mold

20 mm

30 m m / m i n

to

and

was 236°C. As shown

interface moves

in

outward

from the mold as the distance increases. This is exp­ lained

by t h e f a c t t h a t t h e c o o l i n g e f f e c t

mes more effective

result,

ser the cooling

the

between

system

speed

exit temperature

conditions

dur­

cooling

40 mm. The withdrawal the mold

position

position was also

the distance

and t h e w a t e r

ser t o the mold

better

casting

as the cooling

exit. This system crystal

system

beco­

is

clo­

implies that the

clo­

to the mold

exit

is, the

is.

experiment­

results of the previous cooling m e t h o d s .

can

for­

water

decrease

process. Fig.8 shows the

was

shown

and

interface was more

progressively

water

casting

temperature

e x i t , for the former two

ingot diameter would ing c a s t i n g

comparing

air cooling

k e p t at 2 3 6 ° C . T h e c a l c u l a t e d in F i g . 7 .

by

Sn b a r c a s t i n g w h e r e t h e

speed w a s 30 mm/min

al

4.3.2. The effect of cooling The effect of cooling

of cooling method

ced

method.

effect

results

It

PULLING RATE R=30 MM/MIN MOLD T=236°C

agree

ones.

MOLD T=236*C PULLING RATE R= 30 MM/MIN 1 NATURAL-AIR COOLING

COOLING WATER AREA

J

COOLING WATER AREA

FORCED-AIR COOLING

HEATED MOLD COOLING WATER AREA 0 10 20 30 40 50 60 70 80 90 DISTANCE FROM MOLD BOTTOM CMMD

WATER COOLING COOLING AREA HEATED MOLD 0 10 20 30 40 50 60 70 80 90 DISTANCE FROM MOLD BOTTOM CMM3 Figure

7: T h e e f f e c t o f c o o l i n g m e t h o d crystal/melt

on

Figure

9:

The effect of cooling crystal/melt

position on

the

interface

5.

CONCLUSIONS The

solidification

successfully

used

to

analysis

system

investigate

has

calculated

results of casting

demonstrated lts, we can

in p r e v i o u s get

(1)It has good

8: T h e e x p e r i m e n t r e s u l t s o f d i f f e r e n t cooling method on crystal growth: (a) water c o o l i n g , ( b ) forced-air cool­ ing and ( c ) n a t u r a l - a i r c o o l i n g

section.

semi-quantitative

of

The

Sn bar h a v e From the

some conclusions

een the calculated

been

the effects

process variables on the O . C C process.

Figure

the

interface.

been resu­

: agreement

r e s u l t s and

betw­

experimental

ones. (2)As the withdrawal ture

speed

and

the mold

increase, the crystal/melt

tempera­

interface

596

will

move outward

from

the m o l d exit

finally will result in (3)The distance

bettween

necking. the water cooling

and t h e m o l d

exit

to avoid

interface out of the mold

too

the

shall

keep

system

in a p r o p e r

range

value, the optimal

can be

Kim and

ons A,

operating

interface

(5)This analysis other metal

system

materials

copper

can

conditions

also be applied

being cast

such

to

as

etc.

S.

19A(1988)

of Japan

,Sept.(1984) pp.773.

6.

Growth

Company,

Dempa

KOU, Metallurgical

pp.14. Digest,

Tansacti-

pp.1849. Kim

and S.

91(1988)

X. C. Z e n g and R. D. , 93(1985), pp.123.

KOU, Journal

of

pp.50.

Pehlke, AFS

Transactions

7 . J. P. H o l m a n , H e a t t r a n s f e r , 5 t h e d . Hill, New Y o r k ( 1 9 8 1 ) .

,McGraw-

8. X. C. Z e n g , R. D. P e h l k e , " N u m e r i c a l S i m u l a t ­ ion o f S o l i d i f i c a t i o n F o r a C o p p e r - B a s e A l l o y C a s t i n g " , Presented at the 1984 A F S Casting Congress.

REFERENCES 1. A . O h n o , B u l l t e i n

Crystal

and

determined.

aluminum,

4. Y . J.

5. Y . H. W a n g , Y . J. crystal/melt

of Metals,Jan.(1986)

3. T h e F u r u k a w a E l e c t r i c April 2 1 ( 1 9 8 6 ) PP.7

exit

much.

(4)From the calculated G/R

2. A . O h n o , J o u r n a l

and

Institite

of

Metals