Modeling Interfacial Flux layer Phenomena in the Shell

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng

Modeling Interfacial Flux layer Phenomena in the Shell/Mold

Gap Using CON1D

Modeling Interfacial Flux layer Phenomena in the Shell/Mold

Gap Using CON1D

Ya Meng

Department of Materials Science &. EngineeringUniversity of Illinois at Urbana-Champaign

September 25, 2000

Ya Meng

Department of Materials Science &. EngineeringUniversity of Illinois at Urbana-Champaign

September 25, 2000


IntroductionIntroduction

oscillation marks parametersoscillation marks parameters

steel propertiessteel properties

spray zone variablesspray zone variables

mold flux propertiesmold flux properties

cooling water propertiescooling water properties

mold geometrymold geometry

simulation parameterssimulation parameters

casting conditionscasting conditions

input

temperaturestemperatures

shell thickness (breakout shell)shell thickness (breakout shell)

heat flux leaving the shellheat flux leaving the shell

ideal mold taperideal mold taper

flux layer thicknessflux layer thickness

output (Validation Parameters)

mold hot face, cold face and thermocouple

mold hot face, cold face and thermocouple

cooling watercooling water

shell surface (below mold) and interior

shell surface (below mold) and interior

friction force in moldfriction force in mold

Solidification & Heat Transfer Model: CON1D

- 1-D transient finite-difference model of solidifying steel shell

- 2-D steady-state heat conduction within the mold wall


Schematic of Continuous Casting ProcessSchematic of Continuous Casting Process

coppermold

solidifying steel shell

contact resistances

crystalline resolidified flux

oscillation mark

glassy resolidified flux

air gapmolten steel pool

flux rim submerged entry nozzle

ferrostatic pressure

flux powder

liquid flux


Improvements to CON1D5.0Improvements to CON1D5.0

l CON1D version 5.0 manual and new format of input filel New output file XXXX.frc, which out put the phase fractions

of shell surface and a certain depth (user input) under surface

l New spray zone modell New oscillation mark model (optional)l New taper calculation modell Cooling water temperature rise adjustment by the program

itself ∆Τmodified cooling water = ∆Tcooling water

- make model calibration with water ∆T measurement easier

l CON1D version 5.0 manual and new format of input filel New output file XXXX.frc, which out put the phase fractions

of shell surface and a certain depth (user input) under surface

l New spray zone modell New oscillation mark model (optional)l New taper calculation modell Cooling water temperature rise adjustment by the program

itself ∆Τmodified cooling water = ∆Tcooling water

- make model calibration with water ∆T measurement easiertotcharea

widthslabL

dw

ch

chch **


Improvements to CON1D6.1Improvements to CON1D6.1

l CON1D version 6.1 manual and new format of input file

l New shear stress model (subroutine shear.f), predicts shear stress in the shell/mold gap and calculates friction forces during one mold oscillation cycle. Results are written into new output file XXXX.shr.

l New analytical segregation model (optional), is developed by Young Mok Won.

l Add a series of thermocouples below steel shell surface to predict steel shell temperature, results are written into new output file XXXX.sst.

l CON1D version 6.1 manual and new format of input file

l New shear stress model (subroutine shear.f), predicts shear stress in the shell/mold gap and calculates friction forces during one mold oscillation cycle. Results are written into new output file XXXX.shr.

l New analytical segregation model (optional), is developed by Young Mok Won.

l Add a series of thermocouples below steel shell surface to predict steel shell temperature, results are written into new output file XXXX.sst.


Schemetic Profile of Flux VelocitySchemetic Profile of Flux Velocity

VmoldVmold

z

MoldLiquid Flux

Solid Flux Steel

y

V=Vc

V=Vs-Vmold

ddy=0


Friction Model DescriptionFriction Model DescriptionMomentum balance equation of flux flow in the gap:

Assume: - Uncoupled time dependent motion (mold oscillation)- Fully developed laminar flow- Flow of flux only along Z axis (casting direction)Eq. (1) is simplified:

Momentum balance equation of flux flow in the gap:

Assume: - Uncoupled time dependent motion (mold oscillation)- Fully developed laminar flow- Flow of flux only along Z axis (casting direction)Eq. (1) is simplified:

( ) ( )1gPVVDtDV

ρτρ +∇+−∇=

∇⋅+

( )

( )3

20

1cgy

gy

yz

yz

+−=⇒

=+∂

∂

ρτ

ρτ


Friction Model DescriptionFriction Model DescriptionConstitutive equation for shear stress-velocity gradient in flux layer:

Assume:

-

Where: ms is flux viscosity at the interface with steel surface

Ts is steel surface temperatureTsol is flux solidification temperaturen is empirical constant chosen to fit measured data

- Linear temperature gradient across flux layersSo:

Constitutive equation for shear stress-velocity gradient in flux layer:

Assume:

-

Where: ms is flux viscosity at the interface with steel surface

Ts is steel surface temperatureTsol is flux solidification temperaturen is empirical constant chosen to fit measured data

- Linear temperature gradient across flux layersSo:

( )4y

V zyz ∂

∂= µτ

( )5n

sol

solss TT

TT

−−

= µµ

( )6y

Vyd z

n

n

syz ∂∂

= µτ


Friction Model DescriptionFriction Model DescriptionSubstitute Eq.(6) into Eq.(3):

Boundary Conditions: (mold/flux & flux/steel interfaces)

Substitute C1 into Eq.(7) and evaluate at y=d:

Substitute Eq.(6) into Eq.(3):

Boundary Conditions: (mold/flux & flux/steel interfaces)

Substitute C1 into Eq.(7) and evaluate at y=d:

( )711

ns

nnz

dycgy

yV

µρ +

−=∂

∂ +

( ) ( )( )

( ) ( ) ( ) ( )102

11

9|

8|

1

0

++

++−

=⇒

=

−==

=

=

nngd

dnVV

c

VV

tVVVV

ssc

cdyz

moldswyz

ρµ

( )( )( ) ( )11

21

|+

+−+

=∂

∂= n

gdd

VVny

V

s

wcdy

z

µρ


Friction Model DescriptionFriction Model DescriptionAt flux/steel interface when there is liquid flux layer:

At solid/mold or solid/steel interface:

where, F is coefficient of sliding friction (F =0.4)

So the shear stress in mold/steel gap is:

The friction force for one mold face is:

where, w is slab width for wide face, slab thickness for narrow face

At flux/steel interface when there is liquid flux layer:

At solid/mold or solid/steel interface:

where, F is coefficient of sliding friction (F =0.4)

So the shear stress in mold/steel gap is:

The friction force for one mold face is:

where, w is slab width for wide face, slab thickness for narrow face

( )( )( ) ( )12

21

++

−+=

ngd

dVVn wc

sliquidρ

µτ

( )13gzsteelsolid ρφτ ⋅=

( ) ( )14, solidliquidMin τττ =

( )150

zdwfmoldZ

∫ ⋅⋅= τ


Example Application: Case 1Example Application: Case 1l Casting Speed: 1.0m/minl Pour Temperature: 1550 oCl Slab Geometry: 1500mm*230mml Nozzle Submergence depth: 265mml Working Mold Length: 800mm

l Time Step: dt=0.001sl Mesh Size: dx=0.5mml Fraction Solid for Shell Thickness location: 0.3

l Carbon Content: 0.05%

l Mold Powder Solidification Temperature: 1080 oCl Mold Powder Conductivity (solid/liquid): 1.5/1.5W/mKl Mold Powder Viscosity at 1300 oC: 8.72poisel Exponent for temperature dependency of viscosity: 1.65l Mold Powder Consumption Rate: 0.45kg/m2

l Oscillation Mark Geometry (depth*width): 0.45*4.5mm2

l Mold Oscillation Frequency: 83.3cpml Oscillation Stroke: 7.8mml Negative Strip Ratio of Velocity: 0.3

l Mold Thickness (including water channel): 51mml Initial Cooling Water Temperature: 30 oCl Water Channel Geometry (depth*width*distance): 25mm*5mm*29mml Cooling Water Flow rate: 7.8m/s

l Casting Speed: 1.0m/minl Pour Temperature: 1550 oCl Slab Geometry: 1500mm*230mml Nozzle Submergence depth: 265mml Working Mold Length: 800mm

l Time Step: dt=0.001sl Mesh Size: dx=0.5mml Fraction Solid for Shell Thickness location: 0.3

l Carbon Content: 0.05%

l Mold Powder Solidification Temperature: 1080 oCl Mold Powder Conductivity (solid/liquid): 1.5/1.5W/mKl Mold Powder Viscosity at 1300 oC: 8.72poisel Exponent for temperature dependency of viscosity: 1.65l Mold Powder Consumption Rate: 0.45kg/m2

l Oscillation Mark Geometry (depth*width): 0.45*4.5mm2

l Mold Oscillation Frequency: 83.3cpml Oscillation Stroke: 7.8mml Negative Strip Ratio of Velocity: 0.3

l Mold Thickness (including water channel): 51mml Initial Cooling Water Temperature: 30 oCl Water Channel Geometry (depth*width*distance): 25mm*5mm*29mml Cooling Water Flow rate: 7.8m/s


-40

-20

0

20

40

0 0.09 0.18 0.27 0.36

Time (s)

Vel

oci

ty (

mm

/s)

VmoldVcasting

Distance below meniscus (mm)

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

0 0.09 0.18 0.27 0.36

Time (s)

Str

ess

(Pa)

400500600

Shear Stress at Different Position down the Mold during Half Oscillation Cycle (Case 1)

Shear Stress at Different Position down the Mold during Half Oscillation Cycle (Case 1)


Flux Thickness : Case 1Flux Thickness : Case 1

0

0.3

0.6

0.9

1.2

1.5

0 100 200 300 400 500 600 700 800

Total

Liquid Layer

Solid Layer

Thi

ckne

ss (

mm

)

Distance below Meniscus (mm)


Shear Stress down the Mold during Half Period (Case 1)

Shear Stress down the Mold during Half Period (Case 1)

-2 104

-1 104

0

1 104

2 104

0 100 200 300 400 500 600 700 800

0 (Maximum)1/162/163/164/16 (Vmold=0)5/166/167/168/16 (Minimum)Average

Str

ess

(Pa)


Cycle Fraction


-40

-20

0

20

40

0 0.09 0.18 0.27 0.36

Time (s)

Vel

oci

ty (

mm

/s) Vmold

Vcasting

-10000

-5000

0

5000

10000

15000

0 0.09 0.18 0.27 0.36

Time (s)

Fo

rce

(N

)Mold Velocity and Friction Force during Half Period

(Case 1)Mold Velocity and Friction Force during Half Period

(Case 1)


Parametric Study ParametersParametric Study Parameters

17.64

9.29

17.13

Friction Force

Amplitude(KPa)

.15*1.5

.225*2.25

.45*4.5

Osc. Mark Geometry

(mm2)

.230

.315

.450

Consumption Rate

(kg/m2)

0.15

0.19

0.24

Negative Strip Time

(s)

133.3

108.3

83.3

Oscillation Frequency

(cpm)

1.6Case 3

1.3Case 2

1.0Case 1

Casting Speed(m/min)

* Other conditions are same as Case 1* Other conditions are same as Case 1


Parameters ChosenParameters Chosen

Oscillation mark depth

(K. Hamagami etc., Steelmaking Conference

Proceeding, 1982, 65, p358)

Oscillation mark depth

(K. Hamagami etc., Steelmaking Conference

Proceeding, 1982, 65, p358)

Consumption rate

(M. Inagaki etc.,CAMP-ISIJ, 1989, 2, p309;

B. Ho, Master thesis, 1992)

Consumption rate

(M. Inagaki etc.,CAMP-ISIJ, 1989, 2, p309;

B. Ho, Master thesis, 1992)

Mold powder viscosity

(D. Larson, Industrial Heating, 1986, 53, p16)

Mold powder viscosity

(D. Larson, Industrial Heating, 1986, 53, p16)

1

10

100

1000

1100 1200 1300 1400 1500

10% Alumina -Larson

CON1D

Vis

cosi

ty (P

oise

)

Temperature (C)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.8 1 1.2 1.4 1.6

70cpm -Inagaki100cpm -Inagaki80cpm -Ho100cpm -HoCON1D

Mol

d P

owde

r C

onsu

mpt

ion

(kg/

m^2

)

Casting Speed (m/min)

83.3cpm

108.3cpm

133.3cpm 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.15 0.18 0.21 0.24 0.27

HamagamiCON1D

Max

imum

Dep

th o

f Osc

. Mar

k (m

m)

Negative Strip Time (s)


Maximum Shear Stress down the Mold ComparisonMaximum Shear Stress down the Mold Comparison

0

5000

1 104

1.5 104

2 104

2.5 104

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

She

ar S

tres

s (P

a)



Maximum Shear Stress near MeniscusMaximum Shear Stress near Meniscus

0

50

100

150

200

250

300

350

400

0 2 4 6 8 10

Case 1Case 2Case 3

She

ar S

tres

s (N

/m)

Time (s)


Solid Flux Layer VelocitySolid Flux Layer Velocity

1

1.5

2

2.5

3

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

Vel

ocity

(m

m/s

)


0.06Vc

0.06Vc

0.06Vc

0.12Vc

0.12Vc


Average Shear Stress down the Mold ComparisonAverage Shear Stress down the Mold Comparison

0

5000

1 104

1.5 104

2 104

2.5 104

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

She

ar S

tres

s (P

a)



Friction Force during Half Period ComparisonFriction Force during Half Period Comparison

-1

-0.5

0

0.5

1

0 4 8 12 16

Scale

d M

old

Velo

cit

y

Vmold/Vmax

Vcasting/Vmax

-10000

-5000

0

5000

10000

15000

0 4 8 12 16

Time Fraction of Oscillation Cycle(*1/32 period)

Fo

rce

(N

)

Case1

Case 2

Case 3

* Vmax is the amplitude velocity of mold oscillation (=p*stroke*freqency)* Vmax is the amplitude velocity of mold oscillation (=p*stroke*freqency)



0

0.3

0.6

0.9

1.2

1.5

0 100 200 300 400 500 600 700 800

Total

Liquid Layer

Solid Layer

Thi

ckne

ss (

mm

)




0

0.3

0.6

0.9

1.2

1.5

0 100 200 300 400 500 600 700 800

Total

Liquid Layer

Solid Layer

Thi

ckne

ss (

mm

)



Liquid Flux Thickness ComparisonLiquid Flux Thickness Comparison

0

0.1

0.2

0.3

0.4

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

Thi

ckne

ss (

mm

)



Total Flux Thickness ComparisonTotal Flux Thickness Comparison

0.6

0.8

1

1.2

1.4

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

Thi

ckne

ss (

mm

)



Heat Flux ComparisonHeat Flux Comparison

0

0.5

1

1.5

2

2.5

3

3.5

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

Hea

t Flu

x (M

W/m

2 )



Mold Hot Face Temperature ComparisonMold Hot Face Temperature Comparison

150

200

250

300

350

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

Tem

pera

ture

(C

)



Shell Thickness ComparisonShell Thickness Comparison

0

5

10

15

20

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

She

ll T

hick

ness

(m

m)



Shell Surface Temperature ComparisonShell Surface Temperature Comparison

1000

1100

1200

1300

1400

1500

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

Tem

pera

ture

(C

)



Shear Stress Amplitude down the Mold ComparisonShear Stress Amplitude down the Mold Comparison

0

1 104

2 104

3 104

4 104

5 104

0 100 200 300 400 500 600 700 800

Case 1

Case 2

Case 3

She

ar S

tres

s (P

a)



Effect of Casting Speed on Friction Force(From H. Nakato, S. Omiya etc., Journal of Metals. , V36 n3 Mar 1984 p44-50)

Effect of Casting Speed on Friction Force(From H. Nakato, S. Omiya etc., Journal of Metals. , V36 n3 Mar 1984 p44-50)

•• CON1D predicted resultsCON1D predicted results


Consumption RateConsumption RateCONSbasic = Consumption Rate - ∆CONS

where,CONSbasic is the minimum consumption rate without

oscillation mark∆CONS is the increase of consumption rate due to

oscillation mark, in order to satisfy the mass balance:

∆CONS=

CONSbasic = Consumption Rate - ∆CONS

where,CONSbasic is the minimum consumption rate without

oscillation mark∆CONS is the increase of consumption rate due to

oscillation mark, in order to satisfy the mass balance:

∆CONS= ρ∗∗∗

pitchwidthOscdepthOsc ..5.0

.023.053.211∆CONS

.207

Case 3

.239

Case 1

.262CONSbasic

Case 2Unit: kg/m2


ConclusionsConclusionsl In one oscillation cycle, the liquid flux layer has

sinusoidal profile for shear stress, while the solid flux layer has square wave.

l Lower friction exists in top half of mold.l For constant friction coefficient, solid fraction

increases cause huge increase in mold friction.l Liquid layer thickness controls the friction force in

mold: thicker liquid layer has shorter solid fraction which lowers friction force.

l Total flux layer thickness affects heat transfer across gap: thicker total flux layer lowers heat flux, leading to lower mold temperature, thicker shell thickness.

l In one oscillation cycle, the liquid flux layer has sinusoidal profile for shear stress, while the solid flux layer has square wave.

l Lower friction exists in top half of mold.l For constant friction coefficient, solid fraction

increases cause huge increase in mold friction.l Liquid layer thickness controls the friction force in

mold: thicker liquid layer has shorter solid fraction which lowers friction force.

l Total flux layer thickness affects heat transfer across gap: thicker total flux layer lowers heat flux, leading to lower mold temperature, thicker shell thickness.


ConclusionsConclusions

l If friction exceeds solid flux strength, then it will fracture, and increase solid flux velocity, causing possible drop in flux layer thickness in transition region accompanied by rebound heat flux.

l Steel shell surface temperature and hence liquid layer thickness is affected by both total flux thickness and casting speed: thicker layers and higher speeds increase shell temperature.

l Higher casting speed and higher real consumption both tends to lower friction.

l If friction exceeds solid flux strength, then it will fracture, and increase solid flux velocity, causing possible drop in flux layer thickness in transition region accompanied by rebound heat flux.

l Steel shell surface temperature and hence liquid layer thickness is affected by both total flux thickness and casting speed: thicker layers and higher speeds increase shell temperature.

l Higher casting speed and higher real consumption both tends to lower friction.


ConclusionsConclusionsl The fraction of mold with solid flux can be

identified by:- value of friction (more solid flux tends toward higher friction)- shape of cycle (more solid flux tends toward sharper transition)

l Higher casting speed with lower consumption rate has increased transverse crack risk because friction is higher in top liquid portion of mold, where shell is hotter, thinner and weaker.

l The fraction of mold with solid flux can be identified by:- value of friction (more solid flux tends toward higher friction)- shape of cycle (more solid flux tends toward sharper transition)

l Higher casting speed with lower consumption rate has increased transverse crack risk because friction is higher in top liquid portion of mold, where shell is hotter, thinner and weaker.


Future WorkFuture Workl Model calibration with plant measured data

- mold friction- consumption rate- oscillation mark geometry

l Relate flux fracture strength to solid flux velocity transition region

l Investigate coefficient of friction as a function of flux composition

l Incorporate default empirical equations for consumption rate, oscillation mark geometry etc.

l Incorporate the effects of flux crystallization behavior

l Model calibration with plant measured data- mold friction- consumption rate- oscillation mark geometry

l Relate flux fracture strength to solid flux velocity transition region

l Investigate coefficient of friction as a function of flux composition

l Incorporate default empirical equations for consumption rate, oscillation mark geometry etc.

l Incorporate the effects of flux crystallization behavior

Documents

Modeling Interfacial Flux layer Phenomena in the Shell