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Modeling Interfacial Flux Layer Phenomena in the Shell/Mold Gap Using CON1D. Ya Meng Department of Materials Science &. Engineering University of Illinois at Urbana-Champaign October 15, 2002. Outline. Improvements to CON1D7 Ideal mold taper Funnel mold Specific heat in mushy zone Others - PowerPoint PPT Presentation
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University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 1
Modeling Interfacial Flux Layer Phenomena in the Shell/Mold
Gap Using CON1D
Ya Meng
Department of Materials Science &. Engineering University of Illinois at Urbana-Champaign
October 15, 2002
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 2
Outline Improvements to CON1D7
Ideal mold taperFunnel moldSpecific heat in mushy zoneOthers
Friction model description Sample cases discussion and results Conclusions Experiment: measure friction coefficient Future work
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 3
Improvements to CON1D7 Ideal taper calculation, including the effect of
mold distortion, flux layer thickness and funnel mold extra length (if present)
Specific heat in mushy zone based on phase fraction
Update phase diagram according to user input solidus/liquidus temperature
Heat flux input above meniscus Curved mold for 2D mold temperature model Friction model
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 4
Ideal Taper Ideal taper for slab and billet:
xtaper: ideal taper (mm)
xshell: steel shell shrinkage (mm)
xmold: mold wall disortion (mm)
xgap: flux layer thickness (=dliquid+dsolid) (mm)
xother: extra mold geometry change, e.g. funnel mold (mm)
supscript “o” means value at the reference position, where shell shrinkage begins
o o otaper shell mold mold gap gap other otherx x x x x x x x
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 5
Mold Distortion: Billet Billet mold distortion:
mold: mold expansion coefficient (K-1)
W: mold width (mm)Thot: mold hot face temperature (oC)
Tcold: mold cold face temperature (oC)
2 2hot cold
mold moldT TWx
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 6
Mold Distortion: Slab Slab mold distortion:
Wide face distortion, xWF :
T’hot, T’cold : linearized mold hot face and cold face temperature (oC)
Narrow face distortion, xNF :
thot, tcold : mold hot layer and cold layer thickness (mm)
Ehot, Ecold : mold hot layer and cold layer elastic modulus (Pa)
' '
2 2hot cold
WF moldT TWx
mold NF WFx x x
2_2
2 3
3
4 6 4
hot cold hot cold hot coldNF total mold
cold
hot hot hot hot cold cold
cold cold cold cold hot hot
T T t tx Z z z
t K
t t E t E tKt t E t E t
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 7
Funnel Mold - Perimeter Calculation Funnel mold (Nucor Steel)
a: half funnel width
b: funnel depth at given position
R: funnel radius
D: total funnel height
1sin
2 2
2 2
2 2
a +bR=4b
Total perimeter = 2 N +W +2x
extra length x= 2R - a
a +b 2abx a2b a +b
a b
R A
A
D
b
A-A
W
W+2x
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 8
Specific HeatSpecific heat in mushy zone based on phase fraction
1
10
800 1000 1200 1400 1600 1800
Micro Segregation ModelMeasured Data
Spe
cific
Hea
t (kJ
/kgK
)
Temperature (K)
Material: AISI 1026
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 9
Previous Work
Pseudo-transient analytical model of heat flux and flow in interfacial liquid flux layer
Stress model in solid flux layer Mold friction depends on powder flux
consumption rate and solid flux velocity Predicting mold flux critical consumption rate
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 10
Review: Liquid Layer Transient Model
-40
-20
0
20
400 0.05 0.1 0.15 0.2
CON1DFDM Flux Model
Vel
ocity
(mm
/s)
x (mm)
upstroke
Vmold
=0, average solid flux velocity
downstroke
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 11
Review: Solid Layer Stress Model zb
static
z0 (z+z)
s/l
ds
z0 (z)
y y
Upstroke
Maximum static friction limits stress
When friction on mold side can not compensate the shear stress on flux solid/liquid interface, axial stress builds up in solid flux layer.If the axial stress exceeds the flux fracture strength, solid flux breaks and moves along the mold wall.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 12
Review: Critical Consumption Rate
Crystalline mold flux: lower consumption causes fracture near meniscus
Critical consumption rate: 0.28kg/m2 for 1.0m/min casting speed
-2 104
0
2 104
4 104
6 104
8 104
0 100 200 300 400 500 600 700 800
Maximum Up StrokeMaximum Down Stroke
Axi
al S
tress
in S
olid
Flu
x (P
a)
Distance Below Meniscus (mm)
flux fracture strength: 80KPa
-2000
-1000
0
1000
2000
3000
0 20 40 60 80 100
up, sol/liq interfaceup, mold sidedown, sol/liq interfacedown, mold sideMaximum Static Friction on Mold Wall
She
ar S
tress
(Pa)
Distance Below Meniscus (mm)
axial stress builds up
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 13
Review: Critical Consumption Rate
Glassy mold flux: lower consumption causes fracture near mold exit
Critical consumption rate: 0.35kg/m2 for 1.0m/min casting speed
-2 104
0
2 104
4 104
6 104
8 104
0 100 200 300 400 500 600 700 800
Maximum Up StrokeMaximum Down Stroke
Axi
al S
tress
in S
olid
Flu
x (P
a)
Distance Below Meniscus (mm)
flux fracture strength: 80KPa
-1 104
-5000
0
5000
1 104
1.5 104
2 104
2.5 104
3 104
0 100 200 300 400 500 600 700 800
up, sol/liq interfaceup, mold sidedown, sol/liq interfacedown, mold sideMaximum Static Friction on Mold Wall
She
ar S
tress
(Pa)
Distance Below Meniscus (mm)
axial stress builds up
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 14
Objectives
What will happen if the flux fractures? Solid flux layer moves down the mold
What is the solid flux velocity? liquid fills the gap between the top attached part and
bottom moving part What is the gap size? Can liquid fill in the gap?
solid flux re-attaches to mold wall Will it break again? Where and when?
liquid flux runs out Will flux move with the steel shell?
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 15
Phenomena Description
mold and solid flux rim move upward
liquid flux channel gap at meniscus increases
pressure in the channel gap decreases
liquid flux fills in the channel gap
liquid layer thickness below meniscus decreases
flux consumption to meniscus region occurs
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 16
Phenomena Description
mold and solid flux rim move downward
liquid flux channel gap at meniscus decreases
pressure in the channel gap increases
liquid flux is squeezed out of the channel gap
liquid layer thickness below meniscus increases
flux consumption to lower shell region occurs
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 17
Fracture Model Description Fracture happens at the maximum up-stroke due to axial tensile stress After fracture, solid flux moves down the mold wall, with a velocity that
depends on force balance between the two sides:
Mold/solid flux interface:
/mold solid flux moving steelgz
Solid/liquid flux interface:
/
1 12
s l
c ss flux steel l
l
n V V ngd
d n
m/s=s/l Vs can be calculated
-40
-30
-20
-10
0
10
20
30
40-0.2 0 0.2 0.4 0.6 0.8
VmoldVsolidVc
Vel
ocity
(mm
/s)
Time (s)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 18
Fracture Model Description Gap occurs when solid flux layer fractures, gap size:
Part of liquid flux is consumed to fill in the gap:
where q is consumption rate (m2/s)
_
_
t reattach
solid moldt fractctureL V V dt
_total fill in liquid oscq q q q
_solid c
fill inmold
L d Vq
Z
0
liquidd
liquid liquidq V dx,liquid solidd d
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 19
Sample Cases
Case 1: dliquid=constant, never fractures Case 2: dliquid fluctuates from meniscus to 100mm below
meniscus, fractures once Case 3: dliquid fluctuates from meniscus to 150mm below
meniscus, frequently fractures near meniscus and mold exit, liquid flux nearly runs out at
mold exit Case 4: dliquid fluctuates from meniscus to 200mm below
meniscus, more frequently fractures near meniscus, also fractures at the bottom of mold, liquid flux runs out before mold exit
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 20
Example Application: Input Conditions Casting Speed: 1.0 m/min Pour Temperature: 1550 oC Slab Geometry: 1500*230 mm2
Nozzle Submergence depth: 265 mm Working Mold Length: 800 mm Time Step: dt=0.002 s Mesh Size: dx=0.5 mm Fraction Solid for Shell Thickness location: 0.3 Carbon Content: 0.05 % Mold Powder Solidification Temperature: 950 oC Mold Powder Conductivity (solid/liquid): 1.5/1.5 W/mK Mold Powder Density: 2500 kg/m3
Mold Powder Viscosity at 1300 oC: 4.2 poise Exponent for temperature dependency of viscosity: 1.6 - Fracture strength (tensile/compress): 80/8000 KPa Mold Powder Consumption Rate: 0.45 kg/m2
Mold/flux coefficient (static/moving): 0.4/0.4 - Oscillation Mark Geometry (depth*width): 0.45*4.5 mm2
Mold Oscillation Frequency: 83.3 cpm Oscillation Stroke: 7.8 mm Mold Thickness (including water channel): 51 mm Initial Cooling Water Temperature: 30 oC Water Channel Geometry (depth*width*distance): 25*5*29 mm3
Cooling Water Flow rate: 7.8 m/s
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 21
Liquid Flux Layer Thickness: Case 1& 2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600 700 800
transient
average
up stroke
down stroke
Liqu
id L
ayer
Thi
ckne
ss (m
m)
Diatance Below Meniscus (mm)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 100 150
transient
average
up stroke
down stroke
Liqu
id L
ayer
Thi
ckne
ss (m
m)
Diatance Below Meniscus (mm)
Assume bi-linear liquid flux layer amplitude variation with time/distance
(average and frequency are calculated)
Case 1
Case 2
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 22
Liquid Layer Thickness & Shear Stress During Oscillation Cycle: Case 1 &2
-40
-30
-20
-10
0
10
20
30
400 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Vmold
Vc
Vel
ocity
(mm
/s)
Time (s)
17mm below meniscus
-100
0
100
200
300
400
500
600
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Case 1Case 2
She
ar S
tress
(Pa)
Time (s)0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Case 1Case 2
Liqu
id L
ayer
Thi
ckne
ss (m
m)
Time (s)
Max. static friction (axial stress provides rest)
Liquid shear balance drag forces
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 23
Axial Stress in Solid Flux LayerCase 1 & 2
-2 104
0
2 104
4 104
6 104
8 104
0 100 200 300 400 500 600 700 800
Case 1Case 2
Axi
al S
tress
in S
olid
Flu
x La
yer (
Pa)
Diatance Below Meniscus (mm)
-40
-30
-20
-10
0
10
20
30
400 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Vmold
Vc
Vel
ocity
(mm
/s)
Time (s)
0
1 104
2 104
3 104
4 104
5 104
6 104
7 104
8 104
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Case 1Case 2
Axi
al s
tress
(Pa)
Time (s)
17mm below meniscus
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 24
Liquid Flux Layer Thickness: 4 Cases
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 50 100 150 200 250
Case 1
Case 2
Case 3
Case 4
Liqu
id L
ayer
Thi
ckne
ss (m
m)
Diatance Below Meniscus (mm)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600 700 800
Case 1
Case 2
Case 3
Case 4
Liqu
id L
ayer
Thi
ckne
ss (m
m)
Diatance Below Meniscus (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 25
Axial Stress in Solid Flux Layer: 4 Cases
-2 104
0
2 104
4 104
6 104
8 104
0 100 200 300 400 500 600 700 800
Case 1Case 2Case 3Case 4
Axi
al S
tress
in S
olid
Flu
x La
yer (
Pa)
Diatance Below Meniscus (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 26
Flux Layer Thickness: 4 Cases
0
0.5
1
1.5
2
0 100 200 300 400 500 600 700 800
Case1: dsolid
Case1: dtotal
Case 2: dsolid
Case 2: dtotal
Case 3: dsolidl
Case 3: dtotal
Case 4: dsolid
Case 4: dtotal
Thic
knes
s (m
m)
Diatance Below Meniscus (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 27
Solid Flux Layer Dwell Time in Mold
0
40
80
120
160
0 100 200 300 400 500 600 700 800
Case 2
Case 3
Case 4
Tim
e to
Sta
y in
Mol
d (m
in)
Diatance Below Meniscus (mm)
0
5
10
15
20
0 100 200 300 400 500 600 700 800
Case 2
Case 3
Case 4
Tim
e to
Sta
y in
Mol
d (m
in)
Diatance Below Meniscus (mm)
Fracture(s) are assumed to occur once per mold residence time
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 28
Heat Flux Comparison
0.5
1
1.5
2
2.5
3
0 100 200 300 400 500 600 700 800
Case 1Case 2Case 3Case 4
Hea
t Flu
x (M
w/m
2 )
Diatance Below Meniscus (mm)
Assume solid layer is squeezed to fill in gaps after liquid flux runs out:
resulting thinner layer produces a local heat flux increase.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 29
Mold Temperature Comparison
50
100
150
200
250
300
350
0 100 200 300 400 500 600 700 800
Case 1: Hot FaceCase 1: Cold FaceCase 2: Hot FaceCase 2: Cold FaceCase 3: Hot FaceCase 3: Cold FaceCase 4: Hot FaceCase 4: Cold Face
Tem
pera
ture
(o C)
Diatance Below Meniscus (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 30
Shell Temperature Comparison
900
1000
1100
1200
1300
1400
1500
1600
0 100 200 300 400 500 600 700 800
Case 1Case 2Case 3Case 4
Tem
pera
ture
(o C)
Diatance Below Meniscus (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 31
Shell Thickness Comparison
0
5
10
15
20
25
0 100 200 300 400 500 600 700 800
Case 1Case 2Case 3Case 4
Thic
knes
s (m
m)
Diatance Below Meniscus (mm)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 32
ResultsCase 1 Case 2 Case 3 Case 4 unit
Heat Flux 1.189 1.202 1.367 1.456 MW/m2
Friction amplitude 0.56 0.66 7.79 18.32 kPa
dliquid at mold exit 0.35 0.32 0.07 0.0 mm
Liquid layer consumption 0.324 0.309 0.151 0.093 kg/ton
Solid layer consumption 0.0 0.015 0.173 0.278 kg/ton
Osc. marks consumption 0.286 0.286 0.286 0.239 kg/ton
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 33
Solid Flux Consumption Mechanism When friction on mold side can not compensate the shear
stress on flux solid/liquid interface, axial stress builds up in solid flux layer. If the axial stress exceeds the flux fracture strength, solid flux breaks and moves along the mold wall.
After fracture the solid flux moves down the mold wall, the velocity is calculated according to force balance.
When mold velocity equals to solid flux’s, the solid flux re-attaches to the mold wall.
The above procedure may repeat, when accumulated axial stress exceeds the fracture strength.
When solid flux layer fractures, part of liquid flux fills in the gap due to the fracture, which decreases liquid flux layer thickness.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 34
Conclusions Solid flux consumption implies flux fracturing, which can be caused
by drops in either consumption rate or liquid layer thickness. Liquid layer thickness fluctuation at meniscus due to mold oscillation
may cause solid flux layer to fracture. The fracture frequency depends on liquid layer thickness fluctuation region and amplitude.
Fracture happens at the maximum up stroke and when liquid layer thickness is thin.
Gaps due to fracture near meniscus can be re-filled, while gaps due to fracture near mold exit might not due to liquid flux shortage.
When liquid flux nearly runs out, solid flux layer fractures frequently. It may lead to a heat flux peak, and corresponding mold temperature increase and shell temperature decrease (if solid flux can be squeezed).
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 35
Experiment: Flux Friction Coefficient
0
0.2
0.4
0.6
0.8
1
1.2
0 200 400 600 800 1000
Fric
tion
Coe
ffici
ent
Temperature (oC)
Mold Powder: M622/G, 1300=1.32Poise, Tcrystal=1180oC
Experiment Procedure:
1. powder melt in crucible at 1400oC, poured into sample holder
2. sample was in HTT, measure friction coefficient with increasing temperature
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 36
Experiment: Flux Friction Coefficient
Mold Powder: M622-C20, 1300=2.0Poise, Tcrystal=1135oC
Experiment Procedure:
1. powder melt in crucible at 1400oC, poured into sample holder
2. sample was in HTT, measure friction coefficient with decreasing temperature
0.2
0.4
0.6
0.8
1
1.2
1.4
0 200 400 600 800 1000
Fric
tion
Coe
ffici
ent
Temperature (oC)
two 100rpm, others 50rpm
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Ya Meng 37
Future Work
Hydro-dynamic model to predict pressure in liquid flux layer over a cycle, therefore, predict consumption rate and flux layer thickness change over a cycle.
Solid flux layer behavior when liquid flux runs out. Measure flux viscosity and friction coefficient at low
temperature using High Temperature Tribometer. Calculate friction force due to mismatch taper using
normal stress calculation from CON2D.
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