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CCC Annual ReportUIUC, August 14, 2013
Rui Liu
Department of Mechanical Science & Engineering
University of Illinois at Urbana-Champaign
Modeling and Simulation of
Multiphase Flows in CC Mold Region
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 2
Outline
• Determination of slide-gate position (PART 1)– Using a gate-position-based flow rate model to back-calculate gate
position based on measured casting speed and mold dimensions;
• Gas flow through UTN and bubble size (PART 2)– To predict hot argon flow rate entering steel stream;– To estimate active sites number density at UTN inner surface– To predict initial bubble size
• Multi-phase flow modeling (PART 3)– Board 4– Board 11~13– Board 14~16
and Validation with nailboard measurements:– Surface velocity profile– Surface level profile
also, Parametric study on bubble size effects
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 3
Acknowlegements
• Continuous Casting Consortium Members(ABB, ArcelorMittal, Baosteel, Magnesita Refractories, Nippon Steel, Nucor Steel, Postech/ Posco, Severstal, SSAB, Tata Steel, ANSYS/ Fluent)
• J. Powers and T. Henry in Severstal for the help with the plant nail board trials on Oct. 15~16 in Severstal in Dearborn, MI, the caster of which has:– a 203 mm mold thickness– plant operation data recorded for gate position, flow rate,
mold level, casting speed, …
• R. Singh for the help with nail board experiments• Mihir Chavan for the nail board measurements
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 4
PART 1:Gate Position Estimation
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 5
Modeling SEN Flow Rate--Analysis of Bernoulli’s Equation
sgfport hhhzg
v
g
pz
g
v
g
p +++++=++ 3
233
0
200
22 ρρ
50
3 3 0
0 3 1 2 3
1.01 10p Pa
p gH p
z z H H H
ρ= ×= +− = + +
+=−+−h
g
vzz
g
pp
2
23
3030
ρ
0
3H− 321 HHH ++
sgfport hhh ++
22
12
−
port
SENSEN
A
A
g
vg
v
D
Lf SEN
SEN
SEN
2
2
g
v
A
A
A
A
A
A
A
Ah SEN
SG
SEN
SG
GAP
GAP
SG
GAP
SENsg 2
11 22222
−+
−=μ
32
3
618.0
64.0
4807.02762.05864.0
37.063.0
+
−
+
+
==SG
GAP
SG
GAP
SG
GAP
SG
GAP
SG
vc
A
A
A
A
A
A
A
A
A
Aμ
Location 0
Location 3
correlation 1[1]
cor. 2[2]
cor. 3[3]
H1
H2
H3
Ref:[1] Oertel, Herbert; Prandtl, Ludwig, et.al, Prandtl's Essentials of Fluid Mechanics, Springer, ISBN 0387404376. See pp. 163–165.[2] Evangelista Torricelli, 1643; [3] http://en.wikipedia.org/wiki/Vena_contracta
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 6
Gate-position-based Model(considering gas addition)
• Equation for gate-position-based model [1]:
( )1 22 22 2 22
2
11 12
SEN eff
SEN SEN SEN SG GAP SEN SEN
port SEN GAP GAP SG SG port
g H HQ A
A L A A A A Af
A D A A A A Aμ
+=
− + + − + − +
3
0.63 0.37 GAP
SG
A
Aμ
= +
gas
SEN
ceffSEN
c
V WT
Q V WT
A
AA
+
=
single phase flow
two phase flowwhere
For continuous caster, an extra term should be added to account for pressure drop due to clogging:
( )1 22 22 2 22
2
11 12
SEN eff
SEN SEN SEN SG GAP SEN SEN
port SEN GAP GAP SG SG port
g H HQ A
A L A A A A Af C
A D A A A A Aμ
+=
− + + − + − + +
In current study, C=0 is assumed (no clogging).
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 7
Validation for Gate-position-based Model--using full-scale water model measurements at ArcelorMittal, East Chicago
25
50
75
100
125
150
175
200
225
25 30 35 40 45 50 55 60
Wat
er F
low
Rat
e (g
allo
n/m
in)
Distance between Plate Bore Center and SEN Bore Center (mm)
0 pct gas data
2 pct gas data
4 pct gas data
6 pct gas data
8 pct gas data
10 pct gas data
0 pct gas model
2 pct gas model
4 pct gas model
6 pct gas model
8 pct gas model
10 pct gas model
curves for 75 mm Slide Gate Plate Bore Diameter
2 22 21 21 2
1 2
2 2arcsin arcsin ,4 4 2GAP
D DD Dh hA Dh if D
D D
− = + − >
22 2 21 2 1 2
1 2
41
4 2D D D D D
hD D D
+ −= −
• Nice match is observed, analytical SEN flow rate model is validated
• Gap area is [1]:
R. Liu, B.G. Thomas, B. Forman and H. Yin,, AISTech Iron Steel Technol. Conf. Proc., 2012, Atlanta, GA, pp 1317.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 8
Predicted vs. Measured Gate Position at Severstal
15
25
35
45
55
65
75
85
95
105
115
0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
predicted, low gas fractionpredicted, high gas fractionmeasured mean gate position (mm)
Low/High gas fraction indicates the location where the fraction is calculated:Low fraction is calculated at UTN gas injection point;High fraction is calculated at SEN port exit.
Throughput (m3/s)
Gat
e P
osi
tio
n/O
pen
ing
(m
m)
From Severstal Steel, Dearborn, MI
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 9
Predicted vs. Calibrated Measurements
Throughput (m3/s)
Gat
e P
osi
tio
n/O
pen
ing
(m
m)
Cases 11-13
Exact offset for quantitative gate position not recorded, but typically is 40-60mm
From Severstal Steel, Dearborn, MI
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 10
Part 1. Gate-position Conclusions
• Prediction and measurements show the same trend at different throughputs;
• Once the measured gate position is calibrated by subtracting 60 mm, the predicted gate position usually matches closely with measurements; mismatch is restricted to one set of casting conditions (case 11~13);
• Gas flow (< 8%) has little effect on gate position (for range of conditions studied)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 11
PART 2:UTN Gas Flow Simulation and Initial Bubble Size Distribution
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 12
Calculate the Gas Velocity profile at
UTN/SEN inner surface
via empirical equation from G. Lee and B.G. Thomas [2]
Estimation of Mean Diameter of Initial Bubble Formation
via two-stage model from H. Bai and B.G. Thomas [3]
Calculation of Gas Volume Flux per Active Site (Total Flow Rate/cm2)/(Active
sites #/cm2)
for gas injection at UTN orSEN refractory
Active Sites Number Density Distribution at
UTN inner surface
via solving a Porous-Flow /Pressure-Source model for average normal velocity at UTN inner surface (described previously) [1]
Methodology of Initial Bubble Size Estimation in Argon-Steel System
References:[1] R. Liu and B.G. Thomas, Iron and Steel Technology Conference Proceedings, p 2235-2245, 2012, AISTech
[2] G. Lee, B.G. Thomas, et al., Met. Mater. Int., Vol. 16, No. 3 (2010), pp. 501~5063
[3] H. Bai and B.G. Thomas, Metall. Mater. Trans. B 32, 1143(2001).
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 13
Governing Equations-- Pressure-Source Model
Darcy’s Law: (1)pKD∇−=vMass Conservation (or continuity): (2)( ) 0=⋅∇ vρ
( ) 0=∇⋅∇ pKDρ ( ) ( ) 0=∇⋅∇+∇⋅∇ pKpK DD ρρ
( ) ( )[ ]pKpK DD ∇⋅∇−=∇⋅∇ ρρ1
RT
p=ρ( ) ( ) SpK
RT
p
p
RTpK DD
=
∇⋅
∇−=∇⋅∇
-- For Pressure-Source Model • The left hand side of the final equation above (in red box) is the standard diffusion part, while the right hand side is in the form of a source term taking into account the effect of gas expansion due to temperature and pressure gradient.• Using a 3-D FLUENT model, adding a source term to pressure (or a user-defined-scalar) diffusion equation coupling the energy equation
pressure diffusion Pressure source due to gas expansion
Heat Conduction: (3)Ideal Gas Law: (4)
( ) 0k T∇ ⋅ ∇ =p RTρ=
Eqn (1) and (2)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 14
Governing Equations-- Porous Flow Model
-- Porous-Flow Model• Solve a complete set of Navier-Stokes equations, with the momentum equation simplified into equation (1), adopting the ideal gas law to relate density with pressure and temperature.
Full Set of Navier-Stokes Equations for flow in porous media:
Mass Conservation (or continuity): (1)( ) 0=⋅∇ vρHeat Conduction: (2)Ideal Gas Law: (3)
( ) 0k T∇ ⋅ ∇ =p RTρ=
( ) ( ) ( ) 12
p Ct
ρ μρ μ ρα
∂ + ∇ ⋅ = −∇ + ∇ ⋅ ∇ + − + ∂
vvv v F v v v
viscous resistance
inertial resistance
(steady state problem)
0
0 Re ~2.3, C=0 for
laminar flow( )
2 240.3 0.0073 4.6 10
0.035V
r
ρρ −×∇ ⋅ = ≈ ×Δ
vv
0
( )5
42 2
8.1 10 0.0073 4.8 100.035
V
r
μμ−
−× ×∇ ⋅ ∇ = = ×Δ
v
0
1
DK
μα
=
pKD∇−=v
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 15
• About permeability in Darcy’s law:– Permeability measured the viscous resistance of the porous
media to fluid;
– Actual permeability consists of specific permeability and gas dynamic viscosity: specific permeability keeps constant for a chosen refractory and argon dynamic viscosity changes with local temperature.
Ref:[1] R. Dawe and E. Smith. Viscosity of Argon at High Temperatures. Science, Vol. 163, pp 675~676, 1969.
Viscosity Varying with Temperatrue: Ref[1]
Permeability Varying with Temperatrue:
( )DS
D
KK
Tμ=
12 21.01 10DSK m−= × (constant specific permeability, from draft paper)
( )Tμ (gas dynamic viscosity, as a function of local temperature)
( ) ( )20.63842lg 6.9365/ 3374.72/ 1.511960 10 T T T
Tμ μ − − −= ∗or 50 2.228 10 Pa sμ −= × ⋅
Room temperature (20 C) argon viscosity
Permeability Formulation
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 16
180017001600150014001300120011001000900
Temperature (deg. C)
Domain, Mesh and Temperature for Porous Gas Flow Model in Severstal UTN
Total 0.6 million mapped hexahedral cells for quarter domain
Temp (K)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 17
Parameters
Specific Permeability (npm)
Back Pressure (Psi)
Measured Argon Flow Rate (SLPM)
10.1 15.45 5.02
Parameters Values
hinner (W/m2K) 2.5*104
houter (W/m2K) 10
Heat conductivityKs (W/mK)
33
μ (Pa*s) 0.0056
ρ (kg/m3) 7200
Average steel velocityU (m/s)
1.6
Boundary Conditions:
SymmetricB.C.
Pressure B.C. at UTN inner surface(with/without pressure correction using Bernoulli’s equation)
Pressure B.C. at gas slot
Wall B.C. at anywhere else
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 18
Radial Direction (m)
Lo
ng
itu
din
alD
ire
cti
on
(m)
0.05 0.1 0.150
0.05
0.1
0.15
0.2
0.25
10000096000920008800084000800007600072000
Static Pressure(Pa)
Pressure DistributionWith/Without using Bernoulli’s Equation for Inner Surface Pressure Estimation
With Bernoulli’s Equation for Inner Surface Pressure including hydrostatic &velocity terms
Hydrostatic Pressure only on Inner Surface
Radial Direction (m)
Lo
ng
itu
din
alD
ire
cti
on
(m)
0.05 0.1 0.150
0.05
0.1
0.15
0.2
0.25
10000096000920008800084000800007600072000
Static Pressure(Pa)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 19
Gas Velocity Distribution
Radial Direction (m)
Lo
ng
itu
din
alD
ire
cti
on
(m)
0.05 0.1 0.150
0.05
0.1
0.15
0.2
0.25
0.0170.0150.0130.0110.0090.0070.0050.0030.001
Gas VelocityMag. (m/s)
Radial Direction (m)L
on
git
ud
ina
lDir
ec
tio
n(m
)0.05 0.1 0.15
0
0.05
0.1
0.15
0.2
0.25
0.0170.0150.0130.0110.0090.0070.0050.0030.001
Gas VelocityMag. (m/s)
With/Without steel velocity effect on inner surface pressure
using Bernoulli’s Equation for Inner Surface Pressure Estimation
Without using Bernoulli’s Equation
12.1 LPM total16.2 LPM total
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 20
Gas Velocity Distribution (3-D View)
using Bernoulli’s Equation for Inner Surface Pressure Estimation
Without using Bernoulli’s Equation
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 21
Gas Flow Simulation
• Velocity Distribution (with/without pressure correction using Bernoulli’s equation)
Longitudinal Distance from UTN Bottom (m)
Gas
Vel
oci
ty a
t U
TN
Inn
er S
urf
ace
(m/s
)
16.2 LPM total
12.1 LPM total
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 22
Calculating Gas Flow Rate
hot hot std std
hot std
hot hot std std
hot std
hot hot std std
hot stdS S
stdstd hot hot
std hot S
pV nRT
pVnR
Tp V p V
nRT T
p Q t p Q t
T T
p Q t p Q tdS dS
T T
TSQ p Q dS
p T
=
=
= =
Δ Δ=
Δ Δ=
=
Tstd (K) Thot (K) Pstd
(Pa)Kd
(npm)
300 1832 101325 10.1
3-5 5, 4 4*1.9156 10 7.6624 10total std std
mV SQ s−= = × = ×
In SLPM, it is: 7.6624*10-5*1000*60 = 4.6 SLPM, which matches reasonably well with measured gas flow rate of 5.01 SLPM. The mismatch could be caused by using a different permeability in the simulation, or possible gas leakage.
phot and Qhot are the absolute pressure and gas hot flow rate at each of the face centers from the simulated data, then integrate them over the UTN inner surface to evaluate the gas volume flow rate in standard conditions as shown in the equation.Since only a quarter is modeled, the total flow rate will be 4 times of the calculated value of S*Qstd.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 23
Estimation of Active Sites Number at UTN Refractory Inner Surface
Where:Qg: the gas injection flow rate per cm2 (LPM);U: liquid superficial velocity (m/s);Perm: material permeability (npm);θ: contact angle for wettability (rad)
G. Lee and B.G. Thomas suggest[1]:
Ref:[1] G. Lee, B.G. Thomas, et al., Met. Mater. Int., Vol. 16, No. 3 (2010), pp. 501~506
from ref [1]
from ref [1]
0.2635 0.85 0.33087 g ermsite
Q U PN
θ=
So the number of active sites per cm2
is:
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 24
Estimation of Mean Bubble Size using a Two-Stage Model
Active sites function as drilled holes where gas is injected. So based on the number of active sites and gas flow rate over an area, the gas flow rate per active site can be determined.
--Figures from ref [2]
Ref:[2] H. Bai and B. G. Thomas, Metall. Mater. Trans. B 32, 1143(2001).
Hua Bai’s two-stage initial bubble formation model[2]:
1. Expansion stage (solving for r, as re)
2. Elongation stage (solving for rd)
Drag coefficient:
Bubble Reynolds number:
:nozzle inner diameter (m)
Based on the 1/7th law in turbulent flow in the circular pipe
Contact angle function: Empirical correlation with liquid steel superficial velocity
lρ :liquid density (kg/m3)
gρ :gas density (kg/m3)
ND :liquid steel superficial velocity (m/s)U:surface tension (N/m)σ:kinematic viscosity of liquid steel (Pa*s)υ
Expansion stage Elongation stage
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 25
Initial Bubble Size Distribution at UTN Inner Surface
UT
NH
eig
ht
(m)
-0.25
-0.2
-0.15
-0.1
-0.05
0
X
Y
Z
Active Sites # density (1/cm2)
Gas Flow Rate per Site (ml/s)
Initial Bubble Size (mm)
Sauter mean bubble diameter: 2.56 mm
3
32 2
i ii
i ii
n dd
n d=
big bubblesmall bubble
no bubble
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 26
PART 2 Conclusion
• Pressure at UTN inner surface serves as a boundary condition in the simulation of heated gas flow through porous refractory, thus needs careful treatment. Two different treatments of inner surface pressure were applied in current study:– Hydrostatic pressure only;– Hydrostatic pressure with correction using Bernoulli’s
equation (considering fluid kinetic energy change and pressure loss due to flow area change inside UTN)
• Results show:– Without pressure correction, hot argon flow rate is 12.1
LPM;– With pressure correction, hot argon flow rate is 16.2
LPM
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 27
PART 2 Conclusion
• A model system has been established to calculate hot argon flow rate at UTN inner surface, and estimate the active sites number density and eventually initial bubble size distributions.
• The initial bubble size is then used as an input parameter for multiphase flow simulations.
• For Severstal conditions for Nail Board 4, – Active sites number density ranges from 0 to ~7 /cm2;– Initial bubble size ranges from ~2.2 to ~3.5 mm,
with a Sauter-mean diameter = 2.56 mm;– Corresponding bubbling frequency ranges from ~40 to ~180
Hz.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 28
PART 3:Multi-phase Flow Simulations
with Nail-Board Measurements
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 29
Model Assumptions and Computational Details
• Model assumptions:– Isothermal flow
– Argon-steel flow is within bubbly flow regime
– No argon bubble break-up or coalescence, bubble size doesn’t change with local pressure
– Left-right symmetry for nozzle and mold domains
– Relatively calm top surface, no significant gravity waves exist
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 30
Governing Equations for Single-Phase Flow in Nozzle/Mold Region
• Continuity Equation:
• Momentum Conservation – Navier-Stoke Equation:
• Turbulence Model – k-ω SST URANS model [1]:
( ) 0ρ∇ ⋅ =v
( ) ( ) ( )( )Tpt
ρρ ρμ μ
∂+ ∇ ⋅ = −∇ + ∇ ⋅ ∇ +
∂+
vvv v g
( )1
1 2max ,T
T
a k
a SF
μνω ρ
= =
( )( )*k k T
kk P k k
tβ ω ν σ ν∂ + ⋅∇ = − + ∇ ⋅ + ∇
∂v
( )( ) ( ) ( )2 21 2
12 1TS F kt ω ωω ω α βω ν σ ν ω σ ω
ω∂ + ⋅∇ = − + ∇ ⋅ + ∇ + − ∇ ⋅∇∂
v
k equation:
Omega equation:
Values for the closure parameters can be found in [1].
[1] F.R. Menter, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications”, AIAA Journal, 1994, 32(8), pp 1598
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 31
Domain, Mesh and Methods for Fluid Flow in Severstal Caster Nozzle and Mold
Y
X
Z
Models and Schemes
Name
Turbulence Model k-ω model
Multiphase Model Eulerian Model
Advection Discretization
2nd order upwindingscheme
Meniscus Domain Outlet
Free-slip wallwith Gas Sink
Pressure outletB.C.:
Time step: 0.05 sec
Total mesh:0.45 million mapped hexa- cells
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 32
BOARD 4: Single Phase Flow Pattern Evolution -- note jet wobble (~20s period)
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0.5Time = 36 sec m/s
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0.5Time = 25 sec m/s
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0.5Time = 28 sec m/s
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0.5Time = 31 sec m/s
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0.5Time = 42.5 sec m/s
Mold Width (m)
Mo
ldL
eng
th(m
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0.5Time = 46 sec m/s
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 33
Single Phase Liquid Steel Flow Pattern-- Movie
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 34
Multiphase Flow Models – Eulerian Bubble Model
• Eulerian-Eulerian Model, treat argon gas as another continuous phase
( ) ( ) 0a aa a at
α ρα ρ
∂+ ∇ ⋅ =
∂v
( ) ( ) 0s ss s st
α ρα ρ
∂+ ∇ ⋅ =
∂v
Continuity for argon:
Continuity for steel:
Momentum balance for argon:( ) ( ) ( ) ( )a a a
a a a a a a a a as s a a ap Kt
α ρα ρ α α μ α ρ
∂+ ∇ ⋅ = − ∇ + ∇ ⋅ ∇ + − +
∂v
v v v v v g
Momentum balance for liquid steel:( ) ( ) ( )( ) ( )s s s
s s s s s s s t s as a s s sp Kt
α ρα ρ α α μ μ α ρ
∂+ ∇ ⋅ = − ∇ + ∇ ⋅ + ∇ + − +
∂v
v v v v v g
3 ,4
Das s s s a
b
CK
Dα ρ= −v v ( )0.68724 1 0.15Re , Re
Res s a b
D b bb s
DC
ρμ−
= + =v v
2
t sk
Cμμ ρε
=
1s aα α+ =Volume fraction equation:
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 35
• Lagrangian bubble tracking, calculate the bubble trajectories
Another Multiphase Flow Model – Discrete Phase Bubble Model
pp D L added mass G press stress
dm
dt −= + + + + +v
F F F F F F
Drag force
Lift force
Added mass force Gravity
pp
d
dt=
xvMotion:
Pressure & Stressgradient force
( )
( )
2
Re
18
24 ,ReRep
D p f D f p f p
pD p f p
p
d C
dC f
π ρ
ν
= − −
= = −
F v v v v
v v
( )0.687Re 1 0.15Re
p pf = +
3
6f p f
press stress
d D
Dt
ρ π + = −
vF F g
3
6p
G p
dπρ=F g
3
12p p f p
added mass
d d d
dt dt
ρ π−
= −
v vF
( )( ) ( ) ( )( )
12
29 sgn( )4
, sgn( ) ,
0.6765* 1 tanh[2.5lg 0.191] 0.667 tanh[6 0.32 ]
uL p s
s f s p fs
Gd G J
GG G
U
J
μπ ν
νε
ε ε ε
= −
= × ∇× ∇ = = −
= + + + −
F U
U v U v v
Ref:(1) Maxey, M.R. and Riley, J.J.: Physics of Fluids, 1983, vol. 26 (4), pp. 883-889.(2) Crowe, C., Sommerfild, M. and Tsinji, Y.: Multiphase Flows with Droplets and Particles, CRC Press, 1998, pp. 23-95.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 36
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.2 0.4 0.6 0.8
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.471.351.231.100.980.860.740.620.500.370.250.130.01
0.3
SEN
Liquid SteelVelocity Magnitude (m/s)m/s
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.2 0.4 0.6 0.8
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
2.2E-024.4E-038.6E-041.7E-043.4E-056.6E-061.3E-062.6E-075.1E-081.0E-08
0.5
SEN
Argon Volume Fractionm/s
• Eulerian model simulation results:
Typical Argon-Steel Flow Pattern in SEN/Mold Region
Mean bubble diameter: 2.56 mm(constant, based on nozzle flow model and initial bubble size estimation)
• Double-roll flow pattern still exists with argon injection (~4% argon)• Large scale instability (such as jet wobbling) has been reduced by gas
injection comparing with single phase flow pattern in this case
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 37
Comparison with Nail-Board Experiment Results – Board 4 Velocity Magnitude
Distance from SEN (mm)
Liq
uid
Ste
el V
elo
city
Mag
nit
ud
e
(m/s
)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 38
Distance from SEN (mm)
Liq
uid
Ste
el H
ori
zon
tal V
elo
city
(m
/s)
Comparison of Horizontal Velocity Profiles
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 39
BOARD 4: DES with DPM
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 40
Comparison of Horizontal Velocity Profiles – Model vs. Measurements (Board 4)
Distance from SEN (mm)
Liq
uid
Ste
el H
ori
zon
tal V
elo
city
(m
/s)
RANS + Eulerian Model
DES + DPM
NailboardMeasurements
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 41
Distance from SEN (mm)
Mo
ld L
evel
Pro
file
(m
m) 0
L
p ph
gρ−Δ =
Comparison of Mold Level Profile(BOARD 4)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 42
Conclusion – from BOARD 4 Simulation
• Single phase flow simulation results show a wobbling liquid steel jet, which causes a periodical reverse flow away from SEN at regions close to the narrow face;
• Jet wobbling is reduced by adding a small amount of gas into the liquid steel (~4% in current case, board 4), and the double-roll flow pattern still remains;
• Comparison of liquid steel surface velocity with nail board measurements suggests:– the trend of both instantaneous and mean steel surface velocity
distributions from argon-steel two-phase simulations match well with nail-board measurements (with velocities peak closer to narrow face), but with a ~20-30% velocity magnitude difference;
– single phase simulation results suggest an opposite velocity distribution – velocity peaks close to SEN instead of narrow face;
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 43
Conclusion – from BOARD 4 Simulation (CONT.)
• DPM model is promising in multiphase flow modeling, given:– A high resolution mesh
– More accurate turbulence model (LES e.g.)
– A well-educated bubble size distribution
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 44
• In this part of work, the following techniques and parameters are utilized:– RANS model (k-epsilon) for turbulence
– Eulerian model for dispersed bubble phase
– Two mean bubble diameters, 3mm and 5mm, are studied
– Mold top surface profile is calculated using:• Pressure method
• A moving-grid free surface tracking algorithm
Simulations for BOARD 11~13
Date & Time NailboardCase #
Casting Speed
(inch/min)
Strand Width (inch)
Argon Flow Rate
(SLPM)
Argon Back Pressure
(psi)
Submerging Depth (mm)
10/16, 3:28:54 pm 11 65.0 54.99 7.0 18.07 222
10/16, 3:29:20 pm 12 65.0 54.99 7.0 18.07 222
10/16, 3:29:41 pm 13 65.0 54.99 7.0 18.07 222
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 45
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.41.31.11.00.80.70.50.40.20.1
0.5 Velocity Magnitude (m/s)m/s
Liquid Steel Velocity Distribution at Mold Center Plane
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.41.31.11.00.80.70.50.40.20.1
0.5 Velocity Magnitude (m/s)m/s
• Double-roll flow pattern achieved for both 3 mm bubble and 5 mm bubble
• Slightly higher sub-meniscus velocity is found for 5 mm bubble size case
3 mm bubble, Board 11~13 5 mm bubble, Board 11~13
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 46
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
5.5E-021.6E-024.8E-031.4E-034.3E-041.3E-043.8E-051.1E-053.4E-061.0E-06
0.5 Argon Volume Fractionm/s
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
5.5E-021.6E-024.8E-031.4E-034.3E-041.3E-043.8E-051.1E-053.4E-061.0E-06
0.5 Argon Volume Fractionm/s
Argon Gas Velocity / Fraction Distribution at Mold Center Plane
3 mm bubble, Board 11~13 5 mm bubble, Board 11~13
• Gas with 3 mm bubble size spreads further into the liquid pool, closer to the narrow phase, comparing with the case with 5 mm bubble size
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 47
Mold Width (m)
Mo
ldT
hic
kn
es
s(m
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.2
-0.1
0
0.1
0.0 0.1 0.1 0.2 0.3 0.3 0.4 0.4 0.50.5
Velocity Magnitude (m/s)
m/s
Mold Width (m)
Mo
ldT
hic
kn
es
s(m
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.2
-0.1
0
0.1
0.0 0.1 0.1 0.2 0.3 0.3 0.4 0.4 0.50.5
Velocity Magnitude (m/s)
m/s
3 mm bubble, Board 11~13
5 mm bubble, Board 11~13
Liquid Steel Velocity Distribution at Mold Top Surface
• Higher surface velocity found in 5 mm bubble size case
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 48
Mold Width (m)
Mo
ldT
hic
kn
es
s(m
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.2
-0.1
0
0.1
1.0E-06 2.1E-05 4.3E-04 8.9E-030.5
Argon Volume Fraction
m/s
Mold Width (m)
Mo
ldT
hic
kn
es
s(m
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.2
-0.1
0
0.1
1.0E-06 2.1E-05 4.3E-04 8.9E-030.5
Argon Volume Fraction
m/s
3 mm bubble, Board 11~13
5 mm bubble, Board 11~13
Argon Gas Velocity / Fraction Distribution at Mold Top Surface
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 49
Mold Thickness (m)
Mo
ldL
en
gth
(m)
-0.04 -0.02 0 0.02 0.04 0.06
0.8
0.82
0.84
0.86
0.88
5.0E-01
1.9E-01
7.5E-02
2.9E-02
1.1E-02
4.4E-03
1.7E-03
6.6E-04
2.6E-04
1.0E-04
0.5
Argon VolumeFraction
m/s
Mold Thickness (m)
Mo
ldL
en
gth
(m)
-0.04 -0.02 0 0.02 0.04 0.06
0.8
0.82
0.84
0.86
0.88
5.0E-01
1.9E-01
7.5E-02
2.9E-02
1.1E-02
4.4E-03
1.7E-03
6.6E-04
2.6E-04
1.0E-04
0.5
Argon VolumeFraction
m/s
Argon Gas Velocity / Fraction Distribution at Port Exit
3 mm bubble, Board 11~13 5 mm bubble, Board 11~13
• Higher gas rising velocity found in 5 mm bubble size case at port exit
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 50
Mold Thickness (m)
Mo
ldL
en
gth
(m)
-0.04 -0.02 0 0.02 0.04 0.06
0.8
0.82
0.84
0.86
0.88
1.9
1.6
1.3
1.0
0.7
0.4
0.1
0.5
Velocity Magnitude(m/s)
m/s
Mold Thickness (m)
Mo
ldL
en
gth
(m)
-0.04 -0.02 0 0.02 0.04 0.06
0.8
0.82
0.84
0.86
0.88
1.9
1.6
1.3
1.0
0.7
0.4
0.1
0.5
Velocity Magnitude(m/s)
m/s
Liquid Steel Velocity Distribution at Port Exit
3 mm bubble, Board 11~13 5 mm bubble, Board 11~13
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 51
• Pressure Conversion– Wall boundary condition at domain top surface
– Best used for steady / quasi-steady state flows, without gravity waves
• Lifting
• displacement
• Moving-grid Surface Tracking *– Pressure boundary at domain top surface
– Working for both steady state and transient flows, with/without gravity waves
Free Surface Modeling
* R. Liu, B.G. Thomas, L. Kalra, T. Bhattacharya, and A. Dasgupta., Proc. AISTech 2013 Conf.(Pittsburg, PA), p1351-1364, (2013)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 52
Moving Grid Technique using FVM
Ref:
S. Muzaferija and M. Peri´c, Numerical Heat Transfer, Part B: Fundamentals: An International Journal of Computation and Methodology, 1997. Vol 32:4, 369-384
This node moving approach has been adopted and coded into FLUENT udf for free surface modeling in current work
( )( ) 0gρ∇ ⋅ =−v vContinuity equation with moving mesh:
Momentum equation with moving mesh:
( ) ( )( ) ( )g pt
ρρ μ
∂+ ∇ ⋅ = −∇ + ∇ ⋅ ∇ +
∂−
vv v Fv v
V is fluid velocity, while V g is grid velocity (mesh velocity)
Kinematic B.C.:
Figure from reference( ) 0s fs
= − ⋅ v v n or 0fsm =Dynamic B.C.: all forces in equilibrium at fs.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 53
Large Amplitude Sloshing
Vertical Velocity (m/s)
• Free surface nodes moved via UDF, with kinematic and dynamic B.C.s satisfied
• Side wall nodes and internal nodes are smoothed via solution of a Laplace equation diffusing free surface nodes displacements to interior nodes
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 54
Model Validation –Analytical Solution and Case Setup
• 2-D small-amplitude sloshing problem
Where zi is the ith root of the equation below, and zi is defined as:
( )ν ν ν ω+ + + + =3
4 2 2 2 2 4 2202 4 0z k z k z k
( ) ( ) ( )( )ων ν νν ω ν=
+ −
+ −1 22 4 14
2 2 20 02 202 4 2 2 2
10
4a t = exp8
ii i
i i i
azk a erfc k t z k t erfc z tk Z z k
Level Height (mm)
Tank Width (mm)
Initial Perturbation Amplitude
(mm)
1500 1000 201500 mm
20 mm
1000 mm
g
Fluid Kinematic Viscosity
(m2/s)
Gravity Acceleration
(m/s2)
Surface Tension
(N/m)
0.01 1.0 0
Initial Interface:
a0=0.01 m
0 gkω = Prosperetti, A., 1981. “Motion of two superposed viscous fluids”. Physics of Fluids, 24(7), July, pp. 1217–1223.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 55
Model Validation –Comparison with Analytical Solution
0 2 4 6 8 10 12 14 16 18 201.490
1.492
1.494
1.496
1.498
1.500
1.502
1.504
1.506
1.508
1.510
1.512
Cor
ner
Leve
l (m
)
Time (sec)
Analytical Solution FLUENT simulation, 25*40 mesh, time step 0.01 sec FLUENT simulation, 200*80 mesh, time step 0.002 sec
• Excellent match with analytical solution obtained even for simulations using the very coarse mesh
• Using second order (or higher) advection scheme and temporal scheme are crucial for achieving accuracy
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 56
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.41.31.11.00.80.70.50.40.20.1
0.5 m/s Velocity Magnitude (m/s)
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.41.31.11.00.80.70.50.40.20.1
0.5 m/s Velocity Magnitude (m/s)
Single Phase, Board 11~13 Multiphase, Board 11~13(5 mm bubble size)
Liquid Steel Velocity Distribution at Mold Center Plane (Board 11-13)
• Gas injection (with 5 mm bubble size) increases liquid steel surface velocity, and surface level difference
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 57
Moving-Grid Free Surface TrackingSingle Phase vs. Two-Phase Flow
X
ZY
0.5780.5760.5740.5720.5700.5680.5660.5640.5630.5610.5590.5570.555
Surface Level (m)
X
ZY
0.5780.5760.5740.5720.5700.5680.5660.5640.5630.5610.5590.5570.555
Surface Level (m)
Single Phase, Board 11~13 Multiphase, Board 11~13(5 mm bubble size)
• Rising of gas bubbles elevate the surface level near SEN, comparing with the no-gas case
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 58
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
5.5E-021.6E-024.8E-031.4E-034.3E-041.3E-043.8E-051.1E-053.4E-061.0E-06
0.5 m/sArgon Volume Fraction
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
5.5E-021.6E-024.8E-031.4E-034.3E-041.3E-043.8E-051.1E-053.4E-061.0E-06
0.5 Argon Volume Fractionm/s
5 mm bubble, Board 11~13(wall B.C. on top)
5 mm bubble, Board 11~13(free surface tracking, pressure B.C. on top)
Liquid Steel Velocity Distribution – Wall B.C. vs. Pressure B.C.
• No significant change for the gas distribution using either method
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 59
Comparison with Nail Board Measurements – Horizontal Velocity
0 100 200 300 400 500 600 700-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Sur
face
Hor
izon
tal V
eloc
ity (
m/s
)
Distance from SEN (mm)
Nail Board, IR Nail Board, OR Eulerian Model, 3 mm bubble dia. Eulerian Model, 5 mm bubble dia. Eulerian Model, Free Surface, 5 mm bubble dia.
SE
N
(Board 11-13)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 60
Comparison with Nail Board Measurements – Surface Level Profile
SE
N
0 100 200 300 400 500 600 700-20
-10
0
10
20
30
Sur
face
Lev
el P
rofil
e (m
m)
Distance from SEN (mm)
Nail Board, IR Nail Board, OR Eulerian Model, 3 mm bubble dia. Eulerian Model, 5 mm bubble dia. Eulerian Model, Free Surface, 5 mm bubble dia.
(Board 11-13)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 61
Conclusions – from BOARD 11~13
• Single phase flow simulation results does not show any wobbling liquid steel jet, thus narrower mold generates a more stable flow pattern comparing to the wider mold (shown previously in case 4)
• Smaller bubble size (3 mm) increases surface velocity slightly, while larger bubbles (5 mm)– increase the surface velocities significantly and– increase surface level differences
• Simple pressure method and moving-grid method predict similar surface level profiles
• The 5-mm bubble case matches reasonably with measurements (better than with 3mm dia.)
• Better match near NF could be obtained if the nailboard had been tilted
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 62
• In this part of work, the following techniques and parameters are utilized:– RANS model (k-epsilon) for turbulence
– Eulerian model for dispersed bubble phase
– Three mean bubble diameters, 3mm, 5mm and 8mm, are studied
Simulations for BOARD 14~16
Date & Time NailboardCase #
Casting Speed (inch/min)
Strand Width (inch)
Argon Flow Rate(SLPM)
Argon Back Pressure (psi)
Submergence Depth (mm)
10/16, 3:35:50 pm 14 25.5 54.99 6.3 19.18 22210/16, 3:36:16 pm 15 25.5 54.99 6.2 19.18 22210/16, 3:36:36 pm 16 25.5 54.99 6.2 19.18 222
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 63
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
5.5E-021.6E-024.8E-031.4E-034.3E-041.3E-043.8E-051.1E-053.4E-061.0E-06
0.5 Argon Volume Fractionm/s
Mold Width (m)
Mo
ldL
en
gth
(m)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0.50.40.40.30.30.20.20.10.10.0
0.5 Velocity Magnitude (m/s)m/s
Liquid Steel Velocity Distribution at Mold Center Plane – Board 14~165 mm bubble, Board 14~16
Complex flow pattern with partial reversed flow
Rising argon bubbles concentrate near SEN
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 64
Mold Width (m)
Mo
ldT
hic
kn
es
s(m
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.2
-0.1
0
0.1
0.0 0.1 0.1 0.2 0.3 0.3 0.4 0.4 0.50.5
Velocity Magnitude (m/s)
m/s
Mold Width (m)
Mo
ldT
hic
kn
es
s(m
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
-0.2
-0.1
0
0.1
1.0E-06 2.1E-05 4.3E-04 8.9E-030.5
Argon Volume Fraction
m/s
Velocity / Argon Fraction Distribution at Mold Top Surface – Board 14~16
• Two liquid steel surface streams move in opposite directions, and meet in the middle region
• Gas exits to the top surface in a symmetric manner, indicating less affected by the swirling liquid steel jet
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 65
Mold Thickness (m)
Mo
ldL
en
gth
(m)
-0.04 -0.02 0 0.02 0.04 0.06
0.8
0.82
0.84
0.86
0.88
5.0E-01
1.9E-01
7.5E-02
2.9E-02
1.1E-02
4.4E-03
1.7E-03
6.6E-04
2.6E-04
1.0E-04
0.5
Argon VolumeFraction
m/s
Mold Thickness (m)
Mo
ldL
en
gth
(m)
-0.04 -0.02 0 0.02 0.04 0.06
0.8
0.82
0.84
0.86
0.88
1.9
1.6
1.3
1.0
0.7
0.4
0.1
0.5
Velocity Magnitude(m/s)
m/s
Liquid Steel Velocity / Gas Distribution at Port Exit
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 66
Comparison with Nail Board 14~16 Measurements – Horizontal Velocity
SE
N
0 100 200 300 400 500 600 700-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Sur
face
Hor
izon
tal V
eloc
ity (
m/s
)
Distance from SEN (mm)
Nail-board measurements Eulerian model, 3 mm bubble Eulerian model, 5 mm bubble Eulerian model, 8 mm bubble
(Board 14-16)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 67
0 100 200 300 400 500 600 700-6
-4
-2
0
2
4
6
8
Mol
d Le
vel (
mm
)
Distance from SEN (mm)
Nail-board measurements Eulerian model, 3mm bubble Eulerian model,5mm bubble Eulerian model, 8mm bubble
SE
N
Comparison with Nail Board 14~16 Measurements – Mold Level
(Board 14-16)
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 68
Conclusion – from BOARD 14~16
• Excellent match is found between the measured and predicted surface steel velocities, as well as for the mold level, for all three bubble diameters used (3, 5 and 8 mm);
• Detailed comparison between simulations and measurements indicates that utilization of multi-size bubble groups instead of a single mean bubble size would increase the accuracy.
University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Rui Liu • 69
Summary and Future Work
• Methodology of modeling and simulating argon-steel multi-phase nozzle/mold flows has been established
• Models have been validated with many measurements and reasonable accuracy has been achieved for flow patterns, including complex flows with partial surface reversals due to gas bubbles rising
• Future work includes:– Develop and apply criteria for defects formation
– Parametric studies to classify flows
– Use methodology and models in this work to find operation windows to avoid defects