Modeling and Simulation of Multiphase Flows in CC Mold Regionccc.illinois.edu/s/2013_Presentations/04_LIU-R_Multiphase_Mold... · Modeling and Simulation of Multiphase Flows in CC

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


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


PART 1:Gate Position Estimation


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


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).


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.


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


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


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)


PART 2:UTN Gas Flow Simulation and Initial Bubble Size Distribution


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).


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)


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


• 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


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)


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


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


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)


Gas Velocity Distribution


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


Gas Velocity Distribution (3-D View)

using Bernoulli’s Equation for Inner Surface Pressure Estimation

Without using Bernoulli’s Equation


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


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.


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:


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


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


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


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.


PART 3:Multi-phase Flow Simulations

with Nail-Board Measurements


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


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


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


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


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


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


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



Single Phase Liquid Steel Flow Pattern-- Movie


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:


• 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.


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


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

)



Liq

uid

Ste

el H

ori

zon

tal V

elo

city

(m

/s)

Comparison of Horizontal Velocity Profiles


BOARD 4: DES with DPM


Comparison of Horizontal Velocity Profiles – Model vs. Measurements (Board 4)


Liq

uid

Ste

el H

ori

zon

tal V

elo

city

(m

/s)

RANS + Eulerian Model

DES + DPM

NailboardMeasurements



Mo

ld L

evel

Pro

file

(m

m) 0

L

p ph

gρ−Δ =

Comparison of Mold Level Profile(BOARD 4)


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;


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


• 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


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


• 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


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


Argon Gas Velocity / Fraction Distribution at Mold Center Plane


• 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


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


m/s

3 mm bubble, Board 11~13


Liquid Steel Velocity Distribution at Mold Top Surface

• Higher surface velocity found in 5 mm bubble size case


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


m/s



Argon Gas Velocity / Fraction Distribution at Mold Top Surface


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


m/s

Argon Gas Velocity / Fraction Distribution at Port Exit


• Higher gas rising velocity found in 5 mm bubble size case at port exit


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


m/s

Liquid Steel Velocity Distribution at Port Exit



• 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)


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.


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


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.


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


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


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


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


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


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

)


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)


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)


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)


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


• 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


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


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


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


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


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


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


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


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


m/s

Liquid Steel Velocity / Gas Distribution at Port Exit


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

)


Nail-board measurements Eulerian model, 3 mm bubble Eulerian model, 5 mm bubble Eulerian model, 8 mm bubble

(Board 14-16)


0 100 200 300 400 500 600 700-6

-4

-2

0

2

4

6

8

Mol

d Le

vel (

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)


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.


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

Documents

Modeling and Simulation of Multiphase Flows in CC Mold Regionccc.illinois.edu/s/2013_Presentations/04_LIU-R_Multiphase_Mold... · Modeling and Simulation of Multiphase Flows in CC