particle capture in mold including effect of subsurface...

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CCC Annual Report UIUC, August 19, 2015 Kai Jin Department of Mechanical Science & Engineering University of Illinois at Urbana-Champaign Particle Capture in Mold including Effect of Subsurface Hooks University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 2 Objective Develop a model to include effects of hook on particle\bubble capture; Use advanced capture criterion [1-3] combined with hook capture mechanism to study the particle/bubble capture;

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CCC Annual ReportUIUC, August 19, 2015

Kai Jin

Department of Mechanical Science & EngineeringUniversity of Illinois at Urbana-Champaign

Particle Capture in Mold including Effect ofSubsurface Hooks

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 2

Objective

• Develop a model to include effects of hook on particle\bubble capture;

• Use advanced capture criterion[1-3] combined with hook capture mechanism to study the particle/bubble capture;

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 3

Review of Inclusion Measurements (Baosteel Caster #4)

• Cut samples from as-cast slab: WF center, WF quarter, and NF;• Mill away steel layer by layer. • Examine bubbles with 35x optical microscope • Record number and size distributions

SampleLayer

Number123456

Convert visible diameter to true diameter

0.785dtrue = dvisible[4]

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 4

Shell

Schematic of Hook Capture Mechanism

• A particle/bubble enters into a hook zone has three different possible fates

• fo is the mold oscillation frequency

Solidified Shell

Hook zone

z

x

Hookstructure

depth

cv

1ocv f −

Note:1. Particle enter hook zoon may not be captured immediately;2. Particle may escape from the hook zone before it was captured;3. Particles may hit the mushy zone front and be captured by WF/NF before captured by hook;4. In post processing, project hook captured bubble vertically onto the shell

cv

1ocv f −

cv tΔ

Escape from hook zone

Capture by WF/NF

Capture by hook

Time t=t0 Time t = t0+∆t

h

h K t=Shell thickness

Pro

ject

ion

Shell

a bubble or inclusion

Casting direction

Solid-liquid interface

NF or

WF

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 5

Flow Chart of Hook Capture Mechanism

• thook – a critical time, allows particle/bubble to travel before it is captured by the hook, on average, we take

• tc – time of a particle remained in the hood zone since it enters. Reset tc to 0 when particle cross the hook zone boundary (consider a particle re-entering the hook zone)

particle in hook zoneNo

Continue

particle has stayed in hook zone for tc > thook

Yes

Captured by hook

Yes

No

1hook 0.5 ot f −=

cv

1ocv f −

tc=0

tc=0

tc=t1

tc=0

tc=0

tc=t2

tc=0

t1: time taken for particle travel on yellow path; t1<thook, particle escaped from hook zone.t2: time taken for particle travel on green path; t2>thook, particle is captured by the hook.

Particle path

Particle re-entering hook zone

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 6

Add hook capture mechanism into advanced capture criterion [1-3]

• Flow chart showing the modified and original advanced capture criterion;

• Hook capture mechanism are added in to FLUENT using UDF;

( ), 2 cos 0L D Lub Grad IF F F F Fχ θ− − − − <

( ) ( ) ( ), , ,cos sin sin 2D B L D Lub Grad IF F F F F F Fη η χθ θ θ+ + − > − −

( ) ( ) ( ), , ,cos sin sin2D B L D Lub Grad IF F F F F F Fη η χθ θ θ− + − > − −

Particle size larger than PDAS (dp≥PDAS)?no Capture

yes

In solidification direction, repulsive force smaller than attractive force?noDrift back to flow

Particle contacts a boundary representing mushy-zone front?yes

noContinue

yes

Can cross-flow and buoyancy drive particle into motion though rotation?

, if FDη andFBη in same direction

, if FDη andFBη in opposite directionand FDη≥FBη

or

or, if FDη andFBη in opposite direction

and FDη<FBη

yes no

( ) ( ) ( ), , ,cos sin sin2B D L D Lub Grad IF F F F F F Fη η χθ θ θ− + − > − −

Particle in hook zone

Satisfies Hook Capture Criterion

yes

no

yes

no

A Bubble/Particle Touching 3 Dendrite Tips [3] Flow chart for Ar bubble/particle capture criterion [3]

0 0.5 1 1.5 2 2.550

100

150

200

250

Distance below meniscus (m)

PD

AS

(μ m

)

NFWF

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 7

Ar Bubble Distribution

Rosin-Rammler distribution, withmean diameter 3mm*

Step–1, Obtain flow field with two-way coupled Euler-Lagrangian simulation: using 5 largest groups of bubbles

Step–2, Inject and track all 11 groups of all 250,000 bubbles.

Repeat Step-2: 10 times ~2.5 million bubbles tracked using each capture criterion

* Mean based on model by H. Bai & BG Thomas, MMTB, 2001

Bubbles < 1mm total <1% Volume fraction

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 8

Governing Equations• Using Reynolds decomposition, steel velocity u = U + u’

• The time averaged continuity and momentum equations for liquid steel (turbulence viscosity μt modelled by k-ε model [5])

• Force balance equations for each individual bubble (diameter dp , velocity up , density ρp , mass mp and volume Vp )

• Turbulence dispersion of particles: using Random Walk Model [7]

( ) mass-sink 0Sρ∇ ⋅ + =U

tρ ∂

∂U ( ) ( )( )*

momentum- DPMsinkT

tpρ μ μ + ⋅∇ = −∇ +∇⋅ + ∇ ∇ + + U U U+ U S S

( ) ( )p

v p

Re

p p pp p p pDp p p p p2

pp pp

p

d DD0.5d 18d 24 D d D

bD

dm Cm m m m

t d t t t

ρ ρ ρμ ρ ρρ ρμ ρρ

− +

− −= − + +

F F FF

u u gu u uuu u

FD – drag force, and drag coefficient CD from Morsi [6];FV – virtual mass force; Fp – pressure gradient force; Fb – buoyancy/gravity

0

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 9

Random Walk Model[7]

• Gaussian distributed random velocity fluctuation, u’, v’ and w’ are generated from

• Eddy life time: where

• Eddy cross time

where

2' 'u uζ= 2 2 2 ' ' ' 2 / 3u v w k= = =

ζ – standard normal distribution random number.

0.15L L

k kt C= ≈

( )lne Ltt r= −

3/24/3

ln 1cross

p

k

tC

u u

μτ

τ

− −

=

r – uniformly distributed random number from 0 and 1.

2

18p pdρ

τμ

=

use k, ε and ζ to calculate fluctuations

evaluate te and tcross

interaction time tinter = min(te , tcross)

interaction time reached?

Yes No

new ζ

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 10

Simulations and Number of Bubbles Injected

• During the bubble/particle tracking step, 244239 bubbles were injected in each simulation

Groupi

Diameter di (mm)

Number Ni

1 0.025 1196

2 0.040 1622

3 0.080 3589

4 0.100 2826

5 0.200 8973

6 0.300 11521

7 1.000 47564

8 2.000 80911

9 3.000 65022

10 4.000 19714

11 5.000 1301

Total 244239

Hook Depth(mm)

thook

(s)Osc. Frequency

(Hz)

A 0 - -

B 3 0.25 2

C 6 0.25 2

List of Simulations

Note:• All Simulations are based on the some flow field solution• Case A was old results presented in 2014 CCC annual meeting;

Casting Conditions Value

Mold Thickness × Width 230 × 1300mm

Submergence Depth 160 mm

Port Downward Angle 15 deg.

Casting Speed 1.5 m/min

Ar injection 8.2% vol.

Casting ConditionsNumber of Bubbles Tracked

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 11

x(m)

Dis

tan

ce

be

low

top

su

rfa

ce

(m)

0 0.2 0.4 0.6

-0.8

-0.6

-0.4

-0.2

01.31.21.110.90.80.70.60.50.40.30.20.1

m/s

Mold

1

23

U

Flow field [8]

(same for all cases in hook study)

• Predicted cross flow from IR toward OR agrees with the plant measurements

• Cross flow was not observed in the single-phase flow results;

• Plant measurements found even stronger cross flow than predicted;

X (m)

Y(m

)

0 0.1 0.2 0.3 0.4 0.5 0.6

-0.1

-0.05

0

0.05

0.1

0.180.160.140.120.10.080.060.040.02

0.4

OR

IR

m/s

SEN

Ar Volume Fraction

Flow Field[8]

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 12

WF hook captured bubbles (Hook depth 3mm, Simulation B)

X (m)Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.2 0.4 0.6

-0.4

-0.2

0

201101814126

X (m)Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.2 0.4 0.6

-0.4

-0.2

0

4001300120011001

X (m)Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.2 0.4 0.6

-0.4

-0.2

0

201101814126

X (m)Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.2 0.4 0.6

-0.4

-0.2

0

4001300120011001

300200100804025

300200100804025

50004000300020001000

50004000300020001000

Bubble Diameter(µm)

Captured by

IR-hook

Captured by

OR-hook

(28 dp ≤ 300µm)

(48 dp ≤ 300µm) (6 dp > 300µm)

(0 dp > 300µm)

Total 28 bubbles capture by IR-hook.

Total 54 bubbles capture by OR-hook.

• Reduce hook depth from 6 mm to 3 mm leads to:

– Less bubbles captured by hook (10~20X less) especially for large bubbles (≥ 1mm);

– Locations of captured large bubbles are more close to meniscus;

– On WF, no dp > 1mm bubbles were capture by hook with 3mm hook depth;

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 13

WF hook captured bubbles(Hook depth 6mm, Simulation C)

X (m)Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.2 0.4 0.6

-0.4

-0.2

0

201101814126

X (m)Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.2 0.4 0.6

-0.4

-0.2

0

4001300120011001

300200100804025

50004000300020001000

Captured by

OR-hook

Total 1067 bubbles capture by OR-hook.

(153 dp ≤ 300µm) (914 dp > 300µm)

X (m)Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.2 0.4 0.6

-0.4

-0.2

0

201101814126

X (m)Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.2 0.4 0.6

-0.4

-0.2

0

4001300120011001

300200100804025

50004000300020001000

Bubble Diameter(µm)

Captured by

IR-hook

Total 229 bubbles capture by IR-hook.

(148 dp ≤ 300µm) (81 dp > 300µm)

• Many large bubbles were captured by hook;

• Each “point” representing one captured bubble, but the “point” size is much larger than the real size of the captured bubble, so it looks like the “line” passing through the bubbles, however they may not “visible” to those examined layers because the sliced layer really didn’t pass through these tiny bubbles;

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 14

Captured Small Bubble (d ≤ 0.3mm) on WF/NF and Their Distributions without Hook Capture Mechanism

(Simulation A)

X (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.5 1-2.5

-2

-1.5

-1

-0.5

0

201101814126

X (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.5 1-2.5

-2

-1.5

-1

-0.5

0

201101814126

Y (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

-0.2 0 0.2-2.5

-2

-1.5

-1

-0.5

0

201101814126

WF-IR WF-OR NF

po

rt

po

rt

300200100804025

300200100804025

300200100804025

Bubble diameter

(µm)

Bubble diameter

(µm)

Bubble diameter

(µm)

3274Captured

1.3% of total injected

3880Captured

1.6% oftotal injected

6515Captured

2.7% of total injected

• Slide gate open to IR, more capture on IR due to more gas escape from IR side;

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 15

Capture Small Bubbles (d ≤ 0.3mm) on WF and NF with Hook Depth 3mm Simulation B

(Captured by Force Balance and Hook)

X (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.5 1-2.5

-2

-1.5

-1

-0.5

0

201101814126

X (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.5 1-2.5

-2

-1.5

-1

-0.5

0

201101814126

Y (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

-0.2 0 0.2-2.5

-2

-1.5

-1

-0.5

0

201101814126

WF-IR WF-OR NFp

ort

po

rt

300200100804025

300200100804025

300200100804025

Bubble diameter

(µm)

Bubble diameter

(µm)

Bubble diameter

(µm)

3284Captured

1.3% of total injected

3992Captured

1.6% oftotal injected

6577Captured

2.7% of total injected

• Slide gate open to IR, more capture on IR due to more gas escape from IR side;

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 16

Capture Small Bubbles (d ≤ 0.3mm) on WF and NF with Hook Depth 6mm Simulation C

(Captured by Force Balance and Hook)

X (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.5 1-2.5

-2

-1.5

-1

-0.5

0

201101814126

X (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

0 0.5 1-2.5

-2

-1.5

-1

-0.5

0

201101814126

Y (m)

Dis

tan

ce

fro

mM

en

isc

us

(m)

-0.2 0 0.2-2.5

-2

-1.5

-1

-0.5

0

201101814126

WF-IR WF-OR NF

po

rt

po

rt

300200100804025

300200100804025

300200100804025

Bubble diameter

(µm)

Bubble diameter

(µm)

Bubble diameter

(µm)

3434Captured

1.4% of total injected

4154Captured

1.7% oftotal injected

6559Captured

2.7% of total injected

• Slide gate open to IR, more capture on IR due to more gas escape from IR side;

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 17

Effect of Hook Depth on Number of Bubbles Captured (Compare Simulation with Measurements)

0 500 1000 15000

10

20

30

40

50

60

Distance below meniscus (mm)

Num

ber

of b

ubbl

e ca

ptur

ed

NoEMBr-exp.Adv.hook 3mmhook 6mm

0 500 1000 15000

10

20

30

40

50

Distance below meniscus (mm)

Num

ber

of b

ubbl

e ca

ptur

ed

NoEMBr-exp.Adv.hook 3mmhook 6mm

Quarter Region IR Quarter Region OR

0 500 1000 15000

5

10

15

20

25

Distance below meniscus (mm)

Num

ber

of b

ubbl

e ca

ptur

ed

NoEMBr-exp.Adv.hook 3mmhook 6mm

0 500 1000 15000

5

10

15

20

25

Distance below meniscus (mm)

Num

ber

of b

ubbl

e ca

ptur

ed

NoEMBr-exp.Adv.hook 3mmhook 6mm

Center Region IR Center Region OR

0 500 1000 15000

10

20

30

40

50

60

Distance below meniscus (mm)

Num

ber

of b

ubbl

e ca

ptur

ed

NoEMBr-exp.Adv.hook 3mmhook 6mm

NF

• Number of bubbles captured per sample layer;

• thook = 0.25s for cases with hook capture mechanism

• Adv. (no hooks) based on average of 10 simulations

No hook No hook

No hook No hook No hook

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 18

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Distance below meniscus (mm)

Ave

rage

Bub

ble

Dia

met

er (

mm

)

NoEMBr-exp.Adv.hook 3mmhook 6mm

0 500 1000 15000

0.1

0.2

0.3

0.4

0.5

Distance below meniscus (mm)

Ave

rage

Bub

ble

Dia

met

er (

mm

)

NoEMBr-exp.Adv.hook 3mmhook 6mm

Quarter Region IR Quarter Region OR

0 500 1000 15000

0.1

0.2

0.3

0.4

0.5

Distance below meniscus (mm)

Ave

rage

Bub

ble

Dia

met

er (

mm

)

NoEMBr-exp.Adv.hook 3mmhook 6mm

0 500 1000 15000

0.2

0.4

0.6

0.8

1

Distance below meniscus (mm)

Ave

rage

Bub

ble

Dia

met

er (

mm

)

NoEMBr-exp.Adv.hook 3mmhook 6mm

Center Region IR Center Region OR

0 500 1000 15000

0.2

0.4

0.6

0.8

Distance below meniscus (mm)

Ave

rage

Bub

ble

Dia

met

er (

mm

)

NoEMBr-exp.Adv.hook 3mmhook 6mm

NF

Effect of Hook Depth on Size of Bubbles Captured (Compare Simulation with Measurements)

• Size:

– Average diameter of bubbles captured in each sample layer

• Increasing hook depth: causes larger average diameter in first 2 layers due to more large bubbles captured;

No hook No hook

No hook No hook No hook

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 19

Effect of Hook Depth on Capture Fraction

• In all of the measured sample layers, ~500 bubbles were observed;Only one large bubble (1.4 mm diameter) was observed > 0.5 mm. Fraction of captured bubbles with d >1 mm is ψ(1 mm) = 0.2% (1/500).

• Advanced capture criterion prediction of ψ(1 mm) = 0.3% matches plant measurement (0.2%).

• Using 3mm hook depth gives slightly more large bubbles captured;

• Using 6mm hook depth leads to 10X more large bubbles captured near surface;

CaptureCriteria

Injected all

ΣN(di)

Injected 1mm

N(1 mm)

Captured all

Σn(di)

Captured 1mm

n(1 mm)

Fraction capturedφ(1 mm)

Fraction large

ψ(1 mm)Simple* No hook[8] 2,442,390 475,640 208,944 27,799 5.84% 13.3%

Adv. No Hook 2,442,390 475,640 137,372 432 0.09% 0.3%Adv. 3mm Hook 244,239 47,564 13,939 75 0.15% 0.5%Adv. 6mm Hook 244,239 47,564 15,249 848 1.70% 5.6%

Experiment Unknown Unknown ~500 1 Unknown 0.2%

ΣN(di): total number of bubbles injected during the particle tracking step;N(1 mm): number of 1 mm bubbles injected;Σn(di): total number of bubbles captured in the entire caster;n(1 mm): number of 1 mm bubbles captured in the entire caster; φ(1 mm): the fraction of 1 mm bubbles that were captured (captured 1mm / injected 1mm); ψ(1 mm): the fraction of captured bubbles that were 1mm diameter (captured 1mm / captured all).

*Simple: “touch = capture”

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 20

Conclusions

• Hook capture mechanism were added into the model and used with advanced capture criterion to predict particle transport and capture

• The model predicted hook captured bubbles were close to meniscus region

• With 3mm hook depth, model predicted 3% more bubbles captured by shell; with 6mm hook, predicted 10% more bubbles captured on WF-OR and NF

• With 6mm hook depth, the model predicted more large bubbles captured by hook which causes larger average bubble diameter

• Effect of hook is not the main reason for predicting less bubbles captured at region close to meniscus

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 21

Future Work

• Hook is not the main reason for predicting less bubbles captured at region close to meniscus, and other effects may need to be investigated (e.g. bubbles/particles reach steel-slag interface may not be removed immediately)

• Use transient LES model and two-way coupled Lagrangian methods to study the transport and capture of particles in the caster under different EMBr conditions.

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 22

Acknowledgments

• Continuous Casting Consortium Members(ABB, AK Steel, ArcelorMittal, Baosteel, JFE Steel Corp., Magnesita Refractories, Nippon Steel and Sumitomo Metal Corp., Nucor Steel, Postech/ Posco, SSAB, ANSYS/ Fluent)

• Xiaoming Ruan and Baosteel at Shanghai, China for plant measurements

• National Science Foundation Grant CMMI-11-30882

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Kai Jin • 23

References[1] Quan Yuan, PhD Thesis, University of Illinois at Urbana-Champaign, 2004.

[2] Sana Mahmood, MS Thesis, University of Illinois at Urbana-Champaign, 2006.

[3] Brian G. Thomas, Quan Yuan, Sana Mahmood, Rui Liu, and Rajneesh Chaudhary,“Transport and Entrapment of Particles in Steel Continuous Casting,” Metall. Mater. Trans. B, 2014, vol. 45, pp. 22–35.

[4] Simon N. Lekakh, Vivek Thapliyal, and Kent Peaslee, in 2013 AISTech Conf. Proc., “Use of an Inverse Algorithm for 2D to 3D Particle Size Conversion and Its Application to Non-Metallic Inclusion Analysis In Steel,” Association for Iron & Steel Technology, Pittsburgh, PA, 2013

[5] Brian Edward Launder and D. B. Spalding, “The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 1974, vol. 3, pp. 269–89.

[6] Saj Morsi and A. J. Alexander, “An Investigation of Particle Trajectories in Two-Phase Flow Systems,” J. Fluid Mech., 1972, vol. 55, pp. 193–208.

[7] A. D. Gosman and E. Loannides, “Aspects of Computer Simulation of Liquid-Fueled Combustors,” J. Energy, 1983, vol. 7, pp. 482–90.

[8] K. Jin, B. G. Thomas, R. Liu, S. P. Vanka, and X. M. Ruan, “Simulation and Validation of Two-Phase Turbulent Flow and Particle Transport in Continuous Casting of Steel Slabs,” IOP Conf. Ser. Mater. Sci. Eng., 2015, vol. 84, p. 012095.