Asymmetric Fluid Flow and Particle Entrapment in the...

ANNUAL REPORT 2006Meeting date: June 15, 2006

Sana Mahmood (M.S. Student) &Brian G. Thomas

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

Asymmetric Fluid Flow and Particle

Entrapment in the Nozzle and Mold

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Sana Mahmood2

Acknowledgements

• Continuous Casting Consortium Members at University of Illinois at Urbana-Champaign

• Fluent, Inc.

• Jun Aoki, Bret Rietow, Claudio Ojeda, Liefeng Zang, Quan Yuan, Gogi Lee


Outline• Part 1: Flow Asymmetries

– Background and Importance

– Objectives

– Validation

– Results (Asymmetries encountered due to various reasons)

– Conclusions and Future Work

• Part 2: Flow in Mold (with shell) and Particle Entrapment in Nozzle and Mold

– Background and Importance

– Objectives

– Results

• Mold flow validation

• Particle Entrapment Model

• Particle Transport and Entrapment in Mold simulation

– Conclusions and Future Work



Objectives Part 1

• Validate model with LES time averaged results for nozzle

• Investigate various causes of asymmetric fluid flow in a tundish nozzle, including:

– Asymmetric flow entering the nozzle from tundish

– Asymmetric flow due to the presence of slide gate

– Asymmetric flow cased by various types of nozzle clogs

• Introduce Asymmetric flow in the mold with no shell

)( ε−k


Model Formulation (validation)

X

Z

Y

SEN

Well Nozzle

Stopper rod

Tundish Region

d=70

d=220

35

98

290

104

d=30

789

All dimensions are in mm

7.98 x 10-7Fluid Kinematic Viscosity (m2/s)

25.4 Casting Speed (mm/s)

127 SEN Submergence Depth (mm)

32 Bottom nozzle Port Diameter (mm)

75 x 32 (inner bore) Nozzle Port Height x Thickness (mm x mm)

ValueParameter / Property

Inlet Velocity = 0.0312m/s (symmetric velocity)

Angle at side port = 15deg

Pressure at outlet = constant


Validation Nozzle

10.90.80.70.60.50.40.30.20.10

Velocity Magnitude (m/s)

0.0940.092Back Flow Zone Fraction

33.0833.76Angle with the X-axis (deg)

0.6750.68Average Velocity (Jet speed) (m/s)

Right Port outlet

Left Port outlet

Front View Side View


Validation Nozzle

X (m)

Z(m

)

-0.1 -0.05 0 0.05 0.1

0

0.05

0.1

0.15

0.2

0.25

10.80.60.40.20

(Scale : 1.0m/s)

(Vx2 + Vz

2)1/2 (m/s)

Velocity Along center line of side ports (m/s)

Dis

tan

cefr

omn

ozzl

eb

ott

om(m

)

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Vx, Right PortVx, Left PortVz, Right PortVz, Left Port

Velocity along the center line of side ports (m/s)

Dis

tan

cefr

om

no

zzle

bo

tto

m(m

)

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Vx, Right PortVx, Left PortVz, Right PortVz, Left Port

Back Flow Zones

)( ε−k

)( ε−k

LES [ Quan Yuan, 2004]

LES [Quan Yuan, 2004 ]


Asymmetry Caused by Flow in Tundish

A

A

Section AA

XY

Z279.8

279.8

D=115

D=80

1283

Well Length = 160

124

R=11

Nozzle port height x thickness (mm X mm) =110 X 22SEN nozzle angle at side port = 45 deg


0.3m/s 0.2m/s

Asymmetric velocity at the inlet of tundish region modeled


2 m/s

3.532.521.510.50


0.3m/s 0.2m/s

Why shift towards the left ?

Flow goes around the cylindrical portion of the stopper rod and more enters from the right side


Asymmetry Caused Near Stopper Rod


5 m/s

Velocity (Vx2 + Vz

2)1/2 (m/s)D

ista

nce

fro

mp

ort

bott

om

(mm

)0 1 2 3

0

10

20

30

40

50

60

70

80

90

100

110

Right outlet center lineLeft outlet center line

13.313.3Back Flow Zone Fraction

30.6931.15Angle with the X-axis (deg)

2.552.56Average Velocity (Jet speed) (m/s)

Right Port outlet

Left Port outlet

Velocity at Nozzle Bottom

Conclusion:

Asymmetric flow across tundish bottom does not appear to cause significant time-average flow asymmetry


Asymmetry Caused by Slide Gate

35mm

75mm

Y

Z

Slide Gate

X

Z

Y

AA

Slide Gate

Nozzle port height x thickness (mm X mm) =98 X 70SEN nozzle angle at side port = 35 deg

Inlet Velocity = 0.014m/s (symmetric velocity)

Mass Flow Rate = 61.6kg/s

Section A-A


D=400

D=260

D=141.5

400

109.5

279.8

D=72


43.532.521.510.50


1 m/s

Left Port Right Port


-Y -Y

Asymmetry Caused by Slide Gate

11.1kg/s 19.7kg/s 19.7kg/s 11.1kg/s

Asymmetry within each port


Cut Section of Nozzle Bottom

to see Clog Shapes

2.2

1.0 2.0 0.6

1.0

0.9

2.1

2.2

1.5

2.9 2.7

1.1

2.3

2.7

2.1

2.8

Direction 2

Direction 1

SEN outlet port

Top view

after

cutting

direction 1

Top view after

cutting direction 2

All dimensions on pictures are in cm

1.41.3

2.8 2.8 2.12.9

Cut sections measured for 3 nozzles by Gogi Lee, 2005


Asymmetry Due to Clogging

43.532.521.510.50


61.6Kg/s 30.8Kg/s 30.8Kg/s 30.8Kg/s 30.8Kg/s

Un-clogged Clog 1 Clog 2 (a) Clog 2 (b) Clog 3

50% 50% 45% 55%55% 45%53% 47% 53% 47%


Velocity Magnitude on centerline of Left and Right outlet ports for two different clog shapes

(Vx2 + Vz

2)1/2 (m/s)

Dis

tan

cefr

om

the

port

bott

om

(mm

)

0.5 1 1.5 2 2.50

10

20

30

40

50

60

70

80

90

Left outlet center lineRight outlet center line

(Vx2 + Vz

2)1/2 (m/s)

Dis

tan

cefr

om

the

po

rtb

ott

om

(mm

)

0.5 1 1.5 2 2.50

10

20

30

40

50

60

70

80

90

Left outlet center lineRight outlet center line

Clog 1 Clog 3

Velocity Magnitude at Ports


Asymmetry in Mold (no shell)X (m)

Dis

tan

ceb

elo

wm

enis

cus,

Z(m

)-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

1 m/s

Velocity from the outlet of Clog shape 1 was placed as the inlet velocity at mold

inletMold Dimensions = 1300mmx230mmCasting Speed = 0.87m/min

Enlarged View of the Top section of moldVelocity vectors in plane mid way between wide faces

Increased Velocity at the right side


Surface Velocity

0.5 m/s

X (m)

Vel

oci

tyM

agn

itud

e(m

/s)

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

30.8Kg/s

See generation of vortexes on the left side of the mold

Note: asymmetric flow from a clogged bore causes 2X velocity across top surface


Conclusions (Part 1)

• The averaged flow results from LES agree reasonably with resultsfrom k-ℇ model

• Although asymmetry in the tundish does not cause asymmetry at the outlet ports, it increases the likelihood of asymmetric clogging near the nozzle top

• The asymmetry due to the 90deg slide gate orientation causes high swirling within each port, and encourages asymmetric flow at outlet towards the opposite mold wide face

• Clogging of the bore (clog 1) reduces port utilization significantly • Asymmetry between left and right ports increases with increasing

severity of clogging of the well region (Clog 3)• Clogging causes severe asymmetry across the top surface of the

mold (2X velocity difference between sides)


Part 2: Particle Entrapment in Nozzle and Mold

• Particle transport and entrapment are an important phenomenon during continuous casting of steel affecting the steel quality

• Entrapped inclusions cause defects such as internal cracks and blisters in the final product

• The inclusions are carried by the steel jets entering the mold and can either be removed by the top liquid slag layer or can be trapped by the solidifying dendrite arms

• Behavior of transport of particles within the mold depends highly on their size and density

• Entrapment of particle depends on the forces present upon it when close to the dendrite arms


Objectives Part 2

• Validate flow in the mold (with shell) obtained from model with LES time averaged results

• See where inclusions are trapped inside the nozzle to cause clogging

• See how varying casting parameters can affect particle capture based on the entrapment model developed

• See how particle trajectories are affected with variation in particle size and density

• Add capture criterion at the boundary of the mold as boundary condition in the simulation

)( ε−k


Mold Flow Validation

984m m 132m mF ree -S lip Bounary

C asting S peed:2 5 .4 m m /s

zy

x

S hell Boundaries

Je t

2400m m

934m m 80m m

P ressure B.C . a t Bottom

Liquid-pool

7.98 × 10-7Fluid Kinematic Viscosity (m2/s)

25.4Casting Speed (mm/s)

127SEN Submergence Depth (mm)

32Bottom nozzle Port Diameter (mm)

75 × 32 (inner bore)Nozzle Port Height × Thickness (mm × mm)

2400Domain Length (mm)

132 (top)79.48 (domain bottom)

Domain Thickness (mm)

984 (top)934.04 (domain bottom)

Domain Width (mm)

132Mold Thickness (mm)

984Mold Width (mm)

Case 2-SParameter/Property

• Negative Source terms added to mass and momentum equations in Fluent (by writing user defined functions) to model fluid extraction due to solidification down the mold

[ Quan Yuan, 2004]


Velocity vectors in plane mid way b/w wide faces (Mold Validation)

X (m)

Z(m

)

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1 m/s

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

(m)

(m) 1m/s:

Time averaged velocity vectors obtained for full mold (LES) [Quan Yuan, 2004 ]

)( ε−kVelocity vectors obtained for half mold


Velocity down the mold on a line 293mm from the center (validation)

Speed (Vx2+Vz2)1/2 (m/s)

Dis

tance

Bel

owth

eto

psu

rfac

e,z

(m)

0 0.1 0.2 0.3 0.4 0.5 0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Time averaged fluid speed, (vx2+vz

2)1/2 (m/s)

Dis

tan

ceb

elo

wth

eto

psu

rfac

e,z

(m)

0 0.1 0.2 0.3 0.4 0.5 0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Left half in full-mold LES (0.7M cells, no SGS)Right half in full-mold LES (0.7M cells, no SGS)Left half in full-mold LES (0.7M cells, SGS-k)Right half in full-mold LES (0.7M cells, SGS-k)Left half in full-mold LES (0.4M cells, SGS-k)Right half in full-mold LES (0.4M cells, SGS-k)Half-mold LES (1.4M cells, no SGS)

293mm

LES [Quan Yuan, 2004 ] )( ε−k


Validation (cont.)

Depth from meniscus, Z (m)

Do

wn

war

dve

loci

ty,V

z(m

/s)

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Vz (k-e)Vz (LES)

Distance from center, X (m)

Ho

rin

zon

talv

elo

city

tow

ard

sS

EN

(m/s

)

0 0.1 0.2 0.3 0.4 0.5-0.05

0

0.05

0.1

0.15

0.2

0.25

Mold Right (k-e)Mold Right (LES)Mold Left (LES)

Velocity along center jet center line Horizontal velocity towards SEN

LES results obtained by [Quan Yuan, 2004 ]


Particle Transport (validation of Hydrodynamic Forces acting)

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

Time (s) -- For 500 time steps

Forc

e m

agnitude

(N

)

Fd

Fp+FsFb

FaFL

Time (s)

Fo

rce

mag

nitu

de

(N)

20 25 30 35 40 4510-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

FD

FA

Fpress+Fstress

FL

FH

FBdp = 400μm

Drag

Pressure and stress

Buoyancy

Added mass

Shear Lift

Basset History force

Magnitude of hydrodynamic forces acting on a single particle entered into the mold

Magnitude of hydrodynamic forces acting on a single particle entered into the mold (LES) [Quan Yuan, 2004 ]

)( ε−k

d=400μm Alumina d=400μm

Alumina


Particles trapped on nozzle walls

No particles coming out from the recirculation regions

20,000 particles randomly distributed at the inlet of tundish region: 500 particles, diameter 10μm, density 5000kg/m3

500 particles, diameter 40μm, density 5000kg/m3



Most particles are trapped near in the middle of well nozzle and at the bottom of SEN – These are potential clogging areas

Validation nozzle introduced in Part 1

Particles are trapped as they touch the walls - 39% particles are trapped at the walls

Stochastic Random walk method used


pushing entrapment engulfment

Particle Capture by Dendritic Interface

particle pushing and capture by engulfment and entrapment.

χ

η

Forces acting on a spherical particle close to dendriticfront of mushy-zone:

Dendrite shape computed by N. Provatas, N. Goldenfeld, and J. A. Dantzig, 1998.

Buoyancy: FB

Drag force: FDχ and FDηLift force: FL

Lubrication force: FLubVan der Waals force: FI

Concentration Gradient force: FGrad

Reaction force: FN(Press gradient, stress gradientadded mass and Basset forcesneglected.)

Solidification direction


How the Entrapment Model is Incorporated in Fluent

• Particle Entrapment model is incorporated at the mold (with shell) boundaries in Fluent by writing user defined functions

• The η and א directions are evaluated from the solidification front angle and fluid flow direction

– א is in the direction of the vector normal to the face (boundary) that the particle hits– η is in the direction of the component of: sum of buoyancy and flow drag force, lying in

the face plane

• Primary dendrite arm spacing (PDAS) varies down the mold length and is incorporated as the function representing the measured PDAS [B.G.Thomas et al, 1998 ]

• Solidification front velocity also varies down the mold length and is incorporated by using the data obtained from [Quan Yuan, 2003]

• Forces acting on the particles when close to the solidifying front are evaluated

• The entrapment equations (force balance equations) are then used to evaluate the particles fate


0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Distance below meniscus (m)

Pri

mar

y d

end

rite

arm

sp

acin

g (P

DA

S)

(m

)

Narrow Facemeasurement

Narrow Faceapproximationused

Wide Facemeasurement

Wide Faceapproximationused

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Distance below meniscus (m)

Shel

l Gro

wth

spe

ed (

m/s

)

V_ so l_ n arrow _ face

V_ so l_ w id e_ face

Variation of PDAS down the caster on narrow face and wide face

Variation of solidification front velocity down the caster on narrow face and wide face

Variation of PDAS and solidification front velocity used down the caster


Particle Capture Criterion [ Quan Yuan, 2004]

( ), 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 and FBη in same direction

, if FDη and FBη in opposite directionand FDη≥FBη

or

or

, if FDη and FBη in opposite directionand FDη<FBη

yes no

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


Particle Positions

35.0s2 sec LES

2 sec K-ℇ

LES: 40,000 particles were introduced into the mold in 9sec•500 particles, diameter 10μm, density 5000kg/m3

•500 particles, diameter 40μm, density 5000kg/m3



[Quan Yuan, 2004]


Small particles

[Quan Yuan, 2004]


100um Particles

10,000 particles of 100μm diameter introduced into the domain from the nozzle ports (LES) [Quan Yuan]

[Quan Yuan, 2004]


Slag Entrainment

4000 slag particles of 100μm diameter introduced into the domain from the top surface (LES) [Quan Yuan]

[Quan Yuan, 2004]


Particles Trapped (Red dots show the position of trapped particles)

3.5% reach the top surface

~ 3% getting trapped at the top narrow face in K-ℇmodel not present in LES

K-ℇ

48.0s

8% reach the top surface

LES

Particles trap once they touch the boundary

[Quan Yuan, 2004]


Particle capture: parameters investigated

• Particle diameter

• Particle density

• Primary dendrite arm spacing (PDAS)

• Sulfur concentration

• Dendrite tip radius (rd)

• Solidification front velocity (Vsol)

• Solidification front angle: angle of solidifying shell (wall) with the horizontal (ø) (decreases with distance below meniscus and with decreasing machine radius)

• Plots are made for critical cross-flow velocity in– Horizontal direction

– Vertical direction (up and down)

• Fluid velocity across the dendrite tips with magnitude exceeding “critical cross-flow velocity” will prevent particle capture


Diameter = 100μm, Alumina particles entering from nozzle outlet

t = 45.0sdp = 100μm

K-ℇ

LES



10,000 particles in full mold 5,000 particles in half mold

Particles are trapped based on the entrapment model

Red dots show the position of trapped particles

[Quan Yuan, 2004]


Diameter = 400μm, Alumina particles entering from nozzle outlet

t = 45.0sdp = 400μm



LES

K-ℇ

10,000 particles in full mold5,000 particles in half mold

[Quan Yuan, 2004]


Particles Trapped on Narrow Face (K-ℇ)

Diameter=10μm and 40μm Diameter=100μm Diameter=400μm

•Number of Particles Entrapped in the encircled region (where Jet hits the wall) reduces with increasing particle diameter

•Number of particles being trapped on the narrow face reduces


Analysis (K-ℇ)

12.84%Slag (Density ≃ 5000 kg/m3)

25.50%Alumina (Density ≃ 2700 kg/m3)

41.00%Argon (Density ≃ 0 kg/m3)

Particles removed by top surface (K-ℇ)Size (400um)

25.50%400 μm

11.20%250 μm

4.62%100 μm

Particles removed by top surface (K-ℇ)Alumina (Density = 2700 kg/m3)


To Investigate more parameters for any mold (Behavior of Particle)

-0 .12

-0 .1

-0 .08

-0 .06

-0 .04

-0 .02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700 800

Particle diameter (um)

Cri

tica

l d

ow

nw

ard

cro

ss f

low

ve

locit

y (

m/

s)

Arg on

Particle drifts downward

Particle is captured

Particle drifts upwards

Conditions:

Tip radius = 2.13um

Solidification Velocity = 500um/s

PDAS = 150um


-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700 800


Cri

tical

dow

nw

ard

cro

ss-flow

velo

cit

y (m

/s)

PDAS =75umPDAS =100umPDAS =150umPDAS =200umPDAS =300umPDAS =400umPDAS =650um

Effect of dendrite arm spacing on bubble capture

Conditions:

Density Argon gas ≃ 0 kg/m3

Tip radius = 2.13um


PDAS = 150um

Particle drifts upward



• Increasing PDAS, tends to capture larger particles • Larger particles are less likely to be captured (capture region is narrower, because they can rotate more easily) • If cross-flow velocity exactly matches buoyancy, then particle is suspended in front of dendritic interface and is eventually captured


-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700 800


Cri

tical d

ow

nw

ard

cro

ss flo

w v

elo

city (m

/s)

Arg onAlum inaSla g

Effect of particle composition on particle capture(Vertical Cross flow velocity)

• Increasing particle density lowers the buoyancy force

• The chances for the particle to drift upwards are less

• Large argon bubbles can move upward more easily than slag or alumina, and avoid capture

• The fluid velocity “capture window” moves down, but is still significant for all densities

Conditions:

Tip radius = 2.13um


PDAS = 150um





Density Slag = 5000 kg/m3

Density Alumina = 2700 kg/m3


0

0 .02

0 .04

0 .06

0 .08

0 .1

0 .12

0 100 200 300 400 500 600 700 800

Part icle diameter (um)

Cri

tical

hori

zonta

l cro

ss f

low

velo

cit

y(m

/s)

ArgonAlum inaSlag

Conditions:

Tip radius = 2.13um


PDAS = 150um

Effect of particle composition on particle capture (Horizontal Cross Flow Velocity)

Particle moves in the direction of FNet= FB + FD



Effect of steel sulfur content on bubble capture

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700 800


Critical

dow

nw

ard

cro

ss flo

w v

elo

city

(m/s)

Lowsulfur

Highsulfur

Conditions:


rd = 2.13um

Vsol = 500um/s,

Low sulfur = 0.0028 wt pct

High sulfur = 0.03 wt pct

PDAS = 150um

• Increasing sulfur concentration increases the surface gradient force, by lowering surface tension near the solidification front, due to S rejection during solidification

• Increasing sulfur concentration from 0.0028 to 0.03 wt pct only slightly increases particle capture. (capture window expands).





Effect of dendrite tip radius and sol. front velocity

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700 800


Critical dow

nw

ard

cro

ss f

low

velo

city (

m/s)

PDAS = 150um,rd = 2.13um,Vsol =500um/s downPDAS = 150um,rd = 3.3um,Vsol = 200umdown

Condition 1:


Tip radius = 2.13um


PDAS = 150um

Condition 2:


Tip radius = 2.13um


PDAS = 150um

• Increasing solidification velocity only slightly increases lubrication force

• Decreasing dendrite tip radius only slightly increases the surface gradient force

• These two parameters together have negligible effect on increasing particle entrapment near top of caster or at higher casting speed





Particle

Inner radius

φ

Effect of solidification front angle on alumina particle capture (inner radius)

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700 800


Critical

cro

ss f

low

velo

city

dow

n inclin

e a

t in

side

rad

ius

(m/s)

30deg45deg60deg90deg

Conditions:

Density Alumina ≃ 2700 kg/m3

rd = 2.13um

Vsol = 500um/s

PDAS = 150um




Particle capture becomes easier on the inner radius with decreasing solidification front angle (ø)(capture window extends to lower flow velocities)

Curved mold caster: Inner radius

Flow Direction


Effect of solidification front angle on alumina particle capture (outer radius)

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700 800


Critical

cro

ss f

low

velo

city

dow

n inclin

e a

t outs

ide r

adiu

s(m

/s)

30 deg

45 deg

60 deg

90 deg

Conditions:


rd = 2.13um

Vsol = 500um/s

PDAS = 150um




•Lowering solidification front angle (ø) (towards horizontal) decreases capture likelihood (particles rotate away more easily)

•Critical particle size exists that will avoid capture for any flow condition

Curved mold caster: Outer radius

Flow Direction Particle

Outer radius

φ


Critical alumina particle size to avoid capture (outer radius)

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700 800


Critica

l cro

ss flo

w v

eloc

ity

dow

n in

clin

e a

t ou

tsid

era

diu

s

30 deg

45 deg

60 deg

Conditions:


rd = 2.13um

Vsol = 500um/s

PDAS = 150um

•Buoyancy force is high, allowing particles to float upward, away from capture

•Smaller particles may still be captured (must check rotation about dendrite tips)

•Critical particle diameter exists that always escapes!

Particle moves away from thedendrites in radial direction

Rotation of particle about dendrite tips needs to be checked


Conclusions

• The k-ℇ model prediction for steady flow in the nozzle and mold match well with the time averaged results from LES

• Particle transport and entrapment model has been implemented into FLUENT and compared with LES model predictions

• Increasing primary dendrite arm spacing has the most important effect increasing particle capture: small particles are always captured when they touch the solidification front

• Particle composition (density: bubble vs. inclusion) shifts the capture window• Bubbles escape more easily than solid inclusions in stagnant flow regions, but

their capture depends on the flow pattern• Although steels with low sulfur content tend to have less particle entrapment,

the effect is small• The increased ease of particle capture on the inner radius is a large effect

(relative to vertical or outer radius)

Model Validation

Entrapment Model Predictions:


Future Work

• The model uses isotropic velocity fluctuations and the velocity magnitude in all spatial directions is significantly different, so match with LES is not perfect. Therefore better fluid flow / turbulence model is needed (eg. Reynolds Stress)

• The model shows high concentration of particle at the top of the narrow face (not seen in LES results)

• Use model to fully investigate effect of other casting conditions and geometries

Asymmetric Fluid Flow and Particle Entrapment in the...

Documents

Transcript of Asymmetric Fluid Flow and Particle Entrapment in the...