effect of embr on flow in sen and...

CCC Annual ReportUIUC, August 19, 2015

Kai Jin

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

Effect of EMBron Flow in SEN and Mold

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

Objectives

• Use high resolution LES model to study the effect of SEN submergence depth on the molten steel flow in mold

• Understand the transient molten steel flow and transient effect of double-ruler EMBr

• Investigate the effect of SEN submergence depth on EMBr braking efficiency

• Prepare flow field for inclusion transport and capture studies


Casting Conditions and Steel Properties

• Baosteel No. 4 caster, 230×1300mm strand

• Slide gate 80% open at Vc = 1.8m/min, steel first entering IR side

• SEN port downward angle 15º, port area 65×83 mm2

Properties of Molten Steel

Density ρl (kg/m3) 7000

Dynamic Viscosity μl (kg/m-s) 0.0063

Electrical Conductivity σ (S/m) 714000[1]

Magnetic Permeability (h/m) 1.26×10-6

Schematic of slide gate configuration

Note: solid shell conductivity taken as 787000 S/m [1]


Governing Equations For Fluids

• The Navier-Stokes equations in conservation form with LES model

ṡ – Mass sink due to solidifying shellFL – Source from Lorentz force

• Sub-grid scale - Coherent-Structure Smagorinsky Model[2] (CSM)

Wij – vorticity tensor Sij – velocity-strain tensor

( ) 0sρ⋅ + =∇ u

( ) ( )( )Tsgs Lp

tρ ρ μ μ∂ + ⋅ = − + ⋅ + + + ∂u u u u u F∇ ∇ ∇ ∇ ∇

( )3/22 / 1 /s csmC C Q E Q E= −

( )1/ 2 ij ij ij ijQ W W S S= − ( )1/ 2 ij ij ij ijE W W S S= +

( )2/32 2sgs s ij ijC x y z S Sν = Δ Δ Δ


Computational Domain and Boundary Conditions

• Domain slide gate, SEN, mold region

• Cartesian grid ~16 million cells, hexahedral with edge length ~4mm

• Solid shells included

• Boundary Conditions

– velocity inlet, 1.66m/s

– top surface, no slid wall

– shell-molten steel interface, moving wall 0.03m/s with mass sink

– outside of shell insulated wall

– outlet, zero derivative velocity

~2.8m


Shell Profile and Mass Sink

• Shell thickness S = Kt1/2 with K = 3mm·s-1/2 (from a breaking shell)

• Mass sink added at some cells

• Cells in shell are solid cells with downward velocity equals Vc and electrical conductivity of 787000 S/m[1]

0 10 20 30−2.5

−2

−1.5

−1

−0.5

0

Dis

tanc

e be

low

men

iscu

s (m

)

Shell thickness (mm)

Vc = 1.5 m/min

Vc = 1.8 m/min

Shell Profile Mass sink terms


Governing Equations for MHD

• By introducing the electric potential Φ and using Ohm’s law, the current density is:

• A well conducting material the current conservation law

• Therefore, electric potential satisfies the Poisson equation

• The Lorentz force is obtained from

• Equations are solved on the entire domain (including the shell)

( )σ= − Φ + ×J u B∇

0⋅ =J∇

( ) ( )σ σ⋅ ∇Φ = ⋅ × u B∇ ∇

L = ×F J B


List of Simulations and EMBr Profile

• Applied magnetic field B, measured by ABB and Baosteel

• Investigate two submergence depth four different EMBr settings

SEN Submergence Depth (mm)

TopCoil

Current(A)

Bottom Coil

Current(A)

1 170 0 02 170 0 8503 170 400 8504 170 850 8505 200 0 06 200 0 8507 200 400 850

List of Seven Simulations(230×1300mm, slide gate 80% open, Vc = 1.8m/min)

Magnetic Field Profile

Addition Validation Case:230×1200mm strand Vc = 1.3m/min, gate 70% open area, no EMBr, no argon injection


Solver and Computational Details

• Multi-GPU finite volume code CUFLOW written in CUDA Fortran

• Fractional step, 2nd order Adams-Bashforth explicit

• Poisson equations are solved by V-cycle multi-grid method with Red-Black Gauss-Seidel SOR

• Domain decomposed onto 6 GPUs (Nvidia K20) on BlueWaters

• Timesteps are taken as ~0.0002s

• 40s LES simulations (16million cells) takes ~2 days to finish

• Multi-Grid using 5 V-Cycle and 6 sweeps on Poisson equations for pressure and 8 V-Cycle and 8 sweeps for electric potential

• Sum or pressure residual reduced to O(1×10-8) at each timestep(sum of residuals drops 3 or 4 orders of magnitude)


Validation – Compare Predicted Velocity with Plant SVC Results

• SVC[3] measurement provided by Baosteel: No. 4 caster with 230×1200mm strand and a lower casting speed of 1.3m/min, no EMBr, no argon injection

• LES simulations carried out with the same conditions, u velocity (along WF) in the quarter mold center plane and 1cm below top surface are compared with SVC data points

Schematic of SVC measurements Compare u velocity from LES with SVC

0 20 40 60 800

0.1

0.2

0.3

0.4

Time (s)

u ve

loci

ty (

m/s

)

LES uSVC u


Mean Velocity (Validation Case)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0

0.2

0.4

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

2Time80.0s

-0.02 0 0.02

0.18

0.2

0.22

0.24

0.26

1.51.20.90.60.30

-0.3-0.6-0.9-1.2-1.5

1Time83.9s

-0.05 0 0.05

-0.6

-0.4

-0.2

0

0.2

21.81.61.41.210.80.60.40.20

-0.2-0.4-0.6-0.8-1

Time80.1s

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

-0.1

0

0.1

0.1 0.13 0.16 0.19 0.22 0.25 0.28

Time80.0s 0.3m/sOR

|U|

|U|

plane x=-0.45look into port

UX(m/s)

x (m)

y(m)

x(m)

z(m)

z(m)

y(m)y(m)

UZ(m/s)

IR

ORUx = 0

X=-0.45

• Time averaged velocity magnitude |U| = (Ux2+Uy

2+Uz2)1/2

• Back flow - reversal going into the port (towards inside SEN)

• A big swirl at bottom of SEN

Back Flow

Back Flow


Transient Flow in SEN, Port and Shape of the Jet Exiting Port (Validation Case)

Large circulation in SEN bottom causes low pressure in the circulation center and suck in fluid in the mid of port, instantaneous velocity u = (ux , uy , uz)

-0.02 0 0.02

0.18

0.2

0.22

0.24

0.26

1.51.20.90.60.30

-0.3-0.6-0.9-1.2-1.5

1Time64.8s

look into port ux = 0OR

ux (m/s)

y (m)

z(m)

Velocity in port

ux = -0.7m/sux = 0.7m/s

IR

OR

Z

SEN

NF

Iso-surface of u

t = 64.8s

IROR

2m/s

uz (m/s)

z(m)

y (m)Velocity in SEN

Back Flow

Back Flow


Flow Rotation at SEN Bottom and Top Surface Velocity (Validation Case)

SEN bottom, three different rotations (identified by color)

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

Time (s)

u v

elo

city

(m

/s)

LES uSVC u

ux at center plane, quarter mold 1cm below top surface

IROR

Time(s)

slide gate

-0.04 0 0.04

0.18

0.2

0.22

0.24

0.26

-0.04 0 0.04

0.18

0.2

0.22

0.24

0.26

-0.04 0 0.04

0.18

0.2

0.22

0.24

0.26

Symmetric Plane SEN Bottom

-0.04 0 0.04

0.18

0.2

0.22

0.24

0.26

port outlet

well

z

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

uz(m/s)

y

OR OR OR OR

Time Averaged

symmetrical clockwise counter-clockwise

x


Swirls at SEN Bottom and Top Surface Velocity (without EMBr)

• 230×1300mm strand, Vc = 1.8m/min, submergence depth dsub of 170mm and 200mm, No EMBr two circulations at SEN bottom

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

uz in Symmetric Plane SEN Bottom

w(m/s)

0 10 20 30 40Time

(s) dsub = 170mm, No EMBr

dsub = 200mm, No EMBr

IRIR

Animation

symmetricalcounter-clockwise

0 5 10 15 20 25 30 35 40 45 50-0.2

0

0.2

0.4

0.6

0.8

dsub = 170mm dsub = 200mm

u(m

/s)

Time (s)

ux at center plane, quarter mold 1cm below top surface

dsub = 170mm dsub = 200mm

y (m) z (m)

z(m)

uz(m/s)


y

z

-0.025 0 0.025

0.18

0.2

0.22

0.24

0.26

2

y

z

-0.025 0 0.025

0.2

0.22

0.24

0.26

0.28

2

Flow in Port (without EMBr)Submergence depth 170 and 200mm

• At x=-0.045

• Negative ux flow exiting port into moldPositive ux backflow

• White lines show where ux = 0

• Backflow at top 1/4 – 1/3 region

dsub

200mm

dsub

170mm

IR

-2 -1.5 -1 -0.5 0 0.5 1

Uxm/s

IR

z(m)

y(m) y(m)

ux(m/s)

ux(m/s)

dsub = 200mmdsub = 170mm

IRIR OROR

Animation Animation

Back Flow

Back Flow


Effect of Submergence Depth on Flow in Top Surface and Mold

Time-averaged (Without EMBr)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0

0.2

0.4

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

2Time45.9s

• Contour of |U| in middle plane and on top surface (1cm below)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0

0.2

0.4

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

2Time42.0s

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0.1

0

0.1

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

Time42.0s

dsub = 200mm

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

-0.1

0

0.1

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

Time45.9s

dsub = 170mm|U|

(m/s)

|U| (m/s) |U| (m/s)

|U| (m/s)

x (m) x (m)

z (m)

y(m)

IR IR

Note: arrows only shows 1/9 of all cells


Effect of EMBr (in SEN CenterplaneTime-averaged; dsub = 170mm)

• Contour of w velocity in SEN• Size of the recirculation region

(below slide gate) is not affected• Length of the jet is reduced• With EMBr Bottom swirl size is

reduced; with top coil 850A bottom only shows one swirl

• With EMBr, pressure p (modified static pressure) drop in SEN is increased

y

z

-0.050 0.05

-0.6

-0.4

-0.2

0

0.2

32.62.21.81.410.60.2

-0.2-0.6-1

2

y

z

-0.050 0.05

-0.6

-0.4

-0.2

0

0.2

32.62.21.81.410.60.2

-0.2-0.6-1

2

y

z

-0.050 0.05

-0.6

-0.4

-0.2

0

0.2

32.62.21.81.410.60.2

-0.2-0.6-1

2

y

z

-0.050 0.05

-0.6

-0.4

-0.2

0

0.2

32.62.21.81.410.60.2

-0.2-0.6-1

2

IR

Uz(m/s)

No EMBr

0A850A

400A850A

850A850A

Current in Top Coil:Current in Bottom Coil:

(m/s)OR

Note: to make figure clearer, arrows only shows in 1/9 of all cells

P2

P1

Pressure (Pa)

No EMBr

0A850A

400A850A

850A850A

P1 - P2 -8065 11416 52741 95014

P1* - P2

* -46565 -27084 14241 56514

*Including ferrostatic pressure

0.55m


Effect of EMBr on Flow (in Port; Time-Averaged; dsub=170mm)

• Contour of Ux in middle of port, x = - 0.045, • White line shows where Ux = 0• Increasing B leads to:

– More flow exiting at bottom of the port– Area of back flow region at top of port increases– Size of the swirls in port reduce

• With top coil 850A, only one circulation at port bottom IR side

y

z

-0.025 0 0.025

0.18

0.2

0.22

0.24

0.26

2

y

z

-0.025 0 0.025

0.18

0.2

0.22

0.24

0.26

2

y

z

-0.025 0 0.025

0.18

0.2

0.22

0.24

0.26

2

y

z

-0.025 0 0.025

0.18

0.2

0.22

0.24

0.26

2Ux (m/s)

No EMBr 0A850A

400A850A

850A850A

Current in Top Coil:Current in Bottom Coil:

10.50

-0.5-1-1.5-2 IRIRIRIR

Backflow

Outward flow

Backflow

Outward flow

Backflow

Outward flow

Backflow

Outward flow


0 5 10 15 20 25 30 35 40 45 50-0.2

0

0.2

0.4

0.6

0.8

Effect of EMBr on Swirl at SEN Bottom and Mold Top Surface Velocity (Transient; dsub=170mm)

• Rotation at bottom of SEN• With EMBr, flow velocity on

top surface is too small (~0.05m/s)

0 5 10 15 20 25 30 35 40 45Time (s)

No EMBr0A

850A400A850A850A850A

ux at center plane, quarter mold region, 1cm below top surface

Time t (s)

uxm/s

No EMBr 0A 850A 400A 850A 850A 850A

“No swirl”

“No Swirl”symmetrical clockwise counter-

clockwise


Effect of EMBr on Flow in Mold(Time Averaged; dsub=170mm)

• Nozzle flow – EMBr makes flow inside SEN more uniform, with strong EMBr increases downward velocity along NF walls in SEN (M-shape profile, only seen in front view, perpendicular to field)

• With EMBr, jets are flatter and stronger, circulations close to jets

x

z

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0

0.2

0.4

x-0.6 -0.4 -0.2 0 0.2 0.4 0.6

x

z

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

0

0.2

0.4

x-0.6 -0.4 -0.2 0 0.2 0.4 0.6

No EMBr Bottom coil 850A

Top coil 400A and Bottom coil 850A Top coil 850A and Bottom coil 850A

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5|U| (m/s)


Effect of EMBr on Flow in Mold(Transient; dsub = 170mm)

• Contour of velocity magnitude |u|• With EMBr: velocity in mold is reduced; less fluctuations

• Without EMBr, jet travels further to NF. With EMBr, jets only reach quarter mold region

• With EMBr, shedding vortex from jet (at port outlet region) with frequency ~1Hz, those vortex die out quickly

x (m/s) x (m/s)

z(m/s)

2 m/s 2 m/s|u|

(m/s)|u|

(m/s)

Animation AnimationTop coil 400A and Bottom coil 850ANo EMBr


Effect of EMBr on Top Surface Stability and Vortex Motion (dsub = 170mm)

• Without EMBr, top surface velocity 0.1~0.45 m/s

• With EMBr, top surface velocity around 0.03~0.07m/s

• EMBr reduces vortex on top surface, more stable

x

y

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

-0.1

0

0.1

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

x

y

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

-0.1

0

0.1

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

No EMBr

x

y

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

-0.1

0

0.1

x

y

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

-0.1

0

0.1

B850A

T400AB850A

T850AB850A

|U| (m/s)

|U| (m/s)

1m/s

1m/s

OR

OR

0.5 m/s

x (m)

y(m)

y(m)

OR

OR

Animation

AnimationTop coil 400A and Bottom coil 850A

No EMBr


Conclusions

• Swirl exiting SEN depends on casting speed, gate position, and EMBr (in addition to geometry)

• Stronger port swirl with smaller slide gate opening fraction (which also accompanies lower casting speed);

• With no EMBr, strong asymmetric flow inside SEN due to slide gate causes big swirl in port bottom (especially with bottom well), & at port exit

• EMBr makes flow inside SEN more uniform, and even increases downward velocity along NF walls (with strong EMBr)

• EMBr causes tighter faster jet, which exits more towards lower region of port with accompanying larger back-flow in top;

• With EMBr, vortex shedding from upside of jet in the mold at ~1Hz

• With EMBr, jets only penetrates to quarter region of mold; recirculation regions become tighter and closer to jet and new smaller vortices form

• Even with this high casting speed, 1.8m/min: with no argon, EMBr lowers top surface velocity too much (~0.04m/s).


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

• Blue Waters / National Center for Supercomputing Applications (NCSA) at UIUC

• National Science Foundation Grant CMMI-11-30882

• NVIDIA for providing the GPUs through the NVIDIA Professor Partnership program


References

[1] Ramnik Singh, Brian G. Thomas, and Surya P. Vanka, “Large Eddy Simulations of Double-Ruler Electromagnetic Field Effect on Transient Flow during Continuous Casting,” Metall. Mater. Trans. B, 2014, vol. 45, pp. 1098–1115.

[2] Hiromichi Kobayashi, “The Subgrid-Scale Models Based on Coherent Structures for Rotating Homogeneous Turbulence and Turbulent Channel Flow,” Phys. Fluids 1994-Present, 2005, vol. 17, p. 045104.

[3] Rui Liu, J Sengupta, D Crosbie, S Chung, M Trinh, and B. G Thomas: in Sens. Sampl. Simul. Process Control, “Measurement of Molten Steel Surface Velocity with SVC and Nail Dipping during Continuous Casting Process,” John Wiley & Sons, San Diego, 2011.

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