Model of Argon Flow through UTN

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$ANNUAL REPORT 2011 UIUC, August 18, 2011 Model of Argon Flow through UTN Refractory$ Sengupta ** *Department of Mechanical Science and Engineering University of

Sengupta ** *Department of Mechanical Science and Engineering University of

Processing Simulation Lab Rui Liu **ArcelorMittal Global R&D ArcelorMittal Dofasco

into argon-steel two-phase flow in UTN and SEN, which greatly influences flow in

distribution in the argonsteel two phase flow in UTN and SEN, which is needed to

the flow pattern to evaluate/design UTN geometry / material for optimal gas flow

porous-flow model Simulation of argon flow through Dofasco UTN Heat transfer

1 ANNUAL REPORT 2011 UIUC, August 18, 2011 Model of Argon Flow through UTN Refractory and Bubble Size Estimation R. Liu *, B.G. Thomas * and J. Sengupta ** *Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign University of Illinois at Urbana- Champaign Metals Processing Simulation Lab Rui Liu **ArcelorMittal Global R&D ArcelorMittal Dofasco Inc. Simulation of Argon Gas Flow through UTN Purpose of the study: to gain insight into argon-steel two-phase flow in UTN and SEN, which greatly influences flow in the mold (especially asymmetric flow) to obtain a reasonable initial bubble size distribution in the argonsteel two phase flow in UTN and SEN, which is needed to simulate argon-steel flow in the mold to run parametric studies of gas injection on the flow pattern to evaluate/design UTN geometry / material for optimal gas flow This work includes: Description and validation of two models: pressure-source model porous-flow model Simulation of argon flow through Dofasco UTN Heat transfer analysis Gas flow simulation using porous-flow model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 2

2 Governing Equations -- Pressure-Source Model Darcy s Law: v = K D p (1) ( ) 0 ( k T) 0 Mass Conservation (or continuity): ρv = (2) Heat Conduction: = (3) Ideal Gas Law: p= ρrt (4) Eqn (1) and (2) 1 ρ ( ρ p) = 0 ρ ( K p) + ρ ( K p) = 0 K D ( K D p) = [ ρ ( K D p) ] RT p ( K ) = ( K ) = S p D p D p ρ = RT pressure diffusion D p RT D Pressure source due to gas expansion -- For Pressure-Source Model The left hand side of the final equation (in red box) is the standard diffusion term, while the right hand side is in the form of a source term that accounts for the effect of gas expansion due to temperature and pressure gradient. Add the source term into a FLUENT model of 3-D scalar diffusion (with pressure as the scalar) and solve coupled with a 3-D energy equation University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 3 Governing Equations -- Porous Flow Model ( ) 0 ( k T) 0 Mass Conservation (or continuity): ρv = (1) Heat Conduction: = (2) Ideal Gas Law: p= ρrt (3) Full Set of Navier-Stokes Equations for flow in porous media: 2 2 ρv ( ρvv) = viscous Re ~2.3, C=0 for Δr resistance 0 laminar flow ( ρv) μ 1 + ( ρvv) = p+ ( μ v) + F v + C ρ v v μ 1 t α 2 α = K D 0 0 (steady state 5 inertial μv problem) ( μ v) = = resistance Δr v = K D p -- Porous-Flow Model Construct a complete set of 3-D Navier-Stokes equations, with the momentum equation simplified into equation (1), adopting the ideal gas law to relate density with pressure and temperature. Solve with FLUENT (porous-media flow module) with energy University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 4

$Permeability (material property p model) Permeability Varying with Temperature: K D K = μ DS ( T ) Specific permeability, from ArcelorMittal for MgO or Alumina refractory: 0.8 1.$ 51196 ) μ T = μ0 10 5 Dawe 69* μ 0 = 2.228 10 Pa s Room temperature (20 C) argon viscosity Ref: *R. Dawe and E. Smith. Viscosity of Argon at High Temperatures. Science, Vol. 163, pp 675~676, 1969.

51196 ) μ T = μ0 10 5 Dawe 69* μ 0 = 2.228 10 Pa s Room temperature (20 C) argon viscosity Ref: *R. Dawe and E. Smith. Viscosity of Argon at High Temperatures. Science, Vol. 163, pp 675~676, 1969.

Test Problem (2 cases) Model Validation --- 3D FLUENT Models 1-D problem of gas flowing through a porous medium, cylindrical coordinate system, heat conduction from heated inner surface (fixed at T1)

3 Permeability (material property p model) Permeability Varying with Temperature: K D K = μ DS ( T ) Specific permeability, from ArcelorMittal for MgO or Alumina refractory: x10-12 m 2 K 12 2 = ) DS m (constant specific permeability, from Z. Hashisho, μ ( T ) Viscosity Varying with Temperature: ( ( ) lg 2 T / T / T ) μ T = μ Dawe 69* μ 0 = Pa s Room temperature (20 C) argon viscosity Ref: *R. Dawe and E. Smith. Viscosity of Argon at High Temperatures. Science, Vol. 163, pp 675~676, (gas dynamic viscosity, as a function of local temperature) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 5 ) ic Viscos sity (Pa*s) n Dynam Argo Temperature (K) Test Problem (2 cases) Model Validation --- 3D FLUENT Models 1-D problem of gas flowing through a porous medium, cylindrical coordinate system, heat conduction from heated inner surface (fixed at T1) to outer surface (fixed at T2) gas injected into outer radial surface, and exits inner surface; Effects of varying permeability and dynamic viscosity with temperature on pressure distribution are studied; Both pressure and mass flow rate boundary conditions are tested in this simple problem, and three models are implemented for each of the cases. Ttl Total: 2, 2,,( ) hexahedral cells B.C. for Case 1, fixed pressure: R 2, T 2, V, (or P) r=r 1, P=P 1, T=T 1 ; r=r 2, P=P 2, T=T 2. B.C. for Case 2, fixed gas mass flow rate: r=r 1, P=P 1, T=T 1 ; r=r 2, V=V inlet, T=T 2. R 1 (m) R 2 (m) P 1 (Pa) P 2 (Pa) V inlet (m/s) T 1 (K) T 2 (K) Symmetric Plane P 1, T 1, R 1 Symmetric Plane University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 6

1-D Test Problem Matlab Solution 1-D numerical solution is obtained independently via a Matlab code to compare and validate

For the 1-D test problem, the equation above can be written as an ODE, together with the heat conduction equation for heat transfer

the thermal effects on both argon permeability and gas expansion 2 1 T K D P P + + P + = 0 r T K dp dt D P dk P = T = K D = 1 dr dr

4 1-D Test Problem Matlab Solution 1-D numerical solution is obtained independently via a Matlab code to compare and validate solutions from FLUENT. For the 1-D test problem, the equation above can be written as an ODE, together with the heat conduction equation for heat transfer process: constant permeability, considering gas expansion 2 1 T P P + P + = 0 r T P dp dt P = T = 1 ( rt ) = 0 dr dr r considering the thermal effects on both argon permeability and gas expansion 2 1 T K D P P + + P + = 0 r T K dp dt D P dk P = T = K D = 1 dr dr dr ( rt ) = 0 Solver uses: r - Implicit scheme - TDMA method - 2 nd central difference scheme University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 7 D Heat Transfer Calculation Temperature Profile For this 1-D test problem, the heat conduction equation can be solved alone without coupling with any fluid flow equations (one-way coupling assumption). The resultant temperature distribution is shown below: University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 8

) ( 0.63842lg 2 T 6.9365/ T 3374.72/ T 1.51196 ) = μ0 10 μ 0 = 2.

of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui

$gas flowing through UTN refractory is determined by both the$ following relationship: KDS KD = KDS = 1.

5 Argon Viscosity Profile The argon viscosity is related to the local temperature via the correlation stated previously (also below) μ ( T ) ( lg 2 T / T / T ) = μ0 10 μ 0 = e 5 Pa* s Room temperature (20 C) argon viscosity University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 9 Permeability Profile for Argon Gas The permeability for argon gas flowing through UTN refractory is determined by both the specific permeability, and the argon gas dynamic viscosity via the following relationship: KDS KD = KDS = m μ ( T ) 12 2 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 10

6 Model Validation CASE 1 using Pressures as B.C. Comparison of Pressure Distribution (Pressure B.C.) Both the pressure-source model and the porousflow model match with solution from the 1-D ODE; ) Pre essure (Pa) Porous- Flow Model Varying Gas Viscosity Constant Gas Viscosity NO Thermal Effect Pressure- Source Model 1-D ODE Solution Radial Position (m) Largest pressure gradient is found in the case with both gas expansion effect and varying viscosity effect The shape of the curve for the constant gas viscosity case is irrelevant of the value of the gas viscosity, as long as it is constant throughout the domain. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 11 Model Validation CASE 2: -- using Mass Flow Rate as B.C. Considering gas expansion, argon viscosity varying with temperature argon viscosity at 1800 K Ignoring gas expansion, argon viscosity varying with temperature argon viscosity i at 1000 K argon viscosity at 293 K University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 12

Dofasco UTN Gas Flow Model Assumptions Specific permeability units: 1 centi-darcy = 9.869*10-15 m 2 1 npm = 10-13 m 2 Argon Flow Rate (SLPM) 1.

1 Porous-flow model is used in current simulation Heat transfer is modeled donce, then the temperature field is exported to the porous-flow simulation

with local l pressure and temperature t - Argon viscosity varying with temperature - one-way coupling with heat transfer - half of the UTN is adopted

of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 13 Heat Transfer Analysis The heat transfer calculation for the real-world

$the UTN refractory (true if the porosity is not large, maybe less than 50%).$ 88 Nu * K ρα a b h = 4 + Pr Nu = 5 + 0.015 Re Pr 1 inner bore diameter μ b = + 0.5 exp( 0.

7 Dofasco UTN Gas Flow Model Assumptions Specific permeability units: 1 centi-darcy = 9.869*10-15 m 2 1 npm = m 2 Argon Flow Rate (SLPM) 1.0 (for half UTN) Specific Permeability (npm) 10.1 Porous-flow model is used in current simulation Heat transfer is modeled donce, then the temperature field is exported to the porous-flow simulation as a fixed field, due to the assumption of one-way coupling between heat ttransfer and dthe fluid idflow Porous-flow model: - Argon density varying with local l pressure and temperature t - Argon viscosity varying with temperature - one-way coupling with heat transfer - half of the UTN is adopted as computation domain due to symmetry y - both circumferential and vertical gas injection slits are included Total: 180,000 hexahedral cells University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 13 Heat Transfer Analysis The heat transfer calculation for the real-world problem is more complicated than the previous test case, still the assumption is adopted that the heat transfer is not affected by the gas flow through the UTN refractory (true if the porosity is not large, maybe less than 50%). The following parameters are calculated/adopted: -- heat transfer coefficients at both outer and inner bore surface; μ Pr = a = 0.88 Nu * K ρα a b h = 4 + Pr Nu = Re Pr 1 inner bore diameter μ b = exp( 0.6 Pr) ρud 3 (Sleicher-Rouse correlation) Re = μ Parameters Values B.C.: h inner (W/m 2 K) 2.5*10 4 h 2 outer (W/m K) 10 Heat conductivity 33 K s (W/mK) μ (Pa*s) ρ (kg/m 3 ) 7200 Average steel velocity U (m/s) h inner Symmetric Plane Bottom: 0 heat flux Z Y X houter Temperature (K) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 14

Temperature and Argon Density Distribution 0.35 0.35 0.3 0.3 0.25 0.25 (m) UTN Height 0.2 0.

56 0.52 0.48 0.44 0.4 0.36 0.32 0.28 0-0.1-0.0505 0 0.0505 0.1 0.15 Radial Position (m) 0-0.

15 Radial Position (m) University of Illinois at Urbana-Champaign Metals Processing

3 Pressure (Pa) UTN He eight (m) 115000 0.25 114000 113000 112000 0.

Obvious asymmetry of the pressure distribution is found through the UTN cross section, due to

8 Temperature and Argon Density Distribution (m) UTN Height Temperature (K) (m) UTN Height Argon Density (kg/m^3) Radial Position (m) Radial Position (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 15 Pressure Distribution through UTN Pressure (Pa) UTN He eight (m) Maximum pressure occurs at the conjunction of the T -shaped slits Radial Position (m) Obvious asymmetry of the pressure distribution is found through the UTN cross section, due to the asymmetric way of injecting gas into UTN For current case, the maximum pressure found in the domain is about 20 KPa, while the average pressure at the slits is approximately 12 KPa. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 16 0

Average Velocity Contour at Inner Bore Surface 0.35 0.3 0.

009 0.008 0.007 0.1 0.006 0.005 0.004 0.0505 0.003 0.002 0-0.1-0.05 0 0.

15 Radial Position (m) 0 003 Maximum velocity is found at the location

gas velocity entering the UTN inner surface corresponding to the circular

Metals Processing Simulation Lab Rui Liu 17 Slice 7 Slice 6 Average Normal

Slice 3 Slice 2 B Top view Slice 5 Slice 6 Slice 4 Slice 1 Slice 3

(m m/s) Average Slice 7 0.009 0.008 0.007 0006 0.006 0.005 0.004 0.003 0.

001 slice 1, 0 deg (from center plane) slice 2, 15 deg slice 3, 30 deg

9 Average Velocity Contour at Inner Bore Surface UTN Heigh ht(m) 0.2 Velocity Magnitude (m/s) Radial Position (m) Maximum velocity is found at the location corresponding to the conjunction point of the T - shaped slits; The average gas velocity entering the UTN inner surface corresponding to the circular slit is approximately 5~6 mm/s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 17 Slice 7 Slice 6 Average Normal Velocity Profiles at Different Circumferential Locations Slice 5 Slice 4 Slice 3 Slice 2 B Top view Slice 5 Slice 6 Slice 4 Slice 1 Slice 3 circumferential slit vertical slit Normal Veloc city at UTN Inn ner Surface (m m/s) Average Slice slice 1, 0 deg (from center plane) slice 2, 15 deg slice 3, 30 deg slice 4, 45 deg slice 5, 90 deg slice 6, 135 deg slice 7, 180 deg A Distance from UTN Bottom (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 18 Slice 1 Slice 2

008 0.007 0.006 0.005 0 004 0.004 0.003 0.

10 Validation via Static Test water tank upper ring Static bubbling test Vertical slit at outer surface Velocity Magnitude (m/s) Gas injection point (at outer o ter surface) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab 19 Rui Liu Comparison of Bubble Distribution on UTN Inner Surface Y X Z Velocity Magnitude ((m/s)) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 20

11 Methodology of Bubble Size Estimation in Argon-Steel System Calculate Gas Volumetric Flow Rate in Hot Condition at Stopper-Rod Tip Calculate the Gas Velocity profile at UTN/SEN inner surface via solving a Porous-Flow /Pressure-Source model for average normal velocity at UTN inner surface (described previously) for gas injection at stopper-rod tip Estimation of Active Sites Number Distribution via empirical equation from G. Lee and B.G. Thomas for gas injection at UTN and SEN refractory Bubble formation at downward nozzle has been studied by H. Tsuge et al. Calculation of Gas Flow Rate per Active Site (Total Flow Rate/cm 2 )/(Active sites #/cm 2 ) via two-stage model from H. Bai and B.G. Thomas Estimation of Mean Diameter of Initial Bubble Formation University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 21 Estimation of Active Sites Number in UTN/SEN Refractory from ref [1] from ref [1] G. Lee and B.G. Thomas suggest [1] : Where: Q g : the gas injection flow rate per cm 2 (LPM); U: liquid superficial velocity (m/s); P erm : material permeability (npm); θ: contact angle for wettability (rad) So the number of active sites per cm 2 is: Q g U P erm Nsite = θ Ref: [1] G. Lee, B.G. Thomas, et al., Met. Mater. Int., Vol. 16, No. 3 (2010), pp. 501~506 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 22

Calculation of Gas Flow Rate per Active Site Adopting the active sites number correlation at UTN inner surface: 0.2635 0.85 0.

12 Calculation of Gas Flow Rate per Active Site Adopting the active sites number correlation at UTN inner surface: Q Q g U P erm N Qsite = = site = θ N U P Qg 1 Qg θ site 7 erm Flow Rate per Active Site (LPM) Average Normal Velocity (m/s) Active Sites Number (#/cm^2) Y Y Y Z X Z X Z X University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 23 Estimation of Mean Bubble Size using a Two-Stage Model Hua s two-stage initial bubble formation model [2] : 1.Expansion stage (solving for r, as r e ) Drag coefficient: Expansion stage --Figures from ref [2] Elongation stage 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. D Bubble Reynolds number: Contact angle function: 2.Elongation stage (solving for r d ) Based on the 1/7 th law in turbulent flow in the circular pipe Empirical correlation with liquid steel superficial i velocity Ref: :nozzle inner diameter (m) :liquid steel superficial velocity (m/s) N [2] B. Hua and B. G. Thomas, Metall. Mater. ρ l :liquid density (kg/m 3 ) σ :surface tension (N/m) Trans. B 32, 1143(2001). ρ g :gas density (kg/m3 ) υ :kinematic viscosity of liquid steel (Pa*s) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 24 U

Metals Processing Simulation Lab Rui Liu 25

Parameters for this process: Casting speed:

thickness: 10 inches Submergence depth: 8

SLPM Back Pressure: 19 psi SEN inner bore

bottom shape: Cup bottom Gas injection flow

modeling the hot system while considering

13 Estimation of Bubble Size Distribution University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 25 Model Application: Gas Leakage Prediction Parameters for this process: Casting speed: 40 ipm Mold width: 72 inches Mold thickness: 10 inches Submergence depth: 8 inches Dithering amplitude: 14 mm or 7 mm Dithering frequency: 0.4 Hz Total gas injection flow rate: ~20 SLPM Back Pressure: 19 psi SEN inner bore diameter: 80 mm Plate diameter: 75 mm SEN bottom shape: Cup bottom Gas injection flow rate into the nozzle can be determined by modeling the hot system while considering leakage. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 26

Estimation of Gas Flow Rate Entering Nozzle Both argon flow rate and back pressure are measured, though one and only one of these two values is needed to define the problem Use back pressure as B.

Difference between measured total gas flow rate and calculated gas flow rate into the nozzle reveals the amount of gas leakage Numerical Model set up: Heat transfer model coupled porous flow

$04 0.0875 84672 131000 1832 1200 Refractory (specific) permeability (m 2 ): 1.01*10-12 2 ( ) Argon dynamic viscosity (Pa*s): ( ) 0.63842lg T 6.9365/ T 3374.72/ T μ T = μ 1.$ 228 10 Pa* s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 27 Pressure/Velocity Distribution of Gas Flowing Through Heated UTN Wall Simulation suggests 30 LPM

228 10 Pa* s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 27 Pressure/Velocity Distribution of Gas Flowing Through Heated UTN Wall Simulation suggests 30 LPM

14 Estimation of Gas Flow Rate Entering Nozzle Both argon flow rate and back pressure are measured, though one and only one of these two values is needed to define the problem Use back pressure as B.C. for the porous-flow model to calculate gas flow rate into the nozzle inside. Difference between measured total gas flow rate and calculated gas flow rate into the nozzle reveals the amount of gas leakage Numerical Model set up: Heat transfer model coupled porous flow model, with pressure at inner and outer bore surface as boundary conditions. B.C. fixed pressure: r=r 1, P=P 1, T=T 1 ; r=r 2, P=P 2, T=T 2. R 1 (m) R 2 (m) P 1 (Pa) P 2 (Pa) T 1 (K) T 2 (K) Refractory (specific) permeability (m 2 ): 1.01* ( ) Argon dynamic viscosity (Pa*s): ( ) lg T / T / T μ T = μ Room temperature (20 C) argon viscosity μ0 = Pa* s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 27 Pressure/Velocity Distribution of Gas Flowing Through Heated UTN Wall Simulation suggests 30 LPM argon entering nozzle (hot condition) 2.84e e e e e e e e e e e e e e e e e e e e e-03 Radial Velocity (m/s) Note: contour is just for velocity vectors Only about 25% of the total gas enters the nozzle Note: pressure shown in the contour is the gauge pressure University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 28

Temperature p and Viscosity y Profiles Argon

(K) 1700 1600 1500 7.50E-05 7.00E-05 1400 6.

085 Radial Position (m) Radial Position (m)

015 15000 0.01 10000 5000 0.005 0 0.035 0.

065 Radial Position (m) University of Illinois

15 Temperature p and Viscosity y Profiles Argon Viscosity Profile across UTN Wall Temperature Profile across UTN Wall 8.50E E-05 Argon Visc cosity (Pa*s) Tempera ature (K) E E E E Radial Position (m) Radial Position (m) Velocity Profile across UTN Wall Gauge Pressure Profile across UTN Wall Argon Velocity y (m/s) Gauge Pressurre (Pa) Radial Position (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Radial Position (m) Rui Liu 29 Rui Liu 30 Geometry y and Mesh ~250 mesh blocks Total mesh: 1 million mapped hexa-cells University of Illinois at Urbana-Champaign Metals Processing Simulation Lab

Computation Details Models and Schemes Turbulence Model

: Meniscus No-slip wall Domain Outlet Pressure outlet

0 million mapped hexa- cells Sources and Sinks: Mass and

steel adjacent to shell, and escape of argon gas adjacent

University of Illinois at Urbana-Champaign Metals

Center Plane between Wide Faces Gas Velocity (m/s) Gas

flow) 120 LPM argon flow rate (hot) (20 SLPM with no

ports, then rising to meniscus 30 LPM argon flow rate

16 Computation Details Models and Schemes Turbulence Model Multiphase Model Advection Discretization Name k-epsilon with std. wall functions Eulerian Model 1 st order upwinding B.C.: Meniscus No-slip wall Domain Outlet Pressure outlet Bubble size: 2.4 mm Time step: 0.05 sec Total mesh: 1.0 million mapped hexa- cells Sources and Sinks: Mass and momentum sinks are utilized for solidification of liquid steel adjacent to shell, and escape of argon gas adjacent to meniscus Half mold was used as computational domain. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 31 Argon Flow Pattern at Center Plane between Wide Faces Gas Velocity (m/s) Gas taking liquid steel to meniscus (buoyancy force dominated flow) 120 LPM argon flow rate (hot) (20 SLPM with no leakage) Gas taken by liquid steel jet once coming out of ports, then rising to meniscus 30 LPM argon flow rate (hot) (20SLPM with 75% leakage based on porous flow model results) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 32

Liquid Steel Flow Pattern at Center Plane between Broad Faces Single

(hot) (20 SLPM with no leakage) 30 LPM argon flow rate (hot) (20SLPM

Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu

ickness Mold Th 0.2 0.5 m/s 0.26 Horizontal Velocity (m/s) 0.

argon flow rate (no leakage) Mold Thic ckness (m m) 0.26 0.

17 Liquid Steel Flow Pattern at Center Plane between Broad Faces Single Roll Flow Pattern Double Roll Flow Pattern 120 LPM argon flow rate (hot) (20 SLPM with no leakage) 30 LPM argon flow rate (hot) (20SLPM with 75% leakage based on porous flow model results) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 33 Steady State Flow Patterns at Different Gas Injection Rate (m) ickness Mold Th m/s 0.26 Horizontal Velocity (m/s) 0.21 flow towards narrow face Distance from Mold Center (m) Single Roll Flow Pattern 120 LPM hot argon flow rate (no leakage) Mold Thic ckness (m m) Horizontal Velocity (m/s) m/s flow towards SEN Distance from Mold Center (m) Double Roll Flow Pattern 30 LPM hot argon flow rate (75% leakage) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 34

18 Conclusions Nice matches are achieved among the 1-D ODE solutions, pressure-source model and porousflow model for the test problems, with the following factors considered: expansion of heated gas argon viscosity change with temperature Validated models of argon flow through heated UTN can be utilized to predict: asymmetry of gas distribution at UTN inner surface, for design optimization purpose initial bubble size combined with bubble size models (by H. Bai and G. Lee) argon gas leakage, which greatly changes flow pattern University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 35 Acknowledgements Continuous Casting Consortium Members (ABB, ArcelorMittal, Baosteel, Tata Steel, Magnesita Refractories, Nucor Steel, Nippon Steel, Postech, Posco, SSAB, ANSYS-Fluent) Hongbin Yin, Bruce Forman and Yong Lee from ArcelorMittal global R&D at East Chicago Other graduate students in Metals Processing Simulation Lab University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 36

Numerical Simulation of the Hagemann Entrainment Experiments

CCC Annual Report UIUC, August 14, 2013 Numerical Simulation of the Hagemann Entrainment Experiments Kenneth Swartz (BSME Student) Lance C. Hibbeler (Ph.D. Student) Department of Mechanical Science & Engineering