CCC Annual Report UIUC, August 14, 213 Gas Flow Through Upper Tundish Nozzle Refractory and Bubble Size Evolution Inside SEN Rui Liu and Seong-Mook Cho Department of Mechanical Science & Engineering University of Illinois at Urbana-Champaign OUTLINE PART 1: UTN porous gas flow model Review of previous model Model updates: Realistic pressure distribution on UTN inner surface Bubble formation threshold for gas pressure One-way passing pressure boundary condition Effects of back pressure effects Effects of gas leakage at UTN bottom PART 2: Bubble size study in a water model Bubble size distributions in SEN Evolution of gas volume fraction down the SEN University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 2
Development and Validation of Gas Porous Flow Models Review 3-D Coupled Eqns.: RT p = D D p RT ( K p) ( K p) ( k T ) = R. Liu and B.G. Thomas, Proc. AISTech 212 Conf. (Atlanta, GA), p22, (212) R 1 (m) R 2 (m) P 1 (Pa) T 1 (K) T 2 (K) V (m/s).37.7 1 18 1.73 1-D Simplified Eqns.: 2 1 T K P D P + + P + = r T K P D 1 ( rt ) = r University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 3 Schematic and Parameters for the Base Case P P Ref: *R. Daweand E. Smith. Viscosity of Argon at High Temperatures. Science, Vol. 163, pp 67~676, 1969. P in * Inlet pressure P in 2 kpa (abs.) Pressure at nozzle inside wall & ambient Specific permeability Dynamic Viscosity* Permeability (K p / µ) Thermal conductivity University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 4 P 11 kpa (abs.) K p 1.1 npm = 1.1 x1-7 mm² µ 7.42 x1 - Pa.s (at 128C) K D k 1.36x1-8 m²/(pa.s) (at 128C) 18 W/mK Heat transfer coefficient (nozzle exterior) h 4 W/m 2 K 2 ( ) ( ) T 6.93/ T 3374.72/ T µ T = µ 1.1196 1 µ = 2.228 1 Pa s Room temperature (2 C) argon viscosity
Scenarios for the Base Case Further Factors to consider: Hydrostatic pressure profile with steel velocity (Bernoulli s eqn.) Bubble formation pressure threshold at pore (due to surface tension) Scenarios: 1. Base case parameters, with porous flow model, constant gas viscosity, constant pressure 2. Base case parameters, but with temperaturedependent gas viscosity 3. Consider liquid steel pressure distribution at UTN inner surface (using Bernoulli s Eqn) 4. Same with case 3, but consider bubbling pressure threshold due to surface tension..1. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu UTN height (m)..2..1. Temperature (K) 18 1796 1776 176 1737 1717 1698 1678 18 1639 1619 16 8 Pressure Threshold for Bubble Formation In order for gas to intrude into the liquid and form bubbles, surface tension effects have to be considered: Bubble expanding stage (assume bubbles expand slowly in equilibrium): r 2 = r pore r 1 r2 r 3 r r > r 1 2 > r 3 2 p g p l p g p l p g p l step1 step2 step3 p p = σκ g l 2σ p > p g 2 g1 2 p = p + g l κ = r p > p g 2 g 3 r 2σ 2σ Pressure threshold for bubble p = p + = p + g l l formation: r r 2 pore Parameters used in current study: σ = 1.2 N, r = 2µ m pore m University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 6
Pressure Distributions Base Case Scenarios center axis....2.2.2..1. 9 7..1. 9 7..1. 9 7..1...1...1. bottom leakage, constant liquid pressure bottom sealed, Bernoulli-based pressure bottom sealed, Bernoulli-based pressure, and bubbling threshold University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 7 center axis Velocity Distributions Base Case Scenarios....2.1m/s.2.1 m/s.2.2 m/s..1..1..1.....1. bottom leakage, constant liquid pressure..1. bottom sealed, Bernouli-based pressure..1. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 8 bottom sealed, Bernouli-based pressure, and bubbling threshold
Radial Velocity Distributions.6 open bottom, no hydrostatic pressure, constant gas viscosity open bottom, no hydrostatic pressure, varying gas viscosity wall bottom, with hydrostatic pressure, no bubbling threshold wall bottom, with hydrostatic pressure and bubbling threshold Radial Velocity (m/s).4.2....1..2. Distance from UTN Bottom (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 9 Effect of One-Way Passing Pressure B.C. Gas Velocity (m/s) Using One-Way Passing B.C. is NECESSARY! Without the one-way passing B.C. Reversed flow from the steel side, results not physical With the one-way passing B.C. Gas Velocity (m/s) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 1
Model Validation with Static Bubbling Test Gas Normal Velocity (m/s).27.22.18..13.1.8.7.6. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 11 Pressure Distribution Bottom Leakage vs. Sealed. Bottom Leakage.3 94737 94211 93684 938 92632 92 979 93 926 9.2.1 9 7.1...1.4..6.7.8.9.1.4. m/s.2.3.2 Pressure (Pa).1.4..6.7.8.9 9 7.1..1. -.1.. 9 7.2.... Bottom Sealed. m/s.4.1 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 12
Velocity Distributions Bottom Leakage vs. Sealed Bottom Leakage..2.1 m/s..1..4.3.2.m/s.1 -.1.4..6.7.8.9.1..4 Bottom Sealed..2.1 m/s..1...1.3.2.1. m/s...1 -.1.4..6.7.8.9.1 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 13 Evaluation of UTN Gas Injection Bottom Leakage vs. Sealed DEFINE: Radial Velocity (m/s).7.6..4.3.2.1 Open Bottom Case Perfectly Sealed Case θ = L θ = L.86....1..2. Distance from UTN Bottom (m) Gas Leakage Rate m θ = & L m& 1 in total Possible gas leakage through UTN bottom does not affect much gas deliver through the upper slit An 86% gas leakage is found in current case with the complete openbottom case University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 14
Effects of Back Pressure on Gas Velocity Distributions in Refractory. 9 kpa 99 kpa 14 kpa...2.1 m/s.2.2 m/s.2.2 m/s..1. 8998 8994 899 8986 8982 8978 8974 897 8966 8962 898 894..1...1. 98 97 96 9 94 93 92 91 9..1...1. 136 132 128 124 12 116 112 18 14 1 96 92..1. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu Effects of Back Pressure and Sealing on Gas Radial Velocity Distributions.24 9 kpa, perfectly sealed 9 kpa, open bottom 99 kpa, perfectly sealed 99 kpa, open bottom 12 kpa, perfectly sealed 12 kpa, open bottom 14 kpa, perfectly sealed 14 kpa, open bottom.2 Radial Velocity (m/s).16.12.8.4....1..2. Distance from UTN Bottom (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 16
Effects of Back Pressure on Gas Mass Flow Rate and Leakage Ratio 1-3 1. Gas Mass Flow Rate (kg/s) 1-4 1-1 -6 1-7 Total/entering gas flow rate, perfectly sealed Total gas flow rate, open bottom Gas entering flow rate, open bottom 9 1 11 12 13 14 Back Pressure (k Pa) Ratio 9 1 11 12 13 14 Back Pressure (k Pa) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 17.8.6.4.2. Gas leakage Ratio of gas entering rate, open bottom / perfectly sealed For both open-bottom and perfectly-sealed cases, gas mass flow rates increase with increasing back pressure For open-bottom cases, with different back pressures in this work, gas leakage ratio decreases with increasing back pressure, but all above 7%, with ratio of gas entering rate also remaining 7% between openbottom and perfectly sealed cases Part 1: Conclusion UTN Porous Gas Flow Model UTN porous gas flow model has been improved to incorporate realistic conditions, including: Liquid steel pressure distribution on UTN inner surface Bubble formation gas pressure threshold One-way passing pressure boundary condition to eliminate unphysical reversed gas flow on UTN surface Parametric studies on gas injection back pressure reveal: For both open-bottom and perfectly sealed cases, gas flow rates increases with increasing back pressure; Open-bottom cases leaks more than 7% of the gas under normal pressure conditions (14~21 psi) Upper slit in open-bottom cases maintains a gas entering ratio of ~7% compared with the perfectly sealed case University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 18
Bubbles Moving Down in the SEN LPM (Water)_.8 SLPM (Argon) LPM (Water)_ 1.6 SLPM (Argon) - Bubbles look bigger with distance down the nozzle - University Perhaps: bubbles coalesce; or else larger bubbles accumulate with time of Illinois at Urbana-Champaign Metals Processing Simulation Lab Seong-Mook Cho 19 Bubble Size Change Near Nozzle Exit LPM (Water)_1.6SLPM (Argon) - Bubbles smaller at the nozzle bottom - Bubbles coalesce at the top region of nozzle port (stagnant flow region) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Seong-Mook Cho 2
Argon Bubble Size Distribution through the Nozzle LPM (Water)_.8 SLPM (Argon) 24 1 24 1 24 1 9 22 22 9 22 2 nd 3 rd 9 9 2 4 th 2 2 8 18 18 7 7 8 18 7 8 d 7 16 avg =.77 mm d 16 avg =.91 mm 16 d avg = 1.29 mm 14 6 14 6 14 6 n 12 4 3 12 12 1 π ( r k ) 4 1 1 3 4 4 8 8 8 d k=1 3 3 3 3 6 avg = 2 6 6 nπ 2 2 2 4 4 4 2 1 2 1 2 1 ~ 1.6~ 2 1.2~ 3 1.8~2.4~ 4 3.~3.6~ 6 7 4.2~ 8 4.8~ 9.4~ 1 6.~ 11 12 ~ 1.6~ 2 1.2~ 3 1.8~2.4~ 4 3.~3.6~ 6 7 4.2~ 8 4.8~ 9.4~ 1 6.~ 11 12 1 2 3 4 6 7 8 9 1 11 12 ~.6~ 1.2~ 1.8~2.4~ 3.~3.6~ 4.2~ 4.8~.4~ 6.~.6 1.2 1.8 2.4 3. 3.6 4.2 4.8.4 6. 6.6 24 1 9 22 th 9 2 8 18 d 7 16 avg = 1.3 mm 7 14 6 12 1 4 8 3 6 2 4 2 1 ~ 1.6~ 2 1.2~ 3 1.8~2.4~ 4 3.~3.6~ 6 7 4.2~ 8 4.8~ 9.4~ 1 6.~ 11 12.6 1.2 1.8 2.4 Row 3. 3.6 Numbers 4.2 4.8.4 6. 6.6v 24 1 9 22 9 8 th 2 8 18 7 d 16 avg = 2.2 mm 7 14 6 12 1 4 8 3 6 2 4 2 1 1 2 3 4 6 7 8 9 1 11 12 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Seong-Mook Cho 21.6 1.2 1.8 2.4 3. 3.6 4.2 4.8.4 6. 6.6 24 1 9 22 6 th 9 2 8 18 d 7 avg = 1.19 mm 7 16 14 6 12 1 4 8 3 6 2 4 2 1 ~ 1.6~ 2 1.2~ 3 1.8~2.4~ 4 3.~3.6~ 6 7 4.2~ 8 4.8~ 9.4~ 1 6.~ 11 12.6 1.2 1.8 2.4 3. 3.6 4.2 4.8.4 6. 6.6 24 1 9 22 9 9 th 2 8 18 7 d 16 avg = 2.6 mm 7 14 6 12 1 4 8 3 6 2 4 2 1 1 2 3 4 6 7 8 9 1 11 12.6 1.2 1.8 2.4 3. 3.6 4.2 4.8.4 6. 6.6 24 1 9 22 9 7 th 2 8 18 d 7 avg = 1.81 mm 7 16 14 6 12 1 4 8 3 6 2 4 2 1 ~ 1.6~ 2 1.2~ 3 1.8~2.4~ 4 3.~3.6~ 6 7 4.2~ 8 4.8~ 9.4~ 1 6.~ 11 12.6 1.2 1.8 2.4 3. 3.6 4.2 4.8.4 6. 6.6 Gas Volume Fraction Evolution Argon gas volume fraction (%) 3. 2. 2. 1. 1.. Injected gas volume fraction: 2.4%. 2 3 4 6 7 8 9 Region - Bubble accumulation? - Calculating drift flux of bubble is needed to obtain gas void fraction considering argon and water superficial velocities, and bubble size. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Seong-Mook Cho 22
Part 2: Conclusion Bubble Size Distribution in SEN Average bubble size is smaller in SEN upper regions, but larger in lower SEN regions Small gas bubbles appear at SEN bottom, but large bubbles are found close to SEN port upper region Measured gas volume fraction increases in general along the downward SEN direction, but still smaller than the superficial gas volume fraction University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Seong-Mook Cho 23 Acknowledgments Continuous Casting Consortium Members (ABB, ArcelorMittal, Baosteel, Magnesita Refractories, Nippon Steel, Nucor Steel, Postech/ Posco, Severstal, SSAB, Tata Steel, ANSYS/ Fluent) Rob Nunnington at Magnesita University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Rui Liu 24