CCC Annual Report UIUC, August 9, 25 Particle Capture in Mold including Effect of Subsurface Hooks Kai Jin Department of Mechanical Science & Engineering University of Illinois at Urbana-Champaign Objective Develop a model to include effects of hook on particle\bubble capture; Use advanced capture criterion [-3] combined with hook capture mechanism to study the particle/bubble capture; University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 2
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 Sample Layer Number 2 3 4 5 6.785d true = d visible [4] Convert visible to true University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 3 Schematic of Hook Capture Mechanism Casting direction Hook zone A particle/bubble enters into a hook zone has three different possible fates f o is the mold oscillation frequency Time t=t vc Δt Time t = t + t Capture by hook NF or WF Hook structure depth Solidified Shell z x Solid-liquid interface vf c o a bubble or inclusion v c v f Shell Note: Shell. 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 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 4 c o h v c Projection Escape from hook zone Capture by WF/NF Shell thickness h = K t
Flow Chart of Hook Capture Mechanism Continue No No particle in hook zone Yes particle has stayed in hook zone for t c > t hook Yes Particle re-entering hook zone by hook t c =t 2 t c = t c = t hook a critical time, allows particle/bubble to travel before it is captured by the hook, on average, we take thook =.5 f o t c time of a particle remained in the hood zone since it enters. Reset t c to when particle cross the hook zone boundary (consider a particle re-entering the hook zone) vf c o v c t c =t t c = t c = t c = Particle path t : time taken for particle travel on yellow path; t <t hook, particle escaped from hook zone. t 2 : time taken for particle travel on green path; t 2 >t hook, particle is captured by the hook. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 5 PDAS (μm) 25 2 5 Add hook capture mechanism into advanced capture criterion [-3] NF WF 5.5.5 2 2.5 Distance below meniscus (m) Continue Drift back to flow yes Particle contacts a boundary representing mushy-zone front? yes no Particle size larger than PDAS (d p PDAS)? no In solidification direction, repulsive force smaller than attractive force? FL FD, 2 FLub FGrad FI cosθ < ( ) ( FD, η + FB, η) + ( FL FD, χ) > ( FLub FGrad FI) Flow chart showing the modified and original advanced capture criterion; Hook capture mechanism are added in to FLUENT using UDF; no Particle in hook zone Satisfies Hook Capture Criterion University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 6 no χ yes yes Can cross-flow and buoyancy drive particle into motion though rotation? yes cosθ sinθ sin 2θ, if F Dη andf Bη in same direction ( F F ) + D, B, ( F F L D, ) > ( F F F η η χ Lub Grad I ) Capture or cosθ sinθ sin 2θ, if F Dη andf Bη in opposite direction and F Dη F Bη no or FB, η FD, η cosθ+ FL FD, χ sinθ > FLub FGrad FI sin2θ, if F Dη andf Bη in opposite direction and F Dη <F Bη ( ) ( ) ( ) A /Particle Touching 3 Dendrite Tips [3] Flow chart for Ar bubble/particle capture criterion [3] no yes
Ar Distribution Rosin-Rammler distribution, with mean 3mm* Step, Obtain flow field with two-way coupled Euler-Lagrangian simulation: using 5 largest groups of bubbles Step 2, Inject and track all groups of all 25, bubbles. s < mm <% Volume fraction Repeat Step: times ~2.5 million bubbles tracked using each capture criterion * Mean based on model by H. Bai & BG Thomas, MMTB, 2 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 7 Governing Equations Using Reynolds decomposition, steel velocity u = U + u The time averaged continuity and momentum equations for liquid steel (turbulence viscosity μ t modelled by k-ε model [5] ) ρ U t ( ρu ) Smass-sink + = * T ( ) p ( t )( ) + ρ U U = + μ+ μ + momentum-sink + U+ U S S Force balance equations for each individual bubble ( d p, velocity u p, density ρ p, mass m p and volume V p ) Rep dup mp8μ C ρdp up u p p ( p ) D ρ Du du ρ Du g ρ ρ mp = 2 ( u up) +.5mp + mp + mp dt ρpdp 24 μ ρp Dt dt ρp Dt ρp FD Turbulence dispersion of particles: using Random Walk Model [7] University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 8 DPM Fv Fp Fb F D drag force, and drag coefficient C D from Morsi [6] ; F V virtual mass force; F p pressure gradient force; F b buoyancy/gravity
Random Walk Model [7] Gaussian distributed random velocity fluctuation, u, v and w are generated from u' = ζ u' 2 u v w k 2 2 2 ' = ' = ' = 2 /3 ζ standard normal distribution random number. Eddy life time: t = t k k ln ( r e L ) where tl = CL.5 r uniformly distributed random number from and. Eddy cross time 2 ρ pd p where τ = 8μ t cross 4/3 k Cμ = τ ln τ u up 3/2 new ζ Yes use k, ε and ζ to calculate fluctuations evaluate t e and t cross interaction time t inter = min(t e, t cross ) interaction time reached? No University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 9 Simulations and Number of s Injected During the bubble/particle tracking step, 244239 bubbles were in each simulation Number of s Tracked Casting Conditions Group i Diameter d i (mm) Number N i Casting Conditions Mold Thickness Width Value 23 3mm.25 96 Submergence Depth 6 mm 2.4 622 Port Downward Angle 5 deg. 3.8 3589 Casting Speed.5 m/min 4. 2826 Ar injection 8.2% vol. 5.2 8973 List of Simulations 6.3 52 Hook Depth t hook Osc. Frequency 7. 47564 (mm) (s) (Hz) 8 2. 89 A - - 9 3. 6522 B 3.25 2 4. 974 C 6.25 2 5. 3 Note: Total 244239 All Simulations are based on the some flow field solution Case A was old results presented in 24 CCC annual meeting; University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin
Y(m) OR -. -.5.5 SEN...2.3.4.5.6 IR Flow field [8] (same for all cases in hook study).4 m/s Ar Volume Fraction.8.6.4.2..8.6.4.2 Distance below top surface (m) -.2 -.4 -.6 -.8 2 3 U Mold m/s.3.2..9.8.7.6.5.4.3.2..2.4.6 x(m) Flow Field [8] 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; University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin -.2 -.4 WF hook captured bubbles (Hook depth 3mm, Simulation B) Reduce hook depth from 6 mm to 3 mm leads to: Less bubbles captured by hook (~2X less) especially for large bubbles ( mm); Locations of captured large bubbles are more close to meniscus; On WF, no d p > mm bubbles were capture by hook with 3mm hook depth; by IR-hook 3 2 2 8 4 4 (28 d p 3µm) 25 26.2.4.6 -.2 -.4 ( d p > 3µm).2.4.6 -.2 -.2 3 5 2 4 2 4 by 3 3 OR-hook -.4 8 4 -.4 2 2 4 (48 d p 3µm) 25 26 (6 d p > 3µm) Total 54 bubbles.2.4.6.2.4.6 capture by OR-hook. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 2 5 4 4 3 3 2 2 Diameter Total 28 bubbles capture by IR-hook.
by IR-hook by OR-hook -.2 -.4 -.2 -.4 WF hook captured bubbles (Hook depth 6mm, Simulation C) 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; -.2 3 2 5 4 2 4 3 3 8 4 -.4 2 2 4 (48 d p 3µm) 25 26 ( d p > 3µm).2.4.6.2.4.6 -.2 3 2 2 8 4 -.4 4 (53 d p 3µm) 25 26 (94 d p > 3µm).2.4.6.2.4.6 capture by OR-hook. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 3 5 4 4 3 3 2 2 Diameter Total 229 bubbles capture by IR-hook. Total 67 bubbles -.5.5 Small (d.3mm) on WF/NF and Their Distributions without Hook Capture Mechanism (Simulation A) Slide gate open to IR, more capture on IR due to more gas escape from IR side; port 3 2 2 8 4 4 25 26.5 WF-IR WF-OR NF 655 2.7% of -.5.5 port 3 2 2 8 4 4 25 26 388.6% of.5 -.2.2 Y(m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 4 -.5.5 3 2 2 8 4 4 26 25 3274.3% of
-.5.5 Capture Small s (d.3mm) on WF and NF with Hook Depth 3mm Simulation B ( by Force Balance and Hook) Slide gate open to IR, more capture on IR due to more gas escape from IR side; WF-IR WF-OR NF port 3 2 2 8 4 4 25 26 6577 2.7% of.5 -.5.5 port 3 2 2 8 4 4 25 26 3992.6% of.5 -.2.2 Y(m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 5 -.5.5 3 2 2 8 4 4 26 25 3284.3% of -.5.5 Capture Small s (d.3mm) on WF and NF with Hook Depth 6mm Simulation C ( by Force Balance and Hook) Slide gate open to IR, more capture on IR due to more gas escape from IR side; port 3 2 2 8 4 4 25 26.5 WF-IR WF-OR NF 6559 2.7% of -.5.5 port 3 2 2 8 4 4 25 26 454.7% of.5 -.2.2 Y(m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 6 -.5.5 3 2 2 8 4 4 26 25 3434.4% of
Effect of Hook Depth on Number of s (Compare Simulation with Measurements) Number of bubble captured 25 2 5 5 Center Region IR Number of bubble captured 25 2 5 5 Center Region OR Number of bubbles captured per sample layer; t hook =.25s for cases with hook capture mechanism Adv. (no hooks) based on average of simulations 5 5 5 5 Number of bubble captured 6 5 4 3 2 Quarter Region IR 5 6 4 5 4 3 Number of bubble captured 2 Quarter Region OR Number of bubble captured 3 2 NF 5 5 5 5 5 5 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 7 Effect of Hook Depth on Size of s (Compare Simulation with Measurements) Average Diameter (mm).5.4.3.2. Center Region IR 5 5 Average Diameter (mm).8.6.4.2 Center Region OR 5 5 Size: Average of bubbles captured in each sample layer Increasing hook depth: causes larger average in first 2 layers due to more large bubbles captured; Average Diameter (mm).8.6.4.2 Quarter Region IR.8.5.6.4 Average Diameter (mm).3.2. Quarter Region OR 5 5 5 5 5 5 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 8 Average Diameter (mm).4.2 NF
Effect of Hook Depth on Capture Fraction Capture Criteria Injected all ΣN(d i ) Injected mm N( mm) all Σn(d i ) mm n( mm) Fraction captured φ( mm) Fraction large ψ( mm) Simple* No hook [8] 2,442,39 475,64 28,944 27,799 5.84% 3.3% Adv. No Hook 2,442,39 475,64 37,372 432.9%.3% Adv. 3mm Hook 244,239 47,564 3,939 75.5%.5% Adv. 6mm Hook 244,239 47,564 5,249 848.7% 5.6% Experiment Unknown Unknown ~5 Unknown.2% ΣN(d i ): number of bubbles during the particle tracking step; *Simple: touch = capture N( mm): number of mm bubbles ; Σn(d i ): number of bubbles captured in the entire caster; n( mm): number of mm bubbles captured in the entire caster; φ( mm): the fraction of mm bubbles that were captured (captured mm / mm); ψ( mm): the fraction of captured bubbles that were mm (captured mm / captured all). In all of the measured sample layers, ~5 bubbles were observed; Only one large bubble (.4 mm ) was observed >.5 mm. Fraction of captured bubbles with d > mm is ψ( mm) =.2% (/5). Advanced capture criterion prediction of ψ( mm) =.3% matches plant measurement (.2%). Using 3mm hook depth gives slightly more large bubbles captured; Using 6mm hook depth leads to X more large bubbles captured near surface; University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 9 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 % 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 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 2
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 2 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- -3882 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 22
References [] Quan Yuan, PhD Thesis, University of Illinois at Urbana-Champaign, 24. [2] Sana Mahmood, MS Thesis, University of Illinois at Urbana-Champaign, 26. [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, 24, vol. 45, pp. 22 35. [4] Simon N. Lekakh, Vivek Thapliyal, and Kent Peaslee, in 23 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, 23 [5] Brian Edward Launder and D. B. Spalding, The Numerical Computation of Turbulent Flows, Comput. Methods Appl. Mech. Eng., 974, 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., 972, vol. 55, pp. 93 28. [7] A. D. Gosman and E. Loannides, Aspects of Computer Simulation of Liquid-Fueled Combustors, J. Energy, 983, vol. 7, pp. 482 9. [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., 25, vol. 84, p. 295. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Kai Jin 23