Inclusion Entrapment Literature Review and Modeling

Transcription

1 Inclusion Entrapment Literature Review and Modeling Lifeng Zhang Department of Mechanical &. Industrial Engineering University of Illinois at Urbana-Champaign October 8, University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

2 Acknowledgements The authors would like to thank: Accmold AK Steel Allegheny Ludlum Steel Columbus Stainless Steel LTV Steel Hatch Associates Stollberg, Inc. National Science Foundation National Center for the Supercomputing Applications (NCSA) Continuous Casting Consortium (CCC) at UIUC University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

3 Contents Background Review of Inclusions in Steel Fluid Flow and Particle Behavior in : Mold Water Model Fluid Flow and Inclusions Behavior in Steel Caster Pressure and Level Fluctuation of Top Surface of Mold Velocity, Turbulence Energy and Its Dissipation Rate for a Full-Developed Pipe Flow University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

4 Background Review of Inclusions in Steel University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

5 Steps of Inclusions Nucleation, Precipitation, Growth and Removal from Liquid Metals Processes Melting and Mixing of Deoxidizer Simultaneous events in Vessel top slag and refractory walls Phenomena Nucleation, Precipitation, and growth of particles Particle growth by coagulation or agglomeration Particle removal Stable suspension of inclusions in liquid steel Evolution Mechanisms:. Elements Diffusion ([O], [Al], or [Si]) (Ostwald- Ripening). Brownian collision Collision between particles (Brownian, Stokes, and turbulence collision) Rising by buoyancy, bubble flotation and flow transport Inclusion removal by -diffusion deoxidation - Interfacial reactions log (time) t=, Adding of deoxidizer Time for nucleation start Time for collisions to dominate size evolution University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

6 Evolution Mechnisms Related to Particle Size Independent of fluid flow Dependent on fluid flow in Ladles, Tundish and Mold Nucleation Particle growing Particle removal t t t t (rp>.µm) (rp>µm) (rp>4µm) (rp>5µm) log time Ostwald-Ripening (Elements Diffusion) Brownian collision Turbulent collision Stokes collision (no flow) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

7 Evaluation Methods of Steel Cleanliness Steel Cleanliness Inclusions in Steel Size Shape Direct Measurement of Inclusions: Metallographical microscope observation (two dimensional slices) Slime (time consuming) Others (Cone machining, laser, electrical, ultrasonic, sulfur print) Indirect Methods Total Oxygen (T.O.) measurement Nitrogen Pickup Dissolved Al loss for LCAK Steel Analysis of slag composition evolution Sampling difficulties Time consuming University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

8 Inclusions in Tunidsh Steel Samples Showing Liquid Slag Steel grade: LCAK Steel Source: Slime test Residual Typical composition: AlO 4%, SiO 9%, MnO %, FeO 6% CaO 4%, MgO.4%, others 4.6% University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

9 Alumina Inclusions in Continuous Casting Slab Steel grade: LCAK Steel Source: Slime test Residual Typical composition: AlO 96.%, SiO.%, MnO.%, FeO.% University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

10 Alumina Clusters in Carbon Steel [] [] R.Rastogi and A. W. Cramb. Inclusions Formation and Agglomeration in Aluminum Killed Steels. 84 th Steelmaking Conference Proceedings, ISS, Warrendale, PA, USA, P University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

11 Example of Total Oxygen, Al loss, Nitrogen Pickup 4 [] 4 From ladle to mold [] From ladle to tundish [] [4] 8 Sliver Index Al loss (ppm) T.O (ppm) %FeO in ladle slag (%) [] Bonila C. et al. 78 th th Steelmaking Conference Proceedings, Vol.78, 995, p69-65 [] Chakraborty S. et al. 77 th th Steelmaking Conference Proceedings, Vol.77, 994, p89-95 [] Ahlborg K. V. et al. 76 th th Steelmaking Conference Proceedings, Vol.76, 99, p [4] Melville S. D. et al. 78 th th Steelmaking Conference Proceedings, Vol.78, 995, p University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

12 Al O Inclusion Absorption to Mold Flux Al O in mold flux (%) Experiment at Baosteel (99) LCAK Steel 5ton ladle 6ton tundish casting speed.m/min slab section: 5mmXmm casting time (min) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

13 Inclusion Phenomena in Continuous Casting Mold Inclusion Sources: Carrying in through nozzle Deoxidation Products Nozzle clog Entrainment of tundish/ladle slag (reoxidation by SiO, FeO, MnO in slag) Entrainment of mold slag by excessive top surface level fluctuation Reoxidation by air absorption from nozzle leaks Argon bubbles Precipitation of inclusion in low superheat, such as TiO Inclusion Removal: Buoyancy rising Fluid flow transport Attachment to bubble surface and fast rising (Bubble flotation) Inclusion growth by collision and Ostwald-Ripening Absorption from steel to slag at interface Inclusion Destination: Top slag layer (safe removal) Trapped in solidification shell (defect) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

14 Conclusion All inclusions phenomena in mold are greatly affected by bulk fluid flow pattern, thus it is important to study the fluid flow in mold. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

15 Cases of Fluid Flow and Inclusion Motion Simulation in the Current Report Water Model:. Large Eddy Simulation (LES) Random Walk Model for Particle Motion. Reynolds Stress Model (RSM) Random Walk Model for Particle Motion. k-e Model for Fluid Flow Random Walk Model for Particle Motion Streamline Model for Particle Motion 4. k-e Model for Top Surface Pressure and Level Fluctuation Steel Caster:. k-e Model for Fluid Flow Four Cases for Inclusion Motion by Random Walk Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

16 Fluid Flow and Particle Behavior in : Water Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

17 Sketch of : Water Model (a) and Simulation Domain (b) [] Submerged entry nozzle Water x z Free Slip y.8m.965m 5 o down inflow V=.69m/s.5m Inlet Jet: 5 o down A' A Widefaces Narrowfaces Outflow.5m Inlet Port Symmetry plane 5mm A-A' 56mm Outlet Port (a) (b) [] Yuan, Q., S.P. Vanka, and B.G. Thomas. Large Eddy Simulatios of Turbulence Flow and Inclusions Transport in Continuous Casting of Steel. Turbulence and Shear Flow Phenomena Second International Symposium, June 7-9. : KTH, Stockholm University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

18 Experimental and Simulation Parameters Nozzle port size/ Inlet port size (x y) (m) Nozzle angle Inlet jet angle Submergence depth (m) Mold/Domain height (m) Mold/Domain width (m) Mold/Domain thickness (m) Average inlet flow rate (m /s) Casting speed (m/s) Fluid density (kg/m ) Fluid kinetic viscosity (m /s) Particle size (diameter) (mm) Particle density (kg/m ) Corresponding alumina inclusion diameter in steel caster (µm) Inlet condition Experiment Simulation o 5 o LES pipe simulation results [] [] Yuan, Q., S.P. Vanka, and B.G. Thomas. Large Eddy Simulatios of Turbulence Flow and Inclusions Transport in Continuous Casting of Steel. Turbulence and Shear Flow Phenomena Second International Symposium, June 7-9. : KTH, Stockholm University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

19 Mesh for k-e and RSM Water Model Simulations x z NX=4 NY=86 NZ=4 Total Nodes: 6,96 y University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

20 Non-Uniform Inlet Condition (LES Skewed Pipe Flow Simulation) [] x-velocity (m/s) y-velocity (m/s) Y Y Z Turbulent energy (m/s) Z Turbulent energy dissipation rate (m/s) Y Y Z Z [] Yuan, Q., S.P. Vanka, and B.G. Thomas. Large Eddy Simulatios of Turbulence Flow and Inclusions Transport in Continuous Casting of Steel. Turbulence and Shear Flow Phenomena Second International Symposium, June 7-9. : KTH, Stockholm University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

21 du Particle Motion Equations dt pi = 4 u µ C ρ D P p, i = Re d P P ( u u ) ( ρ ρ) u p,i p,i, the particle velocity at i direction; x p,i p,i, the particle position at i direction; µ is the fluids viscosity; ρ p, ρ, the particle density and fluid density respectively; Re p, p,, the particle Reynolds number; C D, the drag force coefficient; dx p. i dt 4 C D = + Re p Pi other, i g, is the gravitational acceleration; a other,i, the other forces acceleration, which is ignored in the present study. i + g.65 (.86 Re ) p x P ρ P + a Boundary condition for particles: Escape from top surface and outlet, reflect from other faces (no entrapment to solidified shell) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

22 Random Walk Model Model: The particle interacts with fluid phase turbulent eddies over the eddy lifetime. When the eddy lifetime is reached, a new value of the fluids instantaneous velocity is obtained by applying a new value of random number ξ. Each eddy is characterized by: a Gaussian distributed random velocity fluctuation u, v, w, keeping constant over the characteristic lifetime of the eddies a lifetime scale, τ e Instantaneous fluid velocity: u = u + u u = ξ u for k-ε model ξ k u : the mean fluid phase velocity ξ : normally distributed random number. The expression of t e : τ e = C L k ε C L =.5. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

23 Effect of Turbulence Fluctuations on Particle Movement (Fluid Flow Simulation is by k-e Turbulence Model) Random Walk Model (Stochastic Model) : u = u + u Streamline Model (Non-Stochastic Model) : u = u u : The instantaneous fluid velocity u : the mean fluid phase velocity u : random velocity fluctuation University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

24 Particle Injection Method.5 Time step is.s, and at every time step, 98 particles are injected into mold through the 98 random positions on SEN port (as right figure). Total injection time is.6s, thus 58 inclusions are injected into the domain cast direction Thickness of the narrow face University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

25 Particle Distribution (Water Model ) Streamline Model Random Walk Model t=.6s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

26 Particle Distribution (Water Model ) Streamline Model.4.4 Random Walk Model t=.6s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

27 Particle Distribution (Water Model ) Streamline Model.4.4 Random Walk Model t=s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

28 Particle Distribution (Water Model ) Streamline Model.4.4 Random Walk Model t=s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

29 Particle Distribution (Water Model ) Streamline Model.4.4 Random Walk Model t=s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

30 Particle Distribution (Water Model ) Streamline Model.4.4 Random Walk Model t=s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

31 Particle Velocities Distribution.5m/s.5m/s Speed (m/s) Speed (m/s Streamline Model t=.6s Random Walk Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

32 Particle Velocities Distribution.5m/s.5m/s Speed (m/s) Streamline Model t=.6s Random Walk Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

33 Particle Velocities Distribution.5m/s.5m/s Speed (m/s) Speed (m/s) Streamline Model t=s Random Walk Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

34 Particle Velocities Distribution.5m/s.5m/s Speed (m/s) Speed (m/s) Streamline Model t=s Random Walk Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

35 Particle Velocities Distribution.5m/s.5m/s Speed (m/s) Speed (m/s) Streamline Model t=s Random Walk Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

36 Particle Velocities Distribution.5m/s.5m/s Speed (m/s) Speed (m/s) Streamline Model t=s Random Walk Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

37 Compare of Particle Velocities and Fluids Flow Velocities.5m/s.5m/s.5m/s Speed (m/s) Speed (m/s) Speed (m/s) Particle velocities (Streamline Model, s) Particle velocities (Random Walk Model, s) Fluid flow velocities (steady) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

38 Particle Escape Fraction Removal fraction to top surface (%) Random Walk Model Streamline Model -s -s -s -s Escape fraction to outlet(%) Random Walk Model Streamline Model -s -s-s-s-s Removal fraction to top surface (%) Random Walk Model Streamline Model Experiments -s -s Conclusions: Random walk model is better than streamline model to predict the inclusions motion in mold because considering the effect of turbulence fluctuation. (In s, Random walk model: 7% removal; Streamline model: 65%; Experiments: 5% ) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

39 Comparison between Different Turbulence Models Non-uniform inlet condition. Large Eddy Simulation (LES). Reynolds Stress Model (RSM). k-e Two Equation Model Uniform inlet condition. k-e Two Equation Model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

40 Comparison between Uniform Inlet and Non-Uniform Inlet (k-e Model) Uniform inlet Vx=.9594 m/s Vy= m/s Vz=-. m/s k=.8 m /s ε=.5786 m /s Non-uniform inlet From LES Simulation scale:.5m/s scale:.5m/s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

41 Comparison between Different Turbulence Models (Non-Uniform Inlet Condition) K-e RSM LES scale:.5m/s scale:.5m/s scale:.5m/s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

42 Speed along Four Vertical Lines by Different Turbulence Models and Measurement. 5mm from SEN. mm from SEN. 46mm from SEN. 9mm from SEN.... distance from top surface (m) distance from top surface (m) distance from top surface (m) distance from top surface (m) Uniform inlet k-ε Non-uniform inlet LES k-ε RSM Experiment Experiment speed (m/s) speed (m/s) speed (m/s) speed (m/s) Conclusion: Uniform inlet k-e underpredicts velocity peaks. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

43 Enlargement of the Speed the line of 46mm from SEN on the central wide section distance from top surface (m) Uniform inlet k-ε Non-uniform inlet LES k-ε RSM Experiment Experiment Peak of RSM and Experiments Peak of k-ε and LES 46mm from SEN speed (m/s) Conclusion: RSM model has slightly better prediction on the position of the peak for the line 46mm from SEN on the central wide section. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

44 Particle Distribution by k-e and LES k-e LES t=.6s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

45 Particle Distribution by k-e and LES k-e LES t=.6s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

46 Particle Distribution by k-e and LES k-e LES t=s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

47 Particle Distribution by k-e and LES k-e LES t=s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

48 Particle Escape Fraction Removal fraction to top surface (%) k-ε LES RSM Experiment 6% 66% 57% -s -s -s 5% Fraction to outlet (%) 4 k-ε LES RSM 7% % -s -s -s 9% Conclusion: RSM model has a best prediction of particle removal fraction compared to the experiments results. LES model overpredicts particle removal fraction and k-e far underpredicts particle removal fraction. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

49 Computation Time Consuming LES: more than days To reach a residual of - 6 as convergence criterion, the computation time are as follows: RSM: 4 hours k-e: hours University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

50 Fluid Flow and Inclusion Behavior in Steel Caster (Random Walk k-e) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

51 Nozzle angle Inlet jet angle Mold/Domain height (m) Mold/Domain width (m) Casting speed (m/s) Fluid density (kg/m ) Particle density (kg/m ) Inlet condition Turbulence model Inclusion motion model Experimental and Simulation Parameters Nozzle port size/ Inlet port size (x y) (m) Submergence depth (m) Mold/Domain thickness (m) Average inlet flow rate (m /s) Fluid kinetic viscosity (m /s) Particle size (diameter) (µm) Boundary condition for inclusions Simulation ,, 5, 5 LES pipe simulation results Random walk model Escape from top surface and open bottom, reflect from other faces University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang () 5 o 5 o k-ε

52 Mesh and Velocity Distribution at Central Face distance fron nozzle center (m) distance from top surface (m) m/s distance fron nozzle center (m) distance from top surface (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

53 Magnified Velocity Distribution on Central face m /s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

54 Different Size Particle distribution diatance from top surface (m).5.5 mm diatance from top surface (m).5.5 5mm diatance from top surface (m).5.5 mm diatance from top surface (m).5.5 5mm distance from nozzle center (m) distance from nozzle center (m) distance from nozzle center (m).6s 4s distance from nozzle center (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

55 Escape Fraction for Different Size Inclusions removal fraction to top surface (%) µm µm 5µm 5µm -s -s -s -4s time period Conclusions: removal fraction (%) s 4 inclusion size (µm) top surface With increasing size, inclusion removal to the top surface becomes easier. Smaller inclusions are much easily transported by the flow out of the bottom. Fraction (%) s 7% 5% % 6% 5µm 5µm µm µm 4% % % open bottom.6% University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

56 mm Inclusion Distribution with Time Increasing diatance from top surface (m).5.5 diatance from top surface (m).5.5 diatance from top surface (m).5.5 diatance from top surface (m).5.5 t=.6s t=.6s t=s t=s distance from nozzle center (m) distance from nozzle center (m) distance from nozzle center (m) distance from nozzle center (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

57 mm Inclusion Distribution with Time Increasing diatance from top surface (m).5.5 diatance from top surface (m).5.5 diatance from top surface (m).5.5 diatance from top surface (m).5.5 t=s t=4s t=s t=68.7s distance from nozzle center (m) distance from nozzle center (m) distance from nozzle center (m) distance from nozzle center (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

58 mm Inclusion Distribution with Time Increasing diatance from top surface (m).5.5 diatance from top surface (m).5.5 diatance from top surface (m).5.5 diatance from top surface (m).5.5 diatance from top surface (m).5.5 t=s t=48.7 t=98.7s t=48.7s t=4s distance from nozzle center (m) distance from nozzle center (m) distance from nozzle center (m) distance from nozzle center (m) distance from nozzle center (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

59 Conclusion about Inclusion Distribution along Slab Wideness 5 Conclusion from simulation: Inclusion amount at the center of mold is less than that at other places. inclusion amount (/cm ) 4 /4 slab wideness / slab wideness Microscope observation S print Proof from industrial experiments University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

60 mm Inclusion Distribution with Time Increasing diatance from top surface (m) diatance from top surface (m) diatance from top surface (m) diatance from top surface (m) diatance from top surface (m) diatance from top surface (m) thickness (m ) -.. thickness (m ) -.. thickness (m ) -.. thickness (m ) -.. thickness (m ) -.. thickness (m ) t=.6s t=.6s t=s t=s t=s t=4s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

61 mm Inclusion Distribution with Time Increasing diatance from top surface (m) diatance from top surface (m) diatance from top surface (m) diatance from top surface (m) diatance from top surface (m) diatance from top surface (m) thickness (m ) -.. thickness (m ) -.. thickness (m ) -.. thic kness (m) -.. thickness (m ) -.. thickness (m ) t=s t=68.7s t=s t=48.7s t=98.7s t=4s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

62 fraction of inclusions remaining in domain, η remain (%) Removal of mm Inclusions with Time Increasing Conclusions Calculation Fitting of calculation η remain = exp[((-t)/5)] time (s) Inclusions require about min to leave the domain of mold region (4m). The total removal fraction to top surface is 6%, escape fraction to open bottom is 7%. In min, the casting length is 8.4m, but the domain is 4m. So if ignoring the inclusions entrapment to solidified shell, the steel in the domain will become dirty more and more with time increasing University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang () Fraction of inclusions remaining in domain (%) Calculation Extroplation t (s) t=54s

63 Removal of mm Inclusions with Time Increasing 4.5 Fraction of inclusions (%) removed to top surface escaped from open bottom remaining in the domain Inclusion diameter: µm d(η r )/dt (%/s) Fraction of inclusions to top surface (%):η r Inclusion diameter: µm. 4 t (s) t (s) 5 Conclusions: After t=7s, inclusions removal to top surface becomes less than.5%. At t=7s, the cast length is 4.m, which is similar with domain length. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

64 Effect of Inclusion Entrapment to Solidified Shell Non-Entrapment Model: previous simulations assume that if inclusions collide with solidified shell, they will be reflected. Entrapment Model: if inclusions collide with solidified shell, they will be entrapped. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

65 Inclusion fraction to faces (%) Effect of Inclusion Entrapment to Solidified Shell (s) Non-Entrapment Model % Top surface Bottom -s -s -s -s University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang () Inclusion fraction to faces (%) Entrapment Model % Top surface Narrow face Wide faces Bottom Entrapment Model: Top surface: %, entrapped to wide faces: 54%, narrow face: 9%, flow away from bottom: %, remain in domain: % (Total escape in s: 97%) Non-Entrapment model: Top surface: 6%, flow away from bottom: %, remain in domain: 8% (Total escape in s: 7%) %

66 Inclusion Distribution (s) diatance from top surface (m) diatance from top surface (m).5.5 diatance from top surface (m) diatance from top surface (m) d ista nce from no zzle ce nte r (m ) -.. thic kness (m ) Non-entrapment model distan ce fro m n ozzle center (m) Entrapment model -.. thick nes s (m ) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

67 Inclusion Distribution (s) diatance from top surface (m) diatancefrom topsurface (m).5.5 diatance from top surface (m) diatancefrom topsurface (m) d istan ce fro m n o zzle ce n te r (m ) -.. thick nes s (m ) d istan ce fro m n o zzle ce n te r (m ) -.. thick nes s (m ) Non-entrapment model Entrapment model University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

68 The Accuracy of the Similarity Criterion of Stokes Velocity for the Particle Motion in Water and in Liquid Steel University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

69 The Accuracy of the Similarity of the Particle Motion between Water and Liquid Steel Stokes Velocity Mold Geometry Outlet Steel Caster Water Model Same (The previous water model case) Two holes on lower part of one wide face Density (kg/m ) Viscosity (m /s) Particle size Particle density (kg/m ) µm mm 988 V s = ( ρ ρ ) P 8µ d P g The Stokes velocity of the particles in water is the same as that of the inclusions in liquid steel. (V s =.786m/s) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

70 Particle Stokes Terminal Rising Velocity in Liquid Force balance on particle: Drag force=gravitational force For Re < p C D C D = ρu P 4 Re A P P = 6 ( ρ ρ) g πd P P V s = ( ρ ρ ) P 8µ d P g V S : Stokes velocity, m/s ρ, ρ p, liquid and particle density, kg/m d p, particle diameter, m µ, liquid viscosity, kg/m.s g, gravitational acceleration, m/s A p : Intersection area of particle, m University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

71 Particle Stokes Terminal Rising Velocity in Liquid Stokes velosity of particles (m/s) Liquid steel system: ρ p =7kg/m ρ=7kg/m µ=.67kg/m.s Water model system: ρ p =988kg/m ρ=998kg/m µ=.kg/m.s d p (m) V s = ( ρ ρ ) P 8µ d V S : Stokes velocity, m/s ρ, ρ p, liquid and particle density, kg/m d p, particle diameter, m µ, liquid viscosity, kg/m.s g, gravitational acceleration, m/s P g University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

72 Comparison Between Liquid Steel and Water Model removal fraction to top surface (%) Particles in water and liquid steel have the same Stokes Velocity d p =47µm, ρ p =7 kg/m in liquid steel d p =.8mm, ρ p =988 kg/m in water -s -s -s Escape fraction in s (%) Particles in water and liquid steel have the same Stokes Velocity top surface d p =47µm, ρ p =7 kg/m in liquid steel d p =.8mm, ρ p =988 kg/m in water s outlet time period The difference of particle removal fraction in water and liquid steel shows that the Stokes rising velocity is not a reasonable criterion for matching the particle behavior in water with inclusion behavior in liquid steel. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

73 Comparison Between Liquid Steel and Water Model Steel caster: Previous Steel caster case (length : 4m, open bottom as outlet) Water Model: Previous Water Model (length:.5m, two holes at under part of wide face as outlet) Stokes Velocity: Inclusions in steel Particles in water.6m/s.786m/s removal fraction to top surface (%) d p =µm, ρ p =7 kg/m in liquid steel d p =.8mm, ρ p =988 kg/m in water -s -s -s time period Escape fraction in s (%) top surface d p =µm, ρ p =7 kg/m in liquid steel d p =.8mm, ρ p =988 kg/m in water s outlet University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

74 Pressure on the Top Surface and Level Fluctuation of Mold University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

75 Experimental and Simulation Parameters [] Nozzle inner diameter (m) Nozzle outer diameter (m) Nozzle port size/ Inlet port size (x y) (m) Nozzle angle Inlet jet angle Submergence depth (m) Mold/Domain height (m) Mold/Domain width (m) Mold/Domain thickness (m) Average inlet flow rate (m /s) Casting speed (m/s) Fluid density (kg/m ) Fluid kinetic viscosity (m /s) Inlet condition (Nozzle) Top oil density Experiment o downward 5 o downward Uniform inlet velocity and k, ε 98 [] J. Anagnostopoulos and G. Bergeles. Metall. Mater. Trans. B., Vol.B, 999, p95-5 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

76 Mesh and Velocity Distribution m/s Y m/s Y Z X Z X Nozzle Mold University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

77 Calculated Pressure Distribution at Top Surface and Measured Surface Level Gauge Pressure (atm) (m) Calculation by Anagostopoulos et al [] [] P-P atm (pascal) mold half width (m) [] J. Anagnostopoulos and G. Bergeles. Metall. Mater. Trans. B., Vol.B, 999, p95-5 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

78 Mold Surface Level Calculated from Pressure at Center Line along Width direction on Top Surface ( p p ) atm Level = ( ρ ρ )g water oil level (m) Calculation Experiment Experiment water: kg/m oil: 98 kg/m mold half width (m) level (m) Calculation Experiment Experiment water: kg/m no oil mold half width (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

79 Turbulence Energy Distribution at Top Surface (m) (m) Turbulent Kinetic Energy (k) (m/s) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

80 Level Fluctuation Calculated from Turbulence Energy at Center Line along Width direction on Top Surface..5 Level Fluctuation = ρwaterk ( ρ ρ )g water oil k (m /s ) X. Huang, B.G.Thomas Modeling Transient Flow Phenomena in Continuous Casting of Steel, in 5 th th Conference of Metallurgist, B, C. Twigge-Molecey eds, (Montreal, Canada: CIM, 996), 9-56 level fluctuation (mm) mold half width (m) water: kg/m oil: 98 kg/m mold half width (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

81 Velocity, Pressure, Turbulent Energy at Top Surface for the Former Liquid Steel System Mold thickness (m). -. m/s Speed (m/s) Mold thickness (m) Mold thickness (m) Mold half width (m) Mold half width (m) Mold half width (m) Gauge Pressure (pascal) Turbulent Energy (m/s) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

82 Calculated Surface Level and Its Fluctuation for the Liquid Steel System P-P atm (pascal) mold half width (m) level (m) 5 liquid steel: 7kg/m 5 powder: kg/m mold half width (m) k (m /s ) mold half width (m) level fluctuation (mm) liquid steel: 7kg/m powder: kg/m mold half width (m) University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

83 Velocity, Turbulence Energy and Its Dissipation Rate for a Full-Developed Pipe Flow University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

84 Velocity Distribution along Radial Direction [] rr x R u u u max r = R.84 n =.8Re u = n ( n + )( n + ) x,max u x Re ud = ν n u: velocity in x axial direction u max : maximum value of u Re: Reynolds number R: radius of pipe u: average velocity along radial direction n: power of velocity distribution r: distance along radial direction [ ] H. Schlichting. Boundary-Layer Theory, 979, 7th ed., p599 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

85 Velocity Distribution along Radial Direction..8.6 u/u max.4.. LES, Re=54 [] DNS, Re=5 [] Schlichting's equation, Re=54 [] r/r [] Bin Zhao s LES simulation [] J. G. M. Eggels et al. J. Fluid Mech. (994), Vol.68, pp75-9 [] H. Schlichting. Boundary-Layer Theory, 979, 7th ed., p599 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

86 Turbulence Energy and Its Dissipation along Radial Direction k u * 4 C max µ u = u * n r.4.8 R r.6 R r R ( n) n 4 max ε u = u * D n u * r.4.8 R r.6 R r R ( n) n k: turbulence energy ε: turbulence energy dissipation rate u*: shear velocity at wall u max : maximum value of u D: diameter of pipe R: radius of pipe n: power of velocity distribution r: distance along radial direction University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

87 Turbulence Energy Distribution along Radial Direction 5 4 LES, Re=54 [] DNS, Re=5 [] Lifeng's equation (k-ε), Re=54 k/u* r/r [] Bin Zhao s LES simulation [] J. G. M. Eggels et al. J. Fluid Mech. (994), Vol.68, pp75-9 University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

88 Conclusions. For the fluid flow calculation in a full scale water model, uniform inlet k-e underpredicts velocity peaks. With non-uniform inlet condition, all of k-e, RSM and LES turbulence models have good agreement with experiment measurement. However, RSM model has slightly better prediction at some places, and k-e model takes least time consuming.. For the particle motion, random walk model is better than streamline model because considering the effect of turbulence fluctuation.. It is concluded that entrapment of inclusions to walls has very strong effect to inclusion removal. The suitable entrapment model needs further development. 4. For the particle motion in full scale water model, RSM model has a best prediction of particle removal fraction compared to the experimental results. LES model overpredicts and k-e far underpredicts. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

89 Conclusions 5. From the calculation of inclusion removal in steel caster (k-e, random walk and without consideration of entrapment to walls), with increasing size, inclusion removal to the top surface becomes easier. Inclusions require about min to leave the domain of mold region (4m), and the total removal fraction to top surface is 6%, escape fraction to open bottom is 7%. After t=7s, inclusions removal to top surface becomes less than.5%. 6. The difference of particle removal fraction in water and liquid steel shows that the Stokes rising velocity is not a reasonable criterion for matching the particle behavior in water with inclusion behavior in liquid steel. 7. The top surface level and its fluctuation can be approximately estimated from the calculated pressure distribution for the flat top surface. 8. The developed models for the velocity and turbulence energy distribution for a full-developed pipe flow agree well with LES and DNS simulation. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()

90 Further Investigations The transient fluid flow simulation for the steel caster mold. The suitable entrapment model of inclusion to the solidified shell. The inclusions collision and coagulation simulation and its contribution to inclusion size growth and removal. 4 The interaction between inclusions and bubbles and its contribution to inclusion motion (removal) from mold. University of Illinois at Urbana-Champaign Metals Processing Simulation Lab Lifeng Zhang ()