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Transport and Entrapment of Particles in Steel Continuous Casting

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Abstract

A particle-capture model based on local force balances has been developed, implemented into computational models of turbulent fluid flow and particle transport, and applied to simulate the entrapment of slag inclusions and bubbles during the continuous casting of steel slabs. Turbulent flow of molten steel is computed in the nozzle and mold using transient computational fluid flow models, both with and without the effects of argon gas injection. Next, the transport and capture of many particles are simulated using a Lagrangian approach. Particles touching the dendritic interface may be pushed away, dragged away by the transverse flow, or captured into the solidifying shell according to the results of a local balance of ten different forces. This criterion was validated by reproducing experimental results in two different systems. The implications of this criterion are discussed quantitatively. Finally, the fluid flow/particle transport model results and capture criterion are applied together to predict the entrapment distributions of different sized particles in a typical slab caster. More large particles are safely removed than small ones, but the entrapment rate into the solidifying shell as defects is still very high.

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Abbreviations

ρ :

Density (kg/m3)

ρ f :

Liquid density (kg/m3)

ρ p :

Particle density (kg/m3)

u :

Liquid velocity (m/s)

v :

Particle velocity (m/s)

t :

Time (s)

p :

Pressure (Pa)

μ :

Dynamic viscosity of fluid (Pa s)

ν :

Kinematic viscosity of fluid (m2/s)

f :

Body force density (per unit volume) (N/m3)

x p :

Particle position vector (m)

m p :

Mass of a particle (kg)

F D :

Drag force (N)

F L :

Lift force (N)

F added-mass :

Added mass force (virtual mass force) (N)

F G :

Gravitational force (N)

F press :

Pressure gradient force (N)

F stress :

Stress gradient force (N)

F I :

Magnitude of Van de Waals interfacial force (N)

F Grad :

Magnitude of surface energy gradient force (N)

F lub :

Magnitude of lubrication force (N)

V sol :

Solidification front advancing speed (m/s)

R p :

Particle radius (m)

r tip :

Dendrite tip radius (m)

a 0 :

Liquid atomic radius (m)

h 0 :

Distance between dendrite tip and particle (m)

Δσ 0 :

Surface energy difference (J/m2)

σ sp :

Surface tension between shell and particle (J/m2)

σ sl :

Surface tension between shell and liquid (J/m2)

σ pl :

Surface tension between particle and liquid (J/m2)

ξ :

Distance between dendrite tip center to particle center (m)

χ :

Solidification direction (m)

η :

Direction across solidification (m)

g :

Gravity acceleration (m/s2)

d p :

Particle diameter (m)

C D :

Drag coefficient

Rep :

Particle Reynolds number

u 1 :

Streamwise liquid velocity (m/s)

v 1 :

Streamwise particle velocity (m/s)

U s :

Relative streamwise velocity between liquid and particle (m/s)

G :

Wall normal velocity gradient of u 1 (1/s)

C A :

Correction factor on added mass force

Ac:

Acceleration parameter

α :

Constant for surface energy gradient force

β :

Constant for surface energy gradient force (m)

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Acknowledgments

The authors wish to thank the National Science Foundation (Grants DMI-01-15486 and CMMI-11-30882) and the Continuous Casting Consortium at the University of Illinois for support of this project. Thanks are also due to the National Center for Supercomputing Applications at the University of Illinois for computing time.

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Authors and Affiliations

  1. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign (UIUC), 1206 W. Green Street, Urbana, IL, 61801, USA

    Brian G. Thomas (C.J. Gauthier Professor), Quan Yuan (Former Graduate Student), Sana Mahmood (Former Graduate Student), Rui Liu (Graduate Student) & Rajneesh Chaudhary (Former Graduate Student)

  2. UOP, A Honeywell Company, 25 E Algonquin Rd, Des Plaines, IL, 60017, USA

    Quan Yuan (Former Graduate Student)

  3. Caterpillar Inc., 100 NE Adams Street, Peoria, IL, 61629, USA

    Sana Mahmood (Former Graduate Student)

  4. ABB Corporate Research Center, Whitefield Road, Bangalore, 560048, Karnataka, India

    Rajneesh Chaudhary (Former Graduate Student)

Authors
  1. Brian G. Thomas
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  2. Quan Yuan
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  3. Sana Mahmood
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  5. Rajneesh Chaudhary
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Corresponding author

Correspondence to Brian G. Thomas.

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Manuscript submitted July 30, 2012.

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Thomas, B.G., Yuan, Q., Mahmood, S. et al. Transport and Entrapment of Particles in Steel Continuous Casting. Metall Mater Trans B 45, 22–35 (2014). https://doi.org/10.1007/s11663-013-9916-7

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