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Coupling of CFD and PBE Calculations to Simulate the Behavior of an Inclusion Population in a Gas-Stirring Ladle

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Abstract

Gas-stirring ladle treatment of liquid metal has been pointed out for a long time as the processing stage is mainly responsible for the inclusion population of specialty steels. A steel ladle is a complex three-phase reactor, where strongly dispersed inclusions are transported by the turbulent liquid metal/bubbles flow. We have coupled a population balance model with CFD in order to simulate the mechanisms of transport, aggregation, flotation, and surface entrapment of inclusions. The simulation results, when applied to an industrial gas-stirring ladle operation, show the efficiency of this modeling approach and allow us to compare the respective roles of these mechanisms on the inclusion removal rate. The comparison with literature reporting data emphasizes the good prediction of deoxidating rate of the ladle. On parallel, a simplified zero-dimensional model has been set-up incorporating the same kinetics law for the aggregation rate and all the removal mechanisms. A particular attention has been paid on the averaging method of the hydrodynamics parameters introduced in the flotation and kinetics kernels.

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Abbreviations

B i :

Birth rate (m−3 s−1)

d :

Diameter (m)

D i :

Death rate (m−3 s−1)

C i :

Capture rate (m−3 s−1)

C 0 :

Total oxygen content (ppm m−3)

D Cu :

Diffusion coefficient of copper in liquid steel (m2 s−1)

F :

Interaction force density (kg m−2 s−2)

g :

Gravitational constant (m s−2)

H :

Reactor height (m)

K :

Kinetic energy of turbulence (m−2 s−2)

K 0 :

Kinetics constant (min−1)

N i :

Number density of inclusion of class i (m−3)

P :

Pressure (Pa)

t :

Time (s)

u :

Fluid velocity (m s−1)

S i :

Settling rate (m−3 s−1)

V :

Volume (m3)

Z bi :

Flotation rate (m−3 s−1)

α :

Volume fraction

β :

Collision kernel (m−3 s−1)

ε :

Dissipation rate of the kinetic energy of turbulence (m2 s−3)

μ :

Dynamic viscosity (kg m−1 s−1)

ρ :

Density (kg m−3)

τ :

Tensor of viscous sheer stress (kg m−1 s−2)

ω :

Mass fraction

d:

Deposition

g:

Gas

i:

Bin

k:

Fluid phase index

l:

Liquid

p:

Particle

s:

Settling

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Authors and Affiliations

  1. Institut Jean Lamour, UMR 7198, CNRS (‘LabEx DAMAS’)/Université de Lorraine, 54011, Nancy, France

    Jean-Pierre Bellot (Professor), Valerio De Felice (Scientist), Bernard Dussoubs (Scientist) & Alain Jardy (Scientist)

  2. Aubert & Duval, Les Ancizes Steel Plant BP1, 63770, Les Ancizes, France

    Stéphane Hans (Scientist)

Authors
  1. Jean-Pierre Bellot
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  2. Valerio De Felice
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  3. Bernard Dussoubs
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  4. Alain Jardy
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  5. Stéphane Hans
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Correspondence to Jean-Pierre Bellot.

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Manuscript submitted August 29, 2012.

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Bellot, JP., De Felice, V., Dussoubs, B. et al. Coupling of CFD and PBE Calculations to Simulate the Behavior of an Inclusion Population in a Gas-Stirring Ladle. Metall Mater Trans B 45, 13–21 (2014). https://doi.org/10.1007/s11663-013-9940-7

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