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A 2D Axisymmetric Mixture Multiphase Model for Bottom Stirring in a BOF Converter

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Abstract

A process model for basic oxygen furnace (BOF) steel converter is in development. The model will take into account all the essential physical and chemical phenomena, while achieving real-time calculation of the process. The complete model will include a 2D axisymmetric turbulent multiphase flow model for iron melt and argon gas mixture, a steel scrap melting model, and a chemical reaction model. A novel liquid mass conserving mixture multiphase model for bubbling gas jet is introduced in this paper. In-house implementation of the model is tested and validated in this article independently from the other parts of the full process model. Validation data comprise three different water models with different volume flow rates of air blown through a regular nozzle and a porous plug. The water models cover a wide range of dimensionless number \( R_{\text{p}} \), which include values that are similar for industrial-scale steel converter. The k–ε turbulence model is used with wall functions so that a coarse grid can be utilized. The model calculates a steady-state flow field for gas/liquid mixture using control volume method with staggered SIMPLE algorithm.

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Abbreviations

ρ :

Density (kg m−3)

V :

Velocity vector (m s−1)

u,v :

Radial and axial velocity components (m s−1)

α :

Phase fraction

p :

Pressure (Pa)

g :

Gravity vector (m s−2)

τ :

Stress tensor

c :

Mass fraction

D :

Diffusion coefficient (m2 s−1)

Ω:

Volume (m3)

\( \varvec{V}_{{{\text{cd}}\infty }} \) :

Bubble terminal velocity (m s−1)

\( A_{\text{CS}} \) :

Bubble cross-section area (m2)

\( C_{\text{D}} \) :

Drag coefficient

d :

Diameter (m)

Re :

Reynolds number (dimensionless)

Mo :

Morton number (dimensionless)

μ :

Viscosity (Pa s)

\( N_{\mu } \) :

Fourth root of Morton number (dimensionless)

σ :

Surface tension (N/m)

k :

Turbulence kinetic energy (m2 s−2)

P :

Turbulence production due to shear flow

\( {\textit{P}}_{{{\text{b}}k}} \) :

Turbulence production due to bubbles

ε :

Turbulence dissipation rate (m2 s−3)

\( C_{\text{f}} \) :

Bubble friction coefficient

S :

Surface area (m2)

r,z :

Radial and axial coordinate (m)

n :

Surface unit normal vector

ϖ:

Weighing factor

M :

Molar mass (mol/kg)

R :

Molar gas constant (J mol−1 K−1)

T :

Temperature (K)

\( c_{\rho } \) :

Conversion coefficient from pressure to density (s2 m−2)

R :

Explicit residual vector

A :

Coefficient matrices for the system of equations

J :

Nozzle momentum source (kg m s−2)

\( \dot{m} \) :

Mass flux (kg s−1)

\( A_{\text{nozzle}} \) :

Nozzle area (m2)

K :

Nozzle turbulence kinetic energy source (kg m2 s−3)

t :

Time (s)

C :

Courant number (dimensionless)

\( C^{\text{vis}} \) :

Visous number (dimensionless)

ω :

Volume ratio (dimensionless)

Q :

Volume flow rate (m3 s−1)

\( d_{\text{nozzle}} \) :

Nozzle diameter (m)

H :

Bath height (m)

\( R_{\text{p}} \) :

Plume momentum ratio (dimensionless)

\( k - \varepsilon \) :

Turbulence model constants

σ k :

 = 1.0

σ ε :

 = 1.3

C μ :

 = 0.09

C ε1 :

 = 1.44

C ε2 :

 = 1.92

C ε3 :

 = 1.825

C k1 :

 = 1.0

m:

Mixture

c:

Continuous phase

d:

Dispersed phase

T:

Turbulence

D:

Diffusion

b:

Bubble

p:

Particle

eff:

Effective

\( {\text{n}},{\text{e}},{\text{s}},{\text{w}},{\text{p}} \) :

north, east, south, west, middle cell

i,j :

Grid coordinate directions

tot:

Total

a:

Air

i :

Initial value

g:

Gas

l:

Liquid

n :

Time level index

*:

Updated velocity value after momentum equation

‘:

Fluctuation of variable also used in pressure-correction algorithm as a correction

L, R:

Left, right

T:

Transpose

p :

Pressure matrix

V :

Momentum equation matrix

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Acknowledgments

This work was partly funded by the Finnish Funding Agency for Technology and Innovation (TEKES). The research was carried out as part of the Finnish Metals and Engineering Competence Cluster (FIMECC)’s SIMP 2.1 subprogram. This research was also supported by a grant from Technology Industries of Finland Centennial Foundation Fund for the Association of Finnish Steel and Metal Producers.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Aalto University, P.O. Box 16200, Vuorimiehentie 2, Espoo, 00076, Finland

    Ari Kruskopf (Doctoral Student)

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  1. Ari Kruskopf
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Correspondence to Ari Kruskopf.

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Manuscript submitted May 24, 2016.

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Kruskopf, A. A 2D Axisymmetric Mixture Multiphase Model for Bottom Stirring in a BOF Converter. Metall Mater Trans B 48, 619–631 (2017). https://doi.org/10.1007/s11663-016-0856-x

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