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Modeling mean flow and turbulence characteristics in gas-agitated bath with top layer

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Abstract

A numerical study is presented of the flow characteristics in a gas-agitated water bath in the presence of a top layer of dissimilar fluid. Two systems are considered, comprised separately of silicon and normal pentane as the top layer, to simulate slag cover in a real steelmaking process. The mathematical model involves solution of transport equations for the variables of each phase, with allowance for interphase transfer of momentum. Turbulence is assumed to be a property of the carrier (liquid) phase and represented through solution of additional transport equations for the turbulence kinetic energy, k, and its rate of dissipation, ɛ. The model also accounts for turbulence modulation by the bubbles through enhancement of the source terms in the equations for k and ɛ. The predicted mean and fluctuating velocities, stresses, and turbulence production are generally in the consensus of the experimental data. Both mean flow and turbulence characteristics are found to be suppressed in the water/silicon system of smaller density ratio, indicating enhanced re-entrainment of the top layer, than the water/normal pentane system.

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Abbreviations

a :

coefficients in the linearized equation

C b :

empirical coefficient for the G kb equation

C d :

drag coefficient

C μ, :

empirical coefficient in the eddy viscosity relation (Eq. [11])

d n :

nozzle diameter

d b :

bubble diameter

D :

phase-mass diffusion coefficient

f :

volume fraction

F :

volumetric interfluid friction

G k :

production of turbulence energy

G kb :

additional production of turbulence energy due to bubble migration

H :

total height of liquid bath (water and slag)

I :

volumetric interphase coefficient in the linearized equation

k :

turbulent kinetic energy

p :

static pressure

Q :

gas flow rate at the nozzle

r :

radial coordinate

r n :

nozzle radius

r*:

dimensionless radial distance (r/R)

R :

radius of cylindrical bath

S :

source term

u :

velocity component in the axial (x) direction

u 0 :

inlet gas velocity at the nozzle

u t :

derivative of turbulence intensity

u τ :

shear velocity

U r :

slip velocity vector

v :

velocity component in the radial (r) direction

x :

axial direction coordinate

x*:

dimensionless axial distance (x/H)

y :

normal distance from the wall

Z :

vertical distance from the nozzle

ɛ :

rate of dissipation of turbulent energy

γ :

interfacial tension

Γ :

transport coefficient

κ :

von Karman constant

φ :

generic flow variable

μ eff :

effective viscosity

μ l :

molecular viscosity

μ t :

turbulent viscosity

ρ :

density

σ :

Schmidt number

τ w :

wall shear stress

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Authors and Affiliations

  1. the Department of Mechanical, Industrial and Manufacturing Engineering, Northeastern University, 02115, Boston, MA

    Olusegun J. Ilegbusi (Associate Professor)

  2. the Division of Materials Science and Engineering, Hokkaiddo University, 060, Sapporo, Japan

    Manabu Iguchi (Professor)

  3. Sumitomo Metal Industries Ltd., 660, Hyogo, Japan

    Keiji Nakajima (Research Scientist)

  4. the Graduate School, Osaka University, 565, Osaka, Japan

    Mitsuhiro Sano (Graduate Student) & Mitsuru Sakamoto (Graduate Student)

Authors
  1. Olusegun J. Ilegbusi
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  2. Manabu Iguchi
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  3. Keiji Nakajima
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  4. Mitsuhiro Sano
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  5. Mitsuru Sakamoto
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Ilegbusi, O.J., Iguchi, M., Nakajima, K. et al. Modeling mean flow and turbulence characteristics in gas-agitated bath with top layer. Metall Mater Trans B 29, 211–222 (1998). https://doi.org/10.1007/s11663-998-0024-z

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  • DOI: https://doi.org/10.1007/s11663-998-0024-z

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