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Modeling of gas-liquid reactions in ladle metallurgy: Part II. Numerical simulation

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Abstract

A combined three-dimensional, Lagrangian-Eulerian model for gas-liquid flow in a ladle was developed. The model compared very well with available experimental results in Wood’s metal in terms of void fraction, liquid velocity, and plume bending. From the model, it was clear that the lateral lift force is responsible for plume spreading, whereas lateral drag forces bend the plume. The model was extended to include mass transfer to rising bubbles and at the free surface. The rate of reaction compared very well with the results of part I on the desorption of carbon dioxide from sodium hydroxide solutions.

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Abbreviations

C D :

drag coefficient

C L :

lifting coefficient

C T :

coefficient for the turbulent energy caused by shear work of bubbles

C VM :

virtual mass coefficient of bubbles

C µ :

constant of turbulent viscosity

G :

source term for turbulent energy caused by shear stress

K :

equilibrium constant

P :

dynamic pressure or turbulent energy caused by shear work of bubbles

S :

source terms

T :

time of bubble tracking

U :

velocity in ϑ direction

V :

velocity in r direction or volume

W :

velocity in z direction

\(\bar d\) :

average equivalent bubble diameter

F :

force

g :

gravitational acceleration

M L :

interfacial momentum exchange for liquid phase

S V :

source term for velocity components

U f :

fluctuation velocity

V :

velocity vector

k :

turbulent kinetic energy or reaction rate constant

r :

radius direction coordinate, or injector’s position

s :

distance in the ϑ direction

t :

time

z :

vertical direction coordinate

Φ:

general variable

Γ:

general diffusion coefficient

α :

volume fraction

δ :

coefficient, =1 for surface, =0 for internal control volumes

ɛ :

turbulent kinetic energy dissipation rate

μ :

dynamic viscosity

μ eff :

effective viscosity

μ t :

turbulent viscosity

ν :

kinematic viscosity

ϑ :

angular direction coordinate

ρ :

density

σ :

constant

ξ :

random number of Gaussian distribution

aq :

aqueous

b, bub:

bubble

e :

equilibrium

f :

fluctuation

g :

gas phase

l :

liquid phase

k :

the kth phase

s :

top surface

t :

turbulence or total

B :

buoyancy

CV :

control volume

D :

drag

EP :

turbulent kinetic energy dissipation rate

L :

lift

M :

mass

R :

relative (velocity)

TK :

turbulent kinetic energy

EP :

turbulent kinetic energy dissipation rate

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Authors and Affiliations

  1. the Department of Materials Science and Engineering, McMaster University, L8S 4L7, Hamilton, ON, Canada

    D. Guo (Senior Research Associate) & G. A. Irons (Dofasco/NSERC Industrial Research Chair in Process Metallurgy)

Authors
  1. D. Guo
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  2. G. A. Irons
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Guo, D., Irons, G.A. Modeling of gas-liquid reactions in ladle metallurgy: Part II. Numerical simulation. Metall Mater Trans B 31, 1457–1464 (2000). https://doi.org/10.1007/s11663-000-0030-2

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  • DOI: https://doi.org/10.1007/s11663-000-0030-2

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