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Modeling of Radiative Heat Transfer in an Electric Arc Furnace

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Abstract

Radiation is an important means of heat transfer inside an electric arc furnace (EAF). To gain insight into the complex processes of heat transfer inside the EAF vessel, not only radiation from the surfaces but also emission and absorption of the gas phase and the dust cloud need to be considered. Furthermore, the radiative heat exchange depends on the geometrical configuration which is continuously changing throughout the process. The present paper introduces a system model of the EAF which takes into account the radiative heat transfer between the surfaces and the participating medium. This is attained by the development of a simplified geometrical model, the use of a weighted-sum-of-gray-gases model, and a simplified consideration of dust radiation. The simulation results were compared with the data of real EAF plants available in literature.

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Abbreviations

Nu:

Nusselt number

Pr:

Prandtl number

Re:

Reynolds number

\( \bar{\alpha } \) :

Geometric-mean absorption coefficient

ε :

Emissivity

θ :

Angle measured from normal of surface (rad)

κ :

Extinction coefficient

λ :

Wave length (m)

ρ :

Density (kg m−3)

σ :

Stefan-Boltzmann constant

\( \bar{\tau } \) :

Geometric-mean transmission coefficient

a :

Absorption coefficient (m−1)

A :

Area (m2)

B d :

Dust load (kg m−3)

c :

Speed of light (m s−1)

c, c v :

Specific heat capacity (J kg−1 K−1)

C :

Parameter of mean beam length

d, D :

Diameter (m)

e :

Emissive power (W m−2)

F :

View factor

h :

Planck constant (J s)

h :

Specific enthalpy (J kg−1)

h 12 :

Coefficient of heat transfer (W m−2 K−1)

H :

Height (m)

i λ :

Spectral radiation intensity (W m−2 µm−1 sr−1)

k :

Boltzmann constant (J K−1)

k 12 :

Pressure loss coefficient

l :

Length (m)

L e :

Mean beam length (m)

m :

Mass (kg)

\( \dot{m} \) :

Mass flow rate (kg s−1)

m λ :

Complex refractive index

n :

Normal direction

n λ :

Refractive index

N :

Number of elements

p :

Pressure (Pa)

P :

Power (W)

q :

Energy flux (W m−2)

\( \dot{Q} \) :

Heat flow rate (W)

Q λ,e/s/a :

Extinction/scattering/absorption efficiency

r :

Radius (m)

r, z, φ :

Cylindrical coordinates

s :

Share

S :

Path of radiation (m)

t:

Time (s)

T :

Temperature (K)

V :

Volume (m3)

w :

Weight of gray gas,

x :

Mass fraction

x p :

Size parameter of Mie theory

Y :

Molar fraction

a:

Arc

b:

Basket

bl:

Black body condition

conv:

Convective

cw:

Cooling water

d:

Dust

g:

Gas

high:

High dust model

in:

Incoming

l:

Liquid phase/melt

low:

Low dust model

out:

Outgoing

p:

Particle

r:

Roof

rad:

Radiation

ref:

Reference value

rv:

Radiation volume

s:

Solid phase/scrap

sl:

Slag

v:

Vessel

w:

Wall

CFD:

Computational fluid dynamics

DC:

Direct current

EAF:

Electric arc furnace

WSGG:

Weighted sum of gray gases

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Acknowledgments

This research project is funded by the German Federal Ministry of Education and Research (BMBF) within the framework concept ‘IngenieurNachwuchs‘ (Grant Number 03FH00212).

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Authors and Affiliations

  1. Offenburg University of Applied Sciences, Badstr. 24, 77652, Offenburg, Germany

    Florian Opitz & Peter Treffinger

  2. University of Freiburg, Georges-Köhler-Allee 102, 79110, Freiburg, Germany

    Jürgen Wöllenstein

  3. Fraunhofer Institute for Physical Measurement Techniques IPM, Heidenhofstr. 8, 79110, Freiburg, Germany

    Jürgen Wöllenstein

Authors
  1. Florian Opitz
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  2. Peter Treffinger
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  3. Jürgen Wöllenstein
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Correspondence to Florian Opitz.

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Manuscript submitted February 20, 2017.

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Opitz, F., Treffinger, P. & Wöllenstein, J. Modeling of Radiative Heat Transfer in an Electric Arc Furnace. Metall Mater Trans B 48, 3301–3315 (2017). https://doi.org/10.1007/s11663-017-1078-6

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