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Simulation of Scrap Melting Process in an AC Electric Arc Furnace: CFD Model Development and Experimental Validation

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Abstract

The electric arc furnace (EAF) is a critical steelmaking facility that melts the scrap by the heat produced from electric arc and burners. Simulation and optimization of EAF scrap melting are of great interest to the steel industry, which helps to improve product quality and production efficiency. However, the relevant computational fluid dynamics (CFD) modeling of this process has not been reported so far. The present study established a three-dimensional (3D) integrated CFD model to simulate the scrap melting process in the alternating current (AC) EAF. The scrap melting model was developed to simulate the dynamic scrap melting and collapse based on the dual-cell approach and the stack approach. The electric arc model and the coherent jet model were introduced and integrated with the scrap melting model to estimate the electrical and chemical energy inputs need for melting. The CFD-compatible Monte Carlo method and electrode regulation strategy were developed respectively to predict the arc radiative heat dissipation and track the instant electrode movement. The experiments for the scrap melting by both electric arc and coherent jet burner were designed and implemented in the industry-scale NLMK 150-ton EAF for the model validation. The proposed model was applied to simulate the scrap melting process under the NLMK EAF typical run, and the scrap melting behavior, the electric arc performance, and the burner performance were evaluated and discussed based on the simulation results.

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Abbreviations

\(h_{t}^{^{\prime}}\) :

Old electrode position

\(C^{\prime}_{D}\) :

Constant in turbulent viscosity calculation

\(\vec{F}_{df}\) :

Drag force

\(\overline{\overline{Q}}_{s}\) :

Volumetric energy exchange with fluid phases

\(\dot{m}_{mt}\) :

Phase mass transfer rate

\(v^{\prime}_{r}\) :

Stoichiometric coefficient

\(h_{fusion}\) :

Latent heat of fusion

\(h_{s}\) :

Current scrap surface position

\(h_{t}\) :

New electrode position

\(C_{1}\) :

Constant in turbulence viscosity correction

\(C_{1\varepsilon }\) :

Constant in turbulence model

\(C_{2}\) :

Constant in turbulence viscosity correction

\(C_{2\varepsilon }\) :

Constant in turbulence model

\(C_{D}\) :

Drag coefficient

\(C_{T}\) :

Function

\(C_{p}\) :

Specific heat capacity

\(C_{s}\) :

Inertial resistance factor of scrap

\(D^{\prime}\) :

Coefficient function

\(D_{T}\) :

Thermal (Soret) diffusion coefficient

\(D_{m}\) :

Mass diffusion coefficient

\(\overline{G}\) :

Gain coefficient

\(G_{1}\) :

Constant in impedance control

\(G_{2}\) :

Constant in impedance control

\(G_{k}\) :

Kinetic energy produced by turbulence

\(I_{RMS}\) :

RMS arc current

\(K_{eff}\) :

Effective thermal conductivity

\(M_{w}\) :

Molecular weight

\(M_{\tau }\) :

Turbulent Mach number

\(M_{\tau 0}\) :

Constant in turbulence viscosity correction

\(N_{i}\) :

Number of radiation beams intercepted by cell

\(N_{tot}\) :

Total number of radiation beam emissions

\(P_{a}\) :

Total arc power

\(P_{l}\) :

Momentum transfer to liquid bath

\(Q_{ht}\) :

Phase heat transfer

\(Q_{arc, i}\) :

Arc radiative heat transfer to cell

\(Q_{rad,tot}\) :

Total arc radiative heat dissipation

\(R_{r}\) :

Net rate of production of each species by chemical reaction

\(Sc_{t}\) :

Turbulent Schmidt number

\(T_{g}\) :

Normalized local total gas temperature gradient

\(T_{liquidus}\) :

Liquidus temperature

\(T_{solidus}\) :

Solidus temperature

\(V_{c}\) :

Cell volume

\(a_{g}\) :

Gas acoustic velocity

\(a_{\varepsilon }\) :

Emissivity weighting factor

\(b_{\varepsilon }\) :

Emissivity gas temperature polynomial coefficients

\(\vec{g}\) :

Acceleration of gravity

\(\vec{j}\) :

Species mass diffusion

\(k^{\prime}\) :

Absorption coefficient of the fictitious gray gas

\(l_{a}\) :

Arc length

\(n^{\prime}\) :

Refractive index

\(\vec{r}\) :

Beam position

\(\vec{s}\) :

Beam direction

\(\vec{v}\) :

Velocity vector

\(\Omega^{\prime}\) :

Solid angle

\(\beta_{s}\) :

Scrap permeability

\(\gamma_{s}\) :

Scrap porosity

\(\varepsilon^{\prime}\) :

Total emissivity

\(\mu_{t}\) :

Turbulent viscosity

\(\sigma_{SB}\) :

Stefan–Boltzmann constant

\(\sigma_{k}\) :

Constant in turbulence model

\(\sigma_{s}\) :

Scattering coefficient

\(\sigma_{\varepsilon }\) :

Constant in turbulence model

\(\mathop \tau \limits^{ \equiv }\) :

Stress-strain tensor

\(h_{c}\) :

Cell height

\(h\) :

Heat transfer coefficient

\(A\) :

Interfacial contact area

\(E\) :

Energy

\(H\left( x \right)\) :

Heaviside function

\(I\) :

Radiation intensity

\(K\) :

Thermal conductivity

\(Pr\) :

Prandtl number

\(R\) :

Arc resistance

\(Re\) :

Reynolds number

\(T\) :

Temperature

\(Y\) :

Local species mass fraction

\(a\) :

Absorption coefficient

\(d\) :

Characteristic diameter

\(i\) :

Phase current

\(k\) :

Turbulent kinetic energy

\(m\) :

Mass

\(p\) :

Pressure of fluid phases

\(s\) :

Path length

\(t\) :

Flow time

\(u\) :

Phase voltage

\(\alpha\) :

Volume fraction

\(\varepsilon\) :

Turbulent dissipation rate

\(\lambda\) :

Thermal conductivity

\(\mu\) :

Molecular viscosity

\(\xi\) :

Constant in turbulence viscosity correction

\(\rho\) :

Density

\(\sigma\) :

Ionized air’s specific conductivity

\(\tau\) :

Arc cooling constant

\(\varphi\) :

Difference between the measured arc voltage and the measured arc current

\(\omega\) :

Constant in Cassie-Mayr arc model

\(\phi\) :

Phase function

\(q\) :

Phase subscript

\(i\) :

Specie subscript

g:

Gas phase

\(l\) :

Liquid phase

\(s\) :

Solid phase

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Acknowledgments

The authors would like to thank the Steel Manufacturing Simulation and Visualization Consortium (SMSVC) members for funding this project. The NLMK Indiana and the Center for Innovation through Visualization and Simulation (CIVS) at Purdue University Northwest are also gratefully acknowledged for providing all the resources for this work. The authors also appreciate the great help from Eugene Pretorius (NUCOR), Yury Krotov (Steel Dynamics, Inc.), Jianghua Li (Cleveland-Cliffs), and Yufeng Wang (SSAB).

Author Contributions

Conceptualization, YC; methodology, YC; model development, YC; model validation, YC; parametric studies, YC; data post processing, YC; experiment, SR; manuscript draft, YC; review and editing, SR, AKS, and YC; project supervision, CQZ; funding acquisition, CQZ.

Conflict of interest

The research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Chen, Y., Ryan, S., Silaen, A.K. et al. Simulation of Scrap Melting Process in an AC Electric Arc Furnace: CFD Model Development and Experimental Validation. Metall Mater Trans B 53, 2675–2694 (2022). https://doi.org/10.1007/s11663-022-02559-6

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