Fluid Flow Modeling of Arc Plasma and Bath Circulation in DC Electric Arc Furnace

 A mathematical model describing the flow field, heat transfer and the electromagnetic phenomenon in a DC electric arc furnace has been developed. First the governing equations in the arc plasma region are solved and the calculated results of heat transfer, current density and shear stresses on the anode surface are used as boundary conditions in a model of molten bath. Then a two dimensional time dependent model is used to describe the flow field and electromagnetic phenomenon in the molten bath. Moreover, the effect of bottom electrode diameter on the circulation of molten bath is studied.     

Modeling of fluid flow and heat transfer in the plasma region of the dc electric arc furnace

A mathematical model describing the transport processes in the plasma arc in dc electric arc furnaces has been developed. The equations of conservation of mass, momentum, and energy are solved numerically in conjunction with Maxwell's equations of the electromagnetic field to calculate the velocity and temperature distributions in the plasma region. The heat transfer from the arc to a rigid anode surface is calculated. The model is applied to obtain quantitative results on the relative importance of the various modes of heat transfer from the electric arc to the anode surface. Computational results were obtained for varying arc current magnitudes and anode-cathode distances. The model predicts higher arc jet velocity and a broader arc core at higher arc current. The shorter arc length is more efficient for transferring heat to the anode.     

Numerical study of dc arc plasma and molten bath in dc electric arc furnace

Abstract

A numerical study of the arc plasma and molten bath in a dc electric arc furnace (EAF) is useful for understanding and improving the production process of the dc EAF. In the present paper, a mathematical model based on conservation equations of mass, momentum and energy along with Maxwell's equations is developed to describe the flow field and heat transfer in the arc and molten bath regions of a dc EAF simultaneously. The governing equations are solved using the PHOENICS software package. The calculated results show good agreement with those of previous studies, giving a useful insight into the factors of arc heat transfer and bath circulation.     

Sustainability–steel and the environment

Abstract

A two-dimensional heat and fluid flow model was used to simulate the plasma arc furnace, where the flow is governed by the steady state incompressible Navier–Stokes equations. The flow has been taken as turbulent and the standard k-epsilon model was used to simulate the turbulence in the flow. The coupled non-linear differential equations were solved with suitable boundary conditions and temperature dependent plasma properties at atmospheric pressure by employing an efficient finite volume method. The calculations and heat transfer to various parts of the furnace were calculated for argon, nitrogen and hydrogen plasmas. The voltage–current characteristic for the different types of plasma and the effect of other process parameters on heat transfer are discussed.     

A mathematical model of gas tungsten arc welding considering the cathode and the free surface of the weld pool

A two-dimensional axisymmetric numerical model, including the influence of the cathode and the free surface of the weld pool, is developed to describe the heat transfer and fluid flow in gas tungsten arc (GTA) welding. In the model, a boundary-fitted coordinate system is adopted to precisely describe the cathode shape and deformed weld-pool surface. The current continuity equation has been solved with the combined arc plasma-cathode system, independent of the assumption of current density distribution on the cathode surface, which was essential in the previous studies of arc plasma. It has been shown that the temperature profile, the current, and the heat flux to the anode show good agreement with the experimental data. Moreover, the current and the heat-flux distributions may be affected by the shape of the cathode and the free surface of the weld pool.     

A Multiscale 3D Model of the Vacuum Arc Remelting Process

A three-dimensional, transient, multiscale model of the VAR process is presented, allowing novel simulations of the influence of fluctuations in arc behavior on the flow and heat transfer in the molten pool and the effect this has on the microstructure and defects. The transient behavior of the arc was characterized using the external magnetic field and surface current measurements, which were then used as transient boundary conditions in the model. The interactions of the magnetic field, turbulent metal flow, and heat transfer were modeled using CFD techniques and this “macro” model was linked to a microscale solidification model. This allowed the transient fluctuations in the dendritic microstructure to be predicted, allowing the first coupled three-dimensional correlations between macroscopic operational parameters and microstructural defects to be performed. It was found that convection driven by the motion of the arc caused local remelting of the mushy zone, resulting in variations in permeability and solute density. This causes variations in the local Rayleigh number, leading to conditions under which freckle solidification defects will initiate. A three-dimensional transient tracking of particle fall-in was also simulated, enabling predictions of “white spot” defects via quantification of the trajectory and dissolution of inclusions entering the melt.     

Mathematical modelling of electroslag remelting P91 hollow ingots process with multi-electrodes

Abstract

Electroslag remelting (ESR) hollow ingot process with T-shape current supplying mould is a new metallurgical technology. A mathematical model was developed to describe the interaction of multiple physical fields of this process for studying the process technology. Maxwell, Navier-Stokes and heat transfer equations have been adopted in the model to analyse the electromagnetic field, magnetic driven fluid flow, buoyancy driven flow and heat transfer using finite element software ANSYS. Moreover, the model has been verified through the metal pool depth measurements, which were obtained during remelting of 10 electrodes into Φ900/500 mm hollow ingots of P91 steel, with a slag composition of 50–60 wt-% CaF₂, 10–20 wt-% CaO, 20–30 wt-% Al₂O₃, ≤8 wt-% SiO₂. There was a good agreement between the calculated results and the measured results. The calculated results show that the distribution of current density, magnetic induction intensity, electromagnetic force, Joule heating, fluid flow and temperature are symmetric but not uniform due to the multi-electrode arrangement in two symmetric groups. Simulation of the ESR hollow ingot process will help to understand the new technology process and optimise operating parameters.     

Magnetohydronamic and thermal behavior of electroslag remelting slags

The paper is based on the development and use of a mathematical model that simulates the electroslag remelting (ESR) operation. The model assumes axisymmetrical geometry and steady state. Maxwell equations are first solved to determine the electromagnetic forces and Joule heating. Next, coupled fluid flow and heat transfer equations are written for the two liquids (slag and liquid metal). Thek-ε model is used to represent turbulence. The system of coupled partial differential equations is then solved, using a control volume method. Using the operating parameters as inputs, the model calculates the current density, velocity, and temperature throughout the fluids. This paper is concerned with fluid flow and heat transfer in the slag phase. After being validated by comparing its results with experimental observation, the model is used to evaluate the influence of operating variables, such as the fill ratio, and the thermophysical properties of the slag.     

Heat transfer and fluid flow in the welding arc

Through the numerical solution of the Navier/Stokes equation, the energy transport equation, and the magnetic diffusion equation, a mathematical model has been developed to predict the velocity, temperature, and current density distributions in inert gas welding arcs. Although the model has one adjustable parameter, the cathode current density, it was found that a single value of this variable was sufficient to provide internally consistent results for a range of arc lengths and arc currents representative of welding. The computed temperature distributions in the arc were found to be in good agreement with spectroscopically measured temperatures taken from the literature, and similar agreement was obtained between the predicted and measured current density distributions at the surface of water cooled copper anodes. The mechanisms of heat and momentum transfer to the anode were investigated in the light of recent findings concerning the anode boundary layer and the presence of negative anode fall voltages. The predicted convective heat fluxes to the anode were found to be generally consistent with experimental data.     

A Model of Liquid Metal Droplet Vaporization in Arc Heated Gas Streams

A model of simultaneous heat and mass transfer has been constructed to describe vaporization of liquid metal droplets in arc heated gas streams. The major assumptions of the model include 1) plug flow, 2) negligible pressure drop, 3) no droplet-droplet interactions, 4) negligible gas radiation, natural convection, thermal diffusion, diffusion-thermo transport and axial conduction and diffusion, and 5) no interfacial discontinuities in temperature or concentration. The latter assumption is discussed in detail in a separate appendix. The analysis is limited to binary, nonreacting gas mixtures. The mathematical formulation results in five nonlinear, first order differential equations with temperature and compositional dependent properties. The model is applied to the vaporization of sodium and magnesium droplets injected into arc heated argon flowing in a cylindrical reactor. The effect of parameters such as initial droplet radius, reactor diameter, and liquid metal flowrate on the reactor length required to achieve a specified degree of vaporization is calculated.     

Nitrogen Removal and Arc Voltage Increase in EAF Steelmaking by Methane Injection into the Arc

Methane injection into the arcs of electric arc furnaces has been shown on pilot scale to lead to a remarkable arc voltage increase at constant arc current and arc length. Recent investigations have been concerned with the associated metallurgical effects making use of a gas‐tight 150‐kg arc furnace operated with two AC plasma torches. A first test with bored graphite electrodes in this furnace confirmed the power increase observed during methane injection. The carburization slowly occurring when 6 % CH₄ were injected into the argon atmosphere of the furnace could be avoided by adding minor amounts of CO₂. A slag layer decreased mass transfer rates without noticeably affecting heat transfer. Manganese loss by evaporation was measured to investigate the influence of power increase and slag layers. From the results, an increase of 200 K was concluded for the melt surface temperature when CH₄ was added to pure argon. Methane injection into the arcs proved to accelerate nitrogen removal considerably. Starting with an intentionally high nitrogen content of about 200 ppm, the nitrogen removal rate was found to be slowest with pure argon plasma arcs, faster with 90 % Ar + 10 % H₂, and fastest with 95 % Ar + 5 % CH₄ reaching final contents of less than 20 ppm of nitrogen. Based on thermodynamic calculations, the denitrogenation reactions appear to take place via atomic nitrogen in pure argon plasma, via NH₃ in Ar + H₂ and via HCN in Ar + CH₄.     

Arc Distribution During the Vacuum Arc Remelting of Ti-6Al-4V

Currently, the temporal distribution of electric arcs across the ingot during vacuum arc remelting (VAR) is not a known or monitored process parameter. Previous studies indicate that the distribution of arcs can be neither diffuse nor axisymmetric about the center of the furnace. Correct accounting for the heat flux, electric current flux, and mass flux into the ingot is critical to achieving realistic solidification models of the VAR process. The National Energy Technology Laboratory has developed an arc position measurement system capable of locating arcs and determining the arc distribution within an industrial VAR furnace. The system is based on noninvasive magnetic field measurements and a VAR specific form of the Biot–Savart law. The system was installed on a coaxial industrial VAR furnace at ATI Albany Operations in Albany, OR. This article reports on the different arc distributions observed during production of Ti-6Al-4V. It is shown that several characteristic arc distribution modes can develop. This behavior is not apparent in the existing signals used to control the furnace, indicating the measurement system is providing new information. It is also shown that the different arc distribution modes observed may impact local solidification times, particularly at the side wall.     

Liquid Metal Pool Behavior during the Vacuum Arc Remelting of INCONEL 718

Non-steady-state ensemble arc behavior has been observed during the Vacuum Arc Remelting (VAR) of 508-mm-diameter ingots of INCONEL 718. The liquid metal flow in the melt pool of a 508-mm ingot during VAR has been simulated under two alternative sets of conditions: (1) a steady-state axisymmetrical arc distribution, as has been typically used in modeling work previously; and (b) a transient asymmetrical arc distribution. Due to the computational requirements, neither mass flux nor solidification were modeled; instead, the pool shape was fixed from measurements from a 508-mm-diameter ingot, and a constant pool wall temperature of 1609 K was used. The transient simulation assumed a localized Gaussian arc whose effective center was located at a distance of 0.1 m from the ingot centerline; this simulation rotated clockwise around the centerline with a period of 36 seconds. The steady-state model was simulated with axisymmetrical distributions of current and power input to the pool top surface calculated by time averaging the transient current and power inputs. The standard k-ε solver of ANSYS CFX 5.6 software was used for both simulations. The transient model results suggest that 5 seconds of asymmetrical arc behavior is enough to change the pool from steady state to transient and that, after 30 seconds, the flow is almost fully developed (at least to the accuracy of the model) and dominated by the Lorentz force. Aspects of the model results agree with key features of the melt pool observed during VAR.     

Heat Transfer Analysis for Industrial AC Electric Arc Furnace

The heat transfer analysis was performed for an AC electric arc furnace (EAF). Heat losses by conduction, convection and radiation from outer surface, roof, bottom and electrodes of EAF were determined in detail. Some suggestions about decreasing heat losses were presented.     

Modeling of Electromagnetic Field and Liquid Metal Pool Shape in an Electroslag Remelting Process with Two Series-Connected Electrodes

A three-dimensional finite-element model has been developed to understand the electromagnetic field and liquid metal pool shape in an electroslag remelting (ESR) process with two series-connected electrodes. The magnetic vector potential is introduced into the Maxwell’s equations, and the nodal-based method is used to solve a three-dimensional harmonic electromagnetic field. The heat transfer of the solidifying processes of ingot is modeled by a source-based enthalpy method, and the Joule heating is included in an inner source. The results show the main part of the current flows through the slag cap and a little enters into ingot in a two-series-connected electrode ESR system. As the interaction of self-induced and mutual-induced of two electrodes occurs, the skin effect is significantly suppressed by the neighbor effect. A symmetrical pattern of magnetic flux density in a two-series-connected electrode ESR system is displayed. The magnetic flux density between two electrodes is reinforced and reduced at the outside of two electrodes. The maximum Joule heat power density is located at the interface of slag and electrodes, and it decreases with an increase of the electrode immersion depth. The averaged Joule heat power density increases when slag cap thickness is reduced. With the increase of ingot height, the liquid metal pool shape changes from arc shaped to “V” shaped. When the ingot height is more than the diameter in the ESR processes, the liquid metal pool shape is constant.     

Modeling of Radiative Heat Transfer in an Electric Arc Furnace

Metallurgical and Materials Transactions B - Radiation is an important means of heat transfer inside an electric arc furnace (EAF). To gain insight into the complex processes of heat transfer...     

The interaction of a DC transferred arc with a melting metal: Experimental measurements and mathematical description

Experimental measurements are reported on the transient development of temperature profiles in a hemispherical metal anode onto which a DC plasma jet is impinging. The main process variables were the arc current, the electrode separation, and the argon flow rate. These experimental measurements were compared with the predictions of a mathematical model, which involved the statement of the turbulent heat and fluid flow equations in the plasma, coupled to the heat flow in the testpiece through the boundary conditions. The experimental measurements were in reasonable agreement with the predictions, and convective heat transfer was found to be dominant in the heat exchange between the plasma and the anode.