Melt azimuthal rotation in direct current electric arc furnace without external axial magnetic field

Abstract

This paper considers the azimuthal rotation of melt about the vertical axis of a DC EAF, which is ensured by an inclined installation of the power supply electrodes, which is a patented solution that is the basis for this article. Near inclined electrodes, the Lorentz force has a pronounced azimuthal component, which is the driver of the melt rotation without an external axial magnetic field – thus, additional energy consumption to create an external magnetic field is not necessary. The main design and technological solutions, formulated in the patent and presented by the authors, were obtained using observations and numerical LES study for a laboratory-scale experimental setup (capacity 4.8 kg of GaInSn), as well as using LES computations for an industrial-scale DC EAF (capacity 3.6 t of molten steel). Basic technological solutions studied: the flow of the melt may be controlled by varying the number of vertical and inclined electrodes of DC EAF, choosing the angle of inclination of the electrodes as well as choosing the sequence of turning on and turning off power supply through the electrodes.

Keywords

Direct current (DC)electric arc furnace (EAF)electro-vortex flow (EVF)large eddy simulation (LES)melt rotation external magnetic field

1. Introduction

1.1. An annual growth of the global market of DC EAF

A recent analysis of the global market of DC EAFs predicts a compound annual growth rate of 13.8% in 2023–2029. The market size is therefore expected to reach US$298.1 million in 2029 [1]. Currently, the number of DC EAFs is approximately 10% of the total number of EAFs in operation worldwide [2]. According to the mentioned forecast, the share of DC EAFs may increase by the end of the decade. The efficiency of DC EAF use depends on the energy-saving electrotechnologies, including implementation of the controlled rotation of the melt at certain stages of melt processing.

1.2. A toroidal vortex – the typical structure of the melt EVF in a DC EAF without an external magnetic field

The structure of the melt EVF in an EAF of industrial capacity, with DC supplied through a vertical top electrode to the melt mirror and through two vertical bottom electrodes, is a toroidal vortex with a jet directed towards the bottom of the bath near its axis (Fig. 1a). A detailed numerical study is presented in [3] together with the results of observation of melt circulation at the melt mirror of a laboratory-scale experimental setup.

Fig. 1.

Industrial DC EAF with a top electrode and two bottom perpendicular (non-inclined) non-submerged electrodes. LES-computed time-averaged (flow-time t = 60 s): (a) velocity vectors for melt toroidal vortex at vertical cross-section x = 0; (b) 3D streamlines of melt rotation due to flow instability near the furnace’s vertical axis (view from arc spot plane).

A similar flow structure is observed in DC EAFs with different geometries and sizes of liquid metal baths as well as different numbers and locations of vertically installed bottom electrodes [4–6] without an external axial magnetic field.

1.3. A weak slow rotation of the melt without an azimuthal component of the Lorentz force

A weak slow rotation (Fig. 1b) of the melt about the bath axis of an industrial DC EAF is found in the arc zone in conditions of the absence of a significant azimuthal component value of the Lorentz force. The cause of the rotation is most likely the presence of small perturbations due to flow instability. In our numerical simulation, such a perturbation most likely results from the inhomogeneity of the computational grid. The rotation of the melt in the time-averaged flow manifested itself only at 55–60 s, although the quasi-stationary regime of the turbulent toroidal flow was established approximately in the first 10 s after the Lorentz force was applied.

The essential results of the series of numerical studies are the following: the spatial shift of non-submerged electrodes, which are perpendicular to top and bottom surfaces of the melt, or variations in the ratio of electrical current values in two bottom electrodes, cannot be the cause of melt azimuthal rotation without an external axial magnetic field.

A similar effect of liquid metal rotation was observed in early experiments [7, Fig. 2a] under the condition of a point source of electrical current from above to a mercury mirror in a hemispherical vessel of a laboratory setup. As possible reasons for this phenomenon, the interaction of the electric current with the external magnetic field of the Earth or the impact of distant non-symmetric parts of the current supply wires, which provide an azimuthal Lorentz force, were mentioned in [7].

1.4. An azimuthal rotation of the melt with external magnetic field

A series of recent experiments and numerical computations of the melt EVF and rotation was carried out using developed laboratory setup with a hemispherical vessel filled with a GaInSn eutectic alloy [8–10]. The melt EVF is driven by Lorentz force, which is the results of interaction of electrical current, supplied to the melt mirror, with self-magnetic field. The melt rotation is driven with the azimuthal component of Lorentz force, which is result of interaction of electrical current in the melt with external axial magnetic field, created by solenoid, located around a hemispherical vessel.

Comparative estimates carried out in [8] showed that the Lorentz force causing the EVF was approximately three orders of magnitude greater than the azimuthal force, arising from the interaction of the vertical component of the Earth’s magnetic field with electric currents in liquid metal. In turn, the Coriolis force, resulting from the daily rotation of the Earth around its axis, is about seven orders of magnitude smaller. Thus, the influence of the Earth’s magnetic field on melt rotation in an external magnetic field provided by a solenoid, which is two orders of magnitude greater than the Earth’s magnetic field, can be neglected [8,9]. It was shown also that the velocity value of the melt azimuthal rotation decreased with distance from the symmetry axis of the experimental setup [8,10].

An estimation of the possibilities of using the experimental results, obtained at a “cold” setup, for the analysis of EVF and azimuthal rotation of the melt in an industrial DC EAF was carried out in [11].

A numerical study of the EVF and azimuthal rotation of the melt for an industrial DC EAF was carried out in [12]. To obtain the intensity of rotation of the melt comparable to that of an EVF toroidal vortex, the external axial magnetic field was three orders of magnitude greater than the Earth’s magnetic field.

1.5. The main disadvantages of creating melt rotation using an external magnetic field

Thus, a brief analysis allows us to formulate the following conclusions:

in industrial-scale EAFs, the Earth’s magnetic field can’t be the reason of azimuthal rotation of the melt;

to obtain a technologically significant effect from the azimuthal rotation of the melt, an external axial magnetic field must be generated, requiring additional power consumption.

1.6. The main goal of the current research

The main goal of the research carried out by the authors is to find a means of creating and controlling the azimuthal rotation of the melt when the azimuthal component of the Lorentz force is not the result of the interaction between the electric current in the melt and an external axial magnetic field. Thus the construction of DC EAF would not require an additional power source to generate the external magnetic field.

2. A proposed patented solution to create and control the melt rotation without external magnetic field

The paper considers the azimuthal rotation of the melt in a DC EAF insured by inclined installation of the power supply electrodes. The found solutions have been formulated in the patent [13]. The main design and technological solutions were obtained using observations and numerical studies for the laboratory-scale experimental setup (capacity 4.8 kg of GaInSn alloy) as well as using numerical studies for an industrial-size DC EAF (capacity 3.6 tons of molten steel).

The 3D schemes of the experimental setup are shown in Figs 2a, 2b; the geometric and physical parameters of the melt and electrodes are outlined in Tables 1, 2.

Fig. 2.

Laboratory-scale setups with a bottom electrode and either one (a,c) or two (b,d) semi-submerged inclined top electrodes: (a,b) schemes of setups; (c,d) photography of melt mirror with bubbles, which visualize melt rotation.

Table 1

Geometric parameters of the melt vessel and electrodes in the experimental setup (see also Figs 2a, 2b)

Melt vessel
Diameter	D = 0.22 m
Depth	H = 0.02 m
Bottom electrode, composed of two cylinders
Diameter of higher cylinder	$d_{bottom}^{higher}=∼0.025$ m
Height of higher cylinder	$h_{bottom}^{higher}=∼0.02$ m
Diameter of lower cylinder	$d_{bottom}^{lower}=∼0.05$ m
Height of lower cylinder	$h_{bottom}^{lower}=∼0.12$ m
Cylindrical part(s) of one (two) top electrode(s)
Diameter	d_cyl = 0.035 m
Height	h_cyl = 0.125 m
Distance between axis of cylindrical part and melt symmetry axis	x_cyl = 0.115 m
Distance between axes of two cylindrical parts	2x_cyl = 0.23 m
Inclined strip part(s) of one (two) top electrode(s)
Length	l_strip = 0.11 m
Width	w_strip = 0.025 m
Thickness	h_strip = 0.0035 m
Distance between axis of strip and melt symmetry axis	x_strip = 0.0725
Distance between axes of two strips	2x_strip = 0.145 m
Depth of submersion of strip(s)	$h_{strip}^{\mathit{depth}}=∼0.01$ m
Angle of inclination from vertical of strip(s)	𝛼 = 65°

Table 2

Physical properties of galistan (GaInSn) melt, copper (Cu) electrodes and supplied direct current (DC) in the experimental setup (see also Figs 2a, 2b)

Galistan (GaInSn)
Density	𝜌_m = 6.361 × 10³ kg/m³
Total mass	m_m = 4.8 kg
Viscosity	𝜂_m = 2.2 × 10⁻³ kg/(m ⋅ s)
Electrical conductivity	𝜎_m ≈ 3 ÷ 3.3 × 10⁶ S/m
Copper (Cu)
Electrical conductivity	𝜎_el = 5.8 × 10⁷ S/m
Direct current (DC)
One (two) top electrode(s)	$I_{el}^{top}=∼700$ A (350 A)
Bottom electrode	$I_{el}^{bottom}=∼700$ A

The 3D schemes of the industrial DC EAF are shown in Figs 6a, 6b; the geometric and physical parameters of the melt and electrodes are outlined in Tables 3, 4.

Table 3

Geometric parameters of the melt vessel and electrodes in an industrial DC EAF (see also Figs 6a, 6b)

Melt vessel (a truncated cone)
Top (melt mirror) radius	$r_{m}^{top}=∼0.9$ m
Bottom radius	$r_{m}^{bottom}=∼0.5$ m
Height	H_m = 0.335 m
Top electrode
Radius of the arc spot at the melt mirror	$r_{el}^{top}=∼0.14$ m
Square of electrode cross-section with bottom of melt	$S_{el}^{top}=∼0.062$ m²
Bottom electrodes* for inclination 𝛼 = 30°
Radius of electrode	$r_{el}^{bottom}=∼0.1$ m
Distance between the axes of electrodes	$L_{el-el}^{bottom}=∼0.6$ m
Offset of the electrode axes from the symmetry plane	$L_{\mathit{shift}}^{bottom}=∼0.1$ m
Angle of inclination from vertical	𝛼 = 30°
Square of electrode cross-section with bottom of melt	$S_{el}^{bottom}=∼0.036$ m²
Bottom electrodes for inclination 𝛼 = 60°
Radius of electrode	$r_{el}^{bottom}=∼0.07$ m
Distance between the axes of electrodes	$L_{el-el}^{bottom}=∼0.6$ m
Offset of the electrode axes from the symmetry plane	$L_{\mathit{shift}}^{bottom}=∼0$
Angle of inclination from vertical	𝛼 = 60°
Square of electrode cross-section with bottom of melt	$S_{el}^{bottom}=∼0.031$ m²

*Differing parameters for vertically installed (𝛼 = 0°) bottom electrodes are the following: $r_{el}^{bottom}=0.115$ m; $S_{el}^{bottom}=∼0.042$ m².

Table 4

Physical properties of steel (Fe) melt, graphite (C) top and steel bottom electrodes supplied direct current (DC) of an industrial DC EAF (see also Figs 6a, 6b)

Steel (Fe) melt
Density	𝜌_m = 6.9 × 10³ kg/m³
Total mass	m_m = 3.6 t
Dynamic viscosity	𝜂_m = 6 × 10⁻³ kg/(m ⋅ s)
Electrical conductivity	𝜎_m = 1.1 × 10⁶ S/m
Graphite (C) top electrode
Electrical conductivity	${\sigma}_{el}^{top}=∼7\times 10^{4}$ S/m
Steel (Fe) bottom electrodes
Electrical conductivity	${\sigma}_{el}^{bottom}=∼1.1\times 10^{6}$ S/m
Direct current (DC)
Top electrode	$I_{el}^{top}=∼40$ kA
Each of two bottom electrodes	$I_{el}^{bottom}=∼20$ kA

The basic designs (i.e. with vertically installed electrodes) of a laboratory setup and an industrial DC EAF are considered in detail in [3].

Experimental verification of the developed numerical model for calculating the electromagnetic (EM) field and the melt turbulent EVF is considered in [14] – the LES model of turbulence is used.

Computations are performed with Ansys Maxwell and Ansys Fluent commercial software packages.

3. Experimental and numerical verification of the patented solution using a laboratory-scale setup

3.1. Peculiarities of the construction of developed experimental laboratory-scale setup

Two variants of the experimental setup are considered – with either one (Fig. 2a) or two (Fig. 2b) top electrodes. Each top electrode consists of a vertical cylindrical part and a semi-submerged inclined strip part. The angle of inclination to the vertical direction is 𝛼 = 65°.

The diameter and height of the cylindrical vessel filled with the eutectic alloy GaInSn are D = 0.22 m and H = 0.02 m, respectively. Other geometric parameters are provided in Table 1.

Photos of both variants of the setup are shown in Figs 2c, 2d. There are bubbles on the mirror, visualizing melt rotation. To enable the observation of the melt flow on the melt mirror, the design of both experimental setup variants (Figs 2a, 2b) reproduces the “upside down” location of the electrodes, which are shown in the design of an industrial EAF (Figs 6a, 6b).

3.2. The Lorentz force for the inclined installation of one or two top electrodes

When the top and bottom electrodes are installed vertically [3, Fig. 8b], the melt flow jet is directed from the bottom electrode (like the top electrode in the industrial furnace) towards the melt free surface with two partly submerged top electrodes (like the bottom electrodes in an industrial furnace). In this case, the azimuthal rotation of the melt about the setup axis does not occur, since the Lorentz force has no azimuthal component near the bottom or near the top electrodes [12, Fig. 8a].

When the top electrodes are installed at an incline (𝛼 = 65°) and the bottom electrode remains vertical (Figs 2a, 2b), the Lorentz force acquires a pronounced azimuthal component (Figs 3b, 3d) near the top inclined electrodes, while near the bottom electrode, the Lorentz force remains axis-symmetric with respect to the vertical axis, without azimuthal component (Figs 3a, 3c).

Fig. 3.

Lorentz force distribution in laboratory-scale setups with one bottom electrode and either one (a,c) or two (b,d) semi-submerged inclined top electrodes: (a,c) bottom of melt near electrode; (b,d) top of melt near inclined electrodes.

Fig. 4.

LES-computed time-averaged (flow time t = 60 s) melt velocity vectors at melt mirror in laboratory-scale setup with bottom electrode and one (a) or two (b) semi-submerged inclined top electrodes.

Fig. 5.

LES-computed time-averaged melt velocity maximum v_max as a function of time t in laboratory-scale setups with one bottom electrode and either one (dotted line) or two (solid line) semi-submerged inclined top electrodes.

Fig. 6.

Schemes of an industrial DC EAF with a top electrode and two bottom inclined non-submerged electrodes: (a) 𝛼 = 30°, (b) 𝛼 = 60°.

In case of one inclined top electrode (Fig. 3b), the maximum value of the Lorentz force (f ≈ 4 × 10⁴ N/m³) is much greater than the value (f ≈ 9 × 10³ N/m³) for case of two inclined top electrodes (Fig. 3a), since because the electrical current (I = 700 A) through one electrode (Fig. 2a) is two times greater than the current (I = 350 A) through each of two electrodes (Fig. 2b). Hence, the maximum value of azimuthal velocity in case of one top electrode is significantly greater (see below).

3.3. The velocity of the melt azimuthal rotation as the function of time

The azimuthal component of the Lorentz force produces clockwise rotation of the melt about the vertical axis (Figs 4a, 4b). The maximum values of the time-averaged LES-computed melt velocity on the mirror in case of one top electrode (v_max ≈ 0.25 m/s) and in case of two top electrodes (v_max ≈ 0.15 m/s) agree well with the estimates obtained from the analysis of observed bubble motion in both variants of the experimental setup (Figs 2c, 2d).

The calculated dependence of the time-averaged maximum velocity in the melt volume on time shows that the quasi-stationary regime of turbulent rotation of the melt is established within about 20 s (Fig. 5) for both variants of the experimental setup (Figs 2c, 2d). The graph of maximum velocity value as a function of time reaches saturation at approximately 60 s.

Note that the maximum value of the axis-symmetrically distributed Lorentz force near the bottom electrode (Fig. 3a or Fig. 3c) is approximately two times smaller or greater than the maximum values of the Lorentz force with an azimuthal component near one or two top inclined electrodes (Fig. 3b or Fig. 3d). Despite this difference, EVF with a toroidal vortex structure is quickly replaced by rotational motion in the entire volume of the melt with total mass m_m = 4.8 kg (Table 2) due to relatively low inertia.

4. Numerical verification of the patented solution for an industrial DC EAF

4.1. Peculiarities of the construction of industrial-scale furnace

A similar series of computations was carried out in order to verify the patented solution for an industrial-size EAF. Two variants were considered – inclination of two bottom non-submerged electrodes are 𝛼 = 30° (Fig. 6a) and 𝛼 = 60° (Fig. 6b). Note that the basic design of EAF is not equipped with any system that would generate an external magnetic field.

The top and bottom radii and height of the truncated cone vessel of the molten steel are $r_{m}^{top}=∼0.9$ m; $r_{m}^{bottom}=∼0.5$ m and H_m = 0.335 m, respectively. Other geometric parameters are provided in Table 3.

4.2. The Lorentz force for different installation of bottom electrodes

The distribution of the Lorentz force near the top vertical electrode remains axis-symmetrical, without an azimuthal component (Figs 7a, 7c).

Fig. 7.

Lorentz force distribution: (a,c) top of melt near top electrode; (b,d) bottom of melt near inclined bottom electrodes in an industrial DC EAF: (a,b) 𝛼 = 30°, (c,d) 𝛼 = 60° (see also schemes in Figs 6a, 6b).

When the bottom electrodes are installed with inclination, the Lorentz force near the bottom electrodes has a pronounced azimuthal component. The maximum value of the Lorentz force is more than twice greater (more accurately ∼ 2.44) for inclination 𝛼 = 60° (Fig. 6b) in comparison with lower inclination 𝛼 = 30° (Fig. 6a) – see visualisation in Figs 7d and 7b and compare the maximum values f ≈ 1.4 × 10⁴ N/m³ and f ≈ 0.6 × 10⁴ N/m³ accordingly.

4.3. The velocity of the melt azimuthal rotation as the function of time

The azimuthal component of the Lorentz force drives clockwise rotation of the melt about the vertical axis. The distributions of time-averaged LES-computed melt 3D streamlines (Fig. 8a) and the melt velocity vectors on the mirror (Fig. 8b) are obtained with greater inclination of the bottom electrodes (𝛼 = 60°, Fig. 6b), which results in a greater maximum value of velocity v_max ≈ 1.86 m/s (the electrical current I = 40 kA is supplied through the top electrode) – compare with a lower maximum value of velocity v_max ≈ 1.21 m/s for lower inclination of the bottom electrodes (𝛼 = 30°, Fig. 6a).

Fig. 8.

Industrial DC EAF with a top electrode and two bottom inclined (𝛼 = 60°) non-submerged electrodes: LES-computed time-averaged (flow time t = 300 s) (a) 3D streamlines, (b) velocity vectors near the mirror of rotating melt.

For an industrial DC EAF with greater inclination of the bottom electrodes (𝛼 = 60°, Fig. 6b), the graph of maximum velocity as a function of time reaches saturation at approximately 360 s = 6 min (Fig. 9) – this is the time required to generate rotation in a volume of molten steel weighing 3.6 t (Table 4), which has enormous inertia.

Fig. 9.

LES-computed time-averaged melt velocity maximum v_max as a function of time t in an industrial DC EAF.

5. The summary of several means of the melt flow control for DC EAF

Now let us list several means of the melt flow control in DC EAF – the characteristic trends for the Lorentz force and the maximum values of the melt velocity are illustrated in previous sections:

$\surd$ The variation of supplied electrical current value for control of intensity of either toroidal vortex flow (vertically installed electrodes) or rotational flow (inclined installed electrodes) of the melt.

$\surd$ Switching on between one or two vertically installed electrodes in order to reach different intensity of the toroidal vortex.

$\surd$ Switching on between vertically installed or inclined installed electrodes in order to reach toroidal vortex flow or rotational flow of the melt.

$\surd$ Variation of angle of inclined installation of electrodes for control of intensity of rotation of the melt.

6. Conclusions and outlook

A patented energy-saving method is presented for creating rotation of the melt about the vertical axis of an industrial DC EAF without the need to generate an external axial magnetic field that would require an additional energy source.

This method relies on the installation of inclined electrodes, near which the Lorentz force has an pronounced azimuthal component, its value depends on the angle of inclination of the electrodes.

The use of inclined electrodes leads to a rearrangement of EVF exhibiting toroidal vortex structure to rotation of the entire volume of the melt. The time to reach the maximum rotation speed depends on the magnitude of the azimuthal component of the Lorentz force and on the mass of the melt.

The presented patented solution allows the flow of the melt to be controlled by varying the number of vertically and inclined installed electrodes used in the design of the electric furnace, choosing the angle of inclination of the electrodes from the vertical direction, as well as the sequence of turning on and off the electrical current supplied through the electrodes.

The patented solutions are substantiated by observing the rotation of liquid metal in a developed and installed laboratory-scale experimental setup, and by analysing the result of numerical calculations for the setup as well as for the industrial DC EAF, performed using a developed and experimentally verified method for numerical study of the EM field and turbulent flow of the melt.

The selection of the optimal geometry and corresponding parameters of DC EAFs will be performed during the design process of electroeffective aggregate, taking into account the necessary parameters for the control of the melt flow and rotation in accordance with the selected technological process for metal production with specified characteristics.

Footnotes

Acknowledgements

The European Regional Development Fund funded this work under the “Development of numerical modelling approaches to study complex multiphysical interactions in electromagnetic liquid metal technologies” (contract No. 1.1.1.1/18/A/108).

References

Global DC electric arc furnaces market 2023; https://www.absolutereports.com/global-dc-electric-arc-furnaces-market-22335018.

Odenthal

H.-J.

Kemminger

Krause

Sankovski

Uebber

and Vog

, Review on modelling and simulation of the electric arc furnace (EAF), Steel Research International89 (2018), 1700098, 1–36, doi:10.1002/srin.201700098.

Pavlovs

Jakovics

and Chudnovsky

, Electrovortex flow and melt homogenization in the industrial direct current electrical arc furnace, Magnetohydrodynamics58 (2022), 305–326, doi:10.22364/mhd.58.3.7.

Smirnov

S.A.

Kalaev

V.V.

Hekhamin

S.M.

Krutyanskii

M.M.

Kolgatin

S.N.

and Nekhamin

I.S.

, Mathematical simulation of electromagnetic stirring of liquid steel in a DC arc furnace, High Temperature48 (2010), 68–76, doi:10.1134/S0018151X10010116.

Kazak

, Modelling of vortex flows in direct current (DC) electric arc furnace with different bottom electrode positions, Metallurgical Material Transactions B44 (2013), 1243–1250, doi:10.1007/s11663-013-9899-4.

Yachikov

I.M.

, Modelling of electrovortex flows and heat/mass transfer in the DC arc furnace bath, Magnetohydrodynamics52 (2016), 301–310, doi:10.22364/mhd.52.1-2.33.

Bojarevics

and Shcherbinin

E.V.

, Azimuthal rotation in the axisymmetric meridional flow due to an electric-current source, Journal of Fluid Mechanics126 (1983), 413–430, doi:10.1017/S0022112083000245.

Vinogradov

D.A.

Ivochkin

Yu.P.

and Teplyakov

I.O.

, Effect of the Earth’s magnetic field on the electric-vortex-flow structure, Doklady Physics63 (2018), 447–450, doi:10.1134/S1028335818110046.

Teplyakov

Vinogradov

Ivochkin

Yu.

Kharicha

and Serbin

, Applicability of different MHD approximations in electrovortex flow simulation, Magnetohydrodynamics54 (2018), 403–416, doi:10.22364/mhd.54.4.8.

10.

Vinogradov

Teplyakov

and Ivochkin

Yu.

, Study of modes of electrovortex flow in a wide range of external magnetic field magnitudes, Magnetohydrodynamics55 (2019), 455–464, doi:10.22364/mhd.55.4.4.

11.

Yachikov

I.M.

Portnova

I.V.

and Karandaev

A.S.

, Investigation of the current carrying melt in the DC-EAF bath under the action of external vertical magnetic field, Magnetohydrodynamics55 (2019), 233–240, doi:10.22364/mhd.55.1-2.28.

12.

Pavlovs

Jakovics

and Chudnovsky

, Melt electrovortex flow in DC EAF model with two bottom electrodes in axial magnetic field, in: Proceeding of the XIX Congress of International Union for Electricity applications (UIE), Pilsen, Czech Republic, University of West Bohemia, Czech Republic, 2021, pp. 67–68.https://dspace5.zcu.cz/handle/11025/45792.

13.

Čudnovskis

Timofejevs

Jakovičs

and Pavlovs

, Direct current electric arc furnace with device for controlling azimuthal rotation of the melt around the bath axis; Invention patent No. 15732A (classes F27B 3/08; F27B 1/20, published 20.05.2023; Application No. LVP2021000063 of 07.10.2021, published 20.04.2023, Inventions, trademarks and industrial designs, 2023, No. 4, 248, No. 5, 310; ISSN 2255-9655.

14.

Pavlovs

Jakovics

Chudnovsky

Ivochkin

Yu.

Teplyakov

and Vinogradov

, Numerical and experimental study of electro-vortex flow and temperature field in liquid metal with bifilar power supply, Magnetohydrodynamics58 (2022), 65–79, doi:10.22364/mhd.58.1-2.7.