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Original article / Оригинальная статья
DOI: http://dx.doi.org/10.21285/1814-3520-2020-3-684-693
Calculation of magnetohydrodynamic electrolyser parameters with various types of cathode shell
Evgeniy Yu. Radionov
RUSAL Engineering and Technological Center LLC, Krasnoyarsk, Russia
Abstract: The aim of the research was to analyse the influence of cathode casing design on electrolytic cells with self-baking anodes taking the following magnetohydrodynamic characteristics into account: magnetic field, speed and circulation direction of cathode metal, margin of magnetohydrodynamic stability. The most common type of electrolysers having a Soderberg anode and S-8BM top current lead, for which both counterforce and cradle cathode shell types were used, was taken as an object of study. To simulate the magnetohydrodynamic phenomena occurring in the electrolyser, we used the specialised Blums v5.07 computer program. The following settings were identical for both versions of the models: type of bus, anode assembly parameters, cathode material properties, formation features of the anode mass sintering cone and form of the working space. The calculation of the magnetic field of the electrolyser was carried out using an analytical research method based on the integration of the Poisson (for regions occupied by current) and Laplace (for regions not occupied by current) equations. According to calculations of the speeds and directions of movement of the cathode metal, both types of cathode casing of the electrolyser were shown to be characterised by a four-circuit circulation system, determined by the corresponding location of the anode risers at the inlet and outlet ends of the electrolyser. The results of mathematical modelling show that for electrolysers with a cathode shell of the cradle type, the transverse and vertical components of the magnetic field are less compensated than for cells having a counterforce shell, which affects the average speeds of the cathode metal: circulation speeds will be 0.02 cm / s below. However, the margin of magnetohydrodynamic stability is almost identical for both cathode shell designs. With the same shape of the working space, as well as interpolar distance (41 mm) and metal level (34 cm), the calculated margin of magneto-hydrodynamic stability was 360-380 mV.
Keywords: electrolyser, mathematical modeling, magnetohydrodynamic parameters, cathode shell, magnetic field, interpolar distances, circulation speeds of the cathode metal
Information about the article: Received January 09, 2020; accepted for publication May 19, 2020; available online June 30, 2020.
For citation: Radionov EYu. Calculation of magnetohydrodynamic electrolyser parameters with various types of cathode shell. Vestnik Irkutskogo gosudarstvennogo tehnicheskogo universiteta = Proceedings of Irkutsk State Technical University. 2020;24(3):684-693. https://doi.org/10.21285/1814-3520-2020-3-684-693
УДК 669.713
Расчет магнитогидродинамических параметров работы электролизеров с различным типом катодного кожуха
© Е.Ю. Радионов
ООО «РУСАЛ Инженерно-технологический центр», г. Красноярск, Россия
Резюме: Цель - проанализировать особенность влияния конструкции катодного кожуха на электролизерах с самообжигающимися анодами на следующие магнитогидродинамические характеристики: магнитное поле, скорости и направления циркуляции катодного металла, запас магнитогидродинамической стабильности. В качестве объекта исследования был взят наиболее распространенный тип электролизеров с анодом Содерберга и верхним токоподводом - С-8БМ, для которого приняты контрфорсный и шпангоутный типы катодного кожуха. Для моделирования магнитогидродинамических явлений, происходящих в электролизере, использовалась специализированная компьютерная программа Blums v5.07. Тип ошиновки, параметры анодного узла, свойства материалов катодного устройства, особенности формирования конуса спекания анодной массы, а также форма рабочего пространства для обоих вариантов моделей задавались одинаковыми. Расчет магнитного поля электролизера выполнялся с использованием аналитического метода исследования, основанного на интегрировании уравнений Пуассона (для областей, занятых током) и Лапласа (для областей, не занятых током). Согласно расчетам скоростей и направлений движения катодного металла установлено, что для обоих типов катодных кожухов электро-
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):684-693
лизера характерна четырехконтурная система циркуляции, определяемая соответствующим расположением анодных стояков на входном и выходном торцах электролизера. По результатам математического моделирования было установлено, что для электролизеров с катодным кожухом шпангоутного типа поперечная и вертикальная составляющие магнитного поля менее скомпенсированы, чем на ваннах с контрфорсным кожухом, что отражается на средних скоростях движения катодного металла: скорости циркуляции будут на 0,02 см/с ниже. Однако запас магнитогидродинамической стабильности практически идентичен для обеих конструкций катодного кожуха. При одинаковой форме рабочего пространства, а также значении межполюсного расстояния (41 мм) и уровне металла (34 см) рассчитанный запас магнитогидродинамической стабильности составил 360-380 мВ.
Ключевые слова: электролизер, математическое моделирование, магнитогидродинамические параметры, катодный кожух, магнитное поле, межполюсное расстояние, скорость циркуляции катодного металла
Информация о статье: Дата поступления 09 января 2020 г.; дата принятия к печати 19 мая 2020 г.; дата он-лайн-размещения 30 июня 2020 г.
Для цитирования: Радионов Е.Ю. Расчет магнитогидродинамических параметров работы электролизеров с различным типом катодного кожуха. Вестник Иркутского государственного технического университета. 2020. Т. 24. № 3. С. 684-693. https://doi.org/10.21285/1814-3520-2020-3-684-693
1. INTRODUCTION
Russia is currently the second largest producer of primary aluminium in the world. The main tasks facing the domestic aluminium industry1 [1] are connected with solving complex problems aimed at obtaining new solutions for minimising the environmental burden on the environment [2-6], improving the raw material base [7, 8], expanding the range of manufactured alloys [9], as well as increasing the profitability of products by reducing production costs.
In the context of a global decline in aluminium prices at all plants engaged in its production, the solution to the issue of reducing production costs has become not just relevant, but also the chief determinant of the continuing existence of such plants. The pricing of aluminium obtained by electrolysis of a cryolite-alumina melt directly depends on the indicator of electricity price. The contribution of this expense item to the cost of a unit of production makes up about 20-40% of the entire production cost for aluminium metal. One of the main reasons for the increase in energy losses in the electrolyser [10] and consequent
decrease in current efficiency is directly related to the complex magnetohydrodynamic (MHD) processes taking place in the bath, which are formed in the melt as a result of the interaction of electric and magnetic fields2. Magnetohydrodynamics plays a crucial role in cathode metal circulation and deformation, leading to the reverse transition of the aluminium already obtained at the cathode into the melt with the formation of its oxide. Therefore, when developing new electrolysers and improving existing designs, special attention is paid to optimising their MHD characteristics.
Features of MHD phenomena in aluminium electrolysers are associated with the formation of a magnetic field by the distribution of currents inside a melt [11, 12], the presence of many different phases associated with the molten metal [13], as well as the configurations of anode and cathode assemblies [14, 15].
The MHD parameters of the operation of the electrolyser are determined on the basis of an analysis of the compensation of magnetic fields, the nature of current distribution, the type of motion and shape of cathode metal deformation, as well as the MHD stability margin (AU) of the electrolyser [16].
1
Galevsky GV, Kulagin NM, Mintsis MYa, Sirazutdinov GA. Metallurgy of aluminium: technology, electricity, automation: textbook. 3rd Ed., Revised and corrected. Moscow. Flinta; Nauka, 2008. 572 p. / Галевский Г.В., Кулагин Н.М., Мин-цис М.Я., Сиразутдинов Г.А. Металлургия алюминия: технология, электроснабжение, автоматизация: учеб. по-соб. 3-е изд., перераб. и доп. М.: Флинта: Наука, 2008. 527 с.
2Vetyukov MM, Tsyplakov AM, Shkolnikov SN. Electrometallurgy of aluminium and magnesium: textbook for higher education. Moscow. Metallurgy, 1987. 360 p. / Ветюков М.М., Цыплаков А.М., Школьников С.Н. Электрометаллургия алюминия и магния: учебник для вузов. М.: Металлургия, 1987. 320 с.
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2. RESEARCH METHODS
The direct study of MHD processes in existing aluminium electrolysers implies measurements and subsequent analysis of various direct and indirect parameters affecting MHD processes in the electrolyser: the shape of the working space, current distribution via the main current-carrying elements, magnetic induction fields, cathode metal circulation velocity and deformation, as well as its MHD stability margin. These measurement methods are described in more detail in [14, 17].
However, when designing new electrolysers or predicting the operation of existing baths with altered technical parameters, possible risks can be optimally minimised using a mathematical model as the object under study [18-20].
To date, there are a number of specific narrowly targeted programs for calculating the MHD characteristics of an electrolyser [12, 14, 21, 22], as well as more universal solutions for calculating various associated physical processes [23].
In order to study the influence of the design of the cathode casing, we selected the Blums v5.07 program, which has been tested on many different types of electrolysers [14, 22]. This program is a domestic software product which, during its period of research and development, brought together the input of various institutions, such as the All-Union Aluminium-Magnesium Institute (St. Petersburg), Kirensky Institute of Physics (Krasnoyarsk), Institute of Physics, Academy of Sciences of the Latvian SSR (Riga). Advanced RUSAL electrolysers, such as RA-300, RA-400 and RA-550, were designed at various times using different versions of this program [1, 2].
Using the program, it is possible to calculate the magnetic field in the molten metal, determine the speed and direction of its movement, as well as to predict the supply of MHD stability of the electrolytic cell at different metallic levels and interpolar distances (ID).
Fig. 1 shows the models of both counterforce and cradle cathode shell types for the Soderberg S-8BM electrolyser [3, 10-12, 14, 15, 22, 23].
3. SIMULATION RESULTS AND DISCUSSION
When comparing the two studied mathematical models, it should be noted that the only design element that underwent changes was the cathode shell itself. In the first case, the cathode shell was made according to a counterforce design; in the second, a cradle approach was used. All other parameters remained unchanged, namely: the type and properties of materials, bus arrangement, as well as anode and cathode assembly design.
It should also be noted that during the modelling process the following assumptions were made:
- calculation of the magnetic field induction and, accordingly, the resulting values of the Lorentz forces taking place at the boundary of the metal and electrolyte phases;
- when calculating the speeds and directions of motion of the cathode metal, as well as the MHD stability maps, the influence of gas-hydrodynamic processes in the electro-lyser was not taken into account.
The analysis of the calculation results involved a comparison of the obtained magnetic field induction data, velocities and directions of metal motion, as well as MHD stability maps.
The magnetic field of the electrolyser comprises both external and internal fields. An external magnetic field is created by the surrounding bus arrangement, anode pins and blooms, adjacent electrolysers, cases and ferromagnetic masses (anode and cathode casing, collector beam on baths with calcined anodes, collector beam supports, sheets, automatic point feeding systems, closely located technological cranes, equipment, etc.). The internal magnetic field, on the other hand, is generated by currents flowing in the melt [21, 24].
Table 1 presents the results of calculating the electrolytic magnetic field for three components: Bx (longitudinal), By (transverse), Bz (vertical).
As can be seen from the data in Table 1, for electrolysers with a cradle cathode shell,
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):684-693
the transverse and vertical components of the magnetic field are less compensated than for baths having a counterforce casing. In turn, this is reflected both in the values of the average and maximum cathode metal velocities, as well as in the magnitude of the MHD stability margin.
Metal circulation. One of the resulting actions of electromagnetic forces formed as a result of the interaction of the magnetic field and currents in the melt is the movement of the cathode metal - or, in other words, its circulation.
The circulation of the metal affects the change in the shape of the side ledge and the scull, which participates in heat and mass transfer. The constant movement of the metal causes erosion of the lining of the cell, ultimately determining its lifespan. In the ideal case, the movement of the metal should consist in many small multidirectional contours that cancel each other out.
The results of calculating the speeds and directions of the cathode metal motion are presented in Fig. 2.
a
b
Fig. 1. Models of cathode shells for an electrolyser having a Söderberg anode: a - counterforce, b - cradle Рис. 1. Модели катодных кожухов электролизера с анодом Содерберга: а - контрфорсного, b - шпангоутного
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):684-693
Analysis of the results of the magnetic field calculation Анализ результатов расчета магнитного поля
Table 1 Таблица 1
Parameter, mT Bx By
Counterforce Cradle A Counterforce Cradle A
Maximum value 9.896 9.669 0.227 12.577 12.931 -0.354
Minimum value -9.83 -9.209 -0.621 -11.205 -12.094 0.889
Absolute modulo value* 5.088 4.999 0.089 4.928 5.114 -0.186
*Calculated as the average of a group of numbers taken for each modulo.
As can be seen from the data in Table
1, for electrolysers with a cradle cathode shell, the transverse and vertical components of the magnetic field are less compensated than for baths having a counterforce casing. In turn, this is reflected both in the values of the average and maximum cathode metal velocities, as well as in the magnitude of the MHD stability margin.
Metal circulation. One of the resulting actions of electromagnetic forces formed as a result of the interaction of the magnetic field and currents in the melt is the movement of the cathode metal - or, in other words, its circulation.
The circulation of the metal affects the change in the shape of the side ledge and the scull, which participates in heat and mass transfer. The constant movement of the metal causes erosion of the lining of the cell, ultimately determining its lifespan. In the ideal case, the movement of the metal should consist in many small multidirectional contours that cancel each other out.
The results of calculating the speeds and directions of the cathode metal motion are presented in Fig. 2.
According to the data presented in Fig.
2, it is clear that both types of cathode casing are characterised by a four-circuit circulation system, determined by the corresponding location of the anode risers at the inlet and outlet ends of the electrolyser. Locations with maximum and minimum values coincide in both cases, both with regard to the circulation velocities as well as the directions of the ve-
locities.
It should be noted that the difference between the average and maximum values for both cases is insignificant, differing by hundredths of a cm/s. However, if we take this figure as an indicator, then for baths with a counterforce cathode shell the average circulation speeds will be 0.02 cm/s lower, while the maximum difference will be 0.18 cm/s.
Magnetohydrodynamic stability margin. The interaction between the Lorentz forces and gravitational waves at the metal-electrolyte interface causes the formation of interphase waves, which are referred to in terms of "MHD instability". In [21, 25], MHD instability was considered as the result of a complex process, including interactions between the motion of the phase boundary, electric currents, melt flow and magnetic fields.
The determination of AU was performed for an electrolyser having a fixed current strength of 175 kA with a change in the values of the interpolar distance and metal level.
The margin of MHD stability was calculated as the difference between the operating voltage of the electrolyser in the normal technological mode of operation of the bath and the voltage when MHD instability occurs, i.e. the state of the cell in which the change in time of the operating voltage can be characterised (with some approximation) as harmonic with an oscillation amplitude of ~ 50 - 100 mV and a frequency of the order of ~ 0.3 - 0.6 Hz (Tables 2, 3). In Tables 2 and 3, the following colour indications apply: white colour -
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):684-693
damped metal vibrations, black colour - undamped metal vibrations; grey colour - waves decay only at a small perturbation amplitude.
As can be seen from the data in Table 2, for an electrolyser having a buttress cath-
ode casing at a metal level of 34 cm, the margin AU was 360 mV (4.49 - 4.15 = 0.36 V).
As can be seen from the data in Table 3, for an electrolyser having a cradle cathode shell AU was 380 mV (4.49 - 4.11 = 0.38 V).
-14 V *.j»* iî* -It Î4 -Î 1*4 И2 -OY -&4 04 »V Т/ 1»* ! 3 4 j't ~ii *14 4* 44
b
Fig. 2. Speeds and directions of metal movement: a - counterforce shell, b - cradle shell Рис. 2. Скорости и направления движения металла: a - контрфорсный кожух,
b - шпангоутный кожух
a
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):684-693
Table 2
Magnetohydrodynamic stability margin for a bath with a counterforce cathode shell
Таблица 2
Запас магнитогидродинамической стабильности для ванны
_с контрфорсным катодным кожухом_
ID, cm (Voltage, V)
3.8 (4.11)
3.85 (4.13)
3.9 (4.15)
3.95 (4.16)
4
(4.18)
4.4 (4.30)
4.7 (4.40)
5
(4.49)
Metal level, cm
35 36 37
Table 3
Magnetohydrodynamic stability margin for a bath with a cradle cathode shell
Таблица 3
Запас магнитогидродинамической стабильности для ванны со шпангоутным
катодным кожухом
ID, cm (Voltage, V) Metal level, cm
33 1 34 ■ 35 36 37
3.8 (4.11)
4.1 (4.21)
4.4 (4.30)
4.7 (4.40)
5 (4.49)
4. CONCLUSION
Magnetohydrodynamics plays a crucial role in cathode metal circulation and deformation, leading to a reverse transition of aluminium already obtained at the cathode into
the melt with the formation of oxide. Features of MHD phenomena in aluminium electrolys-ers are associated with the formation of a magnetic field by the distribution of currents inside a melt, the presence of many different phases associated with the molten metal, as
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):684-693
well as the configurations of anode and cathode assemblies.
The MHD parameters of the mathematical modelling of the electrolyser operation with cradle and counterforce cathode shells are estimated based on an analysis of the compensation of magnetic fields, the nature of current distribution, the speed and direction of motion and the shape of the cathode metal deformation, as well as the MHD stability margin of the electrolyser.
In comparison to the counterforce
cathode shell design, the cradle design leads to a slight increase in the average and maximum circulation speeds of the cathode metal, as well as a decrease in the MHD stability margin of the electrolyser by 20 mV.
In order to clarify the results of calculations of the magnetic field and circulation speeds, it is necessary to verify the mathematical models using the magnetic field measurement data and circulation speeds of the cathode metal on electrolysers with various cathode shell designs.
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Authorship criteria
Radionov E.Yu. has obtained and formalized the scientific results and bears the responsibility for plagiarism.
Conflict of interests
The author declares that there is no conflict of interests regarding the publication of this article.
The final manuscript has been read and approved by the author.
INFORMATION ABOUT THE AUTHOR
Evgeniy Yu. Radionov,
Cand. Sci. (Eng.),
Chief specialist of the Department of Mathematical Modeling and Measurements, RUSAL Engineering and Technology Center LLC, 37/1, Pogranichnikov St., Krasnoyarsk 660111, Russia; H e-mail: EYRadionov1983@gmail.ru
lurgy. 2013. [Электронный ресурс]. URL: http://downloads.hindawi.com/archive/2013/196891.pdf (25.11.2019). https://doi.org/10.1155/2013/196891
20. Wang Fuqiang, Zhang Qinsong, Liu Wei, Yang Youjian, Wang Zhaowen. Impact of Local Cathode Electrical Cut-Off on Bath-Metal Two-Phase Flow in an Aluminum Reduction Cell // Metals. 2020. Vol. 10. Issue 1. [Электронный ресурс]. URL: https://www.mdpi.com/2075-4701/10/1/110 (25.11.2019). https://doi.org/10.3390/met10010110
21. Bojarevics V. and Romerio M.V. Long wave instability of liquid metal-electrolyte interface in aluminium electrolysis cells a generation of Sele's criterion // European Journal of Mechanics - B/Fluids. 1994. Vol. 13. Issue 1. Р. 33-56.
22. Пингин В.В., Третьяков Я.А., Радионов Е.Ю., Немчинова Н.В. Перспективы модернизации ошиновки электролизера С-8БМ(С-8Б) // Цветные металлы. 2016. № 3. С. 35-41. https://doi.org/10.17580/tsm.2016.03.06
23. Пат. № 2505626, Российская Федерация, C25C 3/16. Ошиновка электролизера для получения алюминия / В.В. Пингин, В.В. Платонов, Е.Ю. Радионов; заявитель и патентообладатель ООО «Объединенная Компания РУСАЛ Инженерно-технологический центр». Заявл. 25.10.2012; опубл. 27.01.2014. Бюл. № 3.
24. Dupuis M., Bojarevics V., Freibergs J. Demonstration Thermo-Electric and MHD Mathematical Models of а 500 kA Aluminum Electrolysis Cell // Light Metals. 2004. P. 453-459.
25. Grjotheim K., Welch В. Aluminium Smelter Tec h-nology. Dusseldorf: Aluminium Verlag, 1993. 260 р.
Критерии авторства
Радионов Е.Ю. получил и оформил научные результаты и несет ответственность за плагиат.
Конфликт интересов
Автор заявляет об отсутствии конфликта интересов.
Автор прочитал и одобрил окончательный вариант рукописи.
СВЕДЕНИЯ ОБ АВТОРЕ
Радионов Евгений Юрьевич,
кандидат технических наук,
главный специалист отдела математического
моделирования и измерений,
ООО «РУСАЛ Инженерно-технологический центр»,
660111, г. Красноярск, ул. Пограничников, 37/1,
Россия;
Н e-mail: EYRadionov1983@gmail.ru
ВЕСТНИК ИРКУТСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 2020;24(3):684-693
