<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">vsgiu</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Сибирского государственного индустриального университета</journal-title><trans-title-group xml:lang="en"><trans-title>Bulletin of the Siberian State Industrial University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2304 - 4497</issn><issn pub-type="epub">2307-1710</issn><publisher><publisher-name>Федеральное государственное бюджетное образовательное учреждение высшего образования "Сибирский государственный индустриальный университет"</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.57070/2304-4497-2026-2(56)-106-114</article-id><article-id custom-type="elpub" pub-id-type="custom">vsgiu-958</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Раздел 2. Металлургия и материаловедение</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Section 2. Metallurgy and Materials Science</subject></subj-group></article-categories><title-group><article-title>МОДЕЛИРОВАНИЕ ПРОЦЕССА ФОРМИРОВАНИЯ ШЛАКОМЕТАЛЛИЧЕСКИХ НАСТЫЛЕЙ НА СТВОЛЕ ДВУХЪЯРУСНЫХ КИСЛОРОДНЫХ ФУРМ ПРИ ПРОДУВКЕ В БОЛЬШЕГРУЗНЫХ КОНВЕРТЕРАХ</article-title><trans-title-group xml:lang="en"><trans-title>MODELING OF THE FORMATION OF SLAG-METAL SUPPORTS ON THE TRUNK OF TWO-TIER OXYGEN TUYERES DURING PURGING IN HEAVY-DUTY CONVERTERS</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7554-2168</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Протопопов</surname><given-names>Евгений Валентинович</given-names></name><name name-style="western" xml:lang="en"><surname>Protopopov</surname><given-names>Evgenii V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д.т.н., профессор кафедры металлургии черных металлов и химической технологии</p></bio><bio xml:lang="en"><p>Dr. Sci. (Eng.), Professor of the Department of Ferrous Metallurgy and Chemical Technology</p></bio><email xlink:type="simple">protopopov@sibsiu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Фатьянов</surname><given-names>Сергей Сергеевич</given-names></name><name name-style="western" xml:lang="en"><surname>Fat'yanov</surname><given-names>Sergey S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>магистрант кафедры металлургии черных металлов и химической технологии</p></bio><bio xml:lang="en"><p>Master's Student at the Department of Ferrous Metals and Chemical Technology</p></bio><email xlink:type="simple">pimm@sibsiu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-8098-5895</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Запольская</surname><given-names>Екатерина Михайловна</given-names></name><name name-style="western" xml:lang="en"><surname>Zapolskaya</surname><given-names>Ekaterina M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>к.т.н., с.н.с. лаборатории электронной микроскопии и обработки изображений</p></bio><bio xml:lang="en"><p>Cand. Sci. (Eng.), senior researcher Laboratory of Electron Microscopy and Image Processing</p></bio><email xlink:type="simple">beloglazova-ekat@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Сибирский государственный индустриальный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Siberian State Industrial University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>30</day><month>06</month><year>2026</year></pub-date><volume>0</volume><issue>2</issue><fpage>106</fpage><lpage>114</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Протопопов Е., Фатьянов С., Запольская Е., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Протопопов Е., Фатьянов С., Запольская Е.</copyright-holder><copyright-holder xml:lang="en">Protopopov E., Fat'yanov S., Zapolskaya E.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://vestnik.sibsiu.ru/jour/article/view/958">https://vestnik.sibsiu.ru/jour/article/view/958</self-uri><abstract><p>Рассмотрены основные технологические особенности конвертерной плавки при использовании для продувки двухъярусных кислородных фурм. Проанализированы причины формирования металлошлаковых настылей на стволе фурмы при верхней продувке расплава в большегрузных конвертерах в зависимости от особенностей организации дутьевого режима и различном уровне вспененной шлакометаллической эмульсии в рабочем пространстве агрегата. Предложена сопряженная трехмерная математическая модель гидродинамических и массопереносных процессов в шлаковой и металлической фазах конвертера, которая может быть использована для изучения закономерностей формирования и направленности циркуляционных потоков расплава в ванне при положениях двухъярусной фурмы, количестве сопел в нижнем и верхнем ярусах, углах наклона сопел, расходах кислорода через ярусы сопел и прочих конструктивных и технологических параметрах. Сформулирована физическая модель и выполнено численное моделирование процесса продувки металла в конвертере емкостью 350 т с использованием двухъярусной фурмы с четырьмя соплами Лаваля в нижнем наконечнике и двенадцатью соплами в верхнем ярусе. Представленные данные позволяют получить достоверную информацию о характере движения металлической и газошлаковой фаз при продувке в конвертере и механизме образования шлакометаллической настыли на стволе фурмы.</p></abstract><trans-abstract xml:lang="en"><p>The main technological features of converter melting when used for purging two-tier hydrogen tuyeres are considered. The reasons for the formation of metal slag deposits on the tuyere trunk during upper purging of the melt in heavy-duty converters are analyzed, depending on the specifics of the organization of the blast regime and the different level of foamed slag-metal emulsion in the working space of the unit. A conjugated three-dimensional mathematical model of hydrodynamic and mass transfer processes in the slag and metal phases of the converter is proposed, which can be used to study the patterns of formation and direction of melt circulation flows in a bath at the positions of a two-tier tuyere, the number of nozzles in the lower and upper tiers, the angles of inclination of the nozzles, oxygen consumption through the tiers of nozzles and other design and technological parameters. A physical model is formulated and numerical simulation of the metal purging process in a 350 ton converter is performed using a two-tiered tuyere with four Laval nozzles in the lower tip and twelve nozzles in the upper tier. The presented data make it possible to obtain reliable information about the nature of the movement of the metal and slag phases during purging in the converter and the mechanism of formation of slag-metal deposits on the tuyere trunk.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>конвертер</kwd><kwd>кислородная продувка</kwd><kwd>двухъярусная фурма</kwd><kwd>гидрогазодинамика ванны</kwd><kwd>математическая модель</kwd><kwd>шлакометаллическая настыль</kwd></kwd-group><kwd-group xml:lang="en"><kwd>converter</kwd><kwd>oxygen purge</kwd><kwd>two-tier tuyere</kwd><kwd>hydrogas dynamics of the bath</kwd><kwd>mathematical model</kwd><kwd>slag-metal flooring</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено в рамках государственного задания Министерства науки и высшего  образования Российской Федерации № 075-00087-2401.</funding-statement><funding-statement xml:lang="en">Research was carried out within the framework of the state task of the Ministry of Science and Higher  Edication of the Russian Federation № 075-00087-2401.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Бойченко Б.М., Охотского В.Б., Харлашина П.С. Конвертерное производство стали: теория, технология, качество стали, конструкции агрегатов, рециркуляция материалов и экология. Днепропетровск: Днепр-ВАЛ, 2006:454.</mixed-citation><mixed-citation xml:lang="en">Boichenko B.M., Okhotskogo V.B., Kharlashina P.S. Converter steel production: theory, technology, steel quality, aggregate designs, material recycling and ecology. Dnepropetrovsk: Dnepr-VAL, 2006:454. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Григорович К.В. Современное состояние черной металлургии и направления ее развития в цифровой экономики. В кн.: Труды XV международного конгресса сталеплавильщиков. Москва: РПК Принт АП, 2018:42–59.</mixed-citation><mixed-citation xml:lang="en">Grigorovich K.V. The current state of ferrous metallurgy and the directions of its development in the digital economy. In: Proceedings of the XV International Congress of Steelmakers. Moscow: RPK Print AP, 2018:42–59. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Лякишев Н.П. Сравнительная характери-стика состояния кислородно-конвертерного производства стали в России и за рубежом. Москва: Элиз, 2000:64.</mixed-citation><mixed-citation xml:lang="en">Lyakishev N.P. Comparative characteristics of the state of oxygen converter steel production in Russia and abroad. Moscow: Eliz, 2000:64.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Kishmoto Y., Saito N. Development and prospect of combined blowing converter in Japan. Tetsu-to-hagane (Journal of the Iron and Steel Institute of Japan). 2014;100(4):445‒455.</mixed-citation><mixed-citation xml:lang="en">Kishmoto Y., Saito N. Development and prospect of combined blowing converter in Japan. Tetsu-to-hagane (Journal of the Iron and Steel Institute of Japan). 2014;100(4):445‒455.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Su F., Lampinen H.-O., Robinson R. Recy-cling of sludge and dust to the BOF converter by cold bonded pelletizing. ISIJ International. 2004;44(4):770‒776. https://doi.org/10.2355/isijinternational.44.770</mixed-citation><mixed-citation xml:lang="en">Su F., Lampinen H.-O., Robinson R. Recy-cling of sludge and dust to the BOF converter by cold bonded pelletizing. ISIJ International. 2004;44(4):770‒776. https://doi.org/10.2355/isijinternational.44.770</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Меркер Э.Э., Карпенко Г.А. Физические процессы в конвертере и энергоэкологические показатели производства. Старый Оскол: Изд-во «Тонкие наукоемкие технологии», 2014:328.</mixed-citation><mixed-citation xml:lang="en">Merker E.E., Karpenko G.A. Physical processes in the converter and energy-ecological indicators of production. Stary Oskol: Izd-vo «Tonkie naukoemkie tekhnologii», 2014:328. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Смирнов Л.А., Бабенко А.А., Данилин Ю.А. и др. Освоение технологии комбинированной продувки в 160-т конвертерах. Сталь. 2010;5:43–45.</mixed-citation><mixed-citation xml:lang="en">Smirnov L.A., Babenko A.A., Danilin YU.A. et al. Mastering the technology of combined purging in 160-ton converters. Stal'. 2010;5:43–45. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Протопопов Е.В., Уманский А.А., Беленецкий Е.А., Фатьянов С.С. Высокотемпературное моделирование процессов тепломассообмена при комбинированной продувке конвертерной ванны. Вестник Сибирского государственного индустриального университета. 2024;4(50):100–109.</mixed-citation><mixed-citation xml:lang="en">Protopopov E.V., Umanskii A.A., Belenetskii E.A., Fat'yanov S.S. High-temperature modeling of heat and mass transfer processes during combined purging of a converter bath. Bulletin of the Siberian State Industrial University. 2024;4(50):100–109. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">http://doi.org/10.57070/2304-4497-2024-100-109</mixed-citation><mixed-citation xml:lang="en">http://doi.org/10.57070/2304-4497-2024-100-109</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Stel van der J. Top gas recycling blast furnace benefits and “green” and sustainable ironmaking. Ironmaking and Steelmaking. 2013;40:483‒487.</mixed-citation><mixed-citation xml:lang="en">Stel van der J. Top gas recycling blast furnace benefits and “green” and sustainable ironmaking. Ironmaking and Steelmaking. 2013;40:483‒487.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Puzyrev Yu.A., Puzyrev A.Yu. Installation of purge units for supplying inert gases to the molten metal in converters. Refractories and Industrial Ceramics. 2023;64(3):229‒233.</mixed-citation><mixed-citation xml:lang="en">Puzyrev Yu.A., Puzyrev A.Yu. Installation of purge units for supplying inert gases to the molten metal in converters. Refractories and Industrial Ceramics. 2023;64(3):229‒233.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Протопопов Е.В., Лаврик Д.А., Чернятевич А.Г. Повышение эффективности дожигания отходящих газов в конвертерах с жидкофазным восстановлением. Известия вузов. Черная металлургия. 2001;6:13‒17.</mixed-citation><mixed-citation xml:lang="en">Protopopov E.V., Lavrik D.A., Chernyatevich A.G. Improving the efficiency of exhaust gas afterburning in liquid-phase reduction converters. Izvestiya vuzov. Chernaya metallurgiya. 2001;6:13‒17. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Ярошенко А.В., Суханов Ю.Ф., Долгих Ю.Н. Оптимизация комбинированной продувки в конвертере с применением нового технического обеспечения. Сталь. 2008;8:19–21.</mixed-citation><mixed-citation xml:lang="en">Yaroshenko A.V., Sukhanov Yu.F., Dolgikh Yu.N. Optimization of combined purging in a converter using new technical support. Stal'. 2008;8:19–21. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Бабенко А.А., Челпан С.М., Кокаренко О.Н. Заметалливание кислородных продувочных фурм при выплавке стали из углеродистого полупродукта. Известия вузов. Черная металлургия. 2005;6:33–35.</mixed-citation><mixed-citation xml:lang="en">Babenko A.A., Chelpan S.M., Kokarenko O.N. Crushing of oxygen purge tuyeres during steel smelting from carbonaceous intermediates. Chernaya metallurgiya. 2005;6:33–35. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Singh A.K., Raju M.T., Jha U. Recycling of basic oxygen furnace (BOF) sludge in iron and steel works. International Journal of Environmental Technology and Management. 2011;14(1-4):19‒32. https://doi.org/10.1504/IJETM.2011.039255</mixed-citation><mixed-citation xml:lang="en">Singh A.K., Raju M.T., Jha U. Recycling of basic oxygen furnace (BOF) sludge in iron and steel works. International Journal of Environmental Technology and Management. 2011;14(1-4):19‒32. https://doi.org/10.1504/IJETM.2011.039255</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Stone R.P., Neith D., Koester S. et al. Further process improvements at Severstal Sparrows Point via new technology implementation. AIS Tech 2009 Proceedings. 2009;1:737‒747.</mixed-citation><mixed-citation xml:lang="en">Stone R.P., Neith D., Koester S. et al. Further process improvements at Severstal Sparrows Point via new technology implementation. AIS Tech 2009 Proceedings. 2009;1:737‒747.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Tianjie Fu, Shimin Liu, Peiyu Li. Digital twin-driven smelting process management method for converter steelmaking. Journal of Intelligent Manufacturing. 2025;36:2749‒2765.</mixed-citation><mixed-citation xml:lang="en">Tianjie Fu, Shimin Liu, Peiyu Li. Digital twin-driven smelting process management method for converter steelmaking. Journal of Intelligent Manufacturing. 2025;36:2749-2765.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Pal J., Singh S., Ghose A.K., Mohan S. A mathematical model for end point control of basic oxygen steelmaking furnace. Journal of Metallurgy and Materials Science. 2002;44(1):39‒49.</mixed-citation><mixed-citation xml:lang="en">Pal J., Singh S., Ghose A.K., Mohan S. A mathematical model for end point control of basic oxygen steelmaking furnace. Journal of Metallurgy and Materials Science. 2002;44(1):39‒49.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Cao L.L., Liu Q., Wang Z., Li N. Interaction behavior between top blown jet and molten steel during BOF steelmaking process. Ironmaking and Steelmaking. 2018;45(3):239‒248. https://doi.org/10.1080/03019233.2016.1255373</mixed-citation><mixed-citation xml:lang="en">Cao L.L., Liu Q., Wang Z., Li N. Interaction behavior between top blown jet and molten steel during BOF steelmaking process. Ironmaking and Steelmaking. 2018;45(3):239‒248. https://doi.org/10.1080/03019233.2016.1255373</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Dering D., Swartz C., Dogan N. Dynamic modeling and simulation of basic oxygen furnace (BOF) operation. Processes. 2020;8(4):483. https://doi.org/10.3390/pr8040483</mixed-citation><mixed-citation xml:lang="en">Dering D., Swartz C., Dogan N. Dynamic modeling and simulation of basic oxygen furnace (BOF) operation. Processes. 2020;8(4):483. https://doi.org/10.3390/pr8040483</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Югов П.И. Современное состояние мировой практики конвертерного производства и научные направления его развития в России. Черная металлургия. 2001;9:9‒13.</mixed-citation><mixed-citation xml:lang="en">Yugov P.I. The current state of the world practice of converter production and scientific directions of its development in Russia. Chernaya metallurgiya. 2001;9:9‒13. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Ughadpada K., Briglio S., Mohammed G. Production improvement of No. 2 BOSP at ESAI. Iron and Steel Technology. 2010;11:59‒64.</mixed-citation><mixed-citation xml:lang="en">Ughadpada K., Briglio S., Mohammed G. Production improvement of No. 2 BOSP at ESAI. Iron and Steel Technology. 2010;11:59‒64.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Протопопов Е.В, Чернятевич А.Г., Филиппенко С.А., Фейлер С.В. Перспективная конструкция кислородной фурмы для конвертеров ОАО «ЕВРАЗ ЗСМК» емкостью 350 т. Вестник Сибирского государственного индустриального университета. 2013;(2):4‒7.</mixed-citation><mixed-citation xml:lang="en">Protopopov E.V, Chernyatevich A.G., Fili-penko S.A., Feiler S.V. Prospective design of an oxygen form for converters of EVRAZ ZSMK capacity of 350 t. Bulletin of the Siberian State Industrial University. 2013;(2):4‒7. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Stone R.P., Neith D., Koester S. Further pro-cess improvements at Severstal Sparrows Point via new technology implementation. AIS Tech 2009 Proceeding. 2009;1:737–747.</mixed-citation><mixed-citation xml:lang="en">Stone R.P., Neith D., Koester S. Further pro-cess improvements at Severstal Sparrows Point via new technology implementation. AIS Tech 2009 Proceeding. 2009;1:737–747.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Voraberger B., Wimmer G., Dieguez Salgado U., Wimmer E., Pastucha K., Fleischanderl A. Green LD (BOF) steelmaking ‒ reduced CO2 emissions via increased scrap rate. Metals. 2022;12(3):466. https://doi.org/10.3390/met12030466</mixed-citation><mixed-citation xml:lang="en">Voraberger B., Wimmer G., Dieguez Salgado U., Wimmer E., Pastucha K., Fleischanderl A. Green LD (BOF) steelmaking ‒ reduced CO2 emissions via increased scrap rate. Metals. 2022;12(3):466. https://doi.org/10.3390/met12030466</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Самохвалов С.Е., Сокол А.Н. Квазитрех-мерная математическая модель гидродинамических процессов в полости конвертера. Математическое моделирование. 2008;2(19):67–70.</mixed-citation><mixed-citation xml:lang="en">Samokhvalov S.E., Sokol A.N. Quasi-three-dimensional mathematical model of hydrodynamic processes in the converter cavity. Matematicheskoe modelirovanie. 2008;2(19):67–70. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Сокол А.Н. Математическое моделирование гидродинамических процессов в полости конвертера во время верхней продувки в трехмерной постановке. Вестник Херсонского технического университета. 2010;3(39):448–454.</mixed-citation><mixed-citation xml:lang="en">Sokol A.N. Mathematical modeling of hydrodynamic processes in the converter cavity during upper purging in a three-dimensional formulation. Vestnik Khersonskogo tekhnicheskogo universiteta. 2010;3(39):448–454. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Самохвалов С.Е., Сокол А.М. Математическое моделирование процессов перемешивания в конвертере. Днепродзержинск: изд. ДДТУ, 2013:99.</mixed-citation><mixed-citation xml:lang="en">Samokhvalov S.E., Sokol A.M. Mathematical modeling of mixing processes in a converter. Dneprodzerzhinsk: izd. DDTU, 2013:99. (In Russ.).</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Chen J.D., Zhang C.J., Feng J.H. Static me-chanics model in loading converter and energy saving. Journal of Hebei Institute of Technology. 2007;29(1):32–35.</mixed-citation><mixed-citation xml:lang="en">Chen J.D., Zhang C.J., Feng J.H. Static me-chanics model in loading converter and energy saving. Journal of Hebei Institute of Technology. 2007;29(1):32–35.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
