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<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">vguit</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Воронежского государственного университета инженерных технологий</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Voronezh State University of Engineering Technologies</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-910X</issn><issn pub-type="epub">2310-1202</issn><publisher><publisher-name>VSUET</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.20914/2310-1202-2023-2-38-44</article-id><article-id custom-type="elpub" pub-id-type="custom">vguit-3219</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>Процессы и аппараты пищевых производств</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Processes and equipment for food industry</subject></subj-group></article-categories><title-group><article-title>Перспективы методов вычислительной гидродинамики при исследовании мембранных процессов</article-title><trans-title-group xml:lang="en"><trans-title>Perspectives of computational fluid dynamics methods in the study of membrane processes</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5306-0328</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ключников</surname><given-names>А. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Klyuchnikov</surname><given-names>A. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д.т.н., профессор, кафедра машин и аппаратов пищевых производств, пр-т Революции, 19, г. Воронеж, 394036, Россия</p></bio><bio xml:lang="en"><p>Dr. Sci. (Engin.), professor, machines and apparatuses of food production department, Revolution Av., 19 Voronezh, 394036, Russia</p></bio><email xlink:type="simple">kaivanov@mail.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/0000-0001-9388-6303</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Овсянников</surname><given-names>В. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Ovsyannikov</surname><given-names>V. Y.</given-names></name></name-alternatives><bio xml:lang="ru"><p>д.т.н., профессор, кафедра машин и аппаратов пищевых производств, пр-т Революции, 19, г. Воронеж, 394036, Россия</p></bio><bio xml:lang="en"><p>Dr. Sci. (Engin.), professor, machines and apparatuses of food production department, Revolution Av., 19 Voronezh, 394036, Russia</p></bio><email xlink:type="simple">ows2003@mail.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>Ключникова</surname><given-names>Д. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Klyuchnikova</surname><given-names>D. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>к.т.н., доцент, кафедра технологии переработки продуктов животного происхождения, пр-т Революции, 19, г. Воронеж, 394036, Россия</p></bio><bio xml:lang="en"><p>Cand. Sci. (Engin.), associate professor, processing technology of animal products department, Revolution Av., 19 Voronezh, 394036, Russia</p></bio><email xlink:type="simple">dina.key@mail.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/0000-0001-5308-4752</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Давыдов</surname><given-names>А. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Davydov</surname><given-names>A. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>к.т.н., доцент, кафедра ресторанного бизнеса, пер. Стремянный, 36, г. Москва, 117997, Россия</p></bio><bio xml:lang="en"><p>Cand. Sci. (Engin.), associate professor, restaurant business department, Stremyanny lane, 36, 117997, Moscow, Russia</p></bio><email xlink:type="simple">davydov.am@rea.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Воронежский государственный университет инженерных технологий</institution></aff><aff xml:lang="en"><institution>Voronezh State University of Engineering Technologies</institution></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Российский экономический университет имени Г.В. Плеханова</institution></aff><aff xml:lang="en"><institution>Plekhanov Russian University of Economics</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2023</year></pub-date><pub-date pub-type="epub"><day>26</day><month>10</month><year>2023</year></pub-date><volume>85</volume><issue>2</issue><fpage>38</fpage><lpage>44</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Ключников А.И., Овсянников В.Ю., Ключникова Д.В., Давыдов А.М., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Ключников А.И., Овсянников В.Ю., Ключникова Д.В., Давыдов А.М.</copyright-holder><copyright-holder xml:lang="en">Klyuchnikov A.I., Ovsyannikov V.Y., Klyuchnikova D.V., Davydov A.M.</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://www.vestnik-vsuet.ru/vguit/article/view/3219">https://www.vestnik-vsuet.ru/vguit/article/view/3219</self-uri><abstract><p>При математическом моделировании мембранных процессов изучение структурных особенностей используемых мембран и существенная ограниченность информации при формальном описании их разделительных свойств привели к разработке физических моделей, учитывающих не только особенности строений реальных мембран, но и их особенностей функционирования. При составлении физических моделей мембранных процессов, невозможно объективно провести количественный учет большинства факторов из-за их большого многообразия и изменчивости, что далеко отдаляет математическую модель от реального процесса. Именно поэтому методы вычислительной гидродинамики надежно и эффективно выполняют расчеты для всех физических моделей и типов, включая стационарное или переходное течение, несжимаемое или сжимаемое течение (от малых дозвуковых до гиперзвуковых), моделирование ламинарных или турбулентных потоков, ньютоновских или неньютоновских жидкостей, идеального или реального газа. Авторами проведен анализ возможности использования вычислительной гидродинамики CFD для расчета гидродинамики потоков в мембранном биореакторе на основе полых волокон. Сафаровым Р.Р. и др. была построена электронная геометрическая модель установки, осуществлен выбор геометрии сетки с различной плотностью для оптимизации времени расчетов и точности решения для конкретного случая, рассчитана кинетическая зависимость роста клеток, определены расходы подачи питательной среды во внутриволоконное и межволоконное пространства биореактора, проанализированы гидродинамические условия. Все вышесказанное подтверждает перспективы использования CFD методов для моделирования мембранных процессов, осложненных культивированием клеток на поверхности мембран.</p></abstract><trans-abstract xml:lang="en"><p>In the mathematical modeling of membrane processes, the study of the structural features of the membranes used and the significant limitation of information in the formal description of their separation properties led to the development of physical models that take into account not only the structural features of real membranes, but also their functioning features. When compiling physical models of membrane processes, it is impossible to objectively carry out a quantitative accounting of most factors due to their great diversity and variability, which distances the mathematical model far from the real process. This is why CFD methods reliably and efficiently perform calculations for all physical models and types, including steady or transient flow, incompressible or compressible flow (from small subsonic to hypersonic), laminar or turbulent flow simulations, Newtonian or non-Newtonian fluids, ideal or real gas . The authors analyzed the possibility of using CFD to calculate the hydrodynamics of flows in a membrane bioreactor based on hollow fibers. Safarov R.R. etc., an electronic geometric model of the installation was built, mesh geometry with different densities was selected to optimize the calculation time and solution accuracy for a specific case, the kinetic dependence of cell growth was calculated, the flow rates of the nutrient medium into the intrafiber and interfiber spaces of the bioreactor were determined, and the hydrodynamic conditions were analyzed. All of the above confirms the prospects for using CFD methods for modeling membrane processes complicated by culturing cells on the surface of membranes.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>математическое моделирование</kwd><kwd>вычислительная гидродинамика</kwd><kwd>мембранный модуль</kwd><kwd>мембранный биореактор</kwd><kwd>концентрационная поляризация</kwd><kwd>культивирование</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical modeling</kwd><kwd>computational fluid dynamics</kwd><kwd>membrane module</kwd><kwd>membrane bioreactor</kwd><kwd>concentration polarization</kwd><kwd>cultivation</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Dash S., Mohanty S. Separation of lanthanum and neodymium in a hollow fiber supported liquid membrane: CFD modelling and experimental validation // Minerals Engineering. 2022. 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