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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">alternative</journal-id><journal-title-group><journal-title xml:lang="ru">Альтернативная энергетика и экология (ISJAEE)</journal-title><trans-title-group xml:lang="en"><trans-title>Alternative Energy and Ecology (ISJAEE)</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1608-8298</issn><publisher><publisher-name>Международный издательский дом научной периодики "Спейс</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.15518/isjaee.2024.10.110-128</article-id><article-id custom-type="elpub" pub-id-type="custom">alternative-2528</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>I. ВОЗОБНОВЛЯЕМАЯ ЭНЕРГЕТИКА 5. Энергия биомассы 5-2-0-0 Термохимические газогенераторы</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>I. RENEWABLE ENERGY 5. Energy of biomass 5-2-0-0 Thermochemical gas generators</subject></subj-group></article-categories><title-group><article-title>Влияние свойств частиц на границу раздела между низко- и высоконцентрированными газодисперсными потоками</article-title><trans-title-group xml:lang="en"><trans-title>Particle properties influence on the borderline between gas-dispersed flows with high and low particle concentrations</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Ершов</surname><given-names>М. И.</given-names></name><name name-style="western" xml:lang="en"><surname>Ershov</surname><given-names>M. I.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Ершов Михаил Игоревич, инженер-исследователь лаборатории Новых энергетических технологий Уральского энергетического института; инженер технической поддержки </p><p>620002, г. Екатеринбург, ул. Мира, 19</p><p>620131, г. Екатеринбург, ул. Металлургов, 16б</p></bio><bio xml:lang="en"><p>Ershov Mikhail Igorevich, Research Engineer of the New Energy Technology Laboratory of Ural Power Engineering Institute; technical support engineer</p><p>620002, Yekaterinburg, 19 Mira Street</p><p>620131, Yekaterinburg, 16b Metallurgov Street</p></bio><email xlink:type="simple">miershov@urfu.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>Абаимов</surname><given-names>Н. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Abaimov</surname><given-names>N. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Абаимов Николай Анатольевич, кандидат технических наук, доцент кафедры Тепловых электрических станций Уральскогоэнергетического института </p><p>620002, г. Екатеринбург, ул. Мира, 19</p></bio><bio xml:lang="en"><p>Abaimov Nikolai Anatolevich, Candidate of Technical Sciences,Associate Professor of the Department of Thermal Power Plants of the Ural Power Engineering Institute</p><p>620002, Yekaterinburg, 19 Mira Street</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Осипов</surname><given-names>П. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Osipov</surname><given-names>P. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Осипов Павел Валентинович,  старший преподаватель кафедры Тепловых электрических станций Уральского энергетического института</p><p>620002, г. Екатеринбург, ул. Мира, 19</p></bio><bio xml:lang="en"><p>Osipov Pavel Valentinovich, Currently he is a Senior Lecturer at theThermal Power Plants Department of Ural Power Engineering Institute</p><p>620002, Yekaterinburg, 19 Mira Street</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Тупоногов</surname><given-names>В. Г.</given-names></name><name name-style="western" xml:lang="en"><surname>Tuponogov</surname><given-names>V. G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Тупоногов Владимир Геннадьевич, доктор технических наук, профессор кафедры Теплоэнергетики и теплотехники Уральского энергетического института  </p><p>620002, г. Екатеринбург, ул. Мира, 19</p></bio><bio xml:lang="en"><p>Tuponogov Vladimir Gennadievich, Doctor of Technical Sciences. Currently he is Professor of Department of Heat Power Engineering and Heat Engineering</p><p>620002, Yekaterinburg, 19 Mira Street</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Алексеенко</surname><given-names>С. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Alekseenko</surname><given-names>S. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Алексеенко Сергей Владимирович,доктор физико-математических наук, академик РАН, научный руководитель; главный научный сотрудник лаборатории Новых энергетических технологий Уральского энергетического института </p><p>620002, г. Екатеринбург, ул. Мира, 19</p><p>630090, г. Новосибирск, пр. Академика Лаврентьева, 1 </p></bio><bio xml:lang="en"><p>Alekseenko Sergey Vladimirovich, Doctor of Physical and Mathematical Sciences, Academician of the Russian Academy of Sciences. Currently he is a Scientific Director; Chief Researcher of the New Energy Technology Laboratory</p><p>620002, Yekaterinburg, 19 Mira Street</p><p>630090, Novosibirsk, Academician Lavrentyev Avenue 1 </p></bio><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Рыжков</surname><given-names>А. Ф.</given-names></name><name name-style="western" xml:lang="en"><surname>Ryzhkov</surname><given-names>A. F</given-names></name></name-alternatives><bio xml:lang="ru"><p>Рыжков Александр Филиппович, доктор технических наук, профессор, заведующий лабораторией Новых энергетическихтехнологий, профессор кафедры Тепловых электрических станций Уральского энергетического института</p><p>620002, г. Екатеринбург, ул. Мира, 19</p></bio><bio xml:lang="en"><p>Doctor of Technical Sciences. Currently he is a Head of the New Energy New Energy Technology Laboratory, Professor of the Department of Thermal Power Plants of Ural Power Engineering Institute</p><p>Ryzhkov Alexander Filippovich,</p><p>620002, Yekaterinburg, 19 Mira Street</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Уральский федеральный университет; ООО «ПЛМ Урал»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Ural Federal University; PLM Ural LLC</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Уральский федеральный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Ural Federal University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-3"><aff xml:lang="ru"><institution>Уральский федеральный университет; Институт Теплофизики им. С. С. Кутателадзе СО РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Ural Federal University; Kutateladze Institute of Thermophysics of the SB RAS</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>23</day><month>01</month><year>2025</year></pub-date><volume>0</volume><issue>10</issue><fpage>110</fpage><lpage>128</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Международный издательский дом научной периодики "Спейс, 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Международный издательский дом научной периодики "Спейс</copyright-holder><copyright-holder xml:lang="en">Международный издательский дом научной периодики "Спейс</copyright-holder><license xlink:href="https://www.isjaee.com/jour/about/submissions#copyrightNotice" xlink:type="simple"><license-p>https://www.isjaee.com/jour/about/submissions#copyrightNotice</license-p></license></permissions><self-uri xlink:href="https://www.isjaee.com/jour/article/view/2528">https://www.isjaee.com/jour/article/view/2528</self-uri><abstract><p>На примере задачи обтекания двух последовательно расположенных тел методами CFD проведена сравнительная оценка условий возможной потери гидродинамической устойчивости низконцентрированного газодисперсного потока при вариации физических свойств частиц в диапазоне, характерном для промышленных энергетических установок на биомассе и ископаемом топливе. Выполнена валидация численной модели ламинарного обтекания одиночных частиц на основе результатов экспериментов Роу и Хенвуда для относительного расстояния между шариками 5, 11, 17 и 23. Показано, что профиль скорости перед первым шариком влияет на соотношение сил, действующих на каждый из шариков. Рассчитано относительное межцентровое расстояние (x/d)кр, при котором отношение силы, действующей на вторую частицу (F2) к силе, действующей на первую частицу (F1), равно 0,95 (начало сближения) в условиях установившегося равномерного течения газа в элементарной трубке потока бесконечно большого поточного реактора для частиц сферической и пластинчатой формы. В диапазоне чисел Рейнольдса 2,0·10-1…3,2·103 определено влияние плотности, линейных размеров и формы на соответствующую (x/d)кр объемную концентрацию φкр. Также для сфер рассмотрено соотношение сил F2/F1 = 0,90, что позволило установить переходную зону между поточными установками и котлами с ЦКС.</p><p>Результаты моделирования обтекания газом двух пластинок с тремя различными ориентациями относительно набегающего потока показывают, что взаимная ориентация пластинчатых частиц в потоке влияет на их гидродинамическое взаимодействие, повышая риск сближения в случае ориентации частиц наибольшей гранью перпендикулярно набегающему потоку и понижая риск сближения в случае ориентации частиц наименьшей гранью перпендикулярно набегающему потоку, относительно сценария обтекания двух сфер эквивалентного диаметра. Действенность предложенного метода прошла проверку при анализе ряда объектов, включающих энергетические котлы, промышленные газификаторы и крупные стендовые установки.</p></abstract><trans-abstract xml:lang="en"><p>Computational fluid dynamics (CFD) methods were used to analyze the flow around two sequentially arranged bodies. A comparative assessment was conducted to determine the conditions under which hydrodynamic instability may occur in low-concentration gas-dispersed flows. Variations in the physical properties of particles, typical of those found in industrial biomass and fossil fuel energy installations, were considered in this assessment. The numerical model for laminar flow around individual particles was validated using the experimental data of Rowe and Henwood for dimensionless intersphere distance of 5, 11, 17, and 23. It was demonstrated that the velocity profile upstream of the first sphere influences the ratio of forces acting on each sphere. The critical dimensionless center-to-center distance (x/d)кр was calculated, at which the ratio of the force acting on the second particle (F2) to that on the first particle (F1) equals 0,95 (indicating the onset of convergence), under steady uniform gas flow conditions in an elemental streamtube of an ideal entrained-flow reactor for particles of spherical and plate-like shapes. Within the Reynolds number range 2,0·10-1…3,2·103, the influence of particle density, size, and shape on the corresponding critical volume concentration φкр and (x/d)кр was determined. Additionally, for spheres, the force ratio F2/F1 = 0,90 was considered, which allowed to establish the transition zone between entrained-flow systems and circulating fluidized bed (CFB) boilers. Simulations of gas flow around two plates with three different orientations relative to the incoming flow were conducted. The results demonstrate that the mutual orientation of plate-like particles in the flow affects their hydrodynamic interaction. Specifically, compared to the scenario of flow around two spheres of equivalent diameter, the risk of convergence increases when the particles are oriented with their largest face perpendicular to the incoming flow, and decreases when they are oriented with their smallest face perpendicular to the incoming flow. The effectiveness of the proposed method was verified by analyzing a range of systems, including power boilers, industrial gasifiers, and large-scale test installations.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>моделирование</kwd><kwd>CFD</kwd><kwd>число Рейнольдса</kwd><kwd>сила сопротивления</kwd><kwd>сфера</kwd><kwd>пластинка</kwd><kwd>Ansys Fluent</kwd></kwd-group><kwd-group xml:lang="en"><kwd>modelling</kwd><kwd>CFD</kwd><kwd>Reynolds number</kwd><kwd>drag force</kwd><kwd>sphere</kwd><kwd>plate</kwd><kwd>Ansys Fluent</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено при финансовой поддержке Министерства науки и высшего образования Российской Федерации в рамках Программы развития Уральского федерального университета имени первого Президента России Б. Н. Ельцина в соответствии с программой стратегического академического лидерства «Приоритет-2030». Название проекта: Разработка научно-технологических основ получения синтез-газа из биомассы в несущем потоке с использованием экспериментальных методов, математического моделирования и опытно-промышленных испытаний. Номер проекта: 4.69.</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">. Nascimento F. R. M., González A. M., Lora E. E. S., Ratner A., Palacio J. C. E., Reinaldo R. Benchscale bubbling fluidized bed systems around the world – Bed agglomeration and collapse: A comprehensive review // International Journal of Hydrogen Energy, 2021, vol. 46, no. 36, pp. 18740-18766, doi: 10.1016/j.ijhydene.2021.02.086.</mixed-citation><mixed-citation xml:lang="en">. Nascimento F. R. M., González A. M., Lora E. E. S., Ratner A., Palacio J. C. E., Reinaldo R. Benchscale bubbling fluidized bed systems around the world – Bed agglomeration and collapse: A comprehensive review // International Journal of Hydrogen Energy, 2021, vol. 46, no. 36, pp. 18740-18766, doi: 10.1016/j.ijhydene.2021.02.086.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">. Göktepe B., Umeki K., Gebart R. Does distance among biomass particles affect soot formation in an entrained flow gasification process? // Fuel Processing Technology, 2016, vol. 141, pt. 1, pp. 99-105, doi: 10.1016/j.fuproc.2015.06.038.</mixed-citation><mixed-citation xml:lang="en">. Göktepe B., Umeki K., Gebart R. Does distance among biomass particles affect soot formation in an entrained flow gasification process? // Fuel Processing Technology, 2016, vol. 141, pt. 1, pp. 99-105, doi: 10.1016/j.fuproc.2015.06.038.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">. Бабий В. И., Куваев Ю. Ф. Горение угольной пыли и расчет пылеугольного факела. – М.: Энергоатомиздат, 1986. – 208 с.</mixed-citation><mixed-citation xml:lang="en">. Babij V. I., Kuvaev YU. F. Gorenie ugol’noj pyli i raschet pyleugol’nogo fakela. – M.: Ehnergoatomizdat, 1986. – 208 s.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">. Hasse C., Debiagi P., Wen X., Hildebrandt K., Vascellari M., Faravelli T. Advanced modeling approaches for CFD simulations of coal combustion and gasification // Progress in Energy and Combustion Science, 2021, vol. 86, 100938, doi: 10.1016/j.pecs.2021.100938</mixed-citation><mixed-citation xml:lang="en">. Hasse C., Debiagi P., Wen X., Hildebrandt K., Vascellari M., Faravelli T. Advanced modeling approaches for CFD simulations of coal combustion and gasification // Progress in Energy and Combustion Science, 2021, vol. 86, 100938, doi: 10.1016/j.pecs.2021.100938</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">. Wu X., Guo Q., Gong Y., Cheng C., Ding L., Wang F., Yu G. Visualization study on particle flow behaviors during atomization in an impinging entrained-flow gasifier // Chemical Engineering Science, 2020, vol. 225, 115834, doi: 10.1016/j.ces.2020.115834.</mixed-citation><mixed-citation xml:lang="en">. Wu X., Guo Q., Gong Y., Cheng C., Ding L., Wang F., Yu G. Visualization study on particle flow behaviors during atomization in an impinging entrained-flow gasifier // Chemical Engineering Science, 2020, vol. 225, 115834, doi: 10.1016/j.ces.2020.115834.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">. Cai R., Luo K., Watanabe H., Kurose R., Fan J. Recent advances in high-fidelity simulations of pulverized coal combustion // Advanced Powder Technology, 2020, vol. 31(7), pp. 3062-3079, doi: 10.1016/j.apt.2020.05.001.</mixed-citation><mixed-citation xml:lang="en">. Cai R., Luo K., Watanabe H., Kurose R., Fan J. Recent advances in high-fidelity simulations of pulverized coal combustion // Advanced Powder Technology, 2020, vol. 31(7), pp. 3062-3079, doi: 10.1016/j.apt.2020.05.001.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">. Yerushalmi J. High velocity fluidized beds // in: D. Geldart (Ed) Gas Fluidization Technology, Chapter 7 , John Willey &amp; Sons, New York, 1986.</mixed-citation><mixed-citation xml:lang="en">. Yerushalmi J. High velocity fluidized beds // in: D. Geldart (Ed) Gas Fluidization Technology, Chapter 7 , John Willey &amp; Sons, New York, 1986.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">. Lecner B. Regimes of large-scale fluidized beds for solid fuel conversion // Powder technology, 2017, vol. 308, pp. 362-367, doi: 10.1016/j.powtec.2016.11.070.</mixed-citation><mixed-citation xml:lang="en">. Lecner B. Regimes of large-scale fluidized beds for solid fuel conversion // Powder technology, 2017, vol. 308, pp. 362-367, doi: 10.1016/j.powtec.2016.11.070.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">. Bi H. T., Grasce J. R. Flow regime diagrams for gas-solid fluidization and upward transport // International Journal of Multiphase Flow, 1995, vol. 21, no. 6., pp. 1229-1236, doi: 10.1016/0301-9322(95)00037-X.</mixed-citation><mixed-citation xml:lang="en">. Bi H. T., Grasce J. R. Flow regime diagrams for gas-solid fluidization and upward transport // International Journal of Multiphase Flow, 1995, vol. 21, no. 6., pp. 1229-1236, doi: 10.1016/0301-9322(95)00037-X.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">. Matsen J. M. Mechanism of choking and entrainment // Powder technology, vol. 32(1), pp. 21-33, 1982, doi: 10.1016/0032-5910(82)85003-1.</mixed-citation><mixed-citation xml:lang="en">. Matsen J. M. Mechanism of choking and entrainment // Powder technology, vol. 32(1), pp. 21-33, 1982, doi: 10.1016/0032-5910(82)85003-1.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">. Gidaspow D., Mostofi R. Maximum carrying capacity and granular temperature of A, B and C particles // AIChE Journal, 2003, vol. 49. no. 4. pp. 831-843, doi: 10.1002/aic.690490404.</mixed-citation><mixed-citation xml:lang="en">. Gidaspow D., Mostofi R. Maximum carrying capacity and granular temperature of A, B and C particles // AIChE Journal, 2003, vol. 49. no. 4. pp. 831-843, doi: 10.1002/aic.690490404.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">. Knowlton T. M. Solids transfer in fluidized systems // in: D. Geldart (Ed) Gas Fluidization Technology, Chapter 12, John Willey &amp; Sons, New York, 1986.</mixed-citation><mixed-citation xml:lang="en">. Knowlton T. M. Solids transfer in fluidized systems // in: D. Geldart (Ed) Gas Fluidization Technology, Chapter 12, John Willey &amp; Sons, New York, 1986.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">. Bi H. T., Grasce J. R., Zhu J. X. Types of choking in vertical pneumatic systems // International Journal of Multiphase Flow, 1993, vol. 19, no. 6, pp. 1077-1092, doi: 10.1016/0301-9322(93)90079-A.</mixed-citation><mixed-citation xml:lang="en">. Bi H. T., Grasce J. R., Zhu J. X. Types of choking in vertical pneumatic systems // International Journal of Multiphase Flow, 1993, vol. 19, no. 6, pp. 1077-1092, doi: 10.1016/0301-9322(93)90079-A.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">. Rabinovich E., Kalman H. Flow regime diagram for vertical pneumatic conveying and fluidized bed systems // Powder technology, 2011, vol. 207, no. 1-3, pp. 119-133, doi: 10.1016/j.powtec.2010.10.017.</mixed-citation><mixed-citation xml:lang="en">. Rabinovich E., Kalman H. Flow regime diagram for vertical pneumatic conveying and fluidized bed systems // Powder technology, 2011, vol. 207, no. 1-3, pp. 119-133, doi: 10.1016/j.powtec.2010.10.017.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">. Yang W. C. «Choking» Revisited // Industrial Engineering Chemical Research, 2004, vol. 43, no. 18, pp. 5496-5506, doi: 10.1021/ie0307479.</mixed-citation><mixed-citation xml:lang="en">. Yang W. C. «Choking» Revisited // Industrial Engineering Chemical Research, 2004, vol. 43, no. 18, pp. 5496-5506, doi: 10.1021/ie0307479.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">. M. Smoluchowski. Über die Wechselwirkung von Kugeln, die sich in einer zähen Flüssigkeit bewegen. Bull. Int. Acad. Sci. Cracovie, Cl. Sci. Math. Nat., Sér. A Sci. Math., 1911, pp. 28-39.</mixed-citation><mixed-citation xml:lang="en">. M. Smoluchowski. Über die Wechselwirkung von Kugeln, die sich in einer zähen Flüssigkeit bewegen. Bull. Int. Acad. Sci. Cracovie, Cl. Sci. Math. Nat., Sér. A Sci. Math., 1911, pp. 28-39.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">. Happel J., Brenner H. Low Reynolds Number Hydrodynamics. Prentice-Hall, 1965, 553 pp.</mixed-citation><mixed-citation xml:lang="en">. Happel J., Brenner H. Low Reynolds Number Hydrodynamics. Prentice-Hall, 1965, 553 pp.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">. Rowe P. N., Henwood G. A. Drag forces in a hydraulic model of a fluidized bed. Part I // Transactions of the Institution of Chemical Engineers, 1961, vol. 39, pp. 43-54.</mixed-citation><mixed-citation xml:lang="en">. Rowe P. N., Henwood G. A. Drag forces in a hydraulic model of a fluidized bed. Part I // Transactions of the Institution of Chemical Engineers, 1961, vol. 39, pp. 43-54.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">. Abbas S., Mohammed S., Drag Forces under Longitudinal Interaction of Two Particles // Iraqi Journal of Chemical and Petroleum Engineering, 2007, vol. 8, pp. 1-4, doi:10.31699/IJCPE.2007.2.1.</mixed-citation><mixed-citation xml:lang="en">. Abbas S., Mohammed S., Drag Forces under Longitudinal Interaction of Two Particles // Iraqi Journal of Chemical and Petroleum Engineering, 2007, vol. 8, pp. 1-4, doi:10.31699/IJCPE.2007.2.1.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">. Cocetta F., Szmelter J., Gillard M. Simulations of stably stratified flow past two spheres at Re = 300 // Physics of Fluids, 2021, vol. 33, no. 4, 046602, doi: 10.1063/5.0044801.</mixed-citation><mixed-citation xml:lang="en">. Cocetta F., Szmelter J., Gillard M. Simulations of stably stratified flow past two spheres at Re = 300 // Physics of Fluids, 2021, vol. 33, no. 4, 046602, doi: 10.1063/5.0044801.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">. Abed A. H., Shcheklein S. E., Pakhaluev V. M. Numerical and Experimental Investigation of heat transfer and flow structures around three heated spheres in tandem arrangement // IOP Conference Series: Materials Science and Engineering, 2020, vol. 791, 012002, doi: 10.1088/1757-899X/791/1/012002.</mixed-citation><mixed-citation xml:lang="en">. Abed A. H., Shcheklein S. E., Pakhaluev V. M. Numerical and Experimental Investigation of heat transfer and flow structures around three heated spheres in tandem arrangement // IOP Conference Series: Materials Science and Engineering, 2020, vol. 791, 012002, doi: 10.1088/1757-899X/791/1/012002.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">. Yang J., Zhu X., Liu M., Wang C., Wu Y., Shen Z. Wake bifurcations behind two circular disks in tandem arrangement // Physical Review Fluids, 2022, vol. 7, no. 6, 064102, doi: 10.1103/PhysRevFluids.7.064102.</mixed-citation><mixed-citation xml:lang="en">. Yang J., Zhu X., Liu M., Wang C., Wu Y., Shen Z. Wake bifurcations behind two circular disks in tandem arrangement // Physical Review Fluids, 2022, vol. 7, no. 6, 064102, doi: 10.1103/PhysRevFluids.7.064102.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">. Kotsev T. Numerical Study of Hydrodynamic Interaction between a Row of Spheroids in a Steady Stream of Viscous Fluid // Proceedings of the Bulgarian Academy of Sciences, 2022, vol. 75, no. 1, pp. 19-25, doi: 10.7546/CRABS.2022.01.03.</mixed-citation><mixed-citation xml:lang="en">. Kotsev T. Numerical Study of Hydrodynamic Interaction between a Row of Spheroids in a Steady Stream of Viscous Fluid // Proceedings of the Bulgarian Academy of Sciences, 2022, vol. 75, no. 1, pp. 19-25,  doi: 10.7546/CRABS.2022.01.03.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">. Ahmed A., Wahid A., Manzoor R., Nadeem N., Ullah N., Kalsoom S. Flow Characteristics and Fluid Forces Reduction of Flow Past Two Tandem Cylinders in Presence of Attached Splitter Plate // Mathematical Problems in Engineering, 2021, pp. 1-16, doi: 10.1155/2021/4305731.</mixed-citation><mixed-citation xml:lang="en">. Ahmed A., Wahid A., Manzoor R., Nadeem N., Ullah N., Kalsoom S. Flow Characteristics and Fluid Forces Reduction of Flow Past Two Tandem Cylinders in Presence of Attached Splitter Plate // Mathematical Problems in Engineering, 2021, pp. 1-16, doi: 10.1155/2021/4305731.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">. Ai Y., Zhou L., Zhang H. High-order optimal mode decomposition analysis of the ground effect on flow past two tandem inclined plates // Physics of Fluids, 2023, vol. 35, 013611, doi: 10.1063/5.0133928.</mixed-citation><mixed-citation xml:lang="en">. Ai Y., Zhou L., Zhang H. High-order optimal mode decomposition analysis of the ground effect on flow past two tandem inclined plates // Physics of Fluids, 2023, vol. 35, 013611, doi: 10.1063/5.0133928.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">. Reyes A., Soria J., Saffe A., Zambon M., Echegaray M., Suárez S., Rodriguez R., Mazza G., Fluidization of biomass: a correlation to assess the minimum fluidization velocity considering the influence of the sphericity factor // Particulate Science and Technology, 2021, vol. 39, no. 8, pp. 1020-1040, doi: 10.1080/02726351.2021.1879981.</mixed-citation><mixed-citation xml:lang="en">. Reyes A., Soria J., Saffe A., Zambon M., Echegaray M., Suárez S., Rodriguez R., Mazza G., Fluidization of biomass: a correlation to assess the minimum fluidization velocity considering the influence of the sphericity factor // Particulate Science and Technology, 2021, vol. 39, no. 8, pp. 1020-1040, doi: 10.1080/02726351.2021.1879981.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">. Bagheri G., Bonadonna C. On the drag of freely falling non-spherical particles, Powder Technology, 2016, vol. 301, pp. 526-544, doi: 10.1016/j.powtec.2016.06.015.</mixed-citation><mixed-citation xml:lang="en">. Bagheri G., Bonadonna C. On the drag of freely falling non-spherical particles, Powder Technology, 2016, vol. 301, pp. 526-544, doi: 10.1016/j.powtec.2016.06.015.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">. Ganser G. H. A rational approach to drag prediction of spherical and nonspherical particles // Powder Technology, 1993, vol. 77, no. 2, pp. 143-152, doi: 10.1016/0032-5910(93)80051-B.</mixed-citation><mixed-citation xml:lang="en">. Ganser G. H. A rational approach to drag prediction of spherical and nonspherical particles // Powder Technology, 1993, vol. 77, no. 2, pp. 143-152, doi: 10.1016/0032-5910(93)80051-B.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">. Гидравлические и тепловые основы работы аппаратов со стационарным и кипящим зернистым слоем / М. Э. Аэров, О. М. Тодес. – Л.: Химия, 1968. – 510 с.</mixed-citation><mixed-citation xml:lang="en">. Gidravlicheskie i teplovye osnovy raboty apparatov so stacionarnym i kipyashchim zernistym sloem / M. EH. Aehrov, O. M. Todes. – L.: Khimiya, 1968. – 510 s.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">. Горбис З. Р. Теплообмен и гидромеханика дисперсных сквозных потоков. – М.: Энергия, 1970. – 424 с.</mixed-citation><mixed-citation xml:lang="en">. Gorbis Z. R. Teploobmen i gidromekhanika dispersnykh skvoznykh potokov. – M.: Ehnergiya, 1970. – 424 s.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">. Основы практической теории горения [Учеб. пособие для энерг. спец. вузов / В. В. Померанцев, К. М. Арефьев, Д. Б. Ахмедов и др.]; Под ред. В. В. Померанцева. – 2-е изд., перераб. и доп. – Ленинград: Энергоатомиздат, Ленингр. отд-ние, 1986. – 309 с.</mixed-citation><mixed-citation xml:lang="en">. Osnovy prakticheskoj teorii goreniya [Ucheb. posobie dlya ehnerg. spec. vuzov / V. V. Pomerancev, K. M. Aref’ev, D. B. Akhmedov i dr.]; Pod red. V. V. Pomeranceva. – 2-e izd., pererab. i dop. – Leningrad: Ehnergoatomizdat, Leningr. otd-nie, 1986. – 309 s.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">. Баскаков, А. П. Скоростной безокислительный нагрев и термическая обработка в кипящем слое: научное издание / А. П. Баскаков. – М.: Металлургия, 1968. – 223 с.</mixed-citation><mixed-citation xml:lang="en">. Baskakov, A. P. Skorostnoj bezokislitel’nyj nagrev i termicheskaya obrabotka v kipyashchem sloe: nauchnoe izdanie / A. P. Baskakov. – M.: Metallurgiya, 1968. – 223 s.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">. Abdulally I., Voyles R. W., Lipal F. Multiply Fuel Firing Experience in a Circulating Fluidized Bed Boiler // Proceedings of the American Power Conference – Chicago (USA), 1992, vol. 2, pp 1-11.</mixed-citation><mixed-citation xml:lang="en">. Abdulally I., Voyles R. W., Lipal F. Multiply Fuel Firing Experience in a Circulating Fluidized Bed Boiler // Proceedings of the American Power Conference – Chicago (USA), 1992, vol. 2, pp 1-11.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">. Johansson A. Solids flow pattern in circulating fluidized-bed boilers. Ph. D. Dissertation, Chalmers University of Technology. – 2005. ISBN 91-7291-662-1.</mixed-citation><mixed-citation xml:lang="en">. Johansson A. Solids flow pattern in circulating fluidized-bed boilers. Ph. D. Dissertation, Chalmers University of Technology. – 2005. ISBN 91-7291-662-1.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">. Swieger В. Fluidized bed boilers achieve commercial status worldwide // Power, 1985, vol. 129, no. 2, pp. 1-16.</mixed-citation><mixed-citation xml:lang="en">. Swieger В. Fluidized bed boilers achieve commercial status worldwide // Power, 1985, vol. 129, no. 2, pp. 1-16.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">. Johnsson F., Leckner B. Vertical distribution of solids in a CFB-furnace // Proceedings of the 13-th International Conference on Fluidized-Bed Combustion, vol. 1, pp. 671-679.</mixed-citation><mixed-citation xml:lang="en">. Johnsson F., Leckner B. Vertical distribution of solids in a CFB-furnace // Proceedings of the 13-th International Conference on Fluidized-Bed Combustion, vol. 1, pp. 671-679.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">. The New Romerbrucke FBC Combined Heat and Power Plant: Deutsche Babkock Information, 1990, 9 p., rep. no. 217.</mixed-citation><mixed-citation xml:lang="en">. The New Romerbrucke FBC Combined Heat and Power Plant: Deutsche Babkock Information, 1990, 9 p., rep. no. 217.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">. Рябов Г. А., Фоломеев О. М. Исследование гидродинамики и массообмена на экспериментальной установке с циркуляционным кипящим слоем // Теплоэнергетика. – 1998. – № 6. – С. 8-12.</mixed-citation><mixed-citation xml:lang="en">. Ryabov G. A., Folomeev O. M. Issledovanie gidrodinamiki i massоobmena na ehksperimental’noj ustanovke s cirkulyacionnym kipyashchim sloem // Teploehnergetika. – 1998. – № 6, s. 8-12.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">. Jiradilok V., Gidaspow D., Breault R. W., Shadle L. J., Guenther C., Shi S. Computation of turbulence and dispersion of cork in the NETL riser // Chemical Engineering Science, 2008, vol. 63, no. 8, pp. 2135-2148, doi: 10.1016/j.ces.2008.01.019.</mixed-citation><mixed-citation xml:lang="en">. Jiradilok V., Gidaspow D., Breault R. W., Shadle L. J., Guenther C., Shi S. Computation of turbulence and dispersion of cork in the NETL riser // Chemical Engineering Science, 2008, vol. 63, no. 8, pp. 2135-2148, doi: 10.1016/j.ces.2008.01.019.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">. Рябов Г. А. Научное обоснование использования технологии сжигания твердых топлив в циркулирующем кипящем слое // ОАО «ИТИ» г. Москва. – 2016.</mixed-citation><mixed-citation xml:lang="en">. Ryabov G. A. Nauchnoe obosnovanie ispol’zovaniya tekhnologii szhiganiya tverdykh topliv v cirkuliruyushchem kipyashchem sloe // OAO «ITI» g. Moskva. – 2016.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">. Kashyap M., Gidaspow D. Circulation of Geldart D type particles: Part II—Low solids fluxes: Measurements and computation under dilute conditions // Chemical Engineering Science, 2011, vol. 66. no. 8. pp. 1649-1670, doi: 10.1016/j.ces.2010.12.043.</mixed-citation><mixed-citation xml:lang="en">. Kashyap M., Gidaspow D. Circulation of Geldart D type particles: Part II – Low solids fluxes: Measurements and computation under dilute conditions // Chemical Engineering Science, 2011, vol. 66. no. 8. pp. 1649-1670, doi: 10.1016/j.ces.2010.12.043.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">. Brown B. W., Smoot L. D., Smith P. J., Hedman P. O. Measurement and prediction of entrained-flow gasification processes // AIChE Journal, 1988, vol. 34, no. 3, pp. 435-446, doi: 10.1002/aic.690340311.</mixed-citation><mixed-citation xml:lang="en">. Brown B. W., Smoot L. D., Smith P. J., Hedman P. O. Measurement and prediction of entrained-flow gasification processes // AIChE Journal, 1988, vol. 34, no. 3, pp. 435-446, doi: 10.1002/aic.690340311.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">. Halama S., Spliethoff H. Numerical simulation of entrained flow gasification: Reaction kinetics and char structure evolution // Fuel Processing Technology, 2015, vol. 138, pp. 314-324, doi: 10.1016/j.fuproc.2015.05.012.</mixed-citation><mixed-citation xml:lang="en">. Halama S., Spliethoff H. Numerical simulation of entrained flow gasification: Reaction kinetics and char structure evolution // Fuel Processing Technology, 2015, vol. 138, pp. 314-324, doi: 10.1016/j.fuproc.2015.05.012.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">. Watanabe H., Otaka, M. Numerical simulation of coal gasification in entrained flow coal gasifier // Fuel, 2006, vol. 85, no. 12-13, pp. 1935-1943, doi: 10.1016/j.fuel.2006.02.002.</mixed-citation><mixed-citation xml:lang="en">. Watanabe H., Otaka, M. Numerical simulation of coal gasification in entrained flow coal gasifier // Fuel, 2006, vol. 85, no. 12-13, pp. 1935-1943, doi: 10.1016/j.fuel.2006.02.002.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">. Slezak A., Kuhlman J. M., Shadle L. J., Spenik J., Shi S. CFD simulation of entrained-flow coal gasification: Coal particle density/sizefraction effects // Powder Technology, 2010, vol. 203, no. 1, pp. 98-108, doi: 10.1016/j.powtec.2010.03.029.</mixed-citation><mixed-citation xml:lang="en">. Slezak A., Kuhlman J. M., Shadle L. J., Spenik J., Shi S. CFD simulation of entrained-flow coal gasification: Coal particle density/sizefraction effects // Powder Technology, 2010, vol. 203, no. 1, pp. 98-108, doi: 10.1016/j.powtec.2010.03.029.</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">. Risberg M., Carlsson P., Gebart R. Numerical modeling of a 500 kW air-blown cyclone gasifier // Applied Thermal Engineering, 2015, vol. 90, pp. 694-702, doi: 10.1016/j.applthermaleng.2015.06.056.</mixed-citation><mixed-citation xml:lang="en">. Risberg M., Carlsson P., Gebart R. Numerical modeling of a 500 kW air-blown cyclone gasifier // Applied Thermal Engineering, 2015, vol. 90, pp. 694-702, doi: 10.1016/j.applthermaleng.2015.06.056.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">. Тепловой расчет котлов [Текст] /нормативный метод/. Издание 3-е, переработанное и дополненное. – СПб.: НПО ЦКТИ, 1998. – 256 с.</mixed-citation><mixed-citation xml:lang="en">. Teplovoi raschet kotlov [Tekst] /normativnyi metod/. Izdanie 3-e, pererabotannoe i dopolnennoe. – SPb.: NPO TSKTI, 1998. – 256 s.</mixed-citation></citation-alternatives></ref><ref id="cit48"><label>48</label><citation-alternatives><mixed-citation xml:lang="ru">. Grace J. R. Contacting Modes and Behaviour Classification of Gas-Solid and Other Two-Phase Suspensions // The Canadian Journal of Chemical Engineering, 1986, vol. 64, no. 3, pp. 353-363.</mixed-citation><mixed-citation xml:lang="en">. Grace J.R. Contacting Modes and Behaviour Classification of Gas-Solid and Other Two-Phase Suspensions // The Canadian Journal of Chemical Engineering, 1986, vol. 64, no. 3, pp. 353-363.</mixed-citation></citation-alternatives></ref><ref id="cit49"><label>49</label><citation-alternatives><mixed-citation xml:lang="ru">. Geldart D. Types of gas fluidization // Powder Technology, 1973, vol. 5, no. 7, pp. 285-292, doi: 10.1016/0032-5910(73)80037-3.</mixed-citation><mixed-citation xml:lang="en">. Geldart D. Types of gas fluidization // Powder Technology, 1973, vol. 5, no. 7, pp. 285-292, doi: 10.1016/0032-5910(73)80037-3.</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>
