<?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">ntv</journal-id><journal-title-group><journal-title xml:lang="ru">Научно-технический вестник информационных технологий, механики и оптики</journal-title><trans-title-group xml:lang="en"><trans-title>Scientific and Technical Journal of Information Technologies, Mechanics and Optics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-1494</issn><issn pub-type="epub">2500-0373</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2226-1494-2025-25-5-952-960</article-id><article-id custom-type="elpub" pub-id-type="custom">ntv-524</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>МАТЕМАТИЧЕСКОЕ И КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MODELING AND SIMULATION</subject></subj-group></article-categories><title-group><article-title>Экспериментальное исследование структуры течения и поля температур оптически прозрачной среды посредством  фоново-ориентированного шлирен-метода</article-title><trans-title-group xml:lang="en"><trans-title>Experimental study of the optically transparent gas flow and temperature field using the background oriented Schlieren method</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3710-5116</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Брызгунов</surname><given-names>П. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Bryzgunov</surname><given-names>P. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Брызгунов Павел Александрович — кандидат технических наук, ассистент</p><p>sc 57844836600</p><p>Москва, 111250</p></bio><bio xml:lang="en"><p>Pavel A. Bryzgunov — PhD, Assistant</p><p>sc 57844836600</p><p>Moscow, 111250</p></bio><email xlink:type="simple">bryzgunovpa@mpei.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/0009-0006-3091-4884</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Писарев</surname><given-names>Д. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Pisarev</surname><given-names>D. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Писарев Дмитрий Сергеевич — старший преподаватель</p><p>sc 16239539100</p><p>Москва, 111250</p></bio><bio xml:lang="en"><p>Dmitry S. Pisarev — Senior Lecturer</p><p>sc 16239539100</p><p>Moscow, 111250</p></bio><email xlink:type="simple">pisarevds@mpei.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/0000-0003-0554-4026</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Злывко</surname><given-names>О. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Zlyvko</surname><given-names>O. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Злывко Ольга Владимировна — кандидат экономических наук, доцент, доцент</p><p>sc 57060525900</p><p>Москва, 111250</p></bio><bio xml:lang="en"><p>Olga V. Zlyvko — PhD (Economy), Associate Professor, Associate Professor</p><p>sc 57060525900</p><p>Moscow, 111250</p></bio><email xlink:type="simple">zlyvkoov@mpei.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/0000-0001-7256-0144</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Рогалев</surname><given-names>А. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Rogalev</surname><given-names>A. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Рогалев Андрей Николаевич — доктор технических наук, доцент, заведующий кафедрой</p><p>sc 34980078500</p><p>Москва, 111250</p></bio><bio xml:lang="en"><p>Andrey N. Rogalev —<ext-link xlink:href="http://D.Sc/" ext-link-type="uri"> D.Sc</ext-link>., Associate Professor, Head of Department</p><p>sc 34980078500</p><p>Moscow, 111250</p></bio><email xlink:type="simple">rogalevan@mpei.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/0000-0002-6458-2869</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Рогалев</surname><given-names>Н. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Rogalev</surname><given-names>N. D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Рогалев Николай Дмитриевич — доктор технических наук, профессор, ректор</p><p>sc 6507029432</p><p>Москва, 111250</p></bio><bio xml:lang="en"><p>Nikolay D. Rogalev — <ext-link xlink:href="http://D.Sc/" ext-link-type="uri">D.Sc</ext-link>., Professor, Rector</p><p>sc 6507029432</p><p>Moscow, 111250</p></bio><email xlink:type="simple">rogalevnd@mpei.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный исследовательский университет «МЭИ»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>National Research University “Moscow Power Engineering Institute”</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>27</day><month>10</month><year>2025</year></pub-date><volume>25</volume><issue>5</issue><fpage>952</fpage><lpage>960</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Брызгунов П.А., Писарев Д.С., Злывко О.В., Рогалев А.Н., Рогалев Н.Д., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Брызгунов П.А., Писарев Д.С., Злывко О.В., Рогалев А.Н., Рогалев Н.Д.</copyright-holder><copyright-holder xml:lang="en">Bryzgunov P.A., Pisarev D.S., Zlyvko O.V., Rogalev A.N., Rogalev N.D.</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://ntv.elpub.ru/jour/article/view/524">https://ntv.elpub.ru/jour/article/view/524</self-uri><abstract><sec><title>Введение</title><p>Введение. Представлены результаты экспериментального исследования структуры течения и поля температур в конвективной струе воздуха и продуктов сгорания природного газа, формирующейся над пламенем горелки малой мощности. Проанализированы пульсационные и спектральные характеристики потока в ключевых точках отбора, что позволило сделать вывод о характере течения в основных точках струи. Предложено для анализа спектральных характеристик потока использовать временные ряды изменения поля смещений точек.</p></sec><sec><title>Метод</title><p>Метод. В работе для визуализации течения и определения температур использован фоново-ориентированный шлирен-метод с последующей постобработкой в разработанной в ходе исследования программе. Преимуществом данного подхода в сравнении с традиционным оптическим шлирен-методом является отсутствие необходимости в параболических зеркалах, а также возможность получения результатов в цифровом виде, удобном для дальнейшей обработки. В ходе эксперимента за объектом исследования, который снимался видеокамерой, помещался фон со случайно расположенными черными точками. Колебания плотности среды вызывали изменения коэффициентов преломления среды, вследствие чего точки на фоне на видеокадрах смещались, причем смещение точек пропорционально изменению коэффициента преломления, который в свою очередь пропорционален градиенту плотности и, соответственно, градиенту температуры среды. Смещение точек определялось с применением кросс-корреляционного анализа каждого кадра в сравнении с кадрами при отсутствии возмущений. Далее поле смещений подвергалось фильтрации посредством медианного фильтра с целью минимизации шумов и статистических выбросов. Отфильтрованное поле смещений использовалось для вычисления поля температур, при этом решалась задача Коши относительно температуры с известной производной в точке и заданных граничных условиях.</p></sec><sec><title>Основные результаты</title><p>Основные результаты. Получена совокупность мгновенных полей смещений точек, мгновенных и осредненного полей температуры, позволивших сделать выводы о структуре течения. В характерных точках струи получены осциллограммы величины смещения, а также спектры пульсаций, имеющие инерционный интервал, соответствующий закону «–5/3».</p></sec><sec><title>Обсуждение</title><p>Обсуждение. Предложенный в работе подход позволяет в дополнение к бесконтактному исследованию поля температур также исследовать турбулентные пульсации течения в случае квазидвухмерных или осесимметричных потоков.</p></sec></abstract><trans-abstract xml:lang="en"><p>The article presents the results of an experimental study of the flow structure and temperature field in a plume formed above a low-power burner flame. The pulsation and spectral characteristics of the flow at key sampling points were analyzed, which allowed us to draw a conclusion about the nature of the flow at the main points of the jet. It is proposed to use time series of changes in the point displacement field to analyze the spectral characteristics of the flow. In this work, the Background Oriented Schlieren method was used to visualize the flow and determine temperatures followed by post-processing in the program developed during the study. The advantage of this approach compared to the traditional optical Schlieren method is that there is no need for parabolic mirrors as well as the ability to obtain results in digital form convenient for further processing. During the experiment, a special background with randomly located bright dots was placed behind the object of study which was filmed by a video camera. Fluctuations in the medium density caused changes in the refractive indices of the medium, as a result of which the points on the background of the video frames displaced, and the displacements of the points was proportional to the change in the refractive index which in turn is proportional to the density gradient and, accordingly, to the temperature gradient of the medium. The displacement of the points was determined by cross-correlation analysis of each frame in comparison with the frames in the absence of disturbances. Then the displacement field was filtered by a median filter in order to minimize noise and statistical outliers. The filtered displacement field was used to calculate the temperature field, while solving the Cauchy problem for temperature with a known derivative at a point and specified boundary conditions. A set of instantaneous point displacement fields, instantaneous and time-averaged temperature fields was obtained, which allowed us to draw conclusions about the flow structure. At characteristic points of the jet, oscillograms of the displacement value were obtained as well as pulsation spectra with an inertial interval corresponding to the “–5/3” law. The approach proposed in the work allows, in addition to contactless study of the temperature field, also studying turbulent flow pulsations in the case of close to two-dimensional or axisymmetric flows.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>фоново-ориентированный шлирен-метод</kwd><kwd>поле температур</kwd><kwd>спектральные характеристики потока</kwd><kwd>оптические исследования потока</kwd><kwd>структура течения</kwd></kwd-group><kwd-group xml:lang="en"><kwd>background oriented Schlieren method</kwd><kwd>temperature field</kwd><kwd>spectral characteristics of flow</kwd><kwd>optical studies of flow</kwd><kwd>flow structure</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при финансовой поддержке Министерства науки и высшего образования Российской Федерации в рамках государственного задания № FSWF-2023-0014 (Соглашение № 075-03-2023-383 от 18 января 2023 г.) в сфере научной деятельности на 2023–2025 гг.</funding-statement><funding-statement xml:lang="en">This study conducted by the Moscow Power Engineering Institute was financially supported by the Ministry of Science and Higher Education of the Russian Federation (State Assignment No. FSWF-2023-0014, contract No. 075-03-2023383, 18.01.2023).</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">Braeuer A. Shadowgraph and schlieren techniques. Supercritical Fluid Science and Technology, 2015, vol. 7, pp. 283–312. https://doi.org/10.1016/B978-0-444-63422-1.00004-3</mixed-citation><mixed-citation xml:lang="en">Braeuer A. Shadowgraph and schlieren techniques. Supercritical Fluid Science and Technology, 2015, vol. 7, pp. 283–312. https://doi.org/10.1016/B978-0-444-63422-1.00004-3</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Dalziel S.B., Hughes G.O., Sutherland B.R. Whole-field density measurements by ‘synthetic schlieren’. Experiments in Fluids, 2000, vol. 28, no. 4, pp. 322–335. https://doi.org/10.1007/s003480050391</mixed-citation><mixed-citation xml:lang="en">Dalziel S.B., Hughes G.O., Sutherland B.R. Whole-field density measurements by ‘synthetic schlieren’. Experiments in Fluids, 2000, vol. 28, no. 4, pp. 322–335. https://doi.org/10.1007/s003480050391</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Shimazaki T., Ichihara S., Tagawa Y. Background oriented schlieren technique with fast Fourier demodulation for measuring large densitygradient fields of fluids. Experimental Thermal and Fluid Science, 2022, vol. 134, pp. 110598. https://doi.org/10.1016/j.expthermflusci.2022.110598</mixed-citation><mixed-citation xml:lang="en">Shimazaki T., Ichihara S., Tagawa Y. Background oriented schlieren technique with fast Fourier demodulation for measuring large densitygradient fields of fluids. Experimental Thermal and Fluid Science, 2022, vol. 134, pp. 110598. https://doi.org/10.1016/j.expthermflusci.2022.110598</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Li X., Gong S., Zhang F., Ma Z., Xun G. Three-dimensional tomographic reconstruction for gaseous fuel jets based on background oriented schlieren technique. Journal of the Energy Institute, 2025, vol. 120, pp. 102118. https://doi.org/10.1016/j.joei.2025.102118</mixed-citation><mixed-citation xml:lang="en">Li X., Gong S., Zhang F., Ma Z., Xun G. Three-dimensional tomographic reconstruction for gaseous fuel jets based on background oriented schlieren technique. Journal of the Energy Institute, 2025, vol. 120, pp. 102118. https://doi.org/10.1016/j.joei.2025.102118</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Davami J., Juliano T.J., Moreto J.R., Liu X. Density measurements via background-oriented schlieren and parallel-ray omnidirectional integration. Experiments in Fluids, 2025, vol. 66, no. 4, pp. 78. https://doi.org/10.1007/s00348-025-04012-1</mixed-citation><mixed-citation xml:lang="en">Davami J., Juliano T.J., Moreto J.R., Liu X. Density measurements via background-oriented schlieren and parallel-ray omnidirectional integration. Experiments in Fluids, 2025, vol. 66, no. 4, pp. 78. https://doi.org/10.1007/s00348-025-04012-1</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Martínez-González A., Moreno-Hernández D., Guerrero-Viramontes J.A., León-Rodríguez M., Zamarripa-Ramírez J.C.I., Carrillo-Delgado C. Temperature measurement of fluid flows by using a focusing schlieren method. Sensors, 2019, vol. 19, no. 1, pp. 12. https://doi.org/10.3390/s19010012</mixed-citation><mixed-citation xml:lang="en">Martínez-González A., Moreno-Hernández D., Guerrero-Viramontes J.A., León-Rodríguez M., Zamarripa-Ramírez J.C.I., Carrillo-Delgado C. Temperature measurement of fluid flows by using a focusing schlieren method. Sensors, 2019, vol. 19, no. 1, pp. 12. https://doi.org/10.3390/s19010012</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Ichihara S., Shimazaki T., Tagawa Y. Background-oriented schlieren technique with vector tomography for measurement of axisymmetric pressure fields of laser-induced underwater shock waves. Experiments in Fluids, 2022, vol. 63, no. 11, pp. 182. https://doi.org/10.1007/s00348-022-03524-4</mixed-citation><mixed-citation xml:lang="en">Ichihara S., Shimazaki T., Tagawa Y. Background-oriented schlieren technique with vector tomography for measurement of axisymmetric pressure fields of laser-induced underwater shock waves. Experiments in Fluids, 2022, vol. 63, no. 11, pp. 182. https://doi.org/10.1007/s00348-022-03524-4</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Miao Y., Jia C., Hua Y., Sun L., Xu J., Wu D., Huang G., Liu H. Measurement of the concentration distribution of hydrogen jets using adaptive stream stripe- background oriented schlieren (ASS-BOS). International Journal of Hydrogen Energy, 2024, vol. 77, pp. 281–290. https://doi.org/10.1016/j.ijhydene.2024.06.099</mixed-citation><mixed-citation xml:lang="en">Miao Y., Jia C., Hua Y., Sun L., Xu J., Wu D., Huang G., Liu H. Measurement of the concentration distribution of hydrogen jets using adaptive stream stripe- background oriented schlieren (ASS-BOS). International Journal of Hydrogen Energy, 2024, vol. 77, pp. 281–290. https://doi.org/10.1016/j.ijhydene.2024.06.099</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Wang Q., Mei X.H., Wu Y., Zhao C.Y. An optimization and parametric study of a schlieren motion estimation method. Flow, Turbulence and Combustion, 2021, vol. 107, no. 3, pp. 609–630. https://doi.org/10.1007/s10494-021-00246-1</mixed-citation><mixed-citation xml:lang="en">Wang Q., Mei X.H., Wu Y., Zhao C.Y. An optimization and parametric study of a schlieren motion estimation method. Flow, Turbulence and Combustion, 2021, vol. 107, no. 3, pp. 609–630. https://doi.org/10.1007/s10494-021-00246-1</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Yang S., Zhao L., Wang H., Li M., Xu W. Fluid motion prediction from schlieren for ethanol plume velocity measurement. International Journal of Heat and Fluid Flow, 2025, vol. 115, pp. 109889. https://doi.org/10.1016/j.ijheatfluidflow.2025.109889</mixed-citation><mixed-citation xml:lang="en">Yang S., Zhao L., Wang H., Li M., Xu W. Fluid motion prediction from schlieren for ethanol plume velocity measurement. International Journal of Heat and Fluid Flow, 2025, vol. 115, pp. 109889. https://doi.org/10.1016/j.ijheatfluidflow.2025.109889</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Li J., Xiong Y., Tang Y., Han W., Pan C., Wang J. Three-dimensional diagnosis of lean premixed turbulent swirl flames using tomographic background oriented Schlieren. Physics of Fluids, 2024, vol. 36, no. 5, pp. 055159. https://doi.org/10.1063/5.0209235</mixed-citation><mixed-citation xml:lang="en">Li J., Xiong Y., Tang Y., Han W., Pan C., Wang J. Three-dimensional diagnosis of lean premixed turbulent swirl flames using tomographic background oriented Schlieren. Physics of Fluids, 2024, vol. 36, no. 5, pp. 055159. https://doi.org/10.1063/5.0209235</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Akamine M., Teramoto S., Okamoto K. Formulation and demonstrations of three-dimensional background-oriented schlieren using a mirror for near-wall density measurements. Experiments in Fluids, 2023, vol. 64, no. 7, pp. 134. https://doi.org/10.1007/s00348-023-03672-1</mixed-citation><mixed-citation xml:lang="en">Akamine M., Teramoto S., Okamoto K. Formulation and demonstrations of three-dimensional background-oriented schlieren using a mirror for near-wall density measurements. Experiments in Fluids, 2023, vol. 64, no. 7, pp. 134. https://doi.org/10.1007/s00348-023-03672-1</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Bulat P.V., Volkov K.N. Numerical simulation of shock wave refraction on inclined contact discontinuity. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 3, pp. 550–558. (in Russian). https://doi.org/10.17586/2226-1494-2016-16-3-550-558</mixed-citation><mixed-citation xml:lang="en">Bulat P.V., Volkov K.N. Numerical simulation of shock wave refraction on inclined contact discontinuity. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 3, pp. 550–558. (in Russian). https://doi.org/10.17586/2226-1494-2016-16-3-550-558</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Bulat P.V., Volkov K.N. Numerical simulation of shock wave diffraction over right angle on unstructured meshes. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 2, pp. 354–362. (in Russian). https://doi.org/10.17586/2226-1494-2016-16-2-354-362</mixed-citation><mixed-citation xml:lang="en">Bulat P.V., Volkov K.N. Numerical simulation of shock wave diffraction over right angle on unstructured meshes. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 2, pp. 354–362. (in Russian). https://doi.org/10.17586/2226-1494-2016-16-2-354-362</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Grauer S.J., Unterberger A., Rittler A., Daun K.J., Kempf A.M., Mohri K. Instantaneous 3D flame imaging by background-oriented schlieren tomography. Combustion and Flame, 2018, vol. 196, pp. 284–299. https://doi.org/10.1016/j.combustflame.2018.06.022</mixed-citation><mixed-citation xml:lang="en">Grauer S.J., Unterberger A., Rittler A., Daun K.J., Kempf A.M., Mohri K. Instantaneous 3D flame imaging by background-oriented schlieren tomography. Combustion and Flame, 2018, vol. 196, pp. 284–299. https://doi.org/10.1016/j.combustflame.2018.06.022</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Cowles R.A.P., Molnar J.P., Singh A.K., Grauer S.J. Tomographic background-oriented schlieren facility for buoyancy-driven flows and flames. Proc. of the AIAA Science and Technology Forum and Exposition, AIAA. SciTech Forum, 2025, https://doi.org/10.2514/6.2025-1058</mixed-citation><mixed-citation xml:lang="en">Cowles R.A.P., Molnar J.P., Singh A.K., Grauer S.J. Tomographic background-oriented schlieren facility for buoyancy-driven flows and flames. Proc. of the AIAA Science and Technology Forum and Exposition, AIAA. SciTech Forum, 2025, https://doi.org/10.2514/6.2025-1058</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Liu Y., Xing F., Su L., Tan H., Wang D. A mini-review of recent developments in plenoptic background-oriented schlieren technology for flow dynamics measurement. Aerospace, 2024, vol. 11, no. 4, pp. 303. https://doi.org/10.3390/aerospace11040303</mixed-citation><mixed-citation xml:lang="en">Liu Y., Xing F., Su L., Tan H., Wang D. A mini-review of recent developments in plenoptic background-oriented schlieren technology for flow dynamics measurement. Aerospace, 2024, vol. 11, no. 4, pp. 303. https://doi.org/10.3390/aerospace11040303</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Sasono M., Sakti S.P., Noor J.E., Soetedjo H. Application of checkerboard-based Background-Oriented Schlieren technique for invisible visualization of thermal plumes. AIP Conference Proceedings, 2023, vol. 2720, no. 1, pp. 040035. https://doi.org/10.1063/5.0136943</mixed-citation><mixed-citation xml:lang="en">Sasono M., Sakti S.P., Noor J.E., Soetedjo H. Application of checkerboard-based Background-Oriented Schlieren technique for invisible visualization of thermal plumes. AIP Conference Proceedings, 2023, vol. 2720, no. 1, pp. 040035. https://doi.org/10.1063/5.0136943</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Gao P., Zhang Y., Yu X., Dong S., Chen Q., Yuan Y. Reconstruction method of 3D turbulent flames by background-oriented schlieren tomography and analysis of time asynchrony. Fire, 2023, vol. 6, no. 11, pp. 417. https://doi.org/10.3390/fire6110417</mixed-citation><mixed-citation xml:lang="en">Gao P., Zhang Y., Yu X., Dong S., Chen Q., Yuan Y. Reconstruction method of 3D turbulent flames by background-oriented schlieren tomography and analysis of time asynchrony. Fire, 2023, vol. 6, no. 11, pp. 417. https://doi.org/10.3390/fire6110417</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Vasiliev A., Sukhanovskii A., Frick P., Budnikov A., Fomichev V., Bolshukhin M., Romanov R. High Rayleigh number convection in a cubic cell with adiabatic sidewalls. International Journal of Heat and Mass Transfer, 2016, vol. 102, pp. 201–212. https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.015</mixed-citation><mixed-citation xml:lang="en">Vasiliev A., Sukhanovskii A., Frick P., Budnikov A., Fomichev V., Bolshukhin M., Romanov R. High Rayleigh number convection in a cubic cell with adiabatic sidewalls. International Journal of Heat and Mass Transfer, 2016, vol. 102, pp. 201–212. https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.015</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Liu H.C., Huang J.Q., Li L. Cai W.W. Volumetric imaging of flame refractive index, density, and temperature using background-oriented Schlieren tomography. Science China Technological Sciences, 2021, vol. 64, no. 1, pp. 98–110. https://doi.org/10.1007/s11431-020-1663-5</mixed-citation><mixed-citation xml:lang="en">Liu H.C., Huang J.Q., Li L. Cai W.W. Volumetric imaging of flame refractive index, density, and temperature using background-oriented Schlieren tomography. Science China Technological Sciences, 2021, vol. 64, no. 1, pp. 98–110. https://doi.org/10.1007/s11431-020-1663-5</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Wang G.T., Daniel K.A., Lynch K.P., Guildenbecher D.R., Mazumdar Y.C. High temperature and pressure Gladstone–Dale coefficient measurements in air behind reflected shock waves. Physics of Fluids, 2023, vol. 35, no. 8, pp. 086121. https://doi.org/10.1063/5.0162017</mixed-citation><mixed-citation xml:lang="en">Wang G.T., Daniel K.A., Lynch K.P., Guildenbecher D.R., Mazumdar Y.C. High temperature and pressure Gladstone–Dale coefficient measurements in air behind reflected shock waves. Physics of Fluids, 2023, vol. 35, no. 8, pp. 086121. https://doi.org/10.1063/5.0162017</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Chen Y., Cao R., Chen J., Liu L., Matsushita B. A practical approach to reconstruct high-quality Landsat NDVI time-series data by gap filling and the Savitzky–Golay filter. ISPRS Journal of Photogrammetry and Remote Sensing, 2021, vol. 180, pp. 174–190. https://doi.org/10.1016/j.isprsjprs.2021.08.015</mixed-citation><mixed-citation xml:lang="en">Chen Y., Cao R., Chen J., Liu L., Matsushita B. A practical approach to reconstruct high-quality Landsat NDVI time-series data by gap filling and the Savitzky–Golay filter. ISPRS Journal of Photogrammetry and Remote Sensing, 2021, vol. 180, pp. 174–190. https://doi.org/10.1016/j.isprsjprs.2021.08.015</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>
