<?xml version="1.0" encoding="UTF-8"?>
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" dtd-version="1.4" article-type="research-article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="issn">2411-3336</journal-id>
      <journal-id journal-id-type="eissn">2541-9404</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Записки Горного института</journal-title>
        <journal-title xml:lang="en">Journal of Mining Institute</journal-title>
      </journal-title-group>
      <publisher>
        <publisher-name xml:lang="ru">Санкт-Петербургский горный университет императрицы Екатерины ΙΙ</publisher-name>
        <publisher-name xml:lang="en">Empress Catherine II Saint Petersburg Mining University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.25515/pmi.2017.5.558</article-id>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-11414</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/11414</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Электромеханика и машиностроение</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Electromechanics and mechanical engineering</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Multiphysical model of heterogenous flow moving along а channel of variable cross-section</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Мультифизическая модель течения гетерогенного потока при движении по каналу переменного сечения</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="eastern">
            <surname>Vasileva</surname>
            <given-names>M. A.</given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Васильева</surname>
              <given-names>М. А.</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Vasileva</surname>
              <given-names>M. A.</given-names>
            </name>
          </name-alternatives>
          <email>saturn.sun@mail.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru">Санкт-Петербургский горный университет (Санкт-Петербург, Россия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Saint-Petersburg Mining University (Saint-Petersburg, Russia)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Feit</surname>
            <given-names>S. </given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Фёйт</surname>
              <given-names>С. </given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Feit</surname>
              <given-names>S. </given-names>
            </name>
          </name-alternatives>
          <email>Stefan.Voeth@thga.de</email>
          <xref ref-type="aff" rid="aff2"/>
        </contrib>
        <aff-alternatives id="aff2">
          <aff>
            <institution xml:lang="ru">Университет прикладных наук имени Георга Агриколы (Бохум, Германия)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Technische Hochschule Georg Agricola (Bochum, Germany)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="2017-10-23">
        <day>23</day>
        <month>10</month>
        <year>2017</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>2017</year>
      </pub-date>
      <volume>227</volume>
      <fpage>558</fpage>
      <lpage>562</lpage>
      <history>
        <date date-type="received" iso-8601-date="2017-04-29">
          <day>29</day>
          <month>04</month>
          <year>2017</year>
        </date>
        <date date-type="accepted" iso-8601-date="2017-06-29">
          <day>29</day>
          <month>06</month>
          <year>2017</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2017-10-23">
          <day>23</day>
          <month>10</month>
          <year>2017</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© M. A. Vasileva, S.  Feit</copyright-statement>
        <copyright-year>2017</copyright-year>
        <copyright-holder xml:lang="ru">М. А. Васильева, С.  Фёйт</copyright-holder>
        <copyright-holder xml:lang="en">M. A. Vasileva, S.  Feit</copyright-holder>
        <license xlink:href="http://creativecommons.org/licenses/by/4.0">
          <license-p>CC BY 4.0</license-p>
        </license>
      </permissions>
      <self-uri xlink:type="simple" xlink:href="https://pmi.spmi.ru/pmi/article/view/11414">https://pmi.spmi.ru/pmi/article/view/11414</self-uri>
      <abstract xml:lang="ru">
        <p>В статье рассмотрена задача, направленная на решение фундаментальных проблем разработки эффективных методов и средств проектирования, контроля и управления потоками течения жидкостей в трубопроводах переменного сечения, предназначенных для производства насосного оборудования, медицинских приборов и используемых в таких областях промышленности, как горная, химическая, пищевая и др. Выполнение имитационного моделирования движения потока по схеме скрученного лопастного статического смесителя позволяет оценить эффективность смешивания путем вычисления траектории и скоростей взвешенных частиц через смеситель, а также оценить потери напора на гидравлическое сопротивление потока. Модель исследует смешивание твердых частиц, растворенных в жидкости при комнатной температуре. Для визуализации процесса распределения частиц смеси по сечению и анализа эффективности смешения использовался модуль Poincaréplot программной среды COMSOL Multiphysics. Впервые разработана мультифизическая модель течения гетерогенного потока, которая подробно описывает физическое состояние жидкости во всех точках рассматриваемой области в начальный момент времени, учитывает конструктивные параметры канала (ориентация, размеры, материал и др.), задает законы изменения параметров на границах рассчитываемой области в условиях волнового изменения внутреннего сечения рабочей камеры-канала индукционного перистальтического насосного агрегата под воздействием энергии магнитного поля.</p>
      </abstract>
      <abstract xml:lang="en">
        <p>The article deals with the problem aimed at solving the fundamental problems of developing effective methods and tools for designing, controlling and managing the stream of fluid flowing in variable-section pipelines intended for the production of pumping equipment, medical devices and used in such areas of industry as mining, chemical, food production, etc. Execution of simulation modelling of flow motion according to the scheme of twisted paddle static mixer allows to estimate the efficiency of mixing by calculating the trajectory and velocities of the suspended particles going through the mixer, and also to estimate the pressure drop on the hydraulic flow resistance. The model examines the mixing of solids dissolved in a liquid at room temperature. To visualize the process of distributing the mixture particles over the cross-section and analyzing the mixing efficiency, the Poincaréplot module of the COMSOL Multiphysics software environment was used. For the first time, a multi-physical stream of heterogeneous flow model has been developed that describes in detail the physical state of the fluid at all points of the considered section at the initial time, takes into account the design parameters of the channel (orientation, dimensions, material, etc.), specifies the laws of variation of the parameters at the boundaries of the calculated section in conditions of the wave change in the internal section of the working chamber-channel of the inductive peristaltic pumping unit under the influence of the energy of the magnetic field.</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>гетерогенный  поток</kwd>
        <kwd>математическое  моделирование</kwd>
        <kwd>эластомер</kwd>
        <kwd>смеситель</kwd>
        <kwd>перистальтическое транспортирование</kwd>
      </kwd-group>
      <kwd-group xml:lang="en">
        <title>Keywords</title>
        <kwd>heterogeneous flow</kwd>
        <kwd>mathematical modelling</kwd>
        <kwd>elastomer</kwd>
        <kwd>mixer</kwd>
        <kwd>peristaltic transportation</kwd>
      </kwd-group>
      <funding-group>
        <funding-statement xml:lang="ru">Исследования выполнены при финансовой поддержке Российского фонда фундаментальных исследований, грант No 16-38-00169/16</funding-statement>
        <funding-statement xml:lang="en">The research has been made under financial support of Russian Founda-tion of Basic Research, grant # 16-38-00169/16</funding-statement>
      </funding-group>
    </article-meta>
  </front>
  <body/>
  <back>
    <ref-list>
      <ref id="ref1">
        <label>1</label>
        <mixed-citation xml:lang="ru">Зайцев А.В. Моделирование течения вязкой жидкости в трубе / А.В.Зайцев, Ф.В.Пеленко // Научный электронный журнал НИУ ИТМО. Серия: Процессы и аппараты пищевых производств. 2012. № 1. С. 163-168 Режим доступа: URL: www.processes.open-mechanics.com/</mixed-citation>
        <mixed-citation xml:lang="en">Zaitsev A.V., Pelenko F.V. Modeling of viscous fluid flow in a pipe. Nauchnyi elektronnyi zhurnal NIU ITMO. Seriya: Protsessy i apparaty pishchevykh proizvodstv. 2012. N1, p. 163-168. Rezhim dostupa: URL: www.processes.open-mechanics.com/</mixed-citation>
      </ref>
      <ref id="ref2">
        <label>2</label>
        <mixed-citation xml:lang="ru">A mathematical model of fluid flow in tight porous media based on fractal assumptions / Y.Jin, X.Li, M.Y.Zhao, X.H.Liu, H.Li // International Journal of Heat and Mass Transfer. 2017. № 108. Р. 1078-1088.</mixed-citation>
        <mixed-citation xml:lang="en">Jin Y., Li X., Zhao M.Y., Liu X.H., Li H.A mathematical model of fluid flow in tight porous media based on fractal assumptions. International Journal of Heat and Mass Transfer. 2017.N 108,р. 1078-1088.</mixed-citation>
      </ref>
      <ref id="ref3">
        <label>3</label>
        <mixed-citation xml:lang="ru">Afrasiabikia P. Scenarios for improvement of water distribution in Doroodzan irrigation network based on hydraulic simulation / P.Afrasiabikia, A.P.Rizi, M.Javan // Computers and Electronics in Agriculture. 2017. № 135. Р. 312-320.</mixed-citation>
        <mixed-citation xml:lang="en">Afrasiabikia P.,RiziA. P., Javan M. Scenarios for improvement of water distribution in Doroodzan irrigation network based on hydraulic simulation. Computers and Electronics in Agriculture. 2017. N 135, р. 312-320.</mixed-citation>
      </ref>
      <ref id="ref4">
        <label>4</label>
        <mixed-citation xml:lang="ru">Alexandrov V. Turbulent Transport of Solid Phase in Hydrotransport / V.Alexandrov, M.Vasilyeva // Papers presented at the 15th International Freight Pipeline Society Symposium; The Institute of Hydrodynamics AS CR, Academy of Sciences of the Czech Republic. Prague, 2014. P. 3-9.</mixed-citation>
        <mixed-citation xml:lang="en">Alexandrov V., Vasilyeva M.Turbulent Transport of Solid Phase in Hydrotransport.Papers presented at the 15th International Freight Pipeline Society Symposium;TheInstitute of Hydrodynamics AS CR, Academy of Sciences of the Czech Republic.Prague, 2014,p. 3-9.</mixed-citation>
      </ref>
      <ref id="ref5">
        <label>5</label>
        <mixed-citation xml:lang="ru">Ates S. Hydraulic modelling of control devices in loop equations of water distribution networks // Flow Measurement and Instrumentation. 2017. № 35. Р. 243-260.</mixed-citation>
        <mixed-citation xml:lang="en">Ates S. Hydraulic modelling of control devices in loop equations of water distribution networks.Flow Measurement and Instrumentation. 2017. N 35, р. 243-260.</mixed-citation>
      </ref>
      <ref id="ref6">
        <label>6</label>
        <mixed-citation xml:lang="ru">Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier-Stokes system with competitive kinetics / M.Hirata, S.Kurima, M.Mizukami, T.Yokota // Journal of Differential Equations. 2017. № 263(1). Р. 470-490.</mixed-citation>
        <mixed-citation xml:lang="en">Hirata M., Kurima S., Mizukami M., Yokota T.Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier-Stokes system with competitive kinetics. Journal of Differential Equations. 2017. N 263(1), р. 470-490.</mixed-citation>
      </ref>
      <ref id="ref7">
        <label>7</label>
        <mixed-citation xml:lang="ru">Bruno O.P. On the quasi-unconditional stability of bdf-adi solvers for the compressible Navier-Stokes equations and related linear problems / O.P.Bruno, M.Cubillos // Siam Journal on Numerical Analysis. 2017. № 55(2). Р. 892-922. DOI: 10.1137/15M1042279.</mixed-citation>
        <mixed-citation xml:lang="en">Bruno O.P.,Cubillos M.On the quasi-unconditional stability of bdf-adi solvers for the compressible Navier-Stokes equations and related linear problems.Siam Journal on Numerical Analysis. 2017. N55(2), р.892-922. DOI: 10.1137/15M1042279.</mixed-citation>
      </ref>
      <ref id="ref8">
        <label>8</label>
        <mixed-citation xml:lang="ru">Fang F. Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems / F.Fang, M.W.Ge // Chinese Physics Letters. 2017. № 34(3), № 030501. DOI:10.1088/0256-307X/34/3/030501.</mixed-citation>
        <mixed-citation xml:lang="en">Fang F., GeM.W.Mathematical Constraints in Multiscale Subgrid-Scale Modeling of Nonlinear Systems.Chinese Physics Letters. 2017. No 34(3), N030501. DOI:10.1088/0256-307X/34/3/030501.</mixed-citation>
      </ref>
      <ref id="ref9">
        <label>9</label>
        <mixed-citation xml:lang="ru">Lai M.C. A short note on Navier-Stokes flows with an incompressible interface and its approximations / M.C.Lai, Y.Seol // Applied Mathematics Letters. 2017. № 65. Р. 1-6. DOI:10.1016/j.aml.2016.09.016.</mixed-citation>
        <mixed-citation xml:lang="en">Lai M.C., SeolY.A short note on Navier-Stokes flows with an incompressible interface and its approximations.Applied Mathematics Letters. 2017. N 65, р. 1-6. DOI:10.1016/j.aml.2016.09.016.</mixed-citation>
      </ref>
      <ref id="ref10">
        <label>10</label>
        <mixed-citation xml:lang="ru">Modeling of Perforated Sill-Controlled Hydraulic Jump / M.Fathi-Moghadam, S.Kiani, P.Asiaban, R.Behrozi-Rad // International Journal of Civil Engineering. 2017. № 15(4А). Р. 689-695.</mixed-citation>
        <mixed-citation xml:lang="en">Fathi-Moghadam M., Kiani S., Asiaban P., Behrozi-Rad R.Modeling of Perforated Sill-Controlled Hydraulic Jump.International Journal of Civil Engineering. 2017. N15(4А),р. 689-695.</mixed-citation>
      </ref>
      <ref id="ref11">
        <label>11</label>
        <mixed-citation xml:lang="ru">Non-linear modelling and stability analysis of the PTGS at pump mode / L.Wang, Q.S.Han, D.Y.Chen, C.Z.Wu, X.Y.Wang // IET Renewable Power Generation. 2017. № 11(6). Р. 827-836.</mixed-citation>
        <mixed-citation xml:lang="en">Wang L., Han Q.S., Chen D.Y., Wu C.Z., Wang X.Y. Non-linear modelling and stability analysis of the PTGS at pump mode.IET Renewable Power Generation. 2017. N11(6),р. 827-836. </mixed-citation>
      </ref>
      <ref id="ref12">
        <label>12</label>
        <mixed-citation xml:lang="ru">Nouri A.Z. Mathematical modeling of concrete pipes reinforced with CNTs conveying fluid for vibration and stability analyses // Computers and Concrete, 2017. № 19(3). Р. 325-331.</mixed-citation>
        <mixed-citation xml:lang="en">Nouri A.Z. Mathematical modeling of concrete pipes reinforced with CNTs conveying fluid for vibration and stability analyses.Computers and Concrete. 2017.N19(3), р. 325-331.</mixed-citation>
      </ref>
      <ref id="ref13">
        <label>13</label>
        <mixed-citation xml:lang="ru">Numerical modelling of a point-absorbing wave energy converter in irregular and extreme waves / W.C.Chen, I.Dolguntseva, A.Savin, Y.L.Zhang, W.Li, E.Svensson, M.Leijon // Applied Ocean Research. 2017. № 63. Р. 90-105. DOI: 10.1016/j.apor.2017.01.004.</mixed-citation>
        <mixed-citation xml:lang="en">Chen W.C., DolguntsevaI., Savin A., Zhang Y.L., Li W., Svensson E., Leijon M.Numerical modelling of a point-absorbing wave energy converter in irregular and extreme waves. Applied Ocean Research. 2017. N63, р.90-105. DOI:10.1016/j.apor.2017.01.004. </mixed-citation>
      </ref>
      <ref id="ref14">
        <label>14</label>
        <mixed-citation xml:lang="ru">Olsen J.E. VLES turbulence model for an Eulerian-Lagrangian modeling concept for bubble plumes / J.E.Olsen, P.Skjetne, S.T.Johansen // Applied Mathematical Modelling. 2017. № 44. Р. 61-71.</mixed-citation>
        <mixed-citation xml:lang="en">Olsen J.E., Skjetne P., Johansen S.T.VLES turbulence model for an Eulerian-Lagrangian modeling concept for bubble plumes.Applied Mathematical Modelling. 2017. N44, р. 61-71.</mixed-citation>
      </ref>
      <ref id="ref15">
        <label>15</label>
        <mixed-citation xml:lang="ru">Ottosson A. A mathematical model of heat and mass transfer in Yankee drying of tissue / A.Ottosson, L.Nilsson, J.Berghel // Drying Technology. 2017. № 35(3). P. 323-334.</mixed-citation>
        <mixed-citation xml:lang="en">Ottosson A., Nilsson L., Berghel J.A mathematical model of heat and mass transfer in Yankee drying of tissue.Drying Technology. 2017. N 35(3), p. 323-334.</mixed-citation>
      </ref>
      <ref id="ref16">
        <label>16</label>
        <mixed-citation xml:lang="ru">Vasilyeva M. Justification of the Choice Matrix Material of the Magnetoactive Elastomer for Working Camera-Channel Peristaltic Unit // Materials Science Forum. 2016. № 870. P. 13-19.</mixed-citation>
        <mixed-citation xml:lang="en">Vasilyeva M. Justification of the Choice Matrix Material of the Magnetoactive Elastomer for Working Camera-Channel Peristaltic Unit.Materials Science Forum. 2016. N 870, p. 13-19.</mixed-citation>
      </ref>
      <ref id="ref17">
        <label>17</label>
        <mixed-citation xml:lang="ru">Vasilyeva M. Perspectives of Application of 3D Shape Memory Composite Materials for Peristaltic Transportation of Slurries // Key Engineering Materials. 2015. № 685. P. 291-294.</mixed-citation>
        <mixed-citation xml:lang="en">Vasilyeva M. Perspectives of Application of 3D Shape Memory Composite Materials for Peristaltic Transportation of Slurries.KeyEngineeringMaterials. 2015. N 685, p. 291-294</mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>
