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Theoretical investigation on laminar-turbulent transition of flows through a rectangular duct

Research Project

Project/Area Number 15560052
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionKyoto University

Principal Investigator

NAGATA Masato  Kyoto University, Graduate School of Engineering, Professor, 工学研究科, 教授 (80303858)

Co-Investigator(Kenkyū-buntansha) KAAHARA Genta  Osaka University, Graduate School of Engineering Science, Professor, 基礎工学研究科, 教授 (50214672)
ITANO Tomoaki  Kannsai University, Faculty of Engineering, Lecture, 工学部, 講師 (30335187)
Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2005: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥2,400,000 (Direct Cost: ¥2,400,000)
Keywordsrectangular duct flow / channel Flow / laminar-turbulent transition / linear stability / nonlinear stability / internal heat source / inflection point / Boussinesq approximation / ナヴィエ・ストークス方程式 / 非線形安定性解析 / ノーマル・モード / ニュートン法 / チェビシェフ多項式 / フーリエ級数 / グラスホフ数 / レイノルズ数 / 線形解析 / 円管ポアズイユ流 / 縦渦・横渦解
Research Abstract

(1)Linear and nonlinear stability analyses on a convective flow in a channel produced by a homogeneously distributed heat source are carried out by imposing a periodic boundary condition on the side walls in the spanwise direction. We expect that the transition mechanism from laminar to turbulent flows in this system would not change much from the one in a rectangular duct case. From the linear analysis we find that there are two kinds of infinitesimal disturbances, transverse-roll type and longitudinal-roll type, which destabilise the flow in the case when the channel is placed almost vertically. Also we are able to obtain finite amplitude solutions resulting from the nonlinear interaction of these two kinds of disturbances.
(2)A linear stability on the flow through a duct produced by a homogeneously distributed heat source is examined numerically. We obtain the following results. (i)There are, unexpectedly, several inflection points and reverse-flow points in the basic flow profile. They play important roles for the stability, of the flow. (ii)The flow through a duct at any aspect ratio can become unstable. (iii)The region in the parameter space where the flow becomes unstable coincides with the region where the basic flow profile is inflectional. (iv)The eigenfunction of the unstable mode propagates in the streamwise direction with the phase velocity equal to the average velocity of the basic flow.
(3)As a nonlinear extension of the case (2)we derive higher order terms resulting from the nonlinear interaction of unstable eigenmodes, and the modification terms for the mean flow and the mean temperature. By taking into account the particular spatial symmetry in this system we identify the spatial structure of the finite amplitude solution that may bifurcate as a result of instability. The validity of the numerical code which incorporates the above has been checked partially.

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (14 results)

All 2006 2005 2004 2003 Other

All Journal Article (12 results) Publications (2 results)

  • [Journal Article] Linear stability of flow in an internally heated rectangular duct2006

    • Author(s)
      Uhlmann, M., Nagata, M.
    • Journal Title

      Journal of Fluid Mechanics 551

      Pages: 387-404

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Linear stability of flow in an internally heated rectangular duct2006

    • Author(s)
      Uhlmann, M., Nagata, M.
    • Journal Title

      Journal of Fluid Mechanics Vol.551

      Pages: 387-404

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Nonlinear secondary flow through a rotating channel2006

    • Author(s)
      Wall, D.P., Nagata, M.
    • Journal Title

      Journal of Fluid Mechanics (In press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Characterization of near-wall turbulence in terms of equilibrium and ``bursting'' solutions2005

    • Author(s)
      Jimenez, J., Kawahara, G., Simens, M.P., Nagata, M., Shiba, M.
    • Journal Title

      Physics of Fluids 17-1

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Nonlinear Solutions of Simple Plane Shear Layers with and without a System Rotation2005

    • Author(s)
      Nagata, M., Kawahara, G., Itano, T., Wall, D.P., Mitsumoji, T, Nakamura, R.
    • Journal Title

      Fluid Mechanics and its Applications 77

      Pages: 51-69

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Characterization of near-wall turbulence in terms of equilibrium and "bursting" solutions2005

    • Author(s)
      Jimenez, J., Kawahara, G., Simens, M.P., Nagata, M.Shiba, M.
    • Journal Title

      Physics of Fluids Vol.17-1

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Nonlinear Solutions of Simple Plane Shear Layers with and without a System Rotation2005

    • Author(s)
      Nagata, M., Kawahara, G., Itano, T., Wall, D.P., Mitsumoji, T, Nakamura
    • Journal Title

      Fluid Mechanics and its Applications Vol.77

      Pages: 51-69

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Transition in plane parallel shear flows heated internally2004

    • Author(s)
      Nagata, M., Generalis, S.C.
    • Journal Title

      Comptes Rendus Mecanique 332

      Pages: 9-16

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Transition in plane parallel shear flows heated internally2004

    • Author(s)
      Nagata, M., Generalis, S.C.
    • Journal Title

      Comptes Rendus Mecanique Vol.332

      Pages: 9-16

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Rotating Flows Over Compliant Walls2003

    • Author(s)
      Carpenter, P.W., Thomas, P.J., Nagata, M.
    • Journal Title

      Fluid Mechanics and its Applications 72

      Pages: 167-187

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Rotating Flows Over Compliant Walls2003

    • Author(s)
      Carpenter, P.W, Thomas, P.J., Nagata, M.
    • Journal Title

      Fluid Mechanics and its Application Vol.72

      Pages: 167-187

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Nonlinear secondary flow through a rotating channel

    • Author(s)
      Wall, D.P., Nagata, M.
    • Journal Title

      Journal of Fluid Mechanics (In press)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] S.Generalis, M.Nagata: "Transition in Homogeneously Heated Inclined Plane Parallel Shear Flows"Journal of Heat Transfer. 125. 795-803 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Nagata, S.Generalis: "Transition in plane parallel shear flows heated internally"Comptes Rendus Mecanique. 332. 9-16 (2004)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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