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Genelarized slip flow theory for stationary micro gas flows and its extension to nonstationary problems

Research Project

Project/Area Number 23360083
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Fluid engineering
Research InstitutionKyoto University

Principal Investigator

TAKATA Shigeru  京都大学, 工学(系)研究科(研究院), 教授 (60271011)

Co-Investigator(Kenkyū-buntansha) KOSUGE Shingo  京都大学, 大学院・工学研究科, 助教 (40335188)
TAGUCHI Satoshi  電気通信大学, 情報理工学研究科, 助教 (90448168)
Project Period (FY) 2011-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥18,720,000 (Direct Cost: ¥14,400,000、Indirect Cost: ¥4,320,000)
Fiscal Year 2013: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2012: ¥8,190,000 (Direct Cost: ¥6,300,000、Indirect Cost: ¥1,890,000)
Fiscal Year 2011: ¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000)
Keywords分子流体力学 / 希薄気体力学 / ボルツマン方程式 / すべり流 / 一般すべり流理論 / 希薄気体効果 / 分子気体力学 / 2次すべり / 国際研究者交流
Research Abstract

The present research aims at extending the conventional fluid dynamics to describe the gas behavior in the pressure range from 1 to about 1/10000 atmospheric pressure. This is an extension of the existing theory for time-independent cases to the theory for time-dependent cases. It is found that a new term should be added to the fluid-dynamic type equations due to the compressibility of the gas. A new phenomenon that is peculiar to the time-dependent systems are also found. From a technical viewpoint, the present research makes use of a new methodology that is base on a symmetric property of the Boltzmann equation, the equation which is the fundamental equation for a microscopic description of the gas. A numerical method has been newly developed in order to overcome some mathematical difficulties.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • Research Products

    (34 results)

All 2014 2013 2012 2011

All Journal Article (7 results) (of which Peer Reviewed: 5 results) Presentation (27 results) (of which Invited: 15 results)

  • [Journal Article] A force acting on an oblate spheroid with discontinuous surface temperature in a slightly rarefied gas2014

    • Author(s)
      K. Aoki, S. Takata, T. T omota
    • Journal Title

      J. Fluid Mech

      Volume: 748 Pages: 712-730

    • DOI

      10.1017/jfm.2014.200

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Journal Article] Asymptotic theory for the time-dependent behavior of a slightly rarefied gas over a smooth solid boundary2012

    • Author(s)
      S. Takata and M. Hattori
    • Journal Title

      J. Stat. Phys

      Volume: 147 Issue: 6 Pages: 1182-1215

    • DOI

      10.1007/s10955-012-0512-z

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hagen-Poiseuille and thermal transpiration flows of a highly rarefied gas through a circular pipe2012

    • Author(s)
      H. Funagane and S. Takata
    • Journal Title

      Fluid Dyn. Res

      Volume: 44 Issue: 5 Pages: 55506-55506

    • DOI

      10.1088/0169-5983/44/5/055506

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the second-order slip and jump coefficients for the general theory of slip flow2012

    • Author(s)
      S. Takata and M. Hattori
    • Journal Title

      AIP Conf. Proc

      Volume: 1501 Pages: 59-66

    • DOI

      10.1063/1.4769473

    • NAID

      120005439713

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Journal Article] A simple model for flows around moving vanes in Crookes radiometer2012

    • Author(s)
      S. Taguchi
    • Journal Title

      28th International Symposium on Rarefied Gas Dynamics 2012: AIP Conf. Proc.

      Volume: 1501 Pages: 786-793

    • DOI

      10.1063/1.4769622

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parabolic temperature profile and second-order temperature jump of a slightly rarefied gas in an unsteady two-surface problem2012

    • Author(s)
      S.Takata, K.Aoki, M.Hattori, N.G.Hadjiconstantinou
    • Journal Title

      Phys.Fluids

      Volume: 24 Issue: 3 Pages: 32002-32002

    • DOI

      10.1063/1.3691262

    • NAID

      120004920388

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical demonstration of the reciprocity among elemental relaxation and driven-flow problems for a rarefied gas in a channel2012

    • Author(s)
      S.Takata, M.Oishi
    • Journal Title

      Physics of Fluids

      Volume: 24 Issue: 1 Pages: 12003-12003

    • DOI

      10.1063/1.3678308

    • NAID

      120004920390

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Theory of reciprocity for rarefied gases2013

    • Author(s)
      高田滋
    • Organizer
      IMS PDE seminar
    • Place of Presentation
      The Chinese University of Hong Kong
    • Year and Date
      2013-11-27
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Asymptotic Analyses in Molecular Gas Dynamics : Fluid-dynamic limit and some other topics2013

    • Author(s)
      高田滋
    • Organizer
      IMS PDE seminar
    • Place of Presentation
      The Chinese University of Hong Kong
    • Year and Date
      2013-11-25
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Molecular Gas Dynamics : An approach to non-continuum effects in Fluids2013

    • Author(s)
      高 田 滋
    • Organizer
      Joint Colloquium of the Institute of Mathematical Science and the Department of Mathematics
    • Place of Presentation
      The Chinese University of Hong Kong
    • Year and Date
      2013-11-21
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Elementary rarefied gas flows : thermal effects and reciprocity2013

    • Author(s)
      高 田 滋
    • Organizer
      The Research Away Day
    • Place of Presentation
      University of Strathclyde(イギリス)
    • Year and Date
      2013-09-06
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 微視的視点からの流体現象へのアプローチ2013

    • Author(s)
      高田滋
    • Organizer
      日本航空宇宙学会関西支部第442回航空懇談会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-07-19
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Some applications of symmetry relations for the steady/unsteady linearized Boltzmann equation2013

    • Author(s)
      高 田 滋
    • Organizer
      The 6th Pacific RIM Conference on Mathematics 2013
    • Place of Presentation
      札幌コンベンションセンタ
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Some applications of symmetry relations for the steady/unsteady linearized Boltzmann equation2013

    • Author(s)
      高 田 滋
    • Organizer
      The 5th Workshop on Theory and Numerics of Kinetic Equations
    • Place of Presentation
      Saarland University (ドイツ)
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On a gradient singularity of flow velocity of a rarefied gas over a planar boundary2013

    • Author(s)
      高田滋
    • Organizer
      Workshop on Boundary Phenomena for Evolutionary Partial Differential Equations
    • Place of Presentation
      Academia Sinica(台湾)
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 希薄気体の円筒クエット流における境界条件の影響2013

    • Author(s)
      小菅真吾
    • Organizer
      日本流体力学会年会2013
    • Place of Presentation
      東京農工大学小金井キャンパス
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Elementary rarefied gas flows: thermal effects and reciprocity2013

    • Author(s)
      高田滋
    • Organizer
      The Research Away Day
    • Place of Presentation
      University of Strathclyde (イギリス)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Some applications of symmetry relations for the steady/unsteady linearized Boltzmann equation2013

    • Author(s)
      高田滋
    • Organizer
      The 5th Workshop on Theory and Numerics of Kinetic Equations
    • Place of Presentation
      Saarland University (ドイツ)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On a gradient singularity of flow velocity of a rarefied gas over a planar boundary2013

    • Author(s)
      高田滋
    • Organizer
      Workshop on Boundary Phenomena for Evolutionary Partial Differential Equations
    • Place of Presentation
      Academia Sinica (台湾)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Asymptotic Analyses in Molecular Gas Dynamics: Fluid-dynamic limit and some other topics2013

    • Author(s)
      高田滋
    • Organizer
      IMS PDE seminar
    • Place of Presentation
      The Chinese University of Hong Kong
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Molecular Gas Dynamics: An approach to non-continuum effects in Fluids2013

    • Author(s)
      高田滋
    • Organizer
      Joint Colloquium of the Institute of Mathematical Science and the Department of Mathematics
    • Place of Presentation
      The Chinese University of Hong Kong
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 希薄気体の円筒クエット流における境界条件の影響2013

    • Author(s)
      小菅真吾
    • Organizer
      日本流体力学会年会2013
    • Place of Presentation
      東京農工大学小金井キャンパス
    • Related Report
      2013 Annual Research Report
  • [Presentation] Symmetry relation for the linearized Boltzmann system and its applications2012

    • Author(s)
      S. Takata
    • Organizer
      Workshop on Kinetic Theory and Gas Dynamics
    • Place of Presentation
      Stanford (USA)
    • Year and Date
      2012-07-24
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Invited
  • [Presentation] Reciprocity among elemental relaxation and driven-flow problems for a rarefied gas2012

    • Author(s)
      S. Takata
    • Organizer
      The 23rd International Congress of Theoretical and Applied Mechanics
    • Place of Presentation
      Beijing (China)
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] On the second-order slip and jump coefficients for the general theory of slip flow2012

    • Author(s)
      S. Takata
    • Organizer
      The 28th International Symposium on Rarefied Gas Dynamics
    • Place of Presentation
      Symposium on Rarefied Gas Dynamics
    • Related Report
      2013 Final Research Report
  • [Presentation] A simple model for flows around moving vanes in Crookes radiometer2012

    • Author(s)
      S. Taguchi
    • Organizer
      The 28th International Symposium on Rarefied Gas Dynamics
    • Place of Presentation
      Zaragoza (Spain)
    • Related Report
      2013 Final Research Report 2012 Annual Research Report
  • [Presentation] 非定常系における一般すべり流理論2012

    • Author(s)
      初鳥匡成
    • Organizer
      日本流体力学会年会 2012
    • Place of Presentation
      高知大学(高知)
    • Related Report
      2013 Final Research Report
  • [Presentation] Reciprocity among elemental relaxation and driven-flow problems in the kinetic theory of gases2012

    • Author(s)
      S. Takata
    • Organizer
      Spring School on Kinetic Theory and Fluid Mechanics
    • Place of Presentation
      フランス
    • Related Report
      2013 Final Research Report 2011 Annual Research Report
  • [Presentation] 非定常二平板問題における弱希薄気体の放物型温度分布と温度のとび2012

    • Author(s)
      初鳥匡成
    • Organizer
      第61回理論応用力学講演会
    • Place of Presentation
      東京
    • Related Report
      2013 Final Research Report 2011 Annual Research Report
  • [Presentation] On the second-order slip and jump coefficients for the general theory of slip flow2012

    • Author(s)
      Shigeru Takata
    • Organizer
      The 28th International Symposium on Rarefied Gas Dynamics
    • Place of Presentation
      Zaragoza (Spain)
    • Related Report
      2012 Annual Research Report
  • [Presentation] 非定常系における一般すべり流理論2012

    • Author(s)
      初鳥匡成
    • Organizer
      日本流体力学会年会2012
    • Place of Presentation
      高知大学(高知)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Reciprocity among elemental relaxation and driven-flow problems for a rarefied gas2011

    • Author(s)
      S. Takata
    • Organizer
      Workshop on Boltzmann Models in Kinetic Theory
    • Place of Presentation
      アメリカ合衆国
    • Related Report
      2013 Final Research Report 2011 Annual Research Report
  • [Presentation] Reciprocity among elemental relaxation and driven-flow problems in the kinetic theory of gases2011

    • Author(s)
      S. Takata
    • Organizer
      8th East Asia Conference on Partial Differential Equations
    • Place of Presentation
      韓国
    • Related Report
      2013 Final Research Report 2011 Annual Research Report
  • [Presentation] On the force exerted on the edge of a heated plate : Numerical investigation and considerations2011

    • Author(s)
      S. Taguchi
    • Organizer
      The Eighth International Conference for Mesoscopic Methods in Engineering and Science
    • Place of Presentation
      フランス
    • Related Report
      2013 Final Research Report 2011 Annual Research Report

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Published: 2011-04-06   Modified: 2019-07-29  

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