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Analytical and numerical studies of nonlinear problems of a low density gas

Research Project

Project/Area Number 03452098
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field Aerospace engineering
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

SONE Yoshio  Kyoto University, Faculty of Engineering, Professor, 工学部, 教授 (80025923)

Co-Investigator(Kenkyū-buntansha) SUGIMOTO Hiroshi  Kyoto University, Faculty of Engineering, Instructor, 工学部, 助手 (50222055)
OHWADA Taku  Kyoto University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (40223987)
AOKI Kazuo  Kyoto University, Faculty of Engineering, Professor, 工学部, 教授 (10115777)
田中 貞映  神戸商船大学, 商船学部, 教授 (00031469)
Project Period (FY) 1991 – 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥7,000,000 (Direct Cost: ¥7,000,000)
Fiscal Year 1993: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1992: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1991: ¥4,900,000 (Direct Cost: ¥4,900,000)
KeywordsRarefied Gas Dynamics / Boltzmann equation / Evaporation and condensation / Shock waves / Kinetic theory of gases / Thermophoresis / Numerical analysis / Low density flows / 気体分子運動論 / 低密度(希薄)気体 / 蒸発 / 自由膨張流 / 抗力 / クヌーセン層 / 衝撃波 / 凝縮 / クヌ-セン層
Research Abstract

The result of this project is summarized as follows.
A.Flows accompanying evaporation and condesation
Long-standing problems, evaporating flows from a cylindrical or spherical condensed phase into a vacuum or into a space occupied with its vapor, are analyzed on the basis of the kinetic theory, and the comprehensive feature of the flows, especially the decisive difference between the flow from a cylinder and that from the sphere, are clarified. The drag problem of a volatile particle is also studied.
B.Flows around a body
Various difficulties in carrying out numerical analysis of flows around a body, i.e., discontinuity of the velocity distribution function in a gas, the complicated collision integral, and infinite domain problems, are resolved. With aid of the result, various important flows around bodies are analyzed accurately for the whole range of the Knudsen number.
C.Flows induced by temperature fields
The thermophoresis problem for a spherical particle is analyzed accurately on the basis of the standard Boltzmann equation for the whole range of the Knudsen number, and its comprehensive feature are clarified. The thermal creep flow, which plays an important role in the thermophoresis, is examined experimentally, and fundamental theoretical results are confirmed.
D.Shock waves
The structure of plane shock waves is analyzed accurately on the basis of the standard Boltzmann equation for hard-sphere molecules. Shock waves that appears in expanding flows are also analyzed.
E.Fundamental properties of solutions of Boltzmann equation
Various important properties in analyzing and understanding rarefied gas flows, i.e., existence of discontinuity of the velocity distribution function in a gas around a convex body and its relation with the S layr at the bottom of Knudsen layr, mathematical properties of steady solutions of a highly rarefied gas, nonlinear effects in a nearly uniform equilibrium flow and thier examples, are clarified.

Report

(4 results)
  • 1993 Annual Research Report   Final Research Report Summary
  • 1992 Annual Research Report
  • 1991 Annual Research Report
  • Research Products

    (54 results)

All Other

All Publications (54 results)

  • [Publications] Hiroshi Sugimoto: "Numerical analysis of steady flows of a gas evaporating from its cylindrical condensed phase on the basis of kinetic theory" Physics of Fluids A. 4. 419-440 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 高田 滋: "希薄気体中の球状粒子に働く抗力と熱応力-全希薄度に対する数値解析-" 真空. 35. 143-146 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Taku Ohwada: "Analysis of thermal stress slip flow and negative thermophoresis using the Boltzmann equation for hard-sphere molecules" European Journal of Mechanics,B/Fluids. 11. 389-414 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Discontinuity of the velocity distribution function in a rarefied gas around a convex body and the S layer at the bottom of the Knudsen layer" Transport Theory and Statistical Physics. 21. 501-530 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Taku Ohwada: "Structure of normal shock waves:Direct numerical analysis of the Boltzmann equation for hard-sphere molecules" Physics of Fluids A. 5. 217-234 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 杉元 宏: "球状凝縮相から真空中への定常蒸発流の気体論的解析" 真空. 36. 148-151 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru Takata: "Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules" Physics of Fluids A. 5. 716-737 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum" Physics of Fluids A. 5. 1491-1511 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Kazuo Aoki: "Steady flows of a rarefied gas around arbitrary obstacle distributions" European Journal of Mechanics,B/Fluids. 12. 565-577 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru Takata: "Thermophoresis of a spherical aerosol particle:Numerical analysis based on kinetic theory of gases" Journal of Aerosol Science. 24. S147-148 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "A simple experiment on the basis of the thermal creep flow of a rarefied gas over a flat wall" European Journal of Mechanics,B/Fluids. 13. (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru Takata: "Thermophoresis of a sphere with a uniform temperature:Numerical analysis of the Boltzmann equation for hard-sphere molecules" Rarefied Gas Dynamics. (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Taku Ohwada: "Numerical analysis of normal shock waves on the basis of the Boltzmann equation for hard-sphere molecules" Rarefied Gas Dynamics. (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 杉元 宏: "円柱状凝縮相から真空中への定常蒸発流の気体論的解析" 真空. 37. (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Numerical analysis of a rarefied gas flow past a volatile particles using the Boltzmann equation for hard-sphere molecules" Physics of Fluids. (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Numerical examination of applicability of the linearized Boltzmann equation" European Journal of Mechanics,B/Fluids. (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Hiroshi Sugimoto: "Numerical analysis of steady flows of a gas evaporating from its cylindrical condensed phase on the basis of kinetic theory" Physics of Fluids A. Vol.4. 419-440 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru Takata: "Drag and thermal force on a spherical particle in a rarefied gas - Numerical analysis for all Knudsen numbers -" Journal of the Vacuum Society of Japan. Vol.35. 143-146 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Taku Ohwada: "Analysis of thermal stress slip flow and negative thermophoresis using the Boltzmann equation for hard-sphere molecules" European Journal of Mechanics, B/Fluids. Vol.11. 389-414 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Discontinuity of the velocity distribution function in a rarefied gas around a convex body and the S layr at the bottom of the Knudsen layr" Transport Theory and Statistical Physics. Vol.21. 501-530 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Taku Ohwada: "Structure of normal shock waves : Direct numerical analysis of the Boltzmann equation for hard-sphere molecules" Physics of Fluids A. Vol.5. 217-234 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Hiroshi Sugimoto: "Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum" Journal of the Vacuum Society of Japan. Vol.36. 148-151 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru Takata: "Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules" Physics of Fluids A. Vol.5. 716-737 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum" Physics of Fluids A. Vol.5. 1491-1511 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Kazuo Aoki: "Steady flows of a rarefied gas around arbitrary obstacle distributions" European Journal of Mechanics, B/Fluids. Vol.12. 565-577 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru Takata: "Thermophoresis of a spherical aerosol particle : Numerical analysis based on kinetic theory of gases" Journal of Aerosol Science. Vol.24. S147-148 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "A simple experiment on the strength of the thermal creep flow of a rarefied gas over a flat wall" European Journal of Mechanics, B/Fluids. Vol.13(in press). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Shigeru Takata: "Thermophoresis of a sphere with a uniform temperature : Numerical analysis of the Boltzmann equation for hard-sphere molecules" Rarefied Gas Dynamics. (in press). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Taku Ohwada: "Numerical analysis of normal shock waves on the basis of the Boltzmann equation for hard-sphere molecules" Rarefied Gas Dynamics. (in press). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Hiroshi Sugimoto: "Kinetic theory analysis of steady evaporating flows from a cylindrical condensed phase into a vacuum" Journal of the Vacuum Society of Japan. Vol.37(in press). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Numerical analysis of a rarefied gas flow past a volatile particles using the Boltzmann equation for hard-sphere molecules" Physics of Fluids. (in press). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Numerical examination of applicability of the linearized Boltzmann equation" European Journal of Mechanics, B/Fluids. (in press). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Yoshio Sone: "Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum" Phys.Fluids A. 5. 1491-1511 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Shigeru Takata: "Thermophoresis of a spherical aerosol particle:Numerical analysis based on kinetic theory of gases" J.Aerosol Sci.24. S147-S148 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Shigeru Takata: "Thermophoresis of a sphere with a uniform temperature:Numerical analysis of the Boltzmann equation for hard-sphere molecules" Rarefied Gas Dynamics,AIAA. (印刷中). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yoshio Sone: "A simple experiment on the strength of the thermal creep flow of a rarefied gas over a flat wall" Eur.J.Mech.,B/Fluids. 13(印刷中). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] 杉元 宏: "円柱状凝縮相から真空中への定常蒸発流の気体論的解析" 真空. 37(印刷中). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yoshio Sone: "Numerical analysis of a rarefied gas flow past a volatile particle using the Boltzman equation for hard-sphere molecules" Phys.Fluids. 6(印刷中). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yoshio Sone: "Steady evaporating flows from a spherical condensed phase into a vacuums,Laboratoire SETT" Proceedings of the IUTAM Symposium,Aerothermochemistry of Spacecraft and Associated Hypersonic Flow. 67-72 (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Shigeru Takata: "Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules" Phys.Fluids A. 5. 716-737 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 高田 滋: "希薄気体中の球状粒子に働く抗力と熱流力-粒子の熱伝導率の影響-" 真空. 37(印刷中). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yoshio Sone: "Numerical examination of applicability of the linearized Boltzmann equation" Eur.J.Mech.,B/Fluids. 13(印刷中). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yoshio Sone: "Discontinuity of the velocity distribution function in a rarefied gas around a convex body and the S layer at the bottom of the Knudsen layer" Transport Theory and Statistical Physics. 21. 501-530 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Yoshio Sone: "Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum" Physics of Fluids A. 5. (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] Yoshio Sone: "Steady evaporating flows from a spherical condensed phase into a vacuum" Proceedings of IUTAM symposium, Aerothermochemistry of spacecrafts and associated hypersonic flows,Springer-Verlag. (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] Taku Ohwada: "Analysis of thermal stress slip flow and negative thermophoresis using the Boltzmann equation for hard-sphere molecules" European Journal of Mechanics,B/Fluids. 11. 389-414 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Sigeru Takata: "Thermophoresis of a sphere with a uniform temperature: Numerical analysis of the Boltzmann equation for hard-sphere molecules" Rarefied Gas Dynamics AIAA. (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] Taku Ohwada: "Numerical analysis of normal shock waves on the basis of the Boltzmann equation for hard-sphere molecules" Rarefied Gas Dynamics AIAA. (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] Kazuo Aoki: "Numerical analysis of steady flows of a gas condensing on or evaporating from its plane condensed phase on the basis of kinetic theory:Effect of gas motion along the condensed phase" physics of Fluids A. 3. 2260-2275 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Hiroshi Sugimoto: "Numerical analysis of steady flows of a gas evaporating from its cylindrical condensed phase on the basis of kinetic theory" Physics of Fluids A. 4. 419-440 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Yoshio Sone: "Discontinuity of the velocity distribution function in a rarefied gas around a convex body and the S layer at the bottom of the Knudsen layer" Transport Theory and Statistical Physics. 21. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 高田 滋: "希薄気体中の球状粒子に働く抗力と熱応力ー全希薄度に対する数値解析ー" 真空. 35. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Shigeru Takata: "Rarefied gas flows around a body and discontinuity of the velocity distribution function in the drag and thermal force problem" Rarefied Gas Dynamics. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] Taku Ohwada: "Numerical analysis of normal shock waves on the basis of the Boltzmann equation for hardーsphere molecules" Rarefied Gas Dynamics. (1992)

    • Related Report
      1991 Annual Research Report

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Published: 1991-04-01   Modified: 2016-04-21  

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