2019 Fiscal Year Final Research Report
Slip boundary conditions for micro-scale gas flows induced by a discontinuous wall temperature
| Project/Area Number |
17K06146
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Fluid engineering
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | すべりの境界条件 / 希薄気体 / 不連続 / ボルツマン方程式 / 境界層 / 接合漸近展開 / 特異性 |
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| Outline of Final Research Achievements |
In this study, we aimed at extending the conventional "generalized slip flow theory" that assumes a smooth boundary condition to the case where the boundary condition has a jump discontinuity along the boundary. More specifically, a slightly rarefied gas confined in a two-dimensional channel with a discontinuous wall temperature is considered based on the linearized Boltzmann equation and it was found that the singularity with diverging flow velocity is served as the corresponding slip boundary condition for the overall flow velocity described by the Stokes equation. The strength of the singularity (the multiplicative factor) is determined by the analysis of a newly introduced spatially two-dimensional Knudsen-layer problem.
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| Free Research Field |
流体工学
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| Academic Significance and Societal Importance of the Research Achievements |
気体の振舞いを巨視的に記述する流体力学的方程式系を分子の集団運動を記述するボルツマン方程式の系から導出することは実用上重要であり，気体の接する壁における条件（温度分布や速度分布）が滑らかに変化する場合にはすでに確立されたものがある（一般化すべり流理論）．一方，一般化すべり流理論を壁面温度が不連続的な跳びをもつ場合に対して拡張できるかどうかは，理論の原型が発表されてからほぼ半世紀がたった研究開始時点でも知られていなかった．本研究はこれを肯定的に解決し，従来考えられていたよりも広い範囲のマイクロスケール流体問題が（ボルツマン方程式に立ち返ることなく）流体力学のレベルで解析できることを示した．
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