Slip boundary conditions for micro-scale gas flows induced by a discontinuous wall temperature

• Project/Area Number: 17K06146
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Fluid engineering
• Research Institution: Kyoto University
• Principal Investigator: Taguchi Satoshi 京都大学, 情報学研究科, 教授 (90448168)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• 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 / 滑りの境界条件 / 気体論境界層 / マイクロスケール気体流 / 流体 / マイクロ流体

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.

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．

Research Products

• [Journal Article] A rarefied gas flow around a rotating sphere: diverging profiles of gradients of macroscopic quantities (2019)
  • Author(s): Taguchi Satoshi, Saito Kazuyuki, Takata Shigeru
  • Journal Title: Journal of Fluid Mechanics Volume: 862 Pages: 5-33
  • DOI: 10.1017/jfm.2018.946
  • NAID: 120006876603
  • Peer Reviewed / Int'l Joint Research
• [Presentation] 希薄気体中で自転を始める球により誘起される流れ (2020)
  • Author(s): 小寺雅司
  • Organizer: 桂インテックセンター 先端流体理工学研究部門 第2回公開セミナー
• [Presentation] Motion of a slightly rarefied gas induced by a discontinuous wall temperature (2019)
  • Author(s): Satoshi Taguchi
  • Organizer: INdAM Workshop: Recent Advances in Kinetic Equations and Applications
  • Int'l Joint Research / Invited
• [Presentation] 不連続な壁面温度によって誘起される流れ：特異なすべり境界条件 (2019)
  • Author(s): 田口智清
  • Organizer: 日本流体力学会年会2019
• [Presentation] Cross-coupling effect of flow and heat transfer in a slow flow of a rarefied gas past a sphere (2018)
  • Author(s): S. Taguchi
  • Organizer: 31th International Symposium on Rarefied Gas Dynamics
  • Int'l Joint Research
• [Presentation] 希薄気体における力学的・熱力学的相互作用 (2018)
  • Author(s): 田口智清
  • Organizer: 兵庫県立大学計算機科学連携セミナー～非平衡現象のダイナミ クス～
  • Invited
• [Presentation] Cross-coupling effect in a slow rarefied flow past a heated sphere (2018)
  • Author(s): S. Taguchi
  • Organizer: The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Int'l Joint Research / Invited
• [Presentation] 希薄気体における熱と流れの相互作用 (2018)
  • Author(s): 田口智清
  • Organizer: 日本流体力学会年会2018