| Project/Area Number |
21K03877
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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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| Review Section |
Basic Section 19010:Fluid engineering-related
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| Research Institution | Tottori University |
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Principal Investigator |
Doi Toshiyuki 鳥取大学, 工学研究科, 准教授 (00227688)
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2023: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2022: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 分子気体力学 / マイクロ潤滑 / 非連続体効果 / 偏心円筒間流れ / 平均自由行程 / 曲率 / 希薄気体流 / マイクロマシン / 潤滑 |
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| Outline of Research at the Start |
気体分子の平均自由行程程度(0.1ミクロン以下)よりも狭い超微小隙間の潤滑を記述する巨視的潤滑方程式を、気体分子運動論に基づいて導出する。特に、2つの壁面が任意の温度分布を有する場合において、隙間と温度分布の広い範囲で妥当な方程式を導く。導かれた方程式の妥当性は、気体分子運動論に基づく直接数値計算と比較することによって検証する。
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| Outline of Final Research Achievements |
Microscale lubrication of a gas between circular cylinders with the clearance of the order of the mean free path of the gas is studied on the basis of kinetic theory. The dimensionless curvature, defined as the clearance divided by the radius of the spindle, is small. The Boltzmann equation is studied analytically using a perturbation method. It was clarified that a lubrication equation derived by the direct application of the conventional lubrication theory yields a non-negligible error proportional to the square root of the dimensionless curvature, when the clearance is much smaller than the mean free path. An improved lubrication equation is derived by correctly taking the effect of small curvature into account. It was also demonstrated that the improved equation provides the solution that perfectly agrees with the direct numerical solution of the Boltzmann equation over the entire range of the clearance.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究課題の成果として、本来連続体力学で扱えないようなマイクロ潤滑問題を、連続体潤滑理論と同程度の容易さで解析できる改良潤滑方程式および必要な数値データを社会に提供した。研究詳細を示した文献はオープンアクセス化し、万人が読めるようにした。改良潤滑方程式を実際に使用する際に必要な数値データを研究代表者のホームページから公開した。
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