Kinetic-theoretic studies of the effect of sharp edges of the boundary in low-pressure gases

低压气体边界锐边效应的动力学理论研究

• 批准号: 10650171
• 负责人: AOKI Kazuo
• 金额: $ 1.92万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10650171/
• 关键词: low-pressure gases; Boltzmann equation; velocity distribution function; propagation of singularities; Knudsen number; kinetic theory of gases; rarefied gas dynamics; mean free path; 端的特異性; 熱ほふく流

1. Study of a rarefied gas flow induced around edges of a uniformly cooled or heated plate :In our previous paper, we showed, by means of a numerical analysis using the direct simulation Monte Carlo method, that a fairly strong gas flow is induced around the edges of a uniformly cooled or heated plate placed in a rarefied gas. In the present study, in order to obtain the result with higher reliability, we investigated the flow by an accurate finite-difference analysis of a kinetic equation. As a result, the behavior of the gas was clarified comprehensively. In particular, it was confirmed that the flow has a stronger effect than the thermal creep flow and the flow induced by the thermal stress in the near continuum case.2. Study of a rarefied gas flow caused by a discontinuous wall temperature :We have investigated a rarefied gas flow induced in a container when the temperature of the wall of the container has a discontinuous distribution. The flow was obtained accurately for a wide ra … More nge of the degree of gas rarefaction by applying the finite-difference method developed in 1. We showed that, as the continuum limit is approached, though the region with an appreciable flow shrinks to the discontinuity line of the wall temperature, the maximum speed of the flow tends to approach a finite value. In addition, we have clarified the propagation of singularities, caused by the singularities in the boundary data, mathematically on the basis of a simple transport equation that possesses the feature of the equations in kinetic theory of gases.3. Studies of some other fundamental problems :Paying attention to another aspect of a well-known flow induced by a temperature field (thermal transpiration), we studied the control of the flow in a pipe (e. g., causing a one-way flow) by devising the temperature distribution as well as the configuration of the pipe. We have also investigated the fundamental features of the continuum limit for gas mixtures, the understanding of which facilitates the extension of the analyses of 1 and 2 to the case of the mixtures. Less

1.均匀冷却或加热板边缘周围诱导的稀薄气流的研究：在我们之前的论文中，我们通过使用直接模拟蒙特卡罗方法的数值分析表明，放置在稀薄气体中的均匀冷却或加热板的边缘周围会诱导相当强的气流。在本研究中，为了获得可靠性更高的结果，我们通过对动力学方程进行精确的有限差分分析来研究流动。结果，气体的行为得到了全面阐明。特别是，在近连续介质情况下，证实了该流动比热蠕变流动和热应力诱导流动具有更强的影响。 2．由不连续壁温引起的稀薄气流的研究：我们研究了当容器壁温度具有不连续分布时在容器中引起的稀薄气流。通过应用1中开发的有限差分方法，可以准确地获得大范围气体稀疏度的流动。我们表明，随着接近连续极限，尽管具有明显流动的区域收缩到壁温的不连续线，但流动的最大速度趋于接近有限值。此外，我们还基于一个具有气体动力学方程特征的简单输运方程，从数学上阐明了由边界数据奇点引起的奇点传播。 3．其他一些基本问题的研究：关注由温度场引起的众所周知的流动（热蒸腾）的另一个方面，我们通过设计温度分布和管道的配置来研究管道中流动的控制（例如，引起单向流动）。我们还研究了气体混合物连续介质极限的基本特征，对其的理解有助于将1和2的分析扩展到混合物的情况。较少的

项目成果

K. Aoki: "Numerical analysis of a rarefied gas flow induced near the edges of a uniformly cooled or heated plate"Book of Abstract, 4th International Congress on Industrial and Applied Mathematics (ICIAM99, Edinburgh, 1999). 155

K. Aoki：“均匀冷却或加热板边缘附近引起的稀薄气流的数值分析”摘要书，第四届国际工业与应用数学大会（ICIAM99，爱丁堡，1999 年）。

Kazuo Aoki: "Numerical analysis of a rarefied gas flow induced near the edges of a uniformly cooled or heated plate"Book of Abstract, the Fourth International Congress on Industrial and Applied Mathematics. 155 (1999)

青木一夫：“均匀冷却或加热板边缘附近引起的稀薄气流的数值分析”摘要书，第四届国际工业与应用数学大会。

Kazuo Aoki: "A rarefied gas flow caused by a discontinuous wall temperature"Research Report, Section of Dynamics in Aeronautics and Astronautics Dept. of Aeronautics and Astronautics, Kyoto University. (1999)

青木和夫：“由不连续壁温引起的稀薄气流”研究报告，京都大学航空航天系航空航天动力学部分。

Shigeru Takata: "Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory"Physics of Fluids. Vol.11, No.9. 2743-2756 (1999)

Shigeru Takata：“根据动力学理论，蒸汽和不可凝气体多组分混合物在连续介质极限中的两个表面问题”流体物理学。

K. Aoki: "A rarefied gas flow caused by a discontinuous wall temperature"Research Report, Section of Dynamics in Aeronautics and Astronautics, Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University. 2000

K.青木：“由不连续壁温引起的稀薄气流”研究报告，京都大学工学研究科航空航天系航空航天动力学部。