1999 Fiscal Year Final Research Report Summary
Kinetic-theoretic studies of the effect of sharp edges of the boundary in low-pressure gases
| Project/Area Number |
10650171
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
AOKI Kazuo Kyoto University, Graduate School of Engineering, Professor, 工学研究科, 教授 (10115777)
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| Co-Investigator(Kenkyū-buntansha) |
INAMURO Takaji Kyoto University, Graduate School of Engineering, Associate Professor, 工学研究科, 助教授 (20263113)
SUGIMOTO Hiroshi Kyoto University, Graduate School of Engineering, Lecturer, 工学研究科, 講師 (50222055)
TAKATA Shigeru Kyoto University, Graduate School of Engineering, Associate Professor, 工学研究科, 助教授 (60271011)
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| Project Period (FY) |
1998 – 1999
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| Keywords | low-pressure gases / Boltzmann equation / velocity distribution function / propagation of singularities / Knudsen number / kinetic theory of gases / rarefied gas dynamics / mean free path |
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| Research Abstract |
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
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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
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