2007 Fiscal Year Final Research Report Summary
Mathematical and Physical studies on bifurcation and stability of the solution of the Boltzmann equation
| Project/Area Number |
17360041
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | Kyoto University |
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Principal Investigator |
AOKI Kazuo Kyoto University, GRADUATE SCHOOL OF ENGINEERING, PROFESSOR (10115777)
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| Co-Investigator(Kenkyū-buntansha) |
TAKATA Shigeru KYOTO UNIVERSITY, GRADUATE SCHOOL OF ENGINEERING, ASSOCIATE PROFESSOR (60271011)
SUGIMOTO Hiroshi KYOTO UNIVERSITY, GRADUATE SCHOOL OF ENGINEERING, LECTURER (50222055)
KOSUGE Shingo KYOTO UNIVERSITY, GRADUATE SCHOOL OF ENGINEERING, ASSISTANT PROFESSOR (40335188)
MATSUMURA Akitaka OSAKA UNIVERSITY, GRADUATE SCHOOL OF INFORMATION SCIENCE AND TECHNOLOGY, PROFESSOR (60115938)
SONE Yoshio KYOTO UNIVERSITY, GRADUATE SCHOOL OF ENGINEERING, PROFESSOR EMERITUS (80025923)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Boltzmann equation / Kinetic theory of gases / Stability and instability / Bifurcation theory / Ghost effect / Evaporation and condensation / Cylindrical Couette flow / Taylor vortices |
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| Research Abstract |
1. Stability of cylindrical Couette flow of rarefied gases
A rarefied gas between two coaxial circular cylinders rotating at different angular velocities was considered, and the stability of the axially and circumferentially uniform flow (cylindrical Couette flow) for small perturbations was investigated on the basis of kinetic theory. To be more specific, the parameter range in which the cylindrical Couette flow is unstable was clarified numerically using the BGK model of the Boltzmann equation.
2. Cylindrical Couette flow of a vapor-gas mixture
The cylindrical Couette flow mentioned above was considered for the ram where the cylinders are made of the condensed phase of a substance and the gas is a mixture of the vapor of the substance and another noncondensable gas. In this case, evaporation and condensation take place in general on the surface of the cylinders. The behavior of this flow at small Knudsen numbers, in particular, that in the continuum limit, was investigated on the basis
… More
of kinetic theory. As the result, it was shown that the flow field is affected by infinitesimal evaporation and condensation (that is, the ghost effect manifests itself) and a bifurcation of the flow takes place.
3. Taylor-Couette flow of a vapor-gas mixture between two coaxial cylinders
If the assumption of the axial uniformity is released in the cylindrical Couette flow mentioned in 2., the flow may become unstable and transform into doughnut-shaped vortices arranged in the axial direction (Taylor vortices). The effect of the velocity profile of the cylindrical Couette flow deformed by the ghost effect on this instability was studied numerically, and some typical patterns of the transformation were clarified.
4. Other researches
Some instability phenomena and flow bifurcations peculiar to a vapor-gas mixture in the gravitational field were clarified on the basis of the Boltzmann equation. In addition, flows of a binary mixture of vapors evaporating from a plane condensed phase were investigated theoretically, and their basic properties were clarified. Furthermore, a new model Boltzmann equation for a binary mixture of gases was proposed, and its validity and capability were examined numerically. Less
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[Journal Article] Numerical simulation of a Knudsen pump using the effect of curvature of the channel2007
Author(s)
Kazuo, Aoki, Pierre, Degond, Luc, Mieussens, Masaru, Nishioka, Shigeru, Takata
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Journal Title
Rarefied Gas Dynamics, eds. M. S. Ivanov and A. K. Rebrov (Russian Academy of Sciences)
Pages: 1079-1084
Description
「研究成果報告書概要(欧文)」より
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