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Studies on the stability of low pressure gases on the basis of kinetic theory

基于动力学理论的低压气体稳定性研究

基本信息

批准号：
08455463
负责人：
SONE Yoshio
金额：
$ 4.99万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08455463/
关键词：
rarefied gas stability bifurcation Taylor-Couette flow Boltzmean equation Benard problem evaporation and condensation thermal creep flow テーラー・クェット問題

项目摘要

1.the Benard problem for a rarefied gas is studied numerically on the basis of kinetic theory. The main results are as follows : (1)The range of the parameters for which a steady convection flow exists and steady flow patterns ; 2)transition processes to various steady patterns from various initial conditions ; and 3)stability of multi-roll solutions, which are arrays of several stable single-roll solutions. In (1) there exists a different branch of the stability boundary, not found in the classical gas dynamies.2)The stability of the cylindrical Couette flow for a rarefied flow is studied by the direct simulation Monte Carlo method, and the parameter range where the steady Taylor vortex flow exists and the structure of the flow are clarified. The analysis is extended to the case where there is a temperature difference between the two cylinders. It is found that the temperature difference acts so as to stabikize flow, against the result inferred from the Benard problem.3.The study of the subject 2 is extended to the case where the cylinders are made of the condensed phase of the gas, and a new type of bifurcation of flow is found in a circumferentially and axially uniform flow.4.Asymptotic analysis in the continuum limit of the problem 3 shows that the rerefaction effect which is supposed to vanish in the continuum limit remains in this limit (a ghost effect). This is a striking result showing the incompleteness of the classical (conventional) gas dynamics and necessity of kinetic theory even in the analysis of the continuum limit (a new role of kinetic theory).5.Flows induced around a heated plate in a rarefied gas in a gravitational field is stucied.6.High speed flows of a rarefied gas past a flat plate are studied.

1.本文在动力学理论的基础上对稀薄气体的Benard问题进行了数值研究。主要结果如下：（1）定常对流存在的参数范围和定常流型;（2）从不同初始条件到不同定常流型的过渡过程;（3）多滚解的稳定性，即多个稳定的单滚解的阵列。在（1）中，存在一个不同于经典气体动力学的稳定边界分支。2）用直接模拟Monte Carlo方法研究了稀薄流动下圆柱Couette流的稳定性，阐明了定常Taylor涡流存在的参数范围和流动结构。分析扩展到的情况下，有两个气缸之间的温差。发现温差的作用是使流动稳定，与Benard问题的结果相反。3.将课题2的研究扩展到气体凝相圆柱体的情况，在周向和轴向均匀流中发现了一种新的流动分叉类型。4.对问题3的连续极限的渐近分析表明，假定在连续极限中消失的再折射效应保持在该极限中（鬼效应）。这是一个引人注目的结果，表明了经典（常规）气体动力学的不完备性和动力学理论的必要性，即使在分析连续极限（动力学理论的一个新作用）时也是如此。5.研究了重力场中稀薄气体绕加热平板的流动。6.研究了稀薄气体绕平板的高速流动。