Studies on forces on and energy transfer to bodies in a rarefied gas

I)在过去，我们发展了流体动力系统和玻尔兹曼系统在略微稀薄的气体流过物体时的稳定流动的一般理论。然而，对于BKW模型方程，只给出了滑移系数和努森层修正的显式数据。在本研究中，发展了一种新的标准Boltzmann方程的数值分析方法，分析了硬球分子气体的滑移系数和Knudsen层，完善了一般理论。ii)在整个Knudsen数范围内分析了热蒸腾流动和不同温度下非共轴圆柱之间的流动。这些是在没有外力的情况下由温度场引起的典型稀薄气体流动，这在连续气体中是看不到的。圆柱体上的力表现出一个有趣的特征，它是克努森数的函数。最初均匀的气体受其平面凝缩…约束的瞬变行为利用动力学理论对蒸发过程中更多的Sd相进行了详细的研究。从长时间解出发，阐明了气体的稳态行为，以及无穷远处变量和凝聚相变量之间的关系。这为气体与其凝聚相界面上的流体动力学方程提供了边界条件。在蒸发速率和克努森数的较大范围内，对圆柱体的定常蒸发流动进行了精确的分析。在研究过程中，我们提出了几种新的动力学方程分析方法，如数值核法、速度分布函数间断分析法、修正的克努森数展开法、无限区域问题的修正诺依曼级数法等。v)应用我们的新方法，我们对各种基本稀薄气体流动进行了精确的分析，包括Couette流、Poiseuille流、缝隙流动、非线性波传播以及平板之间的换热。较少

i) In the past we developed the general theory relating the hydrodynamic system and the Boltzmann system in a steady flow of a slightly rarefied gas past bodies. The explicit data of the slip coefficient and Knudsen layer correction, however, were given only for the BKW model equation. In this study, developing a new method of numerical analysis of the standard Boltzmann equation, we analyzed the slip coefficient and the Knudsen layer for a hard-sphere molecular gas and completed the general theory.ii) The thermal transpiration flow and the flow induced between noncoaxial circular cylinders with different temperatures were analyzed for the whole range of the Knudsen number. These are typical flows of rarefied gas induced by temperature field in the absence of external forces, which are not seen in a continuum gas. The force on the cylinder shows an interesting feature as a function of the Knudsen number.iii) The transient behavior of an initially uniform gas bounded by its plane conden … More sed phase was investigated in detail by the kinetic theory when evaporation took place. From the long-time solution the steady behavior of the gas, as well as the relation among the variables at infinity and on the condensed phase, was clarified. This provides the boundary condition for the fluiddynamic equation on the interface between a gas and its condensed phase. Further, steady evaporation flows from a circular cylinder was analyzed accurately for a wide range of the rate of evaporation and the Knudsen number. The discontinuity of the velocity distribution function in gas was first analyzed accurately in this study.iv) In the course of these studies, we proposed several new methods of analysis of the kinetic equation, such as the numerical kernel method, the method of analyzing the discontinuity of the velocity distribution function, the modified Knudsen number expansion method, and the modified Neumann series method for infinite domain problems.v) Applying our new methods, we made accurate analyses of various fundamental rarefied gas flows for the whole range of gas rarefaction, such as the Couette flow, the Poiseuille flow, a flow through a slit, nonlinear wave propagation, and the heat transfer between two plates. Less