Asymptotic theory of a uniform flow of a rarefied gas past a sphere at low Mach numbers
Asymptotic theory of a uniform flow of a rarefied gas past a sphere at low Mach numbers
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稀薄气体以低马赫数均匀流过球体的渐近理论
DOI：
10.1017/jfm.2015.265
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发表时间：
2015
影响因子：
3.7
通讯作者：
Satoshi Taguchi
中科院分区：
文献类型：
--
作者：
Yukihito NARITA;Naoto KATO;Masashi YAMANAKA;Toshiharu KAZAMA;Yasuhiro OSAFUNE;Tomoya MASUYAMA;Yukihito NARITA，Masashi YAMANAKA，Toshiharu KAZAMA，Yasuhiro OSAFUNE，Tomoya MASUYAMA;Yukihito Narita，Toshiharu Kazama，Masashi Yamanaka;成田幸仁，加藤直人，ムハマド ハフィズ，山中将，風間俊治;高木佑太，佐藤亮介，笹川竜哉，成田幸仁，風間俊治;山本大平，笹川竜哉，佐藤亮介，成田幸仁，風間俊治;加藤直人，成田幸仁，山中将，風間俊治;佐藤亮介，成田幸仁，加藤直人，風間俊治;笹川竜哉，成田幸仁，加藤直人，風間俊治;Yukihito Narita，Toshiharu Kazama，Masashi Yamanaka;成田幸仁，加藤直人，ムハマド ハフィズ，山中将，風間俊治;Satoshi Taguchi
考虑稀薄气体缓慢均匀地流过具有均匀温度的球体。本文以玻尔兹曼方程为基础，在Knudsen数有限的情况下，用系统渐近分析方法研究了小马赫数下气体的稳定行为。引入长度变化尺度远大于球体尺寸的慢变解，导出了描述远区气体整体行为的流体动力学型方程。然后，用线性玻尔兹曼方程描述的随球体大小变化的近区域的解，以及用流体动力学型方程描述的远区域的解，以马赫数展开到二阶的形式寻求，以一种将它们连接在中间重叠区域的方式。因此，阻力被推导到马赫数的二阶，这在形式上扩展了Takata等人的线性阻力。流体力学，1993,vol. 5, pp. 716-737)。文中还给出了基于BGK模型的阻力计算结果。
A slow uniform flow of a rarefied gas past a sphere with a uniform temperature is considered. The steady behaviour of the gas is investigated on the basis of the Boltzmann equation by a systematic asymptotic analysis for small Mach numbers in the case where the Knudsen number is finite. Introducing a slowly varying solution whose length scale of variation is much larger than the sphere dimension, the fluid-dynamic-type equations describing the overall behaviour of the gas in the far region are derived. Then, the solution in the near region which varies on the scale of the sphere size, described by the linearised Boltzmann equation, and the solution in the far region, described by the fluid-dynamic-type equations, are sought in the form of a Mach number expansion up to the second order, in a way that they are joined in the intermediate overlapping region. As a result, the drag is derived up to the second order of the Mach number, which formally extends the linear drag obtained by Takata et al. (Phys. Fluids A, vol. 5, 1993, pp. 716–737) to a weakly nonlinear case. Numerical results for the drag on the basis of the Bhatnagar–Gross–Krook (BGK) model are also presented.