The sudden expansion into vacuum of a gas cloud, with initial centrally symmetric density and temperature profiles, is studied theoretically for different values of the specific heat ratio γ. Models treating the expansion are discussed, in particular, a model for isentropic expansion and a model for spatially isothermal expansion. For γ→1, the density of the gas obtained from the former model for late stages of the expansion, approaches a Gaussian spatial profile which is the exact solution to the latter model. A description by a Gaussian profile can be, for some important cases, approximately correct even for large deviations of γ from one. For a spherically symmetric flow, the maximum difference (for any given time and distance from the center of symmetry) between the densities obtained from the above two models is 11% for γ=7/5. For γ=1.28, which corresponds to the expansion of lead azide detonation products previously studied in the author’s laboratory, the difference is 9%. It is also shown that in practice it is more convenient to use the model for isothermal expansion to describe the density profile since it does not depend on γ, which is very often not exactly known. Finally, for γ→1, a relation between the density and the temperature is obtained which is not dependent on their initial distributions.

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再次讨论了气体云突然膨胀成真空的情况

从理论上研究了气体云团突然膨胀到真空中的初始中心对称密度和温度分布，并得出了不同值的气体。 比热比γ。讨论了处理膨胀的模型，尤其是等熵膨胀模型和在空间上等温膨胀。对于γ→1，从前一个模型获得的膨胀后期的气体密度接近高斯分布空间的 个人资料是 确切的解决方案到后一种模型。在某些重要情况下，即使对于γ与γ的较大偏差，使用高斯轮廓进行的描述也可能是近似正确的。对于球形对称流，对于γ= 7/5，从上述两个模型获得的密度之间的最大差值（对于任何给定时间和距对称中心的距离）为11％。对于γ= 1.28（与先前在作者实验室中研究过的叠氮化铅爆炸产物的扩展相对应），相差9％。还表明，实际上，使用等温膨胀模型来描述密度分布图更为方便，因为它不依赖于γ，而γ常常不是很确切。最后，对于γ→1，获得密度和温度之间的关系，该关系不依赖于它们的初始分布。