Abstract

The effect of non-Boltzmann energy distributions on the free propagation of shock waves through a monoatomic gas is investigated via theory and simulation. First, the non-Boltzmann heat capacity ratio \(\gamma \), as a key property for describing shock waves, is derived from first principles via microcanonical integration. Second, atomistic molecular dynamics simulations resembling a shock tube setup are used to test the theory. The presented theory provides heat capacity ratios ranging from the well-known \(\gamma = 5/3\) for Boltzmann energy-distributed gas to \(\gamma \rightarrow 1\) for delta energy-distributed gas. The molecular dynamics simulations of Boltzmann and non-Boltzmann driven gases suggest that the shock wave propagates about 9% slower through the non-Boltzmann driven gas, while the contact wave appears to be about 4% faster if it trails non-Boltzmann driven gas. The observed slowdown of the shock wave through applying a non-Boltzmann energy distribution was found to be consistent with the classical shock wave equations when applying the non-Boltzmann heat capacity ratio. These fundamental findings provide insights into the behavior of non-Boltzmann gases and might help to improve the understanding of gas dynamical phenomena.

Graphical abstract

中文翻译：

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单原子非玻尔兹曼气体自由传播冲击波的理论与模拟

摘要

通过理论和模拟研究了非玻尔兹曼能量分布对冲击波通过单原子气体自由传播的影响。首先，非玻尔兹曼热容比\(\gamma \)作为描述冲击波的关键属性，是通过微正则积分从第一原理推导出来的。其次，使用类似于激波管装置的原子分子动力学模拟来测试该理论。所提出的理论提供的热容比范围从众所周知的玻尔兹曼能量分布气体的\(\gamma = 5/3\)到Delta 能量分布气体的\(\gamma \rightarrow 1\) 。玻尔兹曼和非玻尔兹曼驱动气体的分子动力学模拟表明，冲击波在非玻尔兹曼驱动气体中的传播速度要慢约 9%，而如果接触波跟随非玻尔兹曼驱动气体，接触波的传播速度似乎要快约 4%。发现通过应用非玻尔兹曼能量分布观察到的冲击波减慢与应用非玻尔兹曼热容比时的经典冲击波方程一致。这些基本发现提供了对非玻尔兹曼气体行为的见解，并可能有助于提高对气体动力学现象的理解。

图形概要