Plane shock waves and Haff’s law in a granular gas
Plane shock waves and Haff’s law in a granular gas
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颗粒气体中的平面冲击波和哈夫定律
DOI：
10.1017/jfm.2015.455
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发表时间：
2015
影响因子：
3.7
通讯作者：
Meheboob Alam
中科院分区：
文献类型：
--
作者：
M. H. L. Reddy;Meheboob Alam
通过数值求解欧拉阶方程和纳维-斯托克斯阶方程，分析了稀颗粒气体的平面冲击波黎曼问题。发现密度和温度分布是不对称的，密度和温度的最大值出现在激波层内。密度峰值随着马赫数和非弹性的增加而增加，并且被发现在后期以稳定的速度传播。激波上游端的颗粒温度根据哈夫定律衰减 ( ${\it\theta}(t)\sim t^{-2}$ )，但下游温度比上游温度衰减得更快。对于弱冲击，哈夫定律似乎在一定时间内在冲击内成立，但对于强冲击会出现偏差。最高温度偏离哈夫定律的时间遵循幂律与上游马赫数和恢复系数的关系。讨论了密度随时间不断增加的起源，并表明必须对颗粒能量方程进行“正则化”以阻止最大密度。
The Riemann problem of planar shock waves is analysed for a dilute granular gas by solving Euler- and Navier–Stokes-order equations numerically. The density and temperature profiles are found to be asymmetric, with the maxima of both density and temperature occurring within the shock layer. The density peak increases with increasing Mach number and inelasticity, and is found to propagate at a steady speed at late times. The granular temperature at the upstream end of the shock decays according to Haff’s law ( ${\it\theta}(t)\sim t^{-2}$ ), but the downstream temperature decays faster than its upstream counterpart. Haff’s law seems to hold inside the shock up to a certain time for weak shocks, but deviations occur for strong shocks. The time at which the maximum temperature deviates from Haff’s law follows a power-law scaling with the upstream Mach number and the restitution coefficient. The origin of the continual build-up of density with time is discussed, and it is shown that the granular energy equation must be ‘regularized’ to arrest the maximum density.