具有多个或超音速临界点的范德瓦尔斯激波极
Van der Waals shock polars with multiple or supersonic critical points
摘要：
结果表明，$γ$ -van der Waals状态方程（eos）允许激波极线具有超声速临界点，对应于超声速的临界或强型激波反射，这对理想气体是不可能的。一般范德瓦耳斯方程允许有多个临界点，对应于四个或更多的反射激波相同的偏转角。在这些反射冲击中，至少有两个是弱型的，即偏转角随着冲击强度的增加而增加，因此标准文献没有标准来选择两者之一。这两种现象都可以发现与Hugoniot曲线完全在凸的区域内和稳定的eos，避免共存区域和满足各种冲击稳定性标准。
英文摘要：
It is shown that the $γ$-van der Waals equation of state (eos) permits shock polars with supersonic critical points, corresponding to critical or strong-type shock reflections that are supersonic, which is not possible for ideal gas. It is also shown that general van der Waals eos permit polars with multiple critical points, corresponding to four or more reflected shocks for same deflection angle. Of these reflected shocks at least two are weak-type, i.e.\ deflection angle increasing with increasing shock strength, so that standard literature has no criteria to select one of the two. Both phenomena can be found with Hugoniot curves entirely in the region of convex and thermodynamically stable eos, avoiding the coexistence region and satisfying various shock stability criteria.
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