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首页> 外文会议>International Symposium on Explosion, Shock Wave and Hypervelocity Phenomena(ESHP-2); 20070306-09; Kumamoto(JP) >Reconsideration of the So-called von Neumann Paradox in the Reflection of a Shock wave Over a Wedge
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Reconsideration of the So-called von Neumann Paradox in the Reflection of a Shock wave Over a Wedge

机译：在楔形物上的冲击波反射中对所谓冯·诺依曼悖论的反思

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Numerous experimental investigations on the reflection of plane shock waves over straight wedges indicated that there is a domain, frequently referred to as the weak shock wave domain, inside which the resulted wave configurations resemble the wave configuration of a Mach reflection although the classical three-shock theory does not provide an analytical solution. This paradox is known in the literature as the von Neumann paradox. While numerically investigating this paradox Colella & Henderson [1] suggested that the observed reflections were not Mach reflections but another reflection, in which the reflected wave at the triple point was not a shock wave but a compression wave. They termed them it von Neumann reflection. Consequently, based on their study there was no paradox since the three-shock theory never aimed at predicting this wave configuration. Vasilev & Kraiko [2] who numerically investigated the same phenomenon a decade later concluded that the wave configuration, inside the questionable domain, includes in addition to the three shock waves a very tiny Prandtl-Meyer expansion fan centered at the triple point. This wave configuration, which was first predicted by Guderley [3], was recently observed experimentally by Skews & Ashworth [4] who named it Guderley reflection. The entire phenomenon was re-investigated by us analytically. It has been found that there are in fact three different reflection configurations inside the weak reflection domain: 1. A von Neumann reflection - vNR, 2. A yet not named reflection - ?R, 3. A Guderley reflection - GR. The transition boundaries between MR, vNR, ?R and GR and their domains have been determined analytically. The reported study presents for the first time a full solution of the weak shock wave domain, which has been puzzling the scientific community for a few decades. Although the present study has been conducted in a perfect gas, it is believed that the reported various wave configurations, namely, vNR, ?R and GR, exist also in the reflection of shock waves in condensed matter.
机译：关于平面冲击波在直楔上的反射的大量实验研究表明，存在一个域，通常称为弱冲击波域，尽管经典的三冲击波，在该域中产生的波配置类似于马赫反射的波配置。理论没有提供分析解决方案。该悖论在文献中被称为冯·诺依曼悖论。在对这一悖论进行数值研究时，Collella＆Henderson [1]建议观察到的反射不是马赫反射，而是另一种反射，其中三点处的反射波不是冲击波而是压缩波。他们称其为冯·诺依曼反射。因此，根据他们的研究，没有任何矛盾，因为三震理论从未旨在预测这种波的构造。十年后，Vasilev＆Kraiko [2]对这一现象进行了数值研究，得出的结论是，在可疑范围内，波浪结构除了三个冲击波之外，还包括一个以三点为中心的非常小的Prandtl-Meyer膨胀风扇。这种波状结构最初是由Guderley [3]预测的，最近由Skews＆Ashworth [4]通过实验观察到，他将其命名为Guderley反射。我们通过分析重新调查了整个现象。已经发现，在弱反射域内实际上存在三种不同的反射构型：1.冯·诺伊曼反射-vNR，2.尚未命名的反射-ΔR，3.古德利反射-GR。 MR，vNR，ΔR和GR及其域之间的过渡边界已通过分析确定。报道的研究首次提出了弱冲击波领域的完整解决方案，几十年来一直困扰着科学界。尽管本研究是在理想的气体中进行的，但据信所报道的各种波构型，即vNR，ΔR和GR，也都在凝聚物中冲击波的反射中存在。

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