TY - GEN
T1 - Reconsideration of the So-called von Neumann Paradox in the Reflection of a Shock wave over a Wedge
AU - Vasilev, Eugene I.
AU - Elperin, Tov
AU - Ben-Dor, Gabi
PY - 2008/1/1
Y1 - 2008/1/1
N2 - 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: A von Neumann reflection - vNR, A yet not named reflection - ?R, 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.
AB - 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: A von Neumann reflection - vNR, A yet not named reflection - ?R, 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.
KW - Shock wave reflection
KW - Von neumann paradox
UR - https://www.scopus.com/pages/publications/38349154198
M3 - Conference contribution
AN - SCOPUS:38349154198
SN - 0878494650
SN - 9780878494651
T3 - Materials Science Forum
SP - 1
EP - 8
BT - Explosion, Shock Wave and Hypervelocity Phenomena in Materials II - Selected, peer reviewed papers from the 2nd International Symposium on Explosion, Shock Wave and Hypervelocity Phenomena (ESHP-2)
PB - Trans Tech Publications Ltd
T2 - 2nd International Symposium on Explosion, Shock Wave and Hypervelocity Phenomena, ESHP-2
Y2 - 6 March 2007 through 9 March 2007
ER -