Mach reflection and interaction of weak shock waves under the von Neumann paradox conditions

1996 ◽  
Vol 31 (2) ◽  
pp. 318-324 ◽  
Author(s):  
G. P. Shindyapin
Keyword(s):  
Shock Waves ◽  
Mach Reflection ◽  
Weak Shock ◽  
Von Neumann ◽  
Von Neumann Paradox

Reconsideration of the So-Called von Neumann Paradox in the Reflection of a Shock Wave over a Wedge

2007 ◽  
Vol 566 ◽  
pp. 1-8
Author(s):  
Eugene I. Vasilev ◽  
Tov Elperin ◽  
Gabi Ben-Dor
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Triple Point ◽  
Mach Reflection ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Plane Shock ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Guderley Reflection

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.

scholarly journals Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection

1994 ◽  
Vol 6 (5) ◽  
pp. 1874-1892 ◽  
Author(s):  
Esteban G. Tabak ◽  
Rodolfo R. Rosales
Keyword(s):  
Shock Waves ◽  
Weak Shock ◽  
Oblique Shock ◽  
Shock Reflection ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Oblique Shock Reflection

The von Neumann paradox for the diffraction of weak shock waves

1990 ◽  
Vol 213 (-1) ◽  
pp. 71 ◽  
Author(s):  
P. Colella ◽  
L. F. Henderson
Keyword(s):  
Shock Waves ◽  
Weak Shock ◽  
Von Neumann ◽  
Von Neumann Paradox

Transition from regular to Mach reflection of shock waves Part 2. The steady-flow criterion

1982 ◽  
Vol 123 ◽  
pp. 155-164 ◽  
Author(s):  
H. G. Hornung ◽  
M. L. Robinson
Keyword(s):  
Shock Waves ◽  
Steady Flow ◽  
Mach Reflection ◽  
Strong Shock ◽  
Hysteresis Effect ◽  
Neumann Condition ◽  
Flow Transition ◽  
Von Neumann ◽  
Mach Numbers ◽  
Flow Criterion

It is shown experimentally that, in steady flow, transition to Mach reflection occurs at the von Neumann condition in the strong shock range (Mach numbers from 2.8 to 5). This criterion applies with both increasing and decreasing shock angle, so that the hysteresis effect predicted by Hornung, Oertel & Sandeman (1979) could not be observed. However, evidence of the effect is shown to be displayed in an unsteady experiment of Henderson & Lozzi (1979).

Examination of the von Neumann paradox for a weak shock wave

1995 ◽  
Vol 17 (1) ◽  
pp. 13-25 ◽  
Author(s):  
Susumu Kobayashi ◽  
Takashi Adachi ◽  
Tateyuki Suzuki
Keyword(s):  
Shock Wave ◽  
Weak Shock ◽  
Weak Shock Wave ◽  
Von Neumann ◽  
Von Neumann Paradox

Non-self-similar characteristics of weak Mach reflection: the von Neumann paradox

2004 ◽  
Vol 35 (4) ◽  
pp. 275-286 ◽  
Author(s):  
Susumu Kobayashi ◽  
Takashi Adachi ◽  
Tateyuki Suzuki
Keyword(s):  
Mach Reflection ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Self Similar

An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves

1989 ◽  
Vol 7 (5) ◽  
pp. 289-292 ◽  
Author(s):  
G. D. Lock ◽  
J. M. Dewey
Keyword(s):  
Experimental Investigation ◽  
Shock Waves ◽  
Mach Reflection ◽  
Weak Shock

On the von Neumann paradox of weak Mach reflection

1989 ◽  
Vol 4 (5-6) ◽  
pp. 333-345 ◽  
Author(s):  
Akira Sakurai ◽  
L F Henderson ◽  
Kazuyoshi Takayama ◽  
Zbigniew Walenta ◽  
Philip Colella
Keyword(s):  
Mach Reflection ◽  
Von Neumann ◽  
Von Neumann Paradox

An Analytical Solution for Weak Mach Reflection and Its Application to the Problem of the von Neumann Paradox

2005 ◽  
Vol 74 (5) ◽  
pp. 1490-1495 ◽  
Author(s):  
Akira Sakurai ◽  
Shuji Takahashi
Keyword(s):  
Analytical Solution ◽  
Mach Reflection ◽  
Von Neumann ◽  
Von Neumann Paradox

The von Neumann paradox in weak shock reflection

2000 ◽  
Vol 422 ◽  
pp. 193-205 ◽  
Author(s):  
A. R. ZAKHARIAN ◽  
M. BRIO ◽  
J. K. HUNTER ◽  
G. M. WEBB
Keyword(s):  
Numerical Solution ◽  
Euler Equations ◽  
Triple Point ◽  
Numerical Solutions ◽  
Mach Reflection ◽  
Weak Shock ◽  
Complete Agreement ◽  
Von Neumann ◽  
Weak Shock Reflection ◽  
Expansion Fan

We present a numerical solution of the Euler equations of gas dynamics for a weak-shock Mach reflection in a half-space. In our numerical solutions, the incident, reflected, and Mach shocks meet at a triple point, and there is a supersonic patch behind the triple point, as proposed by Guderley. A theoretical analysis supports the existence of an expansion fan at the triple point, in addition to the three shocks. This solution is in complete agreement with the numerical solution of the unsteady transonic small-disturbance equations obtained by Hunter & Brio (2000), which provides an asymptotic description of a weak-shock Mach reflection. The supersonic patch is extremely small, and this work is the first time it has been resolved in a numerical solution of the Euler equations. The numerical solution uses six levels of grid refinement around the triple point. A delicate combination of numerical techniques is required to minimize both the effects of numerical diffusion and the generation of numerical oscillations at grid interfaces and shocks.

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