Irregular Reflection of Acoustical Shock Waves and von Neumann Paradox

2006 ◽  
Author(s):  
S. Baskar
Keyword(s):  
Shock Waves ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Irregular Reflection

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.

The von Neumann paradox for strong shock waves

Shock Waves ◽  
2009 ◽  
pp. 1539-1542 ◽  
Author(s):  
S. Kobayashi ◽  
T. Adachi ◽  
T. Suzuki
Keyword(s):  
Shock Waves ◽  
Strong Shock ◽  
Von Neumann ◽  
Von Neumann Paradox ◽  
Strong Shock Waves

scholarly journals Interaction between Shock Waves Travelling in the Same Direction

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 315
Author(s):  
Pavel Bulat ◽  
Konstantin Volkov ◽  
Igor Volobuev
Keyword(s):  
Shock Waves ◽  
Contact Discontinuity ◽  
Jet Engines ◽  
Mach Stem ◽  
Regular Reflection ◽  
Reflected Shock ◽  
Different Types ◽  
Irregular Reflection

In this paper, we study the intersection (interaction) between several steady shocks traveling in the same direction. The interaction between overtaking shocks may be regular or irregular. In the case of regular reflection, the intersection of overtaking shocks leads to the formation of a resulting shock, contact discontinuity, and some reflected discontinuities. The type of discontinuity depends on the parameters of incoming shocks. At the irregular reflection, a Mach shock forms between incoming overtaking shocks. Reflected discontinuities come from the points of intersection of the Mach stem with the incoming shocks. We also consider the possible types of shockwave configurations that form both at regular and irregular interactions of several overtaking shocks. The regions of existence of overtaking shock waves with different types of reflected shock and the intensity of reflected shocks are defined. The results obtained in the study can potentially be useful for designing supersonic intakes and advanced jet engines.

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).

Analytical reconsideration of the von Neumann paradox in the reflection of a shock wave over a wedge

2008 ◽  
Vol 20 (4) ◽  
pp. 046101 ◽  
Author(s):  
Eugene I. Vasilev ◽  
Tov Elperin ◽  
Gabi Ben-Dor
Keyword(s):  
Shock Wave ◽  
Von Neumann ◽  
Von Neumann Paradox

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
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