The thermal nature of the triple point of a Mach reflection

1987 ◽  
Vol 30 (5) ◽  
pp. 1287 ◽  
Author(s):  
G. Ben-Dor ◽  
K. Takayama ◽  
C. E. Needham
Keyword(s):  
Triple Point ◽  
Mach Reflection

Further Results on Guderley Mach Reflection and the Triple Point Paradox

2015 ◽  
Vol 64 (3) ◽  
pp. 721-744 ◽  
Author(s):  
Allen M. Tesdall ◽  
Richard Sanders ◽  
Nedyu Popivanov
Keyword(s):  
Triple Point ◽  
Mach Reflection

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.

The Mach reflection triple-point locus for internal and external conical diffraction of a moving shock wave

Shock Waves ◽  
1992 ◽  
Vol 2 (1) ◽  
pp. 5-12 ◽  
Author(s):  
Z. Y. Han ◽  
B. E. Milton ◽  
K. Takayama
Keyword(s):  
Shock Wave ◽  
Triple Point ◽  
Mach Reflection

The non-stationary hysteresis phenomenon in shock wave reflections

2013 ◽  
Vol 732 ◽  
Author(s):  
Meital Geva ◽  
Omri Ram ◽  
Oren Sadot
Keyword(s):  
Shock Wave ◽  
High Resolution ◽  
Triple Point ◽  
Convex Surface ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Concave Surface ◽  
Hysteresis Phenomenon ◽  
Regular Reflection

AbstractThe non-stationary transition from Mach to regular reflection followed by a reverse transition from regular to Mach reflection is investigated experimentally. A new experimental setup in which an incident shock wave reflects from a cylindrical concave surface followed by a cylindrical convex surface of the same radius is introduced. Unlike other studies that indicate problems in identifying the triple point, an in-house image processing program, which enables automatic detection of the triple point, is developed and presented. The experiments are performed in air having a specific heats ratio 1.4 at three different incident-shock-wave Mach numbers: 1.2, 1.3 and 1.4. The data are extracted from high-resolution schlieren images obtained by means of a fully automatically operated shock-tube system. Each experiment produces a single image. However, the high accuracy and repeatability of the control system together with the fast opening valve enables us to monitor the dynamic evolution of the shock reflections. Consequently, high-resolution results both in space and time are obtained. The credibility of the present analysis is demonstrated by comparing the first transition from Mach to regular reflection ($\mathrm{MR} \rightarrow \mathrm{RR} $) with previous single cylindrical concave surface experiments. It is found that the second transition, back to Mach reflection ($\mathrm{RR} \rightarrow \mathrm{MR} $), occurs earlier than one would expect when the shock reflects from a single cylindrical convex surface. Furthermore, the hysteresis is observed at incident-shock-wave Mach numbers smaller than those at which the dual-solution domain starts, which is the minimal value for obtaining hysteresis in steady and pseudo-steady flows. The existence of a non-stationary hysteresis phenomenon, which is different from the steady-state hysteresis phenomenon, is discovered.

Transverse waves in numerical simulations of cellular detonations

2001 ◽  
Vol 447 ◽  
pp. 31-51 ◽  
Author(s):  
GARY J. SHARPE
Keyword(s):  
Numerical Simulations ◽  
Triple Point ◽  
Mach Reflection ◽  
Physical Structure ◽  
Structure Evolution ◽  
Transverse Waves ◽  
Strong Transverse ◽  
Cellular Detonations ◽  
Double Mach Reflection ◽  
Steady Detonation

In this paper the structure of strong transverse waves in two-dimensional numerical simulations of cellular detonations is investigated. Resolution studies are performed and it is shown that much higher resolutions than those generally used are required to ensure that the flow and burning structures are well resolved. Resolutions of less than about 20 numerical points in the characteristic reaction length of the underlying steady detonation give very poor predictions of the shock configurations and burning, with the solution quickly worsening as the resolution drops. It is very difficult and dangerous to attempt to identify the physical structure, evolution and effect on the burning of the transverse waves using such under-resolved calculations. The process of transverse wave and triple point collision and reflection is then examined in a very high-resolution simulation. During the reflection, the slip line and interior triple point associated with the double Mach configuration of strong transverse waves become detached from the front and recede from it, producing a pocket of unburnt gas. The interaction of a forward facing jet of exploding gas with the emerging Mach stem produces a new double Mach configuration. The formation of this new Mach configuration is very similar to that of double Mach reflection of an inert shock wave reflecting from a wedge.

Time history of regular to Mach reflection transition in steady supersonic flow

2011 ◽  
Vol 682 ◽  
pp. 160-184 ◽  
Author(s):  
S. G. LI ◽  
B. GAO ◽  
Z. N. WU
Keyword(s):  
Triple Point ◽  
Early Stage ◽  
Mach Reflection ◽  
Time History ◽  
Mach Stem ◽  
Interaction Structure ◽  
Reflection Transition ◽  
History Of ◽  
Multiple Interaction ◽  
Mach Waves

In this paper, we study the transition from regular to Mach reflection (RR → MR) in the dual solution domain due to the influence of an upstream disturbance, by considering the transition as an evolutionary rather than an abrupt process. From numerical simulation, we observe for the early stage of transition a multiple interaction structure, composed of a triple-shock structure, a type VI shock interaction and a shock/slipline interaction. In the end, we observe a pure unsteady MR structure. Under self-similar assumption of the triple point for the first stage and including additional Mach waves over the slipline for the last stage, we develop an idealized unsteady model to obtain the evolution of the Mach stem height and the time taken for the Mach stem to stabilize. The triple point is found to move at a nearly constant speed in the multiple interaction stage which occupies about one quarter of the transition time. In the pure unsteady MR stage, which occupies the rest of transition, the speed of the triple point drops nonlinearly until the Mach stem stabilizes.

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.

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