8: Shock Wave Triple‒Point Morphology

Numerical simulations were conducted to understand the different wave configurations associated with the shock-wave reflections over double-concave cylindrical surfaces. The reflectors were generated computationally by changing different geometrical parameters, such as the radii of curvature and the initial wedge angles. The incident-shock-wave Mach number was varied such as to cover subsonic, transonic and supersonic regimes of the flows induced by the incident shock. The study revealed a number of interesting wave features starting from the early stage of the shock interaction and transition to transitioned regular reflection (TRR) over the first concave surface, followed by complex shock reflections over the second one. Two new shock bifurcations have been found over the second wedge reflector, depending on the velocity of the additional wave that appears during the TRR over the first wedge reflector. Unlike the first reflector, the transition from a single-triple-point wave configuration (STP) to a double-triple-point wave configuration (DTP) and back occurred several times on the second reflector, indicating that the flow was capable of retaining the memory of the past events over the entire process.

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Shock Wave Triple-Point Morphology

Shock Wave Dynamics ◽

10.1201/b12970-10 ◽

2012 ◽

pp. 91-110

Keyword(s):

Shock Wave ◽

Triple Point

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

Shock Waves ◽

10.1007/bf01414416 ◽

1992 ◽

Vol 2 (1) ◽

pp. 5-12 ◽

Cited By ~ 6

Author(s):

Z. Y. Han ◽

B. E. Milton ◽

K. Takayama

Keyword(s):

Shock Wave ◽

Triple Point ◽

Mach Reflection

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Shock Wave Triple-Point Morphology

Analytical Fluid Dynamics, Third Edition ◽

10.1201/b19392-11 ◽

2015 ◽

pp. 129-145

Keyword(s):

Shock Wave ◽

Triple Point

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Pseudostationary oblique shock-wave reflections in sulphur hexafluoride (SF 6 ): interferometric and numerical results

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1986.0123 ◽

1986 ◽

Vol 408 (1835) ◽

pp. 321-344 ◽

Cited By ~ 3

Keyword(s):

Shock Wave ◽

Mach Number ◽

Triple Point ◽

Wave Reflection ◽

Incident Shock ◽

Oblique Shock Wave ◽

Wave Reflections ◽

Shock Wave Reflection ◽

Wedge Surface ◽

Vibrational Equilibrium

Pseudostationary oblique shock-wave reflections in SF 6 were investigated experimentally and numerically. Experiments were concluded in the UTIAS 10 x 18 cm Hypervelocity Shock Tube in the range of incident shock wave Mach number 1.25 < M s < 8.0 and wedge angle 4° < θ w < 47° with initial pressure 4 < P 0 < 267 Torr (0.53-35.60 kPa) at temperatures T 0 near 300 K. The four major types of shock-wave reflection, i. e. regular reflection (RR), single-Mach (SMR), complex-Mach (CMR) and double-Mach reflections (DMR), were observed. These were studied by using infinite-fringe interferograms from a Mach-Zehnder interferometer with a 23 cm diameter field of view. The isopycnics and the density distributions along the wedge surface are presented for the various types of reflection. The analytical transition boundaries between the four types of shock-wave reflection were established up to M s = 10.0 for frozen and equilibrium vibrational SF 6 . An examination of the relaxation length under the present experimental conditions indicated that a vibrational-equilibrium analysis was required. Comparisons of experiment with analysis for transition-boundary maps, reflection angle δ and the first triple-point trajectory angle X verify that the reflections were in vibrational equilibrium. The excellent agreement between the present interferometric results and the numerical results obtained by H. M. Glaz et al . ( Proc. int. colloq. on dynamics of explosives and reactive systems [ Berkeley ] (1985)) with real-gas effects also supports the vibrational equilibrium hypothesis for shocked SF 6 . The behaviour of the angle between the two triple-point trajectories ( X ' — X ) is discussed and the unique pattern of DMR with X ' = 0 was verified experimentally. A numerical analysis for the second triple-point system is obtained for the first time. It is shown that, for a given incident shock Mach number, the highest wedge-surface pressure is achieved through a DMR instead of an RR at high M s .

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The non-stationary hysteresis phenomenon in shock wave reflections

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.423 ◽

2013 ◽

Vol 732 ◽

Cited By ~ 20

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.

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The Three-Shock Confluence Problem for Normally Impinging, Overexpanded Jets

Aeronautical Quarterly ◽

10.1017/s0001925900007265 ◽

1975 ◽

Vol 26 (2) ◽

pp. 117-132 ◽

Cited By ~ 16

Author(s):

G T Kalghatgi ◽

B L Hunt

Keyword(s):

Shock Wave ◽

Shock Waves ◽

Boundary Conditions ◽

Triple Point ◽

Systematic Study ◽

Flow Patterns ◽

Incident Shock ◽

Free Jet ◽

Alternative Solutions ◽

Impinging Flow

SummaryIn this paper, a systematic study of the triple shock confluence point is presented for the case of an overexpanded jet which impinges on a perpendicular flat plate at small displacements from the nozzle. The jet is uniform upstream of the free jet shock wave. Non-homentropic effects are taken into account and lead to modifications to the accepted flow patterns at a triple point for the case of strong incident shock waves. Where more than one thermodynamically possible solution to the triple point equations exists, the alternative solutions are re-examined, taking non-homentropic effects into consideration. Some discussion of the possibility of infinite shock curvatures is also included. Qualitative flow patterns of the impinging flow are constructed, based on the triple point solutions and the known boundary conditions. The interesting cases where the tail shock flow is supersonic are given particular attention and two possible flow patterns are distinguished. Finally, some experimental evidence in the form of schlieren pictures is presented. Although not conclusive, this evidence supports the theory.

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

Materials Science Forum ◽

10.4028/www.scientific.net/msf.566.1 ◽

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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