scholarly journals Theory of Mach reflection of detonation at glancing incidence

2016 ◽  
Vol 811 ◽  
pp. 269-314 ◽  
Author(s):  
John B. Bdzil ◽  
Mark Short
Keyword(s):  
Heat Release ◽  
Mach Reflection ◽  
Rigid Wall ◽  
Angle Of Incidence ◽  
Reaction Heat ◽  
Von Neumann ◽  
Spatially Resolved ◽  
Reflected Shock ◽  
State Dependent ◽  
Detonation Energy

We present a theory for Mach reflection of a detonation undergoing glancing incidence reflection off of a rigid wall. Our focus is on condensed-phase explosives, which we describe with a constant adiabatic gamma equation of state and an irreversible and either state-independent or weakly state-dependent reaction rate. We consider two detonation models: (1) the instantaneous reaction heat-release Chapman–Jouguet (CJ) limit and (2) the spatially resolved reaction heat-release Zeldovich–von Neumann–Dø̈ring (ZND) limit, where here we only consider that a small fraction of the detonation energy release is spatially resolved (the SRHR limit). We observe a three-shock reflection in the CJ limit case, with a Mach shock that is curved. We develop an analytical expression for the triple-point track angle as a function of the angle of incidence. For the SRHR model, we observe a smooth lead shock, akin to von Neumann reflection, with no reflected shock in the reaction zone. Only at larger angles of incidence is a three-shock Mach reflection observed.

Electron Channeling Patterns

1977 ◽  
Vol 35 ◽  
pp. 12-13
Author(s):  
David C. Joy
Keyword(s):  
Electron Diffraction ◽  
Incidence Angle ◽  
Photographic Plate ◽  
Diffraction Effect ◽  
Angle Of Incidence ◽  
Bulk Single Crystal ◽  
Time Resolved ◽  
Electron Channeling ◽  
Spatially Resolved ◽  
Large Bulk

Electron channeling patterns (ECP) were first found by Coates (1967) while observing a large bulk, single crystal of silicon in a scanning electron microscope. The geometric pattern visible was shown to be produced as a result of the changes in the angle of incidence, between the beam and the specimen surface normal, which occur when the sample is examined at low magnification (Booker, Shaw, Whelan and Hirsch 1967).A conventional electron diffraction pattern consists of an angularly resolved intensity distribution in space which may be directly viewed on a fluorescent screen or recorded on a photographic plate. An ECP, on the other hand, is produced as the result of changes in the signal collected by a suitable electron detector as the incidence angle is varied. If an integrating detector is used, or if the beam traverses the surface at a fixed angle, then no channeling contrast will be observed. The ECP is thus a time resolved electron diffraction effect. It can therefore be related to spatially resolved diffraction phenomena by an application of the concepts of reciprocity (Cowley 1969).

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

Analysis of chemical effects on reflected-shock flow fields in combustible gas

1985 ◽  
Vol 160 ◽  
pp. 29-45 ◽  
Author(s):  
Yasunari Takano ◽  
Teruaki Akamatsu
Keyword(s):  
Heat Release ◽  
Chemical Reactions ◽  
Induction Time ◽  
Combustion Process ◽  
Chemical Species ◽  
Flow Fields ◽  
Rate Equations ◽  
Reflected Shock ◽  
Combustible Gas ◽  
Analytical Results

This paper analyses effects of chemical reactions on reflected-shock flow fields in shock tubes. The method of linearized characteristics is applied to analyse gasdynamic disturbances due to chemical reactions. The analysis treats cases where combustible gas is highly diluted in inert gas, and assumes that flows are one-dimensional and that upstream flows in front of the reflected-shock waves are in the frozen state. The perturbed gasdynamic properties in the reflected-shock flow fields are shown to be expressible mainly in terms of a heat-release function for combustion process. In particular, simple relations are obtained between the heat-release function and the physical properties at the end wall of a shock tube. As numerical examples of the analysis, the present formulation is applied to calculate gasdynamic properties in the reflected-shock region in a H2–O2–Ar mixture. Procedures are demonstrated for calculation of the heat-release function by numerically integrating rate equations for chemical species. The analytical results are compared with rigorous solutions obtained numerically by use of a finite-difference method. It is shown that the formulation can afford exact solutions in cases where chemical behaviours are not essentially affected by gasdynamic behaviours. When the induction time of the combustion process is reduced to some extent owing to gasdynamic disturbances, some discrepancies appear between analytical results and rigorous solutions. An estimate is made of the induction-time reduction, and a condition is written down for applicability of the analysis.

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).

The diffraction of blast. II

1950 ◽  
Vol 200 (1063) ◽  
pp. 554-565 ◽  
Keyword(s):  
Solid Surface ◽  
Speed Of Sound ◽  
Uniform Flow ◽  
Incident Shock ◽  
Plane Shock ◽  
Angle Of Incidence ◽  
Straight Segment ◽  
Reflected Shock ◽  
Perpendicular Distance ◽  
Local Speed

The head-on encounter of a plane shock, of any strength, with a solid corner of angle π - δ is investigated mathematically, when δ is small, by a method similar to that of part I. The incident shock is found to be reflected from each face as a straight segment, the two segments being joined by a shorter curved portion. Behind each straight segment is a region of uniform flow, the two regions being joined by one of non-uniform flow, bounded by arcs of a circle with centre at the corner, which expands at the local speed of sound, and by the shock, which is curved only where intersected by the said circle. The pressure is approximately equal in the two regions of uniform flow, but is less in the region of non-uniform flow between them; and it is found that if the deficiency of pressure therein, divided by the angle δ and by the excess of pressure behind the reflected shock over that of the atmosphere, be plotted at points along the solid surface, after the incident shock has travelled a given perpendicular distance beyond the corner, then the curve is independent of δ and of the precise angle of incidence of the shock, and changes remarkably little in the whole range of incident shock strengths from 0 to ∞ (see figures 5 to 8). It is suggested that some of the above qualitative conclusions may be true even if δ is not small. The case δ<0, when the corner is concave to the atmosphere, is also considered. Shock patterns are found in cases when the incident shock has already been reflected from one, or both, walls before reaching the corner (figures 9 to 11).

Observation and analysis of the Mach reflection of weak uniform plane shock waves. Part 2. Analysis

1985 ◽  
Vol 152 ◽  
pp. 67-81 ◽  
Author(s):  
J. M. Dewey ◽  
D. J. Mcmillin
Keyword(s):  
Mach Reflection ◽  
Grazing Incidence ◽  
Experimental Results ◽  
Plane Shock ◽  
Stationary Model ◽  
Reflected Shock ◽  
Parallel Flows ◽  
Weak Plane ◽  
Spatially Varying ◽  
Limiting Case

A non-stationary approach to the reflection of weak plane shocks is suggested as an alternative to the usual pseudo-stationary transformation. For regular reflection the non-stationary model produces results which are identical to those obtained using the pseudo-stationary assumption, but with simpler algebra. For weak Mach reflections, where the predictions of the pseudo-stationary model are in disagreement with experimental results, the non-stationary model predicts accurately the observed shapes and positions of the reflected and Mach stem shocks and the spatially varying flow properties behind these shocks. However, the non-stationary model predicts that the gas flows above and below the contact surface, relative to the triple point, are not quite parallel. Parallel flows could be obtained only in the limiting case of grazing incidence, when the reflected shock was sonic. The model is based on the experimental results presented in Part 1 of this paper.

The persistence of regular reflection during strong shock diffraction over rigid ramps

2001 ◽  
Vol 431 ◽  
pp. 273-296 ◽  
Author(s):  
L. F. HENDERSON ◽  
K. TAKAYAMA ◽  
W. Y. CRUTCHFIELD ◽  
S. ITABASHI
Keyword(s):  
Stokes Equations ◽  
Mach Reflection ◽  
Strong Shock ◽  
Navier Stokes ◽  
Regular Reflection ◽  
Navier Stokes Equations ◽  
Von Neumann ◽  
Initial Appearance ◽  
Self Similar ◽  
Initial Shock

We report on calculations and experiments with strong shocks diffracting over rigid ramps in argon. The numerical results were obtained by integrating the conservation equations that included the Navier–Stokes equations. The results predict that if the ramp angle θ is less than the angle θe that corresponds to the detachment of a shock, θ < θe, then the onset of Mach reflection (MR) will be delayed by the initial appearance of a precursor regular reflection (PRR). The PRR is subsequently swept away by an overtaking corner signal (cs) that forces the eruption of the MR which then rapidly evolves into a self-similar state. An objective was to make an experimental test of the predictions. These were confirmed by twice photographing the diffracting shock as it travelled along the ramp. We could get a PRR with the first exposure and an MR with the second. According to the von Neumann perfect gas theory, a PRR does not exist when θ < θe. A viscous length scale xint is a measure of the position on the ramp where the dynamic transition PRR → MR takes place. It is significantly larger in the experiments than in the calculations. This is attributed to the fact that fluctuations from turbulence and surface roughness were not modelled in the calculations. It was found that xint → ∞ as θ → θe. Experiments were done to find out how xint depended on the initial shock tube pressure p0. The dependence was strong but could be greatly reduced by forming a Reynolds number based on xint. Finally by definition, regular reflection (RR) never interacts with a boundary layer, while PRR always interacts; so they are different phenomena.

A parametric study of Mach reflection in steady flows

1997 ◽  
Vol 341 ◽  
pp. 101-125 ◽  
Author(s):  
H. LI ◽  
G. BEN-DOR
Keyword(s):  
Present Model ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Incoming Flow ◽  
Steady Flows ◽  
Mach Stem ◽  
Stem Height ◽  
Von Neumann ◽  
Set Up

The flow fields associated with Mach reflection wave configurations in steady flows are analysed, and an analytical model for predicting the wave configurations is proposed. It is found that provided the flow field is free of far-field downstream influences, the Mach stem heights are solely determined by the set-up geometry for given incoming-flow Mach numbers. It is shown that the point at which the Mach stem height equals zero is exactly at the von Neumann transition. For some parameters, the flow becomes choked before the Mach stem height approaches zero. It is suggested that the existence of a Mach reflection not only depends on the strength and the orientation of the incident shock wave, as prevails in von Neumann's three-shock theory, but also on the set-up geometry to which the Mach reflection wave configuration is attached. The parameter domain, beyond which the flow gets choked and hence a Mach reflection cannot be established, is calculated. Predictions based on the present model are found to agree well both with experimental and numerical results.

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
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