Mechanism for the transition from a regular reflection to a mach reflection or a von neumann reflection

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.

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

Entropy ◽

10.3390/e23030314 ◽

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.

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Gaseous detonation propagation in a bifurcated tube

Journal of Fluid Mechanics ◽

10.1017/s0022112007009986 ◽

2008 ◽

Vol 599 ◽

pp. 81-110 ◽

Cited By ~ 8

Author(s):

C. J. WANG ◽

S. L. XU ◽

C. M. GUO

Keyword(s):

Numerical Simulation ◽

Detonation Wave ◽

Mach Reflection ◽

Initial Pressure ◽

Gaseous Detonation ◽

Recirculation Region ◽

Horizontal Branch ◽

Regular Reflection ◽

Detonation Propagation ◽

Wall Geometry

Gaseous detonation propagation in a bifurcated tube was experimentally and numerically studied for stoichiometric hydrogen and oxygen mixtures diluted with argon. Pressure detection, smoked foil recording and schlieren visualization were used in the experiments. Numerical simulation was carried out at low initial pressure (8.00kPa), based on the reactive Navier–Stokes equations in conjunction with a detailed chemical reaction model. The results show that the detonation wave is strongly disturbed by the wall geometry of the bifurcated tube and undergoes a successive process of attenuation, failure, re-initiation and the transition from regular reflection to Mach reflection. Detonation failure is attributed to the rarefaction waves from the left-hand corner by decoupling leading shock and reaction zones. Re-initiation is induced by the inert leading shock reflection on the right-hand wall in the vertical branch. The branched wall geometry has only a local effect on the detonation propagation. In the horizontal branch, the disturbed detonation wave recovers to a self-sustaining one earlier than that in the vertical branch. A critical case was found in the experiments where the disturbed detonation wave can be recovered to be self-sustaining downstream of the horizontal branch, but fails in the vertical branch, as the initial pressure drops to 2.00kPa. Numerical simulation also shows that complex vortex structures can be observed during detonation diffraction. The reflected shock breaks the vortices into pieces and its interaction with the unreacted recirculation region induces an embedded jet. In the vertical branch, owing to the strength difference at any point and the effect of chemical reactions, the Mach stem cannot be approximated as an arc. This is different from the case in non-reactive steady flow. Generally, numerical simulation qualitatively reproduces detonation attenuation, failure, re-initiation and the transition from regular reflection to Mach reflection observed in experiments.

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

Journal of Fluid Mechanics ◽

10.1017/s0022112082003000 ◽

1982 ◽

Vol 123 ◽

pp. 155-164 ◽

Cited By ~ 98

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).

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F-1511 Transition from regular reflection to Mach reflection over a planar wedge

The proceedings of the JSME annual meeting ◽

10.1299/jsmemecjo.iv.01.1.0_335 ◽

2001 ◽

Vol IV.01.1 (0) ◽

pp. 335-336

Author(s):

Takashi ADACHI ◽

Susumu KOBAYASHI ◽

Noriyuki CHIBA

Keyword(s):

Mach Reflection ◽

Regular Reflection

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Transition from mach reflection to regular reflection when strong shock waves interact with cylindrical surfaces

Fluid Dynamics ◽

10.1007/bf01314504 ◽

1982 ◽

Vol 17 (2) ◽

pp. 273-278 ◽

Cited By ~ 2

Author(s):

L. G. Gvozdeva ◽

Yu. P. Lagutov ◽

V. P. Fokeev

Keyword(s):

Shock Waves ◽

Mach Reflection ◽

Strong Shock ◽

Regular Reflection ◽

Strong Shock Waves

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Downstream flow condition effects on the RR → MR transition of asymmetric shock waves in steady flows

Journal of Fluid Mechanics ◽

10.1017/s0022112008004837 ◽

2009 ◽

Vol 620 ◽

pp. 43-62 ◽

Cited By ~ 13

Author(s):

Z. M. HU ◽

R. S. MYONG ◽

M. S. KIM ◽

T. H. CHO

Keyword(s):

Shock Waves ◽

Mach Reflection ◽

Flow Structures ◽

Steady Flows ◽

Regular Reflection ◽

Double Wedge ◽

Asymmetric Reflection ◽

Asymmetric Shock ◽

Downstream Flow ◽

Good Agreement

In this paper, the regular reflection (RR) to Mach reflection (MR) transition of asymmetric shock waves is theoretically studied by employing the classical two- and three-shock theories. Computations are conducted to evaluate the effects of expansion fans, which are inherent flow structures in asymmetric reflection of shock waves, on the RR → MR transition. Comparison shows good agreement among the theoretical, numerical and experimental results. Some discrepancies between experiment and theory reported in previous studies are also explained based on the present theoretical analysis. The advanced RR → MR transition triggered by a transverse wave is also discussed for the interaction of a hypersonic flow and a double-wedge-like geometry.

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A parametric study of Mach reflection in steady flows

Journal of Fluid Mechanics ◽

10.1017/s0022112097005375 ◽

1997 ◽

Vol 341 ◽

pp. 101-125 ◽

Cited By ~ 56

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.

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