Reflexion and diffraction of shocks interacted by yawed wedges

1972 ◽  
Vol 330 (1582) ◽  
pp. 319-330 ◽  
Keyword(s):  
Shock Wave ◽  
Flow Field ◽  
Pressure Distribution ◽  
Small Angle ◽  
Analytic Solution ◽  
Incident Shock ◽  
Oblique Shock Wave ◽  
Reflected Shock ◽  
Wedge Surface ◽  
Perturbation Pressure

In this paper the problem of reflexion and diffraction of an oblique shock wave interacting a yawed wedge of small angle has been attempted. An analytic solution is developed completely, in term s of perturbation pressure, for the non-uniform flow field produced when the relative outflow from the reflected shock is supersonic. Numerical results showing the pressure distribution on the wedge surface for a pair of incident shock strengths have also been obtained.

Evaluation of assumptions and criteria in pseudostationary oblique shock-wave reflections

1986 ◽  
Vol 406 (1830) ◽  
pp. 75-92 ◽  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Mach Reflection ◽  
Wedge Angle ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Reflected Shock ◽  
Wedge Surface

Many experiments in various gases have now been performed on regular and Mach reflection of oblique shock waves in pseudostationary flow. Experimental agreement with the analytical boundaries for such reflec­tions with two- and three-shock theories is reasonable but not precise enough over the entire range of incident shock-wave Mach numbers ( M s ) and compression wedge angle ( θ W ) used in the experiments. In order to improve the agreement, the assumptions and criteria employed in the analysis were critically examined by the use of the experimental data for nitrogen (N 2 ), argon (Ar), carbon-dioxide (CO 2 ), air and sulphurhexa-fluoride (SF 6 ). The assumptions regarding the excitation of the internal degrees of freedom were evaluated based on a relation between the relaxation lengths and a characteristic length of the flow. The ranges in which the frozen-gas and vibrational-equilibrium-gas assumptions can be applied were verified by comparing the experimental and numerical values of δ, the angle between the incident and the reflected shock waves. The deviations of the experimental orientation of the Mach stem at the triple point from a line perpendicular to the wedge surface were considered. A new criterion for the transition from single-Mach to complex-Mach reflection improved the agreement with experiments in the ( M S , θ W )-transition-boundary map. The effects of the shock-induced boundary layer on the wedge surface on the reflected-wave angle and the persistence of regular reflection into the Mach reflection region (‘von Neumann paradox’) were evaluated.

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

1986 ◽  
Vol 408 (1835) ◽  
pp. 321-344 ◽  
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 .

An experimental study of liquefaction shock waves

1979 ◽  
Vol 95 (2) ◽  
pp. 279-304 ◽  
Author(s):  
Georg Dettleff ◽  
Philip A. Thompson ◽  
Gerd E. A. Meier ◽  
Hans-Dieter Speckmann
Keyword(s):  
Shock Wave ◽  
Incident Shock ◽  
Shock Velocity ◽  
Index Of Refraction ◽  
Clear Liquid ◽  
Two Phase ◽  
Condensation Zone ◽  
Temperature Index ◽  
Reflected Shock ◽  
Beam Attenuation

The existence of a liquefaction shock wave, a compression shock which converts vapour into liquid, has recently been predicted on physical grounds. The liquefaction shock was experimentally produced as the reflected shock at the closed end of a shock tube. Measurements of pressure, temperature, index of refraction and shock velocity confirm the existence of the shock and its general conformity to classical Rankine-Hugoniot conditions, with a discrepancy ∼ 10°C between measured and predicted liquid temperatures. Photographic observations confirmed the existence of a clear liquid phase and revealed the (unanticipated) presence of small two-phase torus-form rings. These rings are interpreted as vortices and are formed in or near the shockfront (∼ 50 rings/mm2 are visible near the shockfront at any given time). Separate experiments with the incident shock under conditions of partial liquefaction produced a fog behind the shock: measurements of laser-beam attenuation yielded the thickness of the condensation zone and estimates of the droplet size (∼ 10−7 m).

Weak shock reflection in channel flows for dense gases

2019 ◽  
Vol 874 ◽  
pp. 131-157 ◽  
Author(s):  
A. Kluwick ◽  
E. A. Cox
Keyword(s):  
Shock Wave ◽  
Practical Importance ◽  
Weak Shock ◽  
Normal Incidence ◽  
Incident Shock ◽  
Shock Reflection ◽  
Mach Stem ◽  
Dense Gases ◽  
Reflected Shock ◽  
Guderley Reflection

The canonical problem of transonic dense gas flows past two-dimensional compression/expansion ramps has recently been investigated by Kluwick & Cox (J. Fluid Mech., vol. 848, 2018, pp. 756–787). Their results are for unconfined flows and have to be supplemented with solutions of another canonical problem dealing with the reflection of disturbances from an opposing wall to finally provide a realistic picture of flows in confined geometries of practical importance. Shock reflection in dense gases for transonic flows is the problem addressed in this paper. Analytical results are presented in terms of similarity parameters associated with the fundamental derivative of gas dynamics $(\unicode[STIX]{x1D6E4})$, its derivative with respect to the density at constant entropy $(\unicode[STIX]{x1D6EC})$ and the Mach number $(M)$ of the upstream flow. The richer complexity of flows scenarios possible beyond classical shock reflection is demonstrated. For example: incident shocks close to normal incidence on a reflecting boundary can lead to a compound shock–wave fan reflected flow or a pure wave fan flow as well as classical flow where a compressive reflected shock attached to the reflecting boundary is observed. With incident shock angles sufficiently away from normal incidence regular reflection becomes impossible and so-called irregular reflection occurs involving a detached reflection point where an incident shock, reflected shock and a Mach stem shock which remains connected to the boundary all intersect. This triple point intersection which also includes a wave fan is known as Guderley reflection. This classical result is demonstrated to carry over to the case of dense gases. It is then finally shown that the Mach stem formed may disintegrate into a compound shock–wave fan structure generating an additional secondary upstream shock. The aim of the present study is to provide insight into flows realised, for example, in wind tunnel experiments where evidence for non-classical gas dynamic effects such as rarefaction shocks is looked for. These have been predicted theoretically by the seminal work of Thompson (Phys. Fluids, vol. 14 (9), 1971, pp. 1843–1849) but have withstood experimental detection in shock tubes so far, due to, among others, difficulties to establish purely one-dimensional flows.

scholarly journals Two-dimensional unsteadiness map of oblique shock wave/boundary layer interaction with sidewalls

2019 ◽  
Vol 871 ◽  
Author(s):  
P. K. Rabey ◽  
S. P. Jammy ◽  
P. J. K. Bruce ◽  
N. D. Sandham
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Low Frequency ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Pressure Measurements ◽  
Wave Boundary Layer ◽  
Reflected Shock ◽  
Separation Shock ◽  
Wave Boundary

The low-frequency unsteadiness of oblique shock wave/boundary layer interactions (SBLIs) has been investigated using large-eddy simulation (LES) and high-frequency pressure measurements from experiments. Particular attention has been paid to off-centreline behaviour: the LES dataset was generated including sidewalls, and experimental pressure measurements were acquired across the entire span of the reflected shock foot. The datasets constitute the first maps of low-frequency unsteadiness in both streamwise and spanwise directions. The results reveal that significant low-frequency shock motion (with $St\approx 0.03$) occurs away from the centreline, along most of the central separation shock and in the corner regions. The most powerful low-frequency unsteadiness occurs off-centre, likely due to the separation shock being strengthened by shocks arising from the swept interactions on the sidewalls. Both simulation and experimental results exhibit asymmetry about the spanwise centre. In simulations, this may be attributed to a lack of statistical convergence; however, the fact that this is also seen in experiments is indicative that some SBLIs may exhibit some inherent asymmetry across the two spanwise halves of the separation bubble. There is also significant low-frequency power in the corner separations. The relation of the unsteadiness in the corner regions to that in the centre is investigated by means of two-point correlations: a key observation is that significant correlation does not extend across the attached flow channel between the central and corner separations.

scholarly journals Three-dimensional simulation of combustion, detonation and deflagration to detonation transition processes

2018 ◽  
Vol 209 ◽  
pp. 00003
Author(s):  
Nickolay Smirnov ◽  
Valeriy Nikitin
Keyword(s):  
Shock Wave ◽  
Three Dimensional ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Reflected Shock Wave ◽  
Zone Formation ◽  
Flame Acceleration ◽  
Reflected Shock ◽  
Transient Regimes ◽  
Chemically Reacting

The paper presents results of numerical and experimental investigation of mixture ignition and detonation onset in shock wave reflected from inside a wedge. Contrary to existing opinion of shock wave focusing being the mechanism for detonation onset in reflection from a wedge or cone, it was demonstrated that along with the main scenario there exists a transient one, under which focusing causes ignition and successive flame acceleration bringing to detonation onset far behind the reflected shock wave. Several different flow scenarios manifest in reflection of shock waves all being dependent on incident shock wave intensity: reflecting of shock wave with lagging behind combustion zone, formation of detonation wave in reflection and focusing, and intermediate transient regimes. Comparison of numerical and experimental results made it possible to validate the developed 3-D transient mathematical model of chemically reacting gas mixture flows incorporating hydrogen – air mixtures.

Paper 14: On the Reflection of Shock Waves from Deflector Plates

1965 ◽  
Vol 180 (10) ◽  
pp. 245-259
Author(s):  
W. A. Woods
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Reflected Shock Wave ◽  
Reflected Wave ◽  
Reflected Shock ◽  
Pressure Time ◽  
Wave Travel ◽  
Wave Region

The paper first explains the importance of the reflection of shock waves in the design of certain chemical plant. The theory of the reflection of shock waves is also discussed in the first part of the paper. It is shown that when a shock wave travelling along a pipe containing stationary gas reaches the outlet end of the pipe there may be ( a) a reflected expansion wave, ( b) a reflected shock wave, ( c) a reflected sound wave, ( d) no reflected wave at all, ( e) a standing shock wave situated at the end of the pipe, depending upon the strength of the incident shock wave and the amount of blockage present at the outlet end of the pipe. The conditions for each kind of reflection are determined, and in the case of the reflected shock wave region the strengths and speeds of the reflected shock waves are established throughout the region and the results are presented graphically. In the second part of the paper the results are given of experiments carried out on a shock tube fitted with various kinds of deflector plates. The experiments were performed to study the reflection of shock waves from the deflector plates by measuring pressure/time indicator diagrams near the outlet end of the pipe. The indicator diagrams revealed the approximate pressure amplitudes of the incident and reflected shock waves and also the wave travel times for the shock waves. This information was used in conjunction with the charts given in the first part of the paper to establish the deflector geometry and spacing needed in order to avoid the occurrence of a reflected shock wave.

Application of a High-Resolution Compact Finite Difference Method to Computational Aeroacoustics of Compressible Flows

2011 ◽  
Author(s):  
Zhifeng Zuo ◽  
Hiroshi Maekawa
Keyword(s):  
Shock Wave ◽  
High Resolution ◽  
Flow Field ◽  
Acoustic Wave ◽  
Acoustic Waves ◽  
Compressible Flows ◽  
Compact Finite Difference Method ◽  
Reflected Shock ◽  
Planar Shock ◽  
Planar Shock Wave

WCNS is an efficient high-resolution nonlinear scheme for solving flow-fields including discontinuity. In the present paper, a two-dimensional, unsteady, compressible flow field produced by the interaction between a strong planar shock wave and a strong vortex are simulated numerically using WCNS. The simulation shows the effects of the vortex on a planar shock and the production of acoustic waves by the shock-vortex interaction. At the early times of interaction, the shock wave is perturbed by the vortex and a precursor is produced; with the shock wave emerges from the vortex flow field, a Mach structure was generated and the secondary acoustic wave was formed by the interaction of the reflected shock (MR2) with the precursor. Both components of acoustic wave (the precursor and the second sound wave) propagate radially and have a quadrupolar nature. By this simulation, the ability of WCNS for computational aeroacoustic problems is confirmed.

ON THE GASDYNAMIC MECHANISMS OF EXOTHERMIC REACTION WAVE FORMATION BEHIND SHOCK WAVES

2020 ◽  
Author(s):  
A. Kiverin ◽  
◽  
I. Yakovenko ◽  
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Gas Flow ◽  
Exothermic Reaction ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Wave Formation ◽  
Mixture Flow ◽  
Reflected Shock ◽  
Reaction Wave

The paper analyzes the gasdynamic evolution of the test mixture flow in the shock tube at the stage prior to reaction start. The numerical analysis clearly shows that the incepience of reaction kernels is associated with the specific features of flow development in the boundary layer behind an incident shock wave. It is shown that similar to the processes in the gas flow near a solid surface, the gasdynamic instability arises and develops in the flow behind a shock wave. The linear stage of instability development determines the formation of roll-up vortices at a certain distance behind the shock front. Further, at the nonlinear stage, these roll-up vortices transform in more complex structures that diffuse into the bulk flow. Evolution of vortices causes temperature redistribution on the scales of the boundary layer. On the one hand, there is a certain heating due to the kinetic energy dissipation. On the other hand, there are heat losses to the wall. As a result, the temperature field near the wall becomes nonuniform. The reflected shock amplifies temperature perturbations when interacts with the developed boundary layer. This mechanism determines the formation of hot kernels in which the reaction starts. So, the localized sites of exothermal reaction are arising providing conditions for reaction wave formation and propagation in the precompressed test gas.

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