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.

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.

scholarly journals Experimental investigation of shock waves in liquid helium I and II

1976 ◽  
Vol 75 (2) ◽  
pp. 373-383 ◽  
Author(s):  
John C. Cummings
Keyword(s):  
Shock Wave ◽  
Experimental Investigation ◽  
Shock Waves ◽  
Shock Tube ◽  
Liquid Helium ◽  
Initial Conditions ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Liquid Interface ◽  
Reflected Shock

The flow field produced by a shock wave reflecting from a helium gas-liquid interface was investigated using a cryogenic shock tube. Incident and reflected shock waves were observed in the gas; transmitted first- and second-sound shocks were observed in the liquid. Wave diagrams are constructed to compare the data with theoretical wave trajectories. Qualitative agreement between data and theory is shown. Quantitative differences between data and theory indicate a need for further analysis of both the gas-liquid interface and the propagation of nonlinear waves in liquid helium.This work was a first step in the experimental investigation of a complex non-equilibrium state. The results demonstrate clearly the usefulness of the cryogenic shock tube as a research tool. The well-controlled jump in temperature and pressure across the incident shock wave provides unique initial conditions for the study of dynamic phenomena in superfluid helium.

scholarly journals Experimental and numerical evolution studies for 2D perturbations of the interface accelerated by shock waves

1997 ◽  
Vol 15 (1) ◽  
pp. 101-114 ◽  
Author(s):  
V.V. Bashurov ◽  
Yu.A. Bondarenko ◽  
E.V. Gubkov ◽  
V.I. Dudin ◽  
E.E. Meshkov ◽  
...  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Reflected Shock ◽  
Numerical Studies

In this article, the results of experimental and numerical studies of the behavior of perturbed interface between air and helium are presented. The interface is initially accelerated by the incident shock wave coming from air to helium and then decelerated by a series of reflected shock waves. Two types of initial interface perturbations like “saw” and “step” are considered.

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.

Steady Mach reflection with two incident shock waves

2018 ◽  
Vol 855 ◽  
pp. 882-909 ◽  
Author(s):  
Xiao-Ke Guan ◽  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Mach Reflection ◽  
Lower Surface ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Neumann Condition ◽  
Mach Stem ◽  
Stem Height ◽  
Reflecting Surface

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle.

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.

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.

The influence of the downstream pressure on the shock wave reflection phenomenon in steady flows

1999 ◽  
Vol 386 ◽  
pp. 213-232 ◽  
Author(s):  
G. BEN-DOR ◽  
T. ELPERIN ◽  
H. LI ◽  
E. VASILIEV
Keyword(s):  
Shock Wave ◽  
Wave Reflection ◽  
Numerical Study ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Steady Flows ◽  
Shock Wave Reflection ◽  
Wave Angle ◽  
Good Agreement

The effect of the downstream pressure (defined here as the wake pressure behind the tail of the reflecting wedge) on shock wave reflection in steady flows is investigated both numerically and analytically. The dependence of the shock wave configurations on the downstream pressure is studied. In addition to the incident-shock-wave-angle-induced hysteresis, which was discovered a few years ago, a new downstream- pressure-induced hysteresis has been found to exist. The numerical study reveals that when the downstream pressure is sufficiently high, an inverse-Mach reflection wave configuration, which has so far been observed only in unsteady flows, can be also established in steady flows. Very good agreement between the analytical predictions and the numerical results is found.

Transmission of elastic disturbances caused by air shock waves in a living body

1961 ◽  
Vol 16 (3) ◽  
pp. 426-430 ◽  
Author(s):  
Carl-Johan Clemedson ◽  
Arne Jönsson
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Lead Zirconate Titanate ◽  
Technical Assistance ◽  
Great Part ◽  
Pressure Rise ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
The Body ◽  
Pressure Curve

Anesthetized rabbits were exposed to air shock waves in a detonation chamber. The pressure wave patterns were recorded by means of a small lead zirconate titanate pressure transducer in the following parts of the body: at and under the skin of the side facing the charge, in the pleural sac and in the lung of that side, in the right and left ventricle of the heart, in the lung and in the pleural sac on the side opposite the charge, under the skin of that side, in the stomach, and in the skull between the bone and the brain. When the incident shock wave is propagated through the body the very steep shock front is converted so that the ascending limb of the pressure peak is much less steep, with a duration up to several hundred microseconds. The longest periods of pressure rise were found in the heart ventricles and stomach. The amplitude of the pressure curve generally diminishes as the wave passes through the body. The changes of the original shock wave are due probably in great part to the inhomogeneous structure of the animal body. Note: (With the Technical Assistance of A.-B. Sundqvist) Submitted on October 24, 1960

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