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.

Shock reflection in the presence of an upstream expansion wave and a downstream shock wave

2013 ◽  
Vol 735 ◽  
pp. 61-90 ◽  
Author(s):  
Y. Yao ◽  
S. G. Li ◽  
Z. N. Wu
Keyword(s):  
Shock Wave ◽  
Flow Structure ◽  
Mach Reflection ◽  
Expansion Wave ◽  
Shock Reflection ◽  
Critical Conditions ◽  
Reflected Shock Wave ◽  
Mach Stem ◽  
Turning Angle ◽  
Reflected Shock

AbstractIn this paper, we consider shock reflection problems, occurring in supersonic and hypersonic intake flow under off-design conditions, in which the incident shock wave is disturbed by the lip-generated upstream expansion wave and the reflected shock wave intersects with a downstream cowl-turning deflected shock wave. The expansion wave and deflected shock wave are here generated with the same magnitude of flow deflection angle or turning angle. With the help of shock interaction theory and numerical simulation, the influence of the turning angle of the lip and cowl on the flow structure and the critical conditions for transition between regular reflection and Mach reflection are analysed. It is found that the dual-solution domain is significantly altered by the interference between the expansion wave and shock waves. The flow structure in the condition of Mach reflection is then analysed with a model updated from a previous study. It is shown that the Mach stem height is an increasing function of the turning angle, while the horizontal position of the Mach stem is shifted in the downstream direction for small turning angle and in the upstream direction for large turning angle.

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).

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.

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.

Mach stem deformation in pseudo-steady shock wave reflections

2018 ◽  
Vol 861 ◽  
pp. 407-421 ◽  
Author(s):  
Xiaofeng Shi ◽  
Yujian Zhu ◽  
Jiming Yang ◽  
Xisheng Luo
Keyword(s):  
Shock Wave ◽  
High Temperature ◽  
Wall Jet ◽  
Mach Stem ◽  
Wave Reflections ◽  
Reflected Shock ◽  
Wide Range ◽  
Stem Deformation ◽  
Steady Shock ◽  
High Temperature Gas

The deformation of the Mach stem in pseudo-steady shock wave reflections is investigated numerically and theoretically. The numerical simulation provides the typical flow patterns of Mach stem deformation and reveals the differences caused by high-temperature gas effects. The results also show that the wall jet, which causes Mach stem deformation, can be regarded as a branch of the mainstream from the first reflected shock. A new theoretical model for predicting the Mach stem deformation is developed by considering volume conservation. The theoretical predictions agree well with the numerical results in a wide range of test conditions. With this model, the wall-jet velocity and the inflow velocity from the Mach stem are identified as the two dominating factors that convey the influence of high-temperature thermodynamics. The mechanism of high-temperature gas effects on the Mach stem deformation phenomenon are then discussed.

Application of the minimum entropy production principle to shock reflection induced by separation

2018 ◽  
Vol 857 ◽  
pp. 784-805 ◽  
Author(s):  
Chengpeng Wang ◽  
Longsheng Xue ◽  
Keming Cheng
Keyword(s):  
Entropy Production ◽  
Mach Reflection ◽  
Incident Shock ◽  
Shock Reflection ◽  
Solution Path ◽  
Regular Reflection ◽  
Minimum Entropy ◽  
Reflected Shock ◽  
Minimum Entropy Production ◽  
Shock Configuration

In this paper separation-induced shock reflection is studied theoretically and experimentally. An analytical model is proposed to establish the connections among upstream conditions, downstream conditions and shock configurations. Furthermore, the minimum entropy production principle is employed to determine the incident shock angles as well as the criterion for the transition from regular reflection to Mach reflection, which agrees well with experimental results. Additionally, a solution path for a reflected shock that fulfills the minimum entropy production principle is found in the overall regular reflection domain, based on which the steadiest shock configuration may be determined according to upstream and downstream conditions.

Transition processes in shock wave interactions

1957 ◽  
Vol 2 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Robert G. Jahn
Keyword(s):  
Shock Wave ◽  
Mach Reflection ◽  
Intersection Point ◽  
Incident Shock ◽  
Similar Process ◽  
Wave Interactions ◽  
Wave Refraction ◽  
Shock Interactions ◽  
Reflected Shock ◽  
Shock Wave Interactions

This paper is a discussion of recent experiments in shock-wave refraction which have clarified a special type of shock outflow process appearing to have relevance to other shock interactions, and notably to shock reflection from an oblique wall. For certain incident shock strengths and angles of incidence α, the air/methane refraction problem simulates closely the situation in the trouble-some range of the reflection problem, in which α lies between the value αe at which the theoretical solutions terminate and the value α0 that marks the onset of Mach reflection, and in which the flow deflections cannot be reconciled with theoretically permissible reflected shock strengths. In the analogous refraction cases, the reflected shock is observed to increase in strength along its length to a maximum value at the intersection point, and to be followed by a subsonic rarefaction zone which also increases in severity near the intersection. In fact, this zone appers to coalesce into a subsonic discontinuity, just at the intersection point—a feature which would contradict one of the basic assumptions of the regular reflection and refraction theories. Other refraction experiments suggest that a similar process is relevant to the Mach reflection configuration, and may account for the discrepancies in the three-shock theory for weak incident shocks.

A study on the focusing phenomenon of a weak shock wave

2003 ◽  
Vol 217 (11) ◽  
pp. 1209-1220 ◽  
Author(s):  
H-D Kim ◽  
Y-H Kweon ◽  
T Setoguchi ◽  
S Matsuo
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Peak Pressure ◽  
Weak Shock ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Weak Shock Wave ◽  
Tvd Scheme ◽  
Local Pressure ◽  
Gas Dynamic

When a plane shock wave reflects from a concave wall or when a curved shock wave reflects from a straight wall, it is focused at a certain location, resulting in extremely high local pressure and temperature. This focusing is due to a non-linear phenomenon of a shock wave. This focusing phenomenon has been extensively applied in a variety of engineering and medical areas. In the current study, the focusing phenomenon of a weak shock wave over a reflector is numerically investigated using a computational fluid dynamics (CFD) method. The total variation diminishing (TVD) scheme is used to solve the unsteady, two-dimensional, compressible, Euler equations. The Mach number of the incident shock wave is changed in the range from 1.1 to 1.5. Several different types of reflectors are employed to investigate the effect of the reflector on the focusing phenomenon of the weak shock wave. The focusing characteristics of the shock wave are investigated in terms of peak pressure, gas dynamic and geometrical foci. The results obtained are compared with previous experiment results that are available. The results show that the peak pressure of shock wave focusing and its location strongly depend on the Mach number of the incident shock wave and the reflector geometry. The location of the gas dynamic focus is always shorter than that of the geometrical one. This tendency is more remarkable as the incident shock wave becomes stronger. The present computations predict the experimental results with a very good accuracy.

scholarly journals Unsteady aspects of an incident shock wave/turbulent boundary layer interaction

2009 ◽  
Vol 635 ◽  
pp. 47-74 ◽  
Author(s):  
R. A. HUMBLE ◽  
F. SCARANO ◽  
B. W. van OUDHEUSDEN
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Reflected Shock Wave ◽  
Reversed Flow ◽  
Layer Interaction ◽  
Reflected Shock ◽  
Boundary Layer Interaction

An incident shock wave/turbulent boundary layer interaction at Mach 2.1 is investigated using particle image velocimetry in combination with data processing using the proper orthogonal decomposition, to obtain an instantaneous and statistical description of the unsteady flow organization. The global structure of the interaction is observed to vary considerably in time. Although reversed flow is often measured instantaneously, on average no reversed flow is observed. On an instantaneous basis, the interaction exhibits a multi-layered structure, characterized by a relatively high-velocity outer region and low-velocity inner region. Discrete vortical structures are prevalent along their interface, which create an intermittent fluid exchange as they propagate downstream. A statistical analysis suggests that the instantaneous fullness of the incoming boundary layer velocity profile is (weakly) correlated with the size of the separation bubble and position of the reflected shock wave. The eigenmodes show an energetic association between velocity fluctuations within the incoming boundary layer, separated flow region and across the reflected shock wave, and portray subspace features that represent the phenomenology observed within the instantaneous realizations.

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