Transition processes in shock wave interactions

1957 ◽  
Vol 2 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Robert G. Jahn

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.

2007 ◽  
Vol 575 ◽  
pp. 399-424 ◽  
Author(s):  
R. HILLIER

This paper presents numerical simulations for the interaction of an expansion wave with an incident shock wave of the opposite family, the specific aim being to study the resultant reflection of the now-perturbed shock wave from a solid surface. This problem is considered in the context of an incident flow entering a parallel duct, a situation that commonly arises in a range of flow-turning problems including supersonic intake flows. Once the incident shock conditions are such that Mach reflection must occur, it is shown that stabilization of a simple Mach reflection is only possible for a narrow range of Mach numbers and that this depends sensitively on the relative streamwise positioning of the origins of the shock wave and the expansion wave.


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.


2020 ◽  
Vol 61 (3) ◽  
Author(s):  
David MacLucas ◽  
Beric Skews ◽  
Harald Kleine

1979 ◽  
Vol 95 (2) ◽  
pp. 279-304 ◽  
Author(s):  
Georg Dettleff ◽  
Philip A. Thompson ◽  
Gerd E. A. Meier ◽  
Hans-Dieter Speckmann

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).


2019 ◽  
Vol 874 ◽  
pp. 131-157 ◽  
Author(s):  
A. Kluwick ◽  
E. A. Cox

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.


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