scholarly journals Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation

1979 ◽  
Vol 90 (3) ◽  
pp. 541-560 ◽  
Author(s):  
H. G. Hornung ◽  
H. Oertel ◽  
R. J. Sandeman
Keyword(s):  
Steady Flow ◽  
Dynamic Equilibrium ◽  
Neumann Condition ◽  
Relaxation Length ◽  
Displacement Effect ◽  
Von Neumann ◽  
Transition Condition ◽  
Reflected Shock ◽  
Relaxation Effects ◽  
Mach Reflexion

Experiments were conducted in the free-piston shock tube and shock tunnel with dissociating nitrogen and carbon dioxide, ionizing argon and frozen argon to measure the transition condition in pseudosteady and steady flow. The transition condition in the steady flow, in which the wall was eliminated by symmetry, agrees with the calculated von Neumann condition. In the real gases this calculation assumed thermo-dynamic equilibrium after the reflected shock. In the pseudosteady flow of reflexion from a wedge the measured transition angle lies on the Mach-reflexion side of the calculated detachment condition by an amount which may be explained in terms of the displacement effect of the boundary layer on the wedge surface. A single criterion based on the availability of a length scale at the reflexion point explains the difference between the pseudosteady and steady flow transition condition and predicts a hysteresis effect in the transition angle when the shock angle is varied during steady flow. No significant effects on the transition condition due to finite relaxation length could be detected. However, new experiments in which interesting relaxation effects should be evident are suggested.

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

1982 ◽  
Vol 123 ◽  
pp. 155-164 ◽  
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).

Experiments on the diffraction of strong blast waves

1981 ◽  
Vol 377 (1771) ◽  
pp. 363-378 ◽  
Keyword(s):  
Blast Waves ◽  
Viscous Effects ◽  
Von Neumann ◽  
Reflected Shock ◽  
Self Similar ◽  
Catch Up ◽  
Pass Through ◽  
Weak Shocks ◽  
Mach Reflexion ◽  
Good Agreement

This paper considers the diffraction of strong shocks over rigid concave comers, and complements an earlier paper (Henderson & Siegenthaler 1980), which dealt with weak shocks. It is shown that the von Neumann theory of strong Mach reflexion does not agree with experiment once the comer signal everywhere overtakes the reflected shock. We show that the difficulty is due to the assumption that the flow is self-similar along the trajectory path passing through the comer and that the theory may be reconstructed by choosing a new path that does not necessarily pass through the comer. The flow is assumed to be self-similar with respect to the new path. The reconstructed theory is in good agreement with experiment. One obtains from it a new model of strong Mach reflexion beyond the catch-up condition that features a length scale apparently introduced into the flow by viscous effects at the comer. The reflected shock is weaker according to the new theory which implies that the blast loading on sloping surfaces will be less after catch-up than predicted by the classical theory. Experimental evidence is also presented on transition between regular and Mach reflexions, and it supports the normal shock criterion first proposed by von Neumann but largely ignored by the textbooks.

A note on the pseudo-stationary flow behind a strong shock diffracted or reflected at a corner

1951 ◽  
Vol 209 (1097) ◽  
pp. 238-248 ◽  
Keyword(s):  
Steady Flow ◽  
Compressible Flow ◽  
Complete Solution ◽  
Characteristic Curve ◽  
Strong Shock ◽  
Stationary Flow ◽  
Plane Shock ◽  
Steady Flows ◽  
Reflected Shock ◽  
Concave Corner

It is shown that the equations of an unsteady compressible flow in the ( x, y )-plane, which is expressible in terms of the two variables x/t and y/t only, can be reduced to those of a steady compressible flow with a non-conservative field of external forces and a field of sinks. The steady-flow problems of this type, which correspond to the diffraction or reflexion of a plane shock travelling parallel to a rigid wall and reaching a corner, are discussed qualitatively. It is shown that, under certain conditions, there are regions in the corresponding steady flows which are entirely supersonic and for which a simple solution can be given without determining the whole field of flow. No complete solution for the whole field of flow has yet been given. In the diffraction, at a convex corner, of certain strong shocks, it is shown that there can be an area of Prandtl-Meyer flow, uniformly increasing with time, and that the upper limit to which it can extend is calculable as a characteristic curve in the corresponding steady flow. In the case of regular reflexion beyond a concave comer, or reflexion at a concave corner which gives rise to a reflected shock passing through the corner, it is shown that there can be areas of uniform flow, uniformly increasing with time, and that the upper limits to which they can extend are arcs of circles, which appear as sonic curves in the corresponding steady flows.

Experiments on the diffraction of weak blast waves: the von Neumann paradox

1980 ◽  
Vol 369 (1739) ◽  
pp. 537-555 ◽  
Keyword(s):  
Strong Shock ◽  
Weak Shock ◽  
Blast Waves ◽  
Shock Diffraction ◽  
Self Similarity ◽  
Von Neumann ◽  
Shock System ◽  
Series Of Experiments ◽  
Mach Reflexion ◽  
Good Agreement

This paper presents the results of our experiments with weak incident shocks diffracting over concave corners. For Mach reflexion, the experiments reveal a fundamental difference between weak and strong shock diffraction, namely that for weak shock diffraction the corner signal can always catch up with the three-shock confluence, but this does not happen for strong shock diffraction except for comparatively small corner angles. We show that by taking into account the attenuating effect of the corner signal it is possible in principle to modify the well-known von Neumann theory and that this is then in good agreement with the experimental data. Evidence is presented which shows that another effect of the corner signal is to cause a partial loss of the self-similarity property of the three-shock system. Indeed, for one series of experiments the oncoming flow relative to the Mach stem behaved as though it were parallel to the sloping wall of the corner and therefore did not have the familiar radial distribution centred on the corner. The modified theory can be extended to include the persisted regular reflexion phenomenon suggesting that this is an unresolved Mach reflexion. In that event there is some experi­mental evidence that transition to Mach reflexion would then be consistent with the normal shock point as Henderson and Lozzi found for strong shock diffraction.

The wave system attached to a slender body in a supersonic relaxing gas stream. Basic results: the cone

1977 ◽  
Vol 79 (3) ◽  
pp. 499-524 ◽  
Author(s):  
J. F. Clarke ◽  
Y. L. Sinai
Keyword(s):  
Linear Theory ◽  
The Body ◽  
Slender Body ◽  
Wave System ◽  
Body Of Revolution ◽  
Relaxation Length ◽  
Relaxation Effects ◽  
Mode Energy ◽  
Relaxing Gas ◽  
Slender Body Of Revolution

The results of the linear theory for the flow of a supersonic relaxing gas past a slender body of revolution are analysed in regions where its predictions of wavelet position begin to break down. In this way new variable systems can be found which make it possible to discuss the correct nonlinear wave behaviour far from the body. The situation depends upon three especially important parameters, namely the thickness ratio ε of the body, the ratio δ of relaxing-mode energy to thermal energy and the ratio λ of a relaxation length to a typical body length. After establishing general results from the linear theory, the conical body is treated in some detail. This makes it possible to demote λ as an important parameter, although its restoration does prove useful at one point in the analysis, and results are derived for shock-wave behaviour when ord 1 [ges ] δ > ord ε4, δ = ord ε4and δ < ord ε4. In the first range of δ fully dispersed waves are essential, although they are fully established only at great distances from the cone; in the second range of δ partly dispersed waves seem to be the most likely to appear, and in the third range relaxation effects are second-order modifications of a basically frozen-flow field. Practical situations may well fall into the first of these categories.

Transition study for asymmetric reflection between moving incident shock waves

2021 ◽  
Vol 929 ◽  
Author(s):  
Miao-Miao Wang ◽  
Zi-Niu Wu
Keyword(s):  
Shock Waves ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Neumann Condition ◽  
Plane Shock ◽  
Von Neumann ◽  
Transition Criteria ◽  
Shock Motion ◽  
Reduced Problem

The transition criteria seen from the ground frame are studied in this paper for asymmetrical reflection between shock waves moving at constant linear speed. To limit the size of the parameter space, these criteria are considered in detail for the reduced problem where the upper incident shock wave is moving and the lower one is steady, and a method is provided for extension to the general problem where both the upper and lower ones are unsteady. For the reduced problem, we observe that, in the shock angle plane, shock motion lowers or elevates the von Neumann condition in a global way depending on the direction of shock motion, and this change becomes less important for large shock angle. The effect of shock motion on the detachment condition, though small, displays non-monotonicity. The shock motion changes the transition criteria through altering the effective Mach number and shock angle, and these effects add for small shock angle and mutually cancel for large shock angle, so that shock motion has a less important effect for large shock angle. The role of the effective shock angle is not monotonic on the detachment condition, explaining the observed non-monotonicity for the role of shock motion on the detachment condition. Furthermore, it is found that the detachment condition has a wavefunction form that can be approximated as a hybrid of a sinusoidal function and a linear function of the shock angle.

Sound wave structures downstream of pseudo-steady weak and strong Mach reflections

1996 ◽  
Vol 324 ◽  
pp. 309-332 ◽  
Author(s):  
J. J. Liu
Keyword(s):  
Sound Wave ◽  
Triple Point ◽  
Close Agreement ◽  
Oblique Shock ◽  
Sound Waves ◽  
Reflected Waves ◽  
Von Neumann ◽  
Compression Waves ◽  
Reflected Shock ◽  
Mach Waves

Sound wave structures, downstream of moving incident shocks reflecting from straight compressive wedges, are analysed for both weak and strong Mach reflections (MR) using existing experiments. It is shown that the reflected waves can be well described by using the acoustic criterion or the weak oblique shock approximation, when the classical three-shock theory gives forward-facing reflected shock solutions. The predicted triple-point trajectory angles are found to be in close agreement with the experiments. The distinction between the applicabilities of the two methods is given by an analytically defined ‘smallness’ for the angle of reflecting wedges. The physics of the success of the two methods is discussed. It is concluded that forward-facing reflected shock solutions of pseudo-steady MR should be ruled out physically because sound waves cannot coalesce into Mach waves that propagate upstream of the triple point. In their place, MR-like phenomena occur with the reflected waves being normal Mach waves or finite compression waves for ‘small’ or ‘not-small’ reflecting wedge angles, respectively, and they are classified as the first- or second-king von Neumann reflections, respectively. Boundaries separating regimes between the first and second kinds of von Neumann reflections, and backward-facing MR are determined.

The current emitted by highly conducting Taylor cones

1994 ◽  
Vol 260 ◽  
pp. 155-184 ◽  
Author(s):  
J. Fernández De La Mora ◽  
I. G. Loscertales
Keyword(s):  
Surface Charge ◽  
Capillary Tube ◽  
Fluid Motion ◽  
Surface Current ◽  
Liquid Volume ◽  
Relaxation Length ◽  
Charge Relaxation ◽  
Relaxation Effects ◽  
Cone Apex ◽  
Electrical Permittivity

When a liquid meniscus held at the exit of a metallic capillary tube is charged to a high voltage V, the free surface often takes the form of a cone whose apex emits a steady microjet, and thus injects a certain charge I and liquid volume Q per unit time into the surrounding gas. This work deals with liquids with relatively large conductivities K, for which the jet diameter dj is much smaller than the diameter dn of the capillary tube. In the limit dj/dn → 0, the structure of the jet (dj and I, in particular) becomes independent of electrostatic parameters such as V or the electrode configuration, being governed mostly by the liquid properties and flow rate Q. Furthermore, the measured current is given approximately by I = f(ε) (γQK/ε)½ for a wide variety of liquids and conditions (ε, and γ are, respectively, the dielectric constant of the liquid and the coefficient of interfacial tension; f(ε) is shown in figure 11). The following explanation is proposed for this behaviour. Convection associated with the liquid flow Q transports the net surface charge towards the cone tip. This upsets the electrostatic surface charge distribution slightly at distances r from the apex large compared to a certain charge relaxation length λ, but substantially when r ∼ λ. When the fluid motion is modelled as a sink flow, λ is of the order of r* = (Qεε0/K)$\frac13$ (ε0 is the electrical permittivity of vacuum). If, in addition, the surface charge density is described through Taylor's theory, the corresponding surface current convected towards the apex scales as Is ∼ (γQK/ε)½, as observed for the spray current. The sink flow hypothesis is shown to be realistic for sufficiently small jet Reynolds numbers. In a few photographs of ethylene glycol cone jets, we find the rough scaling dj ∼ 0.4r* for the jet diameter, which shows that the jet forms as soon as charge relaxation effects set in. In the limit ε [Gt ] 1, an upper bound is found for the convected current at the virtual cone apex, which accounts for only one-quarter of the total measured spray current. The rest of the charge must accordingly reach the head of the jet by conduction through the bulk.

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