Experiments on the diffraction of strong blast waves

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.

On the Whitham theory of shock-wave diffraction at concave corners

The well-known Whitham theory may be applied to shocks diffracting over concave corners, provided that the diffraction results in Mach reflexion. This paper compares the theory with data obtained during experiments with diffracting shocks. If an incident shock is classified as weak or strong in the strict sense defined by von Neumann, then it is found that the Whitham theory accurately determines the Mach number of the Mach stem at the wall for both the weak and the strong cases. The theory also has some further value for strong shocks but not for weak; it is not applicable when the diffraction is regular.

On the Mach reflexion of a solitary wave

Miles’ (1977b) model of the Mach reflexion of a solitary wave by a vertical wall is tested by laboratory experiments. The model over-predicts the measured run-up at the wall, and no evidence of the predicted maximum was found. The measurements provide support for the predicted critical angle of incidence at which Mach reflexion is replaced by regular reflexion. It is shown that mass and energy conservation determine the length of the reflected wave in Miles’ model and that this is not consistent with momentum conservation in the neighbourhood of the end point of the reflected wave. It is suggested that the discrepancy between the measurements and the model may result from this failure of the model.

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

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.

Further experiments on transition to Mach reflexion

Our 1975 paper reported the results of experiments on shock reflexion in a wind tunnel and a shock tube; further results are presented here. For strong shocks it is shown that transition to Mach reflexion takes place continuously at the shock wave incidence angle ω0 corresponding to the normal shock point ω0 = ωN, unless the downstream boundaries form a throat. In this event transition can be promoted anywhere within the range ω0 [les ] ωN, and it is even possible to suppress regular reflexion altogether! However when ω0 < ωN the transition is discontinuous and accompanied by hysteresis. Again for strong shocks evidence is presented which suggests that the famous persistence of regular reflexion beyond the ωN point ω0 > ωN is spurious. For weak shocks the transition condition is not known but it is found that even for regular reflexion a marked discrepancy between theory and experiment develops as the shocks become progressively weaker. Also when weak shocks diffract over single concave corners there is a somewhat surprising discontinuity in the regular reflexion range. It seems that none of these phenomena can be adequately explained by real gas effects such as viscosity and variation of specific heats.

Domains and boundaries of non-stationary oblique shock-wave reflexions. 1. Diatomic gas

Interferometric data were obtained in the UTIAS 10 × 18 cm hypervelocity shock tube of oblique shock-wave reflexions in nitrogen at initial temperatures and pressures of about 300 K and 15 torr. The shock-Mach-number range covered was 2 ≤Ms≤ 8 over a series of wedge angles 2° ≤ θw≤ 60°. Dual-wavelength laser interferograms were obtained by using a 23 cm diameter field of view Mach-Zehnder interferometer. In addition to our numerous results the available data for nitrogen, air and oxygen obtained over the last three decades were also utilized. It is shown analytically and experimentally that in non-stationary flows seven domains exist in the (Ms, θw) plane where regular reflexion (RR), single-Mach reflexion (SMR), complex-Mach reflexion (CMR) and double-Mach reflexion (DMR) can occur. In addition, the transition boundaries between these regions were established. The experimental results from many sources substantiate the present analysis, and areas of disagreement which existed in the literature are now clarified and resolved. It is shown that real-gas effects have a significant influence on the size of the regions and their boundaries. The comprehensive, accurate and sensitive isopycnic data will form a base for comparing existing and future numerical analyses of such complex flows.

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

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.

Shock waves at a fast-slow gas interface

This paper presents the results of experiments on plane shock waves refracting at air/SF6and He/CO2interfaces. These are called fast-slow gas combinations because the speed of sound in the incident shock gas is greater than that in the transmitting shock gas. Our work was based on a generalization of the von Neumann (1943) classification of shocks into two classes called weak and strong. We introduced two subclasses of each of these, giving in all four groups of phenomena for study. This is possibly an exhaustive list, at least for conditions where the gases are approximately perfect. We present data on all four groups and study various transition conditions both within and across the groups. Our results appear to conflict with a previously reported irregular refraction; in fact we could apparently completely suppress this wave system by attention to our gas purity and boundary conditions. In its place we found a different system which appears to be a new phenomenon. We found another new system which has the appearance of a Mach-reflexion type of refraction but with its shock dispersed into a band of wavelets. It is interesting that the wavelets remain intense enough to induce identifiable vortex sheets in the flow. Finally we found yet another refraction of the Mach-reflexion type which had no detectable vortex sheet emanating from the triple point: such a system was foreshadowed by von Neumann.

Resonantly interacting solitary waves

Resonant (phase-locked) interactions among three obliquely oriented solitary waves are studied. It is shown that such interactions are associated with the parametric end points of the singular regime for interactions between two solitary waves. The latter include regular reflexion at a rigid wall, which is impossible for ϕi < (3α)½ (ϕ = angle of incidence, α = amplitude/depth [Lt ] 1), and it is shown that the observed phenomenon of ‘Mach reflexion’ can be described as a resonant interaction in this regime. The run-up at the wall is calculated as a function of ϕi/(3α)½ and is found to have a maximum value of 4αd for ϕi = (3α)½. This same resonant interaction also describes diffraction of a solitary wave at a corner of internal angle π − ψi, −(3α)½, and suggests that a solitary wave cannot turn through an angle in excess of (3α)½ at a convex corner without separating or otherwise losing its identity.