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The experimental visualisation of compressible flows has undergone significant development to the point that a large number of optical techniques exist for extracting both qualitative and quantitative information from these flow fields. However, the visualisation, and importantly, validation, of three-dimensional flows requires further attention. This work details the development of a novel validation tool for three-dimensional compressible flows. Oblique experimental imaging techniques used to visualise three-dimensional flow features in a compressible medium are computationally simulated, and corresponding images are constructed from numerical models. The construction technique can be used to generate images for optical orientations in roll, yaw, pitch and any combination of these. Both shadowgraphs and schlieren images may be obtained, with the latter used in this work. Results are presented as a comparison of constructed images with experimental images and discussed for cases in which a range of features are simultaneously present in a three-dimensional flow field, thus thoroughly examining the applicability of the technique to a flow field of significant importance in gas dynamics research.

The interaction of a plane shock wave in air with concave profiles has been used in the past mainly to understand the nature of shock wave focusing. The current study examines the complex two-dimensional flow field resulting from the interaction of a plane shock wave entering a symmetrical cavity with curved walls. Of particular interest are the development of reflection patterns of the incident shock wave at the profile wall and the process of gas dynamic focus. These principal flow features are examined across a wide range of different reflector shapes. This includes a review of previously studied profiles such as cylindrical and parabolic, and also of a number of additional profiles, including compound profiles, where an inlet profile merging with that of the main cavity is shown to have major effects on the focusing mechanism and pressures. The various reflector shapes were specified by varying the shape of the profile and the depth-to-aperture ratio. The strength of the incident plane shock wave was limited between Mach numbers of 1.04 and 1.45. The principal flow features were established and examined experimentally using a variety of qualitative and quantitative flow visualization techniques, supplemented with numerical results. Time-resolved high-speed imaging was used to capture the interaction providing the unique ability to track the various transient flow features over the course of the interaction. The three primary factors that influence the maximum pressure amplification at focus, and the focus mechanism, are the incident shock strength, the depth-to-aperture ratio of the profile and an inlet profile leading into the main cavity, if present. An inlet profile results in higher-pressure amplifications for corresponding shock strengths and depth-to-aperture ratios. Increases in the depth-to-aperture ratio increase the maximum pressure amplification observed at focus. This occurs due to a combination of factors including: the strengthening of the individual shock waves involved in focus; the duration of focus; and the strengthening of a compressive flow field that develops adjacent to the shock system during focus. The compressive flow field adjacent to the shock system at focus is shown to be of great importance to the focus process.

The reflection of a two-dimensional cylindrical shock wave segment on a concave-cylindrical wall segment was investigated from an experimental and numerical perspective. The images obtained from experiment show no qualitative difference between cylindrical shock behavior and how a plane shock would behave in terms of the features developed. The length of the shock’s Mach stem was plotted against subtending angle. Two limits are highlighted, one where the shock’s radius is much larger than the wall’s radius and another where the wall has the larger radius: the former being akin to a plane shock interacting with a cylindrical wall segment. The increase in initial shock Mach number was observed to affect the type of Mach reflection that is formed as well as the transition point to a transitioned Mach reflection.

The reflection of a two-dimensional cylindrical shock wave segment on a concave-cylindrical wall segment was investigated from an experimental and numerical perspective. The images obtained from experiment show no qualitative difference between cylindrical shock behavior and how a plane shock would behave in terms of the features developed. The length of the shock’s Mach stem was plotted against subtending angle. Two limits are highlighted, one where the shock’s radius is much larger than the wall’s radius and another where the wall has the larger radius: the former being akin to a plane shock interacting with a cylindrical wall segment. The increase in initial shock Mach number was observed to affect the type of Mach reflection that is formed as well as the transition point to a transitioned Mach reflection.

The interaction of three-dimensional vortex flows was investigated through vortex shedding off a discontinuous edge. Two wedges of $$14.5^\circ $$ wedge angle (up and downstream edges) were separated by an offset. The size of the offset (5, 10, and 20 mm) and the Mach number (Mach 1.32, 1.42, and 1.6) were the key parameters investigated. Experimental images were taken and computational simulations were run; a close relation was found between the two. This enabled the three-dimensional effects of the flow to be studied and analysed. It was found, as the offset increased in size, the vortices shed off the up and downstream edges took a longer time to merge and the strength of the interaction was weaker. The vortex topology changed with a larger offset; the downstream vortex was thinner (in terms of cross-sectional diameter) adjacent to the offset, which is an indication of a change in density, than the rest of the vortex along the downstream diffraction edge. This particular feature was more prevalent at lower Mach numbers. The effect of a higher Mach number was to increase the rate of dissipation of the vortices, lengthen the shear layer due to the higher upstream velocity, and make the vortex profile elliptical.

The propagation of two-dimensional expansion waves over a corner has received very little attention in the past. It can be studied experimentally in a standard shock tube by placing the test section at the end of the high-pressure section rather than the conventional method with placement at the driven section. It is found that reflected compression and shock waves can form as the wave propagates over the corner. An attached flow separation bubble develops at the corner and for a strong enough wave can develop a region of supersonic flow above it, and, in some cases, a transonic shock wave. Furthermore, for a sufficiently strong expansion wave, the flow behind the trailing edge of the expansion wave becomes supersonic. It has also been shown that when an expansion wave reflects off a wedge, shock waves can also develop due to the induced velocity flowing down the surface of the wedge striking the corner. The development of shock waves can also occur if the expansion wave focuses on a cavity.

The diffraction over a corner normal to the direction of travel of a shock wave has been well documented. This has also been extended to the diffraction of a shock wave over edges with discontinuous profiles in the flow direction. However, these studies have only considered the diffraction of a shock wave travelling over a single, plane surface initially. The current study extends this to consider the dynamics of a plane shock wave travelling simultaneously over two orthogonal surfaces, analogous to a shock wave travelling over the roof and wall of a rectangular building. The flow field bears similarity to the diffraction of a shock wave over a convex diffraction edge whereby there is thickening of the vortex tube formed at the axis defined by the common edge of the two surfaces with outboard thinning. However, as the Mach number of the incident shock wave increases, the vortex tubes shed from the two diffraction edges no longer merge into a single tube but rather each terminates in the downstream face. This also results in curvature of these vortex tubes away from the face rather than remaining approximately parallel to the downstream face as seen in most cases. These results were derived experimentally and computationally for a Mach number in the range M1.3–M1.6.

In this study both qualitative and quantitative flow visualization techniques are used to examine the complex flow field developed during the interaction of a plane shock wave with a compound profile. Shearing interferometry and direction-indicating colour schlieren are implemented in conjunction with high-speed time-resolved imaging. Comparisons between the results provided by the two flow visualization systems are made at incident shock strengths of Mach 1.28 and Mach 1.35. The results from both systems indicate the complex nature of the transient compression and expansion systems developed during the interaction behind the various shock fronts. The direction-indicating results prove valuable in eliminating the ambiguity with respect to the sign of the high-order fringes found in the shearing interferometry results.

There have been numerous studies of the diffraction of a plane shock wave from the normal exit of a shock tube, including studies of tubes with square, lenticular, or other irregular exit shapes. However, in considering the practical case in which such diffraction may spontaneously occur (e.g. the propagation of a blast wave through climate conditioning ducts or of a shock wave through a tuned motor vehicle exhaust system), the more likely geometric boundary condition would be of a curved exit diffraction surface. The current study explored the diffraction of a plane shock wave from the curved exit of a shock tube with a boundary plate to remove the characteristic length of the shock tube thickness. The cases tested all had: separations between the axis of the curved plate and the shock tube axis of between 0.5 and 2.5 shock tube internal diameters; radius ratios of the exit surface to the shock tube inner diameter of 3 or 5; and Mach numbers ranging between 1.2 and 1.6. The flow field was visualised using a high-speed camera operating at 75 kfps capturing schlieren images. It was found that for the case of the exit surface tangent to the inner surface of the shock tube a vortex loop is not formed but rather a horseshoe vortex which convects downstream bound by the tangent exit plate. For higher Mach numbers it seems that the horseshoe vortex may close into a loop, but this cannot be definitely concluded from the available images. An additional feature was noted which is suspected of being the tangent view of a complex shock wave reflection due to the curved edge diffraction.

The interaction between an expansion fan and a shock wave and the resulting flow field are of importance both from a research and an applied perspective. Interesting flow phenomena arise from this interaction which are significant in supersonic engine inlet design and aircraft store carriage and release. This paper focuses on the use of various schlieren techniques to experimentally visualize an expansion fan/shock wave interaction. The expansion fan was generated by a single wedge and the shock wave by another, at various Mach numbers. Three cut-off techniques were investigated: a knife edge, a tri-colour mask and a band lattice mask. Each of these cut-offs was placed in three orientations, parallel to the freestream flow direction, at −45° and perpendicular to the flow, to determine the effects of the directional sensitivity of the system. The different cut-off techniques and respective orientations were evaluated on the efficacy of visualizing flow features of interest, namely the expansion fan and deflection thereof, shock curvature and sliplines formed as a result of the interaction. Each technique produced visualization with varying degrees of clarity. There was a dependence on the system’s directional sensitivity when visualizing both the expansion fan deflection and the shock curvature. The visualization of the expansion fan/shock wave interaction using the band lattice mask parallel to the freestream was particularly effective as it showed all the features of interest (excepting the sliplines as these formed a region of varying entropy rather than occurring as discrete lines). Consequently, it was shown that schlieren is a valuable tool in the experimental visualization of an expansion fan/shock wave interaction.

Experiments were conducted in a shock tube in order to determine the increases in shock wave strength due to reductions in area. Previous work has shown that if the reduction is too sudden significant wave reflections occur and gains are limited. A variety of curved symmetrical contractions are used, made up of parabolic surfaces with different points of inflection. High-speed Schlieren imaging was used to characterize the wave patterns with particular emphasis on wave reflections. Greatest wave amplification is present when Mach reflection of the wave is not reached at all, and this was found to occur with parabolic profiles with inflection point at 60% of the profile length. Clear Mach reflection is evident with the inflection point at 40% and the post shock flow shows significant reflected waves with their associated losses. With an area reduction of 80% and a inflection point at 60% of the contraction, a typical result gives an increase in Mach number from 1.6 to 2.0, corresponding to a 61% increase in post-shock pressure. It is found that profiles with later inflection points provide a more gradual initial area change and allow weaker compression waves to develop which can significantly reduce or even avoid transition to Mach reflection.

Xenon arc lamps have been identified as a suitable continuous light source for high-speed imaging, specifically high-speed Schlieren and shadowgraphy. One issue when setting us such systems is the time that it takes to reduce a finite source to the approximation of a point source for z-type schlieren. A preliminary design of a compact compound lens for use with a commercial Xenon arc lamp was tested for suitability. While it was found that there is some dimming of the illumination at the spot periphery, the overall spectral and luminance distribution of the compact source is quite acceptable, especially considering the time benefit that it represents.

Experiments were conducted in a shock tube to determine the effect of planar wedge inlet geometry on the shock wave reflection pattern that occurred on a wedge. High-speed schlieren imaging was used to visualize the experiments conducted in air with a nominal incident shock strength of Mach 1.31. The experimental test pieces consisted of a wedge mounted above the floor of the shock tube where the underside wedge angle was varied. The upper wedge angle was fixed at 30°, resulting in a Mach reflection. The underside wedge angle was either 30° or 90°, corresponding to a conventional and blunt wedge respectively. For the cases presented here, the reflected shock from the initial interaction reflects off of the shock tube floor and diffracts around the wedge apex. A density gradient is formed at the wedge apex due to this process and results in a vortex being shed for the 90° wedge. It was shown by simple measurements that the diffracted wave could reach the triple point of the upper Mach reflection if the wedge were of sufficient length.

There has been a large amount of work done on the shock wave and boundary layer interaction (SWBLI) as reported by Babinski [1]. In some cases, there is a tendency for the shock to induce separation. In adiabatic and non-reactive flow, the only source of entropy rise is viscosity. The SWBLI is of interest as it establishes a trend. The trend for expansion wave/boundary layer interaction (EWBLI) will have SWBLI as a benchmark, for comparison.

Research on the application of Geometric Shock Dynamics (GSD) to the propagation of plane shockwaves has shown that GSD and experimental data correlate well for stronger shocks (M s > 3) but tends to fail for weak shocks. Bryson and Gross [1] investigated the diffraction of plane shocks (M s ≈ 3) around spheres, cones and cylinders. A comparison of their experimental data with Whitham’s GSD gave a good correlation.

Shock waves and expansion fans form in supersonic flows as a mechanism to allow fluid to flow conformally over a body. When bodies are in close proximity – such as in the aerospace applications of store carriage and release from aircraft, engine inlet design, and formation flying – these shock waves and expansion fans interact and give rise to an interesting flow field warranting further investigation. The present research focused on modelling an expansion fan/shock wave interaction both experimentally and numerically, and these results were used to validate the basic flow physics of the interaction as well as the analytical model to predict the shock curvature originally published by Li and Ben-Dor. From the results, it can be concluded that both the curvature of the shock and the deflection of the expansion fan increase with increasing shock generator angle of attack. The analytical solution for predicting the shock curvature derived by Li and Ben-Dor is valid for predicting the amount of curvature of the shock (i.e., the concavity of the shock, given by the second derivative of the equation for the shock curvature) but underpredicts the range over which the expansion fan/shock wave interaction occurs and is thus invalid for analyses concerned with the extent of the shock curvature and modelling the full interaction.

The effects of gap width and Mach number variation on shock induced flow through a pipe gap are experimentally and numerically investigated. Both were found to have an effect on the propagation conditions in both pipes as well as the development of the flow features in the gap flow. Mach numbers of 1.34, 1.45 and 1.60 as well as gap widths of 40 to 300 mm were used. The incident shock wave accelerated the gas in the upstream pipe to high subsonic speeds and continued in the downstream pipe at a much reduced strength. Expansion waves at the outflow resulted in supersonic speeds as the flow entered the gap for Mach 1.45 and 1.6. This resulted in a number of flow features and interactions in the developing characteristic supersonic jet. In addition to the standing shock, a system of waves of alternating shocks and expansions developed essentially controlling the propagation conditions in the downstream pipe. The development to steady state, the position, and the strength of the standing shock were influenced by both the gap width and Mach the number. For the lower Mach number, no sharp discontinuities were noticed although the width had an effect. Before the downstream pipe end effects, wave propagation and interactions in both pipes were studied. The downstream pipe overpressure is initially unsteady but becomes more uniform, controlled by the developed wave system in the gap. A strong expansion propagated into the flow in the upstream pipe causing a significant pressure drop from the initial post-shock pressure.

Previous research on wave focusing has concentrated on shock wave cavity flows [1]. Expansion wave cavity flows have not been investigated before. This paper looks at the flow resulting from an expansion wave entering a cylindrical cavity. Initially numerical simulations were run with the assumption of a plane diaphragm, however after experimental testing it was found that an investigation of the effect of a curved diaphragm also needed to be done. An expansion wave is a pressure wave which causes the fluid it travels through to decrease in pressure. As expansions cause a decrease in pressure they tend to flatten out (decrease in gradient) as they travel through a fluid. This makes them difficult to visualise as generally they are associated with weak gradients [2]. The interaction between shock and expansion waves has been investigated, as has the diffraction of an expansion wave around a corner [3].

This work evaluates the potential for producing quantitative data of the density field using a two-dimensional colour schlieren system within the test section of a shock tube. Density gradient components, magnitude and direction, form the basis of the quantitative evaluation. These are encoded onto an imaging plane by means of a colour-coded source mask placed along the optical axis of the schlieren system. Direction is indicated by the relative ratios of the three primary colours: red, green and blue (RGB). Magnitude is indicated by the relative intensities of the RGB values. Sensitivity of the system is adjusted by an iris diaphragm placed in the cutoff plane. The method described is applied to the focusing of a shock wave in a parabolic cavity. The experimental results of the schlieren technique are compared to computational simulations with synthetic two-dimensional colour and magnitude coding applied to the results. The source masks designed and used proved to require a greater intensity light source and thus the design of an LED light source was developed. The CFD solutions were converted into an image format directly comparable to the photographic images obtained. Image processing techniques have been employed to deconstruct photographs to allow for quantitative comparisons with a calibration lens. Density gradient direction has been conclusive; however, density gradient magnitude is not yet accurately determined due to light source constraints.

A concept has been developed, and implemented, where the initial shape of a shock wave can, within limits, be arbitrarily set, with a fixed pressure ratio across it, and the duct into which it propagates can also be arbitrarily defined. A narrow slit is positioned on the end wall of a shock tube and is supplied by the essentially constant pressure behind the reflected wave from the shock tube operation. The wave propagating through the slit then enters a narrow test section positioned perpendicular to the main shock tube axis. Initial studies were for a converging cylindrical shock segment, followed by examples of more complex profiles producing waves having both converging (increasing strength), and diverging (decreasing strength) components.

In the unsteady process of shock reflection off convexly curved surfaces, the Reynolds number can have an influence on the development of the irregular reflection pattern. Time-resolved visualizations of the reflection process and high-resolution numerical simulation are used in this investigation to quantify this influence, which manifests itself in a delayed growth of the shock pattern with decreasing Reynolds number. In order to conduct reliable and unambiguous measurements, the present study concentrates on observing the development of the established irregular reflection pattern rather than attempting to determine the transition point directly. It can be seen that the influence of the Reynolds number is highly nonlinear and that changes of two orders of magnitude or more are required to produce a reliably measurable difference in the triple point trajectories, which is considerably more than what has so far been reported in the literature. The results allow one to make inferences regarding the transition process and they help to clarify previously reported discrepancies between predicted and experimentally determined transition angles.

The results of an experimental and numerical investigation into the behaviour of the spiral vortex generated by shock wave diffraction over edges yawed to the incident shock wave are presented. Three-dimensional numerical simulations reveal significant distortion and bending of the free vortex in regions near the boundary of the flow domain, so as to meet it at a right angle. The results of numerical simulations were found to mimic the experimentally obtained photographs very well. The numerical results are used to explain the various features of the resultant flow fields, with particular emphasis placed on the behaviour and properties of the spiral vortex, as it evolves with time. The effects of bending on the structure of the vortex are examined. The rate of circulation production for the three-dimensional shock diffraction cases was calculated, and the trends observed correlated with those for the much published two-dimensional diffraction case.

It is well accepted that the persistence of regular reflection of a shock wave off a wedge beyond the ideal theoretical prediction is due to viscous and thermal boundary layers induced behind the reflection point. Experiments have been done by reflecting two shock waves of equal strength off each other so that the plane of symmetry between them becomes an ideal inviscid and adiabatic reflection plane thereby experimentally mimicking the assumptions of the theory. There is one definitive experiment done at a wall angle of 40° using a bifurcated shock tube that indicates that the actual transition angle is the theoretical detachment condition. This paper extends these results to two cases near limiting conditions; one at a very low incidence shock Mach number and one at a wall angle very close to the theoretical transition limit. The first confirms the reasons for the von Neumann Paradox but cannot discriminate between sonic and detachment conditions, but is within about 0.5% of them, and the second shows transition much closer to the sonic than the detachment condition but with both within the experimental error bounds. In both cases, the results are notably different from transition conditions off a wedge and confirm the effects of transport properties being the cause of persistence of regular reflection.

It has been shown that when a plane shock wave is reflected off a surface consisting of a 75-mm radius circular arc followed by a plane section inclined at 45°, it takes some time for the interaction to reach a pseudosteady reflection configuration. The current study extends this work at a constant Mach number of 1.346, with three compound walls, consisting of leading circular sections of 30, 50 and 75 mm radius, joined to a plane wall section. Testing was done at various wall angles for each of the test pieces. The reflected wave angle was measured and was found to increase along the plane wall section until it reached an asymptotic value, at which time pseudosteady flow was established. The asymptotic values are consistent with reflection off plane wedges and are independent of the leading radius. For lower wall angles which lead to Mach reflection the length required to reach pseudosteady flow increases as the wall angle increases to the pseudosteady transition angle. The reverse occurs when the final pseudosteady reflection is regular, in that as the wall angle increases the distance travelled to reach pseudosteady flow conditions decreases. Additional tests were conducted on a specimen consisting of a plane section at 60° wall angle with 30-mm radius circular arc sections at either end. It is demonstrated how the information from the two slope changes influences the shape of the reflected shock. The trajectories of two perturbations on the reflected shock arising from the joints between the circular sections and the plane wall show that the reflected wave remains linear between these two points, as it received no knowledge from either circular section until the perturbations from the upper and lower joints cross.

An investigation into a three-dimensional, curved shock wave interacting with a three-dimensional, curved boundary layer on a slender body is presented. Three different nose profiles mounted on a cylindrical body were tested in a supersonic wind tunnel and numerically simulated by solving the Navier–Stokes equations. The conical and hemispherical nose profiles tested were found to generate shock waves of sufficient strength to separate the boundary layer on the cylinder, while the shock wave generated by the ogival profile did not separate the boundary layer. For the separated flow, separation was found to occur predominantly on the windward side of the cylinder with the lee-side remaining shielded from the direct impact of the incident shock wave. A thickening of the boundary layer on the lee-side of all the profiles was observed, and in the conical and hemispherical cases this leads to the re-formation of the incident shock wave some distance away from the surface of the cylinder. A complex reflection pattern off the shock wave/boundary layer interaction (SWBLI) was also identified for the separated flow cases. For comparative purposes, an inviscid simulation was performed using the hemispherical profile. Significant differences between the viscous and inviscid results were noted including the absence of a boundary layer leading to a simplified shock wave reflection pattern forming. The behaviour of the incident shock wave on the lee-side of the cylinder was also affected with the shock wave amalgamating on the surface of the cylinder instead of away from the surface as per the viscous case. Test data from the wind tunnel identified two separation lines present on the cylindrical surface of the hemispherical SWBLI generator. The pair of lines were not explicitly evident in the original CFD simulations run, but were later identified in a high-resolution simulation.

An experimental and numerical study of underexpanded free sonic jet flows issuing from rectangular, elliptical and slot nozzles has been undertaken. Aspect ratios (AR) of 1, 2, and 4 are described at pressure ratios (exit plane pressure to ambient pressure), of 2 and 3. There is good qualitative agreement between the experimental observations and the numerical predictions. In the case of rectangular jets, a complex system of shock waves forming the incident shock system is identified. This shock wave system originates at the corners of the nozzle exits, and proceeds downstream. Mach reflections are found to occur on the incident shock wave surface as well as the presence of a Mach disk terminating the first jet cell. This Mach disk has the shape of a square, a hexagon, or an octagon depending on the nozzle shape. For slot and elliptical jets, the formation of the incident shock wave was not observed along the minor axis plane of the nozzle for AR > 2. The incident shock wave was observed to originate downstream of the nozzle exit in the major axis plane. This wave system undergoes a transition to Mach reflection as it propagates downstream of the nozzle exit. In all cases tested, the shape of the jet boundary is significantly distorted. In rectangular jets, the narrowing of the jet boundary along the diagonal axis of the nozzle exit is observed, and in the case of the elliptical and slot jets axis switching is noted.

The reflection of shock waves off cylindrical surfaces of different radii is examined with the help of time-resolved flow visualization. The primary diagnostic is a newly developed technique based on the tracking of deliberately introduced small perturbations in the flow. The main focus of the investigation is to determine at which position the shock wave receives information about the shape of the wall that it reflects off. In the pseudo-steady shock reflection off a plane wall, it is commonly accepted that the reflection changes from regular to irregular as soon as sonic signals generated behind the reflection point catch up with the reflection point, and the common interpretation is that this corresponds to the transition from regular to Mach reflection (the so-called sonic criterion). The results obtained here for convex circular surfaces show that this ‘catch-up’ condition occurs at wall angles considerably higher than in the plane wall case, while a visible Mach stem occurs only further along the surface at wall angles distinctively lower than those for plane walls. Tests are also conducted on a surface where a cylindrical portion is followed by a fixed angle plane section. The Mach numbers are chosen to be on either side of the plane wall transition condition so as to examine the adjustment from reflection on the cylindrical portion to that on the plane wall. These tests confirm that the wall angle at which sonic ‘catch-up’ to the reflection point occurs on the cylindrical surface is much higher than the corresponding wall angle predicted by the sonic criterion for a plane wall. While the transition from regular to irregular reflection is not the main concern of this contribution, the present results show that the transition criteria developed for steady and pseudo-steady flows are only of limited use in the fully unsteady flows such as the one investigated here.

Previous studies of the impact of a blast or shock wave on a layer of textile positioned a short distance in front of a surface have shown that significant pressure amplification can occur. These studies have all dealt with the case of head-on impact on plane textile surfaces. This study extends such work to plane textile specimens inclined to the wave propagation direction, both for the textile freely suspended in order to examine the transmitted wave and with it positioned a short distance in front of a solid surface. Tests are also conducted with the textile suspended in a cylindrical shape positioned in front of a curved surface to approximate a more realistic practical loading case on a torso. Three textile types were used, varying significantly in permeability. In the oblique impact case it is found that the pressure amplification decreases as the wall angle decreases. The behaviour of the wave system in the gap between the textile layer and the body is clarified, showing a succession of oblique shock reflections and transmissions back through the textile layer. Tests on the cylindrical body surface at low Mach number show no significant amplification at the most forward position and steadily decreasing pressure around the sides of the surface. The concern regarding very large increases in pressure which arose from tests on head-on impact on plane surfaces appear to be ameliorated when the body is curved. Computer simulations are used to confirm the wave pattern for the cylindrical case by modeling a curved porous surface a short distance in front of a rigid wall.

This paper examines the shock wave dynamics of a biconvex aerofoil in transonic flight during acceleration and retardation. The aerofoil has a cord length of 1 m and air at infinity is at 101.325 kPa and 300 K. Using Fluent as the CFD software, constant velocity (steady state) simulations were conducted at transonic Mach numbers. The aerofoil was then accelerated at 1041m/s2 (106 g), starting at Mach 0.1, and decelerated at −1041m/s2, starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were found in the transonic region between the steady and the unsteady aerodynamic forces. Analysis of the flow field in this region showed that acceleration-dependent variations in the position of the shock wave on the surfaces of the aerofoil were the main reason for this. As very high accelerations were used in order to emphasize differences, which do not have many practical applications, simulations using accelerations lower than 9 g were also conducted in order to confirm the results. The acceleration-dependent behaviour of other shock waves around the aerofoil, such as the bow shock in front of the aerofoil and the trailing wave were also examined. The trailing wave followed behind the aerofoil changing position with different accelerations at the same Mach number.

Experiments have been conducted in a large shock tube to examine the four-wave shock reflection pattern, now known as Guderley reflection (GR). The fourth wave, an expansion, is clearly identified, as is the supersonic patch behind the reflected wave. A shocklet terminating the supersonic patch behind the reflected wave is identified, which forms a second triple point further down the Mach stem. Evidence is presented showing the presence of more than one expansion wave and more than one shocklet, thus indicating the existence of more than one supersonic patch. In order to distinguish between cases with a single patch without the shocklet as originally proposed by Guderley and found in some computations, and the indications of a multi-patch geometry found here, and also in other computations, this latter case is designated Guderley Mach reflection (GMR). Multi-exposure images of the shock propagation superimposed on a single image frame enable estimates to be made of the strength of the major waves, and it is shown that the reflected wave is very weak.

The examination of the motion of very weak waves generated from small sources on the boundary of a flow domain gives information on how the domain shape influences the flow, both from spatial and temporal perspectives. In the study of shock wave dynamics the shock itself generates a weak wave when passing over a small step, or surface irregularity. The basic principle is that if a particle produces a series of point disturbances in a flow field, the induced perturbations will propagate outwards at the local sonic velocity whilst at the same time being convected along with the local flow velocity. A number of issues may be identified for an unsteady flow. Firstly, the flow field at later times may be influenced by perturbations produced at earlier times. Secondly, if the positions of the perturbations can be monitored as a function of time, then the trajectory and velocity of the particle may be deduced. Thirdly, if a perturbation arises from a point on a boundary, then its influence, if any, on any particular part of the flow can be established. A number of examples are presented to illustrate the value of the technique and its potential to uncover the mechanisms responsible for the formation of certain flow patterns in high-speed compressible flows.

An aircraft travelling at supersonic speeds close to the ground generates a bow wave which is reflected off the ground surface. If a valley is traversed a complex reflection pattern will be generated. Similar patterns will evolve with a plane wave traversing a depression on a surface or structure. To simulate the process a planar shock wave, generated in a shock tube, is moved over several notched wedge configurations. Schlieren photographs were produced to assist in identifying the resulting complex three-dimensional wave structures and then verified and extended by three- dimensional computations. The valley geometries investigated are rectangular, triangular, parabolic and conical with a number of valley floor inclinations. The main features are extracted in surface models to demonstrate the complexity of the flow, and in particular in the case where the reflection is regular on the ground plane and Mach reflection in the valley.

This investigation focuses on the aerodynamic effects caused by acceleration and retardation. It shows that, when an object is accelerated in a compressible fluid, the aerodynamic forces and moments experienced by the object at any instantaneous Mach number are different to those, experienced at the same Mach number, when the object moves at constant velocity. A supersonic biconvex aerofoil was chosen, with Fluent as the computational fluid dynamic (CFD) software. Constant velocity (steady state) simulations were conducted at Mach numbers ranging from 0.1 to 1.6 for the aerofoil. The aerofoil was then accelerated at 1041 m/s2 (106 g) and 86.77 m/s2 (8.845 g), starting at Mach 0.1, and decelerated at −1041 and −86.77 m/s2, starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were shown between the steady and the unsteady cases with the greatest differences observed in the transonic region. In this region, for each specific Mach number, acceleration-dependant variations in the position of the shock wave on the upper surface of the aerofoil were also observed. This was used to explain the great differences in the aerodynamic forces and moments between the steady and the unsteady cases in the transonic region.

A simple model is proposed to describe the main features of the complex phenomena that occur when a plane shock wave strikes a open-cell foam block. The complex two-phase interactions can be simplified using the experimental evidence that the foam face may be treated as a contact surface, that the length of the collapsed foam plug grows linearly in time, and that the gas pressure profile in the region between the head of the plug and the undisturbed material may be treated as being pseudo-stationary. These simplifications enable the prominent features of the compression process to be predicted for a variety of foam types. Analytical results for the reflected shock strength, foam front face velocity, transmitted wave velocity and strength, and maximum peak back wall pressures are presented.

The transition from so-called regular to irregular shock wave reflection has been the subject of considerable research effort over the last seven decades [1]. The most thoroughly investigated case is that of the straight wedge

Shock wave focusing has been of great interest to both researchers and engineers alike. Researchers have concentrated on the fundamental gas dynamics of focus as seen in the studies of Sturtevant and Kulkarny [1] and Skews and Kleine [2]

The Kelvin-Helmholtz Instability (KHI) forms along shear layers and takes the form of repeating wave-like structures. Thus the Mach reflection shear layer has the potential to break down into the KHI.

Many complex and fascinating flow features occur when a shock wave impinges on or around a surface. Understanding of these is important in view of the increasing application in a variety of fields, such as medicine and material modification, besides the more conventional fields of blast loading of structures and supersonic aerodynamics. This paper deals with some of the developments of research in the field of shock wave studies at the Flow Research Unit of the University of the Witwatersrand. It covers both successful and unsuccessful investigations and suggests those that still need further work.

The current work presents the results of an experimental study using a conventional diaphragm-constrained, air-driven, circular cross-section shock tube expanding into ambient conditions producing shockMach numbers between 1.25 and 1.64.

A comprehensive study is made of the influence of the physical properties of compressible open-cell foam blocks exposed to shock-wave loading, and particularly on the pressure distribution on the shock tube walls. Seven different foams are used, with three different shock Mach numbers, and three different slab lengths. Foam properties examined include permeability, density, stiffness, tortuosity and cell characteristics. The investigations concentrate on both side-wall and back-wall pressures, and the peak pressures achieved, as well as collapse velocities of the front face and the strength and nature of the reflected shock wave. The consequences of deviations from one-dimensionality are identified; primarily those due to wall friction and side-wall leakage. The results presented are the most comprehensive and wide ranging series conducted in a single facility and are thus a significant resource for comparison with theoretical and numerical studies. The different foams show significant differences in behavior, both in terms of peak pressure and duration, depending primarily on their density and permeability.

Experiments were conducted on the pressure experienced on a surface underlying a textile layer when exposed to a blast wave environment. Injury to humans subjected to blast loading affects the soft organs of the body, and the effects of clothing on these loads is of interest. It was shown that considerable amplification of the pressure load can occur depending on the textile properties. Shadow photographs of the wave interaction with muslin, cotton, and satin textiles are presented in order to identify the physical processes. As the textile becomes more permeable the transmitted wave increases in strength relative to the reflected wave, gas passage through the specimen is greater, and textile movement is less. The effect of a slab of gelatin under the textile was investigated with a view to simulating the effect of animal tissue covering a hard surface such as a rib. Both single and multiple layers of seven widely different cloth types were also tested for their amplification properties. It was found that pressure amplification of up to four times that of an uncovered surface can be generated. Further investigation is necessary to establish the effects of textile structure on the loads.

The effect relative motion between a shock and supersonic flow has on the Mach number of flow behind a planar shock is considered. It is shown that for multiple moving reference frames, such as that encountered in a shock-wave/moving-body interaction the choice of reference frame can result in a Mach number that can either increase or decrease across the shock. This depends on the relative velocities of the reference frames and under certain conditions can remain unchanged for a given shock of finite strength. Euler simulations run at the various computationally predicted transitions have numerically confirmed the idealised analysis presented here.

The interaction of a planar shock wave with a body moving at supersonic speed has been considered with particular focus on shock-on-shock interactions. Three interaction types were previously identified by Smyrl (1964). This work adds a fourth type to these interactions and restates the interaction type classification and the transitions between the various interaction types. A pseudo-steady analysis of key interaction points and flow features is used to predict the various transitions. The criteria presented here are compared to results from a numerical Euler model of the interactions. A comparison of results from the numerical model with experimental results shows good agreement and thus the existence of the various interaction types and transition criteria have been confirmed using the numerical model.

For many years there has been debate regarding why shock wave reflection off a solid surface has allowed regular reflection to persist beyond the incidence angles where it becomes theoretically impossible. Theory predicts that at some limiting angle the reflection point will move away from the wall and Mach reflection will occur. Previous studies have suggested that the paradox could be due to the presence of the growing viscous boundary layer immediately behind the point of reflection, and some numerical studies support this view. This paper takes the approach of establishing an experimental facility in which the theoretical assumptions regarding the surface of reflection are met, i.e. that the reflecting surface is perfectly smooth, perfectly rigid, and adiabatic. This is done by constructing a bifurcated shock tube facility in which a shock wave is split into two plane waves that are then allowed to reflect off each other at the trailing edge of wedge. The plane of symmetry between the waves then acts as the perfect reflection surface.Through a careful set of visualization experiments, and the use of multivariate analysis to take account of the uncertainty in shock Mach number, triple-point trajectory angle, and slightly different shock wave arrival times at the trailing edge, the current work shows that the transition from one type of reflection to the other does indeed occur at the theoretical value. Conventional tests of reflection off a solid wall show significantly different transition results. Furthermore, it is also shown that the thermal boundary layer plays an important role in this regard. It is thus confirmed that viscous and thermal effects are the reason for the paradox. Reasons are also suggested for the counter-intuitive behaviour of the reflected shock wave angle.

Over the past decade and a half there have been a number of numerical studies of the reflection of oblique axisymmetric shock waves from the axis of symmetry. Many of these have shown a complex Mach reflection pattern together with a strong toroidal vortex which significantly distorts the Mach disk. This geometry has never been captured experimentally. This note describes a special rig for the generation of strong imploding conical shocks, and presents photographs of the predicted reflection pattern.

Experimental studies have been performed to investigate the pressure amplification experienced behind a textile when exposed to a shock wave. Three textiles with different masses and air permeabilities were studied. Mach numbers for tests varied between 1.23 and 1.55. The distance between the back wall and the textile was varied between 3 and 15 mm. It was found that in most cases the presence of the textile led to a pressure amplification at the back wall. This amplification was dependent on the textile, Mach number and distance from the back wall. The processes causing the pressure amplification were identified by analysing pressure traces and contact shadowgraphs. It was found that when the incident wave impinges on the textile, a part is reflected upstream and a part is transmitted through the textile. The transmitted portion reflects back and forth in the gap between the textile and the back wall leading to a back wall pressure trace with a stepped profile. In addition, the textile moves towards the back wall causing compression waves to propagate towards the back wall. The combination of the stepped profile and the compression waves cause the pressure amplification. The contribution of each mechanism depends on the textile properties. Approximate wave diagrams have been constructed. Tests involving multiple layers of textiles are also discussed.

This paper concentrates on establishing the three-dimensional flow geometry associated with studies of shock wave reflection between two symmetrical wedges in supersonic flow. It considers the issue of hysteresis in such flows, and draws a distinction between three different aspects of hysteresis, associated with: ideal two-dimensional flow, flow with noise, and three-dimensional effects. The three-dimensional nature of the flow field is elucidated by the use of oblique shadowgraph photography where the optical axis of the shadowgraph system passes at an oblique angle, of as much as 55°, through the test section. The traces of the wave system reflecting off the tunnel window are identified and are used to assist in identification of wave profiles. The nature of the approach of the peripheral Mach reflections collapsing towards the centre of the flow becomes evident, as does the mechanism of transition from Mach reflection to regular reflection. Distinct evidence of the effects of flow perturbations at the mechanical equilibrium transition point are presented, as are changes in the rate of growth of the Mach stem near this point.It is shown that three-dimensional effects can have a major effect on the wedge angle for transition. In the present tests, at Mach 3.1 and a wedge aspect ratio of 0.5, this occurs at a wedge angle of about 5° higher than the theoretical maximum for the corresponding two-dimensional flow, where the dual solution domain extends over only two degrees.

A new friction operated single piston shock tube driver design that is capable of generating shock waves of Mach number 1.1 to 2 is presented. By using different test gases and evacuating the driven section Mach 5 shock waves can easily be produced. The driver is efficient with shock wave Mach numbers within 9% of that predicted by ideal shock tube theory and the non-dimensional formation length lies between 20 and 40. The brake pad mechanism, that restrains the piston until tests commence, removes the necessity of venting an auxiliary chamber rapidly, thus speeding up the displacement of the piston. It is believed that the design is a practical, simple and cost effective way of generating reproducible shock tube tests with very short test turn around times, while removing the necessity of using a diaphragm and exposing the test gases to the atmosphere. Results for three pistons with masses of 4.4, 0.71 and 0.38 kg (brass, PVC and hollow aluminium respectively) with driver gauge pressures of between 2 and 50 bar (Mach 1.2 to 2) are given.