Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations

Toroidal Imploding Detonation Wave Initiator for Pulse Detonation Engines

Imploding toroidal detonation waves were used to initiate detonations in propane–air and ethylene–air mixtures inside of a tube. The imploding wave was generated by an initiator consisting of an array of channels filled with acetylene–oxygen gas and ignited with a single spark. The initiator was designed as a low-drag initiator tube for use with pulse detonation engines. To detonate hydrocarbon–air mixtures, the initiator was overfilled so that some acetylene oxygen spilled into the tube. The overfill amount required to detonate propane air was less than 2% of the volume of the 1-m-long, 76-mm-diam tube. The energy necessary to create an implosion strong enough to detonate propane–air mixtures was estimated to be 13% more than that used by a typical initiator tube, although the initiator was also estimated to use less oxygen. Images and pressure traces show a regular, repeatable imploding wave that generates focal pressures in excess of 6 times the Chapman–Jouguet pressure.Atheoretical analysis of the imploding toroidal wave performed using Whitham’s method was found to agree well with experimental data and showed that, unlike imploding cylindrical and spherical geometries, imploding toroids initially experience a period of diffraction before wave focusing occurs. A nonreacting numerical simulation was used to assist in the interpretation of the experimental data

Numerical shock propagation using geometrical shock dynamics

A simple numerical scheme for the calculation of the motion of shock waves in gases based on Whitham's theory of geometrical shock dynamics is developed. This scheme is used to study the propagation of shock waves along walls and in channels and the self-focusing of initially curved shockfronts. The numerical results are compared with exact and numerical solutions of the geometrical-shock-dynamics equations and with recent experimental investigations

On Shock Wave Diffraction From Non-orthogonal Apertures

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, January 2018The diffraction of shock waves has been explored in many contexts in which either the shock wave is plane and the confi ning volume has complex geometry or where the shock wave has some non-plane geometry, typically something like spherical since this is the approximate shape of the waves generated by blasts. However, these studies have not considered more complex initial wave shapes or exit geometries. This study therefore addresses this de ciency in two ways. The dynamic conical shock wave was originally proposed as a mechanism for the initiation of fusion whereby the focusing of the shock wave near the axis of symmetry would produce the high temperatures and pressures required. This was explored numerically and theoretically, as no experimental method was considered viable, and it was found that the regular re ection of a shock wave de ned by conical wave geometry is not stable and will revert to an irregular re ection pattern at the axis. Three primary geometries were identi ed distinguished by the number of irregular re ections formed and in uenced by the induced vortical ow. The current study used a developed experimental apparatus to study conical shock waves and an additional, new re ection pattern, named the von Neumann type (vN-type) for the similarity to the von Neumann re ection of weak plane waves, was identi ed. In addition, instability of the conical shear layer present as a result of the irregular re ection at the axis of the shock wave was identi ed experimentally which resembles the Kelvin-Helmholtz instability previously only studied in two-dimensional con gurations of compressible ow. Dynamic bending of the central jet from the re ection axis was also tested as a function of upstream occlusion in the shock tube and this suggests possible future work in compressible jet actuation. The current study also considered the diffraction of plane shock waves at the inclined or curved exits of shock tubes, which are more general examples of duct interaction of the sort that might be found in engines or ventilation systems. This was done experimentally using novel, open test sections for a conventional shock tube and for a limited number of computational cases. These ows are characteristically different from the diffraction of shock waves from tubes of complex cross-section studied to date where the exit plane is still normal to the direction of travel of the wave. This is because the shock wave still undergoes simultaneous diffraction at all points around the edge of the tube in such a case while in this study the wave diffracts at different times around the tube periphery. This affects the strength of both the emerging incident wave and the diffraction and thus an atypical formation of the jet and vortex takes place. In the case of the inclined plane exit of the shock tube, two primary phenomena were noted: de ection of the jet and change of the jet cone angle; and variations in the vortex diffraction behaviour. For the former effect a large inclination of the exit from the normal increased the spread of the jet and the inclination away from the tube axis. Also, a system of secondary shock waves forms in the jet due to the expansion fans formed at the diffraction edge, typical of under expanded jets but becomes weaker as exit surface inclination increases. The second effect noted is of the increased curvature as a function of time after diffraction for higher inclinations, due to the much stronger induced velocities for the portion of the vortex shed on the obtuse upstream edge. The vortex loop also loses coherence with increasing inclination because of the weak vortex shedding at the downstream edge of the tube. The results for the curved exit are similar although the effects are not as extreme since the limiting diffraction angles are lower than for the extreme plane cases due to the characteristics of circular geometry. In the extreme case of part of the shock tube exit being tangent to the exit surface, the vortex again does not form a closed loop but rather terminates in the exit surface. This was particularly tested here with a plane section at the tangent point. However, the secondary re ection of the diffracted shock wave due to the curvature of the surface toward the diffracted wave, which tends to disrupt the vortex, means that an internal diffraction with a fully closed tube would result in a short-lived vortex loop. In both of the latter cases the vortex loop, or arch if it cannot close into a loop, is part of the physical mechanism whereby a jet ow exiting a pipe adjusts to being a di use ow along the exit surface. This is accomplished by the spreading of the sheet of vorticity, which is the boundary layer in the pipe and the jet boundary outside of it, by the origination of turbulence in the breakdown of the vortex arch or loop. The diffraction of shock waves from non-orthogonal apertures demonstrates features previously unidenti ed and suggests complex ow patterns which simpli ed two-dimensional analysis cannot describe.MT 201

Shock-induced flow through a pipe gap

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Master of Science in Engineering. Johannesburg, April 2016An explosive event in an industrial gas transmission pipe stresses the pipe and can result in pipe rupture and separation at weak points. A shock wave results propagating from the high pressure section of the pipe, through the gap and to the low pressure section. The present study simulates numerically and experimentally the resulting ow eld at the position of pipe separation and propagation conditions in both pipe sections. The e ects of gap width, gap geometry and shock Mach number variation are investigated. Shock Mach numbers of 1.34, 1.45,1.60 and 2.2, gap widths of 40mm to 310mm were used. All variations of boundary conditions were found to have an e ect on the propagation conditions as well as the development of the ow features within the gap. The variation of the gap geometry was done for a pipe gap and a anged gap experimentally. Extended geometries were simulated numerically. For the pipe gap, 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. A strong expansion propagated into the ow in the upstream pipe causing a signi cant pressure drop from the initial post-shock pressure. Expansion waves at the out ow resulted in supersonic speeds as the ow entered the gap for Mach 1.45 and 1.6. A notable feature was the formation of a standing shock at the inlet to the downstream pipe. In addition to the standing shock, shock cells of alternating shocks and expansions developed within the gap essentially controlling the propagation conditions in the downstream pipe. For the lower Mach number of 1.3, no sharp discontinuities were noticed. The e ect of the gap width was found on the nature of the shock cells within the gap. The propagation conditions in the downstream pipe showed that the pressure is initially unsteady but becomes more uniform, controlled by the developed wave system in the gap. For the anged gap case, the ow within the gap is con ned for much longer and hence produced much more intense and complex ow feature interactions and an earlier transition of the ow to turbulence. Numerical investigations for a burst pipe gap, for a gap with a di erent diameter downstream pipe and a gap with a 90-degree bend downstream pipe produced peculiar ow features.MT201

Development of a Detonation Diffuser

This research includes an investigation of the mechanisms of diffraction and reinitiation that enable a detonation diffuser. It describes a set of geometric parameters necessary to design a diffuser for a given detonable mixture and initial channel height. Predetonators with channel height less than the critical height are ineffective because detonations in small channels decouple into separate shock and combustion fronts when the channel height increases. A detonation diffuser allows the channel height to increase by utilizing the decoupled shock wave to reinitiate detonation. In the diffuser, a detonation initially decouples into separate shock and combustion fronts, and then the decoupled shock front reflects from an oblique surface initiating a secondary detonation that survives the expansion. This research investigated the three regions of a detonation diffuser: the initial diffraction, the reflecting surface, and the second diffraction corner. Schlieren video of two-dimensional diffracting detonations recorded the position of the detonation, decoupled shock front and flame front. Observations of the decoupled shocks reflecting from surfaces showed that a 45° reflecting surface must be placed less than 80 mm downstream of the initial diffraction corner to initiate a secondary detonation in more than 91% of repeated trials. Observations of the interaction of diffracting detonations with multiple obstacles revealed that the best performance (smallest separation, and highest Mach number) occurred when the decoupled shock reflected from four separate obstacles at approximately the same time

Design and Testing of an H2/O2 Predetonator for a Simulated Rotating Detonation Engine Channel

A study is presented on the relationship between a pre-detonator and a detonation channel of an RDE. Testing was conducted on a straight narrow channel made of clear polycarbonate windows connected to an H2/O2 pre-detonator to simulate the RDE initiation scheme and allow for flow visualization. A comparison is made on decoupling distance and wave velocities for a range of pre-detonator designs, inclination angles, equivalence ratios and geometries placed within the simulated channel. Regardless of inclination angle or equivalence ratio the detonation wave decoupled within 25 mm from the pre-detonator exit into the channel. A step change in diameter 25 mm from the exit of the pre-detonator increased the coupled distance to approximately 40 mm from the pre-detonator exit. A step diameter change also increased the exit velocity of the wave and directionalized the flow. Wedges of 30° , 45° and 60° , placed in the channel next to the pre-detonator exit, increased the distance the shock and flame remained coupled from the pre-detonator exit to 42 mm, 50 mm and 60 mm, respectively

Experimental studies on shock wave interactions with flexible surfaces and development of flow diagnostic tools

Nowadays, light-weight composite materials have increasingly used for high-speed flight vehicles to improve their performance and efficiency. At supersonic speed, sonic fatigue, panel flutter, severe instabilities, and even catastrophic structural failure would occur due to the shock wave impingement on several flexible components of a given structural system either internally or externally. Therefore, investigation on shock wave interaction with flexible surfaces is crucial for the safety and performance of high-speed flight vehicles. This work aims to investigate the mechanism of shock wave interaction with flexible surfaces with and without the presence of the boundary layer. The first part involves the shock wave generated by supersonic starting jets interaction with flexible surfaces and the other one focuses on shock wave and boundary layer interaction (SBLI) over flexible surfaces. A novel miniature and cost-effective shock tube driven by detonation transmission tubing was designed and manufactured to simulate the supersonic starting jet and investigate the interaction of a supersonic starting jet with flexible surfaces. To investigate the characterization of this novel type shock tube, the pressure-time measurement in the driven section and the time-resolved shadowgraph were performed. The result shows that the flow structure from the open end of the shock tube driven by detonation transmission tubing agrees with that of conventional compressed-gas driven shock tubes. Moreover, this novel type of shock tube has good repeatability of less than 3% with a Mach number range of 1.29-1.58 when the weight of the NONEL explosive mixture varies from 3.6mg to 12.6mg. An unsteady background oriented schlieren (BOS) measurement system and a sprayable Polymer-Ceramic unsteady pressure sensitive paint (PC-PSP) system were developed. The preliminary BOS result in a supersonic wind tunnel shows that the sensitivity of the BOS system is good enough to visualize weak density variations caused by expansion waves, boundary layer, and weak oblique shocks. Additionally, compared with the commercial PC-PSP from Innovative Scientific Solutions Incorporated (ISSI), the in-house developed unsteady PSP system has higher pressure sensitivity, lower temperature sensitivity, and photo-degradation rate. To identify the shock movement, distortion and unsteadiness during the processes of the supersonic starting jet impingement and shock wave boundary layer interaction (SBLI) over flexible surfaces, an image processing scheme involving background subtraction in the frequency domain, filtering, resampling, edge detection, adaptive threshold, contour detection, feature extraction, and fitting was proposed and applied to process shadowgraph and schlieren sequences automatically. A large shadowgraph data set characterized by low signal to noise ratio (SNR) and small spatial resolution (312×260-pixel), was used to validate the proposed scheme. The result proves that the aforementioned image processing scheme can detect, track, localize, and fit shock waves in a subpixel accuracy. The mechanism of the interaction between the initial shock wave from a supersonic starting jet and flexible surfaces was investigated based on a square shock tube driven by detonation transmitting tube. Compared with that of the solid plate case, flexible surfaces can delay the shock reflection process because of the flexible panel deformation generated by the pressure difference between the top and the bottom. The delay time is around 8µs in the case of 0.1mm thick flexible surface, whereas it declines to around 4µs in the case of 0.3mm thick flexible surface because of the lower flexibility and deformation magnitude. However, interestingly, the propagation velocity of the reflected shock wave is basically the same for the solid plate and flexible panels, which means the flexible surface doesn’t reduce the strength of the reflection wave, although it delays its propagation. Also, there is not an apparent difference in the velocity of the reflected shock wave in the case of different incident shock Mach numbers when Ms varying from 1.22 to 1.54. These experimental results from this study are useful for validating numerical codes that are used for understanding fluid-structure interaction processes

On the propagation and reflection of curved shock waves

Curved shock waves, particularly converging shock waves, have applications in a wide variety of elds, yet they are severely under-represented in the literature. Shock re ection is typically categorised in terms of the shock Mach number and incident angle, but these parameters both vary with time for a curved shock wave. A facility capable of producing shock waves with an arbitrary two-dimensional pro le was designed and manufactured. A planar shock from the end of a conventional shock tube is passed through a narrow slit and turned through a 90 bend, generating a shock with an initial shape matching the pro le of the slit. The facility was rst used to study the propagation of shock waves of arbitrary shape. This included a brief computational uid dynamics (CFD) study of the interaction between straight and concave segments on a shock front, followed by CFD and experimental studies into the propagation of shock waves consisting of both concave and convex segments, with initially sharp and rounded pro les. Shocks with Mach numbers between 1.2 and 1.45 were generated, and the behaviour of the shock waves produced by the experimental facility agreed favourably with the CFD simulations, particularly for the higher Mach numbers. A detailed study into the re ection of converging cylindrical shock wave segments was then carried out. CFD simulations for Mach numbers at the apex of the wedge varying from 1.2 to 2.1, for wedge angles between 15 and 60 , and experiments with apex Mach numbers between 1.5 and 2.1 and wedge angles between 15 and 50 were carried out. The sonic condition usually used for predicting the planar shock re ection con guration was successful at predicting the initial re ection con guration. If the initial re ection was regular, then the shock was cleanly re ected o the surface, with no discontinuities in the re ected shock front. However, if the initial re ection was a Mach re ection, this would inevitably transition into a transitioned regular re ection, with the residual Mach stem and shear layer still present behind the re ection point. Collision of the Mach stem with the corner at the end of the wedge generated a small region of very high pressure, which lasted for several microseconds. A simple theoretical model was developed for estimating the Mach stem height and transition point for a converging cylindrical shock segment encountering a straight wedge. The model gives reasonable predictions for shocks of moderate strength and wedge angles below 40 , but deviates from experimental results for wedges at 40 and above