Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves. The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.

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The affects of hydrodynamic shock wave treatment on the bacterial flora of raw beef and poultry were evaluated. Hydrodynamic shock waves were generated in an aqueous treatment medium by either the detonation of two types of explosive charges (explosively-generated hydrodynamic shock waves [EHSW]) (a binary or a molecular explosive) or by electrical discharge (high voltage arc discharge Hydrodyne (TM [HVADH; Hydrodyne, Inc.]). A variety of sample types (whole steaks, ground beef, a water and ground beef slurry) were used to determine the lethality affects of EHSW on cells of the marker microorganism Listeria innocua suspended in a simple broth medium. These sample types were used in order to evaluate the affects of the process not only on the surface, but throughout the bulk of the samples in order to determine whether EHSW could also be used as a non-thermal alternative to reduce the bacterial flora of non-intact or ground meats. The levels of psychrotrophic, lactic, and coliform populations on the surface of whole eye of round steaks submitted to EHSW processing did not differ (P> 0.05) from those of untreated whole eye of round steaks. Parameters expected to influence the nature, magnitude, and propagation of the hydrodynamic shock wave were also varied and evaluated in order to determine which individual parameter or combination of parameters affected the bactericidal potential of EHSW or HVADH processing. Treatment with EHSW failed (P > 0.05) to produce lethality effects on the psychrotrophic, lactic, and coliform populations of ground beef, regardless of the composition and mass of explosive used, the number of successive EHSW treatments used, the relative distance between the explosive charge and the top surface of the sample, or the temperature of the water used in the treatment chamber. EHSW processing did not change (P >0.05) the bacterial population of treated ground beef samples when compared to untreated controls during a five day refrigerated storage study. No lethality effects were observed (P >0.05) in ground beef samples treated by HVADH when samples were subjected to one, two, or three successive HVADH treatments. Minimal penetration of surface inoculated bacteria was observed for both beef steaks and boneless skinless chicken breasts subjected to EHSW and HVADH, respectively. In EHSW-treated beef eye of round steaks, marker bacteria were detected within the first 300 um of tissue below the inoculated surface, 50-100 um beyond the depth of untreated surface inoculated steaks. In HVADH-treated boneless skinless chicken breasts, marker bacteria were detected within the first 200 um below the inoculated surface, 50-100 um beyond the depth of untreated surface inoculated boneless skinless chicken breasts. This suggests that although no difference in the bacteriological populations was observed between EHSW treated, HVADH treated, and untreated control samples of whole steaks (and ground beef treated with both HVADH and EHSW), HVADH and EHSW treatments affect the movement of surface bacteria. United States Department of Agriculture (USDA) guidelines suggest intact beef steaks be cooked to achieve a cooked color appearance on the surface and raw poultry be cooked to an internal temperature of 77° C to inactivate the pathogens Escherichia coli O157:H7 and salmonellae which are of concern in beef and poultry, respectively. By following these guidelines during proper cooking, consumers achieve thermal inactivation of these pathogens. Since the movement of the marker bacterium observed in treated steaks and boneless skinless chicken breasts was minimal, proper cooking of the products would be expected to inactivate vegetative bacterial cells at this depth. Therefore, EHSW and HVADH treated whole beef steaks and boneless skinless chicken breasts would not be expected to pose a bacterial hazard if the products were properly cooked. / Ph. D.

USDA Select bovine Biceps femoris (BF) samples were divided into four sections and randomly assigned to three hydrodynamic shock wave (HSW) treatments and a control. Different amounts of explosive (105 g, H1; 200 g, H2; 305 g, H3) were suspended in the center of the hemishell tank, 26.7 cm above the vacuum packaged beef placed on the bottom center of that water-filled tank and detonated, representing three HSW treatments. In addition, BF steaks (2.54-cm thick) from a different and limited common source (2 muscles) were packaged with each HSW designated BF section. These served as internal refernce steaks (IRS) for the six replications to determine if the HSW treatments physically altered the structural integrity of the meat. H1 and H3 decreased (P<0.05) Warner-Bratzler shear values of the IRS from 3.86 and 3.99 kg (controls) to 3.01 and 3.02 kg (HSW), respectively. H2 shear values, 3.86 (control) to 3.46 kg (HSW) were not different (P> 0.05). HSW and control BF sections were analyzed for protein solubility and then used to manufacture frankfurters formulated with 2.0% NaCl, 0.5 % sodium tripolyphosphate, 156 ppm sodium nitrite, 0.42 % sodium erythorbate, 2.0 % sucrose, and 25 % water. Frankfurters (cooked to 71 C) were evaluated for cooking yield, CIE L*a*b*, nitrosylhemochrome, Texture Profile Analysis (hardness, cohesiveness), and stress and strain (torsion testing). Compared to the control samples, the HSW did not affect (P>0.05) myofibrillar or sarcoplasmic protein solubility, cooking yield, or color. Textural properties and gel strength of the frankfurters were not affected (P>0.05) by the HSW. These results indicate that beef trim obtained from HSW processed meat can be used interchangeably with normal meat trim in the production of further processed meats since the functionality of meat protein is not affected significantly by the HSW process. / Master of Science

Converging cylindrical shock waves have been studied experimentally. Numericalcalculations based on the Euler equations and analytical comparisons basedon the approximate theory of geometrical shock dynamics have been made tocomplement the study.Shock waves with circular or polygonal shock front shapes have been createdand focused in a shock tube. With initial Mach numbers ranging from 2 to4, the shock fronts accelerate as they converge. The shocked gas at the centreof convergence attains temperatures high enough to emit radiation which isvisible to the human eye. The strength and duration of the light pulse due toshock implosion depends on the medium. In this study, shock waves convergingin air and argon have been studied. In the latter case, the implosion lightpulse has a duration of roughly 10 μs. This enables non-intrusive spectrometricmeasurements on the gas conditions.Circular shock waves are very sensitive to disturbances which deform theshock front, decreasing repeatability. Shocks consisting of plane sides makingup a symmetrical polygon have a more stable behaviour during focusing,which provides less run-to-run variance in light strength. The radiation fromthe gas at the implosion centre has been studied photometrically and spectrometrically.Polygonal shocks were used to provide better repeatability. Thefull visible spectrum of the light pulse created by a shock wave in argon hasbeen recorded, showing the gas behaving as a blackbody radiator with apparenttemperatures up to 6000 K. This value is interpreted as a modest estimation ofthe temperatures actually achieved at the centre as the light has been collectedfrom an area larger than the bright gas core.As apparent from experimental data real gas effects must be taken intoconsideration for calculations at the implosion focal point. Ideal gas numericaland analytical solutions show temperatures and pressures approaching infinity,which is clearly not physical. Real gas effects due to ionisation of theargon atoms have been considered in the numerical work and its effect on thetemperature has been calculated.The propagation of circular and polygonal have also been experimentallystudied and compared to the self-similar theory and geometrical shock dynamics,showing good agreement. / QC 20110502

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 2016 / An 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. / MT2016

Chen, Chao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 43-46). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.7 / Chapter 3 --- The mathematical formulation of the problem and main results --- p.11 / Chapter 4 --- Reformulation of the problem --- p.17 / Chapter 5 --- Proof of the main theorems --- p.23 / Chapter 5.1 --- Proof of uniqueness --- p.23 / Chapter 5.2 --- Proof of non-existence --- p.31 / Chapter 6 --- Work in future --- p.40 / Chapter 7 --- Appendix --- p.41 / Bibliography --- p.43