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Focusing of strong shock waves in a gas-filled thin test section with various forms of the reflector boundary is investigated. The test section is mounted at the end of the horizontal co-axial shock tube. Two different methods to produce shock waves of various forms are implemented. In the first method the reflector boundary of the test section is exchangeable and four different reflectors are used: a circle, a smooth pentagon, a heptagon and an octagon. It is shown that the form of the converging shock wave is influenced both by the shape of the reflector boundary and by the nonlinear dynamic interaction between the shape of the shock and the propagation velocity of the shock front. Further, the reflected outgoing shock wave is affected by the shape of the reflector through the flow ahead of the shock front. In the second method cylindrical obstacles are placed in the test section at various positions and in various patterns, to create disturbances in the flow that will shape the shock wave. It is shown that it is possible to shape the shock wave in a desired way by means of obstacles. The influence of the supports of the inner body of the co-axial shock tube on the form of the shock is also investigated. A square shaped shock wave is observed close to the center of convergence for the circular and octagonal reflector boundaries but not in any other setups. This square-like shape is believed to be caused by the supports for the inner body. The production of light, as a result of shock convergence, has been preliminary investigated. Flashes of light have been observed during the focusing and reflection process. / QC 20101126

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

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Master of Science / Department of Mechanical and Nuclear Engineering / Steven Eckels / Both cavitating and flashing flows are important phenomena in fluid flow. Cavitating flow, a common consideration in valves, orifices, and metering devices, is also a concern in loss of coolant accidents for liquid water in power plants when saturation pressures are below atmospheric pressure. Flashing flow is a common consideration for devices such as relief and expansion valves and fluid injectors as well as for loss of coolant accidents in which the coolant’s saturation pressure is above atmospheric. Of the two phenomena, flashing flow has received greater interest due to its applicability to safety concerns, though cavitating flow is perhaps of greater interest in terms of energy efficiency. It is possible for cavitating and flashing flow to actually become sonic. That is, the local velocity of a fluid can exceed the local speed of sound due to the unique properties of two-phase mixtures. When a flow becomes sonic, it is possible for the flow to accelerate and impose additional energy losses that would not otherwise occur. Models of this aspect of two-phase flow are not well developed, typically only being presented for the case of constant area ducts. In this paper two models for cavitating sonic flow are developed and described by applying the integral forms of the mass, momentum, and energy equations to a control volume of variable cross-sectional area. These models, based on the homogeneous equilibrium model (HEM) and separated flow model, are then applied to experimental data taken by the author with R-134a as the fluid of interest. Experimental data were taken with four instrumented converging-diverging nozzles of various geometries using a custom testing rig that allowed for precise control and measurement of flow parameters such as mass flow, temperature, and pressure. The resultant data from the models are then examined, focusing on the resultant velocities, Mach numbers, quality, and shear stresses.

[pt] Neste trabalho, desenvolveremos um modelo teórico baseado em extensão do modelo de Misme e Fimbel para a determinação da distribuição cumulativa da atenuação diferencial devida à chuva entre dois enlaces convergentes. Resultados do modelo desenvolvido serão comparados com medidas realizadas na cidade de São Paulo e no Japão. Adicionalmente, apresentaremos previsões do modelo para os efeitos das variações do ângulo entre os enlaces, assim como dos seus comprimentos, sobre a distribuição cumulativa da atenuação diferencial. Em seguida, calcularemos a indisponibilidade do enlace desejado sujeito à interferência de outro enlace convergente, indicando que a consideração da atenuação simultânea nos dois enlaces permite um dimensionamento capaz de utilizar o espectro eletromagnético de forma mais eficiente. / [en] In this work, we will develop a theoretical model based on an extension of the Misme and Fimbel model for the determination of the cumulative distribution of the rain differential attenuation between two converging links. Results from the developed model will be compared with measurements performed in the City of São Paulo and in Japan. Additionally, we will present model predictions for the effects of variations in the angle between the links and in the path lengths on the cumulative distribution of the rain differential attenuation. Next, we will determine the unavailability of a link in the presence of interference from another converging link. It will be indicated that consideration of the possibility of simultaneous attenuation on both links leads to a more efficient use of the electromagnetic spectrum.

Both experimental and numerical investigations of converging shock waves have been performed. In the experiments, a shock tube was used to create and study converging shock waves of various geometrical shapes. Two methods were used to create polygonally shaped shocks. In the first method, the geometry of the outer boundary of the test section of the shock tube was varied. Four different exchangeable shapes of the outer boundary were considered: a circle, a smooth pentagon, a heptagon, and an octagon. In the second method, an initially cylindrical shock wave was perturbed by metal cylinders placed in various patterns and positions inside the test section. For three or more regularly spaced cylinders, the resulting diffracted shock fronts formed polygonal shaped patterns near the point of focus. Regular reflection was observed for the case with three cylinders and Mach refection was observed for cases with four or more cylinders. When the shock wave is close to the center of convergence, light emission is observed. An experimental investigation of the light emission was conducted and results show that the shape of the shock wave close to the center of convergence has a large influence on the amount of emitted light. It was found that a symmetrical polygonal shock front produced more light than an asymmetrical shape. The shock wave focusing was also studied numerically using the Euler equations for a gas obeying the ideal gas law with constant specific heats. Two problems were analyzed; an axisymmetric model of the shock tube used in the experiments and a cylindrical shock wave diffracted by cylinders in a two dimensional test section. The results showed good agreement with the experiments. The temperature field from the numerical simulations was investigated and shows that the triple points behind the shock front are hot spots that increase the temperature at the center as they arrive there. As a practical example of shock wave focusing, converging shocks in an electrohydraulic lithotripter were simulated. The maximum radius of a gas bubble subjected to the pressure field obtained from the lithotripter was calculated and compared for various geometrical shapes and materials of the reflector. Results showed that the shape had a large impact while the material did not influence the maximum radius of the gas bubble. / QC 20100706

[pt] Neste trabalho foi analisado o escoamento de fluidos não Newtonianos através de canais axisimétricos convergentes divergentes. A solução da conservação de massa e de conservação de momento foi obtida numericamente via volumes finitos utilizando o programa de computador Fluent. A equação constitutiva de fluidos Newtonianos generalizados foi utilizada para modelar o comportamento não Newtoniano, utilizando a equação constitucional de Shunk-Scriven para cálculo da viscosidade, que assume como sendo a média geométrica ponderada pelo classificador de escoamento R entre a viscosidade de cisalhamento e a viscosidade de extensão. Os resultados de perda de pressão e vazão são comparados com os resultados calculados pela relação simplificada proposta por Souza Mendes e Naccache, 2002 entre a perda de carga e vazão de fluidos viscoelásticos fluindo através do meio poroso, para analisar a sua performance. / [en] In this work, the flow of non-Newtonian fluids through axisimmetric convergingdiverging channels is analyzed. The solution of mass and momentum conservation equations is obtained numerically via finite volume technique using the Fluent software. The Generalized Newtonian Fluid constitutive equation was used to model the non- Newtonian fluid behavior, using the Shunk-Scriven model for the viscosity, where a weighted geometric mean by the flow classifier R between shear and extensional viscosities is assumed. The results of pressure drop and flow rate are compared to the ones predicted by a previously proposed simplified relation (Souza Mendes and Naccache, 2002) between pressure drop and flow rate, for viscoelastic fluids flow through porous media, in order to analyze its performance.

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