A weak shock theory is developed which allows for dense gas effects when the fundamental derivative of gas dynarnics, Γ , becomes small and possibly negative. The nonclassical behavior in these negative Γ regions has potential applications in turbomachinery design. The weak shock development results in a Burgers equation which is then solved numerically using the well-known MacCormack scheme. The results include the demonstration of many non-classical results such as expansion shocks, compression fans, shock-splitting and shock-fan combinations. Results are shown which could help improve turbine efficiency. / M.S.

Turbine aerodynamic designers are currently focusing on unsteady passage flow to increase turbine performance. In particular, for high pressure turbine stages the effects of wakes and shocks shed from an upstream blade row on the downstream blade row need to be understood. Also, experimental data is needed for comparison with unsteady three-dimensional turbine stage calculations. Previous simulations of the unsteady shock/wake inlet flow field for a turbine rotor or stator used a rotating disk with radial bars upstream of a linear cascade. An alternate method of shock generation is developed here using a capped shock tube with multiple outlets to get a traveling system of three shock waves. Different lengths of tubing are used to get time delays between the shocks, which are then introduced at the top of a linear cascade of turbine blades and travel downwards (tangentially) along the leading edge. Advantages of this method include the absence of wakes and excellent two-dimensionality of the inlet shock waves. The period of the incoming shocks is easily adjustable to simulate different Strouhal numbers. Unsteady measurements of upstream total pressure, blade static pressures, and uncorrected downstream total pressure are made for a transonic mean flow with introduction of traveling shocks at M=1.3. An analytical solution (Bach and Lee, 1970) for the decay of cylindrical shock waves is used to estimate the behavior of flow variables other than pressure at the cascade inlet. The unsteady total pressure loss of the blade passage and the unsteady blade forces are measured with one shock passing and with three shocks passing at periods of 0.055 and 0.200 milliseconds. Loss is estimated as the normalized difference in unsteady total pressures and blade forces are integrated from seventeen unsteady surface pressure measurements. The Strouhal number for the 0.200 msec case is 2.9, which is typical of a high-pressure turbine nozzle or rotor. Periodic behavior in blade force and loss are observed for this case. Blade lift shows peak-to-peak variation of 6% and the estimated loss fluctuates by 100%. No change is observed in the average level of loss due to the incident shock waves. / Ph. D.

A finite difference method of investigating the shock layer in the vicinity of the stagnation point in a two-dimensional supersonic flow past a circular cylinder is analyzed. This method differs from existing methods which have been used in the past for solving this type of problem in that it uses the properties along the stagnation streamline as initial conditions. However, the method can still be classified as one of the direct type. A potential flow solution along the stagnation streamline is used to approximate the initial conditions. The results are compared with existing solutions and available experimental data. / Master of Science

The thesis develops the acoustic theory of the propagation of the shook waves produced by an aircraft in supersonic flight through an atmosphere in which the speed of sound decreases linearly with altitude. The problem is first studied in terms of the geometry of the rays along which the shock wave travels away from its point of origin and into the surrounding atmosphere. The equation of the rays is derived and certain important properties of the rays are discussed. It is shown how these results lead to a systematic graphical procedure for determining the location of the shock wave of a maneuvering aircraft. The theory is then considered in terms of the geometry of the "wave fronts" which represent the instantaneous positions of the individual disturbances created along the flight path. The shape of a wave front and its growth with time are determined. From this the equations for the envelope of a one-parameter family of wave fronts are obtained. The envelope equations are solved in parametric form and several examples are worked out which show some effects of flight maneuvers upon shock wave propagation. / M.S.

No description available.

A shock is essentially a propagating variation in the pressure or density of a medium. If the medium is transparent, such as air, and the shock radially symmetric, the refractive fringe diagnostic can be used to examine its general features. A laser beam probes the shock, the central part of the beam, refracted to different degrees by the different density features within the shock, interferes with itself and with the outer unrefracted part creating a series of coarse and fine fringes. By examining this interference pattern one can gain insight into the density profile underlying the shock. A series of such experiments was conducted by the Plasma Physics Research Institute at the University of Natal in 1990. To model the situation computationally, they developed a ray-tracer which produced interference patterns for modified theoretical density profiles based on those predicted by Sedov. After numerous trials, an intensity pattern was produced which agreed approximately with experimental observations. Thus encouraged, the institute then sought to determine density profiles directly from the interference patterns, but a true mathematical deconvolution proved non-trivial and is still awaited. The work presented in this thesis reconstructs the ray-tracer using software engineering techniques and achieves the desired deconvolution by training a neural network of the back-propagation type to behave as an inverse ray-tracer. The ray-tracer is first used to generate numerous density profile - interference pattern pairs. The neural network is trained with this theoretical data to provide a density profile when presented with an interference pattern. The trained network is then tested with experimental interference patterns extracted from captured images. The density profiles predicted by the neural network are then fed back to the ray-tracer and the resultant theoretically determined interference patterns compared to those obtained experimentally. The shock is examined at various times after the initial explosion allowing its propagation to be tracked by its evolving density profile and interference pattern. The results obtained prove superior to those first published by the institute and confirm the neural network's promise as a research tool. Instead of lengthy trial and error sessions with the unaided ray-tracer, experimental interference patterns can be fed directly to an appropriately trained neural network to yield an initial density profile. The network, not the researcher, does the pattern association. / Thesis (M.Sc.)-University of Natal, 1996.

The focus of this work is on the modeling and simulation of shock wave propagation in reactive metal powder mixtures. Reactive metal systems are non-explosive, solid-state materials that release chemical energy when subjected to sufficiently strong stimuli. Shock loading experiments have demonstrated that ultra-fast chemical reactions can be achieved in certain micron-sized metal powder mixtures. However, the mechanisms of rapid mixing that drive these chemical reactions are currently unclear. The goal of this research is to gain an understanding of the shock-induced deformation that enables these ultra-fast reactions. The problem is approached using direct numerical simulation. In this work, a finite element (FE) model is developed to simulate shock wave propagation in discrete particle mixtures. This provides explicit particle-level resolution of the thermal and mechanical fields that develop in the shock wave. The Ni/Al powder system has been selected for study. To facilitate mesoscale FE simulation, a new dislocation-based constitutive model has been developed to address the viscoplastic deformation of fcc metals at very high strain rates. Six distinct initial configurations of the Ni/Al powder system have been simulated to quantify the effects of powder configuration (e.g., particle size, phase morphology, and constituent volume fractions) on deformation in the shock wave. Results relevant to the degree of shock-induced mixing in the Ni/Al powders are presented, including specific analysis of the thermodynamic state and microstructure of the Ni/Al interfaces that develop during wave propagation. Finally, it is shown that velocity fluctuations at the Ni/Al interfaces (which arise due to material heterogeneity) may serve to fragment the particles down to the nanoscale, and thus provide an explanation of ultra-fast chemical reactions in these material systems.

Shock waves have been used in medicine for more than 30 year. At the beginning was mainly use for lithotripsy, but today is also applied in other fields of medicine, such as orthopedics, rheumatology and others. Single shock wave is one shock that usually is repeated every 1-1.5 seconds. By contrast tandem shock waves are two shocks consecutively (ideal interval between shocks is from 8 to 15 microseconds), that are repeated. In this work we investigated the clinical use of single and tandem shock waves that are generated entirely new source. It is based on the principle of multichannel discharge. It was found that a single shock wave can destroy the union between bone and bone cement, this effect could be used in orthopedics. Single and tandem shock wave can damage the tumor in vivo, but the principle damage is different. Tandem shockwave is able to cause damage in a depth of acoustically homogeneous medium and enhances the effect of chemotherapy. It would therefore be possible to used single and tandem shock waves in oncology either alone, or their combination with other chemicals. Functional sample of clinically usable applicator of shock waves with a new source was made for these applications. Powered by TCPDF (www.tcpdf.org)

Shock waves have been used in medicine for more than 30 year. At the beginning was mainly use for lithotripsy, but today is also applied in other fields of medicine, such as orthopedics, rheumatology and others. Single shock wave is one shock that usually is repeated every 1-1.5 seconds. By contrast tandem shock waves are two shocks consecutively (ideal interval between shocks is from 8 to 15 microseconds), that are repeated. In this work we investigated the clinical use of single and tandem shock waves that are generated entirely new source. It is based on the principle of multichannel discharge. It was found that a single shock wave can destroy the union between bone and bone cement, this effect could be used in orthopedics. Single and tandem shock wave can damage the tumor in vivo, but the principle damage is different. Tandem shockwave is able to cause damage in a depth of acoustically homogeneous medium and enhances the effect of chemotherapy. It would therefore be possible to used single and tandem shock waves in oncology either alone, or their combination with other chemicals. Functional sample of clinically usable applicator of shock waves with a new source was made for these applications. Powered by TCPDF (www.tcpdf.org)

The purpose of this study is to examine the propagation of waves of finite deformation in rubbers through experiments and analysis. First, attention is focused on the propagation of one-dimensional dispersive waves in strips of latex and nitrile rubber. Tensile wave propagation experiments were conducted at high strain-rates by holding one end fixed and displacing the other end at a constant velocity. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in rubber strips. Analysis of the response through the theory of finite wave propagation indicated a need for an appropriate constitutive model for rubber; by quantitative matching between the experimental observations and analytical predictions, an appropriate instantaneous elastic response for the rubbers was obtained. This matching process suggested that a simple power-law constitutive model was capable of representing the high strain-rate response for both rubbers used. Next, the propagation of one-dimensional shock waves in strips of latex and nitrile rubber is examined. Shock waves have been generated under tensile impact in pre-stretched rubber strips; analysis of the response yields the tensile shock adiabat for rubbers. The propagation of shocks is analyzed by developing an analogy with the theory of detonation. Attention is then focused on the propagation of unloading waves of finite deformation in a rubber specimen analytically and experimentally. A rubber strip stretched to many times its initial length is released at one end and the resulting unloading is examined. Dispersive waves as well as shock waves are observed in these experiments. Quantitative discrepancies between the analytical model and experimental observations are again used to motivate a power-law model. Hysteresis in the response is attributed to strain-induced crystallization and melting phase transitions in natural latex rubber, and to nonequilibrium microstructural deformation in nitrile rubber. Finally, a Kolsky experiment is conducted and analyzed under the framework of dispersive loading and unloading waves utilized in the previous experiments. In this experiment, a phase boundary is introduced separating low and high strain phases of the rubber and is demonstrated to persist as a stationary boundary in latex rubber. / text