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Reflection of an obliquely incident solitary wave at a vertical wall is studied experimentally in the laboratory wave tank. Precision measurements of water-surface variations are achieved with the aid of laser-induced fluorescent (LIF) technique and detailed temporal and spatial features of the Mach reflection are captured. During the development stage of the reflection process, the stem wave is formed with the wave crest perpendicular to the wall; this stem wave is not in the form of a Korteweg-de Vries (KdV) soliton but a forced wave, trailing by a continuously broadening depression wave. Evolution of stem-wave amplification is in good agreement with the Kadomtsev-Petviashvili (KP) theory. The asymptotic characteristics and behaviors are also in agreement with the theory of Miles (1977b) except those in the neighborhood of the transition between the Mach reflection and the regular reflection. The maximum fourfold amplification of the stem wave at the transition predicted by Miles is not realized in the laboratory environment: the maximum amplification measured in the laboratory is 2.92, which is however in excellent agreement with the numerical results of Tanaka (1993). The present laboratory study is the first to sensibly analyze validation of the theory; note that substantial discrepancies exist from previous (both numerical and laboratory) experimental studies. Agreement between experiments and theory can be partially attributed to the large-distance measurements that the precision laboratory apparatus is capable of. More important, to compare the laboratory results with theory, the corrected interaction parameter is derived from proper interpretation of the theory in consideration of the finite incident wave angle. Our laboratory data indicate that the maximum stem wave can reach higher than the maximum solitary wave height. The wave breaking along the wall results in the substantial increase in wave height and slope away from the wall. Extending the foregoing study on the reflection of a single solitary wave at a vertical wall, laboratory and numerical experiments are performed on two co-propagating obliquely incident solitary waves with different amplitudes that are reflected at the wall. The larger wave catches up with the smaller wave; hence the two waves collide with the strong interaction. The resulting wave pattern near the wall is complex due to the interaction among the two incident solitons and the two reflected solitons. The numerical predictions of the KP theory are in good agreement with the experimental results. Another comparison of the KP theory with laboratory experiments is demonstrated for one of the exact soliton solutions of the KP equation by Chakravarty and Kodama (2009). This solution is called the T-type solution by Kodama. The theoretically predicted formation of the 'box'-shape wave pattern in the vicinity of two-soliton intersection is realized in the laboratory tank. The agreement between the laboratory observation and the KP theory is found better for the cases with the larger wave amplitude a and smaller oblique angle ψ (i.e. tan ψ/(√3a cos ψ) < 0.6). Subtle and unavoidable differences among the analytical KP solution, the setup of numerical calculation, and the laboratory condition are discussed. / Graduation date: 2013

A numerical investigation of the interaction of a planar shock wave with a rigid wedge and cone in an air-filled shock tube is performed by computing the unsteady flow field of the interaction process. The Euler and Navier-Stokes equations are solved in two dimensions to produce flow solutions for regular and Mach reflections with and without the viscous and thermal boundary layer on the inclined surface. The transition boundary between these two patterns is determined by changing both the shock strength and the angle of the inclined surface so that the simulations are perpendicular to the theoretical transition boundary. The numerically determined boundaries are compared to the theoretical boundaries predicted by two- and three- shock theories and with results obtained from experiments. The results show that the transition boundary between regular and Mach reflection is different not only for wedges and cones but also for inviscid and viscous numerical solutions.

A numerical investigation of the interaction of a planar shock wave with a rigid wedge and cone in an air-filled shock tube is performed by computing the unsteady flow field of the interaction process. The Euler and Navier-Stokes equations are solved in two dimensions to produce flow solutions for regular and Mach reflections with and without the viscous and thermal boundary layer on the inclined surface. The transition boundary between these two patterns is determined by changing both the shock strength and the angle of the inclined surface so that the simulations are perpendicular to the theoretical transition boundary. The numerically determined boundaries are compared to the theoretical boundaries predicted by two- and three- shock theories and with results obtained from experiments. The results show that the transition boundary between regular and Mach reflection is different not only for wedges and cones but also for inviscid and viscous numerical solutions.

A system for recording the trajectories of non-planar shocks and particle tracers within a shock tube flow has been developed. The optics consists of a double-pass schlieren system with a multiply pulsed ruby laser as light source. The laser is synchronized with a high speed framing camera. A grid of ammonium chloride tracers is injected into the flow field, and the motion of the tracers behind the Mach reflection of intermediate strength shocks has been recorded. Analysis of the trajectories has yielded the space and time variation of the physical properties within the flow field. / Graduate / 0605

Detonation waves are supersonic combustion waves that have a multi-shock front structure followed by a spatially non-uniform reaction zone. During propagation, a de-coupled shock-flame complex is periodically re-initiated into an overdriven detonation following a transient Mach reflection process. Past researchers have identified mechanisms that can increase combustion rates and cause localized hot spot re-ignition behind the Mach shock. But due to the small length scales and stochastic behaviour of detonation waves, the important mechanisms that can lead to re-initiation into a detonation requires further clarification. If a detonation is allowed to diffract behind an obstacle, it can quench to form a de-coupled shock-flame complex and if allowed to form a Mach reflection, re-initiation of a detonation can occur. The use of this approach permits the study of re-initiation mechanisms reproducibly with relatively large length scales. The objective of this study is to experimentally elucidate the key mechanisms that can increase chemical reaction rates and sequentially lead to re-initiation of a de-coupled shock-flame complex into an overdriven detonation wave following a Mach reflection. All experiments were carried out in a thin rectangular channel using a stoichiometric mixture of oxy-methane. Three different types of obstacles were used - a half-cylinder, a roughness plate along with the half-cylinder and a full-cylinder. Schlieren visualization was achieved by using a Z-configuration setup, a high speed camera and a high intensity light source. Results indicate that forward jetting of the slip line behind the Mach stem can potentially increase combustion rates by entraining hot burned gas into unburned gas. Following ignition and jet entrainment, a detonation wave first appears along the Mach stem. The transverse wave can form a detonation wave due to rapid combustion of unburned gas which may be attributed to shock interaction with the unburned gas. Alternatively, the Kelvin-Helmholtz instability can produce vortices along the slipline that may lead to mixing between burned-unburned gases and potentially increase combustion rates near the transverse wave. However, the mechanism(s) that causes the transverse wave to re-initiate into a detonation wave remains to be satisfactorily resolved.

Detonation waves are supersonic combustion waves that have a multi-shock front structure followed by a spatially non-uniform reaction zone. During propagation, a de-coupled shock-flame complex is periodically re-initiated into an overdriven detonation following a transient Mach reflection process. Past researchers have identified mechanisms that can increase combustion rates and cause localized hot spot re-ignition behind the Mach shock. But due to the small length scales and stochastic behaviour of detonation waves, the important mechanisms that can lead to re-initiation into a detonation requires further clarification. If a detonation is allowed to diffract behind an obstacle, it can quench to form a de-coupled shock-flame complex and if allowed to form a Mach reflection, re-initiation of a detonation can occur. The use of this approach permits the study of re-initiation mechanisms reproducibly with relatively large length scales. The objective of this study is to experimentally elucidate the key mechanisms that can increase chemical reaction rates and sequentially lead to re-initiation of a de-coupled shock-flame complex into an overdriven detonation wave following a Mach reflection. All experiments were carried out in a thin rectangular channel using a stoichiometric mixture of oxy-methane. Three different types of obstacles were used - a half-cylinder, a roughness plate along with the half-cylinder and a full-cylinder. Schlieren visualization was achieved by using a Z-configuration setup, a high speed camera and a high intensity light source. Results indicate that forward jetting of the slip line behind the Mach stem can potentially increase combustion rates by entraining hot burned gas into unburned gas. Following ignition and jet entrainment, a detonation wave first appears along the Mach stem. The transverse wave can form a detonation wave due to rapid combustion of unburned gas which may be attributed to shock interaction with the unburned gas. Alternatively, the Kelvin-Helmholtz instability can produce vortices along the slipline that may lead to mixing between burned-unburned gases and potentially increase combustion rates near the transverse wave. However, the mechanism(s) that causes the transverse wave to re-initiate into a detonation wave remains to be satisfactorily resolved.

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