Diffraction of shock waves through a non-quiescent medium

An investigation of shock diffraction through a non-quiescent background medium is presented using both experimental and numerical techniques. Unlike diffracting shocks in quiescent media, a spatial distortion of the shock front occurs, producing a region of constant shock angle. An example of this process arises in the exhaust from a pulse-detonation combustor. As the background velocity is increased, such as through the inclusion of a converging nozzle at the exhaust, the spatial distortion becomes more apparent. Numerical simulations using a compressible Euler solver demonstrate that the distortion is not due to the geometrical influence of the nozzle, but rather is a function of the magnitude of the background flow velocity. The distortion is studied using a modified geometrical shock dynamics formulation which includes the background flow and is validated against experiments. A simple model is presented to predict the shock distortion angle in the weak-shock limit. Finally, the axial decay behaviour of the shock is investigated and it is shown that the advection of the shock by the background flow delays the arrival of the head and tail of the expansion characteristic at the centreline. This leads to an increase in the rate of decay of the shock Mach number as the background flow velocity is increased

Uncertainty Quantification of Kiel Probes for RDC Applications

Kiel probes have the potential to be a versatile tool for determining stagnation pressure gain in rotating detonation combustors (RDCs). Although average pressure gain values determined with Kiel probes are comparable to those from thrust stand experiments, one can expect several interferences from the probe in unsteady trans- and supersonic flow. This work investigates the response of a Kiel probe to highly unsteady flow, similar to that in an RDC. The probe is subjected to an underexpanded starting jet behind an incident shock with Mach numbers of 1.6 to 2.7, emanating from a shock tube with a reservoir ratio of about 394. The incidence angle of the probe is varied between 0° and 90°, as is the probe’s axial location with respect to the tube’s exit plane. High-speed schlieren images reveal the Mach number of the moving shock wave and the structure of the detached bow shock at the Kiel head, which is similar to that of a bluff body. It is shown that the measured stagnation pressure signal is independent of inflow angle over a range of 45°, and that signal attenuation is caused by gas processing through the bow shock and viscous losses in the probe’s capillary. Moving the probe downstream of the shock tube’s exit plane causes a 7% reduction in the measured stagnation pressure, due to the expansion process. The frequency response of the Kiel probe to sinusoidal, small-amplitude pressure fluctuations is determined up to 5600 Hz, confirming that no unwanted Helmholtz resonance is present in the probe. A Berg-Tijdeman representation delivers amplitude ratio and phase lag of comparable magnitude

Diffraction of shock waves through a non-quiescent medium

An investigation of shock diffraction through a non-quiescent background medium is presented using both experimental and numerical techniques. Unlike diffracting shocks in quiescent media, a spatial distortion of the shock front occurs, producing a region of constant shock angle. An example of this process arises in the exhaust from a pulse-detonation combustor. As the background velocity is increased, such as through the inclusion of a converging nozzle at the exhaust, the spatial distortion becomes more apparent. Numerical simulations using a compressible Euler solver demonstrate that the distortion is not due to the geometrical influence of the nozzle, but rather is a function of the magnitude of the background flow velocity. The distortion is studied using a modified geometrical shock dynamics formulation which includes the background flow and is validated against experiments. A simple model is presented to predict the shock distortion angle in the weak-shock limit. Finally, the axial decay behaviour of the shock is investigated and it is shown that the advection of the shock by the background flow delays the arrival of the head and tail of the expansion characteristic at the centreline. This leads to an increase in the rate of decay of the shock Mach number as the background flow velocity is increased