Dedicated to Jürg Fröhlich and Tom Spencer on the occasions of their 60th birthdays.Abstract. We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a stationary Markov process, we show that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.

We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation.

Acoustic characteristics of a pulse detonation engine (PDE) with and without an ellipsoidal reflector are numerically and experimentally investigated. A two-dimensional (2D) non-splitting unstructured triangular mesh Euler solver based on the space-time conservation element and solution element (CE/SE) method is employed to simulate the flow field of a PDE. The numerical results clearly demonstrate the external flow field of the PDE. The effect of an ellipsoidal reflector on the flow field characteristic near the PDE exit is investigated. The formation process of reflected shock wave and reflected jet shock are reported in detail. An acoustic measurement system is established for the PDE acoustic testing. The experimental results show that the ellipsoidal reflector changes the sound waveform and directivity of PDE sound. The reflected shock wave and reflected jet shock result in two more positive pressure peaks in the sound waveform. The ellipsoidal reflector changes the directivity of PDE sound from 20 • to 0 • . It is found that the peak sound pressure level (PSPL) and overall sound pressure level (OASPL) each obtain an increment when the PDE is installed with a reflector. The maximum relative increase ratio of PSPL and OASPL are obtained at the focus point F 2 , whose values are 6.1% and 6.84% respectively. The results of the duration of the PDE sound indicate that the reflecting and focusing wave generated by the reflector result in the increment of A duration and B duration before and near focus point F 2 . Results show that the ellipsoidal reflector has a great influence on the acoustic characteristic of PDE sound. The research is helpful for understanding the influence of an ellipsoidal reflector on the formation and propagation process of PDE sound.

Acoustic characteristics of pulse detonation engine (PDE) sound propagating in enclosed space are numerically and experimentally investigated. The finite element software LS-DYNA is utilized to numerically simulate the PDE sound propagating in enclosed space. Acoustic measurement systems are established for testing the PDE sound in enclosed space, and the time-frequency characteristics of PDE sound in enclosed space are reported in detail. The experimental results show that the sound waveform of PDE sound in enclosed space are quite different from those in open space, and the reflection and superposition of PDE sound on the walls of enclosed space results in the sound pressure oscillating obviously. It is found that the peak sound pressure level (PSPL) and overall sound pressure level (OASPL) of PDE sound in enclosed space are higher than those in open space and their difference increases with the rise of propagation distance. The results of the duration of PDE sound indicate that the A duration of PDE sound in enclosed space is higher than that in open space except at measuring points located at 2-m and 5-m while the B duration is higher at each of all measuring points. Results show that the enclosed space has a great influence on the acoustic characteristic of PDE sound. This research is helpful in performing PDE experiments in enclosed laboratories to prevent the PDE sound from affecting the safety of laboratory environment, equipment, and staffs.

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Instantaneous and precise velocity sensing is a critical part of research on detonation mechanism and flow evolution. This paper presents a novel multi-projection tunable diode laser absorption spectroscopy solution, to provide a real-time and reliable measurement of velocity distribution in detonation exhaust flow with obvious nonuniformity. Relations are established between overlapped spectrums along probing beams and Gauss velocity distribution phantom according to the frequency shifts and tiny variations in components of light-of-sight absorbance profiles at low frequencies analyzed by the fast Fourier transform. With simulated optical measurement using H2O feature at 7185.6 cm−1 carried out on a phantom generated using a simulation of two-phase detonation by a two-fluid model, this method demonstrates a satisfying performance on recovery of velocity distribution profiles in supersonic flow even with a noise equivalent absorbance up to 2 × 10−3. This method is applied to the analysis of rapidly decreasing velocity during a complete working cycle in the external flow field of an air-gasoline detonation tube operating at 25 Hz, and results show the velocity in the core flow field would be much larger than the arithmetic average from traditional tunable diode laser doppler velocimetry. This proposed velocity distribution sensor would reconstruct nonuniform velocity distribution of high-speed flow in low cost and simple operations, which broadens the possibility for applications in research on the formation and propagation of external flow filed of detonation tube.

Acoustic characteristics of the detonation sound wave generated by a pulse detonation engine with an annular nozzle, including peak sound pressure, directivity, and A duration, are experimentally investigated while utilizing gasoline as fuel and air as oxidizer. Three annular nozzle geometries are evaluated by varying the ratio of inner cone diameter to detonation tube exit diameter from 0.36 to 0.68. The experimental results show that the annular nozzles have a significant effect on the acoustic characteristics of the detonation sound wave. The annular nozzles can amplify the peak sound pressure of the detonation sound wave at 90 deg while reducing it at 0 deg and 30 deg. The directivity angle of the detonation sound wave is changed by annular nozzles from 30 deg to 90 deg. The A duration of the detonation sound wave at 90 deg is also increased by the annular nozzles. These changes indicate that the annular nozzles have an important influence on the acoustic energy distribution of the detonation sound wave, which amplify the acoustic energy in a direction perpendicular to the tube axis and weaken it along the direction of the tube axis.