Irregular reflection of spark-generated shock pulses from a rigid surface: Mach-Zehnder interferometry measurements in air

Abstract

The irregular reflection of weak acoustic shock waves, known as the von Neumann reflection, has been observed experimentally and numerically for spherically diverging waves generated by an electric spark source. Two optical measurement methods are used: a Mach-Zehnder interferometer for measuring pressure waveforms and a Schlieren system for visualizing shock fronts. Pressure waveforms are reconstructed from the light phase difference measured by the interferometer using the inverse Abel transform. In numerical simulations, the axisymmetric Euler equations are solved using finite-difference time-domain methods and the spark source is modeled as an instantaneous energy injection with a Gaussian shape. Waveforms and reflection patterns obtained from the simulations are in good agreement with those measured by the interferometer and the Schlieren methods. The Mach stem formation is observed close to the surface for incident pressures within the range of 800 to 4000 Pa. Similarly, as for strong shocks generated by blasts, it is found that for spherical weak shocks the Mach stem length increases with distance following a parabolic law. This study confirms the occurrence of irregular reflections at acoustic pressure levels and demonstrates the benefits of the Mach-Zehnder interferometer method when microphone measurements cannot be applied.

Spherical shock waveform reconstruction by heterodyne interferometry

“…20 The objective is to compare the use of the two-and three-point deconvolution operators, Eqs. ( 12), (13), and ( 16), which reconstructs the refraction index field directly from the velocity signal, i.e., the projected field, against the three-point deconvolution operator by Dasch, 17 which reconstructs the index time derivative field from the spatial derivative of the velocity field, as in Eq. (8).…”

“…4 Similarly, measurements over solid and irregular surfaces were used to reconstruct pressure waveforms for spark-generated shockwaves at a range of 130 and 330 mm, respectively. 13,14 The fluctuating index of refraction was reconstructed from the measured temporal change in optical phase differences, giving consideration to spatial variations in the fluctuating index over the probe beam. 4,13,14 A spatial waveform is derived from time-series data by assuming the waveform changes little over the duration of the pulse and that the waveform is effectively scanned by a probe beam propagating at the ambient speed of sound toward the shockwave origin.…”

“…13,14 The fluctuating index of refraction was reconstructed from the measured temporal change in optical phase differences, giving consideration to spatial variations in the fluctuating index over the probe beam. 4,13,14 A spatial waveform is derived from time-series data by assuming the waveform changes little over the duration of the pulse and that the waveform is effectively scanned by a probe beam propagating at the ambient speed of sound toward the shockwave origin. 4 This approximation permits use of the Abel integral transform and inverse integral transform for the processing of measurement data.…”