Characterization of spark-generated N-waves in air using an optical schlieren method

Abstract

Accurate measurement of high-amplitude, broadband shock pulses in air is an important part of laboratory-scale experiments in atmospheric acoustics. Although various methods have been developed, specific drawbacks still exist and need to be addressed. Here, a schlieren optical method was used to reconstruct the pressure signatures of nonlinear spherically diverging short acoustic pulses generated using an electric spark source (2.5 kPa, 33 μs at 10 cm from the source) in homogeneous air. A high-speed camera was used to capture light rays deflected by refractive index inhomogeneities, caused by the acoustic wave. Pressure waveforms were reconstructed from the light intensity patterns in the recorded images using an Abel-type inversion method. Absolute pressure levels were determined by analyzing at different propagation distances the duration of the compression phase of pulses, which changed due to nonlinear propagation effects. Numerical modeling base on the generalized Burgers equation was used to evaluate the smearing of the waveform caused by finite exposure time of the high-speed camera and corresponding limitations in resolution of the schlieren technique. The proposed method allows the study of the evolution of spark-generated shock waves in air starting from the very short distances from the spark, 30 mm, up to 600 mm.

Irregular reflection of weak acoustic shock pulses on rigid boundaries

“…The spatial distribution of the acoustic field is measured using a Z-type schlieren system. [16][17][18] A continuous quartz tungsten halogen white light source (maximum 250 W) creates a light beam between two parallel parabolic mirrors (108 mm diameter, 864 mm focal length) separated by approximately 1.7 m. Optical aberrations are reduced by limiting the off-axis to 2α < 10 • . A spatial filtering is operated with a knife edge located in front of the CMOS camera (Phantom V12), at a distance equal to the focal length f , perpendicularly to the direction of propagation of the shock wave.…”

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

“…Recently, it has been shown that in a homogeneous atmosphere it is possible to accurately reconstruct pressure signals from an electric spark source using optical techniques, in particular from Schlieren images or from interferometer measurements. 20,21 In addition, the temporal resolution of the interferometric method is 0.4 ls, which is 6 times higher than the resolution of a 1/8-in. condenser microphone (2.5 ls).…”

“…The method described for the case of the free field in Ref. 20 to estimate the pressure from the image does not apply here due to the geometry of the wavefront. In addition, the resolution in the temporal and spatial domains is limited by the settings of the camera and the optics.…”

High frequency calibration of MEMS microphones using spherical N-waves

“…At frequencies higher than 100 kHz, it has been observed that the mounting of the sensors and the resonance of their membrane have a great influence on the output signal, which is distorted compared to the incident pressure waveform [3]. This has motivated the development of optical methods to measure weak shock waves [8,9], and a research program to design, fabricate, and characterize MEMS microphones with resonance frequency higher than 500 kHz [10,11]. Hereafter are summarized the methods used to estimate the frequency response of MEMS microphones.…”

“…Both are based on fact that the pressure wave p(r, t) induces locally a variation of the density, and therefore a variation of the local optical index n. If the pressure level is sufficiently high, the deviation of light can be observed. A first optical measurement method of the pressure wave is based on an optical arrangement designed to record Schlieren images as described in reference [8] (Figure 1.b). Under the hypothesis of a spherical wavefront, average light intensity profiles were obtained from the Schlieren photographs.…”