Modeling and measurements of nonlinear spherically divergent N waves in air

Abstract

Propagation of nonlinear N pulses in relaxing medium was studied experimentally and numerically. An electric spark source was used in laboratory‐scale experiments in ambient air to obtain spherically divergent shock pulses of 30‐s duration and 1000‐Pa peak pressure at 15‐cm distance from the source. Pressure waveforms were measured by the broadband 1/8‐in. microphone at the distances varying from 15 cm to 2 m from the spark source. A numerical solution was obtained for an initial analytic N waveform at the same distances based on the modified Burger’s equation for nonlinear spherical waves in dissipative medium with relaxation. The duration of the initial N wave was defined by matching the zero values of the corresponding analytic measured spectra; the amplitude was obtained by matching the experimental and theoretical nonlinear propagation curves for the N‐wave duration. The results of modeling were found to be in good agreement with the experimental data. A frequency response of the microphone was obtained at various distances as a ratio between the measured and modeled spectra and showed a good reproducibility. The relative effects of relaxation, nonlinearity, and microphone filtering on the N‐waveform parameters are discussed. [Work is supported by RFBR and INTAS grants.]