A spark-generated bubble model with semi-empirical mass transport

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Abstract
This paper describes the time evolution of bubbles generated by underwater electrical discharges. The oscillations of these high-temperature vapor and plasma bubbles generate acoustic signatures similar to the signatures generated by air guns, underwater explosions, and combustible sources. A set of model equations is developed that allows the time evolution of the bubble generated by a spark discharge to be calculated numerically from a given power input. The acoustic signatures produced by the model were compared to previously recorded experimental data, and the model was found to agree over wide ranges of energy and ambient pressure on several characteristic values of the acoustic signatures. The bubble period in particular matched very well between model and experiment, indicating that the total energy losses predicted by the model over the oscillation of the bubble were approximately correct, although no reliable information was gained about the relative magnitudes of the individual energy loss mechanisms examined. The bubble period and the minimum rarefaction pressure were found to depend on depth, while the peak pressures in the expansion and collapse pulses and the acoustic energy in the expansion pulse were not found to depend on depth over the parameter ranges investigated.

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