Abstract
In this study, a system of two equations is developed that allows the time evolution of the underwater spark channel to be calculated numerically from a given power input. The proposed mathematical model utilizes the elliptical coordinates. This approach has the advantage of considering the underwater spark as an expanding ellipsoid, which closely corresponds to experimental observations. Similar to spherical or cylindrical models, the proposed method considers only one spatial coordinate as a function of time, which simplifies the analysis. The predictions of this model are compared with the experimental results.
Highlights
An electrical breakdown in liquids is usually accompanied by a formation of underwater spark
The efficiency of shock wave generation depends on impedance matching between the characteristic impedance of a high voltage pulse generator and the resistance of a spark channel
The cylindrical coordinate system is used for the analytical model and the dynamics of the underwater spark is described by the cylinder radius defined as a function of time
Summary
An electrical breakdown in liquids is usually accompanied by a formation of underwater spark. The efficiency of shock wave generation depends on impedance matching between the characteristic impedance of a high voltage pulse generator and the resistance of a spark channel. It is desirable to increase the resistance of the spark channel by having a long distance between the electrodes. A mathematical simulation of underwater discharge generated in long gap attracts a particular interest. In this case, the cylindrical coordinate system is used for the analytical model and the dynamics of the underwater spark is described by the cylinder radius defined as a function of time.. In an effort to mathematically describe the expansion process of an electrical spark in an uncompressible liquid, we study the Rayleigh method using the elliptic coordinates. The model developed in this paper provides a close approximation of the spark observed in the experiment
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