Correlation of the peak pressure generated by an underwater spark discharge with energy absorption in a spark channel

In this paper, we have explained the correlation between the amplitude of the underwater shock pressure generated by a spark discharge in water and the energy absorption in a spark channel. With the well-known theory of shock wave formation by an accelerating piston, the peak pressure is considered to be generated by the energy absorption in the spark channel until the expansion speed of the spark channel reaches its maximum value. To obtain the maximum channel speed, we solve the power balance equation with experimentally measured voltage and current waveforms as a transient heating source of the spark channel. It is found that the experimentally measured peak pressure is well correlated with the energy absorption until the maximum channel expansion speed, irrespective of the operating parameters such as the capacitance and the voltage. It is also found that the energy absorption in the spark channel is significantly influenced by the spark channel resistance, indicating that an appropriate resistance model for the spark channel is necessary for an improved analysis of an underwater spark discharge system. The physics-based estimation of the peak shock pressure presented in this paper is expected to be useful for optimizing underwater spark discharge systems utilized in various application fields.