Approximation of Pressure Fields Generated by High-Voltage Discharges in Liquid on a Flat Wall

Pressure fields in electrohydraulic forming often have a very complex character due to the combination of the many physical phenomena involved. Among several energy-force factors generated by underwater discharge, direct shock waves play a leading role in the deformation of the sheet blank. The measuring method based on a multipoint membrane pressure gauge makes it possible to obtain detailed information about shock-wave pressure distribution over a large area (field). The analysis of pressure fields shows three types of loaded segments: zones of direct shock wave loading, zones of shock waves’ interaction, and zones of concentration along lateral rigid walls. In their profile, the pressure distributions in the above-mentioned zones are very similar to the Gaussian distribution curve. The Laplace exponential normalised function was thus selected as a basis for the test approximation dependencies. In the proposed approximation method, the loaded zones are assumed to be independent pressure sources and the principle of superposition is valid. The resulting pressure value at each point is determined as the sum of pressure values from all the loaded zones. The approximation results correlate well with the test data for two simultaneous discharges in a rectangular chamber. The approximations of pressure fields give more exact data on the configuration of each loading zone and its share in the total field formation and can serve as a technological characteristic of a discharge chamber.