Analysis of shock wave measurements in water by a piezoelectric pressure probe

Abstract

Investigation of underwater electrical wire explosions occurring in the time scale of few microseconds requires a measurement of pressure waves with nanosecond rise time and microsecond fall time. Various types of pressure gauges are used for this purpose, however, none of them seems to be suitable for the task since the frequency range of the pressure waves lies between 107 and 109 Hz, whereas all types of mechanical gauges have a bandwidth below 107 Hz. Therefore, a mathematical processing of measurements is required for reconstruction of the actual pressure wave forms. In this article, a signal processing algorithm, based on energy conservation requirements and Fourier analysis, for reconstruction of the wave form of the pressure wave generated under water by electrical explosion of wires is proposed. The gauge used in the experiments is a PCB 119A12 type pressure gauge with a bandwidth below 1 MHz produced by Piezo-Electronics, Inc. Pressure waves were produced by underwater electrical explosion of a thin wire made of Cu by a current pulse with an amplitude of 30–60 kA having a rise time of a 3 μs. It is shown that the error of the gauge in the measurement of the peak pressure is more than 100%, which leads to an error in the estimation of the energy of almost 300%.

Electrical and Acoustic Parameters of Wire-Guided Discharges in Water: Experimental Determination and Phenomenological Scaling

“…Thus, it is shown that in the case of stabilization of the discharge channel with a thin wire, the acoustic magnitude generated by the discharges is proportional to the length of the wire. This is in agreement with [25], where an analytical equation for the total acoustic energy in the pressure impulse generated by an underwater discharge was shown to be directly proportional to the integral of the squared pressure signal and the length of the wire, . Using (6) and (9), the link between the peak acoustic magnitude, P ac , and the total energy deposited into the plasma channel, W(T), can be derived: Equation (11) follows the form of the empirical relationship between the peak acoustic magnitude produced by a spark discharge in water and the corresponding energy available in the spark discharge used in [26], where it was shown that (11).…”

X-ray radiography of the overheating instability in underwater electrical explosions of wires

“…The latter enables resistive heating to continue efficiently, while the expansion of the wire also drives a strong shock wave through the water, which itself can be used to access high pressure conditions. [5][6][7][8] Monitoring of the current through and voltage across exploding wires has long been used as a basis for resistivity measurements in warm dense matter conditions. However, understanding how the wire expands is crucial to the interpretation of this research.…”

Analytical and Experimental Study of Pressure Dynamics in a Pulsed Water Jet Device

“…This equation has been found to provide an excellent representation of the equation of the state of water for pressures up to 2.5 GPa at temperature range of 20 • -60 • C for n = 7 and B = 321.4 MPa [11]. However, the application of the Tait equation with these empirical constants for lower pressure values between 10-100 MPa has not led to acceptable results [13]. Different constant values have been determined by different scientists based on their experimental data; the comparisons showed that Tait equation is in error at the low pressure range [14].…”