Stress wave analysis of high-voltage pulse discharge rock fragmentation based on plasma channel impedance model

Abstract

High voltage pulse discharge (HVPD) rock fragmentation controls the plasma channel to form inside the rock by adjusting the electrical parameters, electrode type, etc. In this paper, a HVPD rock fragmentation test platform was built and the test waveforms were measured. Considering the effects of temperature, channel expansion and electromagnetic radiation, the impedance model of the plasma channel in the rock was established. The parameters and initial values of the model were determined by an iterative computational process. The model calculation results can reasonably characterize the development of plasma channel in rock and estimate the shock wave characteristics. Based on the plasma channel impedance model, the temporal and spatial distribution characteristics of the radial stress and tangential stress in the rock were calculated, and the rock fragmentation effect of the HVPD was analyzed.

Prediction of plasma path and analysis of axial fracturing properties in rock fragmentation by high-voltage pulsed discharge (RHPD)

“…Assuming that the plasma has a cylindrical cross section with a radius of r(t) and a total length of l plasma , its resistance can be described as R p (t) = l plasma /(πr(t) 2 σ plasma (t)), where σ plasma (t) is the conductivity of the plasma. The conductivity σ plasma (t) of the plasma can be expressed as σ plasma (t) = ξT(t) 3/2 × 10 −5000/T(t) [40], ξ is the experimental constant, T(t) is the plasma temperature, and thus the Kirchhoff voltage equation can be expressed as [41],…”

“…The energy E all injected into the plasma is mainly divided into three parts, namely plasma internal energy E in (t), the plasma mechanical energy E m (t) and electromagnetic radi- ation energy E rad (t), that is, E all = E in (t)+ E m (t)+ E rad (t). These four parts of energy can be described as [41],…”

“…In addition, the total number of particles n(t) inside the plasma and radius r(t) satisfy the following equation set [41],…”

“…ρ 0 is the density of the rock. Assume that the plasma satisfies the ideal gas equation of state, as shown below [41],…”