Modeling And Analysis Of Electro-Hydraulic Pulsed Shock Waves Based On "Piston" Model

The shock waves induced by high current pulsed discharge in liquid have the advantages of safety,convenient controllability,and being reproducible,and have been widely used in the fields of solid crushing,electro-hydraulic forming,oil and gas stimulation and so on.The peak value,pulsed width and other characteristics of shock waves greatly affect the effect of shock waves.In the practical application of electro-hydraulic shock waves,the characteristics of shock waves at the action point should be evaluated first.However,the formation process of shock waves involves the breakdown of liquid medium,the expansion and compression process of plasma channel,and the propagation,attenuation,and mutual compression process of shock waves,there are many influencing factors.At present,an effective shock wave characteristic evaluation method has not been formed.Based on the impedance model of plasma channel,the expansion characteristics of plasma channel are calculated by combining the electrical equation of pulsed discharge circuit with the energy balance equation of plasma channel.A current interception test platform has been established in this paper.By analyzing the current interception test results and the expansion characteristics of plasma channel,the influence of deposited energy on shock wave characteristics at each expansion stage of plasma channel is analyzed.Based on the improved“piston”model,an analysis method for the characteristics of electro-hydraulic pulsed shock waves has been proposed.Based on the Braginskii time-varying resistance empirical model of plasma channel Rpl(t)=?l²/Win(t),considering the energy distribution of plasma channel in the initial stage of discharge,the deposited electrical energy of plasma channel Epl(t)is used to replace the internal energy Win(t)in the empirical model.The improved time-varying resistance empirical model of plasma channel Rpl(t)=?l²/Epl(t)is formed,and the calculation process of electrical characteristics of liquid pulsed discharge circuit is simplified.Since the discharge coefficient?in the empirical model is affected by the nature of the liquid and the form of the electrodes,its value is not fixed.A method is proposed to determine the value of discharge coefficient?in the improved time-varying resistance empirical model by comparing the calculation results with the test results of peak value of shock waves.Taking the test condition of lightly filtered tap water medium(conductivity:330?350?S/cm)and the needle-plate electrodes as an example,the value of discharge coefficient?is 1.3×10⁵V²sm^-2 under this test condition.The accuracy of the electrical characteristic and shock wave peak intensity calculation results can be improved by using the discharge coefficient?which matches the test condition.A current interception test platform has been established.It is found that the shock wave waveforms generated by the expansion of plasma channel can be divided into three parts:wave front,transition area and wave tail when the current oscillation period is large.By analyzing the current interception test results and the expansion characteristics of plasma channel,the expansion process of plasma channel is further divided into four stages.It is found that the peak intensity of wave front increases with the increase of the energy deposited in the plasma channel during the channel acceleration expansion stage(stage?),the intensity at the end of the transition area of shock waves increases with the increase of energy deposited in the plasma channel during channel deceleration expansion stage?and stage?,and the intensity at the end of the transition area of shock waves can be higher than the peak intensity of the wave front and it can become a new peak intensity of shock waves.The energy deposited in the plasma channel only affects the wave tail of the shock waves during the channel deceleration expansion stage IV.The improved one-dimensional“piston”model is formed,which can analyze the shock wave characteristics under different test conditions in more detail.Based on the one-dimensional“piston”model,the difference of shock wave characteristics between water gap breakdown and metal wire explosion is analyzed.Under the condition that the channel initial voltage is the same,because the initial current injected in plasma channel formed by metal wire explosion is larger,the energy deposited in the plasma channel formed by metal wire explosion is higher than the energy deposited in the plasma channel formed by water gap breakdown during channel acceleration expansion stage.Therefore,the peak intensity of wave front of shock waves induced by metal wire explosion is higher.It is also found that the time distribution of the energy deposited in the plasma channel formed by water gap breakdown is dispersive under the test condition in this paper.The energy deposited in the plasma channel formed by metal wire explosion is mainly concentrated in 0?20?s after the channel formation.However,only the energy deposited in the initial stage(about 0?20?s)after the formation of the plasma channel contributes to the mechanical energy of the shock waves.Therefore,the energy conversion efficiency of metal wire explosion is higher than that of water gap breakdown.The energy can be concentrated in the initial stage(the first half oscillation period of current)after the formation of the plasma channel by reasonably adjusting the impedance of the discharge circuit of water gap breakdown to make the state of discharge circuit close to the critical damping,which can effectively improve the conversion efficiency from the electrical energy deposited in the plasma channel to the mechanical energy of the shock waves.