A method for calculating the characteristics and excitation properties of underwater arc discharge plasma channels.

Abstract

The present invention discloses a method for calculating the characteristics of an arc discharge plasma channel and shock wave characteristics in water. The invention regards the arc channel resistivity as a function of temperature, and the arc channel is equivalent to a cylindrical time-varying model; constructs an energy conservation relationship, establishes an energy conservation equation, and describes the energy time-varying characteristics; according to Kirchhoff's law, the arc channel inductance is ignored, and an equivalent discharge loop equation is established; after iterative calculation, the characteristics of the arc discharge plasma channel and shock wave characteristics in water are calculated. Through the present invention, the modeling and analysis of the cylindrical plasma channel of arc discharge in water is realized, which reflects the plasma development and motion characteristics of the main discharge process of the water discharge, and the relationship between the various variables of the cylindrical plasma channel can also be quantitatively calculated. Deepening the understanding of the discharge process of arc discharge in water and the transmission process of pressure waves has guiding significance for revealing the mechanism of arc discharge plasma in water.

Description

Technical Field

[0001] The invention relates to the technical field of liquid dielectric discharge monitoring under high electric field, and in particular to a method for calculating channel characteristics and shock wave characteristics of arc discharge plasma in water. Background Art

[0002] Pulse discharge plasma in water is formed by the charge on a high-power capacitor being discharged to electrodes in water through a discharge switch. High-voltage pulse discharge in water is accompanied by intense force, electromagnetic, acoustic, thermal, optical and chemical effects, known as the "liquid-electric effect". High-power electrical energy is injected in a very short time (microseconds), and the discharge current is as high as 10 4 A order of magnitude, a discharge cavity will be generated in this process. The liquid around the cavity has weak compressibility, and a strong shock wave is radiated outward at the interface between the cavity and the liquid medium. It is precisely because of this characteristic that underwater arc discharge is currently mainly used in the fields of liquid electroforming, water treatment, rock crushing, oil and gas unblocking, etc.

[0003] After the liquid gap is broken down, part of the energy deposited in the arc channel is converted into mechanical energy transmitted outward, part is converted into radiation energy, and another part is power loss. In this process, the arc channel resistance is converted into a time-varying variable. At present, many domestic scholars mainly conduct experimental research, using voltage probes and current probes to monitor the two ends of the electrode in real time to obtain the volt-ampere characteristics of the two ends of the arc; using pressure wave sensors to monitor the shock waves generated in the water to obtain the transmission characteristics of the pressure wave. However, through experimental methods, this phenomenon can only be described and analyzed, and a theoretical model of the characteristics of arc discharge plasma and shock waves in water has not been established, resulting in insufficient theoretical and systematic research in this area.

[0004] Building a model of the characteristics of arc discharge plasma and shock wave characteristics in water has guiding significance for revealing the phenomenon of high-voltage pulse discharge in water, and promotes more systematic and theoretical research in this direction. In the process of engineering practice, it is of great significance for reasonably estimating shock wave energy and shock wave amplitude and improving energy utilization. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the channel characteristics and shock wave characteristics of underwater arc discharge plasma, regard the underwater arc plasma as a cylindrical channel with time-varying conductivity, and use the energy conservation equation and Kirchhoff's law to build a numerical model, so as to simulate the development process and development characteristics of the main discharge stage of underwater arc discharge, reveal the mechanism of the phenomenon of underwater arc discharge, and have guiding significance for improving the energy conversion rate in engineering practice.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A method for calculating arc discharge plasma channel characteristics and shock wave characteristics in water comprises the following steps:

[0008] S1, the arc channel resistivity is regarded as a function of temperature, and the arc channel is equivalent to a cylindrical time-varying model;

[0009] S2, construct the energy conservation relationship, establish the energy conservation equation, and describe the time-varying characteristics of energy;

[0010] S3, according to Kirchhoff's law, ignoring the arc channel inductance, establish the equivalent discharge circuit equation;

[0011] S4, after iterative operation, the calculation of the channel characteristics and shock wave characteristics of the arc discharge plasma in water is realized.

[0012] Optionally, in the step S1, the arc channel resistivity is regarded as a function of temperature, and the arc channel is equivalent to a cylindrical time-varying model, which specifically includes:

[0013] The plasma channel length can be regarded as the electrode spacing, the arc channel volume can be regarded as the cylinder volume, the arc channel surface area and the arc channel resistance value can also be regarded as functions of the cylinder radius, and the arc channel pressure is related to the differential value of the arc channel radius. The formulas are as follows:

[0014] V=πa 2 l

[0015] S=2πal

[0016]

[0017]

[0018] Among them, V represents the volume of the cylindrical arc, S represents the surface area of ​​the cylindrical arc, a represents the radius of the cylindrical arc, l represents the length of the cylindrical arc, R represents the resistance of the cylindrical arc, σ(T) represents the conductivity of the cylindrical arc, α and β represent the shock wave coefficients, and ρ w represents the density of water, and p represents the pressure in the arc channel;

[0019] σ(T) can be regarded as a function of the arc channel temperature, and its differential expression is as follows:

[0020]

[0021] Where T is the arc channel temperature and ξ is the plasma conductivity coefficient.

[0022] Optionally, in step S2, constructing an energy conservation relationship, establishing an energy conservation equation, and describing the time-varying characteristics of energy specifically includes:

[0023] The power of the electric energy injected into the channel converted into Joule heat can be expressed by the sum of the energy change rate in the channel and the mechanical power exerted by the channel on the liquid. The radiation power and thermal conductivity power can be obtained by coupling related physical parameters. The formulas are as follows:

[0024]

[0025]

[0026] Q R =σ s T 4 S

[0027]

[0028] Among them, γ is the isentropic index, I is the arc channel current, Q R is the radiated power, Q T is the thermal conductivity, σ S is the Stefan radiation constant, k is the Boltzmann constant;

[0029] Through the above formula, the qualitative analysis of arc discharge in water can be realized from the energy perspective, and the time-varying characteristics of the arc channel discharge stage can be described.

[0030] Optionally, in step S3, according to Kirchhoff's law, the arc channel inductance is ignored and an equivalent discharge circuit equation is established, which specifically includes:

[0031] Establish an equivalent circuit for arc discharge in water, treat the arc channel as a resistor, and ignore the influence of time-varying inductance. According to Kirchhoff's law, the relationship between current and external circuit can be obtained:

[0032]

[0033] U C =q / C

[0034] I=-dq / dt

[0035] Among them, U c is the voltage of the main capacitor of the external circuit, L is the inductance of the external circuit, q is the charge of the main capacitor of the external circuit, C is the main capacitor of the external circuit, R cir Total resistance of the external circuit.

[0036] Optionally, in step S4, after iterative calculation, the calculation of the arc discharge plasma channel characteristics and shock wave characteristics in water is realized as follows:

[0037] After setting reasonable initial values ​​and performing iterative calculations, the calculation of the characteristics of the arc discharge plasma channel in water can be realized. When the shock wave propagates in water, the cylindrical channel can be equivalent to a sphere using the volume equality principle, and the equivalent radius can be calculated, and then the pressure characteristics at the distant point of the shock wave can be calculated. The specific formula is as follows:

[0038] a s =(3a 2 l) 1 / 3

[0039]

[0040] t r =t+r / c0

[0041] Among them, a s is the equivalent radius of the sphere, p w is the shock wave pressure at distance r, t r is the time at distance r, c0 represents the speed of sound in water. By processing the iterative data through the above formula, the waveform characteristics of the shock wave at any point in the water can be obtained, and the pressure characteristics of the shock wave at the distant point in the water can be calculated.

[0042] The beneficial effect of the present invention is that through the present invention, modeling and analysis of arc discharge plasma in water can be realized, which can not only reflect the development and motion characteristics of the arc plasma channel, but also can quantitatively calculate the equivalent resistance, shock wave pressure, channel current, etc. of the arc channel during the main discharge process. It can promote the theoreticalization and systematization of the arc discharge process in water, and has guiding significance for revealing the arc discharge mechanism in water. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Attached Figure 1 The present invention is a flow chart of a method for calculating channel characteristics and shock wave characteristics of an underwater arc discharge plasma.

[0044] Attached Figure 2 Schematic diagram of a cylindrical arc channel model in an embodiment of the present invention.

[0045] Attached Figure 3 Schematic diagram of the discharge circuit of the main discharge process in an embodiment of the present invention.

[0046] Attached Figure 4 This is a simulation diagram of the current waveform of the main discharge process in an embodiment of the present invention.

[0047] Attached Figure 5 This is a simulation diagram of the shock wave waveform at r=0.5m during the main discharge process in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] like Figure 1 As shown, the present invention is used for a method for calculating the channel characteristics and shock wave characteristics of an arc discharge plasma in water, comprising the following steps:

[0050] S1, the arc channel resistivity is regarded as a function of temperature, and the arc channel is equivalent to a cylindrical time-varying model;

[0051] S2, construct the energy conservation relationship, establish the energy conservation equation, and describe the time-varying characteristics of energy;

[0052] S3, according to Kirchhoff's law, ignoring the arc channel inductance, establish the equivalent discharge circuit equation;

[0053] S4, after iterative operation, the calculation of the channel characteristics and shock wave characteristics of the arc discharge plasma in water is realized.

[0054] Wherein, in the step S1, the arc channel resistivity is regarded as a function of temperature, and the arc channel is equivalent to a cylindrical time-varying model, which specifically includes:

[0055] The plasma channel length can be regarded as the electrode spacing, the arc channel volume can be regarded as the cylinder volume, the arc channel surface area and the arc channel resistance value can also be regarded as functions of the cylinder radius, and the arc channel pressure is associated with the arc channel radius differential value, and the formulas are as follows:

[0056] V=πa 2 l

[0057] S=2πal

[0058]

[0059]

[0060] Wherein, V represents the volume of the cylindrical arc; S represents the surface area of ​​the cylindrical arc; a represents the radius of the cylindrical arc; l represents the length of the cylindrical arc, and in this embodiment, l=0.3 mm; R represents the resistance of the cylindrical arc; σ(T) represents the conductivity of the cylindrical arc; α and β represent the shock wave coefficients, α=0.3001 GPa, β=0.3 GPa; ρ w represents the density of water, ρ w =1000kg / m 3 ; p represents the pressure inside the arc channel.

[0061] σ(T) can be regarded as a function of the arc channel temperature, and its differential expression is as follows:

[0062]

[0063] Where T represents the arc channel temperature; ξ is the plasma conductivity coefficient, ξ=1.411×10 -2 ;

[0064] The schematic diagram of the cylindrical arc channel model in this embodiment is shown in the attached figure. Figure 2 shown.

[0065] The step S2 also includes: constructing an energy conservation relationship, establishing an energy conservation equation, and describing the time-varying characteristics of energy, specifically:

[0066] The power of the electric energy injected into the channel converted into Joule heat can be expressed by the sum of the energy change rate in the channel and the mechanical power exerted by the channel on the liquid. The radiation power and thermal conductivity power can be obtained by coupling related physical parameters. The formulas are as follows:

[0067]

[0068]

[0069] Q R =σ S T 4 S

[0070]

[0071] Where γ is the isentropic index, γ = 1.22; I is the arc channel current; Q R is the radiation power; Q T is the thermal conductivity; σ S is the Stefan radiation constant, σ S =5.67×10 -8 W / (m 2 ·K 4 );k is the Boltzmann constant, k=1.38×10 -23 J / K;

[0072] Through the above formula, the qualitative analysis of arc discharge in water can be realized from the energy perspective, and the time-varying characteristics of the arc channel discharge stage can be described.

[0073] In step S3, according to Kirchhoff's law, ignoring the arc channel inductance, an equivalent discharge circuit equation is established, which specifically includes:

[0074] Establish an equivalent circuit for arc discharge in water, treat the arc channel as a resistor, and ignore the influence of time-varying inductance. According to Kirchhoff's law, the relationship between current and external circuit can be obtained:

[0075]

[0076] U C =q / C

[0077] I=-dq / dt

[0078] Among them, U c is the voltage of the main capacitor of the external circuit; L is the inductance of the external circuit, L = 6.35μH; q is the charge of the main capacitor of the external circuit; C is the main capacitor of the external circuit, C = 0.786μF; R cir Total resistance of external circuit, R cir =403.2mΩ;

[0079] The schematic diagram of the discharge circuit of the main discharge process in this embodiment is shown in the attached figure. Figure 3 As shown; the simulation diagram of the current waveform of the main discharge process in this embodiment is shown in the attached Figure 4 shown.

[0080] In step S4, after iterative calculation, the calculation of the arc discharge plasma channel characteristics and shock wave characteristics in water is realized, which is specifically as follows:

[0081] Reasonable initial values ​​were set for iterative calculations. Among them, the initial radius a = 0.1 mm, the initial current I = 0, the initial current change rate dI / dt = -U0 / L, where U0 = 40000 V, the initial plasma channel resistance R = 200 Ω, and the initial internal pressure p = 1.85 × 10 8 Pa.

[0082] After iterative calculation, the calculation of the characteristics of the arc discharge plasma channel in water can be realized. When the shock wave propagates in water, the cylindrical channel can be equivalent to a sphere using the volume equality principle, and the equivalent radius can be calculated, and then the pressure characteristics at the distant point of the shock wave can be calculated. The specific formula is as follows:

[0083] a s =(3a 2 l) 1 / 3

[0084]

[0085] t r =t+r / c0

[0086] Among them, a s is the equivalent radius of a sphere; p w is the shock wave pressure at distance r; t r is the time at a distance r; c0 represents the speed of sound in water, c0 = 1500m / s.

[0087] By processing the iterated data through the above formula, the waveform characteristics of the shock wave at any point in the water can be obtained, and the pressure characteristics at the distant point of the shock wave in the water can be calculated.

[0088] In this embodiment, the simulation diagram of the shock wave waveform at r = 0.5m during the main discharge process is shown in the attached figure. Figure 5 As shown;

[0089] The beneficial effect of the present invention is that through the present invention, the modeling and analysis of the arc discharge plasma channel in water can be realized, which can not only deeply understand the development and movement characteristics of the arc plasma channel, but also can quantitatively analyze the change characteristics of physical quantities such as voltage, current, channel radius, and distant shock wave during the main discharge stage of the arc discharge in water. The invention is conducive to reasonably estimating the discharge energy and improving the energy conversion efficiency, and has guiding significance for actual engineering practice.

Claims

1. A method for calculating channel characteristics and shock wave characteristics of arc discharge plasma in water, characterized in that: The following steps are involved: S1, the arc channel resistivity is regarded as a function of temperature, and the arc channel is equivalent to a cylindrical time-varying model; S2, construct the energy conservation relationship, establish the energy conservation equation, and describe the time-varying characteristics of energy, including: The power of the electric energy injected into the channel converted into Joule heat can be expressed by the sum of the energy change rate in the channel and the mechanical power exerted by the channel on the liquid. The radiation power and thermal conductivity power can be obtained by coupling the relevant physical parameters. The formulas are as follows: Q R =σ S T 4 S Among them, γ is the isentropic index, I is the arc channel current, Q R is the radiated power, Q T is the thermal conductivity, σ S is the Stefan radiation constant, k is the Boltzmann constant; Through the above formula, the qualitative analysis of arc discharge in water can be realized from the energy perspective, and the time-varying characteristics of the arc channel discharge stage can be described; S3, according to Kirchhoff's law, ignoring the arc channel inductance, establish the equivalent discharge circuit equation; S4, setting a reasonable initial value of the shock wave internal pressure and performing iterative calculations to realize the calculation of the channel characteristics and shock wave characteristics of the arc discharge plasma in water, specifically including: After setting a reasonable initial value of the shock wave internal pressure and performing iterative calculations, the calculation of the characteristics of the arc discharge plasma channel in water can be realized. When the shock wave is transmitted in water, the cylindrical channel can be equivalent to a sphere using the volume equality principle, and the equivalent radius can be calculated, and then the pressure characteristics at the shock wave prospect can be calculated. The specific formula is as follows: a s =(3a 2 l) 1 / 3 t r =t+r / c0 Among them, a s is the equivalent radius of the sphere, p w is the shock wave pressure at distance r, t r is the time at distance r, c0 represents the speed of sound in water; By processing the iterated data through the above formula, the waveform characteristics of the shock wave at any point in the water can be obtained, and the pressure characteristics at the distant point of the shock wave in the water can be calculated; The arc channel deposition energy can be obtained from the above arc channel current equation and arc channel instantaneous power equation.

2. The method for calculating the plasma channel characteristics of the main discharge process of arc discharge in water according to claim 1, characterized in that: In the step S1, the arc channel resistivity is regarded as a function of temperature, and the arc channel is equivalent to a cylindrical time-varying model, which specifically includes: The plasma channel length can be regarded as the electrode spacing, the arc channel volume can be regarded as the cylinder volume, the arc channel surface area and the arc channel resistance value can also be regarded as functions of the cylinder radius, and the arc channel pressure is related to the differential value of the arc channel radius. The formulas are as follows: V=πa 2 l S=2πal Among them, V represents the volume of the cylindrical arc, S represents the surface area of ​​the cylindrical arc, a represents the radius of the cylindrical arc, l represents the length of the cylindrical arc, R represents the resistance of the cylindrical arc, σ(T) represents the conductivity of the cylindrical arc, α and β represent the shock wave coefficients, and ρ w represents the density of water, and p represents the pressure in the arc channel; σ(T) can be regarded as a function of the arc channel temperature, and its differential expression is as follows: Where T is the arc channel temperature and ξ is the plasma conductivity coefficient.

3. The method for calculating channel characteristics and shock wave characteristics of underwater arc discharge plasma according to claim 1, characterized in that: In step S3, according to Kirchhoff's law, ignoring the arc channel inductance, an equivalent discharge circuit equation is established, which specifically includes: Establish an equivalent circuit for arc discharge in water, treat the arc channel as a resistor, and ignore the influence of time-varying inductance. According to Kirchhoff's law, the relationship between current and external circuit can be obtained: U c =q / C I=-dq / dt Among them, U c is the voltage of the main capacitor of the external circuit, L is the inductance of the external circuit, q is the charge of the main capacitor of the external circuit, C is the main capacitor of the external circuit, R cir Total resistance of the external circuit.

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