A method for calculating the amplitude of shock waves in hydro-electric effect

Abstract

The present invention discloses a method for calculating the shock wave amplitude in the hydroelectric effect. The method applies a nanosecond pulse voltage to both ends of the electrode, calculates the ionization generation term at the initial moment based on the field ionization Zener equation; establishes an arc plasma fluid dynamics model, performs iterative operations, and calculates the electric field intensity distribution and particle concentration distribution between the electrodes at any time; uses the data after the model iterative operation to calculate the instantaneous current, instantaneous power, and deposited energy of the plasma arc channel; and realizes the calculation of the amplitude of the shock wave generated in the main discharge stage of the streamer. Through the present invention, modeling and analysis of nanosecond pulse discharge in water can be achieved, which can not only reflect the starting and development characteristics of arc plasma, but also quantitatively calculate the current, instantaneous power, deposited energy and shock wave amplitude after breakdown. Deepening the understanding of the discharge process and shock wave transmission process of nanosecond pulse discharge in water has guiding significance for revealing the connection between the two processes.

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 shock wave amplitude in liquid-electric effect. Background Art

[0002] Based on traditional power technology, pulse power technology has gradually emerged in recent years. As one of its branches, underwater high-voltage pulse discharge produces physical and chemical effects that are widely used in waste treatment, oil production increase, rock crushing and other fields.

[0003] When high voltage pulse discharge occurs in liquid, a strong explosion will occur in the liquid, and the impact pressure can reach 10 2 -10 4 Mpa, which is the so-called hydro-electric effect. During the discharge process, an arc plasma channel will be generated, and the arc channel is the carrier for the conversion of electrical energy into mechanical energy. The electrode spacing will significantly affect the streamer development process, the inter-electrode electric field strength and the distribution of net charge density, thereby affecting the electrode breakdown time and the deposition of arc channel energy, thereby affecting the shock wave amplitude in the hydro-electric effect. As the main product of the hydro-electric effect, the accurate calculation of the shock wave amplitude is of great significance for practical engineering applications.

[0004] A fluid plasma model is established to analyze the ionization of the medium and the convergence of ions before the formation of the streamer, the development speed of the streamer, the migration of ions in the streamer channel, and the distortion of the original electric field by the compound, and the quantitative calculation of the instantaneous power, instantaneous current and energy, so as to achieve the accurate calculation of the shock wave amplitude generated in the main discharge stage of the streamer. Accurate analysis of the factors affecting the hydro-electrochemical effect and the development process of the arc channel can deepen the understanding of the mechanism of shock wave generation in the hydro-electrochemical effect and provide a theoretical basis for the calculation method of the shock wave amplitude in the hydro-electrochemical effect. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the shock wave amplitude in the liquid-electric effect, to establish a physical model for the plasma arc discharge process in water, to describe the field ionization, electric field distortion, particle diffusion, particle adsorption, and particle recombination processes, to quantitatively calculate the plasma current, power, energy, and shock wave amplitude, to deepen the understanding of the discharge process and shock wave transmission process of nanosecond pulse discharge in water, and to have guiding significance for revealing the connection between the two processes.

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

[0007] A method for calculating the amplitude of shock waves in a hydroelectric effect comprises the following steps:

[0008] S1, applying nanosecond pulse voltage to both ends of the electrode, and calculating the ionization generation term at the initial moment based on field ionization;

[0009] S2, establish the arc plasma fluid dynamics model, perform iterative operations, and calculate the electric field intensity distribution and particle concentration distribution between electrodes at any time, as follows:

[0010]

[0011] Among them, ε r Represents the relative dielectric constant of liquid water medium, ε 0 represents the vacuum dielectric constant, q represents the electron charge, n e The three symbols represent H + OH - , the charge density of e, D e are the diffusion rates of the three particles, μ e They represent the mobility of the three particles, τ is the electron-water molecule adsorption time, Respectively represent H + The recombination rate of and e, H + and OH - The compound rate;

[0012] S3, using the data after model iteration operation, calculate the instantaneous current, instantaneous power and deposition energy of the plasma arc channel, as follows:

[0013]

[0014] P(t)=u(t)I(t) (7)

[0015] E pl =∫p(t)dt (8)

[0016] Among them, the streamer radius r after the plasma arc breakdown can be obtained from the radial particle concentration distribution 2 , N A is Avogadro's constant;

[0017] The arc channel deposition energy (8) can be obtained from the arc channel current equation (6) and the arc channel instantaneous power equation (7);

[0018] S4, realizing the calculation of the amplitude of the shock wave generated during the main discharge stage of the streamer, specifically including:

[0019] The empirical expression of deposition energy and shock wave amplitude is obtained by fitting a large number of experimental data obtained from the hydroelectric effect, as follows:

[0020] P=k×E pl 0.54 (9)

[0021]

[0022] Where k is the streamer polarity coefficient in water, which is related to the streamer polarity. 1 Indicates the rising edge time of the applied voltage, t 2 The falling edge time of the applied voltage is represented by formulas (9)-(10), which can be used to calculate the shock wave amplitude.

[0023] Optionally, in the step S1, a nanosecond pulse voltage is applied to both ends of the electrode, and an ionization generation term at the initial moment is calculated based on field ionization, specifically including:

[0024] The nanosecond pulse voltage can use the double exponential pulse lightning wave equation, and the voltage equation, the empirical formula of the field strength at the tip of the needle electrode, and the field ionization calculation equation can be used to calculate the ionization generation term at the initial moment. The formulas are as follows:

[0025] u(t)=U c (e -αt -e -βt ) (11)

[0026]

[0027] Among them, U c is the amplitude of the pulse voltage, α is the wavefront coefficient, and β is the wavetail coefficient. 1 is the tip radius of the needle electrode, L is the distance between electrodes, q is the electron charge, n 0 is the number of ionizable water molecules per unit volume, is the electric field strength, h is Planck's constant, a is the molecular distance, m * is the effective electron mass, and Δ is the ionization energy of water.

[0028] Based on a large amount of experimental data fitting, it is found that μ e The empirical formulas for calculation are as follows (14)-(15):

[0029]

[0030] The specific method for calculating τ is as follows:

[0031]

[0032]

[0033] Among them, k t represents the heat transfer coefficient of water, λ e represents the electron decay length, C vis the specific heat capacity of water.

[0034] Combine the continuity equations (2)-(4) of hydrogen ions, hydroxide ions and electrons to describe the generation, recombination and adsorption mechanisms of the three particles during the flow process;

[0035] The drift and diffusion motion of charged particles will change the original electric field distribution. The Poisson equation (5) is used to express the coupling relationship between the electric field and the space charge, which can specifically express the interaction between the space charges and the distortion effect of the space charge on the electric field. By coupling (1)-(5) and (14)-(18), the updated electric field intensity distribution and particle concentration distribution can be obtained.

[0036] The beneficial effect of the present invention is that through the present invention, modeling and analysis of nanosecond pulse discharge in water can be realized, which can not only reflect the initiation and development characteristics of arc plasma, but also quantitatively calculate the current, instantaneous power, deposition energy and shock wave amplitude after breakdown. It can deepen the understanding of the discharge process and shock wave transmission process of nanosecond pulse discharge in water, and has guiding significance for revealing the connection between the two processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 The present invention is a flow chart of a method for calculating the amplitude of shock waves in the hydro-electric effect.

[0038] Figure 2 2 is a waveform diagram of an externally applied voltage in an embodiment of the present invention.

[0039] Figure 3 This is the underwater needle-plate electrode model in the embodiment of the present invention.

[0040] Figure 4 Graph showing the temporal and spatial distribution of the electric field intensity in an embodiment of the present invention.

[0041] Figure 5 This is a cloud diagram of the electron density distribution of the water stream breakdown in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] 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.

[0043] like Figure 1 As shown, the method for calculating the shock wave amplitude in the hydroelectric effect of the present invention comprises the following steps:

[0044] S1, applying nanosecond pulse voltage at both ends of the electrode, and calculating the ionization generation term at the initial moment based on field ionization;

[0045] S2, establish the arc plasma fluid dynamics mathematical model, perform iterative operations, and calculate the electric field distribution and particle concentration distribution between electrodes at any time, as follows:

[0046]

[0047] Among them, ε r Represents the relative dielectric constant of liquid water medium, ε 0 represents the vacuum dielectric constant, q represents the electron charge, n e The three symbols represent H + OH - , the charge density of e, D e are the diffusion rates of the three particles, μ e They represent the mobility of the three particles, τ is the electron-water molecule adsorption time, Respectively represent H + The recombination rate of and e, H + and OH - The compound rate;

[0048] S3, using the data after model iteration operation, calculate the instantaneous current, instantaneous power and deposition energy of the plasma arc channel, as follows:

[0049]

[0050] P(t)=u(t)I(t) (7)

[0051] E pl =∫p(t)dt (8)

[0052] Among them, the streamer radius r after the plasma arc breakdown can be obtained from the radial particle concentration distribution 2 , N A is Avogadro's constant;

[0053] The arc channel deposition energy (8) can be obtained from the arc channel current equation (6) and the arc channel instantaneous power equation (7);

[0054] S4, realizes the calculation of the amplitude of the shock wave generated by the main discharge process, as follows:

[0055] P=k×E pl 0.54 (9)

[0056]

[0057] Where k is the streamer polarity coefficient in water, which is related to the streamer polarity. 1Indicates the rising edge time of the applied voltage, t 2 The falling edge time of the applied voltage is represented by formulas (9)-(10), which can be used to calculate the shock wave amplitude.

[0058] Wherein, in the step S1, a nanosecond pulse voltage is applied to both ends of the electrode, and the ionization generation term at the initial moment is calculated based on the field ionization, specifically including:

[0059] The nanosecond pulse voltage can use the double exponential pulse lightning wave equation, and the voltage equation, the empirical formula of the field strength at the tip of the needle electrode, and the field ionization calculation equation can be used to calculate the ionization generation term at the initial moment. The formulas are as follows:

[0060] u(t)=U c (e -αt -e -βt ) (11)

[0061]

[0062] Among them, U c is the amplitude of the pulse voltage, α is the wavefront coefficient, and β is the wavetail coefficient. 1 is the tip radius of the needle electrode, L is the distance between electrodes, q is the electron charge, n 0 is the number of ionizable water molecules per unit volume, is the electric field strength, h is Planck's constant, a is the molecular distance, m * is the effective electron mass, and Δ is the ionization energy of water.

[0063] The specific voltage waveform applied in this embodiment is as shown in the attached Figure 2 As shown; the electrode structure is a needle plate electrode, the specific structure is as shown in the attached Figure 3 shown.

[0064] Based on a large amount of experimental data fitting, it is found that μ e The empirical formulas for calculation are as follows (14)-(15):

[0065]

[0066] The specific method for calculating τ is as follows:

[0067]

[0068] Among them, k t represents the heat transfer coefficient of water, λ e represents the electron decay length, C v is the specific heat capacity of water.

[0069] Combine the continuity equations (2)-(4) of hydrogen ions, hydroxide ions and electrons to describe the generation, recombination and adsorption mechanisms of the three particles during the flow process;

[0070] The drift and diffusion motion of charged particles will change the original electric field distribution. The Poisson equation (5) is used to express the coupling relationship between the electric field and the space charge, which can specifically express the interaction between the space charges and the distortion effect of the space charge on the electric field. By coupling (1)-(5) and (14)-(18), the updated electric field intensity distribution and particle concentration distribution can be obtained.

[0071] The temporal and spatial distribution of the electric field intensity in the embodiment of the present invention is shown in the attached figure. Figure 4 As shown, the electron density distribution cloud diagram of the streamer breakdown in water is as follows Figure 5 shown.

[0072] Table 1 Main physical parameters of the control equation

[0073] parameter Symbols and units Numeric Electron charge q(C) <![CDATA[1.602×10 -19 ]]> Number of water molecules per unit volume <![CDATA[n 0 (m -3 )]]> <![CDATA[3.344×10 28 ]]> Distance between water molecules a(nm) 0.31 Planck constant h(J·s) <![CDATA[6.626×10 -34 ]]> Vacuum dielectric constant <![CDATA[ε 0 (F / m)]]> <![CDATA[8.85×10 -12 ]]> Electron effective mass <![CDATA[m * (kg)]]> <![CDATA[9.1×10 -32 ]]> Relative dielectric constant of water <![CDATA[ε r ]]> 83.83 Electron decay length <![CDATA[λ e (mm)]]> 1 Water heat transfer coefficient <![CDATA[k t (W / (m 2 ·K))]]> 0.599 Avogadro's constant <![CDATA[N A ]]> <![CDATA[6.02×10 23 ]]> Specific heat of water <h2 style=";text-align:left;direction:ltr"><![CDATA[C <h2 style=";text-align:left;direction:ltr"> v <h2 style=";text-align:left;direction:ltr"> (J / (kg·K))]]><h2 style=";text-align:left;direction:ltr"> <![CDATA[4.2×10 3 ]]>

[0074] The present invention obtains the values ​​of the physical quantity parameters in each control equation by consulting multidisciplinary data, as shown in Table 1. According to the values ​​of each parameter in Table 1, each formula is substituted and the formula is solved and calculated.

[0075] The beneficial effects of the present invention are as follows: through the present invention, modeling and analysis of nanosecond pulse discharge in water can be realized, which can not only deeply understand the initiation and development characteristics of arc plasma, but also quantitatively calculate the current, instantaneous power, deposition energy and shock wave amplitude after breakdown. From a microscopic perspective, the discharge process and shock wave transmission process of nanosecond pulse discharge in water are deeply understood, providing a new perspective for revealing the connection between the two processes.

Claims

1. A method for calculating the amplitude of shock waves in the hydro-electric effect, It is characterized in that The following steps are involved: S1, applying nanosecond pulse voltage to both ends of the electrode, and calculating the ionization generation term at the initial moment based on the field ionization Zener equation; S2, establish the arc plasma fluid dynamics model, perform iterative operations on equations (1)-(5), and calculate the electric field intensity distribution and particle concentration distribution between electrodes at any time, as follows: Among them, ε r Represents the relative dielectric constant of liquid water medium, ε 0 represents the vacuum dielectric constant, q represents the electron charge, n e The three symbols represent H + OH - , the charge density of e, D e are the diffusion rates of the three particles, μ e They represent the mobility of the three particles, τ is the electron-water molecule adsorption time, Respectively represent H + The recombination rate of and e, H + and OH - The recombination rate, q is the electron charge, n 0 is the number of ionizable water molecules per unit volume, is the electric field strength, h is Planck's constant, a is the molecular distance, m * is the effective electron mass, Δ is the ionization energy of water; S3, using the data after model iteration operation, calculate the instantaneous current, instantaneous power and deposition energy of the plasma arc channel, as follows: P(t)=u(t)I(t) (7) E pl =∫p(t)dt (8) Among them, the streamer radius r after the plasma arc breakdown can be obtained from the radial particle concentration distribution 2 , N A is Avogadro's constant; The arc channel deposition energy (8) can be obtained from the arc channel current equation (6) and the arc channel instantaneous power equation (7); S4, realizing the calculation of the amplitude of the shock wave generated during the main discharge stage of the streamer, specifically including: The empirical expression of deposition energy and shock wave amplitude is obtained by fitting a large number of experimental data obtained from the hydroelectric effect, as follows: P=k×E pl 0.54 (9) Among them, k is the streamer polarity coefficient in water, which is related to the streamer polarity, t 1 Indicates the rising edge time of the applied voltage, t 2 Indicates the falling edge time of the applied voltage, U c represents the amplitude of the pulse voltage, L represents the electrode spacing, and the shock wave amplitude can be calculated using formulas (9)-(10).

2. A method for calculating the amplitude of shock waves in the hydroelectric effect according to claim 1, It is characterized in that In the step S1, a nanosecond pulse voltage is applied to both ends of the electrode, and the ionization generation term at the initial moment is calculated based on the field ionization Zener equation, which specifically includes: The nanosecond pulse voltage can use the double exponential pulse lightning wave equation, and the voltage equation, the empirical formula of the field strength at the tip of the needle electrode, and the field ionization calculation equation can be used to calculate the ionization generation term at the initial moment. The formulas are as follows: u(t)=U c (e -αt -e -βt ) (11) Among them, U c is the amplitude of the pulse voltage, α is the wavefront coefficient, β is the wavetail coefficient, r 1 is the tip radius of the needle electrode, L is the distance between electrodes, q is the electron charge, n 0 is the number of ionizable water molecules per unit volume, is the electric field strength, h is Planck's constant, a is the molecular distance, m * is the effective electron mass, Δ is the ionization energy of water; According to the above formula, the electric field intensity distribution between electrodes at the initial moment and the initial term of field ionization can be calculated to describe the generation of space charge.

3. A method for calculating the amplitude of shock waves in the hydroelectric effect according to claim 1, It is characterized in that The arc plasma fluid dynamics model is established. μ e , The calculation method of τ is as follows: Among them, k t represents the heat transfer coefficient of water, λ e represents the electron decay length, C v Represents the specific heat capacity of water.

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