Breakdown judgment method for discharge in water

Abstract

The invention provides a breakdown judgment method for discharge in water. According to the method, a circuit model, a bubble model and a water discharge breakdown judgment method of a traditional gas discharge breakdown theory are combined, and quantitative analysis and accurate judgment of the breakdown process are achieved through simulation solution of the bubble state. And the dynamic change of the bubble internal breakdown condition during water discharge can be quantitatively calculated. The water discharge breakdown judgment method provided by the invention is suitable for quantitatively judging the occurrence of bubble internal breakdown generated by bubble-shaped stream during discharge.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater pulse discharge, and in particular to a method for judging the breakdown of underwater discharge. Background Art

[0002] Underwater pulse discharge (IPD) involves applying nanosecond to microsecond high-voltage pulses between electrodes immersed in water, causing the water medium to break down and form a plasma channel. Due to its unique physical and chemical effects, IPD technology has been widely used in materials processing, medical treatment, wastewater treatment, and other fields. Under the action of the high-voltage pulse, Joule heating and liquid vaporization at the electrode tip generate tiny bubbles. When the electric field strength exceeds the breakdown threshold of water, the localized liquid water molecules undergo a phase transition, forming an initial bubble. As a low-density region, the internal electric field strength of the bubble is significantly higher than that of the surrounding water medium, causing rapid ionization of the gas molecules. The initial free electrons within the bubble are accelerated by the strong electric field, triggering an electron avalanche through impact ionization, ultimately forming a streamer discharge. After breakdown, the high temperature and pressure within the bubble cause the plasma channel to rapidly expand, accompanied by the release of a shock wave. Accurately determining discharge breakdown is critical to ensuring the stable and efficient operation of this technology.

[0003] However, current methods for determining underwater discharge breakdown primarily rely on statistical methods to summarize breakdown characteristics. These methods, such as the classic Martin equation, are based on empirical relationships between breakdown voltage, gap distance, and water quality parameters, derived through experiments. However, this traditional statistical approach relies on empirical formulas and lacks in-depth physical meaning. This method can only predict breakdown characteristics within a limited range, making it difficult to achieve accurate judgments.

[0004] Therefore, the present invention proposes a method for judging bubble breakdown under underwater discharge, which contributes new research ideas to this technical field. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for determining the breakdown of underwater discharge to solve the problems existing in the prior art.

[0006] The technical solution adopted to achieve the purpose of the present invention is as follows: a method for determining the breakdown of underwater discharge, comprising the following steps:

[0007] 1) Parameter initialization and time determination. c0 , pulse application time t m And the input of bubble initial conditions r0, r′0, r"0 parameters. Determine whether the current time t is greater than or equal to the pulse application time t m If so, the gap is determined to be incapable of breakdown. Otherwise, the initialized parameters are passed to the corresponding circuit model and bubble model.

[0008] 2) Establish a circuit model and a bubble model and solve them. The circuit model includes the circuit topology, impedance characteristic equation, and circuit transient equation. The bubble model includes the energy balance equation, bubble dynamics equation, and saturated steam equation, forming a set of self-consistent differential equations. The bubble power P is obtained by solving the circuit model. b and bubble partial pressure U b ,. Among them, the bubble power P b Input into the bubble model. Obtain the bubble radius r by solving the bubble model b , temperature T b and pressure p b Isostate parameters, where the bubble radius r b input into the circuit model.

[0009] 3) Breakdown judgment. The bubble pressure p obtained in step 2) is b Substitute Paschen's law to obtain the breakdown voltage U br . Make a breakdown judgment and compare U br Is it greater than or equal to U obtained in step 2) b If so, the gap is determined to have broken down, and the process ends. Otherwise, the next breakdown determination process is entered, t becomes t+Δt, and steps 1) to 3 are repeated. The theoretical breakdown voltage is calculated based on Paschen's law for gas discharge breakdown:

[0010]

[0011] Where A and B are constants related to the gas type, and γ is the secondary electron emission coefficient. b Substitute to obtain the corresponding breakdown voltage U br .

[0012] Furthermore, the circuit model regards the bubbles and water as two resistors connected in series or in parallel. s 、L s and discharge capacitor C g The circuit topology that constitutes the second-order RLC.

[0013] Furthermore, when the bubble resistance and water resistance are considered to be in parallel, the circuit transient equation is as follows:

[0014]

[0015] R g =R b ||R l (3)

[0016] Among them, R b 、R lare the air bubble and water medium resistances, respectively, and are determined using the impedance characteristic equation obtained based on finite element simulation results.

[0017] The bubble input power is obtained through the circuit model. The dynamic equation uses the classic RP equation to describe the relationship between pressure and radius. Assuming that the interior of the bubble is saturated steam, the relationship between pressure and temperature is described by the saturated steam equation:

[0018]

[0019] The bubble model is iteratively solved to obtain the bubble radius and pressure r b 、p b Numerical solution of .

[0020] Furthermore, it can be applied to the precise analysis of water switches or the design optimization of pulse power devices.

[0021] The technical effects of the present invention are unquestionable:

[0022] A. Combine the circuit model, bubble model and traditional gas discharge breakdown theory to judge the underwater discharge breakdown. Through the simulation solution of the bubble state, the quantitative analysis and accurate judgment of the breakdown process can be achieved.

[0023] B. Quantitative analysis can clarify the breakdown dispersion of water switches with different structures, and screen the optimal structure to improve the operating stability of the equipment.

[0024] C. Enable pulse power devices to be intelligently optimized from empirical design. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a breakdown judgment flow chart;

[0026] Figure 2 is the impedance characteristic equation curve based on finite element simulation;

[0027] Figure 3 is the simulation result of the bubble model;

[0028] Figure 4 This is the breakdown judgment result. DETAILED DESCRIPTION

[0029] The present invention will be further described below with reference to the following examples, but it should not be understood that the scope of the present invention is limited to the following examples. Without departing from the above technical ideas of the present invention, various substitutions and modifications can be made according to common technical knowledge and customary means in the art, and all should be included in the scope of protection of the present invention.

[0030] Example 1:

[0031] See also Figure 1This embodiment provides a method for determining the breakdown of underwater discharge, comprising the following steps:

[0032] 1) Parameter initialization and time determination; voltage U c0 , pulse application time t m And the input of bubble initial condition radius r0, velocity r′0, acceleration r"0 parameters; determine whether the current time t is greater than or equal to the pulse application time t m If so, it is determined that the gap cannot be penetrated; otherwise, the initialized parameters are passed to the corresponding circuit model and bubble model;

[0033] 2) Establish and solve a circuit model and a bubble model; the circuit model includes the circuit topology, impedance characteristic equation, and circuit transient equation; the bubble model includes the energy balance equation, bubble dynamics equation, and saturated steam equation, forming a set of self-consistent differential equations; the input voltage of the circuit model is the voltage value across the capacitor at the beginning of discharge, and the input of the bubble model is the state of the initial bubble generated when the voltage is applied to the water gap, including the bubble size, expansion speed, and acceleration, which can be observed by a high-speed camera. The bubble power P is obtained by solving the circuit model. b and bubble partial pressure U b ,; where the bubble power P b Input into the bubble model; obtain the bubble radius r by solving the bubble model b , temperature T b and pressure p b Isostate parameters, where the bubble radius r b input into a circuit model; the circuit model regards the air bubble and the water as two resistors in a series or parallel relationship;

[0034] The bubble input power in the energy balance equation is obtained through the circuit model and converted into the bubble's internal energy, mechanical energy, and external heat conduction. The dynamic equation uses the classic RP equation to describe the relationship between pressure and radius. Assuming that the interior of the bubble is saturated steam, the relationship between pressure and temperature is described by the saturated steam equation:

[0035]

[0036] The bubble model is iteratively solved to obtain the bubble radius and pressure r b 、p b Numerical solution of .

[0037] 3) Breakdown judgment; the bubble pressure p obtained in step 2) is b Substituting into Paschen's law, we get the breakdown voltage U br ; Make breakdown judgment and compare U br Is it greater than or equal to U obtained in step 2) bIf yes, the gap is judged to have broken down and the process ends; otherwise, the process enters the next breakdown judgment process, t becomes t+Δt, and steps 1) to 3) are repeated; wherein, the calculation of the theoretical breakdown voltage is based on Paschen's law of gas discharge breakdown:

[0038]

[0039] Among them, A and B are constants related to the gas type, γ is the secondary electron emission coefficient; the bubble pressure p obtained by the bubble model is b Substitute to obtain the corresponding breakdown voltage U br .

[0040] Example 2:

[0041] The main contents of this embodiment are the same as those of embodiment 1. In particular, taking the case of a bubble streamer penetrating the electrode gap as an example, a circuit model of discharge in water is established in combination with the external discharge circuit and the electrode gap. The bubble and water are regarded as two parallel resistors, and the equivalent impedance R of the external circuit is s 、L s and discharge capacitor C g The circuit topology of the second-order RLC circuit is as follows:

[0042]

[0043] R g =R b ||R l (2)

[0044] Among them, R b 、R l are the resistances of the air bubble and water medium, respectively, which are determined by the impedance characteristic equation, which is obtained based on the finite element simulation results. Figure 2 This is the impedance characteristic equation curve based on finite element simulation.

[0045] A self-consistent bubble model is established based on the energy balance equation, bubble dynamics equation, and saturated steam equation, as shown in Equation (3). The bubble input power is obtained through the circuit model and converted into the bubble's internal energy, kinetic energy, and external heat conduction. The dynamics equation uses the classic RP equation to describe the relationship between its pressure and radius. Assuming that the interior of the bubble is saturated steam, the saturated steam equation is used to describe the relationship between its pressure and temperature.

[0046]

[0047] The bubble model is iteratively solved to obtain the bubble radius and pressure r b 、p b The numerical solution of Figure 3 shown.

[0048] When a discharge in water produces a bubble-like streamer, breakdown occurs inside the bubble, which can be considered as gas breakdown. Therefore, the calculation of the theoretical breakdown voltage is based on Paschen's law for gas discharge breakdown:

[0049]

[0050] Among them, A and B are constants related to the gas type, and γ is the secondary electron emission coefficient. It can be seen that the breakdown voltage V b It is a function of the product of gas pressure p and gap distance d. When the gap distance is constant, the breakdown voltage and gas pressure have a one-to-one mapping relationship. The bubble pressure p obtained by the bubble model is b Substituting it into the equation, we can get the corresponding breakdown voltage U br , the comparison results of breakdown voltage and gap voltage are as follows Figure 4 shown.

[0051] Example 3:

[0052] The main content of this embodiment is the same as that of embodiment 1 or 2, wherein this embodiment is applied to the precise analysis of water switches or the design optimization of pulse power devices. The present invention obtains a method for quantitatively judging the breakdown of discharge in water by calculating the state of bubbles generated in the water gap during pulse discharge in water. This method takes into account the influence of the electrical characteristics of the discharge circuit and the state of bubbles on whether breakdown occurs or not. The quantitative judgment method obtained by the present invention can reliably judge the breakdown of the water gap under different discharge conditions, thereby being applied to the application optimization of pulse discharge in water and the design optimization of pulse power devices. When using a breakdown model based on an empirical formula to judge whether a breakdown occurs, a probabilistic judgment can only be made within a fixed and limited parameter range. The method proposed by the present invention can quantitatively calculate the dynamic changes of the breakdown conditions in the bubble during discharge in water. The method for judging the breakdown of discharge in water proposed by the present invention is suitable for quantitatively judging the occurrence of breakdown in the bubble under the generation of bubble-like streamers during discharge.

Claims

1. A method for determining breakdown of underwater discharge, characterized in that: The following steps are involved: 1) Parameter initialization and time determination; voltage U c0 , pulse application time t m And the input of bubble initial conditions r0, r′0, r"0 parameters; determine whether the current time t is greater than or equal to the pulse application time t m ,If it is true, the gap is determined to be impenetrable; Otherwise, the initialized parameters are passed to the corresponding circuit model and bubble model; 2) Establishing a circuit model and a bubble model and solving them; the circuit model includes the circuit topology, impedance characteristic equation, and circuit transient equation; the bubble model includes the energy balance equation, bubble dynamics equation, and saturated steam equation, forming a set of self-consistent differential equations; obtaining the bubble power P by solving the circuit model b and bubble partial pressure U b ,; where the bubble power P b Input into the bubble model; obtain the bubble radius r by solving the bubble model b , temperature T b and pressure p b Isostate parameters, where the bubble radius r b Input into the circuit model; 3) Breakdown judgment; the bubble pressure p obtained in step 2) is b Substitute Paschen's law to obtain the breakdown voltage U br ; Make breakdown judgment and compare U br Is it greater than or equal to U obtained in step 2) b If yes, the gap is judged to have broken down and the process ends; otherwise, the process enters the next breakdown judgment process, t becomes t+Δt, and steps 1) to 3) are repeated; wherein, the calculation of the theoretical breakdown voltage is based on Paschen's law of gas discharge breakdown: Among them, A and B are constants related to the gas type, γ is the secondary electron emission coefficient; the bubble pressure p obtained by the bubble model is b Substitute to obtain the corresponding breakdown voltage U br .

2. The method for determining breakdown of underwater discharge according to claim 1, wherein: The circuit model regards the bubbles and water as two resistors connected in series or in parallel; the circuit model is equivalent to the external circuit impedance R s 、L s and discharge capacitor C g The circuit topology that constitutes the second-order RLC.

3. The method for determining breakdown of underwater discharge according to claim 2, wherein: When the bubble resistance and water resistance are considered to be in parallel, the circuit transient equation is as follows: R g =R b ||R l (3) Among them, R b 、R l are the resistances of air bubbles and water medium respectively, which are determined by the impedance characteristic equation; the impedance characteristic equation is obtained based on the finite element simulation results; The bubble input power is obtained through the circuit model; the dynamic equation uses the classic RP equation to describe the relationship between pressure and radius; assuming that the interior of the bubble is saturated steam, the relationship between pressure and temperature is described by the saturated steam equation: The bubble model is iteratively solved to obtain the bubble radius and pressure r b 、p b Numerical solution of .

4. The application of the breakdown judgment method according to claim 1, characterized in that: Applied to precise analysis of water switches or design optimization of pulse power devices.

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