Analysis method

Abstract

To analyze the discharge occurring in space.SOLUTION: An analysis method includes repeatedly performing electrostatic field analysis processing to acquire an electric field intensity distribution in an analysis space, increase processing to increase negative electric charge particle density and positive electric charge particle density of cells that satisfy the condition that, in each cell of the analysis space, the electric field intensity exceeds a first electric field threshold and the positive electric charge particle density is a predetermined upper limit value or less, reduction processing to reduce the negative electric charge particle density and the positive electric charge particle density of each cell in the analysis space, negative electric charge particle discharge processing to increase the negative electric charge particle density of cells in the surroundings of the surface of the electrode with the lower set potential of the first electrode and the second electrode, and advection processing to update the negative electric charge particle density of each cell by moving the electrons of each cell in the analysis space on the basis of the electric field intensity distribution within the analysis space.SELECTED DRAWING: Figure 34

Description

Technical Field

[0001] The present invention relates to an analysis method for analyzing discharges occurring in space.

Background Art

[0002] For example, Patent Document 1 discloses that lightning may strike an aircraft in flight. In Patent Document 1, electric field sensors are provided at various parts of the aircraft body, and based on the detection results of the electric field sensors, the distribution of the surface electric field strength of the aircraft is derived, and by using the distribution of the surface electric field strength to perform attitude control of the aircraft, the influence of lightning strikes is suppressed.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] By the way, in various electrical devices including aircraft, depending on the shape of each part of the electrical device or the gap length between each part, etc., discharges may occur in space due to each part of the electrical device. A technology for assisting in designing an electrical device that does not generate such discharges is desired.

[0005] Therefore, an object of the present invention is to provide an analysis method capable of analyzing discharges occurring in space.

Means for Solving the Problems

[0006] To solve the above problems, an analysis method according to an embodiment of the present invention is an analysis method for analyzing discharges occurring in the space between a first electrode and a second electrode, dividing an analysis space for performing electrostatic field analysis into a plurality of cells, Set the negative charge particle density indicating the number of negative charge particles having negative charges in one cell and the positive charge particle density indicating the number of positive charge particles having positive charges in one cell for a plurality of cells in the analysis space. Place the first electrode and the second electrode in the analysis space, set a first potential for the first electrode, and set a second potential for the second electrode. Perform an electrostatic field analysis process of obtaining the electric field strength distribution in the analysis space by deriving the electric field strength for each cell in the analysis space through electrostatic field analysis. In each cell of the analysis space, perform an increase process of increasing the negative charge particle density and the positive charge particle density of the cell that satisfies the condition that the electric field strength exceeds a predetermined first electric field threshold value and the positive charge particle density is equal to or less than a predetermined upper limit value by a predetermined first coefficient. Perform a decrease process of decreasing the negative charge particle density and the positive charge particle density of each cell in the analysis space by a predetermined second coefficient. When the electric field strength on the surface of the electrode with the lower set potential among the first electrode and the second electrode exceeds a predetermined second electric field threshold value, perform a negative charge particle emission process of increasing the negative charge particle density of the cells around the surface in the analysis space by a predetermined third coefficient. Perform an advection process of updating the negative charge particle density of each cell by moving the negative charge particles of each cell in the analysis space based on the electric field strength distribution in the analysis space. Repeat the electrostatic field analysis process, the increase process, the decrease process, the negative charge particle emission process, and the advection process.

Advantages of the Invention

[0007] According to the present invention, it becomes possible to analyze the discharge occurring in the space.

Brief Description of the Drawings

[0008]

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Embodiments for Carrying Out the Invention

[0009] Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. The specific dimensions, materials, numerical values, etc. shown in such embodiments are merely examples for facilitating the understanding of the invention and do not limit the present invention unless otherwise specified. In the present specification and drawings, elements having substantially the same functions and configurations are denoted by the same reference numerals to omit redundant explanations, and elements not directly related to the present invention are not shown.

[0010] As an example of the theoretical explanation of discharge, the streamer theory has been proposed. Hereinafter, the outline of the streamer theory will be described.

[0011] Figures 1 to 4 are explanatory diagrams expressing the generation process of discharge in the streamer theory in a deformed manner. In Figures 1 to 4, the first electrode 10 is a rod-shaped electrode, and the second electrode 12 is a flat-plate electrode. The first electrode 10 and the second electrode 12 are separated, and there is a space between the first electrode 10 and the second electrode 12. In the examples of Figures 1 to 4, it is assumed that the first electrode 10 is the negative electrode and the second electrode 12 is the positive electrode.

[0012] Connect the first electrode 10 and the second electrode 12 to a power source, and apply a potential difference to the first electrode 10 and the second electrode 12 such that the first electrode 10 becomes the negative electrode and the second electrode 12 becomes the positive electrode. Then, an electrostatic field is generated in the space between the first electrode 10 and the second electrode 12. And since the first electrode 10 is rod-shaped, the electric field concentrates at the tip of the first electrode 10 on the side of the second electrode 12, and the electric field strength becomes strong.

[0013] As shown in FIG. 1, when the potential difference between the first electrode 10 and the second electrode 12 is increased, the strong electric field at the tip of the first electrode 10 causes dielectric breakdown of the air around the tip, and a filamentous streamer 20 is generated from the tip of the first electrode 10 which is the negative electrode.

[0014] As shown in FIG. 2, the streamer 20 appears to fly from the first electrode 10 which is the negative electrode toward the second electrode 12 which is the positive electrode.

[0015] When the streamer 20 reaches the second electrode 12, as shown in FIG. 3, a leader 22 that appears following the streamer 20 is generated from the second electrode 12 which is the positive electrode. Hereafter, the occurrence of the leader 22 may be called leader conversion.

[0016] As shown in FIG. 4, the leader 22 extends from the second electrode 12 which is the positive electrode toward the first electrode 10 which is the negative electrode and reaches the first electrode 10. When the leader 22 reaches the first electrode 10, a large current flows between the first electrode 10 and the second electrode 12, leading to discharge.

[0017] FIGS. 5 to 8 are other explanatory diagrams that deform and represent the discharge generation process in streamer theory. In the examples of FIGS. 5 to 8, it is assumed that the first electrode 10 is the positive electrode and the second electrode 12 is the negative electrode. Also in this example, the electric field concentrates at the tip of the first electrode 10 on the side of the second electrode 12, and the electric field strength becomes strong.

[0018] As shown in FIG. 5, when the potential difference between the first electrode 10 and the second electrode 12 is increased, the strong electric field at the tip of the first electrode 10 causes dielectric breakdown of the air around the tip, and a string-shaped streamer 20 is generated from the tip of the first electrode 10 which is the positive electrode.

[0019] As shown in FIG. 6, the streamer 20 appears to fly from the first electrode 10 which is the positive electrode toward the second electrode 12 which is the negative electrode.

[0020] When the streamer reaches the second electrode 12, as shown in FIG. 7, a leader 22 that appears following the streamer 20 is generated from the first electrode 10 which is the positive electrode. Thus, when the first electrode 10 is the positive electrode, leader conversion occurs at the first electrode 10 which is the positive electrode.

[0021] As shown in FIG. 8, the leader 22 extends from the first electrode 10 which is the positive electrode toward the second electrode 12 which is the negative electrode and reaches the second electrode 12 which is the negative electrode. When the leader 22 reaches the second electrode 12, a large current flows between the first electrode 10 and the second electrode 12, leading to discharge.

[0022] Here, in order to deepen the understanding of under what conditions such a discharge occurs, an analysis method for analyzing the discharge is desired.

[0023] Therefore, in the present embodiment, an analysis method for analyzing the discharge occurring in the space between the first electrode 10 and the second electrode 12 is disclosed. By using the analysis method of the present embodiment, it becomes possible to estimate whether discharge caused by each part of the electrical device occurs in the space depending on the shape of each part of the electrical device or the gap length between each part.

[0024] FIG. 9 is a schematic diagram showing the configuration of an analysis device 50 for realizing the analysis method of the present embodiment. The analysis device 50 is a computer such as a personal computer, for example. The analysis device 50 includes a user interface 60, a storage device 62, and an arithmetic device 64.

[0025] The user interface 60 includes a display device 70 and an input device 72. The display device 70 is, for example, a liquid crystal display or an organic EL display, and displays various images and information. Note that the user interface 60 may include, in addition to the display device 70, an output device such as a speaker that presents various information to the user. The input device 72 includes, for example, a keyboard or a mouse, and receives input operations from the user.

[0026] The storage device 62 is composed of non-volatile memory elements. Note that the storage device 62 may be composed of electrically rewritable non-volatile memory elements such as flash memory. Various data used for various processes executed by the analysis device 50 are stored in the storage device 62.

[0027] The arithmetic device 64 includes one or more processors 80 and one or more memories 82 connected to the processors 80. The memory 82 includes a ROM in which programs and the like are stored and a RAM as a work area. The processor 80 executes various processes in cooperation with the programs included in the memory 82. The processor 80 also functions as a pre-analysis processing unit 90, an analysis execution processing unit 92, and a determination processing unit 94 by executing programs.

[0028] The pre-analysis processing unit 90 executes pre-processing for performing analysis execution processing by the analysis execution processing unit 92. After the pre-processing is performed, the analysis execution processing unit 92 executes analysis execution processing. The analysis execution processing is a process for analyzing the generation process of discharge. The determination processing unit 94 is a process for determining whether discharge occurs by using the result of the analysis execution processing after the analysis execution processing is performed.

[0029] Here, the inventor interpreted and modeled the discharge generation process independently with reference to the above-mentioned streamer theory. Then, based on the modeled content, the inventor constructed an analysis method for analyzing the discharge generation process. First, the content of the modeling by the inventor will be described below, and then the pre-processing, analysis execution processing, and determination processing according to the analysis method of the present embodiment will be described in detail.

[0030] Figures 10 to 14 are diagrams for explaining the modeled phenomena around the tip of the first electrode 10 which serves as a negative electrode. In Figures 10 to 14, the black circles indicate negative charge particles n having a negative charge, and the circles marked with “+” indicate positive charge particles p having a positive charge. The arrows in Figures 11 to 14 illustrate the moving directions of the negative charge particles n. The negative charge particles n are assumed to be particles having a negative electric charge amount, and physically, for example, they correspond to electrons. The positive charge particles p are assumed to be particles having a positive charge, and physically, for example, they correspond to ions.

[0031] The atmosphere is filled with a gas which is an example of neutral particles showing neutrality. At the tip of the first electrode 10, since the electric field is concentrated, the electric field strength is strong. As shown in Figure 10, in the vicinity of the tip of the first electrode 10, due to the strong electric field strength, the gas in the atmosphere is ionized into electrons having a negative charge and ions having a positive charge. That is, negative charge particles n and positive charge particles p are generated in the vicinity of the tip of the first electrode 10.

[0032] As shown in Figure 11, in this model, it is assumed that the negative charge particles n generated by ionization move in the direction from the first electrode 10 to the second electrode 12 with a certain mobility under the influence of the electric field strength distribution in the space between the first electrode 10 and the second electrode 12. On the other hand, it is assumed that the positive charge particles p generated by ionization stay at the generated positions and do not move. This is because the mass of the ions corresponding to the positive charge particles p is large compared with the electrons corresponding to the negative charge particles n, and the mobility of the ions is extremely small compared with the mobility of the electrons, so that in an extremely short time of less than microseconds for carrying out the simulation, it can be considered that the ions do not move.

[0033] Also, negative charge particles n exist in the first electrode 10 which is a negative electrode. As shown in Figure 11, it is assumed that negative charge particles n are emitted from the first electrode 10 into the atmosphere based on the electric field strength on the surface of the first electrode 10 which is a negative electrode.

[0034] As shown in FIG. 11, the moved negative charge particles n generate an electric field f at the moved position as indicated by the dashed circles. That is, the ionization region, which is the ionized region, grows from the first electrode 10 toward the second electrode 12. The gas is ionized into electrons and ions by the electrons accelerated in the grown ionization region and electromagnetic waves generated by the recombination of the already ionized gas. As a result, as shown in FIG. 12, negative charge particles n and positive charge particles p are generated, and the ionization region expands.

[0035] As shown in FIG. 13, the negative charge particles n in the space move further in the direction from the first electrode 10 toward the second electrode 12 under the influence of the electric field strength distribution in the space. The moved negative charge particles n generate an electric field f at the moved position, and the ionization region further grows. The gas is ionized into electrons and ions by the electrons accelerated in the grown ionization region and electromagnetic waves generated by the recombination of the already ionized gas. As a result, as shown in FIG. 14, negative charge particles n and positive charge particles p are generated, and the ionization region expands.

[0036] In this way, it is considered that negative charge particles n and positive charge particles p are generated, and the ionization region grows as the negative charge particles n move. At this time, positive charge particles p are gradually generated from the first electrode 10 toward the second electrode 12. Therefore, the progress of the streamer 20 is modeled by the positive charge particles p that are gradually generated from the first electrode 10 toward the second electrode 12.

[0037] FIGS. 15 to 20 are diagrams for explaining the modeled phenomena around the second electrode 12 that serves as the positive electrode. FIGS. 15 to 20 show a state in which positive charge particles p are arranged from the first electrode 10 toward the second electrode 12. The arrows in FIGS. 15 to 20 illustrate the moving direction of the negative charge particles n.

[0038] As shown in Fig. 15, the negatively charged particles n that have moved in space enter the second electrode 12 which is the positive electrode, and the electric field strength near the second electrode 12 becomes stronger. Then, as shown in Fig. 16, in the vicinity of the second electrode 12, the gas in the atmosphere ionizes into electrons and ions. It is assumed that the negatively charged particles n generated by ionization move toward the second electrode 12. On the other hand, for the positively charged particles p generated by ionization, it is assumed that they remain at the generated position and do not move due to reasons such as the mass of the ions and the mobility of the ions described above.

[0039] When the generated negatively charged particles n move and enter the second electrode 12, as shown in Fig. 17, a strong electric field f is generated by the positively charged particles p that are generated and do not move. Due to the electric field f, as shown in Fig. 18, the gas on the first electrode 10 side ionizes into electrons and ions, and more negatively charged particles n and positively charged particles p are generated. The generated negatively charged particles n move toward the second electrode 12.

[0040] As shown in Fig. 19, when the negatively charged particles n move, a strong electric field f is generated by the positively charged particles p that are generated in Fig. 18 and do not move. That is, the ionization region grows from the second electrode 12 toward the first electrode 10, and it looks as if the second electrode 12 which is the positive electrode extends toward the first electrode 10 side. Then, due to the grown ionization region, as shown in Fig. 20, the gas on the first electrode 10 side ionizes into electrons and ions, and more negatively charged particles n and positively charged particles p are generated.

[0041] In this way, it is considered that negatively charged particles n and positively charged particles p are generated, and the ionization region grows as the negatively charged particles n move. At this time, positively charged particles p are gradually generated from the second electrode 12 toward the first electrode 10. From this, the progress of the leader 22 is modeled by the positively charged particles p that are gradually generated from the second electrode 12 toward the first electrode 10.

[0042] Figures 21 to 25 are diagrams for explaining the modeled phenomena around the tip of the first electrode 10 which is the positive electrode. The arrows in Figures 21 to 25 illustrate the moving directions of the negative charge particles n.

[0043] At the tip of the first electrode 10, since the electric field is concentrated, the electric field strength is strong. As shown in Figure 21, in the vicinity of the tip of the first electrode 10, due to the strong electric field strength, the gas in the atmosphere is ionized into electrons and ions, generating negative charge particles n and positive charge particles p.

[0044] As shown in Figure 21, it is assumed that the negative charge particles n generated by ionization move toward the first electrode 10 which is the positive electrode and enter the first electrode 10. On the other hand, for the positive charge particles p generated by ionization, it is assumed that they stay at the generated positions and do not move due to reasons such as the mass of the ions and the ion mobility described above. Then, as shown in Figure 22, an electric field f is generated by the positive charge particles p that are generated and do not move. That is, the ionization region grows from the first electrode 10 toward the second electrode 12, taking on a form as if the first electrode 10 which is the positive electrode extends toward the second electrode 12 side.

[0045] Due to the ionization region grown in accordance with Figure 22, as shown in Figure 23, the gas on the second electrode 12 side is ionized into electrons and ions, further generating negative charge particles n and positive charge particles p. The generated negative charge particles n move toward the first electrode 10 which is the positive electrode. Then, as shown in Figure 24, an electric field f is generated by the positive charge particles p that are generated and do not move, and the ionization region grows.

[0046] Due to the ionization region grown in accordance with Figure 24, as shown in Figure 25, the gas on the second electrode 12 side is ionized into electrons and ions, further generating negative charge particles n and positive charge particles p.

[0047] In this way, negative charge particles n and positive charge particles p are generated, and it is considered that the ionization region grows as the negative charge particles n move. At this time, positive charge particles p are gradually generated from the first electrode 10 toward the second electrode 12. From this, the progress of the streamer 20 is modeled by the positive charge particles p that are gradually generated from the first electrode 10 toward the second electrode 12.

[0048] Regarding the progress of the leader 22 from the first electrode 10 that serves as the positive electrode, it is modeled by the positive charge particles p that are gradually generated from the first electrode 10 toward the second electrode 12 in the same manner as described with reference to FIGS. 21 to 25.

[0049] FIG. 26 is a diagram for explaining the analysis space 100. The analysis space 100 is a virtual space for performing electrostatic field analysis. The analysis space 100 has a size sufficient for performing sufficient electrostatic field analysis.

[0050] For example, the first electrode 10 is set near the center of the analysis space 100. The first electrode 10 is set, for example, as a rod electrode having a length of about 30 cm. Note that the size of the first electrode 10 is not limited to the exemplified size and may be set to any size. Also, for example, the second electrode 12 is set above the analysis space 100. The second electrode 12 is set as a flat plate electrode that spreads in a planar shape in the left-right direction of FIG. 26. The length of the second electrode 12 in the left-right direction is sufficiently longer than the diameter of the first electrode 10. The first electrode 10 and the second electrode 12 are arranged to be separated from each other. The distance between the first electrode 10 and the second electrode 12 is set, for example, to about 80 cm, but may be set to any value.

[0051] A first potential is set for the first electrode 10, and a second potential is set for the second electrode 12. For example, the first potential is a negative potential and the second potential is a positive potential. Note that the first potential may be a positive potential and the second potential may be a negative potential. Also, the first potential may be a ground potential and the second potential may be a positive or negative potential. By setting potentials for the first electrode 10 and the second electrode 12 respectively, an electrostatic field can be generated between the first electrode 10 and the second electrode 12.

[0052] The analysis space 100 is divided into a plurality of cells 102. The cell 102 is, for example, a square region of a predetermined size. The size of the cell 102 is set, for example, such that one side is 10 mm, etc., but may be set to any size that enables appropriate execution of the analysis. In the analysis space 100, a plurality of cells 102 are arranged over the entire analysis space 100. In other words, the analysis space 100 is partitioned into a mesh shape by a plurality of cells 102. Note that in FIG. 26, a part of the analysis space 100 is enlarged to illustrate the cell 102.

[0053] Here, the above-described model focusing on the generation of negative charge particles n and positive charge particles p and the movement of negative charge particles n is developed using the cells 102 of the analysis space 100.

[0054] FIGS. 27 to 31 are diagrams for explaining the states of negative charge particles n and positive charge particles p in the cell 102. In FIGS. 27 to 31, for convenience of explanation, two cells 102, namely cell 102a and cell 102b, among the plurality of cells 102 are illustrated. The cell 102a and the cell 102b are adjacent to each other.

[0055] Here, the number of negative charge particles n in one cell is defined as the negative charge particle density, and the number of positive charge particles p in one cell is defined as the positive charge particle density.

[0056] For example, due to the influence of the strong electric field strength at the tip of the first electrode 10, as shown in FIG. 27, it is assumed that the gas in cells 102a and 102b is ionized, and negative charge particles n and positive charge particles p are generated in cells 102a and 102b, respectively. In this case, the negative charge particle density and the positive charge particle density in cell 102a, and the negative charge particle density and the positive charge particle density in cell 102b increase compared to before ionization.

[0057] As shown in FIG. 28, it is assumed that the negative charge particles n in cell 102a move to cell 102b based on the electric field strength distribution around cell 102a. The speed at which the negative charge particles n in cell 102a move to cell 102b depends on the electric field strength distribution around cell 102a. Hereinafter, the movement of the negative charge particles n between cells 102 may be referred to as advection, and the speed at which the negative charge particles n advect may be referred to as the advection speed.

[0058] Also, as shown in FIG. 28, negative charge particles n advect into cell 102a from an unillustrated cell 102 adjacent to cell 102a. Also, as shown in FIG. 28, the negative charge particles n in cell 102b advect to an unillustrated cell 102 adjacent to cell 102b.

[0059] Thus, regarding the advection of the negative charge particles n, the negative charge particle density in cell 102a changes to the negative charge particle density indicated by the difference value between the negative charge particles n entering cell 102a and the negative charge particles n exiting cell 102a. Similarly, regarding the advection of the negative charge particles n, the negative charge particle density in cell 102b changes to the negative charge particle density indicated by the difference value between the negative charge particles n entering cell 102b and the negative charge particles n exiting cell 102b.

[0060] On the other hand, as shown in FIG. 28, the positive charge particles p in cell 102a remain in cell 102a, and the positive charge particles p in cell 102b remain in cell 102b.

[0061] As described above, even if the negative charge particles n undergo advection, the positive charge particles p do not move. Therefore, with respect to the advection of the negative charge particles n, the positive charge particle density in the cell 102a does not change. Similarly, with respect to the advection of the negative charge particles n, the positive charge particle density in the cell 102b does not change.

[0062] In FIG. 28, it is assumed that the negative charge particles n that have advected from the cell 102a into the cell 102b collide with the neutral particles present in the cell 102b. The neutral particles may simulate, for example, any gas in the atmosphere.

[0063] When the negative charge particles n collide with the neutral particles in the cell 102b, the neutral particles are ionized by the collision energy, and as shown in FIG. 29, negative charge particles n and positive charge particles p resulting from the neutral particles are generated in the cell 102b. Then, as shown in FIG. 29, the negative charge particle density and the positive charge particle density in the cell 102b increase compared to the negative charge particle density and the positive charge particle density in the cell 102b of FIG. 28 before the ionization of the neutral particles.

[0064] Similarly, in FIG. 28, it is assumed that the negative charge particles n that have advected into the cell 102a collide with the neutral particles present in the cell 102a.

[0065] When the negative charge particles n collide with the neutral particles in the cell 102a, the neutral particles are ionized by the collision energy, and as shown in FIG. 29, negative charge particles n and positive charge particles p resulting from the neutral particles are generated in the cell 102a. Then, as shown in FIG. 29, the negative charge particle density and the positive charge particle density in the cell 102a increase compared to the negative charge particle density and the positive charge particle density in the cell 102a before the ionization of the neutral particles.

[0066] In this way, due to the ionization caused by the advection of the negative charge particles n, the negative charge particle density and the positive charge particle density in each cell 102 increase. The increase rate of the negative charge particle density and the increase rate of the positive charge particle density of each cell 102 due to this factor may be set to values according to the electric field strength of the cell 102.

[0067] Also, assume that when simulating the recombination of electrons and ions, if there is a pair of negatively charged particles n and positively charged particles p in the cell 102, the negatively charged particles n and the positively charged particles p may recombine. When recombination occurs, the negatively charged particles n and the positively charged particles p used for recombination disappear.

[0068] When the negatively charged particles n and the positively charged particles p in the cell 102a recombine at a predetermined ratio, as shown in FIG. 30, the negatively charged particle density and the positively charged particle density in the cell 102a decrease from the negatively charged particle density and the positively charged particle density in the cell 102a before recombination.

[0069] Similarly, when the negatively charged particles n and the positively charged particles p in the cell 102b recombine at a predetermined ratio, as shown in FIG. 30, the negatively charged particle density and the positively charged particle density in the cell 102b decrease from the negatively charged particle density and the positively charged particle density in the cell 102b before recombination.

[0070] Thus, due to recombination, the negatively charged particle density and the positively charged particle density in each cell 102 decrease. The rate of decrease in the negatively charged particle density and the rate of decrease in the positively charged particle density of each cell 102 due to this factor may be preset to specific values regardless of the electric field strength.

[0071] Also, assume that when simulating ionization by electromagnetic waves caused by the recombination of electrons and ions, neutrons in the cell 102 are ionized at a predetermined ratio, and negatively charged particles n and positively charged particles p in the cell 102 are generated.

[0072] When neutrons in the cell 102a are ionized at a predetermined ratio due to electromagnetic waves, as shown in FIG. 31, the negatively charged particle density and the positively charged particle density in the cell 102a increase.

[0073] Similarly, when neutrons in the cell 102b are ionized at a predetermined ratio due to electromagnetic waves, as shown in FIG. 31, the negatively charged particle density and the positively charged particle density in the cell 102b increase.

[0074] In this way, due to ionization caused by electromagnetic waves, the density of negatively charged particles and the density of positively charged particles in each cell 102 increase. The rate of increase in the density of negatively charged particles and the rate of increase in the density of positively charged particles in each cell 102 due to this factor may be set to values according to the electric field strength of the cell 102.

[0075] Based on these, in each cell 102 of the analysis space 100, by deriving the changes in the density of negatively charged particles and the density of positively charged particles, the generation process of discharge can be analyzed. Hereinafter, the details of each process in the analysis device 50 that realizes the analysis method of the present embodiment will be described.

[0076] FIG. 32 is a flowchart for explaining the operation of the arithmetic unit 64. When the pre-analysis processing unit 90 of the arithmetic unit 64 receives a pre-processing start signal instructing the start of pre-processing, for example, through the input device 72, it executes pre-processing (S11). After the pre-processing, when the analysis execution processing unit 92 of the arithmetic unit 64 receives an analysis execution start signal instructing the start of analysis execution processing, for example, through the input device 72, it executes analysis execution processing (S12). After the analysis execution processing, when the determination processing unit 94 of the arithmetic unit 64 receives a determination start signal instructing the start of determination processing, for example, through the input device 72, it executes determination processing (S13).

[0077] FIG. 33 is a flowchart for explaining the flow of pre-processing (S11). When the pre-processing is started, the pre-analysis processing unit 90 first defines the analysis space 100 (S21). For example, the pre-analysis processing unit 90 sets the size of the analysis space 100, sets the size of the cell 102, and divides the analysis space 100 into a mesh shape by dividing the analysis space 100 with a plurality of cells 102. Note that the user of the analysis device 50 may set the size of the analysis space 100, the size of the cell 102, etc. through the input device 72. Further, since it is assumed that the negatively charged particles n flow between the cells 102, the size of the cell 102 may be set in consideration of the mobility of the negatively charged particles n.

[0078] Next, the pre-analysis processing unit 90 sets the negative charge particle density for each cell 102 (S22), and sets the positive charge particle density for each cell 102 (S23). For example, the pre-analysis processing unit 90 sets the initial value of the negative charge particle density to zero, and the initial value of the positive charge particle density to zero.

[0079] Next, the pre-analysis processing unit 90 sets the first electrode 10 and the second electrode 12 in the analysis space 100 (S24). For example, the pre-analysis processing unit 90 sets a rod electrode as the first electrode 10 approximately at the center of the analysis space 100. The pre-analysis processing unit 90 sets a flat plate electrode as the second electrode 12 at the upper part of the analysis space 100. Note that the user may set the shape, position, and size of each of the first electrode 10 and the second electrode 12 through the input device 72.

[0080] After setting the electrodes, the pre-analysis processing unit 90 sets the first potential for the first electrode 10 and sets the second potential for the second electrode 12 (S25), and ends the pre-processing. For example, when the first electrode 10 is a negative electrode, a negative potential is set as the first potential, and when the second electrode 12 is a positive electrode, a positive potential is set as the second potential. The polarities and values of the first potential and the second potential are set to the polarities and values according to the purpose of the analysis. Note that the user may set the polarities and values of the first potential and the second potential through the input device 72.

[0081] In the pre-processing, the setting of the negative charge particle density, the setting of the positive charge particle density, and the setting of the electrodes are not limited to the illustrated order, and may be performed in any order. Also, the setting of the potential may be performed in any order after the setting of the electrodes is completed.

[0082] FIG. 34 is a flowchart for explaining the flow of the analysis execution process (S12). When the analysis execution process is started, the analysis execution processing unit 92 executes an electrostatic field analysis process (S31). The electrostatic field analysis process (S31) is a process of obtaining the electric field strength distribution in the analysis space 100 by deriving the electric field strength for each cell 102 in the analysis space 100 through electrostatic field analysis.

[0083] More specifically, the analysis execution processing unit 92 acquires the negative charge particle density and the positive charge particle density in the cell 102 at the current time in each cell 102. For example, in the first electrostatic field analysis process since the start of the analysis execution process, the initial value of the negative charge particle density and the initial value of the positive charge particle density are acquired in each cell 102. The analysis execution processing unit 92 selects one cell 102 as a target, subtracts the positive charge particle density from the negative charge particle density in the cell 102, and derives the charge density in the cell 102.

[0084] The analysis execution processing unit 92 uses the derived charge density to solve the Poisson equation shown in the following equation (1) to derive the electric potential in the cell 102. In equation (1), Φ represents the electric potential, ρ represents the charge density, and ε represents the dielectric constant. Note that as the method for solving equation (1), various known analysis methods such as the finite element method can be used.

Equation

[0085] The analysis execution processing unit 92 uses the derived electric potential to solve the relational expression between the electric field and the electric potential shown in the following equation (2) to derive the electric field strength in the cell 102. In equation (2), E represents the electric field and Φ represents the electric potential. Note that as the method for solving equation (2), various known analysis methods such as the finite element method can be used.

Equation

[0086] The analysis execution processing unit 92 performs such derivation of the electric field strength for all cells 102 in the analysis space 100. Thereby, the current electric field strength distribution in the analysis space 100 is obtained.

[0087] Next, the analysis execution processing unit 92 executes an increase process (S32) of increasing the negative charge particle density and the positive charge particle density of the cell 102 that satisfies a predetermined increase condition in each cell 102 of the analysis space 100 by a predetermined first coefficient. Increasing by a predetermined first coefficient means multiplying the negative charge particle density and the positive charge particle density in the cell 102 at the current time by a first coefficient with a value of 1 or more, so as to increase the negative charge particle density and the positive charge particle density in the cell 102 to be higher than the values before multiplying by the first coefficient.

[0088] The predetermined increase condition is that the electric field strength in the cell 102 exceeds a predetermined first electric field threshold value and the positive charge particle density is equal to or less than a predetermined upper limit value. The first electric field threshold value is set, for example, to the lower limit value of the electric field strength at which neutral particles in the cell 102 are ionized. The upper limit value of the positive charge particle density is set to an arbitrary value, for example, to the extent that ions can actually exist in the cell 102.

[0089] The predetermined first coefficient is set as a variable that increases in proportion to the electric field strength in the cell 102, for example. The predetermined first coefficient may be set by comprehensively considering, for example, the probability that neutral particles are ionized based on the electric field strength in the cell 102, the probability that neutral particles are ionized based on the collision of moving negative charge particles n, and the probability that neutral particles are ionized based on electromagnetic waves due to recombination. That is, in the increase process, it is simulated that at least the negative charge particle density and the positive charge particle density increase due to ionization.

[0090] Next, the analysis execution processing unit 92 executes a decrease process (S33) of decreasing the negative charge particle density and the positive charge particle density of each cell 102 in the analysis space 100 by a predetermined second coefficient. Decreasing by a predetermined second coefficient means multiplying the negative charge particle density and the positive charge particle density in the cell 102 at the current time by a second coefficient with a value less than 1, so as to decrease the negative charge particle density and the positive charge particle density in the cell 102 to be lower than the values before multiplying by the second coefficient.

[0091] The predetermined second coefficient is set as a variable that decreases in proportion to, for example, the electric field strength within the cell 102. The predetermined second coefficient is set based on, for example, the probability of recombination that actually occurs within the cell 102. That is, in the decrease process, it is simulated that the negative charge particle density and the positive charge particle density decrease due to recombination.

[0092] Next, the analysis execution processing unit 92 executes a negative charge particle emission process (S34) that simulates the emission of negative charge particles n from the negative electrode.

[0093] The negative electrode corresponds to the electrode with the lower set potential among the first electrode 10 and the second electrode 12. In the negative charge particle emission process, the analysis execution processing unit 92 acquires the electric field strength at the surface of the electrode corresponding to the negative electrode. When the acquired electric field strength exceeds a predetermined second electric field threshold value, the analysis execution processing unit 92 increases the negative charge particle density of the cells 102 around the surface in the analysis space 100 by a predetermined third coefficient. Increasing by the predetermined third coefficient means multiplying the negative charge particle density within the cell 102 at the current time by a third coefficient with a value of 1 or more, thereby increasing the negative charge particle density within the cell 102 compared to the value before multiplying by the third coefficient. The second electric field threshold value is set to a value at which, for example, electrons are actually emitted from the negative electrode.

[0094] The predetermined third coefficient is set as a variable that increases in proportion to, for example, the electric field strength within the cell 102. Note that the predetermined third coefficient may be set as a variable that increases in proportion to the combination of the electric field strength within the cell 102 and the positive charge particle density within the cell 102 of the emission destination. That is, in the negative charge particle emission process, it is simulated that the negative charge particle density increases due to the emission of electrons from the negative electrode.

[0095] Next, the analysis execution processing unit 92 executes an advection process (S35) that simulates the advection of negative charge particles n between the cells 102. In the advection process, the analysis execution processing unit 92 moves the negative charge particles n in each cell 102 of the analysis space 100 based on the electric field strength distribution within the analysis space 100. For example, the analysis execution processing unit 92 compares the electric field strength within the cell 102 where the negative charge particles n to be moved exist with the electric field strength around the cell 102, and determines the moving direction of the negative charge particles n to be moved from the cell 102, that is, the cell 102 to which the negative charge particles n move. Then, the analysis execution processing unit 92 decreases the negative charge particle density in the original cell 102 based on the number of negative charge particles n flowing out, and increases the negative charge particle density in the destination cell 102 based on the number of negative charge particles n flowing in.

[0096] More specifically, the analysis execution processing unit 92 solves the charge advection equation shown in the following equation (3). In equation (3), ρ represents the charge density, μ represents the mobility, and E represents the electric field. Note that as the method for solving equation (3), various known analysis methods such as the CIP (Constrained Interpolation Profile) method can be used.

Equation

[0097] By doing so, in the advection process, the negative charge particle density of each cell 102 is updated.

[0098] Also, in the advection process, the analysis execution processing unit 92 derives the advection time in which the negative charge particles n move by one cell 102 in one advection process based on the mobility of the negative charge particles n and the size of the cell 102. One round of processing from the electrostatic field analysis process (S31) to the advection process (S35) simulates the phenomena occurring within the advection time.

[0099] Also, in the advection process, each time the analysis execution processing unit 92 performs the advection process, it may accumulate the advection time to derive time information indicating the passage of time from the analysis start on the analysis space 100.

[0100] After the advection process, the analysis execution processing unit 92 executes a storage process (S36) of storing various information obtained in a series of processes from the electrostatic field analysis process to the advection process in the memory 82 or the storage device 62 in association with the time information on the analysis space. For example, in the storage process, the time on the analysis space when the electrostatic field analysis process is executed and the negative charge particle density and positive charge particle density in each cell 102 at that time are stored in association with each other.

[0101] Next, the analysis execution processing unit 92 determines whether or not the analysis end condition is satisfied (S37). As the analysis end condition, for example, the analysis execution processing unit 92 may determine that the analysis end condition is satisfied when a predetermined time has elapsed from the analysis start in the analysis space. Note that the analysis execution processing unit 92 may, for example, count the number of times the electrostatic field analysis process is repeatedly executed and determine that the analysis end condition is satisfied when the number of times of the repeated execution reaches a predetermined number of times.

[0102] If it is determined that the analysis end condition is not satisfied (NO in S37), the analysis execution processing unit 92 returns to the electrostatic field analysis process (S31). Then, the analysis execution processing unit 92 repeatedly performs the electrostatic field analysis process (S31), the increase process (S32), the decrease process (S33), the negative charge particle emission process (S34), and the advection process (S35) until the analysis end condition is satisfied. The negative charge particle density and positive charge particle density of each cell 102 are updated by the increase process, the decrease process, the negative charge particle emission process, and the advection process immediately before the repetition. Therefore, in the electrostatic field analysis process performed again by the repetition, an electric field strength distribution reflecting the negative charge particle density and positive charge particle density updated immediately before the repetition can be obtained.

[0103] When it is determined that the analysis end condition is satisfied (YES in S37), the analysis execution processing unit 92 executes notification processing (S38) for notifying the analysis result and ends the analysis execution processing. For example, based on the information stored in the storage processing, the analysis execution processing unit 92 generates an image showing the distribution of the positive charge particle density in the analysis space 100 by the amount of electrostatic field analysis processing performed. Then, the analysis execution processing unit 92 causes the display device 70 to display a moving image that displays the generated images in the order of the passage of time. Thereby, the user can easily grasp the temporal change in the distribution of the positive charge particle density in the analysis space 100.

[0104] In the above example, each time the electrostatic field analysis processing is performed, the storage processing is performed, and the notification processing is performed based on the information stored by the storage processing. However, the storage processing may be omitted. In that case, each time the electrostatic field analysis processing is performed, the analysis execution processing unit 92 may generate an image showing the distribution of the positive charge particle density in the analysis space 100 and cause the display device 70 to display the image in real time.

[0105] FIG. 35 is a flowchart for explaining the flow of the determination processing (S13). When the determination processing starts, the determination processing unit 94 first acquires the analysis result by the analysis execution processing (S41). For example, the determination processing unit 94 may read various information stored in the storage processing (S36) from the memory 82 or the storage device 62.

[0106] Next, the determination processing unit 94 determines whether a predetermined first determination condition is satisfied (S42). The predetermined first determination condition is that the cells 102 in which the positive charge particle density has changed to a predetermined first determination threshold value or more are connected from the first electrode 10 to the second electrode 12. The first determination threshold value is set to a value that can be regarded as the ionization region growing from the first electrode 10 toward the second electrode 12, for example. That is, satisfying the first determination condition corresponds to the streamer 20 advancing from the first electrode 10 reaching the second electrode 12.

[0107] When it is determined that the first determination condition is satisfied (YES in S42), the determination processing unit 94 determines whether the second determination condition is satisfied (S43). The second determination condition is that a cell 102 in which the positive charge particle density has changed to a predetermined second determination threshold value or more occurs anywhere within the analysis space 100. The predetermined second determination threshold value is set to a value higher than the first determination threshold value. The second determination threshold value is set to a value that can distinguish, for example, whether the positive charge particle density indicates either the streamer 20 or the leader 22. That is, satisfying the second determination condition corresponds to the leader 22 having occurred in the analysis space 100.

[0108] Here, when the leader 22 actually occurs, it is then presumed to be difficult to suppress the occurrence of discharge. Therefore, when it is determined that the second determination condition is satisfied after it is determined that the first determination condition is satisfied (YES in S43), the determination processing unit 94 determines that discharge will occur (S44) and proceeds to the process of step S46.

[0109] On the other hand, even if the streamer 20 has advanced from the first electrode 10, if the streamer 20 does not reach the second electrode 12, it is presumed that discharge will not occur. From this, when it is determined that the first determination condition is not satisfied (NO in S42), the determination processing unit 94 determines that discharge will not occur (S45) and proceeds to the process of step S46.

[0110] Also, even if the streamer 20 advancing from the first electrode 10 reaches the second electrode 12, if the leader 22 has not occurred, it is presumed that discharge will not occur. From this, when it is determined that the second determination condition is not satisfied after it is determined that the first determination condition is satisfied (NO in S43), the determination processing unit 94 determines that discharge will not occur (S45) and proceeds to the process of step S46.

[0111] In step S46, the determination processing unit 94 notifies the determination result determined in step S44 or step S45 (S46) and ends the determination process. For example, the determination processing unit 94 causes the determination result to be displayed on the display device 70.

[0112] As described above, in the analysis method of this embodiment, the electrostatic field analysis process (S31), the increase process (S32), the decrease process (S33), the negative charge particle emission process (S34), and the advection process (S35) are repeatedly performed. In the electrostatic field analysis process, the electric field strength is derived for each cell 102 in the analysis space 100 by electrostatic field analysis, thereby obtaining the electric field strength distribution in the analysis space 100. In the increase process, in each cell 102 of the analysis space 100, when the electric field strength exceeds a predetermined first electric field threshold value and the positive charge particle density is equal to or less than a predetermined upper limit value, the negative charge particle density and the positive charge particle density of the cell 102 are increased by a predetermined first coefficient. In the decrease process, the negative charge particle density and the positive charge particle density of each cell 102 in the analysis space 100 are decreased by a predetermined second coefficient. In the negative charge particle emission process, when the electric field strength on the surface of the electrode with the lower set potential among the first electrode 10 and the second electrode 12 exceeds a predetermined second electric field threshold value, the negative charge particle density of the cells 102 around the surface in the analysis space 100 is increased by a predetermined third coefficient. In the advection process, the negative charge particles n in each cell 102 of the analysis space 100 are moved based on the electric field strength distribution in the analysis space 100, thereby updating the negative charge particle density of each cell 102.

[0113] As described above, in the analysis method of this embodiment, each time the electrostatic field analysis process is repeated, the negative charge particle density and the positive charge particle density of each cell in the analysis space are updated. Therefore, in the analysis method of this embodiment, the temporal changes in the negative charge particle density and the positive charge particle density can be obtained. The temporal changes in the negative charge particle density and the positive charge particle density are presumed to simulate the occurrence process of discharge. Therefore, according to the analysis method of this embodiment, the discharge occurring in the space can be analyzed, and the understanding of the occurrence process of discharge can be deepened.

[0114] For example, by using the analysis method of the present embodiment, it is possible to obtain the time evolution of the negative charge particle density and the positive charge particle density when various parameters such as the shape and size of the first electrode and the second electrode, the distance between the electrodes of the first electrode and the second electrode, the first potential, and the second potential are changed. That is, by using the analysis method of the present embodiment, for example, in the design of electrical equipment, it is possible to examine in detail under what conditions leader conversion occurs and leads to discharge, and it is possible to assist in the design of electrical equipment that does not generate discharge.

[0115] Further, in the analysis method of the present embodiment, a determination process (S13) may be performed to determine that discharge occurs when the first determination condition is satisfied and the second determination condition is satisfied after the first determination condition is satisfied. Thereby, in the analysis method of the present embodiment, it is possible to objectively determine whether discharge occurs.

[0116] As described above, the embodiments of the present invention have been described with reference to the accompanying drawings. Needless to say, the present invention is not limited to such embodiments. It is obvious that those skilled in the art can conceive of various modification examples or correction examples within the scope described in the claims, and it is naturally understood that those also belong to the technical scope of the present invention.

Explanation of Reference Numerals

[0117] 10 First electrode 12 Second electrode 100 Analysis space 102 Cell n Negative charge particle p Positive charge particle S13 Determination process S31 Electrostatic field analysis process S32 Increase process S33 Decrease process S34 Negative charge particle emission process S35 Advection process

Claims

1. An analysis method for analyzing a discharge generated in a space between a first electrode and a second electrode, comprising: dividing an analysis space for performing an electrostatic field analysis into a plurality of cells; setting a negative charge particle density indicating the number of negative charge particles having negative charges in one cell and a positive charge particle density indicating the number of positive charge particles having positive charges in one cell for the plurality of cells in the analysis space; placing the first electrode and the second electrode in the analysis space, setting a first potential for the first electrode, and setting a second potential for the second electrode; performing an electrostatic field analysis process of obtaining an electric field strength distribution in the analysis space by deriving an electric field strength for each cell in the analysis space through electrostatic field analysis; performing an increasing process of increasing the negative charge particle density and the positive charge particle density of cells that satisfy the conditions that the electric field strength exceeds a predetermined first electric field threshold value and the positive charge particle density is equal to or less than a predetermined upper limit value in each cell in the analysis space by a predetermined first coefficient; performing a decreasing process of decreasing the negative charge particle density and the positive charge particle density of each cell in the analysis space by a predetermined second coefficient; when the electric field strength on the surface of the electrode with the lower set potential among the first electrode and the second electrode exceeds a predetermined second electric field threshold value, performing a negative charge particle emission process of increasing the negative charge particle density of the cells around the surface in the analysis space by a predetermined third coefficient; performing an advection process of updating the negative charge particle density of each cell by moving the negative charge particles of each cell in the analysis space based on the electric field strength distribution in the analysis space; An analysis method that repeatedly performs the electrostatic field analysis process, the increasing process, the decreasing process, the negative charge particle emission process, and the advection process.

2. By repeatedly performing the electrostatic field analysis process, the increasing process, the decreasing process, the negative charge particle emission process, and the advection process, a first determination condition that a cell in which the positive charge particle density has changed to be equal to or higher than a predetermined first determination threshold value is connected from the first electrode to the second electrode is satisfied, and after the first determination condition is satisfied, a second determination condition that a cell in which the positive charge particle density has changed to be equal to or higher than a predetermined second determination threshold value higher than the first determination threshold value occurs anywhere in the analysis space is satisfied, and further performing a determination process of determining that a discharge has occurred, the analysis method according to Claim 1.

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