Method and apparatus for determining radial power density distribution of fuel rods

Abstract

This application provides a method and apparatus for determining the radial power density distribution of fuel rods, relating to the field of nuclear control technology. The method includes: obtaining the atomic density and neutron flux of each nuclide within each radial ring; determining the volumetric power density function of each radial ring based on the atomic density and neutron flux; normalizing the volumetric power density function to obtain a radial power density distribution factor; determining the local power corresponding to the radial ring by multiplying the average power of the axial segment by the radial power density distribution factor of the radial ring; and using the local power to determine the radial power density distribution of the fuel rod. By using the above method, multiple local powers are determined based on the atomic density and neutron flux of each nuclide, and the radial power density distribution of the fuel rod is determined based on these multiple local powers. This allows for determining the radial power density distribution of the fuel rod not limited to fixed nuclide categories, improving the accuracy of performance analysis and design of fuel rods for new reactor types.

Description

Technical Field

[0001] This invention relates to the field of nuclear control, and more specifically to a method and apparatus for determining the radial power density distribution of fuel rods. Background Technology

[0002] In current fuel rod performance analysis software, the radial power density distribution of the fuel pellets needs to be simulated in order to accurately model the various performance characteristics of the fuel rods.

[0003] Currently, in pressurized water reactor fuel rod performance analysis software, the interpolation method is mainly used to calculate the radial power density distribution of fuel rods. The introduction of this method means that the analysis and calculation of reactor physics software must be completed before fuel rod performance analysis.

[0004] However, for the performance analysis and design of fuel rods in new reactor types (such as lead reactors, fast reactors, and other fourth-generation reactors), the corresponding physics software is still under development and not yet mature, and therefore does not currently have the ability to provide calculation tables for the radial power density distribution of fuel rods. In other words, the corresponding interpolation table method for the radial power density distribution of fuel rods cannot be provided. Furthermore, due to the significant differences in the radial power density distribution of fuel rods between old and new reactor types, using existing calculation tables for the radial power density distribution of fuel rods cannot accurately complete the performance analysis and design of fuel rods for new reactor types. Summary of the Invention

[0005] The purpose of this application is to provide a method and apparatus for determining the radial power density distribution of fuel rods, so as to accurately complete the performance analysis and design of fuel rods for new reactor types.

[0006] In a first aspect, embodiments of this application provide a method for determining the radial power density distribution of a fuel rod, wherein the fuel rod is divided into multiple axial segments along the axial direction, and each axial segment includes multiple radial rings. The method includes:

[0007] Obtain the atomic density of each nuclide within each radial ring;

[0008] Obtain the neutron fluence rate within each radial ring;

[0009] The volume power density function of each radial ring is determined based on the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring.

[0010] The volume power density function of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring.

[0011] For each radial ring, the product of the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring is determined as the local power of the radial ring.

[0012] The radial power density distribution of the fuel rod is determined by utilizing the local power corresponding to each radial ring.

[0013] In some implementations, the volumetric power density function of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring, including:

[0014] The volumetric power density function of each radial ring is integrated by area integration to obtain the integral result of the volumetric power density function of each radial ring.

[0015] For each radial ring, the volume power density function of the radial ring is normalized by integrating the volume power density function of the radial ring to obtain the radial power density distribution function of the radial ring.

[0016] Obtain the density of each radial ring;

[0017] For each radial ring, the product of the radial power density distribution function corresponding to the radial ring and the density of the radial ring is determined as the radial power density distribution function based on the density influence of the radial ring.

[0018] The radial power density distribution function based on density influence of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring.

[0019] In some implementations, the radial power density distribution function based on density influence of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring, including:

[0020] The radial power density distribution function based on density influence for each radial ring is integrated by area integration to obtain the integral result of the radial power density distribution function based on density influence for each radial ring.

[0021] For each radial ring, the radial power density distribution function based on density influence is normalized using the integral result of the radial power density distribution function based on density influence corresponding to the radial ring, so as to obtain the radial power density distribution factor corresponding to each radial ring.

[0022] In some implementations, before determining the local power corresponding to each radial ring by multiplying the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring, the determination method further includes:

[0023] Obtain the average power of the fuel rods and the axial power density distribution factor of each axial segment;

[0024] For each axial segment, the average power of each axial segment is determined by multiplying the average power of the fuel rods by the axial power density distribution factor of the axial segment.

[0025] In some implementations, obtaining the atomic density of each nuclide within each radial ring includes:

[0026] Obtain the radial power density distribution function corresponding to each nuclide within each radial ring;

[0027] The atomic density of each nuclide in each radial ring is determined based on the radial power density distribution function corresponding to each nuclide in each radial ring and the preset burnup equation.

[0028] In some implementations, obtaining the radial power density distribution function corresponding to each nuclide within each radial ring includes:

[0029] Obtain the initial radial power density distribution function for each nuclide within each radial ring;

[0030] The initial radial power density distribution function is integrated by area integration to obtain the integral result of the initial radial power density distribution function;

[0031] By integrating the initial radial power density distribution function, the initial radial power density distribution function is normalized to obtain the radial power density distribution function corresponding to each nuclide in each radial ring.

[0032] In some implementations, obtaining the neutron flux rate of the fuel rods includes:

[0033] Based on the neutron hypothesis theory, the neutron diffusion equation corresponding to the fuel rod is obtained;

[0034] Obtain the general solution of the neutron diffusion equation and the preset boundary conditions of the neutron diffusion equation;

[0035] The neutron flux rate of the fuel rods is determined based on the general solution and preset boundary conditions.

[0036] Secondly, embodiments of this application provide a device for determining the radial power density distribution of a fuel rod, the device comprising:

[0037] The first acquisition module is used to acquire the atomic density of each nuclide in each radial ring;

[0038] The second acquisition module is used to acquire the neutron fluence rate in each radial ring;

[0039] The first determining module is used to determine the volume power density function of each radial ring based on the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring.

[0040] The processing module is used to normalize the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring.

[0041] The second determining module is used to determine the local power of each radial ring by multiplying the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring.

[0042] The third determining module is used to determine the radial power density distribution of the fuel rods by utilizing the local power corresponding to each radial ring.

[0043] Thirdly, embodiments of this application provide an electronic device, including:

[0044] The memory is configured to store instructions; and

[0045] The processor is configured to retrieve instructions from memory and, when executing the instructions, to implement the method for determining the radial power density distribution of fuel rods provided in the first aspect of the embodiments of this application.

[0046] Fourthly, embodiments of this application provide a machine-readable storage medium storing instructions for causing a machine to execute the method for determining the radial power density distribution of the fuel rods as described above.

[0047] In this embodiment, the fuel rod is divided into multiple axial segments along the axial direction, and each axial segment is further divided into multiple radial rings. The atomic density and neutron fluence rate of each nuclide within each radial ring are obtained. Based on the atomic density and neutron fluence rate of each nuclide within each radial ring, the volumetric power density function of each radial ring is determined. The volumetric power density function of each radial ring is then normalized to obtain the radial power density distribution factor corresponding to each radial ring. For each radial ring, the product of the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring is determined as the local power of the radial ring. Finally, the radial power density distribution of the fuel rod is determined using the local power of each radial ring. Thus, by determining the radial power density distribution factor corresponding to each radial ring based on the atomic density and neutron fluence rate of each nuclide within each radial ring, and then determining the local power corresponding to each radial ring, the radial power density distribution of the fuel rod can be determined based on the local power corresponding to each radial ring. This eliminates the need to calculate the radial power density distribution calculation table for the fuel rod, thereby enabling accurate performance analysis and design of the fuel rods for the new reactor type. Attached Figure Description

[0048] Figure 1This is a flowchart illustrating the method for determining the radial power density distribution of fuel rods provided in an embodiment of this application.

[0049] Figure 2 This is a schematic flowchart of a method for determining radial power density distribution according to a specific embodiment of this application;

[0050] Figure 3 This is a flowchart illustrating a local nuclide density calculation method provided in a specific embodiment of this application;

[0051] Figure 4 This is a schematic diagram showing a comparison between a specific embodiment of the present application and an experimentally measured radial power density distribution;

[0052] Figure 5 This is a schematic diagram of the structure of a device for determining the radial power density distribution of a fuel rod according to an embodiment of this application;

[0053] Figure 6 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0054] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0055] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0056] The following description, in conjunction with the accompanying drawings, details the method for determining the radial power density distribution of fuel rods and the electronic equipment provided in this application, through specific embodiments and application scenarios.

[0057] Please see Figure 1 This is a flowchart illustrating a method for determining the radial power density distribution of a fuel rod according to an embodiment of this application. This method is applied to electronic devices, where the fuel rod is divided into multiple axial segments along its axis, and each axial segment includes multiple radial rings. For example... Figure 1 As shown, the method for determining the radial power density distribution of the fuel rod includes the following steps S100 to S600.

[0058] Step S100: Obtain the atomic density of each nuclide within each radial ring.

[0059] In this embodiment, fuel rod refers to a fuel assembly used in a nuclear reactor, such as nuclear fuel rods used in a nuclear power plant. Fuel rods in a nuclear power plant serve to contain and support nuclear fuel. Fuel rods may include, but are not limited to, uranium dioxide fuel rods and uranium-plutonium mixed fuel rods. A fuel rod is a cylindrical structure and can be divided into multiple axial segments along its axis. Each axial segment is a cylindrical structure with a circular cross-section. For any given axial segment, multiple concentric circles are drawn based on the center of the cross-section. The cylindrical structure corresponding to each concentric circle is a radial ring. The radial ring can be a hollow or solid cylinder. The height of the radial ring is the same as the height of the axial segment including the radial ring, and the radius of the radial ring is less than or equal to the maximum radius of the axial segment including the radial ring. Each axial segment may include multiple radial rings.

[0060] Each radial ring contains numerous nuclides. A nuclide is an isotope having a specific number of protons and neutrons. Fuel rods are composed of specific nuclides. In a nuclear reactor, fuel rods contain specific nuclides. After dividing the fuel rod into multiple radial rings, each radial ring contains one or more nuclides. The atomic density of a nuclide refers to the number of atoms of a certain nuclide contained per unit volume. When determining the radial power density distribution of the fuel rod, the atomic density of each nuclide within each radial ring is first obtained.

[0061] Step S200: Obtain the neutron fluence rate within each radial ring.

[0062] In this embodiment, neutron fluence rate refers to the neutron flux passing through a unit area per unit time. In nuclear reactors or other radioactive facilities, neutron fluence rate is used to describe the intensity and density of neutron radiation. Based on neutron diffusion theory and the neutron number conservation equation, an analytical solution for the neutron fluence rate distribution can be obtained.

[0063] Step S300: Determine the volume power density function of each radial ring based on the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring.

[0064] In this embodiment, after obtaining the atomic density of each nuclide and the neutron fluence rate of each radial ring, the volumetric power density function of each radial ring is determined based on the atomic density and neutron fluence rate of each nuclide within the radial ring. The volumetric power density function of the radial ring can be expressed as:

[0065]

[0066] in, The volumetric power density function of the radial ring is represented. This represents the cross section of the nuclide fission, which is a preset parameter. Indicates nuclide Local atomic density, Indicates neutron flux rate, This indicates the radius of the radial ring.

[0067] Step S400: Normalize the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring.

[0068] In this embodiment, the radial power density distribution factor can be used to describe the distribution of radial power density. After obtaining the volumetric power density function of each radial ring, the volumetric power density function of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring.

[0069] In one example, the volumetric power density function of each radial ring can be normalized by scaling its value to a specified range. In another example, the volumetric power density function of each radial ring can be integrated by area integration, and then the volumetric power density function of each radial ring can be normalized based on the area integral results to obtain the radial power density distribution factor for each radial ring.

[0070] Step S500: For each radial ring, the product of the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring is determined as the local power corresponding to the radial ring.

[0071] In this embodiment, to determine the radial power density distribution of the fuel rod, it is first necessary to determine the local power inside the fuel rod, i.e., the local power corresponding to each radial ring. For any radial ring, the average power of the axial segment where the radial ring is located and the radial power density distribution factor corresponding to the radial ring are obtained. The average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring are multiplied, and the resulting product is determined as the local power corresponding to the radial ring.

[0072] When obtaining the average power of the axial segment containing the radial ring, in one example, the average power of the axial segment can be obtained by calculating the power of each axial segment of the fuel rod and determining the average power of all axial segments. In another example, the average power of the fuel rod and the axial power density distribution factor of each axial segment are first obtained. Both the average power of the fuel rod and the axial power density distribution factor of each axial segment are attribute parameters of the fuel rod. For each axial segment, the average power of the fuel rod and the axial power density distribution factor of the axial segment are multiplied, and the product is determined as the average power of that axial segment.

[0073] Step S600: Determine the radial power density distribution of the fuel rods using the local power corresponding to each radial ring.

[0074] In this embodiment of the application, after obtaining the local power corresponding to each radial ring, the local power corresponding to each radial ring is statistically analyzed, and the radial power density distribution of the fuel rod is determined based on the distribution of the local power corresponding to each radial ring.

[0075] Through steps S100-S600, the fuel rod is divided into multiple axial segments along the axial direction, and each axial segment is further divided into multiple radial rings. The atomic density and neutron fluence rate of each nuclide within each radial ring are obtained. Based on the atomic density and neutron fluence rate of each nuclide within each radial ring, the volumetric power density function of each radial ring is determined. The volumetric power density function of each radial ring is then normalized to obtain the radial power density distribution factor corresponding to each radial ring. For each radial ring, the product of the average power of the corresponding axial segment and the radial power density distribution factor is determined as the local power of that radial ring. Finally, the radial power density distribution of the fuel rod is determined using the local power of each radial ring. Thus, by determining the radial power density distribution factor corresponding to each radial ring based on the atomic density and neutron fluence rate of each nuclide within each radial ring, and then determining the local power corresponding to each radial ring, the radial power density distribution of the fuel rod can be determined based on the local power corresponding to each radial ring. This allows for the determination of the radial power density distribution of the fuel rod for the nuclides within the fuel rod, without being limited to fixed nuclide categories, thereby improving the accuracy of performance analysis and design of fuel rods for new reactor types.

[0076] In some implementations, the volumetric power density function of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring, including:

[0077] The volumetric power density function of each radial ring is integrated by area integration to obtain the integral result of the volumetric power density function of each radial ring.

[0078] For each radial ring, the volume power density function of the radial ring is normalized by integrating the volume power density function of the radial ring to obtain the radial power density distribution function of the radial ring.

[0079] Obtain the density of each radial ring;

[0080] For each radial ring, the product of the radial power density distribution function corresponding to the radial ring and the density of the radial ring is determined as the radial power density distribution function based on the density influence of the radial ring.

[0081] The radial power density distribution function based on density influence of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring.

[0082] Specifically, when normalizing the volumetric power density function of each radial ring, the volumetric power density function of each radial ring is first integrated using an area integral to obtain the integral result of the volumetric power density function corresponding to each radial ring. For any radial ring, the volumetric power density function of the radial ring is normalized using the integral result of the volumetric power density function corresponding to the radial ring, thus obtaining the radial power density distribution function corresponding to the radial ring. The radial power density distribution function corresponding to the radial ring can be expressed as:

[0083]

[0084] in, This represents the radial power density distribution function corresponding to the radial loop. The volumetric power density function of the radial loop is represented. This indicates the radius of the radial ring. In the case of annular fuel rods, Indicates the outer diameter of the radial ring. This indicates the inner diameter of the radial ring. When the fuel rod is solid, only one radius exists, i.e. for .because In the process When calculating , the proportional coefficient can be simplified and eliminated, so it is not reflected in the above formula.

[0085] Next, obtain the density of each radial ring. The density of each radial ring is an inherent property of the fuel rod and is a fixed value.

[0086] For each radial ring, the product of the radial power density distribution function corresponding to the radial ring and the density of the radial ring is determined as the radial power density distribution function based on the density influence of the radial ring. The radial power density distribution function based on the density influence can be expressed as: .

[0087] The radial power density distribution function based on density influence for each radial ring is normalized to obtain the radial power density distribution factor for each radial ring. In one example, normalization can be achieved by scaling the values ​​of the radial power density distribution function based on density influence for each radial ring to a specified range. In another example, area integration can be performed on the radial power density distribution function based on density influence for each radial ring to obtain the area integral result. Then, the radial power density distribution function based on density influence for each radial ring is normalized based on the area integral result to obtain the radial power density distribution factor for each radial ring.

[0088] By performing a two-step normalization process on the volumetric power density function of each radial ring, the radial power density distribution factor corresponding to each radial ring can be obtained, which can improve the accuracy of the calculation of the radial power density distribution factor, and thus improve the accuracy of the determination of the radial power density distribution of the fuel rod.

[0089] In some implementations, the radial power density distribution function based on density influence of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring, including:

[0090] The radial power density distribution function based on density influence for each radial ring is integrated by area integration to obtain the integral result of the radial power density distribution function based on density influence for each radial ring.

[0091] For each radial ring, the radial power density distribution function based on density influence is normalized using the integral result of the radial power density distribution function based on density influence corresponding to the radial ring, so as to obtain the radial power density distribution factor corresponding to each radial ring.

[0092] Specifically, when normalizing the radial power density distribution function based on density influence for each radial ring, the area integral of the radial power density distribution function based on density influence for each radial ring is first performed to obtain the integral result of the radial power density distribution function based on density influence for each radial ring. Then, the integral result of the radial power density distribution function based on density influence for each radial ring is used to normalize the radial power density distribution function based on density influence, resulting in the radial power density distribution factor for each radial ring. The radial power density distribution factor can be expressed as:

[0093]

[0094] in, Represents the radial power density distribution factor. This represents the radial power density distribution function based on density effects. This indicates the radius of the radial ring. In the case of annular fuel rods, Indicates the outer diameter of the radial ring. This indicates the inner diameter of the radial ring. When the fuel rod is solid, only one radius exists, i.e. for .

[0095] By further normalizing the radial power density distribution function based on density influence, the accuracy of calculating the radial power density distribution factor can be improved, thereby improving the accuracy of determining the radial power density distribution of the fuel rod.

[0096] In some implementations, before determining the local power corresponding to each radial ring by multiplying the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring, the determination method further includes:

[0097] Obtain the average power of the fuel rods and the axial power density distribution factor of each axial segment;

[0098] For each axial segment, the average power of each axial segment is determined by multiplying the average power of the fuel rods by the axial power density distribution factor of the axial segment.

[0099] Specifically, before determining the local power corresponding to the radial ring based on the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring, it is necessary to first determine the average power of the axial segment corresponding to the radial ring. First, obtain the average power of the fuel rods and the axial power density distribution factor of each axial segment. The average power of the fuel rods and the axial power density distribution factor of each axial segment are properties of the fuel rods and are fixed values. For any axial segment, multiply the average power of the fuel rods by the axial power density distribution factor of that axial segment, and determine the average power of that axial segment as the product. By calculating the product of the axial power density distribution factor of each axial segment and the average power of the fuel rods, the average power of each axial segment can be obtained, and then the local power corresponding to the radial ring can be calculated.

[0100] In some implementations, obtaining the atomic density of each nuclide within each radial ring includes:

[0101] Obtain the radial power density distribution function corresponding to each nuclide within each radial ring;

[0102] The atomic density of each nuclide in each radial ring is determined based on the radial power density distribution function corresponding to each nuclide in each radial ring and the preset burnup equation.

[0103] Specifically, a radial ring can be understood as multiple concentric circles defined by the center of the cross-section of an axial segment. Each axial segment can include multiple radial rings. Each radial ring contains many nuclides. A nuclide refers to an isotope having a specific number of protons and neutrons. Fuel rods are composed of specific nuclides. In a nuclear reactor, fuel rods contain specific nuclides. After dividing the fuel rod into multiple radial rings, each radial ring contains one or more nuclides. The atomic density of a nuclide refers to the number of atoms of a certain nuclide contained per unit volume.

[0104] When obtaining the atomic density of each nuclide within each radial ring, the radial power density distribution function corresponding to each nuclide within each radial ring is first obtained. In one example, the nuclide may include... The corresponding radial power density distribution function can be expressed as:

[0105]

[0106] in, This represents the initial radial power density distribution function corresponding to each nuclide. It can be represented as:

[0107]

[0108] in, , , Refers to a constant. The radius of the radial ring.

[0109] After obtaining the radial power density distribution function for each nuclide within each radial ring, the atomic density of each nuclide within each radial ring is determined based on the radial power density distribution function and the preset burnup equation. In one example, the preset burnup equation can be expressed as:

[0110]

[0111]

[0112] in, Indicates nuclide Local atomic density, Indicates nuclide Local atomic density, Indicates nuclide Local atomic density, This indicates the change in fuel consumption. express Neutron absorption cross section of a nuclide express Neutron capture cross section of nuclide express Nuclide cross section of a nuclide Indicates the conversion factor. This represents the average atomic density. Indicates neutron flux rate, Indicates the density of the fuel rod. They can represent nuclides. 、 and .

[0113] By solving the above set of differential equations, the atomic density of each nuclide in the uranium dioxide fuel rod can be obtained.

[0114] Based on the test data of uranium-plutonium mixed fuel rods, it was observed that, in addition to Besides nuclides There is also a significant spatial self-shielding phenomenon. Spatial self-shielding refers to the phenomenon in certain physical or mathematical problems where, due to the inherent characteristics of an object or environmental limitations, some parts cannot access or influence other parts. Therefore, based on the uranium dioxide fuel rod model, a second distribution function is introduced into the calculation of uranium-plutonium mixed fuel rods. Used to describe, it can be expressed as:

[0115]

[0116] The above distribution function and The forms are the same. Among them, the parameters... and Keep it consistent, parameters This can be approximated as the contribution of the ultrathermal neutron resonance absorption region to the effective cross section, specifically expressed as the ratio of resonance absorption to thermal neutron capture, which can be expressed as:

[0117]

[0118] in, This represents the ratio of resonant absorption to thermal neutron capture. This represents the neutron capturing interface. Represents neutron energy. Indicates neutron flux rate, Represents the resonance region integral of the reaction cross section. This represents the thermal neutron region integral of the reaction cross section.

[0119] By determining the atomic density of each nuclide within each radial ring based on the radial power density distribution function and the preset burnup equation, calculations can be performed on different types of nuclides, improving the accuracy of performance analysis and design of fuel rods for new reactor types.

[0120] In some implementations, obtaining the radial power density distribution function corresponding to each nuclide within each radial ring includes:

[0121] Obtain the initial radial power density distribution function for each nuclide within each radial ring;

[0122] The initial radial power density distribution function is integrated by area integration to obtain the integral result of the initial radial power density distribution function;

[0123] By integrating the initial radial power density distribution function, the initial radial power density distribution function is normalized to obtain the radial power density distribution function corresponding to each nuclide in each radial ring.

[0124] Specifically, when obtaining the radial power density distribution function corresponding to each nuclide within each radial ring, the initial radial power density distribution function corresponding to each nuclide within each radial ring is first obtained, which can be expressed as:

[0125]

[0126] Then, consider the initial radial power density distribution function. Area integration is performed to obtain the integral result of the initial radial power density distribution function. Finally, the initial radial power density distribution function is normalized using the integral result to obtain the radial power density distribution function corresponding to each nuclide within each radial ring. The radial power density distribution function corresponding to each nuclide within each radial ring can be expressed as:

[0127]

[0128] By obtaining the initial radial power density distribution function corresponding to each nuclide within each radial ring, and performing area integration and normalization on the initial radial power density distribution function, the accuracy of calculating the radial power density distribution function corresponding to each nuclide within each radial ring can be improved.

[0129] In some implementations, obtaining the neutron flux rate of the fuel rods includes:

[0130] Based on the neutron hypothesis theory, the neutron diffusion equation corresponding to the fuel rod is obtained;

[0131] Obtain the general solution of the neutron diffusion equation and the preset boundary conditions of the neutron diffusion equation;

[0132] The neutron flux rate of the fuel rods is determined based on the general solution and preset boundary conditions.

[0133] Specifically, the neutron hypothesis theory is a theoretical framework in nuclear and particle physics used to describe the behavior and properties of neutrons in atomic nuclei and nuclear reactions. First, based on the neutron hypothesis theory, the neutron diffusion equations corresponding to the fuel rods are obtained. In one example, the single-group neutron hypothesis theory can be used. This theory treats all neutrons as a single energy group, ignoring the detailed distribution of the neutron energy spectrum, thus simplifying the problem and calculations. In another example, the multi-group neutron hypothesis theory can be used. The multi-group neutron hypothesis theory is a more refined model compared to the single-group hypothesis theory, used to describe the changes and effects of neutron energy distribution in nuclear reactions and neutron transport. The basic idea of ​​the multi-group neutron hypothesis theory is to divide the neutron energy distribution into multiple energy ranges, with neutrons in each energy range considered as an energy group, thereby more accurately simulating and calculating neutron behavior and reactions. Compared to the single-group neutron hypothesis theory, the multi-group neutron hypothesis theory has higher computational complexity, requiring the processing of more equations and data, but it provides more accurate results, especially when the significant influence of the neutron energy spectrum needs to be considered.

[0134] In cylindrical coordinates, the neutron diffusion equation can be expressed as:

[0135]

[0136] in, Represents the Laplace operator. The cross section represents the macroscopic absorption cross section of the neutron, and D represents the neutron diffusion absorption coefficient. This represents the neutron fluence rate.

[0137] Next, we obtain the general solution of the neutron diffusion equation and the preset boundary conditions for the neutron diffusion equation. The general solution of the neutron diffusion equation can be expressed as:

[0138]

[0139] Where A and B represent constants, Represents the 0th order modified Bessel function of the first kind. This represents the 0th order modified Bessel function of the second kind.

[0140] The pre-defined boundary conditions of the neutron diffusion equation can be expressed as:

[0141]

[0142] When the fuel rods are solid fuel rods, due to exist Since time is infinity, B must be 0. Therefore, the analytical solution can be expressed as:

[0143] When the fuel rods are annular, the analytical solution for the neutron flux rate can be expressed as:

[0144]

[0145] in, Represents a constant. This represents the first-order modified Bessel function of the first kind. This represents a first-order modified Bessel function of the second kind. Since the radial power density distribution focuses only on relative values, the constant... The value will not affect the radial power density distribution, therefore It can be any constant. By determining the neutron flux rate of the fuel rod based on the general solution of the neutron diffusion equation and the preset boundary conditions, it can be used to further calculate the radial power density distribution of the fuel rod.

[0146] Please see Figure 2 This is a flowchart illustrating a method for determining radial power density distribution according to a specific embodiment of this application. Figure 2 As shown, the method for determining the radial power density distribution may include the following steps:

[0147] Step S201: Calculation of radial power density distribution;

[0148] Step S202: Fuel consumption increment of axial segment i;

[0149] Step S203: Calculate the local nuclide density;

[0150] Step S204: Calculate the analytical solution for the neutron fluence rate distribution;

[0151] Step S205: Unnormalized radial power density distribution;

[0152] Step S206: Radial power density distribution normalization;

[0153] Step S207: Determine if this is the last axial segment. If yes, proceed to step S208; otherwise, return to step S202.

[0154] Step S208: Power distribution calculation ends.

[0155] In this specific embodiment, when determining the radial power density distribution, the calculation is performed on an axial segment basis, calculating the nuclides within the radial ring of a given axial segment. After the radial power density distribution calculation is completed, it is determined whether the current axial segment is the last axial segment of the fuel rod. If the current axial segment is the last axial segment of the fuel rod, the radial power density distribution calculation of the fuel rod is complete. If the current axial segment is not the last axial segment of the fuel rod, the calculation of the radial power density distribution of the next axial segment continues.

[0156] For details on the implementation, please refer to the aforementioned description, which will not be repeated here.

[0157] Please see Figure 3 This is a flowchart illustrating a local nuclide density calculation method provided in a specific embodiment of this application. Figure 3 As shown, this method for calculating local nuclide density may include the following steps:

[0158] Step S301: Simulation Distributed radially on the fuel rods.

[0159] Step S302: Calculate the normalized radial distribution function.

[0160] Step S303: Calculation Density of each nuclide atom within the fuel rod.

[0161] Step S304: Correct the atomic density of each nuclide in the MOX fuel rod.

[0162] For details on the implementation, please refer to the aforementioned description, which will not be repeated here.

[0163] Please see Figure 4 This is a schematic diagram illustrating a comparison between a specific embodiment of this application and experimentally measured radial power density distribution. Figure 4 As shown,

[0164] The radial power density calculation model for fuel pellets established using the method of this invention generates radial power density distributions under different burnout levels. The correctness of the method is verified by comparing these distributions with experimentally measured radial power density distributions. Furthermore, the method is applied to fuel rod performance analysis software, and its correctness is indirectly proven by comparing the results with experimentally measured pellet center temperatures.

[0165] The entire verification process included two comparisons: one was a comparison between the calculated radial power density distribution at five different burn-out depths and the experimental measurements; the other was a comparison between the pellet center temperature calculated using fuel rod performance analysis software based on this model and the experimental measurements. Figure 4 Table 1 presents the comparative analysis results of the radial power density distribution.

[0166] Table 1

[0167]

[0168] Note: Relative deviation = (Calculated result - Experimental result) / Experimental result

[0169] Table 2 presents the comparative analysis results of the core block center temperature.

[0170] Table 2

[0171]

[0172] The comparison results show that, in this specific embodiment, the radial power density distribution of the pellet calculated by the method of this application deviates from the experimental measurement results by no more than 4%, and the pellet center temperature calculated by the fuel rod performance analysis software using this method is consistent with the measurement results.

[0173] Please see Figure 5 This is a schematic diagram of a device for determining the radial power density distribution of a fuel rod according to an embodiment of this application. A second aspect of this application provides a device 50 for determining the radial power density distribution of a fuel rod, the device 50 comprising:

[0174] The first acquisition module 51 is used to acquire the atomic density of each nuclide in each radial ring;

[0175] The second acquisition module 52 is used to acquire the neutron fluence rate in each radial ring;

[0176] The first determining module 53 is used to determine the volume power density function of each radial ring based on the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring.

[0177] Processing module 54 is used to normalize the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring.

[0178] The second determining module 55 is used to determine the local power of each radial ring by multiplying the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring.

[0179] The third determining module 56 is used to determine the radial power density distribution of the fuel rod by utilizing the local power corresponding to each radial ring.

[0180] The apparatus 50 for determining the radial power density distribution of fuel rods provided in the second aspect of this application can implement the various processes implemented in the above method embodiments and achieve the same beneficial effects. To avoid repetition, it will not be described again here.

[0181] Please see Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. A third aspect of this application provides an electronic device 6000, including a processor 6100 and a memory 6200. The memory 6200 stores machine-executable instructions that can be executed by the processor 6100. The processor 6100 can execute the machine-executable instructions to implement the above-mentioned method for determining the radial power density distribution of fuel rods.

[0182] In some embodiments, this application also provides a machine-readable storage medium storing instructions that, when executed by a processor, cause the processor to implement the above-described method for determining the radial power density distribution of fuel rods.

[0183] In some embodiments, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the method for determining the radial power density distribution of fuel rods according to the above embodiments.

[0184] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0185] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0186] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0187] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0188] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0189] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0190] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

[0191] Furthermore, various different embodiments of the present invention can be combined in any way, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed by the present invention.

Claims

1. A method for determining the radial power density distribution of a fuel rod, characterized in that, The fuel rod is divided into multiple axial segments along its axial direction, and each axial segment includes multiple radial rings. The method for determining these segments includes: Obtain the atomic density of each nuclide within each radial ring; Obtain the neutron fluence rate within each of the radial rings; The volume power density function of each radial ring is determined based on the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring. The volume power density function of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring; For each radial ring, the product of the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring is determined as the local power corresponding to the radial ring. The radial power density distribution of the fuel rod is determined by utilizing the local power corresponding to each radial ring. The normalization of the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring includes: The volume power density function of each radial ring is integrated by area integration to obtain the volume power density function integral result corresponding to each radial ring; For each radial ring, the volume power density function of the radial ring is normalized by integrating the volume power density function corresponding to the radial ring, so as to obtain the radial power density distribution function corresponding to the radial ring. Obtain the density of each radial ring; For each radial ring, the product of the radial power density distribution function corresponding to the radial ring and the density of the radial ring is determined as the radial power density distribution function based on the density influence corresponding to the radial ring. The radial power density distribution function based on density influence of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring.

2. The determination method according to claim 1, characterized in that, The normalization process for the radial power density distribution function based on density influence of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring includes: The area integral of the radial power density distribution function based on density influence for each radial ring is performed to obtain the integral result of the radial power density distribution function based on density influence for each radial ring. For each radial ring, the radial power density distribution function based on density influence is normalized using the integral result of the radial power density distribution function based on density influence corresponding to the radial ring, so as to obtain the radial power density distribution factor corresponding to each radial ring.

3. The method according to claim 1, characterized in that, Before determining the local power corresponding to each radial ring by multiplying the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring, the determination method further includes: Obtain the average power of the fuel rods and the axial power density distribution factor of each axial segment; For each axial segment, the average power of the fuel rod is determined by multiplying the average power of the fuel rod by the axial power density distribution factor of the axial segment.

4. The determination method according to claim 1, characterized in that, The process of obtaining the atomic density of each nuclide within each radial ring includes: Obtain the radial power density distribution function corresponding to each nuclide within each radial ring; The atomic density of each nuclide within each radial ring is determined based on the radial power density distribution function corresponding to each nuclide within each radial ring and the preset burnup equation.

5. The determination method according to claim 4, characterized in that, The step of obtaining the radial power density distribution function corresponding to each nuclide within each radial ring includes: Obtain the initial radial power density distribution function corresponding to each nuclide within each radial ring; The initial radial power density distribution function is integrated by area integration to obtain the integral result of the initial radial power density distribution function; By integrating the initial radial power density distribution function, the initial radial power density distribution function is normalized to obtain the radial power density distribution function corresponding to each nuclide in each radial ring.

6. The determination method according to claim 1, characterized in that, The process of obtaining the neutron flux rate of the fuel rod includes: Based on the neutron hypothesis theory, the neutron diffusion equation corresponding to the fuel rod is obtained; Obtain the general solution of the neutron diffusion equation and the preset boundary conditions of the neutron diffusion equation; The neutron flux rate of the fuel rod is determined based on the general solution and the preset boundary conditions.

7. A device for determining the radial power density distribution of a fuel rod, characterized in that, The fuel rod is divided into multiple axial segments along its axial direction, and each axial segment includes multiple radial rings. The determining device includes: The first acquisition module is used to acquire the atomic density of each nuclide in each radial ring; The second acquisition module is used to acquire the neutron fluence rate within each radial ring; The first determining module is used to determine the volume power density function of each radial ring based on the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring. The processing module is used to normalize the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring. The second determining module is used to determine the local power corresponding to each radial ring by multiplying the average power of the axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring. The third determining module is used to determine the radial power density distribution of the fuel rod by utilizing the local power corresponding to each radial ring; The processing module is further configured to: The volume power density function of each radial ring is integrated by area integration to obtain the volume power density function integral result corresponding to each radial ring; For each radial ring, the volume power density function of the radial ring is normalized by integrating the volume power density function corresponding to the radial ring, so as to obtain the radial power density distribution function corresponding to the radial ring. Obtain the density of each radial ring; For each radial ring, the product of the radial power density distribution function corresponding to the radial ring and the density of the radial ring is determined as the radial power density distribution function based on the density influence corresponding to the radial ring. The radial power density distribution function based on density influence of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring.

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