Method for determining radial power density distribution of fuel rod, and product

Abstract

A method for determining a radial power density distribution of a fuel rod, and a product, relating to the technical field of nuclear control. The method comprises: acquiring an atomic density of each nuclide (S100) and a neutron fluence rate (S200) in each radial ring; on the basis of the atomic density and the neutron fluence rate, determining a volume power density function of each radial ring (S300); normalizing the volume power density function to obtain a radial power density distribution factor (S400); determining the product of the average power of an axial section and the radial power density distribution factor corresponding to the radial ring as a local power corresponding to the radial ring (S500); and determining a radial power density distribution of a fuel rod by using the local power (S600). The above method enables determination of a radial power density distribution of a fuel rod without being limited to a fixed nuclide category, and can improve the accuracy of performance analysis and design of a new reactor-type fuel rod.

Description

Method and product for determining radial power density distribution of fuel rod TECHNICAL FIELD

[0001] The present application relates to the field of nuclear control, in particular to a method and product for determining radial power density distribution of fuel rod. BACKGROUND

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

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

[0004] However, for the performance analysis and design of the fuel rod of a new reactor type (such as a lead reactor, a fast reactor, etc.), the corresponding physical software is still in the development process and has not yet matured, and therefore the ability to provide the calculation table of the radial power density distribution of the fuel rod is temporarily unavailable, that is, the interpolation table method of the radial power density distribution of the fuel rod cannot be provided. Moreover, due to the large difference between the radial power density distribution of the fuel rod of the new and old reactor types, the use of the existing calculation table of the radial power density distribution of the fuel rod cannot accurately complete the performance analysis and design of the fuel rod of the new reactor type. SUMMARY

[0005] The purpose of the embodiments of the present application is to provide a method and product for determining the radial power density distribution of the fuel rod, so as to accurately complete the performance analysis and design of the fuel rod of the new reactor type.

[0006] In a first aspect, the embodiments of the present application provide a method for determining the radial power density distribution of the fuel rod, the fuel rod is divided into a plurality of axial segments along the axial direction, and each axial segment includes a plurality of radial rings, and the method comprises the following steps:

[0007] obtaining the atomic density of each nuclide in each radial ring;

[0008] obtaining the neutron fluence rate in each radial ring;

[0009] determining the volume power density function of each radial ring according to the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring;

[0010] performing normalization processing on the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring;

[0011] For each radial ring, a 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;

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

[0013] In some embodiments, the volume 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 volume power density function of each radial ring is area-integrated to obtain the volume power density function integral result corresponding to each radial ring;

[0015] For each radial ring, the volume power density function of the radial ring is normalized by using the volume power density function integral result corresponding to the radial ring to obtain the radial power density distribution function corresponding to the radial ring;

[0016] The density of each radial ring is obtained;

[0017] For each radial ring, a product of the radial power density distribution function corresponding to the radial ring and the density of the radial ring is determined as the density-influenced radial power density distribution function corresponding to the radial ring;

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

[0019] In some embodiments, the density-influenced radial power density distribution function of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring, including:

[0020] The density-influenced radial power density distribution function of each radial ring is area-integrated to obtain the density-influenced radial power density distribution function integral result corresponding to each radial ring;

[0021] For each radial ring, the density-influenced radial power density distribution function of the radial ring is normalized by using the density-influenced radial power density distribution function integral result corresponding to the radial ring to obtain the radial power density distribution factor corresponding to each radial ring.

[0022] In some embodiments, before 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 for each radial ring, the method further includes:

[0023] obtaining an average power of the fuel rod and an axial power density distribution factor of each axial segment;

[0024] For each axial segment, a product of the average power of the fuel rod and the axial power density distribution factor of the axial segment is determined as an average power of the axial segment.

[0025] In some embodiments, obtaining the atomic density of each nuclide in each radial ring comprises:

[0026] obtaining a radial power density distribution function corresponding to each nuclide in each radial ring;

[0027] determining the atomic density of each nuclide in each radial ring according to the radial power density distribution function corresponding to each nuclide in each radial ring and a preset burnup equation.

[0028] In some embodiments, obtaining the radial power density distribution function corresponding to each nuclide in each radial ring comprises:

[0029] obtaining an initial radial power density distribution function corresponding to each nuclide in each radial ring;

[0030] performing an area integral processing on the initial radial power density distribution function to obtain an initial radial power density distribution function integral result;

[0031] normalizing the initial radial power density distribution function by using the initial radial power density distribution function integral result to obtain the radial power density distribution function corresponding to each nuclide in each radial ring.

[0032] In some embodiments, obtaining the neutron fluence rate of the fuel rod comprises:

[0033] obtaining a neutron diffusion equation corresponding to the fuel rod based on a neutron hypothesis theory;

[0034] obtaining a general solution of the neutron diffusion equation and a preset boundary condition of the neutron diffusion equation;

[0035] determining the neutron fluence rate of the fuel rod according to the general solution and the preset boundary condition.

[0036] In a second aspect, an embodiment of the present application provides a determination device for radial power density distribution of a fuel rod, and the determination device comprises:

[0037] a first obtaining module configured to obtain atomic density of each nuclide in each radial ring;

[0038] a second obtaining module configured to obtain a 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 the embodiment of the present application, the fuel rod is divided into multiple axial segments along the axial direction, and each axial segment is divided into multiple radial rings. The atomic density and the neutron fluence rate of each nuclide in each radial ring are obtained. According to 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 determined. 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. Finally, the radial power density distribution of the fuel rod is determined by using the local power corresponding to each radial ring. In this way, by determining the radial power density distribution factor corresponding to each radial ring according to the atomic density and the neutron fluence rate of each nuclide in each radial ring, and then determining the local power corresponding to each radial ring, and determining the radial power density distribution of the fuel rod according to the local power corresponding to each radial ring, the determination of the radial power density distribution of the fuel rod can be realized without the calculation of the fuel rod radial power density distribution calculation table, so that the performance analysis and design of the new reactor fuel rod can be accurately realized. BRIEF DESCRIPTION OF DRAWINGS

[0048] FIG. 1 is a flowchart of a method for determining the radial power density distribution of a fuel rod according to an embodiment of the present application;

[0049] FIG. 2 is a flowchart of a method for determining the radial power density distribution according to an embodiment of the present application;

[0050] FIG. 3 is a flowchart of a method for calculating the local nuclide density according to an embodiment of the present application;

[0051] FIG. 4 is a schematic diagram of a comparison result of the radial power density distribution measured by the test according to an embodiment of the present application;

[0052] FIG. 5 is a structural schematic diagram of a device for determining the radial power density distribution of a fuel rod according to an embodiment of the present application;

[0053] FIG. 6 is a structural schematic diagram of an electronic device according to an embodiment of the present application. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present application will be clearly described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art belong to the scope of protection of the present application.

[0055] The terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than that illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of a kind and do not limit the number of objects, for example, the first object can be one or more. In addition, "and / or" in the specification and claims indicates at least one of the connected objects, and the character " / " generally indicates that the front and rear associated objects are in an "or" relationship.

[0056] The fuel rod radial power density distribution determination method and the electronic device provided by the embodiments of the present application will be described in detail below in combination with the drawings, specific embodiments and application scenarios.

[0057] Please refer to FIG. 1, which is a flowchart of the fuel rod radial power density distribution determination method provided by the embodiments of the present application. The method is applied to an electronic device. The fuel rod is divided into multiple axial segments along the axial direction, and each axial segment includes multiple radial rings. As shown in FIG. 1, the fuel rod radial power density distribution determination method includes the following steps S100 to S600.

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

[0059] In the embodiments of the present application, the fuel rod refers to a fuel assembly used in a nuclear reactor, such as a nuclear fuel rod used in a nuclear power plant. The fuel rod can serve to contain and support nuclear fuel in a nuclear power plant. The fuel rod can include but is not limited to a uranium dioxide fuel rod and a uranium-plutonium mixed fuel rod, etc. The fuel rod is a cylindrical structure and can be divided into multiple axial segments along the axial direction. Each axial segment is a cylindrical structure, and the cross section of each axial segment is circular. For any one axial segment, based on the center of the cross section, multiple concentric circles are drawn, and each concentric circle corresponds to a cylindrical structure of a radial ring. The radial ring is a hollow cylindrical structure or a solid cylindrical structure, 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 annular ring of the radial ring is less than or equal to the maximum radius of the axial segment including the radial ring. Each axial segment can include multiple radial rings.

[0060] Each radial ring includes many nuclides. Nuclide refers to an isotope with a specific number of protons and neutrons. The fuel rod is composed of specific nuclides. In a nuclear reactor, the fuel rod contains specific nuclides. After the fuel rod is divided into multiple radial rings, each radial ring range includes one or more nuclides. The atomic density of a nuclide refers to the number of atoms of a certain nuclide contained in a unit volume. When determining the radial power density distribution of the fuel rod, the atomic density of each nuclide in each radial ring is first obtained.

[0061] Step S200: Obtain the neutron flux in each radial ring.

[0062] In the embodiments of the present application, the neutron flux is the neutron flux per unit time through a unit area. In a nuclear reactor or other radioactive equipment, the neutron flux is used to describe the intensity and density of neutron radiation. According to the neutron diffusion theory and the neutron number conservation equation, the analytical solution of the neutron flux distribution can be obtained.

[0063] Step S300: Determine the volume power density function of each radial ring according to the atomic density of each nuclide in each radial ring and the neutron flux in each radial ring.

[0064] In the embodiments of the present application, after obtaining the atomic density of each nuclide in each radial ring and the neutron flux in each radial ring, for each radial ring, the volume power density function of the radial ring is determined according to the atomic density of each nuclide in the radial ring and the neutron flux. The volume power density function of the radial ring can be expressed as:

[0065] where q3(r) represents the volume power density function of the radial ring. σ f,k represents the nuclide fission cross section, which is a preset parameter. N k (r) represents the local atomic density of the nuclide k, and φ (r) represents the neutron flux, and r represents the radius of the radial ring.

[0066] 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.

[0067] In the embodiments of the present application, the radial power density distribution factor can be used to describe the distribution of the radial power density. After obtaining the volume power density function of 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.

[0068] In one example, the volume power density function of each radial ring can be scaled to a specified range to realize the normalization of the volume power density function of each radial ring. In another example, the volume power density function of each radial ring can be area-integrated to obtain an area integration result, and then the volume power density function of each radial ring is normalized according to the area integration result of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring.

[0069] Step S500: For each radial ring, a 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.

[0070] In the embodiment of the present application, to determine the radial power density distribution of the fuel rod, the local power inside the fuel rod, i.e., the local power corresponding to each radial ring, needs to be determined first. 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 is multiplied by the radial power density distribution factor corresponding to the radial ring, and the product obtained is determined as the local power corresponding to the radial ring.

[0071] In obtaining the average power of the axial segment where the radial ring is located, 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 value of the 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 obtained first. The average power of the fuel rod and the axial power density distribution factor of each axial segment are both attribute parameters of the fuel rod. For each axial segment, the average power of the fuel rod is multiplied by the axial power density distribution factor of the axial segment, and the product obtained is determined as the average power of the axial segment.

[0072] Step S600: The radial power density distribution of the fuel rod is determined by using the local power corresponding to each radial ring.

[0073] In the embodiment of the present application, after obtaining the local power corresponding to each radial ring, the local power corresponding to each radial ring is counted, and the radial power density distribution of the fuel rod is determined according to the distribution of the local power corresponding to each radial ring.

[0074] By the steps S100-S600, the fuel rod is divided into a plurality of axial segments along the axial direction, and each axial segment is divided into a plurality of radial rings. The atomic density and the neutron fluence rate of each nuclide in each radial ring are obtained. According to 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 determined. 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. Finally, the radial power density distribution of the fuel rod is determined by using the local power corresponding to each radial ring. In this way, by determining the radial power density distribution factor corresponding to each radial ring according to the atomic density and the neutron fluence rate of each nuclide in each radial ring, and then determining the local power corresponding to each radial ring, and determining the radial power density distribution of the fuel rod according to the local power corresponding to each radial ring, the radial power density distribution of the fuel rod can be determined for the nuclides in the fuel rod, which is not limited to a fixed nuclide category, and the accuracy of performance analysis and design of new reactor fuel rods can be improved.

[0075] In some embodiments, the volume power density function of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring, including:

[0076] The volume power density function of each radial ring is area-integrated to obtain the volume power density function integral result corresponding to each radial ring;

[0077] For each radial ring, the volume power density function of the radial ring is normalized by using the volume power density function integral result corresponding to the radial ring to obtain the radial power density distribution function corresponding to the radial ring;

[0078] The density of each radial ring is obtained;

[0079] 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 density-influenced radial power density distribution function corresponding to the radial ring;

[0080] The density-influenced radial power density distribution function of each radial ring is normalized to obtain the radial power density distribution factor corresponding to each radial ring.

[0081] Specifically, in the normalization process of the volume power density function of each radial ring, the volume power density function of each radial ring is first subjected to area integration to obtain the volume power density function integral result corresponding to each radial ring. For any radial ring, the volume power density function of the radial ring is normalized using the volume power density function integral result corresponding to the radial ring, so that the radial power density distribution function corresponding to the radial ring can be obtained. The radial power density distribution function corresponding to the radial ring can be expressed as:

[0082] wherein q nor 3(r) represents the radial power density distribution function corresponding to the radial ring, q3(r) represents the volume power density function of the radial ring, and r represents the radius of the radial ring. In the case of a ring-shaped fuel rod, r out represents the outer diameter of the radial ring, and r in represents the inner diameter of the radial ring. In the case of a solid fuel rod, only one radius exists, i.e. r 2 . Since q3(r)∝∑ k σ f,k ·N k (r)·φ (r) , the proportional coefficient can be simplified and eliminated in the calculation of q nor 3(r), and therefore is not reflected in the above formula.

[0083] The density of each radial ring is then obtained, which is a fixed value and an inherent property of the fuel rod.

[0084] 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, which can be expressed as: q ρ 3(r)=q nor 3(r)·ρ(r).

[0085] The density-influenced radial power density distribution function of each radial ring is normalized to obtain a radial power density distribution factor corresponding to each radial ring. In one example, the density-influenced radial power density distribution function of each radial ring can be normalized by scaling the value of the density-influenced radial power density distribution function of each radial ring to a specified range. In another example, the density-influenced radial power density distribution function of each radial ring can be normalized by area integration of the density-influenced radial power density distribution function of each radial ring to obtain an area integration result, and then the density-influenced radial power density distribution function of each radial ring is normalized according to the area integration result of each radial ring to obtain a radial power density distribution factor corresponding to each radial ring.

[0086] By two-step normalization of the volume power density function of each radial ring, a radial power density distribution factor corresponding to each radial ring is obtained, which can improve the accuracy of the calculation of the radial power density distribution factor, and further improve the accuracy of the determination of the radial power density distribution of the fuel rod.

[0087] In some embodiments, the density-influenced radial power density distribution function of each radial ring is normalized to obtain a radial power density distribution factor corresponding to each radial ring, including:

[0088] The density-influenced radial power density distribution function of each radial ring is area integrated to obtain a density-influenced radial power density distribution function integration result corresponding to each radial ring.

[0089] For each radial ring, the density-influenced radial power density distribution function is normalized using the density-influenced radial power density distribution function integration result corresponding to the radial ring to obtain a radial power density distribution factor corresponding to each radial ring.

[0090] Specifically, when the density-influenced radial power density distribution function of each radial ring is normalized, the density-influenced radial power density distribution function of each radial ring is first area integrated to obtain a density-influenced radial power density distribution function integration result corresponding to each radial ring. Then, the density-influenced radial power density distribution function is normalized using the density-influenced radial power density distribution function integration result corresponding to the radial ring to obtain a radial power density distribution factor corresponding to each radial ring. The radial power density distribution factor can be represented as:

[0091] wherein, denotes the radial power density distribution factor, q ρ3(r) represents a radial power density distribution function based on the density effect, and r represents the radius of the radial ring. In the case of a fuel rod in the form of a ring, r out represents the outer diameter of the radial ring, and r in represents the inner diameter of the radial ring. In the case of a fuel rod in the form of a solid, there is only one radius, i.e. r 2 .

[0092] By further normalizing the radial power density distribution function based on the density effect, the accuracy of the calculation of the radial power density distribution factor can be improved, and the accuracy of the determination of the radial power density distribution of the fuel rod can be improved.

[0093] In some embodiments, for each radial ring, before determining the local power corresponding to the radial ring as the product of the average power of the axial section corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring, the method further comprises:

[0094] obtaining the average power of the fuel rod and the axial power density distribution factor of each axial section;

[0095] For each axial section, the product of the average power of the fuel rod and the axial power density distribution factor of the axial section is determined as the average power of the axial section.

[0096] Specifically, before determining the local power corresponding to the radial ring as the product of the average power of the axial section 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 section corresponding to the radial ring. First, obtain the average power of the fuel rod and the axial power density distribution factor of each axial section. The average power of the fuel rod and the axial power density distribution factor of each axial section are both properties of the fuel rod and are fixed values. For any one axial section, multiply the average power of the fuel rod and the axial power density distribution factor of the axial section, and determine the product obtained as the average power of the axial section. By calculating the product of the axial power density distribution factor of each axial section and the average power of the fuel rod, the average power of each axial section can be obtained, and the local power corresponding to the radial ring can be calculated.

[0097] In some embodiments, obtaining the atomic density of each nuclide in each radial ring comprises:

[0098] obtaining the radial power density distribution function corresponding to each nuclide in each radial ring;

[0099] determining the atomic density of each nuclide in each radial ring according to the radial power density distribution function corresponding to each nuclide in each radial ring and a preset burnup equation.

[0100] Specifically, the radial ring can be understood as a plurality of concentric circles determined by the center of the cross section of the axial segment. Each axial segment can include a plurality of radial rings. Each radial ring includes a plurality of nuclides. A nuclide refers to an isotope with a specific number of protons and neutrons. A fuel rod is composed of specific nuclides. In a nuclear reactor, a fuel rod contains specific nuclides. After dividing the fuel rod into a plurality of radial rings, each radial ring range includes one or more nuclides. The atomic density of a nuclide refers to the number of atoms of a certain nuclide contained in a unit volume.

[0101] In obtaining the atomic density of each nuclide in each radial ring, the corresponding radial power density distribution function of each nuclide in each radial ring is first obtained. In one example, the nuclides can include Pu 239 The corresponding radial power density distribution function can be expressed as:

[0102] where f(r) represents the initial radial power density distribution function corresponding to each nuclide, and f(r) can be expressed as:

[0103] where p1, p2, and p3 are constants, and r is the radius of the radial ring.

[0104] After obtaining the radial power density distribution function corresponding to each nuclide in each radial ring, the atomic density of each nuclide in each radial ring is determined according to the radial power density distribution function corresponding to each nuclide in each radial ring and a predetermined burnup equation. In one example, the predetermined burnup equation can be expressed as:

[0105] where N 235 represents the local atomic density of nuclide U 235 , N 238 represents the local atomic density of nuclide U 238 , N 239 represents the local atomic density of nuclide U 239 , dbu represents the change in burnup, σ a,k represents the neutron absorption cross section of k nuclide, σ c,k represents the neutron capture cross section of k nuclide, σ f,k represents the nuclide fission cross section of k nuclide, and α represents the conversion coefficient. represents the average atomic density, φ represents the neutron fluence rate, and ρ fuel represents the fuel rod density, and j can represent nuclides Pu 240 , Pu 241 , and Pu 242 , respectively.

[0106] By solving the above differential equations, the atomic density of each nuclide in the uranium dioxide fuel rod can be obtained.

[0107] According to the test data of the uranium-plutonium mixed fuel rod, it is observed that the U 238 In addition to U 240 There is also a significant spatial self-shielding phenomenon. Spatial self-shielding phenomenon refers to a phenomenon in which, due to the characteristics of an object itself or the limitations of the environment, some parts cannot contact or affect other parts in certain physical or mathematical problems. Therefore, on the basis of the uranium dioxide fuel rod model, a second distribution function f 240 (r) is introduced in the calculation of the uranium-plutonium mixed fuel rod to describe, which can be expressed as:

[0108] The above distribution function f 240 (r) is the same as f nor (r). The parameters p2 and p3 remain the same, and the parameter p1 can be approximately considered as the contribution degree of the epithermal neutron resonance absorption region to the effective cross section, which can be expressed as the ratio of resonance absorption to thermal neutron capture, which can be expressed as:

[0109] Where p1 represents the ratio of resonance absorption to thermal neutron capture, σ cc represents the neutron capture interface, E represents the neutron energy, φ represents the neutron flux, and ∫ res σ c (E)φ(E)dE represents the resonance region integral of the reaction cross section, and ∫ th σ c (E)φ(E)dE represents the thermal neutron region integral of the reaction cross section.

[0110] By determining the atomic density of each nuclide in each radial ring according to the radial power density distribution function corresponding to each nuclide in each radial ring and the preset burnup equation, the calculation of different types of nuclides can be realized, and the accuracy of performance analysis and design of new fuel rod types can be improved

[0111] In some embodiments, obtaining the radial power density distribution function corresponding to each nuclide in each radial ring includes:

[0112] Obtaining an initial radial power density distribution function corresponding to each nuclide in each radial ring;

[0113] Performing area integral processing on the initial radial power density distribution function to obtain an initial radial power density distribution function integral result;

[0114] Normalizing the initial radial power density distribution function using the initial radial power density distribution function integral result to obtain the radial power density distribution function corresponding to each nuclide in each radial ring.

[0115] Specifically, in obtaining the radial power density distribution function corresponding to each nuclide in each radial ring, first, the initial radial power density distribution function corresponding to each nuclide in each radial ring is obtained, which can be expressed as:

[0116] Then, the initial radial power density distribution function f(r) is subjected to area integration processing to obtain the initial radial power density distribution function integration result. Finally, the initial radial power density distribution function is normalized using the initial radial power density distribution function integration result to obtain the radial power density distribution function corresponding to each nuclide in each radial ring. The radial power density distribution function corresponding to each nuclide in each radial ring can be expressed as:

[0117] By obtaining the initial radial power density distribution function corresponding to each nuclide in each radial ring, and subjecting the initial radial power density distribution function to area integration and normalization processing, the accuracy of the calculation of the radial power density distribution function corresponding to each nuclide in each radial ring can be improved.

[0118] In some embodiments, the neutron fluence rate of the fuel rod is obtained, including:

[0119] Based on the neutron hypothesis theory, a neutron diffusion equation corresponding to the fuel rod is obtained;

[0120] The general solution of the neutron diffusion equation and the preset boundary condition of the neutron diffusion equation are obtained;

[0121] The neutron fluence rate of the fuel rod is determined according to the general solution and the preset boundary condition.

[0122] Specifically, the neutron hypothesis theory refers to a theoretical framework in nuclear physics 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, a neutron diffusion equation corresponding to the fuel rod is obtained. In one example, a single-energy-group neutron hypothesis theory can be used, which treats all neutrons as a single energy group, ignoring the detailed distribution of neutron energy spectrum, simplifying the problem processing and calculation. In another example, a multi-energy-group neutron hypothesis theory can also be used. The multi-energy-group neutron hypothesis theory is a more refined model relative to the single-energy-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-energy-group neutron hypothesis theory is to divide the neutron energy distribution into multiple energy ranges, and the neutrons in each energy range are treated as an energy group, so as to more accurately simulate and calculate the behavior and reactions of neutrons. Compared with the single-energy-group neutron hypothesis theory, the multi-energy-group neutron hypothesis theory has higher computational complexity and needs to handle more equations and data, but can provide more accurate results, especially in cases where the influence of neutron energy spectrum is significant.

[0123] In a cylindrical coordinate system, the neutron diffusion equation can be expressed as:

[0124] where Δ represents the Laplace operator, ∑a represents the neutron macroscopic absorption cross section, D represents the neutron diffusion absorption coefficient, and φ(r) represents the neutron flux.

[0125] The general solution of the neutron diffusion equation and the preset boundary condition of the neutron diffusion equation are obtained. The general solution of the neutron diffusion equation can be expressed as: φ(r) = A·I0(kr) + B·K0(kr)

[0126] where A and B represent constants, I0(kr) represents the 0th order modified Bessel function of the first kind, and K0(kr) represents the 0th order modified Bessel function of the second kind.

[0127] The preset boundary condition of the neutron diffusion equation can be expressed as:

[0128] In the case of a solid fuel rod, since K0 is infinite at r = 0, B must be 0, and the analytical solution can be expressed as: φ(r) = C1·I0(kr)

[0129] In the case of a ring-shaped fuel rod, the analytical solution of the neutron flux can be expressed as:

[0130] where C1 represents a constant, I1(kr) represents the 1st order modified Bessel function of the first kind, and K1(kr) represents the 1st order modified Bessel function of the second kind. Since the radial power density distribution only concerns the relative value, the value of the constant C1 does not affect the radial power density distribution, so C1 can be any constant. By determining the neutron flux of the fuel rod according to the general solution of the neutron diffusion equation and the preset boundary condition, the radial power density distribution of the fuel rod can be further calculated.

[0131] Please refer to FIG. 2, which is a flowchart of a radial power density distribution determination method according to an embodiment of the present application. As shown in FIG. 2, the radial power density distribution determination method can include the following steps:

[0132] Step S201: radial power density distribution calculation;

[0133] Step S202: fuel burnup increment of axial segment i;

[0134] Step S203: calculation of local nuclide density;

[0135] Step S204: calculation of analytical solution of neutron flux distribution;

[0136] Step S205: non-normalized radial power density distribution;

[0137] Step S206: normalizing radial power density distribution;

[0138] Step S207: judging whether it is the last axial segment, if yes, entering step S208, if no, returning to step S202;

[0139] Step S208: power distribution calculation ends.

[0140] In the embodiment, the radial power density distribution is calculated in axial segments, and the nuclides in the radial ring in a certain axial segment are calculated. After the radial power density distribution is calculated, it is judged 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 calculation of the radial power density distribution of the fuel rod ends. If the current axial segment is not the last axial segment of the fuel rod, the radial power density distribution of the next axial segment is calculated.

[0141] The specific implementation can refer to the foregoing description, which will not be repeated here.

[0142] Please refer to FIG. 3, which is a flowchart of a local nuclide density calculation method according to an embodiment of the present application.

[0143] As shown in FIG. 3, the local nuclide density calculation method can include the following steps:

[0144] Step S301: simulating Pu 239 in the fuel rod.

[0145] Step S302: calculating the normalized radial distribution function.

[0146] Step S303: calculating the nuclide atomic density in the UO2 fuel rod.

[0147] Step S304: correcting to obtain the nuclide atomic density in the MOX fuel rod.

[0148] The specific implementation can refer to the foregoing description, which will not be repeated here.

[0149] Please refer to FIG. 4, which is a diagram of the comparison result of the radial power density distribution measured by the test and the radial power density distribution according to an embodiment of the present application. As shown in FIG. 4,

[0150] The core radial power density calculation model established by the method is used to generate radial power density distribution under different burnups, and the correctness of the method is verified by comparing the radial power density distribution results with the test measurement results. The method is applied to the fuel rod performance analysis software, and the correctness of the method is indirectly proved by comparing the core center temperature with the test measurement results.

[0151] The entire verification includes two comparisons: one is to compare the radial power density distribution calculation results under five different burnup depths with the test measurement results. The other is to compare the core center temperature calculated by the fuel rod performance analysis software using the model with the test measurement results. FIG. 4 and Table 1 show the comparative analysis results of the radial power density distribution.

[0152] Table 1

[0153] Note: Relative deviation = (calculated result-test result) / test result

[0154] Table 2 shows the comparative analysis results of the core center temperature.

[0155] Table 2

[0156] From the comparison results, in the specific embodiment of the present application, the deviation of the core radial power density distribution results calculated by the method from the test measurement results is not more than 4%, and the core center temperature calculated by the fuel rod performance analysis software using the method is consistent with the measurement results.

[0157] Please refer to FIG. 5, which is a structural schematic diagram of a determination device for fuel rod radial power density distribution provided by the embodiment of the present application. The second aspect of the embodiment of the present application provides a determination device 50 for fuel rod radial power density distribution, which comprises:

[0158] The first acquisition module 51 is configured to acquire the atomic density of each nuclide in each radial ring.

[0159] The second acquisition module 52 is configured to acquire the neutron fluence rate in each radial ring.

[0160] The first determination module 53 is configured to determine the volume power density function of each radial ring according to the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring.

[0161] The processing module 54 is configured to perform normalization processing on the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring.

[0162] The second determining module 55 is configured to determine, for each radial ring, a product of an average power of the axial segment corresponding to the radial ring and a radial power density distribution factor corresponding to the radial ring as a local power corresponding to the radial ring.

[0163] The third determining module 56 is configured to determine the radial power density distribution of the fuel rod by using the local power corresponding to each radial ring.

[0164] The determination apparatus 50 for the radial power density distribution of the fuel rod provided in the second aspect of the embodiments of the present application can implement each process implemented by the method embodiments and achieve the same beneficial effects. To avoid repetition, details are not described herein.

[0165] Referring to FIG. 6, which is a structural schematic diagram of an electronic device provided in the embodiments of the present application, the third aspect of the embodiments of the present application provides an electronic device 6000, which includes 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 determination method for the radial power density distribution of the fuel rod.

[0166] In some embodiments, the embodiments of the present application further provide a machine readable storage medium, which stores instructions. The instructions are executed by a processor to enable the processor to implement the determination method for the radial power density distribution of the fuel rod.

[0167] In some embodiments, the embodiments of the present application further provide a computer program product, which includes a computer program. The computer program is executed by a processor to implement the determination method for the radial power density distribution of the fuel rod according to the above embodiments.

[0168] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can be in the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can be in the form of a computer program product implemented 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.

[0169] The computer program instructions can 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 such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks or in conjunction with the flowcharts described above.

[0170] In one typical arrangement, the computing device includes one or more processors (CPUs), input / output interfaces, network interfaces, and memory.

[0171] The memory can include non-persistent memory and / or volatile memory, such as a random access memory (RAM) for example. Mass storage can include, in examples, RAM, ROM, flash and / or one or more groups of one or more types of computer-readable media, such as disk storage, a floppy disk, a cassette, a tape, a bubble memory, a racetrack memory, a phase change memory, a polymer memory, a silicon-carbide RAM, and / or the like. The memory is an example of computer-readable media.

[0172] Computer-readable media includes permanent and non-permanent, movable and non-movable media that can be implemented by any method or technology to store information. The information can be computer-readable instructions, data structures, program modules 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, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information accessible to a computing device. According to the definition herein, computer-readable media does not include transitory media such as modulated data signals and carriers.

[0173] It should also be noted that the terms "comprising", "containing", or any other variant thereof are intended to cover non-exclusive inclusions, so that a process, method, article or apparatus that includes a list of elements not only includes those elements, but also includes other elements not explicitly listed, or inherent to such a process, method, article or apparatus. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of additional identical elements in the process, method, article or apparatus that includes the element.

[0174] The above is only an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the scope of claims of the present application.

[0175] In addition, any combination of various embodiments of the present application can also be made, as long as it does not deviate from the idea of the present application, it should also be considered as disclosed by the present application.

Claims

1. A method of determining a radial power density distribution of a fuel rod, characterized by, The fuel rod is divided into multiple axial segments along the axial direction, each axial segment including multiple radial rings, and the determining method comprises: obtaining the atomic density of each nuclide in each radial ring; obtaining the neutron fluence rate in each radial ring; determining the volume power density function of each radial ring according to the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring; normalizing the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring; for each radial ring, determining the local power corresponding to the radial ring as 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; determining the radial power density distribution of the fuel rod by using the local power corresponding to each radial ring.

2. The determination method according to claim 1, characterized in that, The normalization processing of the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring comprises: area integration processing of the volume power density function of each radial ring to obtain the volume power density function integral result corresponding to each radial ring; for each radial ring, normalizing the volume power density function of the radial ring by using the volume power density function integral result corresponding to the radial ring to obtain the radial power density distribution function corresponding to the radial ring; obtaining the density of each radial ring; for each radial ring, determining the radial power density distribution function based on the density influence corresponding to the radial ring as the product of the radial power density distribution function corresponding to the radial ring and the density of the radial ring; normalizing the radial power density distribution function based on the density influence of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring.

3. The determination method according to claim 2, characterized in that, The normalization processing of the radial power density distribution function based on the density influence of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring comprises: area integration processing of the radial power density distribution function based on the density influence of each radial ring to obtain the radial power density distribution function integral result based on the density influence corresponding to each radial ring; for each radial ring, normalizing the radial power density distribution function based on the density influence by using the radial power density distribution function integral result based on the density influence corresponding to the radial ring to obtain the radial power density distribution factor corresponding to each radial ring.

4. The method of claim 1, wherein, Before the determination of the local power corresponding to each radial ring as 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, the determining method further comprises: obtaining the average power of the fuel rod and the axial power density distribution factor of each axial segment; for each axial segment, determining the average power of each axial segment as the product of the average power of the fuel rod and the axial power density distribution factor of the axial segment.

5. The determination method of claim 1, wherein, The obtaining of the atomic density of each nuclide in each radial ring comprises: obtain a radial power density distribution function corresponding to each nuclide in each radial ring; determine the atomic density of each nuclide in each radial ring according to the radial power density distribution function corresponding to each nuclide in each radial ring and a preset burnup equation.

6. The determination method according to claim 5, characterized in that, The obtaining of the radial power density distribution function corresponding to each nuclide in each radial ring comprises: obtaining an initial radial power density distribution function corresponding to each nuclide in each radial ring; performing area integration processing on the initial radial power density distribution function to obtain an initial radial power density distribution function integration result; normalizing the initial radial power density distribution function by using the initial radial power density distribution function integration result to obtain the radial power density distribution function corresponding to each nuclide in each radial ring.

7. The determination method of claim 1, wherein, The obtaining of the neutron fluence of the fuel rod comprises: obtaining a neutron diffusion equation corresponding to the fuel rod based on a neutron hypothesis theory; obtaining a general solution of the neutron diffusion equation and a preset boundary condition of the neutron diffusion equation; determining the neutron fluence of the fuel rod according to the general solution and the preset boundary condition.

8. An apparatus for determining a radial power density distribution of a fuel rod, characterized by The determining device comprises: a first obtaining module configured to obtain the atomic density of each nuclide in each radial ring; a second obtaining module configured to obtain the neutron fluence in each radial ring; a first determining module configured to determine a volume power density function of each radial ring according to the atomic density of each nuclide in each radial ring and the neutron fluence in each radial ring; a processing module configured to perform normalization processing on the volume power density function of each radial ring to obtain a radial power density distribution factor corresponding to each radial ring; a second determining module configured to determine, for each radial ring, a product of an average power of an axial segment corresponding to the radial ring and the radial power density distribution factor corresponding to the radial ring as a local power corresponding to the radial ring; a third determining module configured to determine the radial power density distribution of the fuel rod by using the local power corresponding to each radial ring.

9. An electronic device, comprising: comprise: a memory configured to store instructions; and a processor configured to invoke the instructions from the memory and capable of implementing the method for determining the radial power density distribution of the fuel rod according to any one of claims 1 to 7 when the instructions are executed.

10. A machine-readable storage medium, characterized in that, The machine-readable storage medium has instructions stored thereon, and the instructions are used to cause a machine to execute the method for determining the radial power density distribution of the fuel rod according to any one of claims 1 to 7. The machine-readable storage medium has instructions stored thereon, and the instructions are used to cause a machine to execute the method for determining the radial power density distribution of the fuel rod according to any one of claims 1 to 7.

Images