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

Abstract

The invention provides a method for determining radial power density distribution of a fuel rod and a product, and relates to the technical field of nuclear control. The method comprises the following steps: acquiring the atomic density and neutron fluence rate of each nuclide in each radial ring; determining a volume power density function of each radial ring according to the atomic density and the neutron fluence rate; performing normalization processing on the volume power density function to obtain a radial power density distribution factor; determining the product of the average power of the axial section and the radial power density distribution factor corresponding to the radial ring as the local power corresponding to the radial ring; and determining the radial power density distribution of the fuel rod by using the local power. According to the method, the plurality of local powers are determined according to the atomic density and the neutron fluence rate of each nuclide, and the radial power density distribution of the fuel rod is determined according to the plurality of local powers, so that the radial power density distribution of the fuel rod can be determined without being limited to a fixed nuclide category; and the accuracy of performance analysis and design of the new reactor type fuel rod can be improved.

Description

Technical Field

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

[0002] In the current fuel rod performance analysis software, in order to accurately model the various performances of the fuel rods, it is necessary to simulate the radial power density distribution of the pellets.

[0003] Currently, in the fuel rod performance analysis software of pressurized water reactors, the interpolation method is mainly used to realize the calculation of 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 the fuel rod performance analysis.

[0004] However, for the performance analysis and design of fuel rods of new reactor types (such as lead reactors, fast reactors and other fourth-generation reactors), the corresponding physical software is still in the process of research and development and has not yet matured. It is not yet capable of providing the calculation table of radial power density distribution of fuel rods, that is, the corresponding interpolation table method of radial power density distribution of fuel rods cannot be provided. And because the radial power density distribution of fuel rods of new and old reactor types is quite different, the use of existing calculation tables of radial power density distribution of fuel rods cannot accurately complete the performance analysis and design of fuel rods of new reactor types. Summary of the invention

[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 a fuel rod, so as to accurately complete the performance analysis and design of fuel rods of a new reactor type.

[0006] In a first aspect, an embodiment of the present application provides a method for determining radial power density distribution of a fuel rod, wherein the fuel rod is divided into a plurality of axial segments along an axial direction, each axial segment includes a plurality of radial rings, and the method includes:

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

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

[0009] 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 injection 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 corresponding to the radial ring;

[0012] The radial power density distribution of the fuel rod is determined 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] Performing area integration processing on the volume power density function of each radial ring to obtain the integral result of the volume power density function corresponding to each radial ring;

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

[0016] Get 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 corresponding to the radial ring based on density influence;

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

[0019] In some embodiments, 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] Performing area integration processing on the radial power density distribution function based on density influence of each radial ring, to obtain the integral result of the radial power density distribution function based on density influence corresponding to 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 embodiments, for each radial ring, before determining 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 as the local power corresponding to the radial ring, the determination method further includes:

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

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

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

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

[0027] 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 the preset burnup equation.

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

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

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

[0031] The initial radial power density distribution function is normalized by using the integral result of the initial radial power density distribution function 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 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 injection rate of the fuel rod is determined according to the general solution and preset boundary conditions.

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

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

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

[0039] A first determination module is used 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;

[0040] A processing module, used for normalizing the volume power density function of each radial ring to obtain a radial power density distribution factor corresponding to each radial ring;

[0041] A second determination module is used to determine, 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 as the local power corresponding to the radial ring;

[0042] The third determination module is used to determine the radial power density distribution of the fuel rod by using the local power corresponding to each radial ring.

[0043] In a third aspect, an embodiment of the present application provides an electronic device, including:

[0044] a memory configured to store instructions; and

[0045] The processor is configured to call instructions from the memory and implement the method for determining the radial power density distribution of the fuel rod provided in the first aspect of the embodiment of the present application when executing the instructions.

[0046] In a fourth aspect, an embodiment of the present application provides a machine-readable storage medium, on which instructions are stored, and the instructions are used to enable a machine to execute the method for determining the radial power density distribution of the fuel rod according to the above-mentioned method.

[0047] In an embodiment of the present application, 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 neutron injection 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 injection 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 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 corresponding to the radial ring. Finally, the radial power density distribution of the fuel rod is determined 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 based on the atomic density and neutron injection rate of each nuclide in each radial ring, and then determining the local power corresponding to each radial ring, the radial power density distribution of the fuel rod is determined based on the local power corresponding to each radial ring. The radial power density distribution of the fuel rod can be determined without calculating the radial power density distribution calculation table of the fuel rod, thereby accurately realizing the performance analysis and design of the fuel rods of the new reactor type. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1It is a flow chart of a method for determining radial power density distribution of a fuel rod provided in an embodiment of the present application;

[0049] Figure 2 It is a flowchart of a method for determining radial power density distribution provided by a specific embodiment of the present application;

[0050] Figure 3 It is a flowchart of a method for calculating local nuclide density provided in a specific embodiment of the present application;

[0051] Figure 4 is a schematic diagram of a comparison result of radial power density distribution measured by an experiment provided by a specific embodiment of the present application;

[0052] Figure 5 It is a structural schematic diagram of a device for determining radial power density distribution of a fuel rod provided in an embodiment of the present application;

[0053] Figure 6 It is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0054] The following will be combined with the drawings in the embodiments of the present application to clearly describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments in the present application belong to the scope of protection of this 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 are interchangeable where appropriate, so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of one type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0056] In conjunction with the accompanying drawings, the method for determining the radial power density distribution of the fuel rod and the electronic device provided in the embodiment of the present application are described in detail through specific embodiments and their application scenarios.

[0057] See also Figure 1 , is a flow chart of a method for determining radial power density distribution of a fuel rod provided in an embodiment of the present application, the method is applied to electronic equipment, 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. 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 in each radial ring.

[0059] In the embodiments of the present application, a 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 play the role of containing and supporting nuclear fuel in a nuclear power plant. The fuel rod may include, but is not limited to, uranium dioxide fuel rods and uranium-plutonium mixed fuel rods. The fuel rod is a cylindrical structure and can be divided into a plurality of 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 axial segment, based on the center of the cross-section, a plurality of concentric circles are made, and the cylindrical structure corresponding to each concentric circle is a radial ring, and 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 radial ring is less than or equal to the maximum radius of the axial segment including the radial ring. Each axial segment may include a plurality of radial rings.

[0060] Each radial ring contains many nuclides. Nuclides refer to isotopes with a specific number of protons and neutrons. Fuel rods are composed of specific nuclides. In a nuclear reactor, fuel rods contain specific nuclides. After the fuel rods are divided 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 per 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: obtaining the neutron fluence rate in each radial ring.

[0062] In the embodiments of the present application, the neutron fluence rate refers to the neutron flux passing through a unit area per unit time. In a nuclear reactor or other radioactive equipment, the neutron fluence rate is used to describe the intensity and density of neutron radiation. According to the 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 according to the atomic density of each nuclide in each radial ring and the neutron fluence rate in each radial ring.

[0064] In the embodiment of the present application, after obtaining the atomic density of each nuclide in each radial ring and the neutron fluence rate 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 fluence rate. The volume power density function of the radial ring can be expressed as:

[0065]

[0066] Where q3(r) represents the volume power density function of the radial ring. f,k Represents the nuclide fission cross section, which is a preset parameter. N k (r) represents the local atomic density of nuclide k, φ (r) represents the neutron fluence rate, and r represents the radius of the radial ring.

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

[0068] In the embodiment of the present application, the radial power density distribution factor can be used to describe the distribution of 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.

[0069] In one example, the volume power density function of each radial ring may be normalized by scaling the value of the volume power density function of each radial ring to a specified range. In another example, the volume power density function of each radial ring may be area-integrated to obtain an area integration result, and then the volume power density function of each radial ring may be normalized according to the area integration result of each radial ring to obtain a radial power density distribution factor corresponding to 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 the embodiment of the present application, to determine the radial power density distribution of the fuel rod, it is first necessary to determine the local power inside the fuel rod, that is, 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 obtained product is determined as the local power corresponding to the radial ring.

[0072] When 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 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. 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 and the axial power density distribution factor of the axial segment are multiplied, and the product is determined as the average power of each axial segment.

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

[0074] In the embodiment of the present application, after the local power corresponding to each radial ring is obtained, 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.

[0075] Through the above steps S100-S600, 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 neutron injection 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 injection rate in each radial ring, the volume power density function of each radial ring is determined. Then 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 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 based on the atomic density and neutron injection rate of each nuclide in each radial ring, and then determining the local power corresponding to each radial ring, the radial power density distribution of the fuel rod is determined based on the local power corresponding to each radial ring. This allows the radial power density distribution of the fuel rod to be determined based on the nuclides in the fuel rod, is not limited to fixed nuclide categories, and can improve the accuracy of performance analysis and design of fuel rods of new reactor types.

[0076] 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:

[0077] Performing area integration processing on the volume power density function of each radial ring to obtain the integral result of the volume power density function corresponding to each radial ring;

[0078] For each radial ring, the volume power density function of the radial ring is normalized using the integral result of the volume power density function corresponding to the radial ring to obtain the radial power density distribution function corresponding to the radial ring;

[0079] Get 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 corresponding to the radial ring based on density influence;

[0081] The radial power density distribution function based on the 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 volume power density function of each radial ring, firstly perform area integration on the volume power density function of each radial ring to obtain the integral result of the volume power density function corresponding to each radial ring. For any radial ring, the volume power density function of the radial ring is normalized using the integral result of the volume power density function corresponding to the radial ring to obtain the radial power density distribution function corresponding to the radial ring. Among them, the radial power density distribution function corresponding to the radial ring can be expressed as:

[0083]

[0084] Among them, 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 annular fuel rods, r out Represents the outer diameter of the radial ring, r in represents the inner diameter of the radial ring. In the case of a solid fuel rod, there is only one radius, namely For r 2 Since q3(r)∝∑ k σ f,k ·N k (r)·φ (r) , in the process of q nor When calculating 3(r), the proportional coefficient can be simplified and eliminated, so it is not reflected in the above formula.

[0085] Then, the density of each radial ring is obtained. 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 density influence corresponding to the radial ring. The radial power density distribution function based on density influence can be expressed as: q ρ 3(r)=q nor 3(r)·ρ(r).

[0087] 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. In one example, the radial power density distribution function based on density influence of each radial ring can be normalized by scaling the value of the radial power density distribution function based on density influence of each radial ring to a specified range. In another example, the radial power density distribution function based on density influence of each radial ring can be area-integrated to obtain the area integration result, and then the radial power density distribution function based on density influence 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.

[0088] By performing two-step normalization on the volume power density function of each radial ring, the radial power density distribution factor corresponding to each radial ring is obtained, which can improve the accuracy of calculating the radial power density distribution factor and further improve the accuracy of determining the radial power density distribution of the fuel rod.

[0089] In some embodiments, 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] Performing area integration processing on the radial power density distribution function based on density influence of each radial ring, to obtain the integral result of the radial power density distribution function based on density influence corresponding to 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 of each radial ring, firstly, the radial power density distribution function based on density influence of each radial ring is subjected to area integration processing to obtain the integral result of the radial power density distribution function based on density influence corresponding to each radial ring. Then, 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 to obtain the radial power density distribution factor corresponding to each radial ring. The radial power density distribution factor can be expressed as:

[0093]

[0094] in, represents the radial power density distribution factor, q ρ 3(r) represents the radial power density distribution function based on density effect, and r represents the radius of the radial ring. In the case of annular fuel rods, r out Represents the outer diameter of the radial ring, r in represents the inner diameter of the radial ring. In the case of a solid fuel rod, there is only one radius, namely For r 2 .

[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 embodiments, for each radial ring, before determining 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 as the local power corresponding to the radial ring, the determination method further includes:

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

[0098] For each axial segment, the product of the average power of the fuel rod and the axial power density distribution factor of the axial segment is determined as the average power of each axial segment.

[0099] Specifically, before determining the local power corresponding to the radial ring according to 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 rod and the axial power density distribution factor of each axial segment. The average power of the fuel rod and the axial power density distribution factor of each axial segment are both properties of the fuel rod and are fixed values. For any axial segment, multiply the average power of the fuel rod by the axial power density distribution factor of the axial segment, and determine the obtained product as the average power of the axial segment. By calculating the product of the axial power density distribution factor of each axial segment and the average power of the fuel rod, 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 embodiments, obtaining the atomic density of each nuclide within each radial ring includes:

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

[0102] 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 the preset burnup equation.

[0103] Specifically, radial rings can be understood as multiple concentric circles determined by the center of the cross section of the axial segment. Each axial segment may include multiple radial rings. Each radial ring includes many nuclides. Nuclides refer to isotopes with a specific number of protons and neutrons. Fuel rods are composed of specific nuclides. In a nuclear reactor, fuel rods contain specific nuclides. After the fuel rods are divided into multiple radial rings, each radial ring 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.

[0104] When obtaining the atomic density of each nuclide in each radial ring, first obtain the radial power density distribution function corresponding to each nuclide in each radial ring. In one example, the nuclide may include Pu 239 , the corresponding radial power density distribution function can be expressed as:

[0105]

[0106] Among them, f(r) represents the initial radial power density distribution function corresponding to each nuclide, and f(r) can be expressed as:

[0107]

[0108] Among them, p 1 、p 2 、p 3 refers to a constant, and r refers to the radius of the radial ring.

[0109] 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 the preset burnup equation. In one example, the preset burnup equation can be expressed as:

[0110]

[0111] Among them, N 235 Indicates nuclide U 235 The local atomic density, N 238 Indicates nuclide U 238 The local atomic density, N 239 Indicates nuclide U 239 The local atomic density, dbu represents the change in burnup, σ a,k represents the neutron absorption cross section of the nuclide k, σ c,k represents the neutron capture cross section of the nuclide k, σ f,k represents the nuclide fission cross section of nuclide k, α represents the conversion coefficient, represents the average atomic density, φ represents the neutron injection rate, ρ fuel represents the density of the fuel rod, j can represent the nuclide Pu 240 , Pu 241 Pu 242 .

[0112] By solving the above differential equations, the atomic density of each nuclide in the uranium dioxide fuel rod can be obtained.

[0113] According to the test data of uranium-plutonium mixed fuel rods, it was observed that 238 Nuclide 240 There is also an obvious space self-shielding phenomenon. Space self-shielding refers to the phenomenon that in some physical or mathematical problems, due to the characteristics of the object itself or the limitations of the environment, some parts cannot contact or affect other parts. Therefore, based on the uranium dioxide fuel rod model, a second distribution function f is introduced in the calculation of uranium-plutonium mixed fuel rods. 240 (r) is used to describe and can be expressed as:

[0114]

[0115] The above distribution function f 240 (r) and f nor (r) is of the same form. 2 and p 3 Keep consistent, parameter p 1It can be approximately considered as the contribution of the epithermal neutron resonance absorption region to the effective cross section, which can be specifically expressed as the ratio of resonance absorption to thermal neutron capture. This ratio can be expressed as:

[0116]

[0117] Among them, p 1 represents the ratio of resonant absorption to thermal neutron capture, σ c represents the neutron capture interface, E represents the neutron energy, φ represents the neutron fluence rate, ∫ res σ c (E)φ(E)dE represents the resonance region integral of the reaction cross section, ∫ th σ c (E)φ(E)dE represents the thermal neutron region integral of the reaction cross section.

[0118] 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 reactor fuel rods can be improved.

[0119] In some embodiments, obtaining the radial power density distribution function corresponding to each nuclide in each radial ring includes:

[0120] Obtaining the initial radial power density distribution function corresponding to each nuclide in each radial ring;

[0121] Performing area integration processing on the initial radial power density distribution function to obtain an integral result of the initial radial power density distribution function;

[0122] The initial radial power density distribution function is normalized by using the integral result of the initial radial power density distribution function to obtain the radial power density distribution function corresponding to each nuclide in each radial ring.

[0123] Specifically, when obtaining the radial power density distribution function corresponding to each nuclide in each radial ring, firstly obtain the initial radial power density distribution function corresponding to each nuclide in each radial ring, which can be expressed as:

[0124]

[0125] Then perform area integration on the initial radial power density distribution function f(r) 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 of the initial radial power density distribution function 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:

[0126]

[0127] By obtaining the initial radial power density distribution function corresponding to each nuclide in each radial ring, and performing area integration and normalization processing on the initial radial power density distribution function, the calculation accuracy of the radial power density distribution function corresponding to each nuclide in each radial ring can be improved.

[0128] In some embodiments, obtaining the neutron fluence rate of the fuel rod includes:

[0129] Based on the neutron hypothesis theory, the neutron diffusion equation corresponding to the fuel rod is obtained;

[0130] Obtain the general solution of the neutron diffusion equation and the preset boundary conditions of the neutron diffusion equation;

[0131] The neutron injection rate of the fuel rod is determined according to the general solution and preset boundary conditions.

[0132] Specifically, neutron hypothesis theory refers to a theoretical framework in nuclear physics and particle physics that is 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 equation corresponding to the fuel rod is obtained. In one example, the single-energy group neutron hypothesis theory can be used. The single-energy group neutron hypothesis theory regards all neutrons as one energy group, ignores the detailed distribution of the neutron energy spectrum, and simplifies the processing and calculation of the problem. In another example, the 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, which is 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 regarded as an energy group, so as to more accurately simulate and calculate the behavior and reaction of neutrons. Compared with the single-energy group neutron hypothesis theory, the multi-energy group neutron hypothesis theory has higher computational complexity and requires processing more equations and data, but it can provide more accurate results, especially when the influence of the neutron energy spectrum needs to be considered.

[0133] In cylindrical coordinates, the neutron diffusion equation can be expressed as:

[0134]

[0135] Among them, 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 fluence rate.

[0136] Then obtain the general solution of the neutron diffusion equation and the preset boundary conditions of the neutron diffusion equation. The general solution of the neutron diffusion equation can be expressed as:

[0137] φ(r)=A·I 0 (kr)+B·K 0 (kr)

[0138]

[0139] Among them, A and B are constants, I 0 (kr) represents the modified Bessel function of the first kind of order 0, K 0 (kr) represents the modified Bessel function of the second kind of order 0.

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

[0141]

[0142] In the case of solid fuel rods, due to K 0 When r = 0, it is infinite, so B must be 0, and the analytical solution can be expressed as: φ(r) = C 1 I 0 (kr)

[0143] When the fuel rod is annular, the analytical solution of the neutron injection rate can be expressed as:

[0144]

[0145] Among them, C 1 Represents a constant, I 1 (kr) represents the first-order modified Bessel function of the first kind, K 1 (kr) represents the first-order second-kind modified Bessel function. Since the radial power density distribution only focuses on the relative value, the constant C 1 The value will not affect the radial power density distribution, so C 1 It can be any constant. By determining the neutron injection rate of the fuel rod according to 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] See also Figure 2 , is a flow chart of a method for determining radial power density distribution provided by a specific embodiment of the present application. Figure 2 As shown, the radial power density distribution determination method 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 local nuclide density;

[0150] Step S204: calculating an analytical solution of the neutron fluence rate distribution;

[0151] Step S205: non-normalized radial power density distribution;

[0152] Step S206: normalizing radial power density distribution;

[0153] Step S207: determine whether it is the last axial segment, if so, proceed to step S208, if not, return to step S202;

[0154] Step S208: The power distribution calculation is completed.

[0155] In this specific embodiment, when determining the radial power density distribution, the calculation is performed in units of axial segments, and the nuclides in the radial ring in a certain axial segment are calculated. 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 calculation of the radial power density distribution of the fuel rod is completed. 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 continued to be calculated.

[0156] The specific implementation can be found in the above description and will not be repeated here.

[0157] See also Figure 3 , is a flow chart of a method for calculating local nuclide density provided in a specific embodiment of the present application.

[0158] like Figure 3 As shown, the local nuclide density calculation method may include the following steps:

[0159] Step S301: Simulate Pu 239 Distributed radially on the fuel rods.

[0160] Step S302: Calculate the normalized radial distribution function.

[0161] Step S303: Calculate UO 2 The atomic density of each nuclide in the fuel rod.

[0162] Step S304: Correct and obtain the atomic density of each nuclide in the MOX fuel rod.

[0163] The specific implementation can be found in the above description and will not be repeated here.

[0164] See also Figure 4 , is a schematic diagram of a comparison result of radial power density distribution with experimental measurement provided by a specific embodiment of the present application. Figure 4 As shown,

[0165] The radial power density calculation model of the pellet established by the method of the present invention is used to generate the radial power density distribution under different burnups, and the correctness of the method of the present application is verified by comparing it with the radial power density distribution results measured by the test. The method is also applied to the fuel rod performance analysis software, and the correctness of the method is indirectly proved by comparing it with the pellet center temperature measured by the test.

[0166] The entire verification includes two comparisons: one is to compare the radial power density distribution calculation results at five different burnup depths with the experimental measurement results, and the other is to compare the core temperature of the pellet calculated by the fuel rod performance analysis software using the model with the experimental measurement results. Figure 4 Table 1 gives the comparative analysis results of radial power density distribution.

[0167] Table 1

[0168]

[0169] Note: Relative deviation = (calculated result - test result) / test result

[0170] Table 2 gives the comparative analysis results of the core block center temperature.

[0171] Table 2

[0172] Fuel consumption (MWd / kgU) Standard deviation (℃) Temperature difference at inner diameter (℃) 10 9.71 8.97 40 12.27 10.67 60 13.71 11.12

[0173] From the comparison results, it can be seen that in this specific application embodiment, the radial power density distribution result of the pellet calculated by the method of the application deviates from the experimental measurement result by no more than 4%, and the core temperature of the pellet calculated by the fuel rod performance analysis software using this method is consistent with the measurement result.

[0174] See also Figure 5 , is a schematic diagram of the structure of a device for determining radial power density distribution of a fuel rod provided in an embodiment of the present application. In a second aspect, an embodiment of the present application provides a device 50 for determining radial power density distribution of a fuel rod. The device 50 includes:

[0175] A first acquisition module 51 is used to acquire the atomic density of each nuclide in each radial ring;

[0176] A second acquisition module 52 is used to acquire the neutron injection rate in each radial ring;

[0177] A first determination module 53 is used 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;

[0178] A processing module 54 is used to normalize the volume power density function of each radial ring to obtain a radial power density distribution factor corresponding to each radial ring;

[0179] A second determination module 55 is used to determine, 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 as the local power corresponding to the radial ring;

[0180] The third determination module 56 is used to determine the radial power density distribution of the fuel rod by using the local power corresponding to each radial ring.

[0181] The device 50 for determining the radial power density distribution of the fuel rod provided in the second aspect of the embodiment of the present application can implement each process implemented in the above method embodiment and achieve the same beneficial effects. To avoid repetition, it will not be described here.

[0182] See also Figure 6 , is a structural diagram of an electronic device provided in an embodiment of the present application. The third aspect of the embodiment of the present 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, and the processor 6100 can execute the machine executable instructions to implement the above-mentioned method for determining the radial power density distribution of the fuel rod.

[0183] In some embodiments, the embodiments of the present application further provide a machine-readable storage medium, on which instructions are stored, and when the instructions are executed by a processor, the processor implements the above-mentioned method for determining the radial power density distribution of the fuel rod.

[0184] In some embodiments, the embodiments of the present application further provide a computer program product, including a computer program, which, when executed by a processor, implements the method for determining the radial power density distribution of the fuel rod according to the above-mentioned embodiment.

[0185] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0186] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0187] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0188] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0189] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. 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 technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0190] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0191] The above are only embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included within the scope of the claims of the present application.

[0192] In addition, various embodiments of the present invention may be arbitrarily combined, and as long as they do not violate the concept of the present invention, they should also be regarded as the contents disclosed by the present invention.

Claims

1. A method for determining radial power density distribution of a fuel rod, characterized in that: The fuel rod is divided into a plurality of axial segments along the axial direction, each axial segment includes a plurality of radial rings, and the determination method includes: Obtain 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 a 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 using the local power corresponding to each radial ring.

2. The determination method according to claim 1, characterized in that: The normalizing the volume power density function of each radial ring to obtain the radial power density distribution factor corresponding to each radial ring includes: Performing area integration processing on the volume power density function of each radial ring to obtain an integration result of the volume power density function corresponding to each radial ring; For each radial ring, the volume power density function of the radial ring is normalized by using the integral result of the volume power density function 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, a radial power density distribution function corresponding to the radial ring and a density of the radial ring are multiplied to determine the radial power density distribution function corresponding to the radial ring based on density influence; The radial power density distribution function based on density influence of each radial ring is normalized to obtain a radial power density distribution factor corresponding to each radial ring.

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

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

5. The determination method according to claim 1, characterized in that: The obtaining of the atomic density of each nuclide in each radial ring includes: Obtaining a radial power density distribution function corresponding to each nuclide within 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 the 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 includes: Obtaining an initial radial power density distribution function corresponding to each nuclide within each radial ring; Performing area integration processing on the initial radial power density distribution function to obtain an integration result of the initial radial power density distribution function; The initial radial power density distribution function is normalized by using the integration result of the initial radial power density distribution function to obtain the radial power density distribution function corresponding to each nuclide in each radial ring.

7. The determination method according to claim 1, characterized in that: The obtaining of the neutron fluence rate of the fuel rod comprises: Based on the neutron hypothesis theory, obtaining the neutron diffusion equation corresponding to the fuel rod; Obtaining a general solution of the neutron diffusion equation and preset boundary conditions of the neutron diffusion equation; The neutron injection rate of the fuel rod is determined according to the general solution and the preset boundary conditions.

8. A device for determining radial power density distribution of a fuel rod, characterized in that: The determining device comprises: A first acquisition module is used to acquire the atomic density of each nuclide in each radial ring; A second acquisition module is used to acquire the neutron fluence rate in each radial ring; A first determination module is used 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; 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 determination module is used to determine, 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 as the local power corresponding to the radial ring; The third determination module is used 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, characterized in that: include: a memory configured to store instructions; as well as A processor is configured to call the instructions from the memory and implement the method for determining the radial power density distribution of the fuel rod according to any one of claims 1 to 7 when executing the instructions.

10. A machine-readable storage medium, characterized in that: The machine-readable storage medium stores instructions for causing a machine to execute the method for determining radial power density distribution of a fuel rod according to any one of claims 1 to 7.

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