Reactor core fuel assembly source distribution calculation method, system, equipment and medium

Abstract

The invention provides a reactor core fuel assembly source distribution calculation method, system and equipment and a medium, and relates to the technical field of nuclear reactors. The reactor core fuel assembly source distribution calculation method provided by the invention comprises the following steps: acquiring input parameters, wherein the input parameters comprise power distribution, fission nuclide share, fission spectrum, average release particle number of each fission, and average release energy and source bias factor of each fission; calculating a cumulative distribution function of source particles based on the input parameters; and sampling the source particles based on the cumulative distribution function, and determining distribution parameters of the source particles. The source particles are sampled based on the cumulative distribution function of the source particles, the distribution parameters of the source particles are determined, the shielding calculation efficiency based on the MC method is improved, and support is provided for new heap design.

Description

Technical Field

[0001] The present application relates to the field of nuclear reactor technology, and in particular to a method, system, device and medium for calculating the source distribution of a reactor core fuel assembly. Background Art

[0002] Reactor shielding calculation and analysis usually adopts methods such as discrete ordinate (SN) and Monte Carlo (MC). The SN method has the characteristics of fast calculation speed and wide application range, and can be used for neutron and photon radiation shielding calculation. The MC method is a numerical analysis technique that estimates the solution of physical or mathematical problems through random sampling. It has high calculation accuracy but low calculation efficiency. It is often used for shielding problems of complex geometry and deep penetration.

[0003] The source term is an important input parameter for shielding calculations, and its numerical results directly affect the accuracy of reactor shielding calculations. The source term calculation needs to consider multiple factors such as core power distribution, fuel assembly burnup, and the change of fission neutron number with burnup. It also needs to consider the coordinate transformation between the source term and the shielding calculation model, and the process is relatively complicated. In addition, the distribution and sampling method of source particles also have a great influence on the calculation efficiency of the MC method. Summary of the invention

[0004] In view of this, the present application provides a method, system, device and medium for calculating the source distribution of a reactor core fuel assembly to improve the shielding calculation efficiency based on the MC method.

[0005] In a first aspect, the present application provides a method for calculating source distribution of a reactor core fuel assembly, comprising:

[0006] Acquiring input parameters, wherein the input parameters include power distribution, fissile nuclide fraction, fission spectrum, average number of particles released per fission, average energy released per fission, and source bias factor, wherein the source bias factor includes one or more of a spatial bias factor of a fuel rod grid, an energy bias factor, and a particle bias factor;

[0007] Calculate a cumulative distribution function of source particles based on the input parameters, wherein the cumulative distribution function includes one or more of a spatial cumulative distribution function of a fuel rod grid, an energy cumulative distribution function of a fuel rod grid, and a cumulative distribution function of a particle type;

[0008] Source particle sampling is performed based on the cumulative distribution function to determine distribution parameters of the source particles.

[0009] In a second aspect, the present application provides a reactor core fuel assembly source distribution calculation system, comprising:

[0010] An input parameter acquisition module, used to acquire input parameters, wherein the input parameters include power distribution, fission nuclide fraction, fission spectrum, average number of particles released per fission, average energy released per fission, and source bias factor, wherein the source bias factor includes one or more of the spatial bias factor, energy bias factor, and particle bias factor of the fuel rod grid;

[0011] A cumulative distribution function calculation module, used to calculate the cumulative distribution function of the source particles based on the input parameters, wherein the cumulative distribution function includes one or more of the spatial cumulative distribution function of the fuel rod grid, the energy cumulative distribution function of the fuel rod grid, and the cumulative distribution function of the particle type;

[0012] The source particle distribution parameter calculation module is used to perform source particle sampling based on the cumulative distribution function to determine the distribution parameters of the source particles.

[0013] In a possible implementation, obtaining the input parameters includes:

[0014] The source bias factor is calculated based on the conjugate fluence rate of the fuel rod grid.

[0015] In a possible implementation, the source bias factor includes a spatial bias factor of a fuel rod grid, the cumulative distribution function includes a spatial cumulative distribution function of a fuel rod grid, and the calculating the cumulative distribution function of source particles based on the input parameters includes:

[0016] Calculate the source strength of the fuel rod grid based on the input parameters;

[0017] Calculating a spatial cumulative distribution function of a fuel rod grid based on the source intensity of the fuel rod grid;

[0018] The sampling of source particles based on the cumulative distribution function to determine the distribution parameters of the source particles includes:

[0019] Get A spatial random number within an interval, and determining a fuel rod grid where a source particle is located based on the spatial random number and a spatial cumulative distribution function of the fuel rod grid;

[0020] Uniformly sampling in the radial plane region of the fuel rod grid where the source particles are located to obtain the first coordinate and the second coordinate of the source particles;

[0021] The third coordinate of the source particle is determined based on the lower boundary and the upper boundary of the grid of the fuel rod where the source particle is located in the axial direction, and the axial direction is perpendicular to the radial plane.

[0022] In a possible implementation, the cross-sectional shape of the fuel rod in the radial plane is a first shape, the first shape is divided into a plurality of sub-regions, and the first coordinates and the second coordinates of the source particle obtained by uniformly sampling in the radial plane region of the fuel rod grid where the source particle is located include:

[0023] Get A regional random number within the interval, and determining a sub-region where a source particle is located based on the regional random number;

[0024] The first coordinate and the second coordinate of the source particle are obtained by uniformly sampling in the sub-region where the source particle is located.

[0025] In a possible implementation, the cross-sectional shape of the fuel rod in the radial plane is a second shape, the second shape is located within the first shape, the first shape is divided into a plurality of sub-regions, and the first coordinates and the second coordinates of the source particle obtained by uniformly sampling in the radial plane region of the fuel rod grid where the source particle is located include:

[0026] Get A regional random number within the interval, and determining a sub-region where a source particle is located based on the regional random number;

[0027] Uniformly sample the sub-region where the source particle is located to obtain the first coordinate and the second coordinate of the source particle,

[0028] determining whether the source particle is within the second shape based on the first coordinate and the second coordinate;

[0029] If not, re-obtaining regional random numbers to calculate the first coordinates and the second coordinates of the source particle until the source particle is within the second shape.

[0030] In a possible implementation, the source bias factor includes an energy bias factor, the cumulative distribution function includes an energy cumulative distribution function of a fuel rod grid, and the cumulative distribution function of source particles calculated based on the input parameters includes:

[0031] Calculating an energy probability density function of the fuel assembly based on the input parameters;

[0032] Calculating the energy cumulative distribution function of the fuel assembly based on the energy probability density function of the fuel assembly;

[0033] Obtaining an energy cumulative distribution function of a fuel rod grid based on the energy cumulative distribution function of the fuel assembly;

[0034] The sampling of source particles based on the cumulative distribution function to determine the distribution parameters of the source particles includes:

[0035] Get An energy group random number within an interval, and determining the energy group to which the source particle belongs based on the energy group random number and the energy cumulative distribution function of the fuel rod grid;

[0036] The initial energy of the source particle is determined based on the lower energy boundary and the upper energy boundary of the energy group to which the source particle belongs.

[0037] In a possible implementation, the source bias factor includes a particle bias factor, the cumulative distribution function includes a cumulative distribution function of a particle type, and calculating the cumulative distribution function of source particles based on the input parameters includes:

[0038] Calculate the source strength of the fuel rod grid based on the input parameters;

[0039] Calculating the total source intensity generated by core fission based on the source intensity of the fuel rod grid;

[0040] Calculating a cumulative distribution function of particle types based on the total source intensity;

[0041] The sampling of source particles based on the cumulative distribution function to determine the distribution parameters of the source particles includes:

[0042] Get A type random number within an interval, and determining a particle type of a source particle based on the type random number and a cumulative distribution function of the particle type.

[0043] In a third aspect, the present application provides a computing device, including:

[0044] at least one processor; and

[0045] At least one memory having instructions stored thereon, which, when executed individually or collectively by the at least one processor, cause the computing device to perform the method according to the first aspect.

[0046] In a fourth aspect, the present application provides a computer storage medium having instructions stored thereon, which, when executed individually or collectively by at least one processor of a computing device, causes the computing device to execute the method described in the first aspect.

[0047] Compared with the prior art, this application has the following advantages:

[0048] The reactor core fuel assembly source distribution calculation method provided by the present application includes obtaining input parameters, the input parameters include power distribution, fission nuclide fraction, fission spectrum, average number of particles released per fission, average energy released per fission and source bias factor; calculating the cumulative distribution function of source particles based on the input parameters; sampling source particles based on the cumulative distribution function to determine the distribution parameters of source particles. The present application samples source particles based on the cumulative distribution function of source particles to determine the distribution parameters of source particles, improves the shielding calculation efficiency based on the MC method, and provides support for the design of new reactor types. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings are included to provide a further understanding of the present application. They are included and constitute a part of the present application. The accompanying drawings illustrate embodiments of the present application and together with the present specification serve to explain the principles of the present application. In the accompanying drawings:

[0050] Figure 1A-1B is a schematic diagram of numbering of a fuel assembly provided in an embodiment of the present application;

[0051] Figure 2A-2B is a schematic diagram of numbering of a fuel rod provided in an embodiment of the present application;

[0052] Figure 3 It is a flow chart of a method for calculating source distribution of reactor core fuel assemblies provided in an embodiment of the present application;

[0053] Figure 4 It is a schematic flow chart of a method for calculating the cumulative distribution function of a source particle provided in an embodiment of the present application;

[0054] Figure 5 It is a schematic diagram of a flow chart of source particle sampling provided in an embodiment of the present application;

[0055] Figure 6A-6B is a sampling schematic diagram of a fuel assembly provided in an embodiment of the present application;

[0056] Figure 7A-7B is a sampling schematic diagram of another fuel assembly provided in an embodiment of the present application;

[0057] Figure 8 is a schematic diagram of a reactor core source particle energy cumulative distribution function provided in an embodiment of the present application;

[0058] Fig. 9 This is a schematic diagram of source particle distribution when the source bias factor is not considered, provided in an embodiment of the present application;

[0059] Fig.10 is a schematic diagram of source particle distribution when a source bias factor is considered, provided in an embodiment of the present application;

[0060] Fig.11 It is a structural schematic diagram of a reactor core fuel assembly source distribution calculation system provided in an embodiment of the present application;

[0061] Fig.12 It is a structural diagram of a computing device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0062] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for the description of the embodiments. Obviously, the drawings described below are only some examples or embodiments of the present application. For ordinary technicians in this field, the present application can also be applied to other similar scenarios based on these drawings without creative work. Unless it is obvious from the language environment or otherwise explained, the same reference numerals in the figures represent the same structure or operation.

[0063] As shown in this application, unless the context clearly indicates an exception, the words "a", "an", "a kind" and / or "the" do not refer to the singular, but also include the plural. Generally speaking, the terms "include" and "comprise" only indicate the inclusion of the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.

[0064] At the same time, the present application uses specific words to describe the embodiments of the present application. For example, "one embodiment", "an embodiment", and / or "some embodiments" refer to a certain feature, structure or characteristic related to at least one embodiment of the present application. Therefore, it should be emphasized and noted that "one embodiment" or "an embodiment" or "an alternative embodiment" mentioned twice or more in different positions in this specification does not necessarily refer to the same embodiment. In addition, some features, structures or characteristics in one or more embodiments of the present application can be appropriately combined.

[0065] Unless otherwise specifically stated, the relative arrangement, numerical expressions and numerical values ​​of the parts and steps set forth in these embodiments do not limit the scope of the present application. Meanwhile, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to actual proportional relationships. The technology, methods and equipment known to those of ordinary skill in the relevant art may not be discussed in detail, but in appropriate cases, the technology, methods and equipment should be considered as a part of the specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, and therefore, once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0066] In addition, although the terms used in this application are selected from well-known and commonly used terms, some of the terms mentioned in this application specification may be selected by the applicant at his or her discretion, and their detailed meanings are explained in the relevant parts of the description of this article. In addition, it is required to understand this application not only by the actual terms used, but also by the meaning implied by each term.

[0067] Flowcharts are used in this application to illustrate the operations performed by the apparatus or equipment according to the embodiments of the application. It should be understood that the preceding or following operations are not necessarily performed precisely in order. On the contrary, various steps may be processed in reverse order or simultaneously. At the same time, other operations may be added to these processes, or one or more operations may be removed from these processes.

[0068] Figure 1A-1B is a schematic diagram of the numbering of a fuel assembly provided in an embodiment of the present application, Figure 2A-2B This is a schematic diagram of the numbering of fuel rods provided in the embodiment of the present application. Please refer to Figure 1A-1B The reactor core 100 is composed of a plurality of fuel assemblies 110 of the same size and a certain cross-sectional shape. The cross-sectional shape of the fuel assembly 110 in the radial plane can be a square, a hexagon, etc. Please refer to Figure 2A-2B The fuel assembly 110 is an in-core heat release component composed of a group of fuel rods 111 and other components, and is a reactor fuel loading and unloading unit.

[0069] Compared with the calculation of source terms of square fuel assemblies, the energy processing method of hexagonal fuel assemblies is similar, but the spatial processing method is more complicated. The key problem of calculating the source term of the SN method is to find the fuel assembly number and fuel rod number when the grid coordinates are known, while the key problem of calculating the source term of the MC method is to find the source particle coordinates when the fuel assembly number and fuel rod number are known. The two are exactly the opposite process.

[0070] In an exemplary embodiment, the cross-sectional shape of the fuel assembly 110 in the radial plane is hexagonal, and the fuel assembly number and the fuel rod number of the MC method are respectively as follows: Figure 1A and Figure 2A shown. Figure 1A , m1 and n1 are the numbering directions of the fuel assemblies 110 in the reactor core 100, and the fuel assembly numbers (m1, n1) may be (0, 0), (0, 1), (1, 0), (1, 1), and so on. Figure 2A In the figure, m2 and n2 are the numbering directions of the fuel rods 111 in the fuel assembly 110, and the fuel rod numbers (m2, n2) can be (0, 0), (0, 1), (1, 0), (1, 1), etc. Please refer to Figure 2A, the cross-sectional shape of the fuel rod 111 in the radial plane is a hexagon. Assuming that the side length of the fuel assembly 110 is a cm and the side length of the fuel rod 111 is b cm, then a and b satisfy the relationship: During the calculation process, the fuel rod 111 may be divided into a plurality of grids in the axial direction, and one fuel rod 111 in the radial direction corresponds to one grid.

[0071] In another exemplary embodiment, the cross-sectional shape of the fuel assembly 110 in the radial plane is a square, and the fuel assembly number and the fuel rod number of the MC method are respectively as follows: Figure 1B and Figure 2B shown. Figure 1B , m1 and n1 are the numbering directions of the fuel assemblies 110 in the reactor core 100, and the fuel assembly numbers (m1, n1) may be (0, 0), (0, 1), (1, 0), (1, 1), and so on. Figure 2B In the figure, m2 and n2 are the numbering directions of the fuel rods 111 in the fuel assembly 110, and the fuel rod numbers (m2, n2) can be (0, 0), (0, 1), (1, 0), (1, 1), etc. Please refer to Figure 2B The cross-sectional shape of the fuel rod 111 in the radial plane is a square. Assuming that the side length of the fuel assembly 110 is a cm and the side length of the fuel rod 111 is b cm, a and b satisfy the relationship: b=a / n. n is the number of fuel rods on one side of the fuel assembly. During the calculation process, the fuel rod 111 can be divided into multiple grids in the axial direction, and one fuel rod 111 in the radial direction corresponds to one grid.

[0072] Figure 3 FIG. 1 is a flow chart of a method for calculating the source distribution of a reactor core fuel assembly provided in an embodiment of the present application. Figure 3 As shown, the reactor core fuel assembly source distribution calculation method includes the following steps:

[0073] Step S310: Obtain input parameters.

[0074] The input parameters may be obtained through an input file, or the input parameters set by the user may be obtained through a user interface, or the required input parameters may be calculated based on the obtained original parameters. The embodiment of the present application does not limit the way of obtaining the input parameters.

[0075] The input parameters include power distribution, fission nuclide fraction, fission spectrum, average number of particles released per fission, average energy released per fission and source bias factor. The power distribution can be a two-dimensional power distribution or a three-dimensional power distribution. The three-dimensional power distribution can be expressed as:

[0076]

[0077] Where P(i,j,k) is the power of the (i,j,k)th fuel rod grid, is the power of the radial (i,j)th fuel rod grid, is the power of the mth assembly and the kth axial fuel rod grid. The radial number (i, j) of the fuel rod grid is the numbering of the fuel rods in all the fuel assemblies in the reactor core in a certain order, which can be obtained based on the two-dimensional numbering of the fuel assembly (m1, n1) and the two-dimensional numbering of the fuel rod (m2, n2). The one-dimensional number m of the fuel assembly can be obtained based on the two-dimensional numbering of the fuel assembly (m1, n1), such as first accumulating row by row in the m1 direction and then accumulating column by column in the n1 direction, that is, processing the two-dimensional array into a one-dimensional array.

[0078] In some embodiments, the fissile nuclides include U-235, U-238, Pu-239, Pu-240, Pu-241, and Pu-242. In some other embodiments, the fissile nuclides may also include only U-235.

[0079] Step S320: Calculate the cumulative distribution function of the source particles based on the input parameters, wherein the cumulative distribution function includes one or more of the spatial cumulative distribution function of the fuel rod grid, the energy cumulative distribution function of the fuel rod grid, and the cumulative distribution function of the particle type.

[0080] Based on the input parameters, the cumulative distribution function of each parameter of the source particles, such as the energy cumulative distribution function of the fuel rod grid, the spatial cumulative distribution function of the fuel rod grid, and the cumulative distribution function of the particle type, can be calculated. The source particles may include only neutrons, or only photons, or both neutrons and photons.

[0081] In some embodiments, please refer to Figure 4 , step S320 includes the following steps:

[0082] Step S321, calculating the energy cumulative distribution function of the fuel rod grid.

[0083] In some embodiments, calculating the energy cumulative distribution function of the fuel rod grid includes: calculating the energy probability density function of the fuel assembly based on input parameters; calculating the energy cumulative distribution function of the fuel assembly based on the energy probability density function of the fuel assembly; and obtaining the energy cumulative distribution function of the fuel rod grid based on the energy cumulative distribution function of the fuel assembly.

[0084] The energy probability density function of a fuel assembly can be calculated based on the fissile nuclide fraction of the fuel assembly, the average number of particles released per fission, and the fission spectrum. The calculation formula for the energy probability density function of the mth fuel assembly is as follows:

[0085]

[0086] Where: is the energy group number, m is the fuel assembly number, n is the fissile nuclide number, p is the particle type number, is the pth particle, The probability of the mth fuel assembly being produced in the group can be obtained through the fission spectrum; is the fission share of the nth nuclide and the mth fuel assembly; is the average number of particles released by each fission of the p-th particle and the n-th nuclide; is the production probability of the p-th particle, the g-th group, and the n-th nuclide particle, which can be obtained through the fission spectrum; is the number of nuclides; G(p) is the energy group number of the p-th particle. For example, p=1 represents a neutron, G(1)=47, p=2 represents a photon, G(2)=20.

[0087] is the pth particle, The energy bias factor of the group, the calculation formula is as follows:

[0088]

[0089] Where: To solve the conjugate transport equation, we get the pth particle and the The conjugate injection rate of the group and the qth fuel rod grid; Q is the number of fuel rod grids.

[0090] Based on the energy probability density function of the fuel assembly, the energy cumulative distribution function of the fuel assembly can be calculated. The calculation formula of the energy cumulative distribution function of the fuel assembly is as follows:

[0091]

[0092] In the formula, is the pth particle, Cumulative energy distribution function of the mth fuel assembly in the group.

[0093] Based on the correspondence between fuel assemblies and fuel rod grids, all fuel rod grids in the same fuel assembly have the same energy probability density function, and thus the energy cumulative distribution function of the qth fuel rod grid can be obtained. The calculation formula of the energy cumulative distribution function of the fuel rod grid is as follows:

[0094]

[0095] In the formula, q is the fuel rod grid number, and E(q,g,p) is the energy cumulative distribution function of the pth particle, the gth group, and the qth fuel rod grid. The one-dimensional number q of the fuel rod grid can be obtained based on the three-dimensional number (i,j,k) of the fuel rod grid, such as first accumulating row by row in the i direction, then accumulating column by column in the j direction, and then accumulating in the axial direction k, that is, processing the three-dimensional array into a one-dimensional array.

[0096] Step S322: Calculate the spatial cumulative distribution function of the fuel rod grid.

[0097] In some embodiments, calculating the spatial cumulative distribution function of the fuel rod grid includes: calculating the source intensity of the fuel rod grid based on input parameters; and calculating the spatial cumulative distribution function of the fuel rod grid based on the source intensity of the fuel rod grid.

[0098] The calculation formula for the spatial distribution of each energy group of three-dimensional source particles is as follows:

[0099]

[0100] Where S(i,j,k,g,p) is the source intensity of the p-th particle, the g-th group, and the (i,j,k)-th fuel rod grid, and the unit is particles / (cm 3 ·s); C is the unit conversion factor, which is 6.24×10 12 MeV / (s·W); is the average energy released per fission of the (i,j,k)th fuel rod grid, in MeV; is the fission share of the nth nuclide and the (i,j,k)th fuel rod grid; is the average number of particles released by each fission of the p-th particle and the n-th nuclide; is the production probability of the p-th particle, the g-th group, and the n-th nuclide particle, which can be obtained through the fission spectrum; is the spatial bias factor of the p-th particle and the (i, j, k)-th fuel rod grid; is the number of nuclides.

[0101] Reconstruct the three-dimensional array into a one-dimensional array, that is, process the data of the (i, j, k)th fuel rod grid into the data of the qth fuel rod grid, and you can get the source intensity of the pth particle and the qth fuel rod grid: , and the spatial bias factor B(q,p)=B(i,j,k,p) for the p-th particle and the q-th fuel rod grid.

[0102] is the spatial bias factor of the p-th particle and the q-th fuel rod grid. The calculation formula is as follows:

[0103]

[0104] Based on the source intensity of the fuel rod grid, the spatial cumulative distribution function of the fuel rod grid can be calculated. The calculation formula of the spatial cumulative distribution function of the fuel rod grid is as follows:

[0105]

[0106] In the formula, is the fuel rod grid number, Q is the total number of fuel rod grids; is the pth particle, The spatial cumulative distribution function of a fuel rod grid; is the source intensity of the p-th particle and the q-th fuel rod grid, in particles / (cm 3 s); is the volume of the qth fuel rod grid, in cm 3 .

[0107] Step S323: Calculate the cumulative distribution function of the particle type.

[0108] In some embodiments, calculating the cumulative distribution function of a particle type includes: calculating the source strength of a fuel rod grid based on input parameters; calculating the total source strength produced by core fission based on the source strength of the fuel rod grid; and calculating the cumulative distribution function of the particle type based on the total source strength.

[0109] The calculation of the source strength of the fuel rod grid may refer to the above step S322, which will not be repeated here.

[0110] The total source strength generated by core fission can be calculated based on the source strength of the fuel rod grid. The calculation formula for the total source strength generated by core fission is as follows:

[0111]

[0112] In the formula, is the total source intensity of the pth particle, in particles / s; is the p-th particle bias factor, and the calculation formula is as follows:

[0113]

[0114] Based on the total source intensity generated by core fission, the cumulative distribution function of the particle type can be calculated. The calculation formula of the cumulative distribution function of the particle type is as follows:

[0115]

[0116] In the formula, is the particle type number, For the The cumulative distribution function of the particles.

[0117] Step S330: sampling source particles based on the cumulative distribution function to determine distribution parameters of the source particles.

[0118] After the cumulative distribution functions of the parameters of the source particles are calculated in step S320, source particle sampling can be performed based on the cumulative distribution functions of the parameters to determine the corresponding distribution parameters of the source particles.

[0119] In some embodiments, please refer to Figure 5 , step S330 includes the following steps:

[0120] Step S331: Determine the particle type of the source particle based on the cumulative distribution function of the particle type.

[0121] In actual operation, it is possible to obtain A type random number within the interval, and the particle type of the source particle is determined based on the type random number and the cumulative distribution function of the particle type.

[0122] In an exemplary embodiment, obtaining Type random number in the interval ,like , it means that the source particle is the pth particle, such as p=1 represents a neutron, and p=2 represents a photon.

[0123] Step S332: determine the spatial position of the source particles based on the spatial cumulative distribution function of the fuel rod grid.

[0124] In actual operation, it is possible to obtain A spatial random number within an interval, and a fuel rod grid where a source particle is located are determined based on the spatial random number and the spatial cumulative distribution function of the fuel rod grid; a first coordinate and a second coordinate of the source particle are obtained by uniformly sampling in a radial plane region of the fuel rod grid where the source particle is located; and a third coordinate of the source particle is determined based on the lower and upper boundaries of the grid in the axial direction of the fuel rod grid where the source particle is located, wherein the axial direction is perpendicular to the radial plane.

[0125] In an exemplary embodiment, obtaining Spatial random numbers in the interval ,like , it means that the source particle is in the qth fuel rod grid. Then, the first coordinate and the second coordinate of the source particle are uniformly sampled in the radial plane area of ​​the qth fuel rod grid, that is, the local spatial position coordinates (x, y) of the source particle.

[0126] The local spatial position coordinates (x, y) of the source particle can be obtained by using different sampling methods according to the cross-sectional shape of the fuel rod in the radial plane. If the cross-sectional shape of the fuel rod in the radial plane is a first shape, the first shape is divided into a plurality of sub-areas, and uniform sampling in the radial plane area of ​​the fuel rod grid where the source particle is located to obtain the first coordinate and the second coordinate of the source particle includes: obtaining A regional random number in the interval, determining the sub-region where the source particle is located based on the regional random number; uniformly sampling in the sub-region where the source particle is located to obtain the first coordinate and the second coordinate of the source particle. For another example, the cross-sectional shape of the fuel rod in the radial plane is a second shape, the second shape is located in the first shape, and the first shape is divided into a plurality of sub-regions, uniformly sampling in the radial plane region of the fuel rod grid where the source particle is located to obtain the first coordinate and the second coordinate of the source particle includes: obtaining A regional random number within the interval, determining a sub-region where a source particle is located based on the regional random number; uniformly sampling in the sub-region where the source particle is located to obtain a first coordinate and a second coordinate of the source particle, and judging whether the source particle is within the second shape based on the first coordinate and the second coordinate; if not, re-obtaining the regional random number to calculate the first coordinate and the second coordinate of the source particle until the source particle is within the second shape.

[0127] In some embodiments, the cross-sectional shape of the fuel rod in the radial plane is a square, such as Figure 2B and Fig. 6A As shown, the sampling is uniform within the square, such as Fig. 6A As shown, the local spatial position coordinates (x, y) of the source particle can be determined according to the following formula:

[0128]

[0129] In the formula, for Random numbers within the interval can be generated by a random function; is the lower and upper boundaries of the qth fuel rod grid in the x direction, in cm; is the lower and upper boundaries of the qth fuel rod grid in the y direction, in cm.

[0130] In some other embodiments, the cross-sectional shape of the fuel rod in the radial plane is hexagonal, such as Figure 2A and Figure 6B As shown, the sampling is uniform within the hexagon, such as Figure 6B As shown, the local spatial position coordinates (x, y) of the source particles can be sampled using piecewise continuous functions. The details are as follows:

[0131] 1) First, divide the hexagon into multiple sub-regions. According to the size of each sub-region, the probability density function and cumulative distribution function of each sub-region can be determined.

[0132] 2) Get The regional random number within the interval determines the sub-region where the source particle is located based on the regional random number.

[0133] 3) Uniformly sample the sub-region where the source particle is located to obtain the first coordinate and the second coordinate of the source particle.

[0134] For example, Figure 6B As shown, the hexagon is divided into three sub-areas: left triangular area 1111, middle rectangular area 1112 and right triangular area 1113. According to the area sizes of these three sub-areas, it can be determined that the probability density functions of the left triangular area 1111, middle rectangular area 1112 and right triangular area 1113 are 1 / 6, 4 / 6 and 1 / 6 respectively, and the cumulative distribution functions are 1 / 6, 5 / 6 and 1 respectively. The regional random number in the interval can determine the sub-region where the source particle is located. For example, if the regional random number is 0.125, since 0.125 is less than 1 / 6, it can be determined that the sub-region where the source particle is located is the left triangular region 1111. For another example, if the regional random number is 0.2, since 0.2 is greater than 1 / 6 but less than 5 / 6, it can be determined that the region where the source particle is located is the middle rectangular region 1112. Then uniformly sample the first coordinate and the second coordinate of the source particle in the sub-region where the source particle is located. The local spatial position coordinates (x, y) of the source particle can be determined according to the following formula:

[0135]

[0136] In the formula, for The random number in the interval can be generated by a random function; b is the side length of the fuel rod, in cm.

[0137] In some other embodiments, the cross-sectional shape of the fuel rod in the radial plane is circular, such as Figure 7A-7B As shown, the sample is uniformly sampled within the circle, and the local spatial position coordinates (x, y) of the source particles can be sampled using the inverse transformation method or the discard sampling method. For example, when the inverse transformation method is used, the local spatial position coordinates (x, y) of the source particles can be determined according to the following formula:

[0138]

[0139] In the formula, for Random numbers within the interval can be generated by a random function.

[0140] When adopting the discard sampling method, it can be assumed that the circle is located in a square or hexagon, and the side length of the square or hexagon is b cm. Uniform sampling is performed in the square or hexagon to obtain the first coordinate and the second coordinate of the source particle. It is determined whether the sum of the squares of the first coordinate and the second coordinate is less than or equal to the square of the radius of the circle. If not, the first coordinate and the second coordinate of the source particle are re-sampled uniformly in the square or hexagon until the sum of the squares of the calculated first coordinate and the second coordinate is less than or equal to the square of the radius of the circle. For example, first use piecewise continuous function sampling in the hexagon to obtain the local spatial position coordinates (x, y) of the source particle, and determine whether the local spatial position coordinates (x, y) of the source particle satisfy the following formula. If not, the piecewise continuous function sampling is re-used in the hexagon until the following formula is satisfied:

[0141]

[0142] Where r is the circular radius of the fuel rod, in cm.

[0143] The global spatial position coordinates of the source particles can be calculated based on the local spatial position coordinates (x, y) of the source particles. First, the center coordinates of the fuel assembly and the center coordinates of the fuel rod are obtained, and then the global spatial position coordinates of the source particles are obtained based on the first and second coordinates of the source particles, the center coordinates of the fuel assembly and the center coordinates of the fuel rod.

[0144] In an exemplary embodiment, the coordinates of the center point of the hexagonal fuel assembly can be calculated based on the fuel assembly number and the movement vector of the fuel assembly. The calculation formula is as follows:

[0145]

[0146] In the formula, is the coordinate of the center point of the fuel assembly on the x-axis and y-axis, in cm; (m1,n1) is the fuel assembly number; is the movement vector of the fuel assembly in the m1 direction; is the movement vector of the fuel assembly in the n1 direction.

[0147] The center coordinates of the fuel rod can be calculated based on the fuel rod number and the movement vector of the fuel rod. The calculation formula is as follows:

[0148]

[0149] In the formula, is the coordinate of the center point of the fuel rod on the x-axis and y-axis, in cm; (m2,n2) is the fuel assembly number; is the movement vector of the fuel rod in the m2 direction, is the movement vector of the fuel rod in the n2 direction.

[0150] The local space position coordinates of the source particle Adding the center point coordinates of the fuel assembly and fuel rod, we can get the global space position coordinates of the source particle.

[0151] The calculation formula for the third coordinate of the source particle in the axial direction, that is, the z-axis coordinate of the source particle, is as follows:

[0152]

[0153] In the formula, is the lower and upper boundaries of the qth fuel rod grid in the z direction, in cm; for Random numbers within the interval can be generated by a random function.

[0154] Step S333: Determine the initial energy of the source particles based on the energy cumulative distribution function of the fuel rod grid.

[0155] In actual operation, a random number of energy groups in the interval (0,1] can be obtained, and the energy group of the source particles can be determined based on the random number of energy groups and the energy cumulative distribution function of the fuel rod grid; the initial energy of the source particles can be determined based on the lower and upper energy boundaries of the energy group of the source particles.

[0156] In an exemplary embodiment, obtain an energy group random number ξ in the interval (0,1] g ,like , it means that the source particle is in the gth group. The initial energy of the source particle is determined based on the lower and upper energy boundaries of the gth group. The calculation formula for the initial energy of the source particle is as follows:

[0157]

[0158] In the formula, g is the energy group number; is the initial energy of the source particle, in MeV; Respectively The lower and upper energy boundaries of the group can be input by the user in MeV; for Random numbers within a range can be generated by a random function.

[0159] In addition to determining the particle type, spatial position, and initial energy of the source particles, it is necessary to assign a weight to the source particles. The calculation formula is as follows:

[0160]

[0161] In the formula, is the source particle weight of the p-th particle, the g-th group, and the q-th fuel rod grid; N0 is the total source intensity produced by core fission without considering the source bias factor, in particles / s.

[0162] The direction of the source particles is sampled, such as using isotropic sampling to determine the particle direction. The distribution parameters of the source particles determined can be used as input for shielding calculation by the MC method.

[0163] Figure 8 is a schematic diagram of a reactor core source particle energy cumulative distribution function provided by an embodiment of the present application, wherein the energy cumulative distribution function accumulates from high energy to low energy. Figure 8 It can be seen that compared with unbiased sampling (i.e., not considering the source bias factor), the probability of sampling to produce high-energy particles is greatly improved after bias (i.e., considering the source bias factor). For example, the probability of unbiased sampling to produce high-energy particles with E≥2.0MeV is about 0.45, that is, about 45 out of 100 source particles have energies greater than 2.0MeV. The probability of biased sampling to produce high-energy particles with E≥2.0MeV is about 0.95, that is, about 95 out of 100 source particles have energies greater than 2.0MeV.

[0164] Fig. 9 and Fig.10 The schematic diagrams of the first 1 million unbiased and biased source particle distributions are shown respectively. Fig. 9 and Fig.10 It can be seen that the unbiased source particle distribution is scattered throughout the core area, while the biased source particle distribution produces more source particles near the counting area (i.e., the area where the calculation results are concerned) compared with the unbiased source particle distribution.

[0165] It can be seen that compared with not considering the source bias factor, when the source bias factor is considered, the calculation result accuracy is comparable and the calculation efficiency can be greatly improved.

[0166] Fig.11 Schematic diagram of a reactor core fuel assembly source distribution calculation system provided in an embodiment of the present application. Fig.11 As shown, the reactor core fuel assembly source distribution calculation system 1100 includes:

[0167] An input parameter acquisition module 1110 is used to acquire input parameters, wherein the input parameters include power distribution, fission nuclide fraction, fission spectrum, average number of particles released per fission, and average energy released per fission;

[0168] A cumulative distribution function calculation module 1120 is used to calculate the cumulative distribution function of the source particles based on the input parameters, wherein the cumulative distribution function includes one or more of the spatial cumulative distribution function of the fuel rod grid, the energy cumulative distribution function of the fuel rod grid, and the cumulative distribution function of the particle type;

[0169] The source particle distribution parameter calculation module 1130 is used to perform source particle sampling based on the cumulative distribution function to determine the distribution parameters of the source particles.

[0170] The reactor core fuel assembly source distribution calculation system 1100 provided in this embodiment is used to implement the aforementioned reactor core fuel assembly source distribution calculation method. Therefore, the specific implementation method of the reactor core fuel assembly source distribution calculation system 1100 can be seen in the embodiment part of the reactor core fuel assembly source distribution calculation method in the previous text, and will not be repeated here.

[0171] Fig.12 Schematic diagram of a computing device provided in an embodiment of the present application. Fig.12 As shown, the computing device 1200 includes one or more processors 1210 , one or more memories 1220 coupled to the processors 1210 , and one or more communication modules 1240 coupled to the processors 1210 .

[0172] The communication module 1240 is used for two-way communication. The communication module 1240 has at least one antenna to facilitate communication. The communication interface may represent any interface necessary for communicating with other network elements.

[0173] Processor 1210 may be of any type suitable for the local technology network, and may include, as non-limiting examples, one or more of: a general purpose computer, a special purpose computer, a microprocessor, a digital signal processor (DSP), and a processor based on a multi-core processor architecture. Computing device 1200 may have multiple processors, such as application specific integrated circuit chips, which are driven in time to a clock that synchronizes a main processor.

[0174] The memory 1220 may include one or more non-volatile memories and one or more volatile memories. Examples of non-volatile memories include, but are not limited to, read-only memory (ROM) 1224, electrically programmable read-only memory (EPROM), flash memory, hard disk, compact disk (CD), digital video disk (DVD), and other magnetic and / or optical memories. Examples of volatile memories include, but are not limited to, random access memory (RAM) 1222 and other volatile memories that do not persist during a power outage.

[0175] The computer program 1230 includes computer executable instructions that are executed by the associated processor 1210. The computer program 1230 may be stored in the ROM 1224. The processor 1210 may perform any appropriate actions and processes by loading the computer program 1230 into the RAM 1222.

[0176] The embodiments of the present application can be implemented by a computer program 1230, so that the computing device 1200 can execute the reference Figure 3-Figure 5 Any process disclosed in the discussion. The embodiments of the present application may also be implemented by hardware or by a combination of software and hardware.

[0177] In some embodiments, computer program 1230 may be tangibly embodied in a computer-readable medium, which may be contained in computing device 1200 (e.g., memory 1220) or other storage devices accessible to computing device 1200. Computing device 1200 may load computer program 1230 from the computer-readable medium to RAM 1222 for execution. The computer-readable medium may include any type of tangible non-volatile memory, such as ROM, EPROM, flash memory, hard disk, CD, DVD, etc. The computer-readable medium has program 1230 stored thereon.

[0178] Generally, various embodiments of the present application may be implemented in hardware or dedicated circuits, software, logic, or any combination thereof. Certain aspects may be implemented in hardware, while other aspects may be implemented in firmware or software, which may be performed by a controller, microprocessor, or other computing device. Although various aspects of the embodiments of the present application are shown and described as block diagrams, flow charts, or using some other graphical representations, it should be understood that, as non-limiting examples, the blocks, devices, systems, techniques, or methods described herein may be implemented in hardware, software, firmware, dedicated circuits or logic, general hardware or controllers or other computing devices, or some combination thereof.

[0179] The present application also provides at least one computer program product tangibly stored on a non-transitory computer readable storage medium. The computer program product includes computer executable instructions, such as instructions included in program modules, which are executed in a device on a target real or virtual processor to perform the above-mentioned reference Figure 3-Figure 5 The method described. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform specific tasks or implement specific abstract data types. In various embodiments, the functions of program modules can be combined or separated between program modules as needed. Machine executable instructions for program modules can be executed in local or distributed devices. In distributed devices, program modules can be located in local and remote storage media.

[0180] The program code for executing the method of the present application can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing equipment so that when the program code is executed by the processor or controller, the function / operation specified in the flow chart and / or the block diagram is realized. The program code can be executed completely on the machine as an independent software package, partially on the machine, partially on the machine, partially on a remote machine, partially on a remote machine, or all on a remote machine or server.

[0181] In the context of this application, computer program codes or related data may be carried by any appropriate carrier to enable a device, apparatus or processor to perform various processes and operations as described above. Examples of carriers include signals, computer readable media, etc.

[0182] The computer readable medium may be a computer readable signal medium or a computer readable storage medium. The computer readable medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared or semiconductor systems, devices or apparatuses, or any suitable combination of the foregoing. More specific examples of computer readable storage media include an electrical connection having one or more conductors, a portable computer floppy disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0183] In addition, although the operations are described in a specific order, this should not be construed as requiring to perform these operations in the specific order or sequence shown, or to perform all the operations shown, to obtain the desired result. In some cases, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these details should not be interpreted as limiting the scope of the application, but can be interpreted as a description of the specific features of a particular embodiment. Some of the features described in the context of a separate embodiment may also be implemented in combination in a single embodiment. On the contrary, the various features described in the context of a single embodiment may also be implemented in multiple embodiments individually or in any suitable sub-combination.

[0184] Although the present application has been described in language specific to structural features and / or methodological acts, it should be understood that the present application defined in the appended claims is not necessarily limited to the specific features or acts described above. Instead, the specific features and acts described above are disclosed as example forms of implementing the claims.

Claims

1. A method for calculating the source distribution of reactor core fuel assemblies, characterized in that: include: Acquiring input parameters, wherein the input parameters include power distribution, fissile nuclide fraction, fission spectrum, average number of particles released per fission, average energy released per fission, and source bias factor, wherein the source bias factor includes one or more of a spatial bias factor of a fuel rod grid, an energy bias factor, and a particle bias factor; Calculate a cumulative distribution function of source particles based on the input parameters, wherein the cumulative distribution function includes one or more of a spatial cumulative distribution function of a fuel rod grid, an energy cumulative distribution function of a fuel rod grid, and a cumulative distribution function of a particle type; Source particle sampling is performed based on the cumulative distribution function to determine distribution parameters of the source particles.

2. The method according to claim 1, characterized in that The obtaining of input parameters includes: The source bias factor is calculated based on the conjugate fluence rate of the fuel rod grid.

3. The method according to claim 1 or 2, characterized in that The source bias factor includes a spatial bias factor of a fuel rod grid, the cumulative distribution function includes a spatial cumulative distribution function of a fuel rod grid, and the cumulative distribution function of source particles calculated based on the input parameters includes: Calculate the source strength of the fuel rod grid based on the input parameters; Calculating a spatial cumulative distribution function of a fuel rod grid based on the source intensity of the fuel rod grid; The sampling of source particles based on the cumulative distribution function to determine the distribution parameters of the source particles includes: Acquire a spatial random number within the interval, and determine the fuel rod grid where the source particle is located based on the spatial random number and the spatial cumulative distribution function of the fuel rod grid; Uniformly sampling in the radial plane region of the fuel rod grid where the source particles are located to obtain the first coordinate and the second coordinate of the source particles; The third coordinate of the source particle is determined based on the lower boundary and the upper boundary of the grid of the fuel rod where the source particle is located in the axial direction, and the axial direction is perpendicular to the radial plane.

4. The method according to claim 3, characterized in that The cross-sectional shape of the fuel rod in the radial plane is a first shape, the first shape is divided into a plurality of sub-regions, and the first coordinates and the second coordinates of the source particles obtained by uniformly sampling in the radial plane region of the fuel rod grid where the source particles are located include: Obtaining a regional random number within the interval, and determining a sub-region where a source particle is located based on the regional random number; The first coordinate and the second coordinate of the source particle are obtained by uniformly sampling in the sub-region where the source particle is located.

5. The method according to claim 3, characterized in that The cross-sectional shape of the fuel rod in the radial plane is a second shape, the second shape is located within the first shape, the first shape is divided into a plurality of sub-regions, and the first coordinates and the second coordinates of the source particles obtained by uniformly sampling in the radial plane region of the fuel rod grid where the source particles are located include: Obtaining a regional random number within the interval, and determining a sub-region where a source particle is located based on the regional random number; Uniformly sample the sub-region where the source particle is located to obtain the first coordinate and the second coordinate of the source particle, determining whether the source particle is within the second shape based on the first coordinate and the second coordinate; If not, re-obtaining regional random numbers to calculate the first coordinates and the second coordinates of the source particle until the source particle is within the second shape.

6. The method according to claim 1 or 2, characterized in that: The source bias factor includes an energy bias factor, the cumulative distribution function includes an energy cumulative distribution function of a fuel rod grid, and the cumulative distribution function of source particles calculated based on the input parameters includes: Calculating an energy probability density function of the fuel assembly based on the input parameters; Calculating the energy cumulative distribution function of the fuel assembly based on the energy probability density function of the fuel assembly; Obtaining an energy cumulative distribution function of a fuel rod grid based on the energy cumulative distribution function of the fuel assembly; The sampling of source particles based on the cumulative distribution function to determine the distribution parameters of the source particles includes: Obtaining a random number of an energy group within the interval, and determining the energy group to which the source particle belongs based on the random number of the energy group and the energy cumulative distribution function of the fuel rod grid; The initial energy of the source particle is determined based on the lower energy boundary and the upper energy boundary of the energy group to which the source particle belongs.

7. The method according to claim 1 or 2, characterized in that: The source bias factor includes a particle bias factor, the cumulative distribution function includes a cumulative distribution function of a particle type, and the cumulative distribution function of a source particle calculated based on the input parameters includes: Calculate the source strength of the fuel rod grid based on the input parameters; Calculating the total source intensity generated by core fission based on the source intensity of the fuel rod grid; Calculating a cumulative distribution function of particle types based on the total source intensity; The sampling of source particles based on the cumulative distribution function to determine the distribution parameters of the source particles includes: A type random number within an interval is obtained, and a particle type of a source particle is determined based on the type random number and a cumulative distribution function of the particle type.

8. A reactor core fuel assembly source distribution calculation system, characterized in that: include: An input parameter acquisition module, used to acquire input parameters, wherein the input parameters include power distribution, fission nuclide fraction, fission spectrum, average number of particles released per fission, average energy released per fission, and source bias factor, wherein the source bias factor includes one or more of the spatial bias factor, energy bias factor, and particle bias factor of the fuel rod grid; A cumulative distribution function calculation module, used to calculate the cumulative distribution function of the source particles based on the input parameters, wherein the cumulative distribution function includes one or more of the spatial cumulative distribution function of the fuel rod grid, the energy cumulative distribution function of the fuel rod grid, and the cumulative distribution function of the particle type; The source particle distribution parameter calculation module is used to perform source particle sampling based on the cumulative distribution function to determine the distribution parameters of the source particles.

9. A computing device, characterized in that: include: at least one processor; as well as At least one memory having instructions stored thereon, which, when executed individually or collectively by the at least one processor, cause the computing device to perform the method according to any one of claims 1 to 7.

10. A computer storage medium, characterized in that: The computer storage medium stores instructions, which, when executed individually or collectively by at least one processor of a computing device, cause the computing device to perform the method according to any one of claims 1 to 7.

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