CN116304498A - Method and system for solving multi-group neutron diffusion equation of nuclear reactor core - Google Patents

Method and system for solving multi-group neutron diffusion equation of nuclear reactor core Download PDF

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CN116304498A
CN116304498A CN202310132524.5A CN202310132524A CN116304498A CN 116304498 A CN116304498 A CN 116304498A CN 202310132524 A CN202310132524 A CN 202310132524A CN 116304498 A CN116304498 A CN 116304498A
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王柱
王相龙
王玥
杜翔鹏
万天缘
李天军
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Abstract

The invention provides a method and a system for solving a multi-cluster neutron diffusion equation of a nuclear reactor core, and relates to the technical field of nuclear reactor core calculation. According to the method, a coefficient matrix of an equation is determined according to boundary conditions of a plurality of groups of neutron diffusion equations of a nuclear reactor by reconstructing the plurality of groups of neutron diffusion equations of the nuclear reactor into an elliptic partial differential equation, and a geometric model of an established nuclear reactor core is subjected to grid division by using a non-structural grid to construct a core grid model, so that accurate simulation of a transient process of a core neutron under any geometric shape is realized; a calculation method for establishing a multi-group diffusion equation based on a coefficient matrix and a reactor core grid model calculates the macro-section parameters of the neutrons of the nuclear reactor and substitutes the macro-section parameters into the calculation method of the multi-group diffusion equation, so that the flux distribution of the neutrons of the reactor core of the nuclear reactor is obtained, the numerical stability of calculation is ensured, the calculation precision and speed are improved, the calculation time is shortened, and the method is beneficial to the wide use of neutron diffusion programs of the nuclear reactor in engineering practice.

Description

Method and system for solving multi-group neutron diffusion equation of nuclear reactor core
Technical Field
The invention relates to the technical field of nuclear reactor core calculation, in particular to a method and a system for solving a multi-cluster neutron diffusion equation of a nuclear reactor core.
Background
The nuclear reactor neutron computing research targets a nuclear reactor core, which is composed of many different kinds of components. Depending on the stack type, the geometry and material arrangement inside the assembly is complex and variable. The fast and accurate neutron calculation of the nuclear reactor is a basic guarantee for the design and check of the reactor.
One of the basic problems of nuclear reactor design basic theory is to determine the distribution condition of neutron flux density in a reactor, and common neutron diffusion equation calculation methods, such as a variable segmentation method, have the problems of complex calculation process, overlarge data volume and the like, so that the stability and the accuracy of calculation are poor, and the wide application of a nuclear reactor neutron diffusion program in engineering practice is not facilitated.
Disclosure of Invention
The invention aims to provide a method and a system for solving a multi-cluster neutron diffusion equation of a nuclear reactor core, which are characterized in that the multi-cluster neutron diffusion equation of the nuclear reactor is reconstructed into an elliptic partial differential equation, then a coefficient matrix of the equation is determined according to the boundary condition of the multi-cluster neutron diffusion equation of the nuclear reactor, and a non-structural grid is used for meshing an established geometric model of the nuclear reactor core to construct a core grid model, so that the accurate simulation of the transient process of neutrons of the core under any geometric shape can be realized; further, a calculation method of a multi-cluster diffusion equation is established based on the coefficient matrix and the reactor core grid model, then the macro-cross section parameters of the neutrons in the multi-cluster of the nuclear reactor are calculated and substituted into the calculation method of the multi-cluster diffusion equation, the flux distribution of the neutrons in the reactor core of the nuclear reactor is obtained by solving, the calculation accuracy and speed can be improved while the numerical stability of calculation is ensured, and the calculation time is greatly shortened, so that the method is beneficial to the wide use of neutron diffusion programs in engineering practice.
Embodiments of the present invention are implemented as follows:
in a first aspect, an embodiment of the present application provides a method for solving a multi-cluster neutron diffusion equation of a nuclear reactor core, including the steps of:
reconstructing a plurality of neutron diffusion equations of the nuclear reactor into an elliptic partial differential equation;
determining a coefficient matrix of an equation according to boundary conditions of a plurality of neutron diffusion equations of the nuclear reactor;
establishing a geometric model of a nuclear reactor core, meshing the geometric model of the nuclear reactor core by using grids, and constructing a core grid model;
and establishing a calculation method of a multi-group diffusion equation through the coefficient matrix and the reactor core grid model, and solving to obtain flux distribution of neutrons in the reactor core of the nuclear reactor based on the established calculation method of the multi-group diffusion equation.
In some embodiments of the present invention, the step of determining the coefficient matrix of the equation according to the boundary condition of the nuclear reactor multi-cluster neutron diffusion equation specifically includes:
and mapping the vacuum boundary conditions and the reflectivity boundary conditions of the nuclear reactor multi-group neutron diffusion equation into Dirichlet and Norman boundary conditions respectively, and determining a coefficient matrix of the equation.
In some embodiments of the present invention, after the step of constructing the core grid model, before the step of establishing the calculation method of the multi-group diffusion equation by the coefficient matrix and the core grid model, further comprises:
creating a multi-group database based on the core evaluation library;
based on the multi-cluster database, a subgroup method is adopted to effectively calculate the macroscopic section parameters of the multi-cluster neutrons of the nuclear reactor under different working conditions.
In some embodiments of the present invention, the step of solving the flux distribution of neutrons in the nuclear reactor core based on the established multi-group diffusion equation calculation method specifically includes:
substituting the macroscopic cross-section parameters of the neutrons in the multiple groups into a calculation method of the diffusion equation in the multiple groups to solve, so as to obtain the flux distribution of the neutrons in the reactor core.
In some embodiments of the invention, the grid comprises an unstructured grid.
In a second aspect, embodiments of the present application provide a solution system for a nuclear reactor core multi-cluster neutron diffusion equation, comprising:
the reconstruction module is used for reconstructing the nuclear reactor multi-group neutron diffusion equation into an elliptic partial differential equation;
the determining module is used for determining a coefficient matrix of an equation according to boundary conditions of the nuclear reactor multi-group neutron diffusion equation;
the construction module is used for establishing a geometric model of the nuclear reactor core, meshing the geometric model of the nuclear reactor core by using grids, and constructing a core grid model;
and the solving module is used for establishing a calculation method of a multi-group diffusion equation through the coefficient matrix and the reactor core grid model and solving the flux distribution of neutrons in the reactor core of the nuclear reactor based on the established calculation method of the multi-group diffusion equation.
In a third aspect, embodiments of the present application provide an electronic device comprising a memory for storing one or more programs; a processor, when the one or more programs are executed by the processor, implementing a method as described in any one of the first aspects.
In a fourth aspect, embodiments of the present application provide a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements a method as described in any of the first aspects above.
Compared with the prior art, the embodiment of the invention has at least the following advantages or beneficial effects:
the embodiment of the invention provides a solving method of a nuclear reactor core multi-group neutron diffusion equation, which comprises the steps of reconstructing the nuclear reactor multi-group neutron diffusion equation into an elliptic partial differential equation, determining a coefficient matrix of the equation according to boundary conditions of the nuclear reactor multi-group neutron diffusion equation, and meshing an established geometric model of the nuclear reactor core by using a non-structural mesh to construct a core mesh model, so that accurate simulation of a neutron transient process of the core under any geometric shape can be realized; further, a calculation method of a multi-cluster diffusion equation is established based on the coefficient matrix and the reactor core grid model, then the macro-cross section parameters of the neutrons in the multi-cluster of the nuclear reactor are calculated and substituted into the calculation method of the multi-cluster diffusion equation, the flux distribution of the neutrons in the reactor core of the nuclear reactor is obtained by solving, the calculation accuracy and speed can be improved while the numerical stability of calculation is ensured, and the calculation time is greatly shortened, so that the method is beneficial to the wide use of neutron diffusion programs in engineering practice.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an embodiment of a method for solving a multi-cluster neutron diffusion equation in a nuclear reactor core according to the present invention;
FIG. 2 is a flowchart showing the steps of the method for solving the multi-cluster neutron diffusion equation of the nuclear reactor core after the step of constructing the core grid model and before the step of establishing the method for calculating the multi-cluster diffusion equation by using the coefficient matrix and the core grid model according to the embodiment of the present invention;
FIG. 3a is a schematic diagram of a transverse neutron flux distribution obtained by solving in an embodiment of the invention;
FIG. 3b is a schematic diagram of a longitudinal neutron flux distribution obtained by solving in an embodiment of the invention;
FIG. 4 is a block diagram illustrating one embodiment of a solution system for a multi-cluster neutron diffusion equation of a nuclear reactor core in accordance with the present invention;
fig. 5 is a block diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, which are generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations.
Example 1
Referring to fig. 1-3, an embodiment of the present application provides a method for solving a multi-cluster neutron diffusion equation of a nuclear reactor core, which comprises reconstructing the multi-cluster neutron diffusion equation of the nuclear reactor into an elliptic partial differential equation, determining a coefficient matrix of the equation according to boundary conditions of the multi-cluster neutron diffusion equation of the nuclear reactor, and meshing an established geometric model of the nuclear reactor core by using a non-structural mesh to construct a core mesh model, so as to achieve accurate simulation of a neutron transient process of the core under any geometric shape; further, a calculation method of a multi-cluster diffusion equation is established based on the coefficient matrix and the reactor core grid model, then the macro-cross section parameters of the neutrons in the multi-cluster of the nuclear reactor are calculated and substituted into the calculation method of the multi-cluster diffusion equation, the flux distribution of the neutrons in the reactor core of the nuclear reactor is obtained by solving, the calculation accuracy and speed can be improved while the numerical stability of calculation is ensured, and the calculation time is greatly shortened, so that the method is beneficial to the wide use of neutron diffusion programs in engineering practice.
As shown in fig. 1, the method for solving the above-mentioned nuclear reactor core multi-cluster neutron diffusion equation includes the following steps:
step S101: reconstructing a nuclear reactor multi-group neutron diffusion equation into an elliptic partial differential equation.
Wherein, for any system containing value added medium, including a nuclear reactor system, the neutron diffusion equation related to energy can be given as:
Figure BDA0004084789610000061
the neutron diffusion equation contains space variables
Figure BDA0004084789610000062
With the energy variable E, the solution cannot be used in most cases, but can be performed based on the idea of "group approximation", specifically as follows: the energy size of the neutrons is divided into G energy regions, i.e., G energy groups, numbered g=1. The specific difference of neutron energy is not paid attention to in each energy group, and is regarded as an overall discussion of the action rule with atomic nuclei.
At each energy group interval delta E g Integrating the equations, and eliminating the variable E in the equations to obtain G neutron diffusion equations without energy variable, wherein the diffusion equation of the G group is as follows:
Figure BDA0004084789610000071
wherein: Δe=e g-1 -E g ，E g-1 、E g The upper and lower energy bounds of the g-group are respectively.
Some energy group average parameters can then be defined to simplify the equation. First define in space
Figure BDA0004084789610000078
The neutron flux density at group g is:
Figure BDA0004084789610000072
as may be made by definition of the terms,
Figure BDA0004084789610000073
namely space->
Figure BDA0004084789610000074
Total flux density of neutrons at various energies.
The total cross section of the redefined g group is as follows:
Figure BDA0004084789610000075
the diffusion coefficient of group g is defined as:
Figure BDA0004084789610000076
after the energy group division is completed, the scattering source in the equation can be written as:
Figure BDA0004084789610000077
defining a group transfer section as:
Figure BDA0004084789610000081
thus, Σ g'→g φ g' That is, the number of neutrons in g' group per second and per unit volume, the energy of which falls into g group after scattering collision, is shown g'→g Should include elastic and inelastic transfer sections, while the g-th group scatter section Σ s,g The following relationship exists between the group transfer section:
Figure BDA0004084789610000082
for fission reactions, the neutron production cross section (v Σ of g group is defined as follows f ) g And neutron fission spectrum:
Figure BDA0004084789610000083
Figure BDA0004084789610000084
and obtaining a steady-state multi-group neutron diffusion equation under the condition of no external source by using the newly defined energy group average parameter formula:
Figure BDA0004084789610000085
g＝1,2,…,G
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0004084789610000098
is a differential calculation operator, D g Is the diffusion coefficient of the energy group, +.>
Figure BDA0004084789610000091
Is the absorption cross section of the energy group g,
Figure BDA0004084789610000092
is the scattering cross section of the energy groups g to g' -, and->
Figure BDA0004084789610000093
Is the fission cross section of the energy group g, phi g Scalar neutron flux, χ, of energy group g g Is the percentage of newly added neutrons, k, in each energy group eff Is the multiplication coefficient, v is the neutron velocity in cm/s, and a is the MATLAB sign of the flux coefficient.
The elliptic partial differential equation is as follows:
Figure BDA0004084789610000095
in the obtained steady-state multi-group neutron diffusion equation under the condition without an external source, the second term (scattering source) on the right of the equation equal sign is moved to the left of the equal sign, the second term is combined with the second term on the left of the equation equal sign to convert the steady-state multi-group neutron diffusion under the condition without the external source, and then the converted multi-group neutron diffusion equation is compared with an elliptic partial differential equation to obtain the following relation:
Figure BDA0004084789610000096
Figure BDA0004084789610000097
Figure BDA0004084789610000101
Figure BDA0004084789610000102
where u is a column vector of length G, c is a diagonal matrix of size G, a and d are coefficient matrices of size G, subscript gg 'represents the G' th column element of the G-th row, k eff Is a multiplication factor.
Step S102: and determining a coefficient matrix of the equation according to boundary conditions of the nuclear reactor multi-group neutron diffusion equation.
The step of determining the coefficient matrix of the equation according to the boundary condition of the nuclear reactor multi-group neutron diffusion equation specifically comprises the following steps:
and mapping the vacuum boundary conditions and the reflectivity boundary conditions of the nuclear reactor multi-group neutron diffusion equation into Dirichlet and Norman boundary conditions respectively, and determining a coefficient matrix of the equation.
In the above step, the reflectance boundary condition is defined as:
Figure BDA0004084789610000103
where n is the surface normal, J is the neutron flux, and α is the reflectance coefficient. For the reflectivity boundary condition, neutron stream j=0, and thus α=0.
The Neumann or second type of boundary condition in the MATLAB software PDE solver is given by,
Figure BDA0004084789610000111
by comparing these two boundary condition equations, it can be deduced that c is the same diagonal matrix defined above, and the variables q and p are respectively:
q＝diag(α 1 ,α 2 ,…α g ,…,α G )
p＝[0，0，…，0，…，0] T
where q is a diagonal matrix of G x G and p (not to be confused with the energy group symbol) is a column vector of length G.
The vacuum boundary conditions are
Figure BDA0004084789610000112
So α= 0.46922.
U under zero flux boundary conditions g ＝Φ g =0, which can be mapped to Dirichlet or first class boundary conditions defined as hu=r in the PDE solver, and comparing the two equations of the vacuum boundary conditions, h is an identity matrix with size g×g, r is a column vector with all elements being zero, as shown in the following formula:
h＝diag(1,1,…,1,…,1)
r＝[0,0,…,0,…,0] T
and then mapping the vacuum boundary condition and the reflectivity boundary condition to a matrix and a vector obtained by the Dirichlet boundary condition and the Neumann boundary condition respectively to serve as a coefficient matrix of the equation of the multi-group neutron diffusion equation.
Step S103: establishing a geometric model of the nuclear reactor core, meshing the geometric model of the nuclear reactor core by using grids, and constructing a core grid model.
In the steps, the used grids comprise unstructured grids, the unstructured grids have arbitrary geometric adaptability, the grid division mode is free, the robustness is good, the calculation speed is high, the unstructured grids are used for carrying out grid division on the geometric model of the nuclear reactor core, an unstructured reactor core grid model is constructed, accurate simulation of the neutron transient process of the reactor core under any geometric shape can be achieved, and the model has better geometric compatibility.
Step S104: and establishing a calculation method of a multi-group diffusion equation through the coefficient matrix and the reactor core grid model, and solving to obtain flux distribution of neutrons in the reactor core of the nuclear reactor based on the established calculation method of the multi-group diffusion equation.
Accordingly, as shown in fig. 2, after the step of constructing the core grid model, before the step of establishing the calculation method of the multi-cluster diffusion equation by the coefficient matrix and the core grid model, the method of solving the multi-cluster neutron diffusion equation of the nuclear reactor core further includes:
step S201: creating a multi-group database based on the core evaluation library;
step S202: based on the multi-cluster database, a subgroup method is adopted to effectively calculate the macroscopic section parameters of the multi-cluster neutrons of the nuclear reactor under different working conditions.
In the steps, a multi-group database based on WIMS format can be manufactured by adopting a nuclear data processing program NIOY-99 based on a nuclear evaluation library of ENDF/B-VIL, then effective self-shielding section calculation is performed by adopting a subgroup method based on the multi-group database, and macroscopic section parameters of multiple groups of neutrons under different moderator temperature, fuel temperature and boron concentration working conditions after the homogenization of a nuclear reactor component are calculated, so that the flux distribution of neutrons in a nuclear reactor core under different working conditions can be calculated quickly based on the parameters, and the calculation time is shortened.
Further, the step of obtaining the flux distribution of the neutrons in the reactor core by solving the calculation method based on the established multi-group diffusion equation specifically includes:
substituting the macroscopic cross-section parameters of the neutrons in the multiple groups into a calculation method of the diffusion equation in the multiple groups to solve, so as to obtain the flux distribution of the neutrons in the reactor core.
Substituting the macroscopic section parameters of the plurality of groups of neutrons into a calculation method of a plurality of groups of diffusion equations established through a coefficient matrix and a reactor core grid model, and solving the plurality of groups of diffusion equations by utilizing a workflow function built in a MATLAB software PDE solver, so that neutron flux distribution conditions at different positions of a reactor core of a nuclear reactor and overall effective increment coefficients can be calculated, wherein the specific conditions of the neutron flux distribution are shown in a transverse neutron flux distribution shown in FIG. 3a and a longitudinal neutron flux distribution shown in FIG. 3 b; through the solving process of the steps, the calculating precision and speed can be improved while the numerical stability of calculation is ensured, and the calculating time is greatly shortened, so that the nuclear reactor neutron diffusion program is widely used in engineering practice.
It should be noted that, in the embodiment of the present invention, the technical content that is not specifically described in the embodiment of the present invention may be implemented by using the existing related technology, which belongs to the prior art, and is not described in detail in the embodiment of the present invention.
Example 2
Accordingly, referring to fig. 4, an embodiment of the present application provides a solution system for a multi-cluster neutron diffusion equation of a nuclear reactor core, which includes:
the reconstruction module 1 is used for reconstructing a plurality of neutron diffusion equations of the nuclear reactor into an elliptic partial differential equation; a determining module 2, configured to determine a coefficient matrix of an equation according to boundary conditions of a plurality of neutron diffusion equations of the nuclear reactor; a construction module 3, configured to establish a geometric model of a nuclear reactor core, and to grid-divide the geometric model of the nuclear reactor core by using grids, so as to construct a core grid model; and the solving module 4 is used for establishing a calculation method of a multi-group diffusion equation through the coefficient matrix and the reactor core grid model and solving and obtaining flux distribution of neutrons in the reactor core based on the established calculation method of the multi-group diffusion equation.
The specific implementation process of the system is referred to the method for solving the multi-cluster neutron diffusion equation of the nuclear reactor core provided in embodiment 1, and is not described herein.
Example 3
Referring to fig. 5, an embodiment of the present application provides an electronic device comprising at least one processor 5, at least one memory 6 and a data bus 7; wherein: the processor 5 and the memory 6 complete the communication with each other through the data bus 7; the memory 6 stores program instructions executable by the processor 5, the processor 5 invoking the program instructions to perform a method of solving a diffusion equation in a plurality of clusters of neutrons in a nuclear reactor core. For example, implementation:
reconstructing a plurality of neutron diffusion equations of the nuclear reactor into an elliptic partial differential equation; determining a coefficient matrix of an equation according to boundary conditions of a plurality of neutron diffusion equations of the nuclear reactor; establishing a geometric model of a nuclear reactor core, meshing the geometric model of the nuclear reactor core by using grids, and constructing a core grid model; and establishing a calculation method of a multi-group diffusion equation through the coefficient matrix and the reactor core grid model, and solving to obtain flux distribution of neutrons in the reactor core of the nuclear reactor based on the established calculation method of the multi-group diffusion equation.
The Memory 6 may be, but is not limited to, a random access Memory (Random Access Memory, RAM), a Read Only Memory (ROM), a programmable Read Only Memory (Programmable Read-Only Memory, PROM), an erasable Read Only Memory (Erasable Programmable Read-Only Memory, EPROM), an electrically erasable Read Only Memory (Electric Erasable Programmable Read-Only Memory, EEPROM), etc.
The processor 5 may be an integrated circuit chip with signal processing capabilities. The processor 5 may be a general-purpose processor including a central processing unit (Central Processing Unit, CPU), a network processor (Network Processor, NP), etc.; but also digital signal processors (Digital Signal Processing, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), field programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.
It will be appreciated that the configuration shown in fig. 5 is merely illustrative, and that the electronic device may also include more or fewer components than shown in fig. 5, or have a different configuration than shown in fig. 5. The components shown in fig. 5 may be implemented in hardware, software, or a combination thereof.
Example 4
The present invention provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor 5, implements a method of solving a multi-cluster neutron diffusion equation in a nuclear reactor core. For example, implementation:
reconstructing a plurality of neutron diffusion equations of the nuclear reactor into an elliptic partial differential equation; determining a coefficient matrix of an equation according to boundary conditions of a plurality of neutron diffusion equations of the nuclear reactor; establishing a geometric model of a nuclear reactor core, meshing the geometric model of the nuclear reactor core by using grids, and constructing a core grid model; and establishing a calculation method of a multi-group diffusion equation through the coefficient matrix and the reactor core grid model, and solving to obtain flux distribution of neutrons in the reactor core of the nuclear reactor based on the established calculation method of the multi-group diffusion equation.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other manners as well. The apparatus embodiments described above are merely illustrative, for example, flow diagrams and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In addition, the functional modules in the embodiments of the present application may be integrated together to form a single part, or each module may exist alone, or two or more modules may be integrated to form a single part.
It will be evident to those skilled in the art that the present application is not limited to the details of the foregoing illustrative embodiments, and that the present application may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the application being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Claims (8)

1. A method of solving a nuclear reactor core multi-cluster neutron diffusion equation, comprising:
reconstructing a plurality of neutron diffusion equations of the nuclear reactor into an elliptic partial differential equation;
determining a coefficient matrix of an equation according to boundary conditions of a plurality of neutron diffusion equations of the nuclear reactor;
establishing a geometric model of a nuclear reactor core, meshing the geometric model of the nuclear reactor core by using grids, and constructing a core grid model;
and establishing a calculation method of a multi-group diffusion equation through the coefficient matrix and the reactor core grid model, and solving to obtain flux distribution of neutrons in the reactor core of the nuclear reactor based on the established calculation method of the multi-group diffusion equation.
2. The method of solving a nuclear reactor core multi-cluster neutron diffusion equation according to any one of claim 1, wherein the step of determining the coefficient matrix of the equation according to the boundary condition of the nuclear reactor multi-cluster neutron diffusion equation specifically comprises:
and mapping the vacuum boundary conditions and the reflectivity boundary conditions of the nuclear reactor multi-group neutron diffusion equation into Dirichlet and Norman boundary conditions respectively, and determining a coefficient matrix of the equation.
3. The method of claim 2, wherein after said step of constructing a core grid model, said step of constructing a calculation method of a multi-cluster diffusion equation from said coefficient matrix and said core grid model further comprises:
creating a multi-group database based on the core evaluation library;
based on the multi-cluster database, a subgroup method is adopted to effectively calculate the macroscopic section parameters of the multi-cluster neutrons of the nuclear reactor under different working conditions.
4. The method for solving a multi-cluster neutron diffusion equation of a nuclear reactor core according to claim 3, wherein the step of solving flux distribution of neutrons of the nuclear reactor core based on the established calculation method of the multi-cluster diffusion equation specifically comprises:
substituting the macroscopic cross-section parameters of the neutrons in the multiple groups into a calculation method of the diffusion equation in the multiple groups to solve, so as to obtain the flux distribution of the neutrons in the reactor core.
5. The method of solving a multi-cluster neutron diffusion equation of a nuclear reactor core of any of claims 1-4, wherein the grid comprises an unstructured grid.
6. A system for solving a nuclear reactor core multi-cluster neutron diffusion equation, comprising:
the reconstruction module is used for reconstructing the nuclear reactor multi-group neutron diffusion equation into an elliptic partial differential equation;
the determining module is used for determining a coefficient matrix of an equation according to boundary conditions of the nuclear reactor multi-group neutron diffusion equation;
the construction module is used for establishing a geometric model of the nuclear reactor core, meshing the geometric model of the nuclear reactor core by using grids, and constructing a core grid model;
and the solving module is used for establishing a calculation method of a multi-group diffusion equation through the coefficient matrix and the reactor core grid model and solving the flux distribution of neutrons in the reactor core of the nuclear reactor based on the established calculation method of the multi-group diffusion equation.
7. An electronic device comprising at least one processor, at least one memory, and a data bus; wherein: the processor and the memory complete communication with each other through the data bus; the memory stores program instructions for execution by the processor, the processor invoking the program instructions to perform the method of any of claims 1-5.
8. A computer readable storage medium, on which a computer program is stored, which computer program, when being executed by a processor, implements the method according to any of claims 1-5.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116821588A (en) * 2023-07-06 2023-09-29 四川大学 Reactor working condition judging and predicting method based on DSMF fusion algorithm

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116821588A (en) * 2023-07-06 2023-09-29 四川大学 Reactor working condition judging and predicting method based on DSMF fusion algorithm
CN116821588B (en) * 2023-07-06 2024-05-03 四川大学 Reactor working condition judging and predicting method based on DSMF fusion algorithm

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