Quasi-three-dimensional transportation method and system based on multi-layer coarse mesh improvement, and medium

Abstract

The invention relates to the technical field of nuclear reactor core design and safety, in particular to a quasi-three-dimensional transportation method and system based on multi-layer coarse net improvement and a medium, a pressurized water reactor three-dimensional reactor core to be simulated is divided into a plurality of transportation layers, and each transportation layer is radially divided into a plurality of fine nets; dividing each transport layer of the pressurized water reactor into a plurality of differential layers; radially dividing a plurality of coarse nets in each difference layer, and establishing a coarse net finite difference model on each coarse net; adopting rhombus difference in each difference layer to assume linear change of neutron angular flux density; and establishing a new quasi-three-dimensional transport model for surface neutron standard flux density correction of the differential layer central surface and the interface surface on each transport layer. According to the method, the axial height of quasi-three-dimensional transport calculation can be expanded, the number of modeling layers of quasi-three-dimensional transport calculation is reduced, the memory is saved, the calculation efficiency is improved, and the method can be used for pressurized water reactor numerical reactor simulation calculation and engineering application.

Description

Technical Field

[0001] The invention relates to the field of nuclear reactor core design and safety technology, and in particular to an improved quasi-three-dimensional transportation method and system and medium based on a multi-layer coarse mesh. Background Art

[0002] With the continuous development of the nuclear power industry, high-fidelity numerical simulation methods use direct solutions of the entire core to reduce approximations in the calculation methods, improve design accuracy, and thus reduce unnecessary safety margins in pressurized water reactors. This is an important technical development direction, ensuring the safety of pressurized water reactors while improving their economy.

[0003] In the high-fidelity numerical simulation method, compared with the traditional two-dimensional and one-dimensional coupled transport model, the quasi-three-dimensional transport model avoids the leakage term generated by the transverse integral, and there is no problem of inconsistency between the two-dimensional equation and the one-dimensional equation, and the calculation process is more stable. In the transport layer of the quasi-three-dimensional method, the diamond difference approximation is often used to deal with the neutron angular flux density. In order to ensure the calculation accuracy, the diamond difference approximation requires that the layer height of the transport layer of the quasi-three-dimensional method cannot be too high, resulting in a very large number of layers for direct solution of the entire core using the quasi-three-dimensional method, high calculation cost and low calculation efficiency, which seriously restricts the engineering application of high-fidelity numerical simulation methods.

[0004] In order to expand the height of the transport layer of the quasi-three-dimensional transport method and ensure the calculation accuracy, the second-order expansion of the axial neutron angular flux is currently often used. This method significantly increases the height of the transport layer while ensuring the calculation accuracy, but it requires coupling calculation of two two-dimensional equations in each transport layer, which increases the calculation cost. Summary of the invention

[0005] The purpose of the present invention is to provide a quasi-three-dimensional transportation method, system and medium based on a multi-layer coarse mesh improvement to solve the above-mentioned problems in the prior art.

[0006] The embodiments of the present invention are implemented by the following technical solutions:

[0007] In a first aspect, the present invention provides a quasi-three-dimensional transportation method based on a multi-layer coarse mesh improvement, comprising:

[0008] Obtaining basic information of a pressurized water reactor core to be simulated, wherein the basic information includes geometric information, material information, and boundary condition information;

[0009] According to the basic information of the pressurized water reactor core, the three-dimensional core of the pressurized water reactor is axially divided into a number of transport layers, and each transport layer is radially divided into a number of fine grids;

[0010] Then, a number of differential layers are divided axially in each transport layer, a number of coarse meshes are divided radially in each differential layer, and a coarse mesh finite difference model is established on the radial coarse meshes of the differential layer;

[0011] Diamond differencing is adopted to assume that the radial fine-grid neutron angular flux density varies linearly in each difference layer;

[0012] According to the coarse-mesh finite difference model, the neutron mark flux density at each coarse-mesh center point and the net neutron flow at the axial interface are obtained. Among them, the product of the neutron mark flux density at the center point of the coarse-mesh and the center plane is taken as the surface neutron mark flux density at the center plane of the difference layer; the net neutron flow at the axial interface is taken as the surface neutron mark flux density at the axial interface of the coarse-mesh. Taking the ratio of the surface neutron mark flux density at the center plane and the interface of each difference layer as the coefficient, according to the neutron angular flux density on the center plane of the transport layer, the fine-mesh neutron angular flux density on the center plane of the difference layer and the interface in the next iteration step is updated;

[0013] A new quasi-three-dimensional transport model is established on each fine mesh of the transport layer, which is related to the fine mesh neutron angular flux density on the center plane and interface of the differential layer.

[0014] Solve the new quasi-three-dimensional transport model, obtain the fine-grid neutron angular flux density on the central plane of the transport layer, calculate the fine-grid neutron standard flux density, and output the neutron angular flux density and neutron standard flux density.

[0015] Preferably, the establishing of the coarse-grid finite difference model comprises:

[0016]

[0017]

[0018] Where n is the coarse mesh number, ix is ​​the number of the coarse mesh along the x-axis, iy is the number of the coarse mesh along the y-axis, iz is the number of the coarse mesh along the z-axis, u is the direction of the coordinate axis, x, y, z are three coordinate directions, g is the neutron energy group number, G is the total number of neutron energy groups, l is the number of external iterations of the transport calculation, is the eigenvalue of the l+1th iteration step, Σ t,n,g is the total neutron cross section of the nth coarse grid of the gth group of the three-dimensional core of the pressurized water reactor, and t is the symbol of the total neutron cross section; Σ s,n,g′→g is the neutron scattering cross section of the nth coarse mesh from the g′th group to the gth group in the three-dimensional core of a pressurized water reactor, s is the neutron scattering cross section, Σ f,n,g′ is the neutron fission cross section of the g′th group and the nth coarse grid of the three-dimensional core of the pressurized water reactor, f is the neutron fission cross section, v is the average number of neutrons per fission; χg is the ratio of the number of neutrons in the gth fission group to the total number of fission neutrons; is the coarse-grid neutron flux density provided by transport calculations for the nth coarse-grid, g′th group, and the l+1 / 2th outer iteration; is the coarse-grid neutron flux density of the nth coarse-grid in the l+1th outer iteration, the gth group, and the nth coarse-grid, is the coarse-grid neutron flux density of the n-1th coarse-grid in the l+1th outer iteration, the gth group; is the coarse-grid neutron flux density of the n+1th coarse-grid in the l+1th outer iteration, the gth group, Δ n,u is the nth coarse mesh, the coarse mesh size along the u axis; is the diffusion coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the positive direction of the u-axis; is the diffusion coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the negative direction of the u-axis; is the neutron flux correction coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the positive direction of the u axis; is the neutron flux correction coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the negative direction of the u-axis.

[0019] Preferably, the method of using diamond difference to assume that the fine mesh neutron angular flux density varies linearly in each difference layer comprises:

[0020]

[0021] Where i is the number of the fine mesh along the x-axis, j is the number of the fine mesh along the y-axis, k is the number of the fine mesh along the z-axis, ik is the number of the difference layers in the transport layer from bottom to top, nz is the total number of difference layers in the transport layer, p is the angle number of the neutron angular flux density, and m is the number of inner iterations of the transport calculation; is the neutron angular flux density along direction p of the ikth differential layer center in the ith x-axis direction and the jth y-axis direction in the kth transport layer of the three-dimensional core of the pressurized water reactor in the l+1 / 2th outer iteration and the mth inner iteration; is the neutron angular flux density along direction p at the bottom of the ikth differential layer in the ith fine mesh in the x-axis direction and the jth fine mesh in the y-axis direction in the kth transport layer, the l+1 / 2th outer iteration, the mth inner iteration of the three-dimensional core of the pressurized water reactor; It is the l+1 / 2th outer iteration and the mth inner iteration of the three-dimensional core of a pressurized water reactor. It is the neutron angular flux density along direction p on the top surface of the ikth difference layer in the ith fine grid in the x-axis direction and the jth fine grid in the y-axis direction in the kth transport layer.

[0022] Preferably, the step of obtaining the surface neutron mark flux density of the center plane and the interface of each differential layer, and updating the neutron angular flux density of the center plane and the interface of the fine mesh radially located in the coarse mesh in the next iteration step by using the surface neutron mark flux density ratio as a coefficient comprises:

[0023]

[0024] In the formula, is the sub-scalar flux density of the coarse mesh at the interface between the ixth coarse mesh in the x direction and the y direction of the ikth difference layer in the kth transport layer, in the gth group, in the lth outer iteration; is the coarse-grid neutron flux density of the g-th group in the l-th outer iteration, located at the center plane of the ix-th coarse-grid in the x-direction and the y-direction of the ik-th difference layer in the k-th transport layer; is the coarse-grid neutron flux density of the ixth coarse-grid in the x-direction and the iyth coarse-grid in the y-direction at the center plane of the kth transport layer in the lth outer iteration, the gth group; is the neutron angular flux density at the interface of the ikth difference layer in the ith x-direction and the jth y-direction fine mesh in the kth transport layer, the mth inner iteration, the gth group, and the l+1 / 2th outer iteration; It is the neutron angular flux density of the center plane of the ikth difference layer in the i-th fine mesh in the x-direction and the j-th fine mesh in the y-direction in the k-th transport layer, the m-th inner iteration, the g-th group, and the l+1 / 2-th outer iteration, the m-th inner iteration.

[0025] Preferably, the establishment of a new quasi-three-dimensional transport model related to the neutron angular flux density at the coarse mesh center plane and the interface includes a new quasi-three-dimensional transport equation scanning from bottom to top, a new quasi-three-dimensional transport equation scanning from top to bottom, and half of the total number of difference layers in the transport layer.

[0026] Preferably, the new quasi-three-dimensional transport equation scanning from bottom to top includes:

[0027]

[0028] The new quasi-3D transport equations for scanning from top to bottom include:

[0029]

[0030] In the formula, μ p is the cosine of the angle between direction p and the positive direction of the x-axis, η p is the cosine value of the angle between direction p and the positive direction of the y-axis; ξ p is the cosine of the angle between direction p and the positive direction of the z axis, z k is the thickness of the kth transport layer in the positive direction of the z axis; Σ t,i,j,k,g is the total neutron cross section of the g-th group of the i-th, j-th, and k-th fine meshes in the three-dimensional core of the pressurized water reactor, and t is the symbol of the total neutron cross section; Σ s,i,j,k,g′→gis the neutron scattering cross section from the g′th group to the gth group in the i-th, j-th, and k-th fine meshes in the x-axis direction, the y-axis direction, and the z-axis direction of the three-dimensional core of the pressurized water reactor, s is the symbol of the neutron scattering cross section; Σ f,i,j,k,g is the neutron fission cross section of the g-th group of the i-th, j-th, and k-th fine meshes in the three-dimensional core of a pressurized water reactor, and f is the symbol of the neutron fission cross section; is the eigenvalue of the lth iteration step; is the neutron angular flux density of the g-th group of the i-th, j-th, and k-th fine meshes in the x-axis direction, the y-axis direction, and the z-axis direction in the 3D core of the PWR for the l+1 / 2-th outer iteration and the m-th inner iteration along the center plane of the direction p; is the neutron angular flux density of the gth group along direction p on the top surface of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction of the three-dimensional core of the pressurized water reactor for the l+1 / 2-th outer iteration and the m-th inner iteration; is the neutron angular flux density of the gth group along direction p at the bottom of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction of the three-dimensional core of the pressurized water reactor for the l+1 / 2-th outer iteration and the m-th inner iteration; is the neutron angular flux density of the g-th group of the i-th, j-th, and k-th fine meshes in the x-axis direction, the y-axis direction, and the z-axis direction in the three-dimensional core of the pressurized water reactor in the l+1-th outer iteration and the m-th inner iteration along the center plane of the direction p; is the neutron flux density of the g-th group located in the i-th fine grid in the x-axis direction, the j-th fine grid in the y-axis direction, and the k-th fine grid in the z-axis direction in the l-th outer iteration and the m-1-th inner iteration of the three-dimensional core of the pressurized water reactor; is the 1st outer iteration, the 0th inner iteration of the three-dimensional core of the pressurized water reactor, the gth group neutron flux density located in the i-th fine grid in the x-axis direction, the j-th fine grid in the y-axis direction, and the k-th fine grid in the z-axis direction, half_nz is half of the total number of differential layers in the transport layer, 2(-1) ik+1 is the coefficient introduced by the difference layer number in the transport layer, (-1) half_nz A coefficient introduced to account for half the total number of difference layers in the transport layer.

[0031] Preferably, half of the total number of differential layers in the transport layer comprises:

[0032]

[0033] Where nz is the total number of difference layers in the transport layer, and the parity of nz determines the different values ​​of half_nz.

[0034] Preferably, the step of calculating the neutron target flux density of the fine grid includes:

[0035]

[0036] In the formula, ω p is the weight of the neutron angular flux density in direction p, is the neutron flux density of the g-th group center plane of the i-th, j-th, and k-th fine meshes in the three-dimensional core of the pressurized water reactor in the l+1-th outer iteration and the m-th inner iteration, It is the l+1th outer iteration and the mth inner iteration of the three-dimensional core of the pressurized water reactor, and the angular neutron flux density of the gth group along the center plane of the direction p of the i-th, j-th, and k-th fine grids in the x-axis direction, the y-axis direction, and the z-axis direction.

[0037] In a second aspect, the present invention provides a quasi-three-dimensional transportation system based on a multi-layer coarse network improvement, comprising:

[0038] The partitioning module is configured to obtain basic information of the pressurized water reactor core to be simulated, wherein the basic information includes geometric information, material information and boundary condition information, and divide the three-dimensional core of the pressurized water reactor into several transport layers according to the basic information of the pressurized water reactor core, radially divide a plurality of fine meshes in each transport layer, obtain the partitioning into several transport layers, and then divide the several transport layers into several differential layers, radially divide a plurality of coarse meshes in each differential layer, and establish a coarse mesh finite difference model on the coarse mesh of the differential layer.

[0039] The flux density calculation module is configured to adopt the diamond difference assumption that the neutron angular flux density in the fine grid changes linearly in each differential layer, obtain the surface neutron standard flux density of the center plane and the interface of each differential layer according to the coarse grid finite difference model, and use the ratio of the surface neutron standard flux density of the center plane and the interface of each differential layer as a coefficient, and update the fine grid neutron angular flux density on the center plane and the interface of the differential layer in the next iteration step according to the neutron angular flux density on the center plane of the transport layer;

[0040] An output module is configured to establish a new quasi-three-dimensional transport model related to the neutron angular flux density at the center plane and interface of the coarse mesh on each fine mesh of the transport layer, solve the new quasi-three-dimensional transport model, obtain the neutron angular flux density at the center plane of the fine mesh, calculate the neutron target flux density of the fine mesh, and output the neutron angular flux density and the neutron target flux density;

[0041] The main control module is connected with the division module, the flux density calculation module and the output module, and is used to execute the above-mentioned quasi-three-dimensional transportation method based on the improvement of the multi-layer coarse network.

[0042] In a third aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the improved quasi-three-dimensional transportation method based on a multi-layer coarse mesh is implemented.

[0043] The technical solution of the embodiment of the present invention has at least the following advantages and beneficial effects:

[0044] The present invention provides a quasi-three-dimensional transport method based on a multi-layer coarse mesh improvement, which divides each transport layer into multiple difference layers, establishes a coarse mesh finite difference model in the coarse mesh of the difference layer, and uses diamond difference approximation to process the neutron angular flux density, and establishes a new quasi-three-dimensional transport model related to the neutron angular flux density of the coarse mesh center plane and interface in the fine mesh of the transport layer to obtain the neutron standard flux density in the fine mesh. Compared with the traditional method, the quasi-three-dimensional transport model based on the multi-layer coarse mesh improvement uses the difference layer to perform multiple linear approximations in the transport layer, which can significantly increase the height of the transport layer while ensuring the calculation accuracy, and only needs to calculate one two-dimensional transport equation in each transport layer, which not only saves the modeling cost but also improves the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0046] Figure 1 It is a schematic diagram of the process of the present invention;

[0047] Figure 2 This is a schematic diagram of a new quasi-three-dimensional transport model for a pressurized water reactor core according to the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0049] The modules or submodules described independently may be physically separated or not: they may be implemented by software or hardware, and some modules or submodules may be implemented by software, and the processor may call the software to implement the functions of these modules or submodules, and other modules or submodules may be implemented by hardware, such as by hardware circuits. In addition, some or all of the modules may be selected according to actual needs to achieve the purpose of the present application.

[0050] Please refer to Figure 1-Figure 2The present invention provides a quasi-three-dimensional transportation method based on a multi-layer coarse mesh improvement, comprising:

[0051] S101: acquiring basic information of a pressurized water reactor core to be simulated, wherein the basic information includes geometric information, material information, and boundary condition information;

[0052] The geometric information includes the core structure: the shape of the core, the size of the core, and the arrangement of the fuel assemblies; the fuel assembly layout: such as the number of fuel rods, the arrangement, the diameter and height of the fuel rods, and other geometric information.

[0053] Material information includes fuel materials: such as uranium dioxide (UO2) or other forms of nuclear fuel, including their physical and chemical properties (such as density, melting point, thermal conductivity, etc.); cladding materials: the properties of the material used to wrap the fuel (such as zirconium alloy), including its strength, corrosion resistance, etc.; coolant materials: such as the properties of water (temperature, pressure, chemical composition), flow characteristics, etc.; control rod materials: neutron-absorbing materials used in control rods (such as lead, bismuth, etc.) and their properties, and other material information.

[0054] Boundary condition information includes thermal boundary conditions: including heat exchange conditions between the core and the coolant, such as heat transfer coefficient, temperature boundary conditions, etc.; fluid dynamic boundary conditions: inlet and outlet conditions of coolant flow (flow rate, pressure, etc.); neutron boundary conditions: such as reflecting surface, shielding thickness and neutron scattering and absorption conditions; mechanical boundary conditions: structural fixing conditions, force action and other information.

[0055] S102: dividing the three-dimensional core of the pressurized water reactor into a plurality of transport layers according to the basic information of the pressurized water reactor core, and radially dividing a plurality of fine grids in each transport layer;

[0056] According to the geometric information such as the grid element size and component size of the three-dimensional core of the rod-shaped pressurized water reactor obtained in step S101 and the material information such as the nuclear density of the fuel and the moderator, Figure 2 In the SHARK program, the three-dimensional core of a pressurized water reactor is divided into three transport layers, and each transport layer is divided radially into multiple fine grids in a cross-shaped pattern.

[0057] S103: obtaining a plurality of transport layers, dividing the plurality of transport layers into a plurality of coarse grids, radially dividing a plurality of coarse grids in each difference layer, and establishing a coarse grid finite difference model on each coarse grid;

[0058] According to each transport layer divided in step S102, Figure 2 The grid is divided into four difference layers, and each difference layer is radially divided into several square coarse grids (one radial coarse grid contains several radial fine grids). A coarse grid finite difference model is established on each coarse grid based on the SHARK program.

[0059] Among them, the radial dimension of the coarse mesh is generally larger than that of the fine mesh.

[0060] S104: Diamond difference is used to assume that the neutron angular flux density in the fine grid varies linearly in each difference layer;

[0061] According to the axial division method in step S102 and step S103, the axial coarse mesh height is smaller than the transport fine mesh height, so the diamond difference is adopted to assume that the neutron angular flux density in the fine mesh changes linearly in each differential layer.

[0062] S105: according to the coarse-grid finite difference model, the surface neutron mark flux density of the center plane and the interface of each differential layer is obtained, and the neutron angular flux density of the radial coarse-grid center plane and the interface located in the differential layer in the next iteration step is updated by using the surface neutron mark flux density ratio as a coefficient;

[0063] S106: Establish a new quasi-three-dimensional transport model on each fine mesh of the transport layer that is related to the neutron angular flux density at the center plane and interface of the coarse mesh;

[0064] S107: Solve the new quasi-three-dimensional transport model, obtain the neutron angular flux density of the fine mesh, calculate the neutron target flux density of the fine mesh, and output the neutron angular flux density and the neutron target flux density.

[0065] The present invention divides each transport layer into multiple difference layers, adopts diamond difference approximation to process the neutron angular flux density, and uses the difference layer to perform multiple linear approximations in the transport layer. Compared with the traditional method of performing linear approximation in the transport layer, the height of the transport layer can be significantly increased while ensuring the calculation accuracy; compared with the second-order expansion method of the axial neutron angular flux in the transport layer, the linear approximation of the coupled difference layer in each transport layer only needs to calculate a two-dimensional transport equation, which not only saves modeling costs but also improves calculation efficiency, laying a foundation for the engineering application of quasi-three-dimensional methods in full-core numerical reactor simulation calculations.

[0066] In an exemplary embodiment of the present invention, establishing a coarse-grid finite difference model includes:

[0067]

[0068] Where n is the coarse mesh number, ix is ​​the number of the coarse mesh along the x-axis, iy is the number of the coarse mesh along the y-axis, iz is the number of the coarse mesh along the z-axis, u is the direction of the coordinate axis, x, y, z are three coordinate directions, g is the neutron energy group number, G is the total number of neutron energy groups, l is the number of external iterations of the transport calculation, is the eigenvalue of the l+1th iteration step, Σ t,n,g is the total neutron cross section of the nth coarse grid of the gth group of the three-dimensional core of the pressurized water reactor, and t is the symbol of the total neutron cross section; Σs,n,g′→g is the neutron scattering cross section of the nth coarse mesh from the g′th group to the gth group in the three-dimensional core of a pressurized water reactor, s is the neutron scattering cross section, Σ f,n,g′ is the neutron fission cross section of the g′th group and the nth coarse grid of the three-dimensional core of the pressurized water reactor, f is the neutron fission cross section, v is the average number of neutrons per fission; χg is the ratio of the number of neutrons in the gth fission group to the total number of fission neutrons; is the coarse-grid neutron flux density provided by transport calculations for the nth coarse-grid, g′th group, and the l+1 / 2th outer iteration; is the coarse-grid neutron flux density of the nth coarse-grid in the l+1th outer iteration, the gth group, and the nth coarse-grid, is the coarse-grid neutron flux density of the n-1th coarse-grid in the l+1th outer iteration, the gth group; is the coarse-grid neutron flux density of the n+1th coarse-grid in the l+1th outer iteration, the gth group, Δ n,u is the nth coarse mesh, the coarse mesh size along the u axis; is the diffusion coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the positive direction of the u-axis; is the diffusion coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the negative direction of the u-axis; is the neutron flux correction coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the positive direction of the u axis; is the neutron flux correction coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the negative direction of the u-axis.

[0069] in.

[0070]

[0071] Where D n,g,u is the coarse mesh diffusion coefficient of the g-th group, the n-th coarse mesh, along the u-axis direction, D n-1,g,u is the coarse mesh diffusion coefficient of the g-th group, the n-1th coarse mesh, along the u-axis direction, D n+1,g,u is the coarse mesh diffusion coefficient of the gth group, the n+1th coarse mesh, along the u-axis direction, is the coarse-grid neutron flux density provided by transport calculation at the interface along the positive direction of u axis in the l+1 / 2th outer iteration, the gth group, the nth coarse-grid, is the coarse-grid neutron flux density provided by transport calculation at the interface along the negative u-axis in the l+1 / 2th outer iteration, the gth group, the nth coarse-grid, and along the negative u-axis. is the coarse-grid neutron flux density provided by transport calculations for the nth coarse-grid, the gth group, and the l+1 / 2th outer iteration, is the coarse-grid neutron flux density provided by transport calculations for the l+1 / 2th outer iteration, the gth group, and the n-1th coarse-grid, is the coarse-grid neutron flux density provided by transport calculations for the l+1 / 2th outer iteration, the gth group, and the n+1th coarse-grid, Δ n-1,u is the size of the coarse mesh along the u axis of the n-1th coarse mesh, Δ n+1,u It is the (n+1)th coarse mesh, the size of the coarse mesh along the u-axis.

[0072] In an exemplary embodiment of the present invention, the diamond difference assumption that the neutron angular flux density in the fine grid changes linearly in each difference layer includes:

[0073]

[0074] Where i is the number of the fine mesh along the x-axis, j is the number of the fine mesh along the y-axis, k is the number of the fine mesh along the z-axis, ik is the number of the difference layers in the transport layer from bottom to top, nz is the total number of difference layers in the transport layer, p is the angle number of the neutron angular flux density, and m is the number of inner iterations of the transport calculation; is the neutron angular flux density along direction p of the ikth differential layer center in the ith x-axis direction and the jth y-axis direction in the kth transport layer of the three-dimensional core of the pressurized water reactor in the l+1 / 2th outer iteration and the mth inner iteration; is the neutron angular flux density along direction p at the bottom of the ikth differential layer in the ith fine mesh in the x-axis direction and the jth fine mesh in the y-axis direction in the kth transport layer, the l+1 / 2th outer iteration, the mth inner iteration of the three-dimensional core of the pressurized water reactor; It is the l+1 / 2th outer iteration and the mth inner iteration of the three-dimensional core of a pressurized water reactor. It is the neutron angular flux density along direction p on the top surface of the ikth difference layer in the ith fine grid in the x-axis direction and the jth fine grid in the y-axis direction in the kth transport layer.

[0075] In an exemplary embodiment of the present invention, the process of obtaining the surface neutron mark flux density of the center plane and the interface of each differential layer, and updating the neutron angular flux density of the center plane and the interface of the fine mesh radially located in the coarse mesh in the next iteration step by using the surface neutron mark flux density ratio as a coefficient comprises:

[0076]

[0077]

[0078] In the formula, is the sub-scalar flux density of the coarse mesh at the interface between the ixth coarse mesh in the x direction and the y direction of the ikth difference layer in the kth transport layer, in the gth group, in the lth outer iteration; is the coarse-grid neutron flux density of the g-th group in the l-th outer iteration, located at the center plane of the ix-th coarse-grid in the x-direction and the y-direction of the ik-th difference layer in the k-th transport layer; is the coarse-grid neutron flux density of the ixth coarse-grid in the x-direction and the iyth coarse-grid in the y-direction at the center plane of the kth transport layer in the lth outer iteration, the gth group; is the neutron angular flux density at the interface of the ikth difference layer in the i-th fine mesh in the x-direction and the j-th fine mesh in the y-direction in the k-th transport layer, the m-th inner iteration, the g-th group, and the l+1 / 2-th outer iteration, the m-th inner iteration; It is the neutron angular flux density of the center plane of the ikth difference layer in the i-th fine mesh in the x-direction and the j-th fine mesh in the y-direction in the k-th transport layer, the m-th inner iteration, the g-th group, and the l+1 / 2-th outer iteration, the m-th inner iteration.

[0079] An exemplary embodiment of the present invention establishes a new quasi-three-dimensional transport model related to the neutron angular flux density at the center plane and interface of the coarse mesh, including a new quasi-three-dimensional transport equation scanning from bottom to top and a new quasi-three-dimensional transport equation scanning from top to bottom.

[0080] In an exemplary embodiment of the present invention, the quasi-three-dimensional transport equation includes:

[0081] New quasi-3D transport equation for bottom-to-top scanning:

[0082]

[0083] The new quasi-3D transport equation scanning from top to bottom:

[0084]

[0085] In the formula, μ p is the cosine of the angle between direction p and the positive direction of the x-axis, η p is the cosine value of the angle between direction p and the positive direction of the y-axis; ξ p is the cosine of the angle between direction p and the positive direction of the z axis, z k is the thickness of the kth transport layer in the positive direction of the z axis; Σ t,i,j,k,g is the total neutron cross section of the g-th group of the i-th, j-th, and k-th fine meshes in the three-dimensional core of the pressurized water reactor, and t is the symbol of the total neutron cross section; Σ s,i,j,k,g′→g is the neutron scattering cross section from the g′th group to the gth group in the i-th, j-th, and k-th fine meshes in the x-axis direction, the y-axis direction, and the z-axis direction of the three-dimensional core of the pressurized water reactor, s is the symbol of the neutron scattering cross section; Σ f,i,j,k,g is the neutron fission cross section of the g-th group of the i-th, j-th, and k-th fine meshes in the three-dimensional core of a pressurized water reactor, and f is the symbol of the neutron fission cross section; is the eigenvalue of the lth iteration step; is the neutron angular flux density of the g-th group along direction p of the i-th, j-th, and k-th fine meshes in the x-axis direction, the y-axis direction, and the z-axis direction in the 1+1 / 2-th outer iteration and the m-th inner iteration of the three-dimensional core of the pressurized water reactor; is the neutron angular flux density of the gth group along direction p on the top surface of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction of the three-dimensional core of the pressurized water reactor for the l+1 / 2-th outer iteration and the m-th inner iteration; is the neutron angular flux density of the gth group along direction p at the bottom of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction of the three-dimensional core of the pressurized water reactor for the l+1 / 2-th outer iteration and the m-th inner iteration; is the neutron flux density of the g-th group located in the i-th fine grid in the x-axis direction, the j-th fine grid in the y-axis direction, and the k-th fine grid in the z-axis direction in the l-th outer iteration and the m-1-th inner iteration of the three-dimensional core of the pressurized water reactor; is the 1st outer iteration, the 0th inner iteration of the three-dimensional core of the pressurized water reactor, the gth group neutron flux density located in the i-th fine grid in the x-axis direction, the j-th fine grid in the y-axis direction, and the k-th fine grid in the z-axis direction, half_nz is half of the total number of differential layers in the transport layer, 2(-1) ik+1 is the coefficient introduced by the difference layer number in the transport layer, (-1) half_nz A coefficient introduced to account for half the total number of difference layers in the transport layer.

[0086] In an exemplary embodiment of the present invention, half of the total number of differential layers in the transport layer comprises:

[0087]

[0088] Where, the total number of difference layers in the transport layer and the parity of nz determine the different values ​​of half_nz.

[0089] In an exemplary embodiment of the present invention, the calculation of the neutron target flux density of the fine grid includes:

[0090]

[0091] In the formula, ω p is the weight of the neutron angular flux density in direction p, is the neutron flux density of the g-th group center plane of the i-th, j-th, and k-th fine meshes in the three-dimensional core of the pressurized water reactor in the l+1-th outer iteration and the m-th inner iteration, It is the l+1th outer iteration and the mth inner iteration of the three-dimensional core of the pressurized water reactor, and the angular neutron flux density of the gth group along the center plane of the direction p of the i-th, j-th, and k-th fine grids in the x-axis direction, the y-axis direction, and the z-axis direction.

[0092] The key points are the diamond difference assumption in each differential layer in step S104, which assumes that the neutron angular flux density changes linearly in each differential layer; and the calculation model of the surface neutron flux density of the central plane and interface of the differential layer in step S105; and based on this, a new quasi-3D transport model for correcting the neutron angular flux density of the coarse mesh central plane and interface in the differential layer in step S106 is established on each transport layer. The method of the present invention can expand the axial height of the quasi-3D transport calculation, reduce the number of modeling layers of the quasi-3D transport calculation, save memory, improve calculation efficiency, and can be used for numerical reactor simulation calculations and engineering applications of pressurized water reactors.

[0093] In a second aspect, the present invention further provides a quasi-three-dimensional transportation system based on a multi-layer coarse network improvement, comprising:

[0094] The partitioning module is configured to obtain basic information of the pressurized water reactor core to be simulated, wherein the basic information includes geometric information, material information and boundary condition information, and divide the three-dimensional pressurized water reactor core into a number of transport layers according to the basic information of the pressurized water reactor core, radially divide a plurality of fine meshes in each transport layer, obtain the divided transport layers, and then divide the transport layers into a number of coarse meshes, radially divide a number of coarse meshes in each differential layer, and establish a coarse mesh finite difference model on the coarse mesh of the differential layer.

[0095] The flux density calculation module is configured to adopt the diamond difference assumption that the neutron angular flux density in the fine mesh changes linearly in each differential layer, obtain the surface neutron standard flux density of the center plane and the interface of each differential layer according to the coarse mesh finite difference model, and use the ratio of the surface neutron standard flux density of the center plane and the interface of each differential layer as a coefficient, and update the fine mesh neutron angular flux density on the center plane of the differential layer and the interface in the next iteration step according to the neutron angular flux density on the center plane of the transport layer. The output module is configured to establish a new quasi-three-dimensional transport model related to the neutron angular flux density of the center plane and the interface of the coarse mesh on each fine mesh of the transport layer, solve the new quasi-three-dimensional transport model, obtain the neutron angular flux density of the fine mesh, calculate the neutron standard flux density of the fine mesh, and output the neutron angular flux density and the neutron standard flux density;

[0096] The main control module is connected with the division module, the flux density calculation module and the output module, and is used to execute the above-mentioned quasi-three-dimensional transportation method based on the improvement of the multi-layer coarse network.

[0097] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0098] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. The computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods of various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0099] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A quasi-three-dimensional transportation method based on a multi-layer coarse net improvement, characterized in that: include: Obtaining basic information of the pressurized water reactor core to be simulated, and dividing the three-dimensional pressurized water reactor core axially into a number of transport layers according to the basic information of the pressurized water reactor core; Divide each transport layer into multiple fine meshes radially, divide each transport layer into multiple differential layers axially, divide each differential layer into multiple coarse meshes radially, and establish a coarse mesh finite difference model on the radial coarse mesh of the differential layer; Diamond differencing is adopted to assume that the radial fine-grid neutron angular flux density varies linearly in each difference layer; According to the coarse-grid finite difference model, the neutron flux density at each coarse-grid center point and the neutron net flow at the axial interface are obtained; The product of the neutron mark flux density at the center point of the coarse mesh and the center plane is used as the surface neutron mark flux density of the center plane of the differential layer, and the net neutron flow at the axial interface is used as the surface neutron mark flux density of the axial interface of the coarse mesh; Taking the ratio of the neutron standard flux density between the center plane and the interface of each differential layer as a coefficient, the fine mesh neutron angular flux density on the center plane of the transport layer is updated in the next iteration step according to the neutron angular flux density; A new quasi-three-dimensional transport model is established on each fine mesh of the transport layer, which is related to the fine mesh neutron angular flux density on the center plane and interface of the differential layer. Solve the new quasi-three-dimensional transport model, obtain the fine-grid neutron angular flux density on the central plane of the transport layer, calculate the fine-grid neutron standard flux density, and output the neutron angular flux density and neutron standard flux density.

2. According to claim 1, a quasi-three-dimensional transportation method based on multi-layer coarse net improvement is characterized in that: The establishment of the coarse-grid finite difference model comprises: Where n is the coarse mesh number, ix is ​​the number of the coarse mesh along the x-axis, iy is the number of the coarse mesh along the y-axis, iz is the number of the coarse mesh along the z-axis, u is the direction of the coordinate axis, x, y, z are three coordinate directions, g is the neutron energy group number, G is the total number of neutron energy groups, l is the number of external iterations of the transport calculation, is the eigenvalue of the l+1th iteration step, Σ t,n,g is the total neutron cross section of the nth coarse grid of the gth group of the three-dimensional core of the pressurized water reactor, and t is the symbol of the total neutron cross section; Σ s,n,g′→g is the neutron scattering cross section of the nth coarse mesh from the g′th group to the gth group in the three-dimensional core of a pressurized water reactor, s is the neutron scattering cross section, Σ f,n,g′ is the neutron fission cross section of the g′th group and the nth coarse grid of the three-dimensional core of the pressurized water reactor, f is the neutron fission cross section, v is the average number of neutrons per fission; χg is the ratio of the number of neutrons in the gth fission group to the total number of fission neutrons; is the coarse-grid neutron flux density provided by transport calculations for the nth coarse-grid, g′th group, and the l+1 / 2th outer iteration; is the coarse-grid neutron flux density of the nth coarse-grid in the l+1th outer iteration, the gth group, and the nth coarse-grid, is the coarse-grid neutron flux density of the n-1th coarse-grid in the l+1th outer iteration, the gth group; is the coarse-grid neutron flux density of the n+1th coarse-grid in the l+1th outer iteration, the gth group, Δ n,u is the nth coarse mesh, the coarse mesh size along the u-axis; is the diffusion coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the positive direction of the u-axis; is the diffusion coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the negative direction of the u-axis; is the neutron flux correction coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the positive direction of the u axis; is the neutron flux correction coefficient of the coarse mesh interface of the g-th group, the n-th coarse mesh, along the negative direction of the u-axis.

3. A quasi-three-dimensional transportation method based on multi-layer coarse net improvement according to claim 2, characterized in that: The diamond difference assumption that the fine mesh neutron angular flux density changes linearly in each difference layer includes: Where i is the number of the fine mesh along the x-axis, j is the number of the fine mesh along the y-axis, k is the number of the fine mesh along the z-axis, ik is the number of the difference layers in the transport layer from bottom to top, nz is the total number of difference layers in the transport layer, p is the angle number of the neutron angular flux density, and m is the number of inner iterations of the transport calculation; is the neutron angular flux density along direction p of the ikth differential layer center in the ith x-axis direction and the jth y-axis direction in the kth transport layer of the three-dimensional core of the pressurized water reactor in the l+1 / 2th outer iteration and the mth inner iteration; is the neutron angular flux density along direction p at the bottom of the ikth differential layer in the ith fine mesh in the x-axis direction and the jth fine mesh in the y-axis direction in the kth transport layer of the three-dimensional core of the pressurized water reactor at the l+1 / 2th external iteration and the mth internal iteration; It is the l+1 / 2th outer iteration and the mth inner iteration of the three-dimensional core of a pressurized water reactor. It is the neutron angular flux density along direction p on the top surface of the ikth difference layer in the ith fine grid in the x-axis direction and the jth fine grid in the y-axis direction in the kth transport layer.

4. The quasi-three-dimensional transportation method based on multi-layer coarse net improvement according to claim 3 is characterized in that: The updating of the fine mesh neutron angular flux density on the differential layered center plane and the interface in the next iteration step includes: In the formula, is the sub-scalar flux density of the coarse mesh at the interface between the ixth coarse mesh in the x direction and the y direction of the ikth difference layer in the kth transport layer, in the gth group, in the lth outer iteration; is the coarse-grid neutron flux density of the g-th group in the l-th outer iteration, located at the center plane of the ix-th coarse-grid in the x-direction and the y-direction of the ik-th difference layer in the k-th transport layer; is the coarse-grid neutron flux density of the ixth coarse-grid in the x-direction and the iyth coarse-grid in the y-direction at the center plane of the kth transport layer in the lth outer iteration, the gth group; is the neutron angular flux density at the interface of the ikth difference layer in the ith x-direction and the jth y-direction fine mesh in the kth transport layer, the mth inner iteration, the gth group, and the l+1 / 2th outer iteration; is the neutron angular flux density of the center plane of the ikth difference layer in the ith x-direction and the jth y-direction fine mesh in the kth transport layer, the mth inner iteration, the gth group, and the l+1 / 2th outer iteration, the mth inner iteration, It is the neutron angular flux density of the gth group along the direction p at the center plane of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction for the l-th outer iteration and the m-th inner iteration of the core.

5. The quasi-three-dimensional transportation method based on multi-layer coarse net improvement according to claim 4 is characterized in that: The new quasi-3D transport model includes: New quasi-3D transport equations scanning from bottom to top. New quasi-3D transport equations scanning from top to bottom.

6. The improved quasi-three-dimensional transportation method based on multi-layer coarse mesh according to claim 5, characterized in that: The new quasi-3D transport equations for scanning from bottom to top include: The new quasi-3D transport equations for scanning from top to bottom include: In the formula, μ p is the cosine of the angle between direction p and the positive direction of the x-axis, η p is the cosine value of the angle between direction p and the positive direction of the y-axis; ξ p is the cosine of the angle between direction p and the positive direction of the z axis, z k is the thickness of the kth transport layer in the positive direction of the z axis; Σ t,i,j,k,g is the total neutron cross section of the g-th group of the i-th, j-th, and k-th fine meshes in the three-dimensional core of the pressurized water reactor, and t is the symbol of the total neutron cross section; Σ s,i,j,k,g′→g is the neutron scattering cross section from the g′th group to the gth group in the i-th, j-th, and k-th fine meshes in the x-axis direction, the y-axis direction, and the z-axis direction of the three-dimensional core of the pressurized water reactor, s is the symbol of the neutron scattering cross section; Σ f,i,j,k,g is the neutron fission cross section of the g-th group of the i-th, j-th, and k-th fine meshes in the three-dimensional core of a pressurized water reactor, and f is the symbol of the neutron fission cross section; is the eigenvalue of the lth iteration step; is the neutron angular flux density of the g-th group of the i-th, j-th, and k-th fine meshes in the x-axis direction, the y-axis direction, and the z-axis direction in the 3D core of the PWR for the l+1 / 2-th outer iteration and the m-th inner iteration along the center plane of the direction p; is the neutron angular flux density of the gth group along direction p on the top surface of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction of the three-dimensional core of the pressurized water reactor for the l+1 / 2-th outer iteration and the m-th inner iteration; is the neutron angular flux density of the gth group along direction p at the bottom of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction for the l+1 / 2-th outer iteration and the m-th inner iteration of the three-dimensional core of the pressurized water reactor; is the neutron angular flux density of the g-th group along direction p in the center plane of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction for the l+1-th outer iteration and the m-th inner iteration of the three-dimensional core of the pressurized water reactor, is the neutron angular flux density of the gth group along direction p in the center plane of the i-th fine mesh in the x-axis direction, the j-th fine mesh in the y-axis direction, and the k-th fine mesh in the z-axis direction for the l+1 / 2-th outer iteration and the m-th inner iteration of the core, is the neutron flux density of the g-th group located in the i-th fine grid in the x-axis direction, the j-th fine grid in the y-axis direction, and the k-th fine grid in the z-axis direction in the l-th outer iteration and the m-1-th inner iteration of the three-dimensional core of the pressurized water reactor; is the 1st outer iteration, the 0th inner iteration of the three-dimensional core of the pressurized water reactor, the gth group neutron flux density located in the i-th, j-th, and k-th fine grids in the x-axis direction, the y-axis direction, and the z-axis direction, half_nz is half of the total number of differential layers in the transport layer, 2(-1) ik+1 is the coefficient introduced by the difference layer number in the transport layer, (-1) half_nz A coefficient introduced to account for half the total number of difference layers in the transport layer.

7. The improved quasi-three-dimensional transportation method based on multi-layer coarse mesh according to claim 6 is characterized in that: Half of the total number of differential layers in the transport layer includes: Where nz is the total number of difference layers in the transport layer, and the parity of nz determines the different values ​​of half_nz.

8. The quasi-three-dimensional transportation method based on multi-layer coarse net improvement according to claim 7 is characterized in that: The calculation of the neutron flux density of the fine grid includes: In the formula, ω p is the weight of the neutron angular flux density in direction p, is the neutron flux density of the g-th group of the i-th, j-th, and k-th fine grids in the x-axis direction, the y-axis direction, and the z-axis direction in the l+1-th outer iteration and the m-th inner iteration of the three-dimensional core of the pressurized water reactor, It is the neutron angular flux density of the g-th group along direction p of the i-th, j-th, and k-th fine meshes in the x-axis direction, the y-axis direction, and the z-axis direction for the l+1-th outer iteration and the m-th inner iteration of the three-dimensional core of a pressurized water reactor.

9. A quasi-three-dimensional transportation system based on a multi-layer coarse network improvement, characterized in that: include: The partitioning module is configured to obtain basic information of the pressurized water reactor core to be simulated, wherein the basic information includes geometric information, material information and boundary condition information, and divide the three-dimensional core of the pressurized water reactor into a number of transport layers according to the basic information of the pressurized water reactor core, radially divide a plurality of fine meshes in each transport layer, obtain the divided transport layers, and then divide the transport layers into a number of differential layers, radially divide a number of coarse meshes in each differential layer, and establish a coarse mesh finite difference model on the coarse mesh of the differential layer. The flux density calculation module is configured to adopt a diamond difference assumption that the neutron angular flux density in the fine grid changes linearly in each differential layer, obtain the surface neutron mark flux density of the center plane and the interface of each differential layer according to the coarse grid finite difference model, and use the ratio of the surface neutron mark flux density of the center plane and the interface of each differential layer as a coefficient, and update the fine grid neutron angular flux density on the center plane and the interface of the differential layer in the next iteration step according to the neutron angular flux density on the center plane of the transport layer; An output module is configured to establish a new quasi-three-dimensional transport model related to the neutron angular flux density at the center plane and interface of the coarse mesh on each fine mesh of the transport layer, solve the new quasi-three-dimensional transport model, obtain the neutron angular flux density at the center plane of the fine mesh, calculate the neutron target flux density of the fine mesh, and output the neutron angular flux density and the neutron target flux density; The main control module is connected to the division module, the flux density calculation module and the output module, and is used to execute the quasi-three-dimensional transportation method based on the multi-layer coarse network improvement as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the computer program implements a quasi-three-dimensional transportation method based on a multi-layer coarse mesh improvement as claimed in any one of claims 1 to 8.

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