A method for calculating steady-state neutron diffusion in a hexagonal assembly pressurized water reactor core
By combining the coarse mesh finite difference method, the nodal expansion method, and conformal transformation technology, the accuracy and efficiency problems of neutron diffusion calculation in the core of a hexagonal component pressurized water reactor were solved, achieving high-precision and high-efficiency calculation results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- XI AN JIAOTONG UNIV
- Filing Date
- 2023-03-29
- Publication Date
- 2026-05-12
AI Technical Summary
Existing technologies cannot simultaneously guarantee the accuracy and efficiency of neutron diffusion calculations in hexagonal component pressurized water reactor cores, leading to difficulties in engineering applications.
A nonlinear iterative strategy combining the coarse mesh finite difference method and the nodal expansion method is adopted. Hexagonal nodal blocks are converted into rectangular nodal blocks by conformal transformation. The computation process is optimized by combining the BICGSTAB algorithm and the Wielandt iterative method.
High-precision and high-efficiency neutron diffusion calculations were achieved for the core of a hexagonal pressurized water reactor, meeting the needs of engineering applications.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of physical calculations of pressurized water reactor cores, specifically to a method for calculating steady-state neutron diffusion in a hexagonal pressurized water reactor core. Background Technology
[0002] With the introduction of VVER-type hexagonal module commercial pressurized water reactors and the development of other advanced hexagonal module small modular reactors, the demand for hexagonal module core calculation software that can meet the needs of engineering applications is increasing. Among these, accurate and efficient core neutron diffusion calculations are of great significance for the operation of commercial pressurized water reactors and the research and development of new technologies.
[0003] The core of reactor core physics calculations lies in solving the three-dimensional neutron diffusion equations to obtain the effective multiplication factor and power distribution under steady-state or transient conditions. The nodal method is widely used for solving the diffusion equations due to its good performance. This method divides the reactor core axially into layers and radially into a grid of component-sized nodes. A high-order expansion of the neutron flux density within each node is then performed to obtain an accurate solution. The nodal method typically employs transverse integration to decompose the three-dimensional neutron diffusion equations into multiple one-dimensional equations in different directions for solution. This technique has proven to have suitable accuracy and efficiency. However, when applying transverse integration to hexagonal nodes, the hypotenuses of the hexagons lead to extremely complex equations and the appearance of non-physical singularities, causing the solution process to stall.
[0004] To address the aforementioned issues, one class of methods modifies the transverse integral neutron diffusion equation and introduces approximations. These methods maintain the efficiency of transverse integration, but their computational accuracy is relatively low. Another class of methods does not employ transverse integration techniques, instead directly solving the three-dimensional neutron diffusion equation. These methods circumvent physically singular terms and achieve higher computational accuracy; however, due to their higher computational complexity, their efficiency is generally lower.
[0005] It is difficult to simultaneously guarantee the accuracy and efficiency of neutron diffusion calculations using the hexagonal core block method in pressurized water reactors, which poses certain challenges to the engineering application of hexagonal core neutron diffusion programs. Summary of the Invention
[0006] In order to overcome the problems existing in the prior art, the purpose of this invention is to provide a method for calculating steady-state neutron diffusion in the core of a hexagonal pressurized water reactor. This method has high accuracy and efficiency, thereby meeting the engineering application requirements of neutron diffusion procedures in hexagonal reactor cores.
[0007] To achieve the above objectives, the present invention adopts the following technical solution:
[0008] A method for calculating steady-state neutron diffusion in a hexagonal pressurized water reactor core employs a nonlinear iterative strategy combining the coarse-grid finite difference method and the nodal expansion method. It applies conformal mapping to the hexagonal nodal expansion method, enabling accurate and efficient steady-state neutron diffusion calculations. The main steps include:
[0009] Step 1: Complete the core modeling based on the geometric and material information of the hexagonal component core. Each hexagonal component in the core represents a hexagonal node. Calculate the node coupling factor based on the material information of each hexagonal node, as shown in formula (1).
[0010]
[0011] In the formula:
[0012] k — represents the block number index;
[0013] g — indicates the energy group number index;
[0014] —The nodal coupling factor on the surface of the g-th energy group in the positive x direction of the k-th nodal;
[0015] —The diffusion coefficient of the g-th energy group in the k-th block;
[0016] —The diffusion coefficient of the g-th energy group in the (k+1)-th block;
[0017] —Discontinuity factor on the surface of the g-th energy group in the positive x direction of the k-th block;
[0018] —Discontinuity factor on the surface of the g-th energy group in the negative x direction of the k+1th block;
[0019] Δx k —The intercept of the k-th block;
[0020] Δx k+1 —The intercept of the (k+1)th block;
[0021] Step 2: If this is the first time step 2 is executed, initialize the nodal coupling correction factor; if this is not the first time step 2 is executed, update the nodal coupling correction factor according to the accurate neutron flux density in step 8 of the previous iteration, as shown in formula (2).
[0022]
[0023] In the formula:
[0024] —The nodal coupling correction factor on the surface of the g-th energy group in the positive x direction of the k-th nodal block;
[0025] —The precise neutron flux density obtained by NEM on the surface of the g-th energy group in the positive x direction of the k-th block; —The average neutron flux density of the g-th energy group in the k-th block;
[0026] —The average neutron flux density of the g-th energy group in the (k+1)-th block;
[0027] Step 3: Based on the nodal coupling factor in Step 1 and the nodal coupling correction factor in Step 2, obtain the nine coefficients of the CMFD nodal coupling equation in each hexagonal nodal. The coupling equation is shown in Formula (3).
[0028]
[0029] In the formula:
[0030] h — indicates the energy group number before scattering;
[0031] G represents the total energy group number;
[0032] — The coefficients of the k-th block in the x-direction of the g-th energy group;
[0033] — The coefficients of the k-th block in the k-th energy group u direction;
[0034] — The coefficients of the k-th block in the v direction of the g-th energy group;
[0035] — The coefficients of the k-th block in the z-direction of the g-th energy group;
[0036] — The coefficients of the g-th energy group of the k-th block;
[0037] — The coefficients of the k+1th block in the x-direction of the g-th energy group of the k-th block;
[0038] — The coefficients of the k+1th block in the direction of the g-th energy group u of the k-th block;
[0039] — The coefficients of the k+1th block in the direction of the g-th energy group of the k-th block;
[0040] — The coefficients of the k+1th block in the z direction of the g-th energy group of the k-th block;
[0041] —The average neutron flux density of the g-th energy group in the (k-1)-th block along the x-direction; —The average neutron flux density of the g-th energy group in the (k-1)-th block along the u direction; —The average neutron flux density of the g-th energy group in the (k-1)-th block along the v direction; —The average neutron flux density of the g-th energy group in the (k-1)-th block along the z-direction; —The average neutron flux density of the g-th energy group in the (k+1)-th block along the x-direction; —The average neutron flux density of the g-th energy group in the (k+1)-th block along the u direction; —The average neutron flux density of the g-th energy group in the (k+1)-th block along the v direction; —The average neutron flux density of the g-th energy group in the (k+1)-th block along the z-direction; —The exit section of the g-th energy group of the k-th block;
[0042] —The scattering cross section from the h-th energy group to the g-th energy group in the k-th block;
[0043] —The product of the fission fraction of the h-th energy group in the k-th block and the fission cross section; χ g —The fission energy spectrum of the g-th energy group;
[0044] k eff —Effective multiplication coefficient;
[0045] By simultaneously establishing the coupling equations of all hexagonal nodules and all energy groups in three-dimensional space, a CMFD linear system is constructed.
[0046] Step 4: Use the BICGSTAB algorithm to solve the CMFD linear system established in Step 3 to obtain the average neutron flux density of each hexagonal block in the current iteration step; when implementing the BICGSTAB algorithm, ignore the 0 elements in the matrix to reduce the running memory and improve the computational efficiency;
[0047] Step 5: Update the fission source term and effective multiplication coefficient based on the average neutron flux density of each hexagonal nodal obtained in Step 4; the Wielandt iterative method was used in Steps 3 to 5 to accelerate the iterative convergence efficiency;
[0048] Step 6: Determine if convergence has occurred. If the difference between the fission source term and the effective multiplication coefficient and the previous step is within the convergence limit, then convergence has occurred. If convergence has occurred, proceed directly to step 9. If convergence has not occurred, implement the local block expansion method based on conformal transformation: First, construct the mapping relationship from hexagonal blocks to rectangular blocks using conformal transformation, and use this to avoid non-physical singular terms introduced by transverse integration. The transverse integral equation in the rectangular block after conformal transformation of the hexagonal block is shown in formula (4).
[0049]
[0050] In the formula:
[0051] — Lateral leakage term in the v direction of the g-th energy group of the k-th block — Lateral leakage term in the z-direction of the g-th energy group of the k-th block
[0052] Δv — Length of the rectangular section in the v direction;
[0053] Δz k — Height of the k-th rectangular segment;
[0054] —Average neutron flux density of the transverse integral along the u direction of the g-th energy group in the k-th block —Mapping area scaling function of transverse integral
[0055] The neutron flux density of each hexagonal segment surface is obtained from the calculation results of the CMFD linear system in step 4. Then, the neutron flux slope of the radial surface is estimated. The transverse leakage integral term in each moment equation is calculated. The estimation method of the neutron flux slope of the hexagonal radial surface is adopted: the average neutron flux density of each corner point is estimated by the average neutron flux density of three adjacent surfaces, and then the neutron flux slope of the radial surface is estimated by the average neutron flux density of each corner point.
[0056] Step 7: Perform transverse integration in the x, u, and v directions respectively, expand the transverse integral neutron flux density within each hexagonal block into a fourth-order polynomial, and establish moment equations between each pair of adjacent blocks; by solving the even-order expansion coefficients first and then the odd-order expansion coefficients, the solution complexity is further reduced; the transverse leakage term obtained in Step 6 is applied to the solution of the moment equations.
[0057] Step 8: Based on the expansion coefficients of the transverse integral neutron flux density within each block obtained in Step 7, the accurate neutron flux density on each surface is obtained and used to update the block coupling correction factor in Step 2, thereby obtaining a more accurate result in the next iteration step.
[0058] Step 9: End the steady-state neutron diffusion calculation for the hexagonal component pressurized water reactor core.
[0059] To balance computational accuracy and efficiency, this invention employs a conformal transformation technique for nodal components, which has been refined and developed. This method conformally transforms hexagonal nodal components into rectangular nodal components, thereby avoiding physical singularities encountered during lateral integration. The conformal transformation ensures that the form of the Laplace operator remains unchanged, resulting in almost no approximations introduced by the transformation, thus guaranteeing computational accuracy. Simultaneously, the lateral integration technique ensures computational efficiency. This method has been experimentally applied to advanced pressurized water reactor core programs internationally and has demonstrated excellent results in practical applications.
[0060] Compared with the prior art, the present invention has the following advantages:
[0061] 1. A nonlinear iterative strategy combined with conformal mapping is employed for diffusion calculations of the hexagonal component core. The conformal mapping method ensures computational accuracy while maintaining the computational efficiency of lateral integration techniques, while the nonlinear iterative strategy coupling the CMFD and NEM algorithms further improves computational efficiency. The calculation process utilizes the BICGSTAB algorithm and Wielandt accelerated iteration, among other optimization algorithms, to further enhance computational efficiency. This allows the proposed algorithm to possess both high computational accuracy and efficiency, meeting the requirements of engineering applications.
[0062] 2. A novel first-order expansion method for the transverse leakage term under conformal transformation of hexagonal nodules is proposed. First, the neutron flux slope of each radial surface is estimated: the average neutron flux density at each corner point is estimated using the average neutron flux density of three adjacent surfaces, and then the neutron flux slope of the surface is estimated using the corner neutron flux density. This slope is then mapped onto the conformal-transformed rectangular nodules to obtain the integrals of the transverse leakage term in each order of the moment equations, which are used to solve the moment equations. This method significantly improves computational accuracy while maintaining accuracy even under vacuum boundary conditions without a reflector layer. Attached Figure Description
[0063] Figure 1 The calculation process for the nodal method of the nonlinear iterative strategy;
[0064] Figure 2 This is a schematic diagram of conformal transformation from a hexagonal segment to a rectangular segment;
[0065] Figure 3 The results are for the VVER-1000 reactor benchmark test. Detailed Implementation
[0066] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0067] This invention employs a nodal method based on a nonlinear iterative strategy to calculate steady-state neutron diffusion in the core of a hexagonal pressurized water reactor (PWR) to obtain the effective core multiplication factor and the average neutron flux density per nodal. The global solution is obtained using the hexagonal coarse-mesh finite difference method (CMFD); a local two-nodal solution is then performed using the nodal expansion method (NEM) based on conformal mapping to obtain an accurate neutron flux density and correct the global solution result. Specific steps are as follows: Figure 1 As shown.
[0068] Step 1: Complete the core modeling based on the geometric and material information of the hexagonal component core. Each hexagonal component in the core represents a hexagonal node. Calculate the node coupling factor based on the material information of each hexagonal node, as shown in formula (1).
[0069]
[0070] In the formula:
[0071] k — represents the block number index;
[0072] g — indicates the energy group number index;
[0073] —The nodal coupling factor on the surface of the g-th energy group in the positive x direction of the k-th nodal;
[0074] —The diffusion coefficient of the g-th energy group in the k-th block;
[0075] —The diffusion coefficient of the g-th energy group in the (k+1)-th block;
[0076] —Discontinuity factor on the surface of the g-th energy group in the positive x direction of the k-th block;
[0077] —Discontinuity factor on the surface of the g-th energy group in the negative x direction of the k+1th block;
[0078] Δx k —The intercept of the k-th block;
[0079] Δx k+1 —The intercept of the (k+1)th block;
[0080] Step 2: If this is the first time step 2 is executed, initialize the nodal coupling correction factor; if this is not the first time step 2 is executed, update the nodal coupling correction factor according to the accurate neutron flux density in step 8 of the previous iteration, as shown in formula (2).
[0081]
[0082] In the formula:
[0083] —The nodal coupling correction factor on the surface of the g-th energy group in the positive x direction of the k-th nodal block;
[0084] —The precise neutron flux density obtained by NEM on the surface of the g-th energy group in the positive x direction of the k-th block;
[0085] —The average neutron flux density of the g-th energy group in the k-th block;
[0086] —The average neutron flux density of the g-th energy group in the (k+1)-th block;
[0087] Step 3: Based on the nodal coupling factor in Step 1 and the nodal coupling correction factor in Step 2, obtain the nine coefficients of the CMFD nodal coupling equation in each hexagonal nodal. The coupling equation is shown in Formula (3).
[0088]
[0089] In the formula:
[0090] h — indicates the energy group number before scattering;
[0091] G represents the total energy group number;
[0092] — The coefficients of the k-th block in the x-direction of the g-th energy group;
[0093] — The coefficients of the k-th block in the k-th energy group u direction;
[0094] — The coefficients of the k-th block in the v direction of the g-th energy group;
[0095] — The coefficients of the k-th block in the z-direction of the g-th energy group;
[0096] — The coefficients of the g-th energy group of the k-th block;
[0097] — The coefficients of the k+1th block in the x-direction of the g-th energy group of the k-th block;
[0098] — The coefficients of the k+1th block in the direction of the g-th energy group u of the k-th block;
[0099] — The coefficients of the k+1th block in the direction of the g-th energy group of the k-th block;
[0100] — The coefficients of the k+1th block in the z direction of the g-th energy group of the k-th block;
[0101] —The average neutron flux density of the g-th energy group in the (k-1)-th block along the x-direction;
[0102] —The average neutron flux density of the g-th energy group in the (k-1)-th block along the u direction;
[0103] —The average neutron flux density of the g-th energy group in the (k-1)-th block along the v direction;
[0104] —The average neutron flux density of the g-th energy group in the (k-1)-th block along the z-direction;
[0105] —The average neutron flux density of the g-th energy group in the (k+1)-th block along the x-direction;
[0106] —The average neutron flux density of the g-th energy group in the (k+1)-th block along the u direction;
[0107] —The average neutron flux density of the g-th energy group in the (k+1)-th block along the v direction;
[0108] —The average neutron flux density of the g-th energy group in the (k+1)-th block along the z-direction;
[0109] —The exit section of the g-th energy group of the k-th block;
[0110] —The scattering cross section from the h-th energy group to the g-th energy group in the k-th block;
[0111] —The product of the fission fraction of the h-th energy group in the k-th block and the fission cross section;
[0112] χ g —The fission energy spectrum of the g-th energy group;
[0113] k eff —Effective multiplication coefficient;
[0114] By simultaneously establishing the coupling equations of all hexagonal nodules and all energy groups in three-dimensional space, a CMFD linear system is constructed.
[0115] Step 4: Use the BICGSTAB algorithm to solve the CMFD linear system established in Step 3 to obtain the average neutron flux density of each hexagonal block in the current iteration step; when implementing the BICGSTAB algorithm, ignore the 0 elements in the matrix to reduce the running memory and improve the computational efficiency;
[0116] Step 5: Update the fission source term and effective multiplication coefficient based on the average neutron flux density of each hexagonal nodal obtained in Step 4; the Wielandt iterative method was used in Steps 3 to 5 to accelerate the iterative convergence efficiency;
[0117] Step 6: Determine if the steps converge. If the differences between the fission source term and the effective multiplication coefficient from the previous step are both within the convergence limit, then convergence is achieved. If convergence is achieved, proceed directly to step 9. If convergence is not achieved, implement the local block expansion method based on conformal transformation: such as... Figure 2 As shown, firstly, conformal transformation is used to construct the mapping relationship from hexagonal blocks to rectangular blocks, thereby avoiding non-physical singularities introduced by transverse integration; the transverse integral equation within the rectangular blocks after conformal transformation of the hexagonal blocks is shown in formula (4):
[0118]
[0119] In the formula:
[0120] — Lateral leakage term in the v direction of the g-th energy group of the k-th block — Lateral leakage term in the z-direction of the g-th energy group of the k-th block
[0121] Δv — Length of the rectangular section in the v direction;
[0122] Δz k — Height of the k-th rectangular segment;
[0123] —Average neutron flux density of the transverse integral along the u direction of the g-th energy group in the k-th block —Mapping area scaling function of transverse integral
[0124] The neutron flux density of each hexagonal segment surface is obtained from the calculation results of the CMFD linear system in step 4. Then, the neutron flux slope of the radial surface is estimated. The transverse leakage integral term in each moment equation is calculated. The estimation method of the neutron flux slope of the hexagonal radial surface is adopted: the average neutron flux density of each corner point is estimated by the average neutron flux density of three adjacent surfaces, and then the neutron flux slope of the radial surface is estimated by the average neutron flux density of each corner point.
[0125] Step 7: Perform transverse integration in the x, u, and v directions respectively, expand the transverse integral neutron flux density within each hexagonal block into a fourth-order polynomial, and establish moment equations between each pair of adjacent blocks; by solving the even-order expansion coefficients first and then the odd-order expansion coefficients, the solution complexity is further reduced; the transverse leakage term obtained in Step 6 is applied to the solution of the moment equations.
[0126] Step 8: Based on the expansion coefficients of the transverse integral neutron flux density within each block obtained in Step 7, the accurate neutron flux density on each surface is obtained and used to update the block coupling correction factor in Step 2, thereby obtaining a more accurate result in the next iteration step.
[0127] Step 9: End the steady-state neutron diffusion calculation for the hexagonal component pressurized water reactor core.
[0128] The method of this invention can accurately and efficiently perform steady-state neutron diffusion calculations on hexagonal component cores, meeting the requirements of engineering applications.
[0129] Benchmarking
[0130] Based on the above methods, a core program was developed and validated as a benchmark problem for the VVER-1000 reactor configuration, which features a 1 / 6 rotationally symmetric core arrangement. The calculation results of VioletHexP1, a hexagonal component core neutron diffusion program developed by the NECP Laboratory of Xi'an Jiaotong University based on the variable segmentation block method, were used as the reference solution. This program has been verified to have high computational accuracy. The verification results are as follows: Figure 3 As shown; among them, the error of the effective proliferation coefficient is 10.8 pcm; the error of the maximum power of the nodule is -0.72%; in On a Gold 6230 CPU@2.10GHz computing platform, the computation time for VioletHexP1 and the method of this invention is 39.91s and 0.53s, respectively. The test results demonstrate that the method of this invention possesses excellent computational accuracy and efficiency, making it suitable for engineering applications in hexagonal core processing.
Claims
1. A method for calculating steady-state neutron diffusion in the core of a hexagonal pressurized water reactor, characterized in that: A nonlinear iterative strategy combining the coarse mesh finite difference method and the nodal expansion method is adopted; the conformal transformation method is applied to the hexagonal nodal expansion method; this enables accurate and efficient steady-state neutron diffusion calculations; the main steps are as follows: Step 1: Complete the core modeling based on the geometric and material information of the hexagonal component core. Each hexagonal component in the core represents a hexagonal node. Calculate the node coupling factor based on the material information of each hexagonal node, as shown in formula (1). In the formula: k — represents the block number index; g — indicates the energy group number index; —The nodal coupling factor on the surface of the g-th energy group in the positive x direction of the k-th nodal; —The diffusion coefficient of the g-th energy group in the k-th block; —The diffusion coefficient of the g-th energy group in the (k+1)-th block; —Discontinuity factor on the surface of the g-th energy group in the positive x direction of the k-th block; —Discontinuity factor on the surface of the g-th energy group in the negative x direction of the k+1th block; Δx k —The intercept of the k-th block; Δx k+1 —The intercept of the (k+1)th block; Step 2: If this is the first time step 2 is executed, initialize the nodal coupling correction factor; if this is not the first time step 2 is executed, update the nodal coupling correction factor according to the accurate neutron flux density in step 8 of the previous iteration, as shown in formula (2). In the formula: —The nodal coupling correction factor on the surface of the g-th energy group in the positive x direction of the k-th nodal block; —The precise neutron flux density obtained by NEM on the surface of the g-th energy group in the positive x direction of the k-th block; —The average neutron flux density of the g-th energy group in the k-th block; —The average neutron flux density of the g-th energy group in the (k+1)-th block; Step 3: Based on the nodal coupling factor in Step 1 and the nodal coupling correction factor in Step 2, obtain the nine coefficients of the CMFD nodal coupling equation in each hexagonal nodal. The coupling equation is shown in Formula (3). In the formula: h — indicates the energy group number before scattering; G represents the total energy group number; — The coefficients of the k-th block in the x-direction of the g-th energy group; — The coefficients of the k-th block in the k-th energy group u direction; — The coefficients of the k-th block in the v direction of the g-th energy group; — The coefficients of the k-th block in the z-direction of the g-th energy group; — The coefficients of the g-th energy group of the k-th block; — The coefficients of the k+1th block in the x-direction of the g-th energy group of the k-th block; — The coefficients of the k+1th block in the direction of the g-th energy group u of the k-th block; — The coefficients of the k+1th block in the direction of the g-th energy group of the k-th block; — The coefficients of the k+1th block in the z direction of the g-th energy group of the k-th block; —The average neutron flux density of the g-th energy group in the (k-1)-th block along the x-direction; —The average neutron flux density of the g-th energy group in the (k-1)-th block along the u direction; —The average neutron flux density of the g-th energy group in the (k-1)-th block along the v direction; —The average neutron flux density of the g-th energy group in the (k-1)-th block along the z-direction; —The average neutron flux density of the g-th energy group in the (k+1)-th block along the x-direction; —The average neutron flux density of the g-th energy group in the (k+1)-th block along the u direction; —The average neutron flux density of the g-th energy group in the (k+1)-th block along the v direction; —The average neutron flux density of the g-th energy group in the (k+1)-th block along the z-direction; —The exit section of the g-th energy group of the k-th block; —The scattering cross section from the h-th energy group to the g-th energy group in the k-th block; —The product of the fission fraction of the h-th energy group in the k-th block and the fission cross section; χ g —The fission energy spectrum of the g-th energy group; k eff —Effective multiplication coefficient; By simultaneously establishing the coupling equations of all hexagonal nodules and all energy groups in three-dimensional space, a CMFD linear system is constructed. Step 4: Use the BICGSTAB algorithm to solve the CMFD linear system established in Step 3 to obtain the average neutron flux density of each hexagonal block in the current iteration step; when implementing the BICGSTAB algorithm, ignore the 0 elements in the matrix to reduce the running memory and improve the computational efficiency; Step 5: Update the fission source term and effective multiplication factor based on the average neutron flux density of each hexagonal nodal obtained in Step 4; Step 6: Determine if convergence has occurred. If the difference between the fission source term and the effective multiplication coefficient and the previous step is within the convergence limit, then convergence has occurred. If convergence has occurred, proceed directly to step 9. If convergence has not occurred, implement the local block expansion method based on conformal transformation: First, construct the mapping relationship from hexagonal blocks to rectangular blocks using conformal transformation, and use this to avoid non-physical singular terms introduced by transverse integration. The transverse integral equation in the rectangular block after conformal transformation of the hexagonal block is shown in formula (4). In the formula: — Lateral leakage term in the v direction of the g-th energy group of the k-th block — Lateral leakage term in the z-direction of the g-th energy group of the k-th block Δv — Length of the rectangular section in the v direction; Δz k — Height of the k-th rectangular segment; —The average neutron flux density of the transverse integral in the u direction of the g-th energy group of the k-th block; —The mapping area scaling function of the transverse integral; The neutron flux density of each hexagonal segment surface is obtained from the calculation results of the CMFD linear system in step 4. Then, the neutron flux slope of the radial surface is estimated. The transverse leakage integral term in each moment equation is calculated. The estimation method of the neutron flux slope of the hexagonal radial surface is adopted: the average neutron flux density of each corner point is estimated by the average neutron flux density of three adjacent surfaces, and then the neutron flux slope of the radial surface is estimated by the average neutron flux density of each corner point. Step 7: Perform transverse integration in the x, u, and v directions respectively, expand the transverse integral neutron flux density within each hexagonal block into a fourth-order polynomial, and establish moment equations between each pair of adjacent blocks; by solving the even-order expansion coefficients first and then the odd-order expansion coefficients, the solution complexity is further reduced; the transverse leakage term obtained in Step 6 is applied to the solution of the moment equations. Step 8: Based on the expansion coefficients of the transverse integral neutron flux density within each block obtained in Step 7, the accurate neutron flux density on each surface is obtained and used to update the block coupling correction factor in Step 2, thereby obtaining a more accurate result in the next iteration step. Step 9: End the steady-state neutron diffusion calculation for the hexagonal component pressurized water reactor core.
2. The method for calculating steady-state neutron diffusion in a hexagonal pressurized water reactor core according to claim 1, characterized in that: When implementing the local nodal expansion method based on conformal transformation, the transverse leakage adopts a first-order step expansion; the neutron flux slope of the hexagonal radial surface is estimated based on the average neutron flux density at the corner points.
3. The method for calculating steady-state neutron diffusion in a hexagonal pressurized water reactor core according to claim 1, characterized in that: The Wielandt iterative method was used in steps 3 to 5 to accelerate the iterative convergence efficiency.