CN-116340709-B - Method for calculating steady neutron diffusion of reactor core of hexagonal assembly pressurized water reactor

CN116340709BCN 116340709 BCN116340709 BCN 116340709BCN-116340709-B

Abstract

The invention discloses a steady-state neutron diffusion calculation method of a pressurized water reactor core of a hexagonal assembly, which adopts a nonlinear iteration strategy to carry out steady-state neutron diffusion calculation, wherein an effective proliferation coefficient and a node average neutron flux density are obtained through a global hexagonal node coarse net finite difference method (CMFD), the accurate neutron flux density of each surface is obtained through a local Node Expansion Method (NEM), a node coupling correction factor is updated to correct the node average neutron flux density obtained through the CMFD, and the high-order precision of a calculation result is ensured, wherein the local NEM adopts a conformal transformation method to map the hexagonal node into a rectangular node, so that non-physical singular terms caused by transverse integration are avoided, a transverse leakage term adopts first-order step approximation, and neutron flux slope is estimated through the neutron flux density. The method is suitable for the physical calculation of the reactor core of the pressurized water reactor with the hexagonal assembly, has higher calculation precision and calculation efficiency, and meets the application requirements of the pressurized water reactor engineering with the hexagonal assembly.

Inventors

YANG HAOZHE
WAN CHENGHUI
CAO LIANGZHI
WU HONGCHUN

Assignees

西安交通大学

Dates

Publication Date: 20260512
Application Date: 20230329

Claims (3)

1. A steady-state neutron diffusion calculation method for a pressurized water reactor core of a hexagonal assembly is characterized by adopting a nonlinear iteration strategy combining a coarse mesh finite difference method and a section expansion method, applying a conformal transformation method to the hexagonal section expansion method, and being capable of accurately and efficiently carrying out steady-state neutron diffusion calculation, and mainly comprising the following steps of: Step 1, completing core modeling according to the geometric information and the material information of a hexagonal assembly core, wherein each hexagonal assembly in the core represents a hexagonal joint block, and calculating a joint block coupling factor according to the material information of each hexagonal joint block, as shown in a formula (1); wherein: k-represents the segment number index; g-represents the energy group number index; -a kth segment, a g-th energy group, a segment coupling factor on the x-forward surface; -the diffusion coefficient of the kth segment, the kth energy group; -the diffusion coefficient of the kth+1st block g energy group; -a discontinuity factor on the positive surface of the kth segment, g-th energy group x; -a discontinuity factor on the negative direction surface of the kth+1th segment, g-th energy group x; Δx k —kth section block intercept; deltax k+1 -kth +1 section block intercept; Step 2, if the step 2 is executed for the first time, initializing a segment coupling correction factor, and if the step 2 is not executed for the first time, updating the segment coupling correction factor according to the accurate neutron flux density in the step 8 in the previous iteration step, as shown in a formula (2); wherein: -the kth segment, the g energy group, x, is coupled to the correction factor on the forward surface; -the accurate neutron flux density obtained by NEM on the positive surface of the kth segment, g-th energy cluster x; -average neutron flux density of the kth segment, g-th energy group; -average neutron flux density of the kth+1th segment, g-th energy group; Step 3, nine coefficients of a CMFD node block coupling equation in each hexagonal node block are obtained according to the node block coupling factor in the step 1 and the node block coupling correction factor in the step 2, wherein the coupling equation is shown in a formula (3); wherein: h-represents the scattering front energy group number; G-represents the total energy group number; -coefficients of a kth segment and a kth energy group x-direction k-1 segment; -coefficients of the kth segment and the kth energy group u-1 segment in the direction k; -coefficients of the kth segment and the kth energy group v direction k-1 segment; -coefficients of the kth segment and the kth energy group z-direction k-1 segment; -coefficients of the kth segment, the kth energy group; -coefficients of the kth block and the kth energy group x-direction k+1 blocks; -coefficients of the kth block and the kth group u direction k+1 block; -coefficients of the kth block and the kth energy group v direction k+1 block; -coefficients of the kth block and the kth energy group k+1 blocks in the z direction; -average neutron flux density of the kth-1 segment in the x-direction, the g-th energy group; -average neutron flux density of the g-th energy group of the k-1 th section in the u direction; -average neutron flux density of the g-th energy group of the k-1 th section in the v direction; -average neutron flux density of the kth-1 segment of the kth energy group in the z direction; -average neutron flux density of the (k+1) th energy group of the segments in the x direction; -average neutron flux density of the (k+1) th energy group of the (g) th section in the u direction; -average neutron flux density of the (k+1) th energy group of the segments in the v direction; -average neutron flux density of the kth+1th energy group of the segments in the z direction; -a removed section of the kth segment, g-th cluster; -a scattering cross section from the h energy group to the g energy group of the kth segment; -the product of the fission fraction of the kth energy group and the fission cross section of the kth segment; Chi g -the crack energy spectrum of the g energy group; k eff -effective proliferation coefficient; Establishing a CMFD linear system by combining the coupling equations of all hexagonal joint blocks and all energy groups in the three-dimensional space; Step 4, solving the CMFD linear system established in the step 3 by adopting BICGSTAB algorithm to obtain the average neutron flux density of each hexagonal section under the current iteration step, and ignoring 0 element in the matrix when BICGSTAB algorithm is implemented to reduce the running memory and improve the calculation efficiency; step 5, updating the fission source item and the effective proliferation coefficient according to the average neutron flux density of each hexagonal segment obtained in the step 4; Step 6, judging whether convergence is carried out, if the differences between the fission source term and the effective multiplication coefficient are within the convergence limit, converging, if convergence is carried out, directly entering into step 9, otherwise, implementing a local section expansion method based on angle-preserving transformation, namely firstly constructing a mapping relation from a hexagonal section to a rectangular section by using the angle-preserving transformation, and avoiding a non-physical singular term introduced by transverse integration, wherein a transverse integral equation in the rectangular section after the angle-preserving transformation of the hexagonal section is shown as a formula (4): wherein: -transverse leakage term in v direction of g energy group of kth segment -Kth segment kth energy group z-direction lateral leakage term Deltav-the length of the rectangular section in the v direction; Δz k -kth rectangular section height; -the average neutron flux density of the transverse integration of the kth segment in the kth energy group u direction; -a cross-integrated mapping area scale function; obtaining neutron flux density of each hexagonal joint surface through the calculation result of the CMFD linear system in the step 4, further estimating neutron flux slope of the radial surface, calculating a transverse leakage integral term in each moment equation, and adopting an estimation method of the neutron flux slope of the hexagonal radial surface to estimate average neutron flux density of each corner point through average neutron flux density of three adjacent surfaces, further estimating neutron flux slope of the radial surface through average neutron flux density of each corner point; Step 7, respectively performing transverse integration in the x, u and v directions, expanding the flux density of the transverse integration neutrons in each hexagonal section by a 4-order polynomial, and establishing a moment equation between every two adjacent sections; step 8, obtaining accurate neutron flux density on each surface according to each step of expansion coefficient of the transverse integral neutron flux density in each section obtained in the step 7, and updating the section coupling correction factor in the step 2 so as to obtain a more accurate result in the next iteration step; And 9, ending the steady-state neutron diffusion calculation of the pressurized water reactor core of the hexagonal assembly.
2. The method for calculating steady-state neutron diffusion of a pressurized water reactor core with a hexagonal assembly according to claim 1, wherein the lateral leakage adopts a first-order step expansion when a local segment expansion method based on angle-preserving transformation is implemented, and the neutron flux slope of the hexagonal radial surface is estimated according to the average neutron flux density of corner points.
3. The method for calculating steady-state neutron diffusion of a pressurized water reactor core with a hexagonal assembly according to claim 1, wherein Wielandt iteration methods are adopted in the steps 3 to 5 to accelerate iteration convergence efficiency.

Description

Method for calculating steady neutron diffusion of reactor core of hexagonal assembly pressurized water reactor Technical Field The invention relates to the field of pressurized water reactor core physical calculation, in particular to a method for calculating steady-state neutron diffusion of a pressurized water reactor core with a hexagonal assembly. Background With the introduction of VVER type hexagonal component commercial pressurized water reactors and the development of other advanced hexagonal component stacks, there is an increasing demand for hexagonal component core calculation software capable of meeting engineering application requirements. The neutron diffusion calculation of the reactor core is accurately and efficiently carried out, and the method has important significance for the operation of commercial pressurized water reactors and the research and development of new technologies. The core of the reactor core physical calculation is to obtain effective multiplication factors and power distribution under steady state or transient state by solving a reactor core three-dimensional neutron diffusion equation. The block method is widely applied to the solution of a diffusion equation because of good effects. The method axially and radially divides the reactor core into grids (segments) with the size of the assembly, and carries out high-order expansion on neutron flux density in the segments to obtain an accurate solution. The method of the section is usually to use a transverse integration technology to decompose a three-dimensional neutron diffusion equation into a plurality of one-dimensional equations in different directions for solving, and the technology is proved to have proper precision and efficiency. However, when the transverse integration technique is applied to hexagonal blocks, the hexagonal hypotenuse may result in extremely complex equation form and the occurrence of non-physical singular terms, resulting in the inability of the solution flow to continue. To solve the above problems, one class of methods modifies the neutron diffusion equation of the transverse integral and introduces approximations. This type of method maintains the efficiency of the transverse integration, but its calculation accuracy is relatively low. Another type of method does not use a transverse integration technique, and instead directly solves the three-dimensional neutron diffusion equation. The method avoids physical singular terms and has higher calculation accuracy, but the efficiency is generally lower due to higher calculation complexity. The accuracy and efficiency of neutron diffusion calculation by the hexagonal assembly pressurized water reactor core segment method are difficult to ensure simultaneously, so that a certain difficulty is brought to engineering application of a hexagonal reactor core neutron diffusion program. Disclosure of Invention In order to overcome the problems of the prior art, the invention aims to provide a method for calculating steady-state neutron diffusion of a reactor core of a hexagonal assembly pressurized water reactor, which has higher precision and efficiency, thereby meeting the engineering application of a neutron diffusion program of the hexagonal reactor core. In order to achieve the above purpose, the invention adopts the following technical scheme: A steady-state neutron diffusion calculation method of a hexagonal assembly pressurized water reactor core adopts a nonlinear iteration strategy combining a coarse mesh finite difference method and a section expansion method, applies a conformal transformation method to the hexagonal section expansion method, can accurately and efficiently perform steady-state neutron diffusion calculation, and mainly comprises the following steps: Step 1, completing core modeling according to the geometric information and the material information of a hexagonal assembly core, wherein each hexagonal assembly in the core represents a hexagonal joint block, and calculating a joint block coupling factor according to the material information of each hexagonal joint block, as shown in a formula (1); wherein: k-represents the segment number index; g-represents the energy group number index; -a kth segment, a g-th energy group, a segment coupling factor on the x-forward surface; -the diffusion coefficient of the kth segment, the kth energy group; -the diffusion coefficient of the kth+1st block g energy group; -a discontinuity factor on the positive surface of the kth segment, g-th energy group x; -a discontinuity factor on the negative direction surface of the kth+1th segment, g-th energy group x; Δx k —kth section block intercept; deltax k+1 -kth +1 section block intercept; Step 2, if the step 2 is executed for the first time, initializing a segment coupling correction factor, and if the step 2 is not executed for the first time, updating the segment coupling correction factor according to the accurate neutron flux density in the