Method for generating few-group cross sections and three-dimensional real-time simulation of pebble-bed high-temperature gas-cooled reactor

Abstract

This invention discloses a method for generating few-group cross sections and performing three-dimensional real-time simulation of a pebble bed high-temperature gas-cooled reactor. The method first calculates a non-uniform fine geometric model using the Monte Carlo method to construct a component-level multi-group homogenized cross section library. Then, core calculations are performed using a core physics analysis program, and neutron leakage and neutron flow correction iterations are executed under the target state to reconstruct the energy spectrum and generate a few-group cross section library related to burnup and core state. In the real-time simulation stage, real-time cross sections are obtained through temperature interpolation, and a three-dimensional multi-group neutron diffusion nodal expansion method based on transverse integration under cylindrical geometry is used for core steady-state calculations. For transient processes, a prediction-correction quasi-static method is coupled to solve the three-dimensional neutron spatiotemporal dynamics, obtaining the three-dimensional power distribution and evolution state in real time, achieving online high-precision simulation of the core physical characteristics. This invention effectively solves the problem of balancing accuracy and real-time computation in pebble bed reactor simulation.

Description

Technical Field

[0001] This invention relates to the field of physical calculation technology for pebble bed high-temperature gas-cooled reactors, specifically to a method for generating small group cross sections and performing three-dimensional real-time simulation of pebble bed high-temperature gas-cooled reactors. Background Technology

[0002] Due to the use of TRISO particulate fuel, pebble bed high-temperature gas-cooled reactors exhibit significant dual inhomogeneities, making it difficult for traditional deterministic methods to accurately describe their cross-sectional characteristics. Furthermore, the elongated core of a high-temperature gas-cooled reactor leads to pronounced neutron leakage effects. Traditional "offline" cross-section generation methods typically assume total internal reflection at component boundaries, neglecting the impact of spatial neutron leakage on the energy spectrum during actual core operation, thus limiting computational accuracy. Simulators used for operational support and training require response times in the millisecond range, contradicting the substantial resources required for high-precision computation.

[0003] Existing simulation methods often struggle to balance accuracy and efficiency. While the Monte Carlo method can accurately handle inhomogeneities, its computational time is too long to meet real-time requirements. Traditional deterministic core programs, although computationally fast, typically generate cross-sections based on simplified models, and this cross-section generation is disconnected from the full-scale reactor calculation. This fails to feed back full-scale leakage effects to the cross-sections, leading to "neutronics-geometry" decoupling errors that affect the accuracy of calculations for key parameters such as core power distribution and control rod value. Furthermore, the spatial variation of neutron flux caused by voids between spheres in a pebble bed reactor also needs special consideration.

[0004] Therefore, developing a physical simulation method for pebble bed-type high-temperature gas-cooled reactor cores that can meet real-time requirements while ensuring high accuracy has become a technical challenge in this field. Summary of the Invention

[0005] To overcome the problems existing in the prior art, the present invention aims to provide a method for generating few-group cross sections and performing three-dimensional real-time simulation of a pebble bed type high-temperature gas-cooled reactor. The method includes: firstly, calculating a non-uniform fine geometric model based on the Monte Carlo method to construct a component-level multi-group homogenized cross section library; then, performing core calculations using a core physics analysis program, and performing neutron leakage and neutron flow correction iterations under the target state to reconstruct the energy spectrum and generate a few-group cross section library related to burnup and core state; in the real-time simulation stage, obtaining real-time cross sections through temperature interpolation, and performing core steady-state calculations using a three-dimensional multi-group neutron diffusion nodal expansion method based on transverse integration under cylindrical geometry; for transient processes, a prediction-correction quasi-static method is coupled to solve the three-dimensional neutron spatiotemporal dynamics, obtaining the three-dimensional power distribution and evolution state in real time, and achieving online high-precision simulation of the core physical characteristics. To achieve the above objectives, the present invention adopts the following technical solution: The method for generating the few-group cross section and performing real-time 3D simulation of a pebble bed type high-temperature gas-cooled reactor includes the following steps: Step 1: Based on the continuous energy nuclear database, the Monte Carlo method is used to establish refined geometric models for fuel spheres containing randomly distributed TRISO particles, graphite spheres using a meta-component model, and fan-shaped reflector models containing control rods and absorption sphere channels. Neutron transport calculations are performed, and multi-group homogenized cross-sectional data of each component under different temperatures and burnup states are statistically generated to form a multi-group homogenized cross-section library. The Monte Carlo method is used to establish refined models to accurately handle the unique dual inhomogeneity of TRISO particles and complex control rod geometry of pebble bed high-temperature gas-cooled reactors, ensuring the physical fidelity of cross-sectional data from the source and eliminating the systematic bias caused by geometric simplification in traditional methods. Step 2: Using the multi-group homogenized cross-section library generated in Step 1 as input, perform core diffusion and online refueling simulation calculations through a core physics analysis program. After reaching the target core state, execute the neutron leakage and neutron flow correction iterative process in this state. The process includes: S21. Using the minority group cross section obtained by directly merging the multi-group homogenized cross sections as the initial value, perform three-dimensional whole-reactor diffusion calculation to obtain the neutron leakage rate of each block in the reactor core space; S22. For each computational region of the reactor core, based on the currently obtained neutron leakage rate and combined with the multi-group homogenization cross section, a regional infinite medium moderation equation incorporating leakage correction is constructed, in the following form: (1) In the formula: ——No. Leakage cross section of the energy group; — Ball court area Homogenization flux of an energy group; — Ball court area The homogenized total cross section of the energy group; — The ball court area starts from the first Energy group transition to the first Homogenized scattering cross section of the energy group; — Ball court area Homogenization flux of an energy group; — Effective multiplication coefficient; — Ball court area Homogenized fission energy spectrum of the energy group; — Ball court area Homogenization of the energy group and fission neutron generation cross section; Among them, the Leakage cross section of the energy group The formula is derived from the leakage rate of the current area: (2) In the formula: — The first in this region The diffusion coefficient of the energy group; — The first in this region The equivalent geometric curvature of the energy group; — The first in this region Neutron leakage rate of the energy group; — The first in this region Neutron flux of the energy group; The introduction of online leakage correction solves the problem that offline cross-section libraries cannot respond to changes in the macroscopic state of the reactor core and local energy spectrum. Its technical effect is to enable cross-sections to have state-aware capabilities, which significantly improves the calculation accuracy of the effective multiplication factor and power distribution. S23. Solving the above moderation equation yields the leakage-corrected multi-group neutron spectrum, followed by online merging to obtain the updated few-group cross-section. The merging formula is: (3) In the formula: — The first ball court area Energy Group Type of homogenized few-group cross section, in which Indicates the type of neutron reaction, including overall reaction, scattering, fission, and transport; — Indicates belonging to the first Indices of all multigroup energy groups within the energy range of a few groups A set; S24. Based on the updated minority group cross section, perform three-dimensional whole-pile diffusion calculation again to obtain the new neutron leakage rate; S25. Substitute the updated minority cross section into the three-dimensional whole-reactor diffusion calculation to obtain the whole-reactor leakage rate and core parameters again. Determine whether the minority cross section has converged. If it has not converged, iteratively execute steps S22 to S24 until the minority cross section converges. S26. Perform neutron flow effect correction on the converged minority cross sections to obtain a minority cross section library that matches the current core burnup and core state; Step 3: 3D Real-Time Simulation Calculation: S31. Based on the current real-time operating parameters, obtain the corresponding state of the minority section from the minority section library generated in step 2 by interpolation; S32. Based on the aforementioned minority cross section, the core steady-state calculation is performed using the three-dimensional multi-group neutron diffusion block expansion method based on transverse integration to obtain the three-dimensional power distribution, effective multiplication coefficient, and control rod value physical quantities. The nodal expansion method can accurately describe the nodal flux gradient using high-order polynomials. While maintaining real-time computation speed, it effectively captures the physical characteristics of strongly non-uniform regions, achieving a balance between computational efficiency and accuracy. Step 4: During the transient calculation, the coupled prediction-correction quasi-static method is used to solve the three-dimensional neutron spatiotemporal dynamics. By decomposing the neutron dynamics equation into amplitude function equations and shape function equations and iterating them separately, the three-dimensional power distribution and fission poison concentration distribution evolving over time can be obtained in real time. The coupled prediction-correction quasi-static method overcomes the problem of strong rigidity of the dynamics equation by solving the amplitude and shape functions separately. Its technical effect is to ensure that the single-step time is stable within the simulation step size while ensuring the accuracy of transient power response, thus meeting the real-time requirements. The above steps enable online high-precision simulation of the physical properties of the reactor core.

[0006] Compared with existing technologies, this invention has the following advantages: This invention uses the Monte Carlo method to accurately handle the dual inhomogeneities of the pebble bed core from the source. Through the collaborative correction and iterative process of leakage and neutron flow, the minority group cross section truly reflects the actual neutron environment of the entire reactor, and the calculation accuracy of key core parameters is significantly improved. This invention adopts an architecture of "offline high-precision minority group cross section generation and online fast interpolation solution", combined with the three-dimensional multi-group neutron diffusion block expansion method based on transverse integration and the prediction-correction quasi-static transient solution method, which greatly improves the computational efficiency and can meet the requirements of real-time simulation. Attached Figure Description

[0007] Figure 1 This is a flowchart illustrating the overall process of generating the few-group cross section and performing real-time three-dimensional simulation of the pebble bed type high-temperature gas-cooled reactor of the present invention.

[0008] Figure 2 This is a schematic diagram illustrating the detailed modeling of some components used in the verification of this invention.

[0009] Figure 3 This is a schematic diagram illustrating the changes in flux amplitude and xenon toxicity concentration after the rod lifting process in this invention. Detailed Implementation

[0010] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: The present invention relates to a method for generating a few-group cross section and performing real-time three-dimensional simulation of a pebble bed type high-temperature gas-cooled reactor, such as... Figure 1As shown, firstly, the non-uniform fine geometric model is calculated based on the Monte Carlo method to construct a component-level multi-group homogenized cross-section library; then, core calculations are performed using a core physics analysis program, and neutron leakage and neutron flow correction iterations are executed under the target state to reconstruct the energy spectrum and generate a few-group cross-section library related to burnup and core state; in the real-time simulation stage, real-time cross-sections are obtained through temperature interpolation, and the three-dimensional multi-group neutron diffusion block expansion method based on transverse integration under cylindrical geometry is used for core steady-state calculation; for the transient process, the prediction-correction quasi-static method is coupled to solve the three-dimensional neutron spatiotemporal dynamics, and the three-dimensional power distribution and evolution state are obtained in real time, realizing online high-precision simulation of core physical characteristics.

[0011] The following examples use a pebble bed modular high-temperature gas-cooled reactor (HTR-PM) core as the application object to describe the method for generating the few-group cross section and performing three-dimensional real-time simulation of the pebble bed high-temperature gas-cooled reactor. The specific steps include: Step 1: Based on a continuous energy kernel database (e.g., ENDF / B-VII), generate an ACE-format continuous energy point cross-section library, then as follows... Figure 2 A refined geometric model was established, which included fuel spheres with randomly distributed TRISO particles, graphite spheres using a meta-component model, and a fan-shaped reflector model containing control rods and absorption sphere channels. Neutron transport calculations were performed using Monte Carlo software (such as the Monte Carlo particle transport calculation software NECP-MCX), and multi-group homogenized cross-sectional data of each component under different temperatures and burnup states were statistically generated to form a multi-group homogenized cross-sectional library. Step 2: Using the multi-group homogenized cross-section library generated in Step 1 as input, perform core diffusion and online refueling simulation calculations through a core physics analysis program (such as the pebble bed high-temperature gas-cooled reactor physics and thermal calculation program NECP-Panda). After reaching the target core state, execute the neutron leakage and neutron flow correction iterative process in this state. The process includes: S21. Using the small group cross section obtained by directly merging the multi-group homogenized cross section data as the initial value, perform three-dimensional whole-reactor diffusion calculation to obtain the neutron leakage rate of each block in the core space; S22. For each computational region of the reactor core, based on the currently obtained neutron leakage rate and combined with the multi-group homogenization cross section, a regional infinite medium moderation equation incorporating leakage correction is constructed, in the following form: (1) In the formula: ——No. Leakage cross section of the energy group; — Ball court area Homogenization flux of an energy group; — Ball court area The homogenized total cross section of the energy group; — The ball court area starts from the first Energy group transition to the first Homogenized scattering cross section of the energy group; — Ball court area Homogenization flux of an energy group; — Effective multiplication coefficient; — Ball court area Homogenized fission energy spectrum of the energy group; — Ball court area Homogenization of the energy group and fission neutron generation cross section; Among them, the Leakage cross section of the energy group The formula is derived from the leakage rate of the current area: (2) In the formula: — The first in this region The diffusion coefficient of the energy group; — The first in this region The equivalent geometric curvature of the energy group; — The first in this region Neutron leakage rate of the energy group; — The first in this region Neutron flux of the energy group; S23. Solving the above moderation equation yields the leakage-corrected multi-group neutron spectrum, followed by online merging to obtain the updated few-group cross-section. The merging formula is: (3) In the formula: — The first ball court area Energy Group Type of homogenized few-group cross section, in which Indicates the type of neutron reaction, including overall reaction, scattering, fission, and transport; — Indicates belonging to the first Indices of all multigroup energy groups within the energy range of a few groups A set; S24. Based on the updated minority group cross section, perform three-dimensional whole-pile diffusion calculation again to obtain the new neutron leakage rate; S25. Substitute the updated minority cross section into the three-dimensional whole-reactor diffusion calculation to obtain the whole-reactor leakage rate and core parameters again. Determine whether the minority cross section has converged. If it has not converged, iteratively execute steps S22 to S24 until the minority cross section converges. S26. Perform neutron flow effect correction on the converged minority cross sections to obtain a minority cross section library that matches the current core burnup and core state; Step 3: 3D Real-Time Simulation Calculation: S31. Based on the current real-time operating parameters, obtain the corresponding state of the minority section from the minority section library generated in step 2 by temperature interpolation; S32. Based on the aforementioned minority cross section, the core steady-state calculation is performed using the three-dimensional multi-group neutron diffusion block expansion method based on transverse integration to obtain the three-dimensional power distribution, effective multiplication coefficient, and control rod value physical quantities. Step 4: Based on the forward and conjugate fluxes obtained from steady-state calculations, the three-dimensional neutron spatiotemporal dynamics is solved using the predictor-corrector quasi-static method during transient calculations. By decomposing the neutron dynamics equations into amplitude function equations and shape function equations and iterating them separately, the three-dimensional power distribution and fission poison concentration distribution evolving over time can be obtained in real time.

[0012] Next, the proposed method for generating a few-group cross section and performing real-time 3D simulation of a pebble bed modular high-temperature gas-cooled reactor (HTR-PM) is verified using a pebble bed modular high-temperature gas-cooled reactor core as the application object. The core condition is selected as full-power balanced xenon operation. The maximum relative deviation between the 3D power distribution calculated by the method of this invention and the reference design value is 5.4%, and the average deviation is 2.1%. The relative deviation of the control rod value calculation is within 5%. In simulating the transient process of lifting a single control rod 50mm from the critical position, the method of this invention can correctly reflect the physical trend of xenon toxicity reduction and flux increase (e.g., ...). Figure 3 (As shown), and the single-step calculation time is consistently within 0.05 seconds. All indicators meet and exceed the requirements of the engineering specifications.

[0013] In summary, the method for generating the few-group cross section and performing three-dimensional real-time simulation of the pebble bed type high-temperature gas-cooled reactor proposed in this invention can combine high computational accuracy, real-time response capability, and engineering practicality.

[0014] The innovation of this invention lies in the following: This method uses the Monte Carlo method to accurately address the dual inhomogeneities of the pebble bed core from the source. Through a collaborative correction and iterative process of leakage and neutron flow, the minority group cross section truly reflects the actual neutron environment of the entire reactor, significantly improving the calculation accuracy of key core parameters. This invention adopts an architecture of "offline high-precision minority group cross section generation and online fast interpolation solution," combined with a three-dimensional multi-group neutron diffusion block expansion method based on transverse integration and a prediction-correction quasi-static transient solution method, which greatly improves computational efficiency and can meet the requirements of real-time simulation.

Claims

1. A method for generating the few-group cross section and performing three-dimensional real-time simulation of a pebble bed type high-temperature gas-cooled reactor, characterized in that: Includes the following steps: Step 1: Based on the continuous energy nuclear database, the Monte Carlo method is used to establish refined geometric models for fuel spheres containing randomly distributed TRISO particles, graphite spheres using a meta-component model, and fan-shaped reflector models containing control rods and absorption sphere channels. Neutron transport calculations are performed and multi-group homogenized cross-sectional data of each component under different temperatures and burnup states are statistically generated to form a multi-group homogenized cross-sectional library. Step 2: Using the multi-group homogenized cross-section library generated in Step 1 as input, perform core diffusion and online refueling simulation calculations through a core physics analysis program. After reaching the target core state, execute the neutron leakage and neutron flow correction iterative process in this state. The process includes: S21. Using the minority group cross section obtained by directly merging the multi-group homogenized cross sections as the initial value, perform three-dimensional whole-reactor diffusion calculation to obtain the neutron leakage rate of each block in the reactor core space; S22. For each computational region of the reactor core, based on the currently obtained neutron leakage rate and combined with the multi-group homogenization cross section, a regional infinite medium moderation equation incorporating leakage correction is constructed, in the following form: (1) In the formula: ——No. Leakage cross section of the energy group; — Ball court area Homogenization flux of an energy group; — Ball court area The homogenized total cross section of the energy group; — The ball court area starts from the first Energy group transition to the first Homogenized scattering cross section of the energy group; — Ball court area Homogenization flux of an energy group; — Effective multiplication coefficient; — Ball court area Homogenized fission energy spectrum of the energy group; — Ball court area Homogenization of the energy group and fission neutron generation cross section; Among them, the Leakage cross section of the energy group The formula is derived from the leakage rate of the current area: (2) In the formula: — The first in this region The diffusion coefficient of the energy group; — The first in this region The equivalent geometric curvature of the energy group; — The first in this region Neutron leakage rate of the energy group; — The first in this region Neutron flux of the energy group; S23. Solving the above moderation equation yields the leakage-corrected multi-group neutron spectrum, followed by online merging to obtain the updated few-group cross-section. The merging formula is: (3) In the formula: — The first ball court area Energy Group Type of homogenized few-group cross section, in which Indicates the type of neutron reaction, including overall reaction, scattering, fission, and transport; — Indicates belonging to the first Indices of all multigroup energy groups within the energy range of a few groups A set; S24. Based on the updated minority group cross section, perform three-dimensional whole-pile diffusion calculation again to obtain the new neutron leakage rate; S25. Substitute the updated minority cross section into the three-dimensional whole-reactor diffusion calculation to obtain the whole-reactor leakage rate and core parameters again. Determine whether the minority cross section has converged. If it has not converged, iteratively execute steps S22 to S24 until the minority cross section converges. S26. Perform neutron flow effect correction on the converged minority cross sections to obtain a minority cross section library that matches the current core burnup and core state; Step 3: 3D Real-Time Simulation Calculation: S31. Based on the current real-time operating parameters, obtain the corresponding state of the minority section from the minority section library generated in step 2 by interpolation; S32. Based on the aforementioned minority cross section, the core steady-state calculation is performed using the three-dimensional multi-group neutron diffusion block expansion method based on transverse integration to obtain the three-dimensional power distribution, effective multiplication coefficient, and control rod value physical quantities. Step 4: During the transient calculation process, the coupled prediction-correction quasi-static method is used to solve the three-dimensional neutron spatiotemporal dynamics. By decomposing the neutron dynamics equation into amplitude function equation and shape function equation and iterating them separately, the three-dimensional power distribution and fission poison concentration distribution that evolve over time can be obtained in real time. Achieve high-precision online simulation of the physical properties of the reactor core.

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