Cross section data calculation method and device and rod position prediction method and system

Abstract

The invention discloses a cross section data calculation method and device and a rod position prediction method and system.The cross section data calculation method comprises the steps that according to a reactor core structure of a micro reactor, initial cross section data of the micro reactor under target working conditions are determined, and the target working conditions comprise working conditions corresponding to different insertion states of a control rod; determining a target SPH factor according to the initial cross section data and an SPH factor iteration method based on flux comparison; and correcting the initial section data according to the target SPH factor to obtain corrected section data under the target working condition. Therefore, the calculation precision of the section data of the micro reactor is improved.

Description

Technical Field

[0001] This invention belongs to the field of nuclear power technology, specifically relating to a method, apparatus, rod position prediction method and system for cross-sectional data calculation. Background Technology

[0002] The control rods of the gas-cooled microreactor are arranged in the side reflector outside the core. The reflector is made of graphite with a small neutron absorption cross section, while the control rods are made of boron carbide with a large neutron absorption cross section. This results in very strong non-uniform, anisotropic scattering and leakage effects near the control rods.

[0003] Due to the small size and large mean free path of neutrons in gas-cooled microreactors, the insertion of control rods significantly impacts the overall energy spectrum of the gas-cooled microreactor, thereby affecting the cross-section of components near the control rod location. However, traditional transient calculation models for pressurized water reactors neglect the cross-sectional changes of other non-control rod components after the insertion of control rods. This approach leads to significant deviations in the calculation results of gas-cooled microreactor cores using diffusion methods.

[0004] Therefore, existing technologies have significant errors in calculating the parameters of gas-cooled microreactors. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the above-mentioned shortcomings of the prior art by providing a cross-sectional data calculation method, device, rod position prediction method and system. Using the cross-sectional data calculation method can improve the accuracy of cross-sectional data calculation for micro-reefs.

[0006] In a first aspect, embodiments of the present invention provide a method for calculating cross-sectional data, applied to a microreactor, the method comprising:

[0007] Based on the core structure of the micro-recharger, the initial cross-sectional data of the micro-recharger under the target operating conditions are determined, and the target operating conditions include the operating conditions corresponding to different insertion states of the control rods.

[0008] Based on the initial cross-sectional data, the target SPH factor is determined using an iterative method for SPH factor based on flux comparison.

[0009] The initial cross-sectional data are corrected based on the target SPH factor to obtain the corrected cross-sectional data under the target working condition.

[0010] Optionally, determining the target SPH factor based on the flux comparison-based SPH factor iterative method using the initial cross-sectional data specifically includes:

[0011] S201. Let n = 0, and obtain the nth SPH factor and the initial cross-sectional data;

[0012] S202. Correct the initial cross-sectional data according to the nth SPH factor to obtain the nth corrected cross-sectional data;

[0013] S203. Determine the nth neutron flux density of each energy group in the core based on the nth corrected section data;

[0014] S204. Determine the (n+1)th SPH factor based on the nth neutron flux density and Monte Carlo reference neutron flux of each energy group.

[0015] S205. If the nth SPH factor and the (n+1)th SPH factor of each energy group do not meet the convergence condition, let n = n+1, and return to execute steps S202 to S204.

[0016] The nth SPH factor and the (n+1)th SPH factor of each block are determined as the target SPH factor until the convergence condition is met.

[0017] Secondly, embodiments of the present invention also provide a rod position prediction method, the method comprising:

[0018] The corrected cross-sectional data under the target working condition is obtained by using the cross-sectional data calculation method described in the first aspect;

[0019] Based on the corrected cross-sectional data under the target operating condition, the control rod position is predicted for the micro-recharger.

[0020] Thirdly, embodiments of the present invention also provide a cross-sectional data calculation device for use in a micro-relay, the device comprising:

[0021] The determination module is used to determine the initial cross-sectional data of the micro-recharger under the target operating condition based on the core structure of the micro-recharger. The target operating condition includes the operating conditions corresponding to different insertion states of the control rods.

[0022] An iterative module, connected to the determining module, is used to determine the target SPH factor based on the flux comparison SPH factor iterative method according to the initial cross-sectional data.

[0023] The first correction module, connected to the iteration module, is used to correct the initial cross-sectional data according to the target SPH factor to obtain the corrected cross-sectional data under the target working condition.

[0024] Fourthly, embodiments of the present invention also provide a rod position prediction system, the system comprising:

[0025] The cross-section data calculation device described in the third aspect is used to acquire corrected cross-section data under the target working condition;

[0026] The prediction module is used to predict the control rod position of the micro-recharger based on the corrected cross-sectional data under the target working condition.

[0027] The cross-sectional data calculation method of this invention obtains the target SPH factor through an iterative method of flux comparison and corrects the initial cross-sectional data, effectively compensating for errors caused by non-uniformity effects and structural complexity in diffusion calculations using homogenized cross-sectional data. By accurately calculating the target SPH factor and using it to correct the cross-sectional data, a high degree of consistency between the neutron flux distribution in diffusion calculations and the flux results from high-precision Monte Carlo calculations can be ensured, thereby significantly improving the accuracy of minority group cross-sectional data. This improves the accuracy of cross-sectional data calculations for microreactors. Attached Figure Description

[0028] Figure 1 This is a flowchart of a cross-sectional data calculation method according to Embodiment 1 of the present invention;

[0029] Figure 2 : This is a flowchart of another method for calculating cross-sectional data according to Embodiment 1 of the present invention;

[0030] Figure 3 : This refers to the steady-state calculation of the block-level power distribution and relative deviation under the conditions of full lifting and full insertion of the control rods in the gas-cooled microreactor core of Embodiment 1 of the present invention;

[0031] Figure 4 : This refers to the cross-sectional parameterized segment-level power distribution and relative deviation of the gas-cooled microreactor core control rod under full lifting conditions in Embodiment 1 of the present invention;

[0032] Figure 5 The cross-sectional parameterized segment-level power distribution and relative deviation of the gas-cooled microreactor core control rods under the condition of 1 / 3 insertion in the reactor core of the present invention, as described in Embodiment 1 of the present invention;

[0033] Figure 6 : This refers to the cross-sectional parameterized segment-level power distribution and relative deviation of the gas-cooled microreactor core control rods under the condition of 2 / 3 insertion in the reactor core of Embodiment 1 of the present invention;

[0034] Figure 7 : This refers to the cross-sectional parameterized segment-level power distribution and relative deviation of the gas-cooled microreactor core control rods under the fully inserted condition in Embodiment 1 of the present invention;

[0035] Figure 8(a): Relative deviation of detector readings under the condition that the control rod is 47.35cm in position according to Embodiment 1 of the present invention;

[0036] Figure 8(b): Root mean square deviation of detector readings under the condition that the control rod is 47.35 cm in position according to Embodiment 1 of the present invention;

[0037] Figure 9(a): The relative deviation of the detector readings under the condition that the control rod position is 97.35cm in Embodiment 1 of the present invention;

[0038] Figure 9(b): shows the root mean square deviation of the detector readings under the condition that the control rod position is 97.35cm in Embodiment 1 of the present invention;

[0039] Figure 10(a): shows the relative deviation of the detector readings when the control rod is positioned at 147.35 cm in Embodiment 1 of the present invention.

[0040] Figure 10(b): Root mean square deviation of detector readings under the condition of control rod position 147.35cm in Embodiment 1 of the present invention;

[0041] Figure 11 : This is a structural diagram of a cross-sectional data calculation device according to Embodiment 3 of the present invention. Detailed Implementation

[0042] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0043] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes said element.

[0044] Cross-section data refers to the observations of the same characteristic variable of a group (or all) of individuals in a population at the same time (period or point in time), and is one of the common types of sample data.

[0045] Energy groups refer to the division of the continuous energy range of neutrons into several discrete intervals (groups), such as two-group models (fast group, hot group) or multi-group models (such as group 30). Neutrons in different energy groups have different nuclear reaction cross sections (absorption, scattering, fission, etc.).

[0046] Nodes refer to the spatial division of the reactor core into several small regions (nodes), and the material composition, temperature and other parameters within each node are considered to be uniform.

[0047] The minority group cross section refers to the cross section data in the neutron transport equations used in core calculations. These cross sections are used to describe the interaction between neutrons and materials in different energy groups (neutron energy ranges).

[0048] Few-group homogenized cross-sectional data refers to the cross-sectional data used in nuclear reactor calculations to describe the neutron behavior of fewer energy groups by simplifying and homogenizing the initial fine-group cross-sectional data. During core calculations, preliminary few-group cross-sectional data is first obtained through a two-step grid / assembly homogenization method. This is the result of simulation using the Monte Carlo program, which considers the neutron behavior of different nodes in the core (such as fuel assemblies, reflector assemblies, etc.) and generates the few-group cross-section for each region.

[0049] Smoothed particle hydrodynamics (SPH) is a computational method for simulating fluid dynamics. Its main idea is to simulate the fluid by analyzing the forces acting on and the motion of each infinitesimal element. By simulating the forces and motion of each element, it calculates forces such as gravity and pressure.

[0050] Unlike traditional pressurized water reactors (PWRs), the six control rods of a gas-cooled microreactor are arranged in a side reflector layer outside the core. The reflector layer is made of graphite with a small neutron absorption cross-section, while the control rods are made of boron carbide with a large neutron absorption cross-section. This results in very strong non-uniform, anisotropic scattering and leakage effects near the control rods. However, the two-step calculation program for grid assembly homogenization based on neutron diffusion theory in traditional PWRs introduces significant errors, while the one-step full-reactor calculation program is too time-consuming and cannot meet the computational requirements of current nuclear design and online core monitoring programs. Therefore, developing a core calculation program with higher accuracy and computational efficiency is of great significance for the core design of gas-cooled microreactors.

[0051] For steady-state core calculation examples, research institutions both domestically and internationally have adopted a two-step approach based on cell / assembly homogenization. This involves using the Monte Carlo program to replace the assembly program for full-reactor calculations, obtaining the homogenized minority group cross-section. The SPH factor is then used to correct the minority group cross-section before core calculations. The results obtained by this method show good agreement with those obtained directly from the one-step method, demonstrating high computational efficiency. Furthermore, this method has been tested and validated on advanced reactor types such as heat pipe reactors, gas-cooled microreactors, and fast reactors, proving its good accuracy and universality. For transient core calculation examples, research is limited both domestically and internationally, primarily relying on pressurized water reactor (PWR) calculation approaches. Transient calculations are performed by solving the spacetime dynamics equations, using a reference cross-section, cross-section parameterization, and delayed neutron data to construct a transient calculation database. Unlike traditional large PWR systems, gas-cooled microreactors are small in size and have a large neutron mean free path. After the insertion of control rods, the control rods significantly affect the overall energy spectrum of the gas-cooled microreactor, thus influencing the cross-section of the components near the control rod location. However, the traditional transient calculation model for pressurized water reactors ignores the cross-sectional changes of the remaining non-control rod components after the control rods are inserted. This approach leads to significant deviations in the calculation results of gas-cooled microreactor cores using the diffusion method.

[0052] Therefore, a global cross-section parameterization method based on neutron diffusion theory is needed to address the compact core structure of gas-cooled microreactors. This method can quickly and accurately calculate core parameters such as the in-core power distribution and effective multiplication factor under different control rod positions. It can also predict the control rod positions of gas-cooled microreactors based on actual nuclear detection signals from detectors.

[0053] Example 1:

[0054] Based on the above research, in order to solve the aforementioned technical problems, such as Figure 1 As shown, this embodiment provides a method for calculating cross-sectional data, which can be applied to micro-relays.

[0055] Specifically, it includes the following steps 101 to 104.

[0056] Step 101: Determine the initial cross-sectional data of the microreactor under the target operating conditions based on the core structure of the microreactor.

[0057] The target operating conditions include the operating conditions corresponding to different insertion states of the control rod.

[0058] Specifically, firstly, a complete three-dimensional microreactor core model is constructed, including internal structures such as fuel assemblies, reflectors, control rods, and coolant, and material composition and geometric parameters are set.

[0059] Then, determine the target operating conditions: select the micro-stacking conditions of different insertion states of the control rods (such as full insertion, full lifting, and other typical states); define the relevant parameters of the operating conditions (temperature, power, etc.).

[0060] Finally, perform full-stack calculations: use Monte Carlo methods (such as the RMC program) to perform high-precision calculations to obtain the initial homogenized minority cross-section data (including absorption cross-section, scattering cross-section, fission cross-section, etc.) for each nodal region. At the same time, it can also obtain benchmark data such as accurate power distribution and effective multiplication factor for verification.

[0061] Step 102: Determine the target SPH factor based on the flux comparison-based SPH factor iterative method according to the initial cross-sectional data.

[0062] The SPH factor, or super homogenization factor, is a correction coefficient used in this application to adjust for errors caused by the non-conservation of neutron leakage rate and reaction rate during the homogenization process.

[0063] The target SPH factor is the convergent SPH factor after iterative optimization; that is, it is the stable correction coefficient finally determined through multiple corrections and flux comparisons. It is used to quantify physical deviations in the homogenization process and adjust cross-sectional parameters (such as diffusion coefficient, total cross-section, etc.).

[0064] The flux comparison SPH factor iterative method compares the reference flux (baseline flux) obtained by high-precision Monte Carlo calculation with the flux obtained by diffusion calculation using homogenized cross-sectional data, and iteratively adjusts the SPH (SuperHomogenization) factor to make the flux distribution calculated by diffusion consistent with the reference flux distribution, thereby eliminating the systematic errors introduced by homogenization and diffusion approximation.

[0065] Step 103: Correct the initial cross-sectional data according to the target SPH factor to obtain the corrected cross-sectional data under the target working condition.

[0066] The convergent SPH factor is applied to the initial cross-sectional data to generate a high-precision corrected cross-sectional database.

[0067] By combining the target SPH factor of the control rod in full insertion / full lifting state, the cross-sectional parameters of arbitrary rod positions are generated by linear interpolation to achieve dynamic simulation.

[0068] In this embodiment, the initial cross-sectional data is corrected using an iterative SPH factor method based on flux comparison, effectively compensating for errors caused by non-uniformity and structural complexity in diffusion calculations of homogenized cross-sectional data. By accurately calculating the target SPH factor and using it to correct the cross-sectional data, a high degree of consistency between the neutron flux distribution in the diffusion calculation and the flux results from the high-precision Monte Carlo calculation can be ensured, thereby significantly improving the accuracy of the few-group cross-sectional data and avoiding the high time consumption problem of traditional "one-step" full-reactor calculations. Therefore, this method significantly improves computational efficiency while ensuring computational accuracy, providing a reliable basis and theoretical support for core parameter calculations and subsequent power monitoring and simulation in microreactors.

[0069] Optionally, S102 above may specifically include the following steps:

[0070] S201. Let n = 0, and obtain the nth SPH factor and initial cross-sectional data;

[0071] S202. Correct the initial cross-sectional data according to the nth SPH factor to obtain the nth corrected cross-sectional data;

[0072] S203. Determine the nth neutron flux density of each energy group in the core based on the nth corrected section data;

[0073] S204. Determine the (n+1)th SPH factor based on the nth neutron flux density and Monte Carlo reference neutron flux of each energy group.

[0074] S205. If the nth and (n+1)th SPH factors of each energy group do not meet the convergence condition, let n = n+1, and return to execute steps S202 to S204.

[0075] The process continues until the nth and (n+1)th SPH factors of each block meet the convergence condition, at which point the (n+1)th SPH factor is determined as the target SPH factor.

[0076] Specifically, S201 is the initialization phase, where the iteration counter n = 0, and the initial SPH factor is set. For example, the 0th SPH factor is usually initialized to 1.0 (for all energy groups and all nodes). Then, the initial cross-sectional data is obtained. The homogenization cross-sectional data of the micro-reactance stack can be calculated using the Monte Carlo method, including: absorption cross-section, scattering cross-section, fission cross-section, transport cross-section, diffusion coefficient, etc.

[0077] Step S202 is the cross-sectional data correction step. The initial cross-sectional data is corrected using the nth SPH factor. The corrected cross-sectional data is then used as the nth corrected cross-sectional data for subsequent calculations.

[0078] Step S203 is the neutron flux calculation step. By establishing the diffusion equation, the neutron flux density of each energy group's sub-blocks is calculated using the corrected cross-sectional data.

[0079] Step S204 is the SPH factor update step. The new SPH factor is calculated based on the neutron flux density of the subblocks in each energy group and the baseline flux calculated by Monte Carlo.

[0080] Step S205 performs convergence judgment and iteration. It judges convergence and decides whether to continue iteration. If the convergence condition is not met, it sets n = n+1 and returns to S202 to continue iteration; if the convergence condition is met, the iteration ends, and the n+1 SPH factors are taken as the final target SPH factor.

[0081] In this embodiment, starting from the initial factor setting, a systematic loop of neutron flux calculation, baseline flux comparison, and factor update is used to achieve accurate correction of the cross-sectional data. This structured iterative method not only provides a clear computational path and convergence criteria but also efficiently compensates for systematic errors introduced during cross-sectional homogenization, while avoiding the risk of iterative divergence. Through this carefully designed iterative strategy, the accuracy of the group constant calculation for the microreactor is significantly improved, especially in strongly inhomogeneous regions such as the control rods, enabling subsequent diffusion calculations based on the corrected cross-section to accurately reflect the true neutron distribution.

[0082] Optionally, the aforementioned initial cross-section data includes the initial diffusion coefficient, initial total cross-section, initial neutron production cross-section, and initial scattering matrix.

[0083] The aforementioned S202 specifically includes:

[0084] The initial diffusion coefficient is corrected based on the nth SPH factor to obtain the nth corrected diffusion coefficient.

[0085] The initial cross-sectional data are corrected based on the nth SPH factor to obtain the nth corrected total cross-section.

[0086] The initial neutron production cross section is corrected according to the nth SPH factor to obtain the nth corrected neutron production cross section;

[0087] The initial scattering matrix is ​​corrected according to the nth SPH factor to obtain the nth corrected scattering matrix;

[0088] The nth correction cross section data includes the nth correction diffusion coefficient, the nth correction total cross section, the nth correction neutron production cross section, and the nth correction scattering matrix.

[0089] In this embodiment, a coordinated correction of the cross-sectional data is achieved by systematically correcting the diffusion coefficient, total cross-section, neutron production cross-section, and scattering matrix. This ensures the physical consistency between the terms of the neutron balance equations and effectively compensates for the spatial self-shielding effect and spectral distortion in regions such as control rods and reflectors in the microreactor. In particular, the precise correction of the scattering matrix accurately captures the influence of the control rods on the neutron energy spectrum, overcoming the accuracy deficiencies of traditional homogenization methods in simulating neutron behavior around strong absorbers. The complete cross-sectional data correction system significantly improves the accuracy of diffusion calculations, enabling it to achieve near-Monte Carlo accuracy while maintaining computational efficiency.

[0090] Optionally, the initial diffusion coefficient is corrected according to the nth SPH factor to obtain the nth corrected diffusion coefficient, specifically including:

[0091] The nth corrected diffusion coefficient is obtained using formula (1):

[0092]

[0093] Where g is the energy group number, For geometric position, For the nth corrected diffusion coefficient, It is the nth SPH factor of the g-th group. The initial diffusion coefficient of the g-th group can usually be obtained from the homogenization results calculated by Monte Carlo. Let g be the transport cross section of the g-th group.

[0094] Formula (1) uses the relationship between diffusion coefficient and transport cross section to obtain the modified diffusion coefficient based on n SPH factors and transport cross section.

[0095] In this embodiment, formula (1) adopts a treatment method consistent with physical relationships (proportional to the SPH factor rather than inversely proportional), which avoids physical contradictions that may be introduced during the correction process and ensures the mathematical consistency of the modified diffusion equation system.

[0096] Optionally, the initial cross-sectional data is corrected based on the nth SPH factor to obtain the nth corrected total cross-section, specifically including:

[0097] The nth corrected total cross section is obtained using formula (2):

[0098]

[0099] Where g is the energy group number, For geometric position, For the nth corrected total cross section, It is the nth SPH factor of the g-th group. Let be the initial total cross section of the g-th group. Let g be the initial absorption cross section of the g-th group. Let g be the initial scattering cross section of the g-th group.

[0100] Here, the total cross section represents the total probability of a neutron interacting with the medium, comprising two basic parts: the absorption cross section, which describes the probability of a neutron being absorbed by the material; and the scattering cross section, which describes the probability of a neutron undergoing a scattering reaction. Modifying the total cross section effectively adjusts the strength of both of these fundamental interactions simultaneously.

[0101] In this embodiment, the overall intensity of the interaction between neutrons and the medium is precisely adjusted by formula (2), effectively solving the problem of neutron flux calculation in the non-uniform region of the microreactor. It can accurately capture the steep gradient and rapid change characteristics of neutron flux in the strong absorption regions such as the control rods in the microreactor. Through precise correction of the total cross section, the absorption term in the diffusion equation is reasonably adjusted, achieving balance with the leakage term (corrected by the diffusion coefficient) and the source term (corrected by the neutron generation cross section). This allows the entire calculation system to achieve calculation results close to the accuracy of the transport equation while maintaining high efficiency, providing a reliable computational basis for the nuclear design and safety analysis of the microreactor.

[0102] Optionally, the initial neutron production cross section is corrected according to the nth SPH factor to obtain the nth corrected neutron production cross section, specifically including:

[0103] The nth modified neutron generation cross section is obtained using formula (3):

[0104]

[0105] Where g is the energy group number, For geometric position, To generate a cross section for the nth modified neutron of the g-th group, It is the nth SPH factor of the g-th group. To generate a cross section for the initial neutrons of the g-th group.

[0106] Neutron generation cross section is a key parameter describing the neutron generation rate during fission. denoted by , which represents the fission cross section, i.e., the probability of fission caused by a neutron; v represents the average number of neutrons produced in each fission; the product of the two directly determines the intensity of the fission chain reaction.

[0107] In this embodiment, since the fission source directly affects the neutron flux distribution, accurate correction of the neutron generation cross section can effectively solve the calculation bias problem of traditional homogenization methods in regions with strong spatial inhomogeneity (such as near the control rods). Accurate correction of the neutron generation cross section can ensure that the diffusion calculation is close to the accuracy level of transport theory, while maintaining the high-efficiency computational advantage of the diffusion method, providing a reliable computational basis for the safe operation monitoring of the microreactor throughout its entire life cycle.

[0108] Optionally, the initial scattering matrix is ​​corrected according to the nth SPH factor to obtain the nth corrected scattering matrix, specifically including:

[0109] The nth corrected scattering matrix is ​​obtained using formula (4):

[0110]

[0111] Where g is the energy group number, For geometric position, For the nth corrected scattering matrix, For the nth SPH factor, ∑ g'→g (r) is the initial scattering matrix.

[0112] The scattering matrix describes the probability distribution of neutrons scattering from one energy group to another. Using the above formula (4), the scattering matrix in the diffusion equation can be corrected according to the nth SPH factor.

[0113] In this embodiment, the neutron transfer probability between energy groups is precisely corrected by formula (4), so that diffusion calculation can accurately capture the energy spectrum effects in complex geometries.

[0114] Since the scattering process directly affects the energy distribution and spatial migration of neutrons, accurate scattering matrix correction can significantly improve the accuracy of power distribution calculations, the reliability of control rod reactivity assessments, and burnup analysis in microreactor design. This allows for accurate simulation of the neutron moderation process, providing a powerful computational tool for the design optimization and safety analysis of small modular reactors, while maintaining the high efficiency of diffusion calculations.

[0115] Optionally, S203 above specifically includes:

[0116] The flux density of the nth neutron is obtained using formula (5):

[0117]

[0118] Where g is the energy group number, For geometric position, For the nth SPH factor, Let n be the neutron flux density of the g-th group. For the fission spectrum, k eff The effective proliferation coefficient, The nth corrected diffusion coefficient for the g-th group. This is the nth corrected total cross section for the g-th group. To generate a cross section for the nth modified neutron of the g-th group, Let be the nth corrected scattering matrix from group g' to group g.

[0119] In this embodiment, formula (5) is the expression for the multi-group diffusion equation, which includes leakage, loss, fission source, and scattering source terms. By integrating all the corrected cross-sectional data into the standard multi-group diffusion equation, the flux distribution after the correction of the cross-section is accurately solved in each SPH factor iteration, providing a reliable basis for the update of the SPH factor, thereby ensuring the convergence and accuracy of the entire iteration process. It can accurately capture the neutron behavior in key regions such as control rods and reflectors.

[0120] Optionally, S204 specifically includes:

[0121] The (n+1)th SPH factor is calculated using formulas (6) to (8):

[0122]

[0123] Among them, C g Let g be the normalization constant of the g-th group. As the reference flux density, φ node,g Let V be the neutron flux density of the g-th energy group node. node This represents the volume of the node.

[0124]

[0125] in, The normalized neutron flux density;

[0126]

[0127] Where n+1 is the number of iterations. It is the (n+1)th SPH factor of the g-th group. This represents the baseline flux density during the (n+1)th iteration. This is the normalized neutron flux density calculated during the (n+1)th iteration.

[0128] In this embodiment, a strategy combining global normalization and local correction ensures the physical consistency and numerical stability of the iterative process. It accurately captures the differences in neutron behavior in strongly inhomogeneous regions such as control rods and reflectors within the microreactor, providing customized correction factors for each spatial point and energy group. Through iterative updates, the diffusion calculation results can achieve precise spatial distribution matching with high-precision transport calculations or Monte Carlo calculations while maintaining high computational efficiency. This significantly improves the reliability of core parameter calculations.

[0129] Optionally, S204 may further include:

[0130] The (n+1)th SPH factor is corrected using formula (9):

[0131]

[0132] Where n+1 is the iteration number, and w is the relaxation factor, which controls the weight ratio between the old and new SPH factors. The relaxation factor w typically ranges from 0 to 1.

[0133] w close to 1: More adoption of the newly calculated SPH factor, faster iterative convergence but potentially unstable.

[0134] When w approaches 0, more SPH factors from the previous iteration are retained, resulting in stable iteration but slow convergence.

[0135] The value of w depends on the specific characteristics of the problem and usually requires a balance between convergence speed and stability.

[0136] In this embodiment, the SPH factor iteration process is optimized by introducing a relaxation factor, thereby enhancing the numerical stability and robustness of the entire calculation process.

[0137] For microreactor systems containing strong absorbing materials or with complex geometries, traditional SPH iteration is prone to numerical oscillations or even divergence in areas such as near the control rods and the core-reflector interface. However, by introducing relaxation techniques, the iteration trajectory of the SPH factor can be smoothed, preventing numerical instability caused by over-correction.

[0138] Optionally, the above convergence condition is that the nth SPH factor and the (n+1)th SPH factor satisfy formula (10):

[0139]

[0140] Where ε is the relative deviation, used to measure the degree of convergence; It is the nth SPH factor of the g-th group. Let be the (n+1)th SPH factor of the g-th group. The threshold of 0.001 (0.1%) is the accuracy requirement for judging convergence.

[0141] In this embodiment, a convergence criterion for the SPH factor iteration process is defined, providing a precise termination mechanism for the entire calculation method. By using relative error as the judgment standard, SPH factors of different magnitudes can be fairly evaluated, enhancing the robustness of the algorithm under various operating conditions. The explicit termination condition enables the entire calculation process to be automated, reducing human intervention and improving computational efficiency.

[0142] Optionally, the target operating conditions include the control rod fully inserted state and the control rod fully raised state, and the above cross-sectional data calculation method further includes:

[0143] The rate of change of cross section of the micro-pile is determined by formula (11):

[0144]

[0145] Where, ∑ cr =1 represents the corrected cross-sectional data for the control rod in its fully inserted state. The corrected cross-sectional data is for the control rod fully extended state. Cr is the control rod insertion fraction. Cr=1 indicates that the control rod is fully inserted, and Cr=0 indicates that the control rod is fully extended.

[0146] Based on the rate of change of cross section, the cross section of the entire stack segment of the micro-stack is corrected to obtain the corrected cross section data of the entire stack segment.

[0147] In this embodiment, an improved linear correction method for control rod cross-sections is implemented. Only the SPH factor for the two extreme states of full insertion and full withdrawal needs to be calculated to quickly and accurately obtain corrected cross-section data for any intermediate control rod position, significantly reducing computational complexity and resource requirements. This method can rapidly assess the reactive effects and power distribution impact of different control rod operation schemes. In safety analysis, this method can efficiently simulate transient behavior during control rod movement, providing a reliable basis for accident analysis and safety limit setting.

[0148] Example 2: This example provides a rod position prediction method, specifically including:

[0149] The cross-sectional data calculation method provided in any of the above embodiments is used to obtain the corrected cross-sectional data under the target working condition.

[0150] Based on the corrected cross-section data under the target operating conditions, the control rod position of the microreactor is predicted.

[0151] Specifically, the modified section data of the target working condition is obtained by using the method provided in the above embodiments. By calculating the reactivity of the control rod under the two states of full insertion and full lifting, assuming that the reactivity is linearly related to the rod position, the control rod position can be solved by interpolation.

[0152] In this embodiment, high-precision optimization of the micro-relay control system can be achieved by establishing a direct mapping from the corrected cross-section data to the precise control rod position.

[0153] To facilitate understanding of the cross-sectional data calculation method provided in this embodiment, a practical application description of the above method is provided here.

[0154] A typical gas-cooled microreactor core model is described below: The core consists of hexagonal prism fuel assemblies, control rod assemblies, and a reflector layer with identical geometry within the active zone. Outside the core, boron-carbon bricks, a basket, a pressure vessel, a shielding layer, and a car frame are arranged. External neutron detectors are located outside the steel shielding layer, with three radially asymmetrical locations. Each location has four sets of detectors axially, for a total of 12 sets of external detectors. The core has 12 radial rows of fuel assemblies, each row having three axial layers of fuel assemblies, resulting in a total of 36 fuel assemblies. Each fuel assembly contains 18 fuel rods, and each fuel rod contains 15 fuel pellets axially. Two sets of control rods are arranged. The first set, located outside the active zone, has six sets of control rods and is used for core operation control, cold shutdown, hot shutdown, and emergency shutdown. The second set, located at the core center, has one set of control rods as a backup shutdown method, used only when the first set of control rods fails to shut down the core, enabling hot shutdown.

[0155] Specific steps are as follows: Figure 2 As shown:

[0156] Step 1: Construct initial homogenization data for the gas-cooled microreactor.

[0157] (1) Core model construction

[0158] Based on a typical gas-cooled microreactor design, a detailed 3D core model was constructed for gas-cooled microreactors operating under different control rod insertion states (fully inserted and fully lifted). The model includes the dispersion distribution of TRISO fuel particles in the fuel pellets, the fuel rod structure, the fuel assemblies and their internal blind sections, end plugs, etc., the arrangement of fuel assemblies, control rod assemblies, and reflectors within the reactor core, and the external structures such as boron-carbon bricks, baskets, pressure vessels, shielding layers, external detectors, and vehicle frames. The model was set according to the actual dimensions, materials, and design schemes of each component.

[0159] (2) Monte Carlo program full-heap calculation under full insertion and full lifting of control rods.

[0160] Step 2: Obtain the initial homogenized minority group cross-sectional data under the 25-group structure.

[0161] This yields 25 groups of initial homogenized cross sections for different segments.

[0162] The reactor was calculated using the Monte Carlo program RMC to obtain initial homogenized minority cross section data, as well as baseline data such as accurate power distribution and effective multiplication factor for core program verification.

[0163] Specifically, based on the accurate core model in step 1, Monte Carlo calculations were performed on gas-cooled microreactors under different control rod insertion states (control rod fully lifted and control rod fully inserted) to obtain initial homogenized minority group cross-section data under the 25-group structure, as well as core parameters such as radial and axial segment-level power distribution and effective multiplication factor for core program verification.

[0164] Step 3: Construct the SPH factor iterative calculation process.

[0165] The convergent SPH factor is obtained by calling the core program to perform SPH iteration.

[0166] (I) The specific theoretical model is as follows:

[0167] The steady-state neutron transport equation is expressed as follows:

[0168]

[0169] Where: g is the energy group number. Geometric position;

[0170] Let g be the neutron flux, describing the spatial location of neutrons in the g-th energy group. Net flow rate at the location;

[0171] This is the total cross-section;

[0172] Let be the neutron flux density, used to describe the spatial location of neutrons in the g-th energy group. flux density at the location;

[0173] For the fission spectrum, the normalized probability distribution of neutrons produced by fission in different energy groups g can be generated by Monte Carlo interpolation based on material composition using fission spectrum data in a kernel database (such as ENDF / B).

[0174] k eff The effective multiplication factor is the neutron multiplication capacity of the reactor core.

[0175] The neutron production cross section is obtained by multiplying the neutron yield v by the fission cross section.

[0176] ∑ g'→g (r) is the scattering matrix from group g' to group g, which is the macroscopic cross section of neutrons scattered from energy group g′ to energy group g. It can be calculated by Monte Carlo program based on material composition and scattering nucleus data (such as thermal cross section).

[0177] After introducing Fick's law, the formula is... Substituting into formula (1), we get the following formula (13):

[0178]

[0179] Theoretically, the core calculation program will use formula (13) for calculation, and the cross-section data in this equation mainly comes from the minority cross-section data generated by the Monte Carlo program through the "two-step method" in step 1. However, in actual calculations, the calculation results obtained by this process deviate significantly from the baseline values. This is mainly because the leakage rate and reaction rate are not conserved during the homogenization process of the "two-step method". The SPH factor can be used to adjust the minority cross-section data. Therefore, the SPH factor is introduced, and formula (13) is transformed into formula (14) according to formulas (15) to (18):

[0180]

[0181] Among them: Among them: The diffusion coefficient is a parameter describing the neutron diffusion capability. It can be calculated using the transport cross section output by the Monte Carlo program or directly approximated using diffusion theory.

[0182] μ g is the SPH correction factor for the g-th energy group, used to adjust the minority group cross-section data to conserve the reaction rate and leakage rate;

[0183]

[0184] To ensure the conservation of reaction rate and leakage rate in formula (14), minority group constants need to be corrected using formulas (15) to (18). Typically, the minority group cross-section library in the core program does not directly provide the diffusion coefficient and total cross-section; they are generally represented by the sum of the transport cross-section, absorption cross-section, and scattering cross-section. Therefore, in the process of correcting the minority group constant using the SPH factor, the minority transport cross-section generated by the Monte Carlo program needs to be divided by the SPH factor, while the remaining absorption, scattering, fission, and scattering matrices need to be multiplied by the SPH factor for use by the core program.

[0185] (ii) Call the core program to perform SPH iteration and obtain the converged SPH factor. The specific steps are as follows:

[0186] 1) Initialize the SPH factor

[0187] Set the SPH factor to 1 for all nodal positions corresponding to minority cross sections.

[0188] 2) Flux normalization

[0189] The initial few-group cross section library is loaded into the core program for calculation to obtain the neutron flux density at each node location. Then, it is multiplied by the volume of the corresponding node to obtain the total flux for each energy group.

[0190] By using formula (19), the reference total flux calculated by the Monte Carlo program in one step is divided by the total flux calculated by the core program to obtain the normalization constant.

[0191]

[0192] in, The reference flux density, i.e., the reference neutron flux density output by the Monte Carlo program, can be directly generated through Monte Carlo whole-reactor calculations; φ node,g V represents the neutron flux density of the g-th energy group node. node This represents the volume of the node.

[0193] Then, by multiplying the normalization constant by the neutron flux density of each block calculated by the core program using the following formula (20), the normalized neutron flux density can be obtained.

[0194]

[0195] 3) Calculation of SPH factor

[0196] The SPH factor for the current iteration number can be obtained by dividing the reference neutron flux density of the Monte Carlo program by the normalized neutron flux density of the core program, as shown in formula (21).

[0197]

[0198] Where n is the number of iterations.

[0199] In addition, in order to ensure convergence of different nodes and cross sections, a relaxation factor needs to be introduced to further modify the SPH factor, as shown in formula (22).

[0200]

[0201] Where n is the number of iterations; w is the relaxation factor, which is a weighting factor to smooth the iteration process and prevent oscillations, and its value ranges from 0.4 to 0.6. (In this application, w = 0.5).

[0202] 4) Minority section correction

[0203] Based on the SPH factor obtained in this calculation, the minority cross section is corrected using formulas (15) to (18), and the corrected minority cross section library is loaded into the core program for calculation to obtain the new neutron flux density.

[0204] 5) Calculation of relative deviation of SPH factor

[0205] Based on the SPH factor obtained from the previous calculation and the current SPH factor, calculate the relative deviation ε, as shown in formula (23). If formula (23) is not true, return to step 2) for iterative calculation until formula (23) is true.

[0206]

[0207] 6) SPH factor correction for minority cross sections in different examples

[0208] Based on the full insertion and full extraction of control rods in the gas-cooled microreactor, steps 1)-5) are repeated to obtain the convergence SPH factor for different examples. Finally, the SPH factor is used to correct the cross section for different nodes and energy groups. The 25 energy group structures selected in this invention are shown in Table 1 below.

[0209] Table 1

[0210]

[0211] Step 4: Use convergent SPH to correct the homogenized cross section of group 25.

[0212] The essence of this step is to correct the homogenized cross-sectional data of the Monte Carlo program using the SPH factor, thereby achieving reactivity and flux conservation. The corrected control rod full-lift cross-section is used as the baseline cross-sectional data.

[0213] Step 5: Calculate the cross-sectional parameterized data, that is, calculate the cross-sectional parameterized data of different sections of the entire stack.

[0214] Formula (11) was used to calculate the minority cross section of all segments (fuel assemblies, reflector assemblies, etc.) of the gas-cooled microreactor after SPH correction, and the parameterized cross section data of all segments were obtained. This data reflects the change process of the cross section of different segments under different control rod positions.

[0215] Specifically, the traditional pressurized water reactor calculation program simulates the control rod insertion process by using the cross-section parameterization method. That is, the cross-sectional change rate of the control rod segment is calculated by formula (11), and then the cross-section of the control rod segment is corrected using this data. The cross-sections of the remaining segments are all based on the cross-sectional data of the control rod not being inserted.

[0216]

[0217] Where, ∑ cr＝1 This represents the corrected minority group cross section under the fully inserted control rod state;

[0218] This represents the corrected few-group cross section under the fully lifted control rod state;

[0219] Cr represents the control rod insertion percentage; Cr=1 indicates the control rod is fully inserted, and Cr=0 indicates the control rod is fully withdrawn.

[0220] Due to the small size, strong leakage, and large mean free path of neutrons in gas-cooled microreactors, the overall energy spectrum and cross-section of the reactor core change during the insertion of control rods. Ignoring the change in the cross-section of non-fuel assemblies with the proportion of control rod insertion would introduce a large deviation. Therefore, this invention incorporates formula (11) into all nodes of the entire reactor core to obtain parameterized cross-section data for all nodes of the entire reactor core.

[0221] Step 6: Construct the small group cross-section database. That is, the core diffusion procedure group 25 cross-section database.

[0222] Based on the reference cross section and cross section parameterization data obtained in steps 4 and 5, a minority cross section database for use by the core program is constructed. The core program interpolates the problem-related minority cross section database according to the actual problem (control rod position and burn-out depth) so that it can be used by the core program.

[0223] Step 7: Comparison of gas-cooled microreactor core parameters.

[0224] Based on the problem-related minority cross-section database obtained in step 6, a core program based on neutron diffusion theory is used to perform calculations to obtain core parameters such as power distribution and effective multiplication factor of the gas-cooled microreactor core under different burn-up points and different control rod insertion states. The calculation results are then compared with the Monte Carlo program to test the accuracy and reliability of the present invention.

[0225] In one example, Table 2 shows the calculated effective proliferation factor for different control rod insertion states. Figure 3 The power distribution and relative deviations under full control rod lift and full insertion conditions are shown. Calculation results show that the SPH-corrected minority cross section proposed in this invention is accurate, with relative deviations of the effective multiplication factor of 120.9 pcm (per mille) and 208 pcm, respectively. The relative deviation of the core power distribution is within ±0.5%, and the calculation time is within 1 second, proving that the reference cross section data of this invention is accurate and reliable.

[0226] Table 2

[0227]

[0228] 1 pcm = 0.00001

[0229] For the calculation examples with different control rod positions, this invention selected four control rod positions of a gas-cooled microreactor (control rod fully extended, control rod inserted 1 / 3, control rod inserted 2 / 3, and control rod fully inserted), mainly to test the correctness of the cross-section parameterization data of this invention. The traditional method, used in pressurized water reactor core design, ignores the change in the cross-section of non-control rod components with the control rod insertion percentage; the improved method used in this invention is a global cross-section parameterization method, which simultaneously considers the change in the cross-section of all core components with the control rod insertion percentage.

[0230] Table 3 shows the calculation results of different processing methods under different control rod positions. Figures 4 to 7 This demonstrates the power distribution and relative deviation of different processing methods under different control rod positions.

[0231] in, Figure 4 The cross-sectional parameterization of segment-level power distribution and relative deviation of the gas-cooled microreactor core control rod under full lifting conditions is used to determine the cross-sectional parameterization of the segment-level power distribution and relative deviation. Figure 5 The cross-sectional parameterization of the segment-level power distribution and relative deviation of the gas-cooled microreactor core control rods at 1 / 3 insertion point is presented. Figure 6 The cross-sectional parameterized segment-level power distribution and relative deviation of the gas-cooled micro reactor core control rods at 2 / 3 insertion point; Figure 7 The cross-sectional parameterization of segment-level power distribution and relative deviation of the gas-cooled microreactor core control rods under full insertion conditions is used to determine the cross-sectional parameterization of the segment-level power distribution and relative deviation.

[0232] from Figures 4 to 7 As shown in Table 3, the calculation results indicate that when using the core diffusion calculation program to calculate different control rod positions, the traditional method ignores the change in the cross-section of non-control rod components with the control rod insertion ratio, leading to a maximum deviation of the effective multiplication factor exceeding 1000 pcm and a maximum deviation of the power distribution exceeding 4%. However, after processing with the global cross-section parameterization method, the calculation results agree well with the benchmark values, with the relative deviation of the effective multiplication factor within 200 pcm and the relative deviation of the power distribution within 2%. This proves that the global cross-section parameterization method proposed in this paper is stable and reliable, and can accurately simulate the operating conditions of different control rod positions in a gas-cooled microreactor.

[0233] Table 3

[0234]

[0235] 1 pcm = 0.00001

[0236] Step 8: Prediction of control rod position in gas-cooled microreactor

[0237] Due to the harsh environment and mechanical wear, the detected values ​​at the end of the system's lifespan may deviate from the actual rod positions by more than 10 steps. Furthermore, the gas-cooled microreactor has a small number of control rods with high differential value, requiring high accuracy in control rod position. This invention uses the core calculation program in step 6 to calculate the core power distribution data of the control rod positions near the detector's measured signal, converting it into detection readings. The calculated detector readings are then compared with the actual detector readings. Finally, it is determined whether the minimum relative deviation and root mean square error of all detector readings corresponds to the actual rod position.

[0238] In one example, to test the accuracy of the control rod position prediction function of this invention, three different rod positions (the length of the control rod inserted into the core) in a gas-cooled microreactor were selected for testing: 47.35 cm, 97.35 cm, and 147.35 cm. The RMC power distribution of these three rod positions was pre-converted into a reference detector reading using the detector response function. Then, the power of the rod position within ±10 cm of the actual rod position was calculated using a core diffusion program. Finally, this power was converted into a detector reading and compared with the reference detector reading of the actual rod position. Figures 8(a) to 10(b) The relative deviations and root mean square errors (RMSEs) of the 12 detector readings at different rod positions compared to the reference detector reading are shown. Specifically, Figures 8(a) and 8(b) show the relative and RMS deviations of the detector readings at a control rod position of 47.35 cm, respectively. Figures 9(a) and 9(b) show the relative and RMS deviations of the detector readings at a control rod position of 97.35 cm, respectively. Figures 10(a) and 10(b) show the relative and RMS deviations of the detector readings at a control rod position of 147.35 cm, respectively.

[0239] Calculation results show that the power of the global cross-section parameterization method proposed in this invention will show a concave trend near the actual rod position, and the relative deviation and root mean square error are minimized near 46.35cm, 98.35cm and 147.35cm. This is only 1cm away from the actual control rod position, which fully demonstrates that this invention can achieve accurate prediction of the control rod position of the gas-cooled microreactor.

[0240] Example 3:

[0241] like Figure 11 As shown, this embodiment provides a cross-sectional data calculation device 1100, applied to a micro-relay, the device comprising:

[0242] The determination module 1101 is used to determine the initial cross-sectional data of the microreactor under the target operating conditions based on the core structure of the microreactor. The target operating conditions include the operating conditions corresponding to different insertion states of the control rods.

[0243] The iteration module 1102, connected to the determination module, is used to determine the target SPH factor based on the flux comparison-based SPH factor iteration method according to the initial cross-sectional data.

[0244] The first correction module 1103 is connected to the iteration module and is used to correct the initial cross-sectional data according to the target SPH factor to obtain the corrected cross-sectional data under the target working condition.

[0245] Optionally, the iteration module 1102 includes:

[0246] The first acquisition unit is used to execute S201, set n=0, and acquire the nth SPH factor and the initial cross-sectional data;

[0247] The first correction unit is used to perform S202, correct the initial cross-sectional data according to the nth SPH factor, and obtain the nth corrected cross-sectional data;

[0248] The first determining unit is used to perform S203 and determine the nth neutron flux density of each energy group in the core based on the nth correction section data.

[0249] The second determining unit is used to perform S204 and determine the (n+1)th SPH factor based on the nth neutron flux density and Monte Carlo reference neutron flux of each energy group.

[0250] The control unit is used to execute S205, where, if the nth SPH factor and the (n+1th)th SPH factor of each energy group do not meet the convergence condition, n = n+1, and controls the first correction unit, the first determination unit, and the second determination unit to repeat steps S202 to S204.

[0251] The process continues until the nth and (n+1)th SPH factors of each block meet the convergence condition, at which point the (n+1)th SPH factor is determined as the target SPH factor.

[0252] Optionally, the first correction unit includes:

[0253] The first correction subunit is used to correct the initial diffusion coefficient according to the nth SPH factor to obtain the nth corrected diffusion coefficient;

[0254] The second correction sub-unit is used to correct the initial cross-sectional data according to the nth SPH factor to obtain the nth corrected total cross-section;

[0255] The third correction subunit is used to correct the initial neutron production cross section according to the nth SPH factor to obtain the nth corrected neutron production cross section;

[0256] The fourth correction sub-unit is used to correct the initial scattering matrix according to the nth SPH factor to obtain the nth corrected scattering matrix;

[0257] The nth correction cross section data includes the nth correction diffusion coefficient, the nth correction total cross section, the nth correction neutron production cross section, and the nth correction scattering matrix.

[0258] Optionally, the first correction subunit is specifically used for:

[0259] The nth corrected diffusion coefficient is obtained using formula (4):

[0260]

[0261] Where g is the energy group number, For geometric position, For the nth corrected diffusion coefficient, It is the nth SPH factor of the g-th group. Let be the initial diffusion coefficient of the g-th group. Let g be the transport cross section of the g-th group.

[0262] Optionally, the second correction subunit is specifically used for:

[0263] The nth modified total cross section is obtained using formula (5):

[0264]

[0265] Where g is the energy group number, For geometric position, For the nth corrected total cross section, It is the nth SPH factor of the g-th group. Let be the initial total cross section of the g-th group. Let g be the initial absorption cross section of the g-th group. Let g be the initial scattering cross section of the g-th group.

[0266] Optionally, the aforementioned third correction subunit is specifically used for:

[0267] The nth modified neutron production cross section is obtained using formula (6):

[0268]

[0269] Where g is the energy group number, For geometric position, To generate a cross section for the nth modified neutron of the g-th group, It is the nth SPH factor of the g-th group. To generate a cross section for the initial neutrons of the g-th group.

[0270] Optionally, the aforementioned fourth correction subunit is specifically used for:

[0271] The nth corrected scattering matrix is ​​obtained using formula (7):

[0272]

[0273] Where g is the energy group number, For geometric position, For the nth corrected scattering matrix, For the nth SPH factor, ∑ g'→g (r) is the initial scattering matrix.

[0274] Optionally, the first determining unit described above is specifically used for:

[0275] The flux density of the nth neutron is obtained using formula (8):

[0276]

[0277] Where g is the energy group number, For geometric position, For the nth SPH factor, Let n be the neutron flux density of the g-th group. For the fission spectrum, k eff The effective proliferation coefficient, The nth corrected diffusion coefficient for the g-th group. This is the nth corrected total cross section for the g-th group. To generate a cross section for the nth modified neutron of the g-th group, Let n be the nth corrected scattering matrix of the g-th group.

[0278] Optionally, the second determining unit described above is specifically used for:

[0279] The (n+1)th SPH factor is calculated using formulas (9) to (11):

[0280]

[0281] Among them, C g Let g be the normalization constant of the g-th group. As the reference flux density, φ node,g Let V be the neutron flux density of the g-th energy group node. node The volume of the node;

[0282]

[0283] in, The normalized neutron flux density;

[0284]

[0285] Where n+1 is the number of iterations. It is the (n+1)th SPH factor of the g-th group. This represents the baseline flux density during the (n+1)th iteration. This is the normalized neutron flux density calculated during the (n+1)th iteration.

[0286] Optionally, the second determining unit described above is further configured to:

[0287] The (n+1)th SPH factor is corrected using formula (9):

[0288]

[0289] Where n+1 is the number of iterations and w is the relaxation factor.

[0290] Optionally, the above convergence condition is that the nth SPH factor and the (n+1)th SPH factor satisfy formula (10):

[0291]

[0292] Where ε is the relative deviation. It is the nth SPH factor of the g-th group. It is the (n+1)th SPH factor of the g-th group.

[0293] Optionally, the target operating conditions include the control rod fully inserted state and the control rod fully raised state, and the above-mentioned device further includes:

[0294] The calculation module is used to determine the rate of change of the cross section of the micro-pile using formula (11):

[0295]

[0296] Where, ∑ cr＝1 Corrected cross-sectional data for the control rod in its fully inserted state. The corrected cross-sectional data is for the control rod fully extended state. Cr is the control rod insertion fraction. Cr=1 indicates that the control rod is fully inserted, and Cr=0 indicates that the control rod is fully extended.

[0297] The second correction module is used to correct the cross-sectional area of ​​the entire stack segment of the micro-stacking according to the cross-sectional change rate, so as to obtain the corrected cross-sectional area data of the entire stack segment.

[0298] The cross-sectional data calculation device in this embodiment obtains the target SPH factor through an iterative method of flux comparison and corrects the initial cross-sectional data, effectively compensating for errors caused by non-uniformity and structural complexity in diffusion calculations of homogenized cross-sectional data. By accurately calculating the target SPH factor and using it to correct the cross-sectional data, a high degree of consistency between the neutron flux distribution in the diffusion calculation and the flux results from the high-precision Monte Carlo calculation can be ensured, thereby significantly improving the accuracy of minority group cross-sectional data. This improves the accuracy of cross-sectional data calculations for microreactors.

[0299] Example 4:

[0300] This embodiment provides a rod position prediction system, which includes:

[0301] The cross-section data calculation device provided in any of the above embodiments is used to obtain corrected cross-section data under the target working condition;

[0302] The prediction module is used to predict the position of control rods in the microreactor based on the corrected cross-section data under the target operating conditions.

[0303] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0304] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0305] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0306] The aspects of this disclosure have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable scheduling apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable scheduling apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by special-purpose hardware performing the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0307] The above are merely specific embodiments of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for calculating cross-sectional data, characterized in that, Applied to microheaps, the method includes: Based on the core structure of the micro-recharger, the initial cross-sectional data of the micro-recharger under the target operating conditions are determined, and the target operating conditions include the operating conditions corresponding to different insertion states of the control rods. Based on the initial cross-sectional data, the target SPH factor is determined using an iterative method for SPH factor based on flux comparison. The initial cross-sectional data are corrected based on the target SPH factor to obtain the corrected cross-sectional data under the target working condition.

2. The method according to claim 1, characterized in that, The step of determining the target SPH factor based on the flux comparison-based SPH factor iterative method using the initial cross-sectional data specifically includes: S201. Let n = 0, and obtain the nth SPH factor and the initial cross-sectional data; S202. Correct the initial cross-sectional data according to the nth SPH factor to obtain the nth corrected cross-sectional data; S203. Determine the nth neutron flux density of each energy group in the core based on the nth corrected section data; S204. Determine the (n+1)th SPH factor based on the nth neutron flux density and Monte Carlo reference neutron flux of each energy group. S205. If the nth SPH factor and the (n+1)th SPH factor of each energy group do not meet the convergence condition, let n = n+1, and return to execute steps S202 to S204. The nth SPH factor and the (n+1)th SPH factor of each block are determined as the target SPH factor until the convergence condition is met.

3. The method according to claim 2, characterized in that, The initial cross-section data includes the initial diffusion coefficient, initial total cross-section, initial neutron production cross-section, and initial scattering matrix. The step of correcting the initial cross-sectional data according to the nth SPH factor to obtain the nth corrected cross-sectional data specifically includes: The initial diffusion coefficient is corrected based on the nth SPH factor to obtain the nth corrected diffusion coefficient; The initial cross-sectional data are corrected according to the nth SPH factor to obtain the nth corrected total cross-section. The initial neutron production cross section is modified according to the nth SPH factor to obtain the nth modified neutron production cross section; The initial scattering matrix is ​​corrected according to the nth SPH factor to obtain the nth corrected scattering matrix; The nth corrected cross section data includes the nth corrected diffusion coefficient, the nth corrected total cross section, the nth corrected neutron production cross section, and the nth corrected scattering matrix.

4. The method according to claim 3, characterized in that, The step of correcting the initial diffusion coefficient based on the nth SPH factor to obtain the nth corrected diffusion coefficient specifically includes: The nth corrected diffusion coefficient is obtained using formula (1): Where g is the energy group number, For geometric position, For the nth corrected diffusion coefficient, It is the nth SPH factor of the g-th group. Let be the initial diffusion coefficient of the g-th group. Let g be the transport cross section of the g-th group.

5. The method according to claim 3, characterized in that, The step of correcting the initial cross-sectional data according to the nth SPH factor to obtain the nth corrected total cross-section specifically includes: The nth corrected total cross section is obtained using formula (2): Where g is the energy group number, For geometric position, For the nth corrected total cross section, It is the nth SPH factor of the g-th group. Let be the initial total cross section of the g-th group. Let g be the initial absorption cross section of the g-th group. Let g be the initial scattering cross section of the g-th group.

6. The method according to claim 3, characterized in that, The step of correcting the initial neutron production cross section according to the nth SPH factor to obtain the nth corrected neutron production cross section specifically includes: The nth modified neutron generation cross section is obtained using formula (3): Where g is the energy group number, For geometric position, To generate a cross section for the nth modified neutron of the g-th group, It is the nth SPH factor of the g-th group. To generate a cross section for the initial neutrons of the g-th group.

7. The method according to claim 3, characterized in that, The step of correcting the initial scattering matrix according to the nth SPH factor to obtain the nth corrected scattering matrix specifically includes: The nth corrected scattering matrix is ​​obtained using formula (4): Where g is the energy group number, For geometric position, For the nth corrected scattering matrix, For the nth SPH factor, ∑ g'→g (r) is the initial scattering matrix.

8. The method according to claim 2, characterized in that, The determination of the nth neutron flux density of each energy group in the reactor core based on the nth corrected cross section data specifically includes: The flux density of the nth neutron is obtained using formula (5): Where g is the energy group number, For geometric position, For the nth SPH factor, Let n be the neutron flux density of the g-th group. For the fission spectrum, k eff The effective proliferation coefficient, The nth corrected diffusion coefficient for the g-th group. This is the nth corrected total cross section for the g-th group. To generate a cross section for the nth modified neutron of the g-th group, Let n be the nth corrected scattering matrix of the g-th group.

9. The method according to claim 2, characterized in that, The determination of the (n+1)th SPH factor based on the nth neutron flux density and Monte Carlo baseline neutron flux of each energy group specifically includes: The (n+1)th SPH factor is calculated using formulas (6) to (8): Among them, C g Let g be the normalization constant of the g-th group. As the reference flux density, φ node,g Let V be the neutron flux density of the g-th energy group node. node The volume of the node; in, The normalized neutron flux density; Where n+1 is the number of iterations. For the (n+1)th SPH factor of the g-th group, This represents the baseline flux density during the (n+1)th iteration. This is the normalized neutron flux density calculated during the (n+1)th iteration.

10. The method according to claim 9, characterized in that, The determination of the (n+1)th SPH factor based on the nth neutron flux density and Monte Carlo reference neutron flux of each energy group also includes: The (n+1)th SPH factor is corrected using formula (9): Where n+1 is the number of iterations and w is the relaxation factor.

11. The method according to claim 2, characterized in that, The convergence condition is that the nth SPH factor and the (n+1)th SPH factor satisfy formula (10): Where ε is the relative deviation. It is the nth SPH factor of the g-th group. It is the (n+1)th SPH factor of the g-th group.

12. The method according to claim 1, characterized in that, The target operating conditions include the control rod fully inserted state and the control rod fully lifted state, and the method further includes: The rate of change of the cross section of the micro-pile is determined by formula (11): Where, ∑ cr＝1 Corrected cross-sectional data for the control rod in its fully inserted state. The corrected cross-sectional data is for the control rod fully extended state. Cr is the control rod insertion fraction. Cr=1 indicates that the control rod is fully inserted, and Cr=0 indicates that the control rod is fully extended. Based on the cross-sectional change rate, the cross-sectional area of ​​the entire stack segment of the micro-stack is corrected to obtain the corrected cross-sectional area data of the entire stack segment.

13. A method for predicting rod position, characterized in that, The method includes: The cross-sectional data calculation method according to any one of claims 1 to 12 is used to obtain the corrected cross-sectional data under the target working condition. Based on the corrected cross-sectional data under the target operating condition, the control rod position is predicted for the micro-recharger.

14. A cross-sectional data calculation device, characterized in that, Applied to micro-stacking, the device includes: The determination module is used to determine the initial cross-sectional data of the micro-recharger under the target operating condition based on the core structure of the micro-recharger. The target operating condition includes the operating conditions corresponding to different insertion states of the control rods. An iterative module, connected to the determining module, is used to determine the target SPH factor based on the flux comparison SPH factor iterative method according to the initial cross-sectional data. The first correction module, connected to the iteration module, is used to correct the initial cross-sectional data according to the target SPH factor to obtain the corrected cross-sectional data under the target working condition.

15. The apparatus according to claim 14, characterized in that, The iteration module includes: The first acquisition unit is used to execute S201, set n=0, and acquire the nth SPH factor and the initial cross-sectional data; The first correction unit is used to perform S202, correcting the initial cross-sectional data according to the nth SPH factor to obtain the nth corrected cross-sectional data; The first determining unit is used to perform S203 and determine the nth neutron flux density of each energy group in the core based on the nth corrected section data. The second determining unit is used to perform S204 and determine the (n+1)th SPH factor based on the nth neutron flux density and Monte Carlo reference neutron flux of each energy group. The control unit is configured to execute step S205, where, if the nth SPH factor and the (n+1)th SPH factor of each energy group do not meet the convergence condition, set n = n+1, and control the first correction unit, the first determination unit, and the second determination unit to repeat steps S202 to S204. The nth SPH factor and the (n+1)th SPH factor of each block are determined as the target SPH factor until the convergence condition is met.

16. A rod position prediction system, characterized in that, The system includes: The cross-section data calculation device according to any one of claims 14 to 15 is used to acquire corrected cross-section data under target working conditions; The prediction module is used to predict the control rod position of the micro-recharger based on the corrected cross-sectional data under the target working condition.

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