Reactor scattering matrix correction method and device, electronic equipment and storage medium

Abstract

The present disclosure provides a reactor scattering matrix correction method and device, electronic equipment and storage medium, which relates to the technical field of nuclear reactors, and through the adoption of particle transport simulation to obtain the statistical quantity of mean square displacement of neutrons in the reactor medium and to obtain the average scattering angle cosine by inversion to determine the initial first-order scattering matrix, at the same time, the equivalent relationship between the infinite medium model and the target finite geometry is established and the geometric correction factor is calibrated, and in the group constant calculation of the target finite geometry, the correction factor is applied to correct the average scattering angle cosine obtained based on the flux proportionality assumption, and then the corrected first-order scattering matrix is generated, so that the problem that the anisotropic scattering is systematically underestimated due to the dependence on the flux proportionality assumption in the prior art, and the mean square displacement derivation of the infinite medium model cannot adapt to the finite geometric structure such as the reflection layer or super-component, thereby causing the large calculation error of the effective multiplication factor and the significant neutron flux deviation in the reflection layer region, can be solved.

Description

Technical Field

[0001] This disclosure relates to the field of nuclear reactor technology, and in particular to a reactor scattering matrix correction method and apparatus, electronic equipment and storage medium. Background Technology

[0002] Nuclear reactor physics and thermal calculations are the core support for the design of advanced reactors (such as fourth-generation high-temperature gas-cooled reactors and fast-spectrum reactors). Its technical system covers key aspects such as neutron transport modeling, group constant generation, and anisotropic scattering processing.

[0003] Traditional scattering matrix calculations rely on the assumption that "flux moment is proportional to scalar flux," substituting scalar flux for flux moment in the merging calculation, leading to a systematic underestimation of anisotropic scattering characteristics. In systems such as fast-spectrum reactors (where the neutron spectrum is hard and leakage effects are significant), this defect causes substantial errors: the calculation error of the effective multiplication factor can reach 588 pcm, and the relative deviation of neutron flux in the reflector region exceeds 9%.

[0004] Meanwhile, existing technologies also have two limitations: first, Monte Carlo statistics of flux moments are difficult to converge, resulting in low computational efficiency; second, the mean square displacement derivation is based on an infinitely large medium model, which cannot directly adapt to the computational needs of finite geometric structures such as reflectors and meta-components. These problems not only affect the accuracy of core criticality analysis and safety assessment, but also significantly increase engineering verification costs, necessitating the establishment of new physical constraint mechanisms to achieve neutron leakage rate conservation calculations. Summary of the Invention

[0005] This disclosure provides a method and apparatus for correcting reactor scattering matrix, electronic equipment, and storage medium. Its main objective is to at least partially address one of the technical problems in the related art.

[0006] According to a first aspect of this disclosure, a reactor scattering matrix correction method is provided, comprising: The mean square displacement statistics of neutrons in the reactor medium were obtained through particle transport simulation. Based on the mean square displacement statistic, the cosine of the neutron's average scattering angle is calculated by inversion. The initial first-order scattering matrix is ​​determined based on the average scattering angle cosine. An equivalence relationship is established between the infinite medium model and the finite geometry of the target. By comparing the calculation results of the average scattering angle cosine of the two, the geometric correction factor is calibrated. In the calculation of the group constant of the target finite geometry, the geometric correction factor is applied to correct the average scattering angle cosine obtained based on the flux proportionality assumption, thereby generating the corrected first-order scattering matrix.

[0007] Optionally, obtaining the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation includes: The Monte Carlo method was used to simulate the multiple collisions and migrations of neutrons in this medium; The expected value of the square of the straight-line distance between the termination position and the starting position of a neutron after multiple collisions is used as the mean square displacement statistic.

[0008] Optionally, the step of inverting and calculating the mean scattering angle cosine of the neutron based on the mean square displacement statistic includes: Based on the monotonic functional relationship between mean square displacement and average scattering angle cosine in neutron transport theory; The mean scattering angle cosine numerical solution satisfying the mean square displacement statistic is obtained by using a numerical iterative algorithm.

[0009] Optionally, establishing the equivalence between the infinite medium model and the target's finite geometry, and calibrating the generated geometric correction factor by comparing the calculated results of the average scattering angle cosine of the two models, includes: For a specified region within the finite geometry of the target, establish an infinitely large homogeneous medium model with the same material composition. The average scattering angle cosine was calculated on the infinite medium model using the flux proportionality assumption method and the neutron mean square displacement conservation method, respectively. The ratio of the cosine of the average scattering angle obtained by the two methods is determined as the geometric correction factor.

[0010] Optionally, applying the geometric correction factor to correct the average scattering angle cosine obtained based on the flux proportionality assumption includes: The average scattering angle cosine directly calculated under the flux proportionality assumption is multiplied by the geometric correction factor to obtain the corrected average scattering angle cosine. Multiplying the corrected average scattering angle cosine by the corresponding zero-order scattering cross section yields the corrected first-order self-scattering cross section.

[0011] Optional, also includes: After generating the corrected first-order scattering matrix, the corrected first-order scattering matrix is ​​deployed in the multi-group neutron transport calculation of the reactor core to obtain the reactor's effective multiplication factor and neutron flux distribution.

[0012] According to a second aspect of this disclosure, a reactor scattering matrix correction device is provided, comprising: The acquisition unit is used to acquire the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation; The calculation unit is used to invert and calculate the average scattering angle cosine of the neutron based on the mean square displacement statistic. A determining unit is used to determine an initial first-order scattering matrix based on the average scattering angle cosine; The calibration unit is used to establish the equivalence between the infinite medium model and the finite geometry of the target. By comparing the calculation results of the average scattering angle cosine of the two, the geometric correction factor is generated. The generation unit is used to apply the geometric correction factor to correct the average scattering angle cosine obtained based on the flux proportionality assumption in the group constant calculation of the target finite geometry, thereby generating the corrected first-order scattering matrix.

[0013] Optionally, the acquisition unit is also used for: The Monte Carlo method was used to simulate the multiple collisions and migrations of neutrons in this medium; The expected value of the square of the straight-line distance between the termination position and the starting position of a neutron after multiple collisions is used as the mean square displacement statistic.

[0014] Optionally, the computing unit is also used for: Based on the monotonic functional relationship between mean square displacement and average scattering angle cosine in neutron transport theory; The mean scattering angle cosine numerical solution satisfying the mean square displacement statistic is obtained by using a numerical iterative algorithm.

[0015] Optionally, the calibration unit is also used for: For a specified region within the finite geometry of the target, establish an infinitely large homogeneous medium model with the same material composition. The average scattering angle cosine was calculated on the infinite medium model using the flux proportionality assumption method and the neutron mean square displacement conservation method, respectively. The ratio of the cosine of the average scattering angle obtained by the two methods is determined as the geometric correction factor.

[0016] Optionally, the generating unit is also used for: The average scattering angle cosine directly calculated under the flux proportionality assumption is multiplied by the geometric correction factor to obtain the corrected average scattering angle cosine. Multiplying the corrected average scattering angle cosine by the corresponding zero-order scattering cross section yields the corrected first-order self-scattering cross section.

[0017] Optional, also includes: The deployment unit is used to deploy the corrected first-order scattering matrix in the multi-group neutron transport calculation of the reactor core after generating the corrected first-order scattering matrix, so as to obtain the effective multiplication factor and neutron flux distribution of the reactor.

[0018] According to a third aspect of this disclosure, an electronic device is provided, comprising: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method described in the first aspect above.

[0019] According to a fourth aspect of this disclosure, a non-transitory computer-readable storage medium is provided storing computer instructions, wherein the computer instructions are configured to cause the computer to perform the method described in the first aspect above.

[0020] According to a fifth aspect of this disclosure, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the method described in the first aspect above.

[0021] The reactor scattering matrix correction method, apparatus, electronic equipment, and storage medium disclosed herein obtain the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation and invert the mean scattering angle cosine to determine the initial first-order scattering matrix. Simultaneously, an equivalence relationship is established between the infinite medium model and the target finite geometry, and a geometric correction factor is calibrated. This correction factor is then applied to correct the mean scattering angle cosine obtained based on the flux proportionality assumption in the group constant calculation of the target finite geometry, thereby generating the corrected first-order scattering matrix. Therefore, this method can solve the problems in existing technologies where the reliance on the flux proportionality assumption leads to a systematic underestimation of anisotropic scattering, and the inability of the mean square displacement derivation of the infinite medium model to adapt to finite geometric structures such as reflectors or supercomponents, resulting in large calculation errors of the effective multiplication factor and significant neutron flux deviations in the reflector region. This method achieves the technical effects of eliminating the error introduced by the assumption that the flux moment is proportional to the scalar flux in traditional methods, significantly reducing the calculation error of the effective multiplication factor, improving neutron flux distribution deviation, achieving neutron leakage rate conservation, and improving the accuracy and engineering adaptability of core neutronics calculations in finite geometric scenarios.

[0022] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0023] The accompanying drawings are provided to better understand this solution and do not constitute a limitation of this disclosure. Wherein: Figure 1 A schematic flowchart illustrating a reactor scattering matrix correction method provided in this embodiment of the disclosure; Figure 2 This is a schematic diagram of the structure of a reactor scattering matrix correction device provided in an embodiment of the present disclosure; Figure 3 A schematic block diagram of an example electronic device provided for embodiments of this disclosure. Detailed Implementation

[0024] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0025] The reactor scattering matrix correction method, apparatus, electronic device, and storage medium of this disclosure are described below with reference to the accompanying drawings.

[0026] Figure 1 This is a schematic flowchart of a reactor scattering matrix correction method provided in an embodiment of the present disclosure.

[0027] like Figure 1 As shown, the method includes the following steps: Step 101: Obtain the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation.

[0028] In the embodiments of this disclosure, in obtaining the mean square displacement statistics of neutrons, particle transport simulation techniques are first employed. For the medium involved in reactor operation (i.e., the various material environments that neutrons encounter during transport within the reactor), the transport behavior of neutrons within this medium is simulated to obtain the mean square displacement statistics, which reflect the positional changes of neutrons during transport. This statistic characterizes the square of the linear distance between the final position and the initial position of the neutron after a certain transport process, and is crucial foundational data for subsequent derivation of neutron scattering-related parameters. As one implementation method, a Monte Carlo-type particle transport calculation program (such as the NECP-MCX program) can be used to simulate the transport process of monoenergetic neutrons in a specific reactor medium (e.g., an infinitely large homogeneous medium), and the mean square displacement statistics of neutrons in that scenario can be directly obtained through the program's statistical functions.

[0029] By directly obtaining the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation, direct and accurate basic data can be provided for subsequent related calculations based on these statistics (such as cosine inversion of the mean scattering angle). This avoids the errors that may be introduced by relying on empirical assumptions to indirectly obtain relevant parameters in traditional methods, and effectively ensures the reliability of the initial data in subsequent neutronics calculations.

[0030] Step 102: Based on the mean square displacement statistics, the cosine of the neutron's average scattering angle is calculated by inversion.

[0031] In the embodiments of this disclosure, after obtaining the mean square displacement statistics of neutrons, an inversion calculation logic is established between the two based on the inherent correlation (such as monotonic correspondence) between the mean square displacement statistics and the cosine of the neutron average scattering angle (i.e., a key parameter characterizing the directional change characteristics during neutron scattering). This logic processes and calculates the mean square displacement statistics to invert and obtain the cosine of the average scattering angle, which reflects the neutron scattering direction characteristics. The core of this inversion process lies in utilizing the neutron transport position information contained in the mean square displacement statistics to transform it into a parameter characterizing the neutron scattering direction, providing crucial basic data for the subsequent construction of the scattering matrix. As one implementation method, based on the monotonic relationship between the mean square displacement statistics and the cosine of the average scattering angle, a search algorithm or other calculation method can be used to invert the mean square displacement statistics of neutrons in an infinitely large homogeneous medium obtained through Monte Carlo simulation, directly obtaining the cosine of the neutron scattering angle in that medium scenario.

[0032] The mean scattering angle cosine is obtained by inverting the mean square displacement statistics. By leveraging the inherent correlation between the two, the complex process of directly calculating the flux moment to obtain the scattering angle-related parameters in traditional methods is avoided. This reduces the errors introduced by flux moment calculation or assumptions, and provides reliable scattering direction characteristic parameters to support the accurate construction of the subsequent first-order scattering matrix.

[0033] Step 103: Determine the initial first-order scattering matrix based on the average scattering angle cosine.

[0034] In the embodiments of this disclosure, after obtaining the average scattering angle cosine of the neutron, based on the inherent physical correlation between the average scattering angle cosine and the initial first-order scattering matrix (i.e., the first-order scattering characteristic matrix used to characterize the scattering transfer law of neutrons between different energy groups or within the same energy group, and which has not been modified by the geometric scene), corresponding calculation logic and relational formulas are constructed. The average scattering angle cosine is then processed and calculated using this logic and relational formulas to determine the initial first-order scattering matrix that can initially reflect the neutron scattering transfer characteristics. The core of this process lies in transforming the average scattering angle cosine, which characterizes the neutron scattering direction, into a matrix form describing the neutron scattering energy or spatial transfer law, providing a basic model for subsequent scattering matrix correction adapted to finite geometric scenes. As one implementation method, based on the calculation formula corresponding to the neutron mean square displacement conservation method, combined with parameters such as the average scattering angle cosine and the zero-order scattering cross section, the first-order scattering cross section for the transfer from a specific energy group to a target energy group can be calculated, and then the initial first-order scattering matrix can be determined from this first-order scattering cross section.

[0035] Determining the initial first-order scattering matrix based on the cosine of the average scattering angle allows for the direct construction of a scattering transfer model using key characteristic parameters of the neutron scattering direction. This avoids the systematic errors that may be introduced by relying on the flux proportionality assumption in traditional methods to construct the scattering matrix, ensuring that the initial first-order scattering matrix can more realistically reflect the neutron scattering characteristics and laying a reliable foundation for the accurate correction of the scattering matrix in subsequent finite geometric scenarios.

[0036] Step 104: Establish the equivalence relationship between the infinite medium model and the target's finite geometry. By comparing the calculation results of the average scattering angle cosine of the two models, calibrate the generated geometric correction factor.

[0037] In the embodiments of this disclosure, after determining the initial first-order scattering matrix, the differences in neutron transport characteristic calculations between the infinite medium model upon which the initial calculations rely and the finite geometry of the target commonly used in actual reactor applications (i.e., geometric structures with clearly defined boundaries and size constraints, such as reflectors and meta-components) are addressed. By analyzing the commonalities and characteristics of both in the neutron scattering process, an equivalence relationship is established that can link the calculation logic of the scattering parameters of the two. Based on this, the mean scattering angle cosine is calculated under the infinite medium model and the target finite geometry, respectively. By comparing the differences between these two sets of calculation results, a geometric correction factor is determined to compensate for changes in neutron transport characteristics under the finite geometry scenario. This correction factor can quantify the impact of the infinite medium assumption and the actual situation of finite geometry on the mean scattering angle cosine calculation results, providing key parameter support for subsequent scattering matrix correction adapted to finite geometry. As one implementation method, an infinitely large model can be established for each homogenized region based on the arrangement of the reflective layer or the super-component model. The average scattering angle cosine of the infinite model can be calculated by using the flux proportionality assumption method and the neutron mean square displacement conservation method respectively. Then, the average scattering angle cosine obtained based on the flux proportionality assumption under the finite geometry of the target can be combined with the difference comparison calibration to generate a geometric correction factor.

[0038] By establishing equivalent relationships and comparing the geometric correction factor calibrated by the cosine of the average scattering angle, the problem that the infinite medium model cannot be directly adapted to the calculation of finite geometric structures is effectively solved. This provides a reliable basis for subsequently correcting the initial first-order scattering matrix to a form that conforms to the actual finite geometric scenario, and significantly improves the adaptability of the scattering matrix calculation to the actual geometric structure of the reactor.

[0039] Step 105: In the calculation of the group constant of the target finite geometry, the geometric correction factor is applied to correct the average scattering angle cosine obtained based on the flux proportionality assumption, thereby generating the corrected first-order scattering matrix.

[0040] In the embodiments of this disclosure, during the calculation of group constants for the target finite geometry (group constants are core parameters characterizing the interaction between neutrons and matter in the reactor medium and supporting the calculation of multi-group neutron transport), the initial average scattering angle cosine under this scenario is first obtained using the flux proportionality assumption. Then, the calibrated geometric correction factor is applied to this initial average scattering angle cosine. Through correction operations, the parameter deviation caused by the flux proportionality assumption underestimating anisotropic scattering and the difference between the infinite medium model and the actual finite geometry is compensated for, resulting in a corrected average scattering angle cosine that conforms to the actual transport characteristics of the target finite geometry. Based on this, combined with the inherent physical relationship between the corrected average scattering angle cosine and the first-order scattering matrix (such as through the derivation logic of the first-order self-scattering cross section), further computational processing is carried out to finally generate a corrected first-order scattering matrix that adapts to the target finite geometry scenario and can accurately reflect the neutron scattering and transfer law. As one implementation method, in the calculation of the finite geometric group constants of targets such as the reflector layer or supercomponents of a fast-spectrum reactor, the average scattering angle cosine under the geometry can be obtained first based on the flux proportionality assumption, and then the geometric correction factor calibrated in the previous step can be substituted to complete the correction. Then, the corrected first-order self-scattering cross section can be calculated based on the corrected average scattering angle cosine, and finally, the corrected first-order scattering matrix can be generated based on the cross section relationship.

[0041] By applying a geometric correction factor to correct the mean scattering angle cosine in the calculation of the target finite geometry group constant, the errors caused by the traditional flux proportionality assumption and the adaptation of the infinite medium model to finite geometry are effectively eliminated. The generated corrected first-order scattering matrix can better fit the neutron scattering characteristics of the actual reactor geometry, significantly improving the accuracy of neutronics calculations in finite geometry scenarios and providing reliable support for key engineering calculations such as core criticality analysis and leakage rate assessment.

[0042] The reactor scattering matrix correction method disclosed herein obtains the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation and inverts to obtain the mean scattering angle cosine to determine the initial first-order scattering matrix. Simultaneously, it establishes an equivalence relationship between the infinite medium model and the target finite geometry and calibrates the geometric correction factor. This correction factor is then applied to correct the mean scattering angle cosine obtained based on the flux proportionality assumption in the group constant calculation of the target finite geometry, thereby generating the corrected first-order scattering matrix. Therefore, it can solve the problems in existing technologies where the reliance on the flux proportionality assumption leads to a systematic underestimation of anisotropic scattering, and the inability of the mean square displacement derivation of the infinite medium model to adapt to finite geometric structures such as reflectors or supercomponents, resulting in large calculation errors of the effective multiplication factor and significant neutron flux deviations in the reflector region. This method achieves the technical effects of eliminating the error introduced by the assumption that the flux moment is proportional to the scalar flux in traditional methods, significantly reducing the calculation error of the effective multiplication factor, improving neutron flux distribution deviation, achieving neutron leakage rate conservation, and improving the accuracy and engineering adaptability of core neutronics calculations in finite geometric scenarios.

[0043] As a specific embodiment of this disclosure, based on the basic scheme, the method of obtaining the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation is further defined as follows: using the Monte Carlo method to simulate the multiple collisions and migration processes of neutrons in the medium; and calculating the expected value of the square of the straight-line distance between the termination position and the starting position of the neutron after multiple collisions, as the mean square displacement statistics.

[0044] Specifically, when obtaining the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation, the Monte Carlo method is used for simulation calculation. During the simulation, a physical model is first constructed to determine the transport behavior of neutrons within the reactor medium. This model clarifies that each "single flight" of a neutron from its initial position to the next collision point must follow an exponential decay law of the neutron's single flight length. Based on this law, multiple collisions and migration paths of neutrons in the medium are simulated sequentially. After each collision and migration to a new position, the neutron's current spatial position is recorded in real time. Coordinates; after the neutron completes a preset number of collisions and migrations, the square of the straight-line distance between the starting and ending positions is calculated based on the recorded starting and ending position coordinates; subsequently, under the same reactor medium conditions and simulation parameters, the above neutron collision and migration simulation process is repeated to collect multiple sets (such as thousands or even tens of thousands of sets) of "square values ​​of the straight-line distance between the ending and starting positions" under different simulation scenarios; finally, all collected square values ​​are statistically analyzed, and the expected value of the square value is obtained by calculating the arithmetic mean, and this expected value is directly used as the required neutron mean square displacement statistic.

[0045] By using the Monte Carlo method to simulate the neutron collision migration process with high fidelity, and combining the expectation method of statistical calculation of multiple sets of data, the actual transport physics of neutrons in the reactor medium can be fully reproduced. This effectively avoids the statistical bias caused by the simplified model, and makes the obtained mean square displacement statistics more accurate and reliable. It provides high-precision data support for the subsequent inversion calculation of the mean scattering angle cosine, and further ensures the reliability of the subsequent scattering matrix calculation.

[0046] As a specific embodiment of this disclosure, based on the basic scheme, the step of inverting and calculating the average scattering angle cosine of the neutron according to the mean square displacement statistic includes: based on the monotonic functional relationship between the mean square displacement and the average scattering angle cosine in neutron transport theory; and solving for the numerical solution of the average scattering angle cosine that satisfies the mean square displacement statistic through a numerical iterative algorithm.

[0047] Specifically, when calculating the cosine of the average scattering angle of neutrons based on the mean square displacement statistic, the monotonic functional relationship between the mean square displacement and the cosine of the average scattering angle, established in neutron transport theory, is first clarified. This relationship is specifically expressed as follows: Where is the statistically obtained mean square displacement of neutrons, and n is the number of neutron flights in the medium. Let λ be the mean free path of neutrons in the medium, and λ be the cosine of the mean scattering angle to be calculated. Since the mean free path decreases monotonically with increasing λ, there is a unique monotonic relationship between the two. A numerical iterative algorithm is then used to solve the problem. First, the initial iteration range of the mean scattering angle cosine is set according to its physical meaning (usually 0 to 1, since the physical range of the scattering angle cosine is [-1, 1], and neutron scattering in the reactor medium is mostly forward scattering, so the initial range can be limited to 0 to 1). The midpoint of the interval is taken as the initial iteration value and substituted into the above monotonic function relationship to calculate the theoretical mean square displacement. The theoretical mean square displacement is compared with the actual mean square displacement statistics obtained through particle transport simulation. If the theoretical value is greater than the actual statistical value, it indicates that the mean scattering angle cosine of the current iteration is too small, and the upper boundary of the iteration interval needs to be adjusted to the current iteration value; otherwise, the lower boundary is adjusted. The above iterative steps of "substitution calculation - difference comparison - interval adjustment" are repeated, and the interval range is reduced after each iteration until the relative deviation between the theoretical mean square displacement and the actual statistical value is less than a preset threshold (e.g., 10). -6 At this point, the corresponding iteration value is the numerical solution of the mean scattering angle cosine that satisfies the mean square displacement statistic.

[0048] Based on the clearly defined monotonic function relationship in neutron transport theory, the uniqueness of the solution during the inversion process is ensured, avoiding the confusion of multiple solutions or no solution. At the same time, the numerical iterative algorithm can accurately approximate the true value of the average scattering angle cosine by gradually narrowing the iteration interval. Compared with the traditional empirical formula estimation method, this significantly reduces the inversion error and provides high-precision parameter support for the subsequent determination of the initial first-order scattering matrix based on the average scattering angle cosine, further ensuring the accuracy of the scattering matrix calculation.

[0049] As a specific embodiment of this disclosure, based on the basic scheme, the equivalence relationship between the established infinite medium model and the target finite geometry is further defined. By comparing the calculation results of the average scattering angle cosine of the two, a geometric correction factor is calibrated and generated, including: establishing an infinitely large homogeneous medium model with the same material composition for a specified region in the target finite geometry; calculating the average scattering angle cosine on the infinite medium model using the flux proportionality assumption method and the neutron mean square displacement conservation method respectively; and determining the ratio of the average scattering angle cosine obtained by the two methods as the geometric correction factor.

[0050] Specifically, when establishing the equivalence between the infinite medium model and the target finite geometry and calibrating the geometric correction factor, firstly, for a designated homogenized region (e.g., fuel zone or reflector region) within the target finite geometry (e.g., the reflector layer or meta-component model of a reactor), the material composition of this region (including nuclide types, mass fraction, or atomic fraction of each nuclide) is analyzed. Based on this, an infinitely large homogenized medium model with the exact same material composition as this designated region is constructed—ensuring that the model is infinitely large only in terms of geometric scale, and that its material properties are completely consistent with the designated region of the target finite geometry, thus establishing an equivalence between the two at the material level. Next, the mean scattering angle cosine is calculated on this infinitely large homogenized medium model: on the one hand, the traditional flux proportionality assumption method is adopted, that is, assuming that the neutron flux moment is proportional to the scalar flux. Through the group constant calculation logic under this assumption, the mean scattering angle cosine of the corresponding region in the infinite medium model is statistically obtained and denoted as . On the other hand, using the neutron mean square displacement conservation method, and based on the mean square displacement statistics obtained through previous particle transport simulations, the mean scattering angle cosine is calculated for the same region in this infinite medium model (denoted as ). Finally, based on the calculation results of the two methods mentioned above, the calculation is performed... and The ratio (i.e.) This ratio is directly determined as the geometric correction factor for the specified finite geometry of the target region.

[0051] By constructing an infinite medium model with the same material composition, it is ensured that the infinite model and the specified region of the target finite geometry are consistent in terms of the fundamental material properties of neutron scattering, providing an equivalent benchmark for subsequent comparative calculations. At the same time, by determining the correction factor through the ratio of the calculation results of the two methods, the difference between the flux proportionality assumption method and the neutron mean square displacement conservation method in the infinite medium scenario can be accurately quantified. This provides a clear and reliable quantitative basis for subsequent correction of the average scattering angle cosine obtained based on the flux proportionality assumption in the finite geometry, effectively improving the accuracy of scattering parameter correction in the finite geometry scenario.

[0052] As a specific embodiment of this disclosure, based on the basic scheme, the application of the geometric correction factor to correct the average scattering angle cosine obtained based on the flux proportionality assumption includes: multiplying the average scattering angle cosine directly calculated under the flux proportionality assumption with the geometric correction factor to obtain the corrected average scattering angle cosine; and multiplying the corrected average scattering angle cosine with the corresponding zero-order scattering cross section to obtain the corrected first-order self-scattering cross section.

[0053] Specifically, when applying a geometric correction factor to correct the average scattering angle cosine obtained based on the flux proportionality assumption, firstly, in the group constant calculation scenario of the target finite geometry (such as a reactor reflector or a supercomponent), following the calculation logic of the traditional flux proportionality assumption method, and combining the structural parameters (such as size and boundary conditions) and the properties of the medium material of the finite geometry, the average scattering angle cosine of the neutron in this scenario is directly calculated and denoted as . Subsequently, the geometric correction factors previously calibrated for a finite geometrically specified region of the target were retrieved. ,Will and Perform multiplication, that is This calculation compensates for the underestimation of anisotropic scattering due to the flux proportionality assumption, yielding a corrected mean scattering angle cosine that conforms to the actual transport characteristics of the target's finite geometry. Next, the zero-order scattering cross section related to neutron scattering is obtained in a finite geometrically specified region of the target. (This cross section is a fundamental parameter characterizing the scattering probability of neutrons within the same energy group in group constant calculations, and can be obtained through nuclear database queries or previous basic calculations.) The corrected mean scattering angle cosine is then used. and To perform multiplication, that is: Finally, the corrected first-order self-scattering cross section is obtained.

[0054] By applying a geometric correction factor through simple and direct multiplication, the cosine deviation of the average scattering angle introduced by the flux proportionality assumption in finite geometric scenarios can be efficiently eliminated, ensuring that the corrected average scattering angle cosine closely matches the actual transport characteristics. At the same time, based on the multiplication of this correction parameter with the zero-order scattering cross section, the corrected first-order self-scattering cross section can be accurately obtained, providing key cross section parameter support for the subsequent generation of a corrected first-order scattering matrix adapted to finite geometry, and further improving the accuracy of the scattering matrix in characterizing the actual neutron scattering process in the reactor.

[0055] As a specific embodiment of this disclosure, based on the basic scheme, the embodiment of this disclosure further includes: after generating the corrected first-order scattering matrix, deploying the corrected first-order scattering matrix in the multi-group neutron transport calculation of the reactor core to obtain the effective multiplication factor and neutron flux distribution of the reactor.

[0056] Specifically, after generating the corrected first-order scattering matrix, when deploying it in the multi-group neutron transport calculation of the reactor core, the basic input parameters required for the multi-group neutron transport calculation are first defined, including the core's geometric model (such as core dimensions, fuel assembly arrangement, reflector position, etc.), the multi-group constants of each region (in addition to the corrected first-order scattering matrix, these also include absorption cross-section, fission cross-section, zero-order scattering cross-section, etc.), and core boundary conditions (such as reflection boundaries, vacuum boundaries, etc.). Subsequently, the corrected first-order scattering matrix is ​​used as the core scattering parameter and imported into the multi-group neutron transport calculation program (such as the NECP-MCX multi-group mode), replacing the uncorrected first-order scattering matrix obtained based on the traditional flux proportionality assumption. This ensures that the program uses scattering matrix data adapted to the actual characteristics of the finite geometry when simulating the scattering and transfer process of neutrons between different energy groups within the reactor core. During the calculation, the program simulates the entire life cycle of neutrons from generation and transport (including collisions, scattering, absorption, leakage, etc.) to their destruction, based on the input geometric model and boundary conditions. At the same time, the program records the neutron multiplication and leakage in the reactor core in real time through the built-in statistical module to calculate the reactor's effective multiplication factor (Keff). In addition, the program also counts the number of neutrons at different spatial locations in the reactor core (such as different coordinate points in the fuel zone and reflector zone) under each energy group, thereby generating neutron flux distribution data of the reactor core (including the spatial distribution law and energy spectrum distribution characteristics of the flux).

[0057] By deploying the corrected first-order scattering matrix in multi-group neutron transport calculations, the errors introduced by the traditional uncorrected matrix are effectively avoided. This makes the calculated effective multiplication factor closer to the actual critical characteristics of the reactor core, and the neutron flux distribution more closely matches the real transport law. This provides high-precision data support for reactor core criticality analysis, power distribution optimization, and safety assessment, and reduces engineering design risks caused by calculation deviations.

[0058] It should be noted that the embodiments of this disclosure may include multiple steps. For ease of description, these steps are numbered, but these numbers are not a limitation on the execution time slots or execution order between the steps; these steps can be implemented in any order, and the embodiments of this disclosure do not limit this.

[0059] Corresponding to the reactor scattering matrix correction method described above, this disclosure also proposes a reactor scattering matrix correction device. Since the device embodiments of this disclosure correspond to the method embodiments described above, details not disclosed in the device embodiments can be referred to the method embodiments described above, and will not be repeated here.

[0060] Figure 2 This is a schematic diagram of the structure of a reactor scattering matrix correction device provided in an embodiment of this disclosure, as shown below. Figure 2 As shown, it includes: The acquisition unit 21 is used to acquire the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation; The calculation unit 22 is used to invert and calculate the average scattering angle cosine of the neutron based on the mean square displacement statistic. The determining unit 23 is used to determine the initial first-order scattering matrix based on the average scattering angle cosine; Calibration unit 24 is used to establish the equivalence relationship between the infinite medium model and the finite geometry of the target. By comparing the calculation results of the average scattering angle cosine of the two, the geometric correction factor is generated. The generation unit 25 is used to apply the geometric correction factor to correct the average scattering angle cosine obtained based on the flux proportionality assumption in the group constant calculation of the target finite geometry, thereby generating the corrected first-order scattering matrix.

[0061] The reactor scattering matrix correction device disclosed herein obtains the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation and inverts to obtain the mean scattering angle cosine to determine the initial first-order scattering matrix. Simultaneously, it establishes an equivalence relationship between the infinite medium model and the target finite geometry and calibrates the geometric correction factor. This correction factor is then applied to correct the mean scattering angle cosine obtained based on the flux proportionality assumption in the group constant calculation of the target finite geometry, thereby generating the corrected first-order scattering matrix. Therefore, it can solve the problems in existing technologies where the reliance on the flux proportionality assumption leads to a systematic underestimation of anisotropic scattering, and the inability of the mean square displacement derivation of the infinite medium model to adapt to finite geometric structures such as reflectors or super-components, resulting in large calculation errors of the effective multiplication factor and significant neutron flux deviations in the reflector region. This achieves the technical effects of eliminating the error introduced by the assumption that the flux moment is proportional to the scalar flux in traditional methods, significantly reducing the calculation error of the effective multiplication factor, improving neutron flux distribution deviation, achieving neutron leakage rate conservation, and improving the accuracy and engineering adaptability of core neutronics calculations in finite geometric scenarios.

[0062] Furthermore, in one possible implementation of this embodiment, the acquisition unit 21 is also used for: The Monte Carlo method was used to simulate the multiple collisions and migrations of neutrons in this medium; The expected value of the square of the straight-line distance between the termination position and the starting position of a neutron after multiple collisions is used as the mean square displacement statistic.

[0063] Furthermore, in one possible implementation of this embodiment, the computing unit 22 is also used for: Based on the monotonic functional relationship between mean square displacement and average scattering angle cosine in neutron transport theory; The mean scattering angle cosine numerical solution satisfying the mean square displacement statistic is obtained by using a numerical iterative algorithm.

[0064] Furthermore, in one possible implementation of this embodiment, the calibration unit 24 is also used for: For a specified region within the finite geometry of the target, establish an infinitely large homogeneous medium model with the same material composition. The average scattering angle cosine was calculated on the infinite medium model using the flux proportionality assumption method and the neutron mean square displacement conservation method, respectively. The ratio of the cosine of the average scattering angle obtained by the two methods is determined as the geometric correction factor.

[0065] Furthermore, in one possible implementation of this embodiment, the generation unit 25 is also used for: The average scattering angle cosine directly calculated under the flux proportionality assumption is multiplied by the geometric correction factor to obtain the corrected average scattering angle cosine. Multiplying the corrected average scattering angle cosine by the corresponding zero-order scattering cross section yields the corrected first-order self-scattering cross section.

[0066] Furthermore, in one possible implementation of this embodiment, such as Figure 2 As shown, it also includes: Deployment unit 26 is used to deploy the corrected first-order scattering matrix in the multi-group neutron transport calculation of the reactor core after generating the corrected first-order scattering matrix, so as to obtain the effective multiplication factor and neutron flux distribution of the reactor.

[0067] It should be noted that the foregoing explanation of the method embodiments also applies to the apparatus of this embodiment, and the principle is the same, so it is not limited in this embodiment.

[0068] According to embodiments of this disclosure, this disclosure also provides an electronic device, a readable storage medium, and a computer program product.

[0069] Figure 3 A schematic block diagram of an example electronic device 300 that can be used to implement embodiments of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0070] like Figure 3As shown, the electronic device 300 includes a computing unit 301, which can perform various appropriate actions and processes based on a computer program stored in ROM (Read-Only Memory) 302 or a computer program loaded from storage unit 308 into RAM (Random Access Memory) 303. The RAM 303 may also store various programs and data required for the operation of the electronic device 300. The computing unit 301, ROM 302, and RAM 303 are interconnected via a bus 304. An I / O (Input / Output) interface 305 is also connected to the bus 304.

[0071] Multiple components in electronic device 300 are connected to I / O interface 305, including: input unit 306, such as keyboard, mouse, etc.; output unit 307, such as various types of displays, speakers, etc.; storage unit 308, such as disk, optical disk, etc.; and communication unit 309, such as network card, modem, wireless transceiver, etc. Communication unit 309 allows electronic device 300 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0072] The computing unit 301 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 301 include, but are not limited to, CPUs (Central Processing Units), GPUs (Graphics Processing Units), various special-purpose AI (Artificial Intelligence) computing chips, various computing units running machine learning model algorithms, DSPs (Digital Signal Processors), and any suitable processor, controller, microcontroller, etc. The computing unit 301 performs the various methods and processes described above, such as the reactor scattering matrix correction method. For example, in some embodiments, the reactor scattering matrix correction method can be implemented as a computer software program tangibly contained in a machine-readable medium, such as storage unit 308. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 300 via ROM 302 and / or communication unit 309. When the computer program is loaded into RAM 303 and executed by the computing unit 301, one or more steps of the methods described above can be performed. Alternatively, in other embodiments, the computing unit 301 may be configured to perform the aforementioned reactor scattering matrix correction method by any other suitable means (e.g., by means of firmware).

[0073] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, FPGAs (Field Programmable Gate Arrays), ASICs (Application-Specific Integrated Circuits), ASSPs (Application-Specific Standard Products), SOCs (System-on-Chips), CPLDs (Complex Programmable Logic Devices), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0074] The program code used to implement the methods of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0075] In the context of this disclosure, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, RAM, ROM, EPROM (Electrically Programmable Read-Only Memory) or flash memory, optical fiber, CD-ROM (Compact Disc Read-Only Memory), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0076] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (Cathode-Ray Tube) or LCD (Liquid Crystal Display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0077] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or computing systems that include middleware components (e.g., application servers), or computing systems that include frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include LANs (Local Area Networks), WANs (Wide Area Networks), the Internet, and blockchain networks.

[0078] Computer systems can include clients and servers. Clients and servers are generally geographically separated and typically interact via communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. A server can be a cloud server, also known as a cloud computing server or cloud host, a hosting product within the cloud computing service system that addresses the shortcomings of traditional physical hosts and VPS (Virtual Private Server) services, such as high management difficulty and weak business scalability. Servers can also be servers for distributed systems or servers incorporating blockchain technology.

[0079] It's important to note that artificial intelligence (AI) is the study of enabling computers to simulate certain human thought processes and intelligent behaviors (such as learning, reasoning, thinking, and planning). It encompasses both hardware and software technologies. AI hardware technologies generally include sensors, dedicated AI chips, cloud computing, distributed storage, and big data processing. AI software technologies primarily include computer vision, speech recognition, natural language processing, machine learning / deep learning, big data processing, and knowledge graph technologies.

[0080] The various numerical designations such as "first," "second," etc., used in this disclosure are merely for ease of description and are not intended to limit the scope of the embodiments of this disclosure, nor do they indicate a sequential order.

[0081] At least one of the features described in this disclosure can also be described as one or more, and multiple features can be two, three, four or more, and this disclosure does not impose any limitations. In the embodiments of this disclosure, for a technical feature, the technical features in that technical feature are distinguished by "first", "second", "third", "A", "B", "C" and "D", etc., and there is no sequential order or size order among the technical features described by "first", "second", "third", "A", "B", "C" and "D".

[0082] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0083] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for correcting a reactor scattering matrix, characterized in that, include: The mean square displacement statistics of neutrons in the reactor medium were obtained through particle transport simulation. Based on the mean square displacement statistic, the cosine of the neutron's average scattering angle is calculated by inversion. The initial first-order scattering matrix is ​​determined based on the average scattering angle cosine. An equivalence relationship is established between the infinite medium model and the finite geometry of the target. By comparing the calculation results of the average scattering angle cosine of the two, the geometric correction factor is calibrated. In the calculation of the group constant of the target finite geometry, the geometric correction factor is applied to correct the average scattering angle cosine obtained based on the flux proportionality assumption, thereby generating the corrected first-order scattering matrix.

2. The method according to claim 1, characterized in that, The process of obtaining the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation includes: The Monte Carlo method was used to simulate the multiple collisions and migrations of neutrons in this medium; The expected value of the square of the straight-line distance between the termination position and the starting position of a neutron after multiple collisions is used as the mean square displacement statistic.

3. The method according to claim 1, characterized in that, The step of inverting and calculating the cosine of the neutron's average scattering angle based on the mean square displacement statistic includes: Based on the monotonic functional relationship between mean square displacement and average scattering angle cosine in neutron transport theory; The mean scattering angle cosine numerical solution satisfying the mean square displacement statistic is obtained by using a numerical iterative algorithm.

4. The method according to claim 1, characterized in that, The process of establishing an equivalence relationship between the infinite medium model and the finite geometry of the target, and calibrating the generated geometric correction factor by comparing the calculated results of the average scattering angle cosine of the two models, includes: For a specified region within the finite geometry of the target, establish an infinitely large homogeneous medium model with the same material composition. The average scattering angle cosine was calculated on the infinite medium model using the flux proportionality assumption method and the neutron mean square displacement conservation method, respectively. The ratio of the cosine of the average scattering angle obtained by the two methods is determined as the geometric correction factor.

5. The method according to claim 1, characterized in that, The application of the geometric correction factor to correct the average scattering angle cosine obtained based on the flux proportionality assumption includes: The average scattering angle cosine directly calculated under the flux proportionality assumption is multiplied by the geometric correction factor to obtain the corrected average scattering angle cosine. Multiplying the corrected average scattering angle cosine by the corresponding zero-order scattering cross section yields the corrected first-order self-scattering cross section.

6. The method according to claim 1, characterized in that, Also includes: After generating the corrected first-order scattering matrix, the corrected first-order scattering matrix is ​​deployed in the multi-group neutron transport calculation of the reactor core to obtain the reactor's effective multiplication factor and neutron flux distribution.

7. A reactor scattering matrix correction device, characterized in that, include: The acquisition unit is used to acquire the mean square displacement statistics of neutrons in the reactor medium through particle transport simulation; The calculation unit is used to invert and calculate the average scattering angle cosine of the neutron based on the mean square displacement statistic. A determining unit is used to determine an initial first-order scattering matrix based on the average scattering angle cosine; The calibration unit is used to establish the equivalence between the infinite medium model and the finite geometry of the target. By comparing the calculation results of the average scattering angle cosine of the two, the geometric correction factor is generated. The generation unit is used to apply the geometric correction factor to correct the average scattering angle cosine obtained based on the flux proportionality assumption in the group constant calculation of the target finite geometry, thereby generating the corrected first-order scattering matrix.

8. An electronic device, characterized in that, include: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-6.

9. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to perform the method according to any one of claims 1-6.

10. A computer program product, characterized in that, Includes a computer program that, when executed by a processor, implements the method according to any one of claims 1-6.

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