A method and system for simultaneous synchronization solving of a nuclear reactor critical boron concentration

Abstract

The application belongs to the technical field of nuclear reactor multi-physical field coupling calculation, and discloses a nuclear reactor critical boron concentration simultaneous synchronization solving method and system, which first determines a critical state parameter constraint relationship and a multi-physical field coupling calculation model; then assembles boron concentration, critical state parameters and other physical field variables into global unknowns; then constructs a residual calculation method corresponding to the global unknowns, wherein the boron concentration residual is constructed according to the corresponding relationship between the boron concentration and the critical state parameters; finally, simultaneous nonlinear iteration solving is adopted, all variables are updated synchronously by calculating the correction amount of the global unknowns, and the critical boron concentration and the reactor state are output until the convergence criterion is met. The application unifies the critical boron concentration solving and the multi-physical field state solving into the same nonlinear simultaneous framework, avoids the nested loop of the traditional hierarchical search, and significantly improves the solving stability and the calculation efficiency under the strong coupling scene.

Description

Technical Field

[0001] This invention belongs to the technical field of multiphysics coupling calculation of nuclear reactors, and more specifically, relates to a method and system for simultaneous solution of critical boron concentration in nuclear reactors. Background Technology

[0002] In the steady-state analysis of nuclear reactors, especially pressurized water reactors, the critical boron concentration is a crucial parameter characterizing the reactor's reactive equilibrium state. It is also a fundamental quantity for determining the core power distribution, temperature distribution, coolant state, and initial conditions for subsequent transient analyses. For actual core operating conditions, solving for the critical boron concentration is not simply a neutronics reactivity problem, but a strongly nonlinear multiphysics coupling problem involving neutronics, thermal-hydraulic feedback, and boron concentration.

[0003] Existing methods for determining the critical boron concentration typically employ a hierarchical iterative structure. This involves searching for the boron concentration in the outer layer, and then performing a multi-physics coupling iteration involving neutronics and thermal-hydraulic fields in the inner layer for each candidate boron concentration. Once the coupling converges, the boron concentration is updated based on the effective multiplication coefficient or the deviation of reactivity from the critical condition. While this approach is relatively straightforward, its drawbacks become increasingly apparent as core model refinement increases and feedback coupling strengthens.

[0004] First, the nested outer boron concentration search and inner multiphysics coupling iteration lead to repeated calls to the neutronics and thermohydraulic solutions, resulting in a deep computational hierarchy and high computational cost. Second, traditional hierarchical solution structures typically treat boron concentration as an external control parameter, failing to integrate it with critical state parameters and feedback state variables as unknowns within the same nonlinear system. This necessitates approximating the consistency between critical conditions and feedback states through multiple iterations, which can lead to slow convergence, coupling lag, and even oscillations in strongly nonlinear scenarios. Third, using Newton-like methods to improve convergence speed usually requires explicitly constructing the global Jacobian matrix of the coupled system. However, in large-scale, multiphysics coupled nuclear reactor analysis problems, the global Jacobian matrix is ​​large, complex, and difficult to construct, often requiring intrusive modifications to each independent physics solution module, hindering the reuse and maintenance of existing program modules.

[0005] Therefore, a new method for solving the critical boron concentration of nuclear reactors is needed. Without disrupting the independent encapsulation structure of the existing neutronics and thermal-hydraulic solution modules, the boron concentration, critical state parameters, and reactor state-related physical field variables should be integrated into the same simultaneous solution framework to improve the solution efficiency and convergence stability of strongly coupled nonlinear problems. Summary of the Invention

[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method and system for simultaneously solving the critical boron concentration of nuclear reactors. This solves the technical problems of nested outer-layer boron concentration search and inner-layer coupled iteration, numerous repeated solutions, and slow convergence, oscillation, or instability under strong nonlinear feedback conditions.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for simultaneously solving the critical boron concentration of a nuclear reactor is provided, comprising the following steps: S1: Determine the critical state parameter constraints and multiphysics coupling calculation model used for solving the critical boron concentration. The critical state parameters are used to characterize the degree to which the reactor deviates from the critical state. S2: Based on the critical state parameter constraint relationship and multi-physics field coupling calculation model determined in step S1, select boron concentration, critical state parameters and other physical field variables related to reactor state as variables to be solved, and assemble them into global unknowns. S3: Based on the critical state parameter constraint relationship determined in step S1, the multiphysics coupling calculation model, and the global unknowns assembled in step S2, construct the residual calculation method corresponding to the global unknowns; wherein, the residual corresponding to the boron concentration is constructed according to the correspondence between the boron concentration and the critical state parameter, and the residuals corresponding to the other physical field variables are constructed according to the corresponding physical field solution model or solution module. S4: Based on the residual calculation method constructed in step S3, the global unknown is solved nonlinearly and iteratively using a simultaneous synchronous solution method, and the global unknown is updated synchronously by calculating the correction amount of the global unknown; S5: Determine whether the updated global unknowns meet the preset convergence criteria; if they do, output the critical boron concentration and its corresponding reactor state; if they do not, return to step S4 and continue execution until the preset convergence criteria are met.

[0008] Preferably, the critical state parameter is the effective proliferation coefficient. or reactivity coefficient The critical state parameter constraints are as follows: .

[0009] Preferably, the global unknowns include at least the boron concentration and the critical state parameters, and the other physical field variables related to the reactor state include one or more of neutronics variables and thermal-hydraulic variables; the global unknowns are expressed as:

[0010] in, For boron concentration, The critical state parameter is... These are the physical field variables related to the reactor state.

[0011] Preferably, the neutronics variables include one or more of neutron flux density, power distribution, and reaction rate distribution; the thermal-hydraulic variables include one or more of coolant temperature, coolant density, coolant enthalpy, fuel temperature, and cladding temperature; the critical state parameters are calculated by the neutronics solution module and are explicitly introduced as separate key unknowns in the simultaneous solution.

[0012] Preferably, in step S3, the residual calculation corresponding to the boron concentration is constructed based on the boron concentration response update relationship, which is established using the pseudo-secant method. That is, an approximate solution relationship for the deviation of the boron concentration from the critical state parameter is established based on the approximately linear relationship between the boron concentration and the critical state parameter. The approximate solution relationship satisfies:

[0013] in, This is the correction amount for boron concentration. This represents the deviation of the critical state parameters from the target critical condition. These are approximation coefficients.

[0014] Preferably, in step S3, the residual calculation method is constructed based on a first-order coupled response calculation for the current global unknown; let... Based on the current global unknowns The updated global unknowns obtained from performing a single coupled response calculation are then expressed as: .

[0015] Preferably, the simultaneous solution in step S4 is achieved using a nonlinear iterative solution method; the nonlinear iterative solution method is achieved using the Jacobi-Newton-Krylov method; before performing the nonlinear iterative solution, the initial boron concentration or initial global unknown is determined by a finite number of conventional boron linear search calculations.

[0016] Preferably, the approximation coefficient The correspondence between boron concentration and critical state parameters is determined based on a finite number of conventional boron linear search calculations performed before the simultaneous synchronous nonlinear iterative solution begins:

[0017] in, , The boron concentrations obtained from two conventional linear boron search calculations are shown below. , These are the corresponding critical state parameters; Alternatively, it can be preset to a fixed value based on experience.

[0018] Preferably, the convergence determination in step S5 is based on both the update amount of the global unknown and the residual or response results corresponding to the physical field variables.

[0019] According to another aspect of the present invention, a simultaneous solution system for the critical boron concentration of a nuclear reactor is provided, employing the above-described method, comprising: The initialization configuration module is used to configure the critical state parameter constraint relationship and multiphysics coupling calculation model for solving the critical boron concentration, and to determine the initial values ​​of boron concentration, critical state parameters and other physical field variables required for simultaneous solution. The variable assembly module is used to select boron concentration, critical state parameters, and reactor state-related physical field variables as variables to be solved, assemble them into global unknowns, and establish the correspondence between the variables to be solved and the global unknowns. The residual construction module is used to construct the residual calculation method corresponding to the global unknown based on the critical state parameter constraint relationship, the multi-physics field coupled calculation model and the global unknown. The residual corresponding to the boron concentration is constructed according to the correspondence between the boron concentration and the critical state parameter, and the residuals corresponding to the other physical field variables are constructed according to the corresponding physical field solution model or solution module. The solution module is used to perform nonlinear iterative solution of the global unknowns based on the residual calculation method and using a simultaneous synchronous solution method. By calculating the correction amount of the global unknowns, the global unknowns are updated synchronously. The convergence determination module is used to determine whether the updated global unknowns meet the preset convergence criteria, and outputs the critical boron concentration and its corresponding reactor state when the preset convergence criteria are met.

[0020] In summary, compared with the prior art, the method and system for simultaneous solution of critical boron concentration in nuclear reactors provided by this invention have the following advantages: 1. This invention integrates boron concentration, critical state parameters, and reactor state-related physical field variables into a unified global unknown and solves them simultaneously, avoiding the multi-layered loop structure formed by the traditional outer boron concentration search and inner coupled iteration, thereby reducing redundant calculations and improving solution efficiency.

[0021] 2. This invention constructs a unified residual calculation method, which incorporates critical condition deviations and multi-physics field state deviations into the same framework for characterization and correction, enabling all unknowns to converge collaboratively in the same nonlinear system, thereby improving the consistency of the solution and the stability of convergence.

[0022] 3. This invention does not require explicit construction of the globally coupled Jacobian matrix and can maintain the encapsulation structure of each independent physics solution module, thus having good engineering implementability and program compatibility.

[0023] 4. The convergence determination of this invention considers both the global unknown update quantity and the physical field residual or coupling response result, which can take into account the consistency between numerical iteration convergence and critical state and multi-physics coupling state, thereby improving the reliability of the solution result.

[0024] 5. This invention is applicable to the search problem of critical boron concentration in nuclear reactors, especially to the combined analysis of neutronics and thermal-hydraulic processes in large-scale, high-fidelity and strongly coupled scenarios, and has good scalability and engineering application value. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the overall process for the simultaneous solution of the critical boron concentration in a nuclear reactor as described in this invention.

[0026] Figure 2 This is a schematic diagram of the radial model when performing three-dimensional pin-by-pin level fine modeling of the entire core of a pressurized water reactor according to the present invention.

[0027] Figure 3 This is a comparison chart of the total computation time of the method of the present invention and the traditional method under example working condition 1.

[0028] Figure 4 This is a comparison chart of the total computation time of the method of the present invention and the traditional method under example working condition 2. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0030] Please see Figure 1 This embodiment provides a method for simultaneously solving the critical boron concentration in a nuclear reactor. This method is used to simultaneously solve for the critical boron concentration, critical state parameters, and reactor state-related physical field variables within a unified nonlinear iterative framework. The method includes the following steps: S1: Determine the critical state parameter constraints and multiphysics coupling calculation model used for solving the critical boron concentration. The critical state parameters are used to characterize the degree to which the reactor deviates from the critical state. Specifically, the first step is to determine the critical state parameter constraints and the multiphysics coupled calculation model used to solve for the critical boron concentration. It should be noted that step S1 does not establish a complete set of simultaneous solution equations, but rather provides the basic physical description and computational capabilities for subsequent global unknown assembly and residual calculation methods.

[0031] The critical state parameter characterizes the degree to which the reactor deviates from the critical state. In this embodiment, the critical state parameter can be taken as the effective multiplication coefficient. or reactivity coefficient When the critical state parameter is taken as the effective multiplication coefficient, the critical state parameter constraint can be expressed as follows: .

[0032] When the critical state parameter is taken as reactive, the critical state constraint can also be equivalently expressed as: .

[0033] The multiphysics coupling model employs neutronics and thermo-hydraulic coupling to describe the coupling relationship between the neutronics state and the thermo-hydraulic state under given boron concentration and feedback conditions. The neutronics solution module solves for the neutronics state based on the current feedback parameters and outputs the power distribution; the thermo-hydraulic solution module solves for the thermo-hydraulic state based on the power distribution; then, based on the thermo-hydraulic state and boron concentration, cross-sectional feedback calculations are performed to update the cross-sectional parameters required for neutronics, and the results are returned to the neutronics solution module, forming a closed-loop coupling relationship.

[0034] In this embodiment, the neutronics solution module and the thermal-hydraulic solution module maintain independent encapsulation structures and achieve collaborative calls through variable mapping interface, data transfer interface and residual calculation interface.

[0035] It should be noted that the critical state parameter constraint relationship and multiphysics coupling calculation model mentioned in step S1 can be obtained based on existing reactor analysis models, existing solution programs or corresponding solution modules. The improvement focus of this invention is not on the basic model itself, but on constructing a unified residual based on the basic model and solving the boron concentration and coupled physical fields simultaneously.

[0036] S2: Based on the critical state parameter constraint relationship and multi-physics field coupling calculation model determined in step S1, select boron concentration, critical state parameters and other physical field variables related to reactor state as variables to be solved, and assemble them into global unknowns. Specifically, after establishing the simultaneous solution model, the variables to be solved are selected and assembled to form a global unknown. The global unknown includes at least boron concentration and critical state parameters, and may further include other physical field variables related to the reactor state; these other physical field variables may include one or more of neutronics variables and thermal-hydraulic variables. Within the general framework of this invention, the global unknown can be expressed as:

[0037] in, Indicates boron concentration. Represents the critical state parameters. Other physical field variables related to the reactor state.

[0038] In this embodiment, the critical state parameter is calculated by the neutronics solution module and can therefore be regarded as one of the neutronics-related quantities; however, since it is used to characterize the degree to which the reactor deviates from the critical state, it is explicitly introduced as a separate key unknown in the simultaneous solution.

[0039] In this embodiment, the critical state parameter is taken as the effective multiplication coefficient. Combining neutronics and thermo-hydraulic coupling in a multiphysics field, the global unknowns are specifically taken as follows:

[0040] in, Neutron flux density For coolant enthalpy and This refers to the fuel temperature. It should be noted that the effective multiplication coefficient... From a physical perspective, it can be regarded as one of the neutron science related quantities. However, since it is used to characterize the degree to which a reactor deviates from the critical state, it is proposed as a critical state parameter and explicitly included in the global unknown quantity in the simultaneous solution framework of this invention.

[0041] The above expressions are merely examples. This invention does not limit the global unknowns to include all variables, nor does it limit the order of the variables. As long as the selected variables, together with the boron concentration and critical state parameters, can characterize the simultaneous state in the critical boron concentration search process, the method of this invention can be used to solve the problem.

[0042] S3: Based on the critical state parameter constraint relationship determined in step S1, the multiphysics coupling calculation model, and the global unknowns assembled in step S2, construct the residual calculation method corresponding to the global unknowns; wherein, the residual corresponding to the boron concentration is constructed according to the correspondence between the boron concentration and the critical state parameter, and the residuals corresponding to the other physical field variables are constructed according to the corresponding physical field solution model or solution module. Specifically, for the boron concentration variable, in this embodiment, the residual calculation corresponding to the boron concentration is preferably constructed based on the boron concentration response update relationship. Further, the boron concentration response update relationship can be established using the pseudo-secant method, that is, based on the approximately linear relationship between the boron concentration and the critical state parameter, the following approximate solution relationship can be established:

[0043] in, This is the correction amount for boron concentration. This represents the deviation of the critical state parameters from the target critical condition. These are approximation coefficients.

[0044] In this embodiment, the approximation coefficient The boron concentration and critical state parameters can be determined based on the correspondence between the boron concentration and the critical state parameters obtained from a finite number of traditional boron linear search calculations prior to the start of the simultaneous synchronous nonlinear iterative solution. For example:

[0045] in, , The boron concentrations obtained from two conventional linear boron search calculations are shown below. , These are the corresponding critical state parameters. Further, the approximation coefficients... Alternatively, it can be preset as a fixed value based on experience, or determined using other equivalent approximation relationships.

[0046] In this embodiment, the critical state parameter is taken as the effective multiplication coefficient. Therefore, the response update relationship for boron concentration is:

[0047]

[0048] in, , The boron concentrations obtained from two conventional linear boron search calculations are respectively. , The corresponding effective multiplication coefficient.

[0049] For the physical field variables other than boron concentration, optionally, a coupled response calculation can be performed on the current global unknowns by calling the corresponding physical field solution model or solution module to obtain the updated physical field variables. Let... Indicates based on the current global unknowns The updated global unknowns obtained from performing a single coupled response calculation can be expressed as: .

[0050] In this embodiment, the global residual vector can be specifically represented as:

[0051] in, This is the residual component of boron concentration. For the residual components of the effective proliferating line, The residual component of neutron flux density This is the residual component of the coolant enthalpy. This represents the residual component of fuel temperature.

[0052] In this embodiment, for the current global unknown, the specific implementation process of the residual calculation method includes the following operations: (1) Obtain the boron concentration, effective multiplication coefficient, neutron flux density, coolant enthalpy and fuel temperature from the current global unknowns, and start a coupled response calculation; (2) Calculate the boron concentration correction based on the approximate solution relationship between boron concentration and critical state parameters, and update the boron concentration accordingly; (3) Calculate the required thermal-hydraulic feedback parameters for cross-sectional feedback based on the coolant enthalpy and fuel temperature, such as coolant density and Doppler temperature; (4) Based on the updated boron concentration and thermal-hydraulic feedback parameters, reconstruct and update the neutronics cross-section parameters; (5) Call the neutronics solution module to solve for the updated effective multiplication coefficient and neutron flux density distribution; (6) Calculate the power distribution based on the updated neutron flux density distribution and transfer the power distribution to the thermal-hydraulic calculation module; (7) Call the thermal hydraulics solution module to solve for the updated coolant enthalpy and fuel temperature; (8) Combine the updated boron concentration, effective multiplication factor, neutron flux density, coolant enthalpy and fuel temperature to form the updated global unknowns, and end the coupled response calculation; (9) For the current global unknown and the updated global unknown after the coupled response calculation, the difference between them is used to obtain the residual corresponding to the current global unknown.

[0053] The characteristic of this residual construction method is that it does not require explicit access to the complete form of the discrete equations inside each physical solution module, nor does it require explicit construction of the global coupling Jacobian matrix. It only needs to be able to complete a coupling response calculation based on a given state and return the updated result.

[0054] S4: Based on the residual calculation method constructed in step S3, the global unknown is solved nonlinearly and iteratively using a simultaneous synchronous solution method, and the global unknown is updated synchronously by calculating the correction amount of the global unknown; In this embodiment, the simultaneous solution in step S4 is implemented using a nonlinear iterative solution method. This nonlinear iterative solution method can be a Newton-like method, a quasi-Newton-like method, a Krylov-like nonlinear solution method, or other algorithms suitable for simultaneous nonlinear problems.

[0055] Preferably, the simultaneous solution in step S4 is implemented using the Jacobi-less Newton-Krylov method. Let the global unknowns of the current Newton iteration step be... The correction amount is The residual is Then the following Newton correction relationship can be established:

[0056] in, Let be the Jacobian matrix of the residuals with respect to the global unknowns. The global unknowns can be updated based on the calculated corrections, i.e.:

[0057] in, This is the updated global unknown.

[0058] To avoid explicitly constructing a globally coupled Jacobian matrix, in some embodiments, the Jacobian-vector product can be approximated using a finite difference approach, for any vector. ,have:

[0059] in, For perturbations, Indicates to Along vector Direction applied amplitude is The residual vector is calculated after a small perturbation. In this embodiment, the perturbation amount... Determined based on machine precision, the scale of unknowns, and the vector norm.

[0060] In the solution phase of the linear subproblem, the correction amount can be obtained using the Krylov subspace method. For example, the generalized minimum residual method.

[0061] Furthermore, before performing the aforementioned nonlinear iterative solution, the initial boron concentration or initial global unknown can be determined through a finite number of conventional boron linear search calculations for simultaneous solution. Specifically, a finite number of conventional boron concentration searches and coupled calculations can be performed first to obtain several sets of data corresponding to boron concentration and critical state parameters, and based on this, the initial boron concentration, initial global unknown, and approximate coefficients in the boron concentration response calculation relationship can be determined.

[0062] S5: Determine whether the updated global unknowns meet the preset convergence criteria; if they do, output the critical boron concentration and its corresponding reactor state; if they do not, return to step S4 and continue execution until the preset convergence criteria are met.

[0063] In this embodiment, convergence is determined based on both the update of the global unknowns and the residuals or responses corresponding to the physical field variables. Preferably, at least one of the following can be used as the convergence criterion:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] in, This is the residual convergence threshold. The threshold for the change in boron concentration. The convergence threshold for the critical state parameter. The neutron flux density convergence threshold. The convergence threshold of coolant enthalpy. This is the fuel temperature convergence threshold.

[0070] When the preset convergence criteria are met, the output results may include: critical boron concentration, corresponding effective multiplication coefficient, corresponding neutron flux density distribution, corresponding coolant enthalpy distribution, corresponding fuel temperature distribution, power distribution, and other thermal-hydraulic feedback parameter field distributions.

[0071] This invention also provides a simultaneous solution system for the critical boron concentration of a nuclear reactor for implementing the above method, comprising: The initialization configuration module is used to configure the critical state parameter constraint relationship and multiphysics coupling calculation model for solving the critical boron concentration, and to determine the initial values ​​of boron concentration, critical state parameters and other physical field variables required for simultaneous solution. The variable assembly module is used to select boron concentration, critical state parameters, and reactor state-related physical field variables as variables to be solved, assemble them into global unknowns, and establish the correspondence between the variables to be solved and the global unknowns. The residual construction module is used to construct the residual calculation method corresponding to the global unknown based on the critical state parameter constraint relationship, the multi-physics field coupled calculation model and the global unknown. The residual corresponding to the boron concentration is constructed according to the correspondence between the boron concentration and the critical state parameter, and the residuals corresponding to the other physical field variables are constructed according to the corresponding physical field solution model or solution module. The solution module is used to perform nonlinear iterative solution of the global unknowns based on the residual calculation method and using a simultaneous synchronous solution method. By calculating the correction amount of the global unknowns, the global unknowns are updated synchronously. The convergence determination module is used to determine whether the updated global unknowns meet the preset convergence criteria, and outputs the critical boron concentration and its corresponding reactor state when the preset convergence criteria are met.

[0072] The system can be deployed on a general-purpose computer platform, a parallel computing platform, or a high-performance computing platform for the simultaneous solution of the critical boron concentration and coupled feedback state of a nuclear reactor.

[0073] To further illustrate the effectiveness of the method of the present invention, this embodiment selects a core-coupled critical boron concentration calculation scenario based on a discrete ordinate neutron transport model and a single-channel thermal-hydraulic model to compare and illustrate the method of the present invention with the traditional hierarchical iterative method. It should be understood that this embodiment is only used to illustrate the application effect of the method of the present invention under a specific model combination and does not constitute a limitation on the scope of protection of the present invention.

[0074] For the three-dimensional pin-by-pin level fine-grained modeling of the entire pressurized water reactor core, please refer to the radial model. Figure 2 The calculations were performed under Example Condition 1 (full power operation) and Example Condition 2 (zero power operation), respectively. Table 1 shows the comparison results between the method of this invention and the traditional method under the above two typical conditions. The critical boron concentration is expressed in ppm (parts per million), and the effective multiplication coefficient error is expressed in pcm (per 10^10). -5 The magnitude of the reactive change; Figure 3 This demonstrates a comparison of the total computation time of the two methods under Example Condition 1. Figure 4 The comparison of the total computation time of the two methods is shown under Example Condition 2.

[0075]

[0076] As shown in Table 1, under Example Condition 1, the critical boron concentration obtained by the method of this invention is 1678.29 ppm, while the critical boron concentration obtained by the traditional method is 1678.25 ppm, and the two results are basically consistent. The corresponding effective multiplication coefficient errors are 2.4 pcm and 2.1 pcm, respectively, both achieving high calculation accuracy. Based on this, the total calculation time of the method of this invention is 18.88 minutes, while the total calculation time of the traditional method is 125.70 minutes, corresponding to a speedup ratio of 6.66.

[0077] Under Example Condition 2, the critical boron concentration obtained by the method of this invention is 1335.61 ppm, while the critical boron concentration obtained by the conventional method is 1335.51 ppm, showing good consistency between the two. The corresponding effective multiplication coefficient errors are 1.5 pcm and 2.5 pcm, respectively, indicating that the method of this invention can maintain high critical solution accuracy even under zero-power conditions. Meanwhile, the total computation time of the method of this invention is 14.32 minutes, while the total computation time of the conventional method is 105.48 minutes, corresponding to a speedup ratio of 7.36.

[0078] The above results demonstrate that the method of this invention can significantly shorten the total computation time under both full-power and zero-power typical operating conditions, while ensuring the accuracy of the critical boron concentration solution and critical state parameters. This is because the method of this invention integrates boron concentration, critical state parameters, and reactor state-related physical field variables into the same global unknown, and performs simultaneous and synchronous solutions based on a unified residual calculation method. This avoids the redundant calculations caused by the nested outer-layer boron concentration search and inner-layer multi-physics coupling iteration in traditional methods. Especially for scenarios with large computational scales and strong coupling feedback, such as the full-core three-dimensional pin-by-pin level refined model, the method of this invention can more fully demonstrate the computational efficiency advantages of the simultaneous and synchronous solution framework.

[0079] Combination Figure 3 and Figure 4 The results show that, under different operating conditions, the total computation time of the method of the present invention is significantly lower than that of the traditional method, indicating that the method of the present invention is not only effective under a specific operating condition, but also has good versatility and stability under different power levels and different feedback characteristics.

[0080] It should be noted that the above comparative embodiments are only used to illustrate the effects of the method of the present invention, and do not mean that the present invention is only applicable to the combination of discrete ordinate neutron transport model and single-channel thermal-hydraulic model. For other physical model combinations such as diffusion model, characteristic line neutron transport model, sub-channel thermal-hydraulic model, fuel performance model, etc., as long as the global unknown assembly, residual calculation method and simultaneous synchronous solution framework described in the present invention are used, the corresponding technical effects can also be obtained.

[0081] In summary, this invention proposes a method and system for simultaneously solving the critical boron concentration in nuclear reactors. This method unifies the boron concentration, critical state parameters, and reactor state-related physical field variables into a global unknown quantity, and constructs a residual calculation method corresponding to this global unknown quantity. This allows for the collaborative solution of the critical boron concentration and coupled feedback state within a unified simultaneous solution framework.

[0082] Compared with existing hierarchical boron concentration search and separate coupling iterative methods, this invention can reduce the repetitive calculations caused by multi-layered loops, improve the solution stability and efficiency of strongly nonlinear coupled problems, and achieve engineering solutions while maintaining the encapsulation structure of independent neutronics and thermal-hydraulic solution modules. It has good engineering application value and scalability.

[0083] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for simultaneously solving the critical boron concentration of a nuclear reactor, characterized in that: Includes the following steps: S1: Determine the critical state parameter constraints and multiphysics coupling calculation model used for solving the critical boron concentration. The critical state parameters are used to characterize the degree to which the reactor deviates from the critical state. S2: Based on the critical state parameter constraint relationship and multi-physics field coupling calculation model determined in step S1, select boron concentration, critical state parameters and other physical field variables related to reactor state as variables to be solved, and assemble them into global unknowns. S3: Based on the critical state parameter constraint relationship determined in step S1, the multiphysics coupling calculation model, and the global unknowns assembled in step S2, construct the residual calculation method corresponding to the global unknowns; wherein, the residual corresponding to the boron concentration is constructed according to the correspondence between the boron concentration and the critical state parameter, and the residuals corresponding to the other physical field variables are constructed according to the corresponding physical field solution model or solution module. In step S3, the residual calculation corresponding to the boron concentration is constructed based on the boron concentration response update relationship. This boron concentration response update relationship is established using the pseudo-secant method, that is, based on the approximately linear relationship between the boron concentration and the critical state parameter, an approximate solution relationship for the deviation of the boron concentration from the critical state parameter is established. This approximate solution relationship satisfies: in, This is the correction amount for boron concentration. This represents the deviation of the critical state parameters from the target critical condition. These are approximate coefficients; The residual calculation method is constructed based on a single coupled response calculation for the current global unknown; let... Based on the current global unknowns The updated global unknowns obtained from performing a single coupled response calculation are then expressed as: ; The approximation coefficient The correspondence between boron concentration and critical state parameters is determined based on a finite number of conventional boron linear search calculations performed before the simultaneous synchronous nonlinear iterative solution begins: in, , The boron concentrations obtained from two conventional linear boron search calculations are shown below. , These are the corresponding critical state parameters; or they can be preset to fixed values ​​based on experience. S4: Based on the residual calculation method constructed in step S3, the global unknown is solved nonlinearly and iteratively using a simultaneous synchronous solution method, and the global unknown is updated synchronously by calculating the correction amount of the global unknown; S5: Determine whether the updated global unknowns meet the preset convergence criteria; if they do, output the critical boron concentration and its corresponding reactor state; if they do not, return to step S4 and continue execution until the preset convergence criteria are met.

2. The method for simultaneously solving the critical boron concentration of a nuclear reactor as described in claim 1, characterized in that: The critical state parameter is the effective proliferation coefficient. or reactivity The corresponding critical state parameter constraints are as follows: .

3. The method for simultaneously solving the critical boron concentration of a nuclear reactor as described in claim 1, characterized in that: The global unknowns include at least the boron concentration and the critical state parameters, and the other physical field variables related to the reactor state include one or more of neutronics variables and thermo-hydraulic variables; the global unknowns are expressed as follows: in, For boron concentration, The critical state parameter is... These are the physical field variables related to the reactor state.

4. The method for simultaneously solving the critical boron concentration of a nuclear reactor as described in claim 3, characterized in that: The neutronics variables include one or more of neutron flux density, power distribution, and reaction rate distribution; the thermal-hydraulic variables include one or more of coolant temperature, coolant density, coolant enthalpy, fuel temperature, and cladding temperature; the critical state parameters are calculated by the neutronics solution module and are explicitly introduced as separate key unknowns in the simultaneous solution.

5. The method for simultaneously solving the critical boron concentration of a nuclear reactor as described in claim 1, characterized in that: The simultaneous solution in step S4 is achieved using a nonlinear iterative solution method; the nonlinear iterative solution method is achieved using the Jacobi-Newton-Krylov method; before performing the nonlinear iterative solution, the initial boron concentration or initial global unknown is determined by a finite number of conventional boron linear search calculations.

6. The method for simultaneously solving the critical boron concentration of a nuclear reactor as described in claim 1, characterized in that: The convergence determination in step S5 is based on both the update of the global unknown and the residual or response results corresponding to the physical field variables.

7. A system for simultaneously solving the critical boron concentration in a nuclear reactor, comprising the method for simultaneously solving the critical boron concentration in a nuclear reactor as described in any one of claims 1-6, characterized in that, include: The initialization configuration module is used to configure the critical state parameter constraint relationship and multiphysics coupling calculation model for solving the critical boron concentration, and to determine the initial values ​​of boron concentration, critical state parameters and other physical field variables required for simultaneous solution. The variable assembly module is used to select boron concentration, critical state parameters, and reactor state-related physical field variables as variables to be solved, assemble them into global unknowns, and establish the correspondence between the variables to be solved and the global unknowns. The residual construction module is used to construct the residual calculation method corresponding to the global unknown based on the critical state parameter constraint relationship, the multi-physics field coupled calculation model and the global unknown. The residual corresponding to the boron concentration is constructed according to the correspondence between the boron concentration and the critical state parameter, and the residuals corresponding to the other physical field variables are constructed according to the corresponding physical field solution model or solution module. The solution module is used to perform nonlinear iterative solution of the global unknowns based on the residual calculation method and using a simultaneous synchronous solution method. By calculating the correction amount of the global unknowns, the global unknowns are updated synchronously. The convergence determination module is used to determine whether the updated global unknowns meet the preset convergence criteria, and outputs the critical boron concentration and its corresponding reactor state when the preset convergence criteria are met.

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