Simulation method, prediction method and system for operating state of integrated small reactor

Abstract

The disclosure provides a simulation method, a running state prediction method and system of an integrated small reactor, the simulation method comprising: establishing mathematical models of a plurality of physical fields of the integrated small reactor based on design parameters and running parameters of the integrated small reactor; wherein the mathematical models comprise at least one of a natural circulation driving force model, a two-phase flow heat transfer correlation model and an emergency cooling water natural injection model; performing simulation calculation on each physical field based on the mathematical models to obtain a first simulation result corresponding to each physical field; and obtaining a target simulation result corresponding to the integrated small reactor based on the first simulation result. The disclosure introduces mathematical models of multiple physical fields dedicated to the integrated small reactor, adds a special model library such as the natural circulation driving force model, the two-phase flow heat transfer correlation model and the emergency cooling water natural injection model, accurately reproduces the coupled thermal hydraulic characteristics under the arrangement of the integrated small reactor, and ensures the accuracy and reliability of the simulation result.

Description

Technical Field

[0001] This disclosure relates to the field of nuclear energy engineering simulation technology, and in particular to an integrated simulation method, a method for predicting operating status, and a system for small modular reactors. Background Technology

[0002] Nuclear reactor simulation is a crucial technical support in nuclear engineering. Traditional simulations of large pressurized water reactors generally rely on full-range simulators and partial-range simulation platforms. While designed for the forced circulation and active safety system design of large reactors, these platforms cannot accurately simulate the natural circulation flow characteristics, passive safety system operation, and highly coupled structures of integrated small reactors (SMRs), making them unsuitable for application to integrated SMRs. Furthermore, the lack of dedicated model libraries for aspects such as pressurizer pressure fluctuations, natural circulation thermosiphon, and gravity injection of emergency cooling water in SMRs leads to significant deviations in simulation results, resulting in inaccurate and unreliable simulation outcomes. Summary of the Invention

[0003] The technical problem to be solved by this disclosure is to overcome the shortcomings of existing large pressurized water reactor simulation, which is designed for the forced circulation and active safety system of large reactors and is not suitable for application to integrated small reactors, resulting in inaccurate and unreliable simulation results. This disclosure provides a simulation method, a method for predicting the operating status of an integrated small reactor.

[0004] This disclosure solves the above-mentioned technical problems through the following technical solution:

[0005] This disclosure provides a simulation method for an integrated small-scale reactor, the simulation method comprising:

[0006] Based on the design and operating parameters of the integrated small reactor, a mathematical model of several physical fields of the integrated small reactor is established.

[0007] The mathematical model includes at least one of the following: natural circulation driving force model, two-phase heat transfer correlation model, and emergency cooling water natural injection model.

[0008] The natural circulation driving force model is used to simulate the natural circulation intensity of the integrated small reactor based on the fluid state of the integrated small reactor;

[0009] The two-phase flow heat transfer correlation model is used to simulate the two-phase flow heat transfer coefficient of the integrated small reactor.

[0010] The emergency cooling water natural injection model is used to simulate the natural injection state of the cooling water tank of the integrated small reactor under accident conditions.

[0011] Based on the mathematical model, simulation calculations are performed on each physical field to obtain the first simulation result corresponding to each physical field.

[0012] Based on the first simulation result, the target simulation result corresponding to the integrated small reactor is obtained.

[0013] Optionally, the natural circulation driving force model is constructed based on parameters such as natural circulation driving force, average density difference of fluid in hot and cold sections, effective height difference of hot and cold sections, loop mass flow rate, flow channel cross-sectional area, local flow resistance coefficient, friction coefficient, and pipe length-to-diameter ratio.

[0014] And / or,

[0015] The two-phase heat transfer correlation model is constructed based on parameters such as Reynolds number, Prandtl number, correction factor for the geometric density characteristics of the integrated small reactor, convective heat transfer coefficient, nucleus boiling heat transfer coefficient, inhibition factor, and enhancement factor.

[0016] And / or,

[0017] The emergency cooling water natural injection model is constructed based on parameters such as flow coefficient, injection port cross-sectional area, height difference between water tank level and core inlet, cooling water density, and pressure drop caused by local core resistance.

[0018] And / or,

[0019] The mathematical model includes a coefficient matrix, a system of equations, and initial conditions;

[0020] And / or,

[0021] The first simulation results include at least one of the following: temperature field, pressure, flow rate, and neutron flux distribution;

[0022] And / or,

[0023] The mathematical model also includes a neutron dynamics model;

[0024] The neutron dynamics model includes a point-pile dynamics model and a spatial partitioning analysis model;

[0025] The point-pile dynamics model is used to adjust the steady-state power of the integrated small reactor and to simulate the global transients of the core of the integrated small reactor.

[0026] The spatial partitioning analysis model is used to analyze the impact of local power distribution changes of the integrated small reactor on the safety margin of the integrated small reactor.

[0027] And / or,

[0028] The mathematical model also includes a finite volume method multilayer heat conduction model, which is used to simulate the multilayer heat conduction behavior of the fuel rods, pressure vessel walls and heat exchange tubes of the integrated small reactor.

[0029] And / or,

[0030] The mathematical model also includes a thermal stress coupling model, which is used to calculate the thermal stress and structural strength margin caused by cyclic temperature changes under preset operating conditions.

[0031] And / or,

[0032] The mathematical model also includes a sensor feedback correction model, which is used to correct the temperature data in the mathematical model other than the sensor feedback correction model based on the surface temperature measurement data of the sensor.

[0033] Optionally, the step of performing simulation calculations on each physical field based on the mathematical model to obtain a first simulation result corresponding to each physical field includes:

[0034] Within each computation time step, the mathematical model is iteratively coupled to obtain a set of coupled equations;

[0035] Based on the set of coupled equations, the first simulation result corresponding to each physical field is obtained;

[0036] And / or,

[0037] The step of performing simulation calculations on each physical field based on the mathematical model to obtain the first simulation result corresponding to each physical field includes:

[0038] Obtain the simulation duration;

[0039] In response to the simulation duration reaching a preset simulation period and / or the corresponding simulation result satisfying a preset convergence condition, the currently obtained simulation result is taken as the first simulation result.

[0040] And / or,

[0041] After the step of performing simulation calculations on each physical field based on the mathematical model to obtain the first simulation result corresponding to each physical field, the method further includes:

[0042] Based on the first simulation results, the coefficient matrix and initial conditions of the mathematical model are corrected;

[0043] And / or,

[0044] The step of obtaining the target simulation result corresponding to the integrated small reactor based on the first simulation result includes:

[0045] An MPI (Message Passing Interface) distributed computing framework is adopted to allocate independent computing nodes to the mathematical model corresponding to each integrated mini-heap in order to obtain the target simulation results corresponding to each integrated mini-heap.

[0046] Optionally, the simulation method further includes:

[0047] Obtain several actual measurement data;

[0048] The mathematical model is modified based on several of the actual measurement data.

[0049] Optionally, before the step of correcting the mathematical model based on several of the actual measurement data, the method further includes:

[0050] In response to the actual measurement data not falling within the first preset range, the corresponding actual measurement data is removed from the plurality of actual measurement data;

[0051] And / or,

[0052] Based on the preset prediction model, the prediction data is obtained;

[0053] Obtain the difference between the actual measurement data and the predicted data;

[0054] In response to the difference being greater than a preset threshold, the corresponding actual measurement data is removed from a plurality of actual measurement data.

[0055] This disclosure also provides a method for predicting the operating status of an integrated small stack, the prediction method comprising:

[0056] Obtain several actual measurement data;

[0057] Based on several actual measurement data and target simulation results, the preset operating parameters are predicted.

[0058] The target simulation results are obtained based on the simulation method of the integrated small stack described above.

[0059] Optionally, the prediction method further includes:

[0060] Based on several actual measurement data and the target simulation results, the operational deviation state of the integrated small reactor is determined.

[0061] This disclosure also provides an integrated simulation system for small modular reactors, the simulation system comprising:

[0062] The physical modeling layer is used to establish mathematical models of several physical fields of the integrated mini-relay based on the design and operating parameters of the integrated mini-relay.

[0063] The mathematical model includes at least one of the following: natural circulation driving force model, two-phase heat transfer correlation model, and emergency cooling water natural injection model.

[0064] The natural circulation driving force model is used to simulate the natural circulation intensity of the integrated small reactor based on the fluid state of the integrated small reactor;

[0065] The two-phase flow heat transfer correlation model is used to simulate the two-phase flow heat transfer coefficient of the integrated small reactor.

[0066] The emergency cooling water natural injection model is used to simulate the natural injection state of the cooling water tank of the integrated small reactor under accident conditions.

[0067] The simulation solution layer is used to perform simulation calculations on each of the physical fields based on the mathematical model, and obtain the first simulation result corresponding to each physical field; based on the first simulation result, the target simulation result corresponding to the integrated small reactor is obtained.

[0068] Optionally, the natural circulation driving force model is constructed based on parameters such as natural circulation driving force, average density difference of fluid in hot and cold sections, effective height difference of hot and cold sections, loop mass flow rate, flow channel cross-sectional area, local flow resistance coefficient, friction coefficient, and pipe length-to-diameter ratio.

[0069] And / or,

[0070] The two-phase heat transfer correlation model is constructed based on parameters such as Reynolds number, Prandtl number, correction factor for the geometric density characteristics of the integrated small reactor, convective heat transfer coefficient, nucleus boiling heat transfer coefficient, inhibition factor, and enhancement factor.

[0071] And / or,

[0072] The emergency cooling water natural injection model is constructed based on parameters such as flow coefficient, injection port cross-sectional area, height difference between water tank level and core inlet, cooling water density, and pressure drop caused by local core resistance.

[0073] And / or,

[0074] The mathematical model includes a coefficient matrix, a system of equations, and initial conditions;

[0075] And / or,

[0076] The first simulation results include at least one of the following: temperature field, pressure, flow rate, and neutron flux distribution;

[0077] And / or,

[0078] The mathematical model also includes a neutron dynamics model;

[0079] The neutron dynamics model includes a point-pile dynamics model and a spatial partitioning analysis model;

[0080] The point-pile dynamics model is used to adjust the steady-state power of the integrated small reactor and to simulate the global transients of the core of the integrated small reactor.

[0081] The spatial partitioning analysis model is used to analyze the impact of local power distribution changes of the integrated small reactor on the safety margin of the integrated small reactor.

[0082] And / or,

[0083] The mathematical model also includes a finite volume method multilayer heat conduction model, which is used to simulate the multilayer heat conduction behavior of the fuel rods, pressure vessel walls and heat exchange tubes of the integrated small reactor.

[0084] And / or,

[0085] The mathematical model also includes a thermal stress coupling model, which is used to calculate the thermal stress and structural strength margin caused by cyclic temperature changes under preset operating conditions.

[0086] And / or,

[0087] The mathematical model also includes a sensor feedback correction model, which is used to correct the temperature data in the mathematical model other than the sensor feedback correction model based on the surface temperature measurement data of the sensor.

[0088] Optionally, the simulation solution layer includes:

[0089] The coupling calculation module is used to perform iterative coupling calculations on the mathematical model in each calculation time step to obtain a set of coupled equations;

[0090] The first result acquisition module is used to obtain the first simulation result corresponding to each physical field based on the coupled equation set;

[0091] And / or,

[0092] The simulation solution layer includes:

[0093] The simulation duration acquisition module is used to acquire the simulation duration.

[0094] The second result acquisition module is used to take the currently obtained simulation result as the first simulation result in response to the simulation duration reaching a preset simulation cycle and / or the corresponding simulation result satisfying a preset convergence condition.

[0095] And / or,

[0096] The simulation solution layer also includes:

[0097] The model correction module is used to correct the coefficient matrix and initial conditions of the mathematical model based on the first simulation results.

[0098] And / or,

[0099] The simulation solution layer includes:

[0100] The target result acquisition module is used to assign independent computing nodes to the mathematical model corresponding to each integrated mini-heap using the MPI distributed computing framework, so as to obtain the target simulation result corresponding to each integrated mini-heap.

[0101] Optionally, the simulation system further includes:

[0102] The data interface layer is used to acquire several actual measurement data; and to modify the mathematical model based on the several actual measurement data.

[0103] Optionally, the data interface layer is further configured to remove the corresponding actual measurement data from a plurality of actual measurement data in response to the actual measurement data not belonging to a first preset range;

[0104] And / or,

[0105] Based on the preset prediction model, the prediction data is obtained;

[0106] Obtain the difference between the actual measurement data and the predicted data;

[0107] In response to the difference being greater than a preset threshold, the corresponding actual measurement data is removed from a plurality of actual measurement data.

[0108] This disclosure also provides an integrated small modular reactor (SMR) operation status prediction system, the prediction system comprising:

[0109] The application function layer is used to acquire several actual measurement data; based on the several actual measurement data and the target simulation results, it predicts the preset operating parameters;

[0110] The target simulation results are obtained based on the integrated small reactor simulation system described above.

[0111] The application function layer is also used to determine the operational deviation state of the integrated small reactor based on several of the actual measurement data and the target simulation results.

[0112] This disclosure also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and for running on the processor, wherein the processor executes the computer program to implement the above-described integrated small stack simulation method, or to implement the above-described integrated small stack operating state prediction method.

[0113] This disclosure also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described simulation method for an integrated small stack, or the above-described method for predicting the operating state of an integrated small stack.

[0114] This disclosure also provides a computer program product, including a computer program that, when executed by a processor, implements the simulation method for an integrated small heap as described above, or implements the prediction method for the operating state of an integrated small heap as described above.

[0115] Based on common knowledge in the field, the above-mentioned preferred conditions can be combined arbitrarily to obtain various preferred embodiments of this disclosure.

[0116] The positive and progressive effects of this disclosure are as follows:

[0117] This disclosure introduces a multiphysics mathematical model specifically for integrated small modular reactors (SMRs), and incorporates a dedicated model library including a natural circulation driving force model, a two-phase heat transfer correlation model, and an emergency cooling water natural injection model. This accurately reproduces the coupled thermal-hydraulic characteristics of an integrated SMR layout, ensuring the accuracy and reliability of the simulation results. Attached Figure Description

[0118] Figure 1 This is a first flowchart of the simulation method for the integrated small stack according to Embodiment 1 of this disclosure;

[0119] Figure 2 This is a schematic diagram illustrating the working principle of the multiphysics mathematical model of the integrated small stack in Embodiment 1 of this disclosure.

[0120] Figure 3 This is a schematic diagram illustrating the working principle of the simulation solution of the mathematical model in Embodiment 1 of this disclosure;

[0121] Figure 4 This is the first flowchart of step S102 in the simulation method of the integrated small stack of the present disclosure embodiment 1;

[0122] Figure 5 This is the second flowchart of step S102 in the simulation method of the integrated small stack of Embodiment 1 of this disclosure;

[0123] Figure 6 This is a schematic diagram illustrating the working principle of the data interface in Embodiment 1 of this disclosure;

[0124] Figure 7 This is a second flowchart of the simulation method for the integrated small stack of the present disclosure in Embodiment 1;

[0125] Figure 8 This is the third flowchart of the simulation method for the integrated small stack according to Embodiment 1 of this disclosure;

[0126] Figure 9 This is the fourth flowchart of the simulation method for the integrated small stack according to Embodiment 1 of this disclosure;

[0127] Figure 10 This is a flowchart of the method for predicting the operating status of the integrated small reactor according to Embodiment 2 of this disclosure;

[0128] Figure 11 This is a schematic diagram of the module of the integrated small reactor simulation system according to Embodiment 3 of this disclosure;

[0129] Figure 12 This is a schematic diagram of the architecture of the integrated small reactor operation status prediction system of Embodiment 4 of this disclosure;

[0130] Figure 13 This is a schematic diagram of the structure of the electronic device according to Embodiment 5 of this disclosure. Detailed Implementation

[0131] The present disclosure is further illustrated below by way of embodiments, but the present disclosure is not limited to the scope of the embodiments described herein.

[0132] The prefixes such as "first" and "second" used in this disclosure are merely for distinguishing different descriptive objects and do not limit the position, order, priority, quantity, or content of the described objects. The use of ordinal numbers and other prefixes used to distinguish descriptive objects in this disclosure does not constitute a limitation on the described objects. The description of the described objects is given in the context of the embodiments, and the use of such prefixes should not constitute unnecessary restrictions. Furthermore, in the description of this embodiment, unless otherwise stated, "multiple" means two or more.

[0133] Example 1

[0134] This embodiment provides a simulation method for an integrated small stack, such as... Figure 1 As shown, the simulation method includes:

[0135] S101. Based on the design and operating parameters of the integrated small-scale reactor, establish a mathematical model of several physical fields of the integrated small-scale reactor.

[0136] The mathematical model includes at least one of the following: natural circulation driving force model, two-phase heat transfer correlation model, and emergency cooling water natural injection model.

[0137] The natural circulation driving force model is used to simulate the natural circulation intensity of an integrated small reactor based on the fluid state of the integrated small reactor.

[0138] Two-phase flow heat transfer correlation model is used to simulate the two-phase flow heat transfer coefficient of integrated small reactor;

[0139] The emergency cooling water natural injection model is used to simulate the natural injection state of the cooling water tank of an integrated small modular reactor under accident conditions.

[0140] S102. Based on the mathematical model, perform simulation calculations for each physical field to obtain the first simulation result for each physical field.

[0141] S103. Based on the first simulation result, the target simulation result corresponding to the integrated small reactor is obtained.

[0142] Specifically, unlike traditional large PWRs (Pressurized Water Reactors), integrated small modular reactors (SMRs) integrate the main reactor components, such as steam generators, pumps, and the reactor core, into a single pressure vessel. By reducing piping and vessel welds, the risk of leakage is lowered, resulting in higher passive safety performance. SMRs emphasize natural circulation and short-loop thermal-hydraulic characteristics. The thermal-hydraulic models for SMRs include a natural circulation driving force model, a two-phase heat transfer correlation model, and an emergency cooling water natural injection model.

[0143] The natural circulation driving force model is constructed based on parameters such as natural circulation driving force, average density difference of fluid in hot and cold sections, effective height difference between hot and cold sections, loop mass flow rate, flow channel cross-sectional area, local flow resistance coefficient, friction coefficient, and pipe length-to-diameter ratio.

[0144] The two-phase heat transfer correlation model is constructed based on parameters such as Reynolds number, Prandtl number, correction factor for geometric density characteristics of integrated small reactor, convective heat transfer coefficient, nucleate boiling heat transfer coefficient, inhibition factor, and enhancement factor.

[0145] The emergency cooling water natural injection model is constructed based on parameters such as flow coefficient, injection port cross-sectional area, height difference between water tank level and core inlet, cooling water density, and pressure drop caused by local core resistance.

[0146] Natural circulation driving force model: An equation set based on gravitational head difference and local flow resistance is established to simulate the intensity of natural circulation under different fluid conditions. Based on the momentum balance equation, the mass flow rate of the loop is determined by the static pressure difference and frictional resistance.

[0147] ;

[0148] ;

[0149] in, This represents the driving force of natural circulation (Pa). This represents the acceleration due to gravity (m / s²). H represents the average density difference of the fluid between the cold and hot sections (kg / m³), and H represents the effective height difference between the cold and hot sections (m). The value represents the loop mass flow rate (kg / s), and A represents the cross-sectional area of ​​the flow channel (m²). The sum of local flow resistance coefficients (for bends, valves, etc.) is represented by f, the coefficient of friction is represented by L / D, and the length-to-diameter ratio of the pipe is represented by L / D.

[0150] Two-phase flow heat transfer correlation model: Considering the low power density of the small stack but the small volume of the regulator, a two-phase flow boiling heat transfer correlation correction is set. The modified Dittus-Boelter (correlation for turbulent forced convection heat transfer) and Chen model (correlation for boiling two-phase flow heat transfer in the tube) are adopted to make the heat transfer simulation in the saturation zone more realistic.

[0151] One-way relative heat transfer: ;

[0152] Two-way relative heat transfer: ;

[0153] Where Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number. To account for the correction factor of small stack geometry / power density characteristics, The two-phase heat transfer coefficient (W / m²K) The convective heat transfer coefficient is... denoted as the nucleation boiling heat transfer coefficient, S as the inhibition factor, and F as the enhancement factor.

[0154] First, the adapted values ​​for the mini-heap condition are calculated using the modified Dittus-Boelter algorithm. Then input it into the corrected Chen model, nucleus boiling heat transfer coefficient By superimposing the results, the overall heat transfer coefficient in the two-phase flow region is obtained, which is closer to the actual performance of the small reactor. .

[0155] Emergency cooling water natural injection model: This is an enhanced passive safety condition in-plant cooling water tank-core natural injection model. The calculation takes into account water level difference, sudden flow resistance change, and thermosiphon effect. The corresponding calculation formula is as follows:

[0156] ;

[0157] in, Mass flow rate (kg / s) injected into the reactor core. For flow coefficient, This represents the cross-sectional area of ​​the injection port (m²). The height difference (m) between the water tank level and the reactor core inlet. The density of cooling water (kg / m³) This refers to the pressure drop (Pa) caused by local drag in the reactor core.

[0158] Combination Local flow resistance and core steam siphon effect can simulate the natural injection of cooling water tanks under accident conditions.

[0159] Based on the mathematical model, simulation calculations are performed on each physical field to obtain the first simulation result corresponding to each physical field; the first simulation results corresponding to all physical fields are used as the target simulation results corresponding to the integrated small reactor.

[0160] This scheme introduces a multiphysics mathematical model specifically for integrated small modular reactors (SMRs), and incorporates a dedicated model library including a natural circulation driving force model, a two-phase heat transfer correlation model, and an emergency cooling water natural injection model. This accurately reproduces the coupled thermal-hydraulic characteristics of the integrated SMR layout, ensuring the accuracy and reliability of the simulation results.

[0161] In a feasible scheme, the mathematical model includes a coefficient matrix, a system of equations, and initial conditions.

[0162] The first simulation results include at least one of the following: temperature field, pressure, flow rate, and neutron flux distribution.

[0163] Specifically, a multiphysics mathematical model of the small reactor is established, including a neutron dynamics model, a thermal-hydraulic model, a thermal structure and heat transfer model, and a control system model. The mathematical model is generated based on input information such as design parameters, operating conditions, geometric structure, and material properties, and includes a coefficient matrix, a system of equations, and boundary or initial conditions. Numerical methods are used to perform simulation calculations based on the data model, obtaining multiphysics calculation results including temperature field, pressure, flow rate, and neutron flux distribution, i.e., the first simulation result. The first simulation result shows the temporal and spatial distribution of each physical quantity. The first simulation result is then transmitted to the data interface.

[0164] In this scheme, the mathematical model includes a coefficient matrix, a system of equations, and initial conditions, which ensures the accuracy and reliability of the mathematical model; the first simulation results include temperature field, pressure, flow rate, and neutron flux distribution, which ensures the diversity and reliability of the simulation results.

[0165] In a feasible approach, the mathematical model also includes a neutron dynamics model;

[0166] Neutron dynamics models include point-pile dynamics models and spatial partitioning analysis models;

[0167] Among them, the point-pile dynamics model is used to adjust the steady-state power of the integrated small reactor and to simulate the global transient of the core of the integrated small reactor.

[0168] The spatial partitioning analysis model is used to analyze the impact of local power distribution variations of integrated small modular reactors (SMRs) on the safety margin of SMRs.

[0169] Specifically, in the neutron dynamics model of the integrated small reactor, the dynamic behavior of nuclear reactions is adopted by combining the point reactor dynamics model with the spatial partitioning analysis model.

[0170] Point-pile dynamics models include neutron flux density dynamics models and delayed neutron precursor dynamics models.

[0171] The calculation formula corresponding to the neutron flux density dynamics model is as follows:

[0172] ;

[0173] The calculation formula corresponding to the delayed neutron precursor dynamics model is as follows:

[0174] i = 1, 2, ..., M;

[0175] Where n(t) represents the instantaneous neutron density in the reactor core, which is proportional to the core power P(t); Indicates reactivity, the amount of deviation from the critical value caused by factors such as the insertion and removal of control rods, coolant temperature, and density; Indicates the total delayed neutron share; Indicates the share of delayed neutrons in the i-th group; This represents the average neutron generation time. Indicates the concentration of the i-th delayed neutron precursor; Let represent the decay constant of the i-th precursor group; M represents the number of delayed neutron groups, usually taken as 6 groups; t represents time.

[0176] The spatial partitioning analysis model divides the reactor core into K spatial regions. The point-pile equations for each region include the regional neutron density dynamics equation and the regional delayed neutron precursor equation.

[0177] The calculation formula corresponding to the regional neutron density dynamics equation is as follows:

[0178] ;

[0179] The calculation formula for the regional delayed neutron precursor is as follows:

[0180] ;

[0181] in, This represents the local neutron density of the k-th region; This represents the local reactivity of the k-th region, taking into account local feedback effects such as fuel temperature and coolant density. This represents the share of delayed neutrons in the i-th group of the k-th region; When representing the average neutron generation of the k-th region; This represents the concentration of the i-th delayed neutron precursor in the k-th region; The coupling coefficient between regions represents the influence of neutron migration in region j on region k, and can be modified... The value is used to simulate the effect of changes in coolant flow distribution on neutron flux coupling between different regions; K represents the total number of spatial divisions.

[0182] Point-based reactor dynamics models are used for fast real-time calculations and are suitable for steady-state power regulation and large-scale transient simulations. Large-scale refers to global transients that affect the entire reactor core, such as coolant flow loss or the introduction of positive reactivity throughout the reactor.

[0183] The spatial partitioning analysis model is activated when necessary to study the impact of local power distribution variations on the safety margin of small reactors.

[0184] The neutron dynamics model switches between point reactor and spatial partitioning, and performs integrated fuel assembly correction on delayed neutron parameters to improve the accuracy of transient response simulation.

[0185] In this scheme, the delayed neutron approximation method is optimized based on the point reactor dynamics model, and special parameter corrections for the integrated small reactor fuel assembly are introduced, so that the simulation results can more realistically reproduce the dynamic response of the core power as the control rods are inserted and removed, the coolant density changes, and other operating conditions.

[0186] In one feasible approach, the mathematical model also includes a finite volume method multilayer heat conduction model, which is used to simulate the multilayer heat conduction behavior of the fuel rods, pressure vessel walls, and heat exchange tubes of an integrated small reactor.

[0187] Specifically, the core assemblies and steam generators of an integrated small modular reactor (SMR) are typically housed closely within a pressure vessel, where changes in material temperature significantly impact system safety. The thermal structure and heat transfer models of an SMR include a finite volume method multilayer heat conduction model.

[0188] The finite volume method was used to simulate the multilayer heat conduction behavior of fuel rods, pressure vessel walls, and heat exchange tubes.

[0189] The radial heat conduction equation in cylindrical coordinates is discretized using energy conservation, and the corresponding calculation formula is as follows:

[0190] ;

[0191] Discretized into a finite volume form, the corresponding calculation formula is as follows:

[0192] ;

[0193] in, Let the density of the j-th layer material be (kg / m³). Specific heat capacity (J / kg·K), To control the volume (m³), Temperature (K), Thermal conductivity (W / m·K) The interface area (m²) Radial thickness (m), The volumetric heat source term (non-zero in the fuel zone, zero in the coolant / container wall) allows for simultaneous stratified heat transfer simulation of the fuel rods, pressure vessel wall, and heat exchanger tube wall.

[0194] In this scheme, a multi-layer heat conduction model using the finite volume method is designed for small piles, ensuring the precision and accuracy of heat transfer effect calculation.

[0195] In a feasible approach, the mathematical model also includes a thermal stress coupling model.

[0196] The thermal stress coupling model is used to calculate the thermal stress and structural strength margin caused by cyclic temperature changes under preset operating conditions.

[0197] Specifically, the thermal structure and heat transfer model of the integrated small reactor also includes a thermal stress coupling model.

[0198] A thermal stress coupling model is used for structural safety assessment under long-term operating conditions.

[0199] The formula for calculating thermal strain is as follows:

[0200] ;

[0201] The formula for calculating the total stress is as follows:

[0202] ;

[0203] in, For thermal strain, The coefficient of thermal expansion (1 / K) For reference temperature (K), Let Pa be the stress tensor. This is the elastic stiffness matrix, which is related to the material's Young's modulus and Poisson's ratio. Let Kroneck's δ tensor be... For total strain.

[0204] In this scheme, the thermal stress coupling model can calculate the thermal stress and structural strength margin caused by cyclic temperature changes under long-term operating conditions, ensuring the accuracy and reliability of the thermal stress and structural strength margin.

[0205] In one feasible approach, the mathematical model also includes a sensor feedback correction model, which is used to correct the temperature data in the mathematical model other than the sensor feedback correction model based on the surface temperature measurement data of the sensor.

[0206] Specifically, the thermal structure and heat transfer model of the integrated small reactor also includes a sensor feedback correction model.

[0207] The surface temperature measured by the sensor is fed back in real time to correct the simulation results. The numerical model is corrected in real time using the surface temperature data from the sensor. The observation-prediction difference method is employed, and the corresponding calculation formula is as follows:

[0208] ;

[0209] in, This is the corrected temperature, used to update subsequent iterations; To simulate and predict temperature; γ represents the actual temperature measured by the sensor; γ is the correction gain factor, with a value range of 0 to 1, which can be dynamically adjusted through a filtering algorithm.

[0210] In this scheme, a sensor feedback correction model is added, which can realize the fusion of model and measurement, and automatically reduce the deviation between simulation and reality during long-term operation.

[0211] In addition, considering the simplified operation and high level of automation of small modular reactors, the integrated small modular reactor also includes a control system model, which is used for reactor power regulation control, control rod control, feedwater and exhaust control, alarm and protection.

[0212] Reactor power regulation and control: Real-time response to grid demand and reactor power.

[0213] Control rod control: Built-in insertion or removal speed curves and emergency stop logic.

[0214] Water supply and exhaust control: Simulate changes in the operating conditions of the secondary loop.

[0215] Alarms and Protection: Implements the complete logical process of triggering a stack shutdown when parameters exceed limits.

[0216] These control logics not only simulate the operation of a real reactor, but also allow for custom designs during training or research, enabling the testing of different control strategies.

[0217] In summary, such as Figure 2 As shown, the multiphysics mathematical model of the integrated small reactor includes sub-models such as a neutron dynamics model, a thermal-hydraulic model, a thermal-structure and heat transfer model, and a control system model. These sub-models achieve fully coupled closed-loop operation through parameter transfer and feedback mechanisms.

[0218] The neutron dynamics model is used to calculate the spatiotemporal distribution of neutron flux, reactivity variations, and power within the reactor core. The model's inputs include operating parameters such as fuel temperature, coolant density and temperature, and control rod positions. The model's output is the core power distribution, which is input as a heat source to the thermal-hydraulic model, thermal-structural model, and heat transfer model. The fuel temperature calculation considers the Doppler effect, and the coolant density and temperature calculations incorporate density feedback.

[0219] The thermal-hydraulic model is used to simulate the flow state, temperature distribution, pressure changes, and density field of the coolant, as well as the heat exchange process between the fluid and the solid structure. Its inputs include the power distribution heat source provided by the neutron dynamics model and the flow and pressure boundary conditions for small reactor operation; its outputs are the coolant temperature field, density field, and velocity field. These results are used as density feedback inputs back to the neutron dynamics model to influence reactivity calculations, and as fluid boundary conditions provided to the thermal structure and heat transfer models.

[0220] The thermal structure and heat transfer model is used to calculate the temperature distribution inside solid structures such as fuel pellets and cladding, as well as the heat transfer process between them and the coolant. The model's inputs include the heat source distribution from the neutron kinetics model and boundary conditions such as coolant temperature and flow velocity provided by the thermal-hydraulic model. Its outputs are key structural temperature parameters such as the fuel pellet center temperature and cladding surface temperature, and it feeds the fuel temperature back to the neutron kinetics model for Doppler effect correction of reactivity.

[0221] The control system model, based on real-time monitoring signals such as power, reactivity, temperature, pressure, and flow rate from the neutron dynamics model and the thermal-hydraulic model, calculates and issues control commands according to predetermined control logic, such as power regulation and protection actions, to drive actuators, such as control rods, main pumps, and valves, for regulation. These actions directly change the reactivity input of the neutron dynamics model and the flow or pressure boundary conditions of the thermal-hydraulic model, thus affecting the physical calculations of the next cycle.

[0222] During closed-loop operation, the above sub-models interact and update in the following order:

[0223] The core power distribution output by the neutron dynamics model is used as a heat source input to the thermal-hydraulic model and the thermal-structure and heat transfer model;

[0224] The coolant temperature, density, and velocity distribution calculated by the thermal-hydraulic model are used to feed back the density effect to the neutron dynamics model and serve as the fluid boundary conditions for the thermal structure and heat transfer model.

[0225] The thermal structure and heat transfer model calculates the temperature distribution of fuel pellets and cladding, and feeds the fuel temperature back to the neutron kinetics model to correct the influence of the Doppler effect on reactivity.

[0226] The control system model obtains operating parameters in real time from neutron dynamics and thermal-hydraulic models, and issues control commands to adjust the position of control rods, pump speed or valve status, thereby changing the flow boundary conditions of neutron dynamics reactive input and thermal-hydraulic flow.

[0227] After adjustment by the control system model, the new boundary conditions and state variables re-enter the neutron dynamics model and enter the next calculation cycle, achieving a fully coupled closed-loop simulation between neutronics, thermal hydraulics, heat transfer in thermal structures, and the control system. This coupling mechanism can accurately reflect the multi-physics interactions and feedback effects in fast and slow transient processes, ensuring the physical realism and engineering applicability of the simulation results.

[0228] The mathematical model of several physical fields of the integrated small modular reactor (SMR) needs to be solved efficiently under limited computing resources and real-time requirements. Unlike traditional large pressurized water reactor simulations, the online simulation of the integrated SMR needs to simultaneously meet two objectives:

[0229] In terms of accuracy, it can accurately reflect the coupled behavior of complex natural circulation, multiphase flow boiling heat transfer, and reactor neutron dynamics under integrated layout.

[0230] In terms of speed, it can guarantee real-time or near real-time calculations in practical applications. That is, when the core physical process changes, the simulation platform can complete the corresponding calculation results within a few seconds, which can be used to support operation prediction, accident drills or digital twin applications.

[0231] Therefore, such as Figure 3 As shown, the simulation solution of the mathematical model covers functions such as multiphysics equation coupling strategy, numerical calculation scheme, real-time guarantee mechanism, parallel computing architecture, fault tolerance and robustness mechanism.

[0232] The various functions of the simulation solution work together in a time-step driven, data-interactive, and feedback-corrected manner to form a high-precision, high-real-time, stable, and reliable simulation solution closed loop.

[0233] First, the multiphysics equation coupling strategy iteratively couples the neutron dynamics equations, thermal-hydraulic equations, heat conduction equations, and control logic equations at each computation time step, ensuring consistency in energy transfer, flow state, and reactivity changes across the various physics fields. After coupled iterative optimization, a complete set of equations and coefficient matrices are generated and used as input for numerical computation.

[0234] Subsequently, based on the characteristics of the input coupled equations, numerical computation selects appropriate numerical solution methods, including implicit or explicit finite difference methods, finite volume methods, multi-group neutron diffusion approximations, the SIMPLEC algorithm (Semi-Implicit Method for Pressure-Linked Equations Consistent, a numerical algorithm for solving momentum-pressure coupling problems), and two-fluid models, to obtain numerical solutions for key physical quantities within the current time step, such as neutron flux, fuel temperature, coolant flow rate, and pressure. The results are not only passed to the real-time performance guarantee mechanism for scheduling and optimization but also provide a state snapshot to the fault-tolerant and robust mechanisms for recovery in abnormal situations.

[0235] Upon receiving the calculation results, the real-time performance guarantee mechanism dynamically adjusts the calculation time step based on the running status and application needs, switches the simulation accuracy mode (including high-precision, real-time, or fast mode), and optimizes the iterative convergence speed to ensure that the results are output within the specified time. The real-time performance guarantee mechanism passes the optimized calculation rhythm and necessary boundary condition adjustment schemes to the parallel computing architecture for execution, and simultaneously feeds back the scheduling strategy to the multiphysics equation coupling strategy and numerical calculation, influencing the solution method for subsequent time steps.

[0236] The parallel computing architecture is responsible for parallelizing the solution process of different physics fields in computing environments such as multi-threaded, GPU (Graphics Processing Unit) accelerated, or MPI distributed computing environments, accelerating matrix operations and data exchange, thereby significantly shortening the overall running time. The accelerated solution results are fed back to the real-time guarantee mechanism in real time to determine performance targets, and the data is directly provided to the fault tolerance and robustness mechanism for storage and monitoring.

[0237] Fault tolerance and robustness mechanisms continuously monitor the above results and key physical quantities. Once numerical anomalies or operational instability are detected, snapshot rollback, physical quantity correction strategies, or redundant channel switching are immediately implemented to prevent simulation interruption. The stable state after correction or rollback will be fed back to the multiphysics equation coupling strategy for iterative calculation, providing a stable operating foundation for the parallel computing architecture and real-time guarantee mechanism.

[0238] Through the sequential driving, data interaction, and feedback correction of the above five functions, the simulation solution can achieve high-precision, real-time, and stable online simulation calculation of complex multi-physics processes of integrated small stacks under limited computing resources, providing reliable data support and prediction functions for upper-level applications.

[0239] The simulation solution of the mathematical model is illustrated below through a specific scheme.

[0240] In a feasible solution, such as Figure 4 As shown, step S102 includes:

[0241] S1021. In each computation time step, the mathematical model is iteratively coupled to obtain a set of coupled equations.

[0242] S1022. Based on the coupled equation set, the first simulation result corresponding to each physical field is obtained.

[0243] Specifically, the simulation solution of mathematical models encompasses multiphysics equation coupling strategies. In reactor simulations, it is typically necessary to simultaneously address the following types of equations: neutron kinetic equations, thermal-hydraulic equations, heat conduction equations, and control system logic equations.

[0244] Neutron dynamics equations include point pile dynamics and space neutron flux transport equations; thermal-hydraulic equations include mass, momentum, and energy conservation equations in single-phase / two-phase model form; heat conduction equations include heat transfer and heat capacity effects within solid heat exchange structures; and control system logic equations, namely electrical logic and automatic control algorithms.

[0245] In traditional large-scale heap simulation systems, the weak coupling method is often used, where each sub-model is solved separately and then data is exchanged through relaxation iteration. However, this approach may lead to convergence difficulties and insufficient stability in the natural loop and highly coupled systems of integrated small heaps.

[0246] This scheme employs a coupled time-step propagation method, iteratively coupling the neutron, thermal-hydraulic, and heat transfer equations within a single time step to ensure energy conservation and fluid driving force balance. A hybrid prediction and correction method is introduced: first, a prediction model is used to derive a rough solution for the next step, and then the correction equations are iteratively refined to reduce numerical oscillations. For the strongly nonlinear problem in the natural circulation loop, a diagonal splitting iterative algorithm is used, which diagonally processes the liquid and gas phase equations to improve the iterative convergence speed. This approach reduces the number of iterations while maintaining accuracy, laying the foundation for real-time performance.

[0247] For the numerical calculation scheme of the mathematical model simulation solution, a dedicated solver is selected according to the characteristics of different equations to balance computational accuracy, stability, and efficiency. Specifically, this includes: the neutron dynamics equation is solved using an implicit finite difference method to ensure numerical stability; the spatial partitioning analysis model uses the finite volume method and introduces a multi-group neutron diffusion approximation under high-power transient conditions to improve accuracy; the thermal-hydraulic equation uses a two-fluid model to handle the vapor and liquid phases separately and introduces a modified source term to better fit actual working conditions; the momentum equation uses a semi-implicit pressure coupling method, such as the improved SIMPLEC algorithm, to ensure the coupling convergence of the velocity and pressure fields; the energy equation uses an upwind scheme supplemented with anti-diffusion correction to effectively avoid numerical oscillations; for the heat conduction equation, the fuel rod heat transfer model adopts the radial finite difference method, while the pressure vessel structure is simplified through three-dimensional slicing and adaptive mesh refinement is used in the high-temperature gradient region to improve local accuracy; for the control logic equation, an event-driven logic is introduced to combine discrete and continuous equations, enabling the simulation of typical transient processes such as control rod insertion and valve opening. By employing this classification-based solution and coupled iterative design method, this scheme not only ensures the stability and accuracy of the calculation results but also takes into account the rational allocation and optimized utilization of computing resources.

[0248] To achieve online simulation, strict requirements must be met in terms of real-time performance. This solution achieves this through a real-time guarantee mechanism, including adaptive time step control, multi-level simulation accuracy mode, and numerical stability optimization.

[0249] Adaptive time step control: Automatically detects the magnitude of variable changes and uses a larger time step to improve efficiency under stable operating conditions. During rapid transient conditions, such as reactor shutdown or loss of water, the time step is reduced to ensure the stability and accuracy of the calculation results.

[0250] Multi-level simulation accuracy modes: Three calculation levels are designed: a high-precision mode for research, a real-time mode for operational prediction, and a fast mode for teaching and training. Users can flexibly choose between accuracy and speed according to their application needs.

[0251] Numerical stability optimization: The preconditional conjugate gradient (PCG) method is used to accelerate convergence of the coupled equations, and matrix diagonal preprocessing is used to avoid numerical divergence in large-scale sparse matrix iteration.

[0252] Using these methods, in single-pile-scale simulations, it is possible to achieve the performance of completing a simulation in less than 5 minutes after running a real pile for 1 hour on ordinary workstation hardware, which is far superior to traditional simulation platforms.

[0253] The method employs time-step coupling iteration and a hybrid prediction and correction approach, combined with a diagonal splitting iteration algorithm to handle the strongly nonlinear problem of natural loops. It achieves strong coupling of all multiphysics fields with a second-level response. It is a customized optimization for the natural loop characteristics of mini-heaps, which improves real-time performance and coupling effect.

[0254] In this scheme, the neutron, thermal-hydraulic, and heat transfer equations are iteratively coupled within one time step, ensuring energy conservation and fluid driving force balance. This scheme is customized and optimized for the natural circulation characteristics of small reactors, improving real-time performance and coupling effect.

[0255] In one feasible embodiment, step S103 includes:

[0256] The MPI distributed computing framework is used to allocate independent computing nodes to the mathematical model corresponding to each integrated mini-heap in order to obtain the target simulation results for each integrated mini-heap.

[0257] Specifically, to further accelerate computation, a hierarchical parallel computing architecture is introduced into the simulation solution design. First, at the multi-threaded parallelism level, the model is divided according to its functional modules, with neutronics, fluid dynamics, and heat conduction calculations allocated to different threads. Efficient communication is achieved through a shared memory mechanism, enabling stable and efficient simulation tasks to be completed on small-scale servers or high-performance PCs. At the GPU acceleration level, the most time-consuming matrix operations, such as Jacobian matrix updates and discrete solutions of fluid equations, are ported to GPU processing, which can improve simulation performance by up to 5-10 times, thus strongly supporting the system's real-time operation goals.

[0258] Furthermore, at the distributed parallel level, when simulating the parallel operation of multiple heap modules, the MPI distributed computing framework is adopted. Each heap module is assigned an independent computing node, and the nodes exchange thermodynamic quantities through a message passing mechanism, thereby ensuring the computational scalability in multi-heap operation scenarios. Therefore, the parallel architecture proposed in this solution not only takes into account the real-time performance of single-heap simulation but also provides a flexible and scalable solution for future multi-heap joint simulation.

[0259] In online simulation scenarios, a complete system outage due to local numerical instability would severely impact its practicality. Therefore, this solution proposes a comprehensive fault-tolerance and robustness mechanism. First, an automatic snapshot rollback mechanism is implemented at the data management level. By periodically saving the system's operating state, rapid rollback is achieved, quickly restoring the system to the most recent stable state in the event of computational anomalies, avoiding a global shutdown. Second, at the numerical stability level, physical limits are set for key variables such as pressure, temperature, and flow rate. Automatic corrections are made when abnormal fluctuations are detected to prevent error propagation. Third, at the computational execution level, a parallel redundancy channel mechanism is introduced. Redundant subroutines are configured for critical modules. When the main program encounters an anomaly, the system immediately switches to the redundant channel, ensuring the continuity and reliability of the system results.

[0260] Through the aforementioned multi-layered fault-tolerant design, this solution enables long-term stable online operation, ensuring uninterrupted simulation even under complex operating conditions. This mechanism offers advantages over traditional nuclear power simulation platforms: traditional simulators typically only provide training snapshots for manually triggered state recovery, emphasizing teaching and training rather than real-time fault tolerance; while this solution's snapshot mechanism features automatic triggering, real-time monitoring, and rapid rollback capabilities to guarantee the stability and robustness of the system during autonomous operation, thus significantly improving its applicability in digital twin and online operation scenarios.

[0261] In this scheme, multi-heap parallel simulation is achieved through the MPI distributed framework, where each heap module independently computes nodes and shares coupling parameters, thus realizing synchronous simulation of the operating status of multiple modules.

[0262] In a feasible solution, such as Figure 5 As shown, step S102 includes:

[0263] S1023, Obtain simulation duration;

[0264] S1024. In response to the simulation duration reaching the preset simulation period and / or the corresponding simulation result satisfying the preset convergence condition, the currently obtained simulation result is taken as the first simulation result.

[0265] Specifically, the preset convergence condition is that the calculated simulation results are inconsistent with the actual results, and the difference between the two is, for example, less than 2%; if the difference between the two is not less than 2%, the parameters of the mathematical model are adjusted and the simulation is performed again.

[0266] The preset simulation cycle is, for example, 10,000 times. If the simulation time reaches 10,000 times, the current simulation result will be used as the first simulation result.

[0267] In this scheme, the first simulation result is determined based on the simulation duration reaching the preset simulation cycle and the corresponding simulation result satisfying the preset convergence condition. The number and duration of simulation iterations are reasonably set to ensure the accuracy and reliability of the simulation results.

[0268] In one feasible solution, after step S102, the following is also included:

[0269] Based on the first simulation results, the coefficient matrix and initial conditions of the mathematical model were revised.

[0270] Specifically, the mathematical model, simulation solution, and data interface sequentially transmit data, forming a closed-loop interaction through the bidirectional transmission of data and information.

[0271] In this scheme, the mathematical model is corrected by the first simulation result, forming a closed-loop interaction, which ensures the accuracy and reliability of the mathematical model, and thus ensures the accuracy and reliability of the first simulation result.

[0272] Simulation solutions and real-world applications require a data interface for connection. This data interface must not only connect to various synchronous or asynchronous data sources, but also ensure high data consistency and real-time performance, while providing communication and computational support for digital twin functionality. Unlike traditional full-range simulations that rely solely on hypothetical control signals, this solution's data interface emphasizes a design philosophy that integrates models and data.

[0273] like Figure 6 As shown, this data interface can realize functions such as online data acquisition, industrial standard protocol adaptation, construction of parameter database and model library, data preprocessing and anomaly detection, feedback correction and digital twin interface, scalable cloud interface and remote data access.

[0274] The data interface sits between the simulation solution and application functions, responsible for transmitting, converting, formatting, and exchanging bidirectional commands for simulation results and real-time monitoring data. It can call databases, real-time data streams, and communication protocols. The data interface sends the standardized data stream to the application functions, while also receiving control commands or physical parameters from the application functions and returning them for simulation solution or mathematical model updates and calculation adjustments.

[0275] The various functions of the data interface achieve sequential processing and bidirectional feedback through standardized data flow and control signals, forming a stable closed-loop interaction system.

[0276] The online data acquisition system is used to obtain operating parameters in real time from the small reactor power plant site, covering data from process systems, core measurements, control systems, and safety systems. It supports three acquisition modes: high frequency, low frequency, and event-triggered. The acquired raw data will be transmitted to an industry standard protocol adapter. The adapter adapts the data communication protocol according to the characteristics of different plant DCS / SCADA (Distributed Control System / Supervisory Control and Data Acquisition) systems, supporting multiple industry standards such as OPC UA (Open Platform Communications Unified Architecture), MODBUS TCP (MODBUS Transmission Control Protocol, based on TCP / IP; TCP / IP, Transmission Control Protocol / Internet Protocol; MODBUS, Modicon Bus), PROFINET (Process Field Network), and MQTT (Message Queuing Telemetry Transport), enabling plug-and-play data, unified data formatting, and cross-platform transmission.

[0277] After protocol adaptation, the data is sent to data preprocessing and anomaly detection. This process filters and reduces noise, detects abnormal data, and repairs missing values, ensuring the accuracy and robustness of the input data. The cleaned, high-reliability data is then combined with static parameters stored in the parameter database and model library, including fuel, core, working fluid, materials, and control logic, before entering the feedback correction and digital twin interface. Filtering and noise reduction include low-pass, high-pass, and Kalman filtering; anomaly detection uses a combination of thresholding and trend prediction; and missing value repair employs time interpolation and multi-source correlation compensation.

[0278] The parameter database and model library are used to store core, fuel, material, working fluid, and control logic parameters and mathematical models.

[0279] The feedback correction and digital twin interface corrects the parameters of the simulation data model based on real-time data and generates short- to medium-term operational trend predictions. Specifically, it dynamically corrects the simulation data model using the latest measured data, improving the model's prediction accuracy by adjusting key parameters such as the friction coefficient and heat transfer coefficient. Based on this, the feedback correction and digital twin interface can generate operational trend predictions and optimization suggestions for 30 minutes to 48 hours, write the corrected model parameters back to the parameter database, pass the optimized state variables to the simulation solution, and output the prediction results and suggested solutions to the module containing the scalable cloud interface and remote data access functionality.

[0280] The scalable cloud interface and remote data access capabilities, via an edge computing gateway and encrypted communication protocols, upload processed and corrected core data and operational prediction data to the cloud. This enables multi-terminal, multi-user collaborative access, supporting remote collaboration and decision support for maintenance, monitoring, and training personnel, as well as allowing remote users to acquire and issue control commands. At the application level, users can receive real-time prediction and operational status data through this module, while simultaneously transmitting control commands or parameter adjustment requirements back via the cloud interface and industry standard protocol adaptation module for simulation solving, thus influencing data acquisition strategies or simulation operating conditions. Control commands can also be directly fed back to online data acquisition to guide data collection.

[0281] In the closed-loop interaction process, the working order and feedback relationship of each function are as follows:

[0282] Online data acquisition obtains various types of operational data from the field in real time;

[0283] The raw data is adapted and converted into a unified standard format using industry standard protocols;

[0284] Standardized data is cleaned, repaired, and anomaly flagged through data preprocessing and anomaly detection.

[0285] The high-reliability data, parameter database, and model library are combined and then fed into the feedback correction and digital twin interface;

[0286] The digital twin interface dynamically corrects the simulation model and generates trend predictions, writes the correction parameters back to the database and outputs them to the simulation core;

[0287] Correction results and prediction information are distributed to users at the application functional level through cloud interfaces and remote data access;

[0288] User decisions or remote commands return data to the interface, which is then adapted to industry standard protocols and sent to online data acquisition or simulation solutions to start the next cycle of calculations.

[0289] Through the above functional design and closed-loop logic, the data interface in this solution can achieve efficient, stable, and real-time simulation data access, processing, and feedback in a multi-source heterogeneous data environment, ensuring the reliability and versatility of the integrated small stack simulation method in various application scenarios such as operation prediction, fault simulation, and remote operation and maintenance.

[0290] The data interface is explained below with a specific solution.

[0291] In a feasible solution, such as Figure 7 As shown, the simulation method also includes:

[0292] S104. Obtain several actual measurement data;

[0293] S105. The mathematical model is modified based on several actual measurement data.

[0294] Specifically, steps S104 and S105 can be executed between steps S101 and S102. Unlike traditional simulation methods that rely solely on independent calculations of physical equations, this scheme introduces a digital twin mechanism to achieve dynamic correction of the data-driven simulation model, thereby improving the consistency and foresight between simulation results and actual operation.

[0295] First, in terms of real-time data feedback, key measurement data from the reactor core and primary loop, such as pressure, coolant flow rate, and core power factor, are input into the simulation solver in real time to correct state variables and ensure that the simulation calculations are based on the latest operating conditions.

[0296] Secondly, regarding model bias correction, when there are discrepancies between simulation results and measured data, a dynamic adjustment mechanism for model parameters is automatically triggered. For example, by correcting key parameters such as the friction resistance coefficient and heat transfer coefficient, the simulation curve gradually converges to the measured curve, thereby reducing model bias.

[0297] Furthermore, in the predictive diagnostic function, the modified model can not only accurately reflect the current operating status, but also predict the operating trend over the next 30 minutes to 48 hours. If the prediction results indicate that the safety margin is about to decrease, a corresponding early warning will be generated, providing a basis for early intervention in operation and scheduling.

[0298] Finally, through digital twin extension, this solution achieves the fusion of the physical model and the data-driven model, constructing an online digital twin system for integrated small modular reactors. This system provides operations and maintenance personnel with flexible accident simulation tools, namely, when specific hypothetical failure conditions are input, it immediately outputs possible evolution trends and operational consequence predictions.

[0299] The feedback correction and digital twin interface proposed in this solution not only ensures the real-time accuracy of simulation calculations, but also provides prediction and rehearsal functions, breaking through the limitations of traditional simulation platforms and demonstrating significant practical value.

[0300] In this scheme, the mathematical model is corrected by actual measurement data, realizing data-driven dynamic correction of the simulation model, which improves the consistency and foresight of the simulation results with actual operation.

[0301] In a feasible solution, such as Figure 8 As shown, before step S105, the following steps are also included:

[0302] S1051. In response to the actual measurement data not belonging to the first preset range, the corresponding actual measurement data is removed from a number of actual measurement data.

[0303] like Figure 9 As shown, before step S105, the following steps are also included:

[0304] S1052. Based on the preset prediction model, obtain the prediction data;

[0305] S1053. Obtain the difference between the actual measurement data and the predicted data;

[0306] S1054. In response to a difference greater than a preset threshold, remove the corresponding actual measurement data from a number of actual measurement data.

[0307] Specifically, in actual power plant operation, the collected monitoring data often suffers from signal corruption, transmission delays, or measurement noise. If these data are directly input into mathematical models for simulation calculations without processing, it can easily lead to distorted simulation results or even numerical divergence. Therefore, this solution's data interface is specially designed and implements data preprocessing and anomaly detection functions to ensure the reliability and robustness of the input data.

[0308] First, in terms of signal filtering, high-pass or low-pass filters are used to reduce noise in the data, and the Kalman filtering method is introduced to achieve smooth estimation of key dynamic signals, such as neutron flux, thereby effectively suppressing instantaneous disturbances.

[0309] Secondly, in terms of anomaly detection, statistical and intelligent methods are combined: on the one hand, a statistical threshold comparison mechanism is used to judge anomalies when real-time data deviates from the mean by more than three times the standard deviation; on the other hand, a machine learning prediction model trained on historical data is used to compare the trends of real-time operating signals to further identify potential abnormal deviations.

[0310] Finally, regarding missing value repair, for short-term signal loss, time interpolation and compensation based on proximity sensors are used for repair; if data is interrupted for a long period of time, the system automatically switches to virtual simulation input mode, where the simulation system predicts and replaces the missing information based on its internal model to ensure computational continuity.

[0311] This solution enables efficient preprocessing and anomaly shielding at the data acquisition level, effectively preventing erroneous signals from interfering with simulation calculations and improving the stability and reliability of the simulation.

[0312] The online data acquisition function of the data interface is used to access the operational data from the integrated small modular reactor (SMR) power plant site, which typically includes the following categories:

[0313] Process parameters: coolant temperature, pressure, flow rate, steam quality at the steam generator outlet, etc.

[0314] Core parameters: neutron flux, power distribution, reactivity margin, etc.

[0315] Control system parameters: control rod position, valve opening signal, pump start / stop status, etc.

[0316] Safety system parameters: emergency water injection level, cooling system water tank pressure, and accident signal triggering status.

[0317] To accommodate data acquisition needs at different frequencies on-site, this module supports:

[0318] High-frequency sampling channels: such as neutron flux, key temperature points, 50~100Hz per second;

[0319] Low-frequency sampling channels: such as system pressure changes, stack power measurement points, 1~10Hz per second;

[0320] Event triggering channels: such as emergency shutdown signals, valve switching information.

[0321] This multi-channel design achieves full data coverage, ensuring that the environment seen by the simulation method is consistent with the actual heap operation.

[0322] During nuclear power plant operation, common control and monitoring methods are typically based on DCS or SCADA systems and follow various industry communication protocols, such as OPC (OLE for Process Control), MODBUS, and PROFINET. To ensure that the simulation method in this solution can achieve plug-and-play online operation with the actual unit, this solution is specifically designed with industrial protocol adaptation functionality.

[0323] The industrial protocol adaptation features include: a built-in OPC UA client / server for seamless integration with mainstream DCS / SCADA systems; support for the MODBUS TCP protocol for exchanging high-frequency monitoring data with external devices; and support for a lightweight MQTT-based message channel suitable for rapid interaction in remote deployment and cloud environments.

[0324] Through the above design, the industrial protocol adaptation of this solution ensures the universality and portability of the simulation method in different plant environments, laying a technical foundation for building a cross-platform, flexibly deployable nuclear power simulation platform.

[0325] To ensure the long-term stable operation of the simulation method, this solution establishes a comprehensive parameter database and model library for its data interface. These include:

[0326] Fuel and core parameter database: fuel type, abundance, burnup curve; core geometry, coolant volume.

[0327] Thermal-hydraulic property database: physical properties of different working fluids, such as saturation line, viscosity, and thermal conductivity of water / steam.

[0328] Material performance parameter database: thermal conductivity, coefficient of thermal expansion, and stress resistance of key structural materials, such as alloys, cladding, and container steel.

[0329] Control logic model library: including power regulation rules, protection action logic, and control strategy configuration under different national standards.

[0330] These databases form the knowledge base for simulation methods, serving both for simulation initialization and for real-time support of digital twin computations.

[0331] Considering that integrated small modular reactors may be deployed in remote or non-urbanized areas, and that R&D, operation and maintenance, and monitoring teams may be located in different locations, this solution designs a scalable cloud interface and remote data access architecture in its simulation methodology. This architecture is implemented by: deploying an edge computing gateway on-site to preprocess and perform preliminary analysis on real-time collected data, and uploading it to the cloud via a secure protocol; and configuring a high-performance simulation engine in the cloud to handle some complex computational processes, thereby reducing the computational burden on the on-site system and improving overall response speed.

[0332] In terms of application features, this solution supports multi-user collaborative access, allowing operations and maintenance personnel, regulatory agencies, and trainers to simultaneously access and utilize simulation results, enabling real-time collaboration across departments and regions. Regarding data privacy and security, it employs encrypted transmission mechanisms and role-based access control to ensure that data exchange and access processes meet the high-level network and information security requirements of nuclear facilities. Leveraging scalable cloud interfaces and remote data access capabilities, the small modular reactor (SMR) simulation method maintains real-time performance on-site while also enabling remote sharing and collaborative operations and maintenance, thereby significantly improving operation and maintenance efficiency.

[0333] The simulation method in this embodiment overcomes the limitations of existing nuclear power simulation methods in terms of real-time performance, coupling accuracy, and application scope, demonstrating significant practical benefits. First, this embodiment highly couples neutron dynamics, thermal hydraulics, and fuel heat transfer processes through GPU parallel computing and an adaptive time-step algorithm. While satisfying the realistic mechanisms of multiphysics, it achieves real-time calculations at the second level, enabling rapid prediction and dynamic response of reactor operating conditions, significantly improving operational safety margins. Second, this simulation method supports multiple industrial protocols such as OPC UA, MODBUS, and MQTT in its data interface, allowing seamless integration with power plant control systems. Furthermore, by leveraging digital twin technology, it achieves real-time correction and model adaptation of operating data, keeping the deviation between predicted results and actual operating curves within the engineering allowable range, thereby effectively improving diagnostic accuracy.

[0334] Example 2

[0335] This embodiment provides a method for predicting the operating status of an integrated small stack, such as... Figure 10 As shown, the prediction method includes:

[0336] S201. Obtain several actual measurement data;

[0337] S202. Based on several actual measurement data and target simulation results, predict the preset operating parameters;

[0338] The target simulation results were obtained based on the simulation method of the integrated small stack in Example 1.

[0339] Specifically, the prediction method, as the direct application of the simulation method, is built upon mathematical models, simulation solutions, and data interfaces. It directly serves application users, addressing multiple scenarios such as nuclear power plant operation, maintenance, training, and management. Compared to existing large pressurized water reactor simulation and prediction methods, this solution offers significant improvements in functionality, flexibility, and intelligence.

[0340] The predictive method receives standardized simulation data and real-time signals from a data interface, analyzes and processes them to generate user decisions or control commands, such as adjusting control rod positions or changing cooling pump operating conditions. These commands are then fed back through the data interface for simulation solving, thereby altering the simulation scenario or operating parameters and achieving real-time interaction and closed-loop control. Based on real-time standardized simulation data, the predictive method generates functional information for operation monitoring, optimized scheduling, accident drills, and training, while simultaneously outputting control commands to the data interface to adjust simulation conditions and model input parameters.

[0341] The prediction method in this solution can realize online operation prediction and status monitoring, accident emergency simulation and drills, operation and maintenance support and predictive maintenance, operator training and public education, multi-stack parallel simulation and grid adaptation, visualization and human-computer interaction.

[0342] Online operation prediction and status monitoring are divided into real-time prediction capability and operation deviation diagnosis.

[0343] Regarding real-time prediction capabilities, it can generate short-term predictions of future operating states based on real-time collected operational data and simulation calculations.

[0344] During steady-state operation, key parameters such as coolant outlet temperature, pressure, and secondary circuit steam parameters can be predicted for the next 10 to 30 minutes.

[0345] In load variation scenarios, it can predict the power stabilization time, peak fuel temperature, and thermal margin after power point tracking.

[0346] In the event of abnormal minor disturbances, such as a pump power outage, the system can predict the parameter trend several seconds later within a few seconds, assisting operators in making judgments.

[0347] Supported by simulation methods, this prediction method achieves real-time operational prediction and monitoring at the application level. Firstly, in short-term prediction, based on transient simulation models, it dynamically predicts key operating parameters such as temperature, pressure, and power for the next few minutes to tens of minutes, helping operators to promptly identify operational risks, such as approaching saturation pressure or other critical conditions. Secondly, in medium- and long-term prediction, by using digital twin models combined with fuel consumption patterns and reactivity loss curves, it can predict core lifespan evolution and operational trends over one to three months, providing a basis for core component lifespan management.

[0348] Building upon this foundation, the predictive method further provides operational optimization suggestions, such as automatically generating power control or cooling adjustment plans based on predictions to prevent critical parameters from exceeding limits. Simultaneously, the predictive method also features multi-dimensional visualization alarm capabilities, displaying prediction results in a 3D scene or virtual reality (VR) and visually representing fuel temperature distribution through color or gradient methods, enabling operators to intuitively identify operational anomalies. Through this design, the predictive method achieves an organic combination of real-time monitoring, forward-looking prediction, and intelligent optimization, effectively improving the operational safety and maintenance efficiency of small modular reactors (SMRs).

[0349] In this scheme, key operating parameters of the integrated small modular reactor are dynamically predicted based on several actual measurement data and target simulation results, which helps operators to identify operational risks in a timely manner and ensures the safety and reliability of the integrated small modular reactor.

[0350] In one feasible approach, the prediction method also includes:

[0351] Based on several actual measurement data and target simulation results, the operational deviation state of the integrated small reactor was determined.

[0352] Specifically, for operational deviation diagnosis based on online operation prediction and condition monitoring, not only is prediction performed, but potential problems can also be diagnosed by comparing simulation results with actual measurements. For example:

[0353] If the actual outlet temperature is higher than the simulated predicted temperature, there may be local heat exchange blockage.

[0354] If the pressure drop exceeds that of the simulation model, it can prompt maintenance personnel to check for leakage risks.

[0355] In this scheme, the operational deviation status is determined based on several actual measurement data and target simulation results, providing additional information redundancy for the operation monitoring of the integrated small reactor, diagnosing potential problems, and ensuring the safety and reliability of the integrated small reactor.

[0356] Since safety is the core objective of nuclear energy applications, the prediction method places particular emphasis on the simulation, drills and emergency training of accident scenarios, that is, providing accident emergency simulation and drill functions.

[0357] Accident emergency simulation and drills are divided into typical design baseline accident simulation, beyond design baseline accident simulation, and online emergency drills.

[0358] For simulation of typical design baseline accidents, including reactor shutdown accidents, coolant pump failure accidents, and secondary loop breaches.

[0359] Reactor shutdown accident: Simulation of power drop curve and residual heat removal path after rapid insertion of control rods.

[0360] Coolant pump failure accident: natural circulation establishment process and prediction of core temperature rise.

[0361] Secondary loop rupture: steam release dynamics, pressure changes, and safety system response.

[0362] The predictive method supports simulations of severe operating conditions such as total power failure (SBO) and core meltdown trends, providing a basis for operators and regulators to conduct drills, namely, simulations of accidents beyond design baselines.

[0363] For online emergency drills, the prediction method can be integrated with the power plant accident simulation platform. The interface parameters received by operators are consistent with those of the actual unit, while the backend is calculated and generated using simulation methods. This approach is more realistic than traditional pre-set script drills and can dynamically adjust the accident process based on real-time operator feedback.

[0364] Unlike traditional prediction methods, this solution's prediction method for operation and maintenance support and predictive maintenance is not limited to training, but has direct value in operation and maintenance.

[0365] Operations support and predictive maintenance include functions such as online digital twins, device-level health management, and remote operations and maintenance.

[0366] Online digital twin: By collecting sensor data from equipment, such as pump speed, valve opening, pipe wall temperature, and heat exchanger temperature difference, and fusing it with simulation results, a digital twin of the reactor is established.

[0367] If the simulation model deviates from the measured data over a long period of time, it may indicate material aging, deposits of dirt, or sensor drift.

[0368] Digital twins can also predict the timing of the next major overhaul, such as the frequency of cleaning the secondary heat exchanger tubes.

[0369] Equipment-level health management: In addition to simulation, it also includes built-in small module models of equipment such as pumps, valves, and heat exchangers. By comparing with real-time operation, quantitative evaluation of equipment performance can be made to assist in maintenance decisions.

[0370] Remote operation and maintenance: Since integrated small stack applications are often distributed in remote areas, this prediction method has remote access and cloud computing support. The operation and maintenance center can view simulation data in real time in a remote location and conduct remote inspections.

[0371] Operator training and public education include training functions and VR / AR (Augmented Reality) immersive environments.

[0372] Training Function: Through a human-machine interface, operators can conduct basic training on daily reactor startup, load changes, and normal reactor shutdown. Predictive methods provide a wealth of accident scenario drills, including coolant loss, secondary circuit breaches, and fuel temperature surges. Upon completion of training, an assessment report is automatically generated, including parameter deviations, operation duration, and records of misoperations.

[0373] VR / AR immersive environment: With a built-in 3D visualization engine, it can be used in conjunction with VR / AR devices, allowing users to "walk into the reactor building" in a virtual environment and observe the reactor vessel, steam generator, control console, etc.

[0374] In VR training, trainees use controllers to perform actions such as valve adjustment and switch triggering, enhancing the sense of immersion. It also has a positive impact on public education, providing a more accessible and engaging explanation of the principles and safety of small stacks.

[0375] For multi-reactor parallel simulation and grid adaptability, small modular reactor (SMR) designs generally emphasize the parallel operation of multiple modules. For example, 4 to 12 SMRs can be connected to a single turbine system to achieve flexible output adjustment and system redundancy backup. This solution addresses this characteristic by implementing multi-reactor parallel simulation functionality in the simulation platform. The hardware architecture employs a distributed parallel computing approach, with each reactor module corresponding to an independent high-performance computing node to perform refined numerical solutions for in-reactor neutronics, thermal hydraulics, etc., in parallel. The software architecture establishes a unified system bus interface for sharing key coupling parameters between different computing nodes, including steam pressure and flow rate, secondary loop load distribution, etc., thereby ensuring the synchronization and coupling accuracy of the operating states of multiple units.

[0376] Based on this architecture, the prediction method can not only recreate the operating conditions of multiple reactors operating together, but also support performance analysis under different load allocation strategies, study the mutual interference effects of sudden failures of a single reactor or some units on the overall system, and conduct grid connection stability assessments. Compared with traditional prediction methods that only support single-reactor operation models, this solution can fully reproduce the collaborative characteristics of multi-module small reactors operating in distributed power sources or flexible grids in a virtual environment, which helps to provide a means of verifying optimization methods and operating strategies for practical engineering deployments.

[0377] Regarding visualization and human-machine interaction functions, the predictive approach focuses on real-time visualization of operational information and user-friendly interaction in terms of human-machine interface design. Through real-time 3D animation rendering, the interface can dynamically present the core structure, coolant flow path, and temperature gradient distribution, enabling operators to intuitively perceive the system's operating status and trends in a visualized environment. In terms of operational safety alerts, a visual alarm mechanism is provided. Once critical parameters such as pressure, temperature, and power exceed limits, color flashing alerts and audible warnings will be automatically triggered, ensuring that operators can detect and respond to abnormal situations immediately.

[0378] Meanwhile, to support operational analysis and post-event evaluation, the forecasting method provides trend curves and reporting functions, enabling real-time plotting of the time evolution curves of multiple operational parameters and automatic export of standardized reports as needed. Furthermore, this forecasting method is equipped with an expandable data interface, supporting the transmission of real-time data and visualization results to external teaching displays or regulatory cloud platforms, achieving information sharing and cross-domain applications, and demonstrating significant advantages in scenarios such as training, supervision, and remote technical support.

[0379] The prediction method in this embodiment is applicable not only to steady-state and transient calculations but also supports design-baseline accident simulations such as coolant pump tripping and water loss. It provides an immersive and interactive environment for operator emergency training, significantly improving the realism and efficiency of the training. Simultaneously, the prediction method also possesses remote operation and maintenance capabilities, predicting the degradation trends of critical equipment such as heat exchangers, assisting in the development of optimized maintenance plans, and reducing the risk of unplanned reactor outages. Finally, this prediction method's multi-reactor parallel simulation and cloud deployment can meet the needs of future multi-module operation and distributed applications of small modular reactors (SMRs). In summary, this embodiment is not only technically advanced and feasible but also has outstanding economic and social benefits in reducing operation and maintenance costs, improving safety levels, and increasing social acceptance. Furthermore, this embodiment has good practicality and economy; it can be integrated into existing integrated SMR control systems with only software upgrades, without hardware modifications, and is applicable to distributed energy supply, seawater desalination, and other fields. Overall, this method promotes the commercialization of SMR technology, is expected to reduce maintenance costs, and provides an innovative paradigm for the autonomous control of next-generation nuclear energy systems, possessing broad application prospects and significant socio-economic benefits.

[0380] Example 3

[0381] Corresponding to the aforementioned integrated small-scale reactor simulation method embodiment, this embodiment provides an integrated small-scale reactor simulation system, such as... Figure 11 As shown, the simulation system includes:

[0382] Physical modeling layer 1 is used to establish mathematical models of several physical fields of the integrated mini-relay based on the design and operating parameters of the integrated mini-relay.

[0383] The mathematical model includes at least one of the following: natural circulation driving force model, two-phase heat transfer correlation model, and emergency cooling water natural injection model.

[0384] The natural circulation driving force model is used to simulate the natural circulation intensity of an integrated small reactor based on the fluid state of the integrated small reactor.

[0385] Two-phase flow heat transfer correlation model is used to simulate the two-phase flow heat transfer coefficient of integrated small reactor;

[0386] The emergency cooling water natural injection model is used to simulate the natural injection state of the cooling water tank of an integrated small modular reactor under accident conditions.

[0387] Simulation solution layer 2 is used to perform simulation calculations on each physical field based on the mathematical model to obtain the first simulation result corresponding to each physical field; based on the first simulation result, the target simulation result corresponding to the integrated small reactor is obtained.

[0388] In a feasible scheme, the natural circulation driving force model is constructed based on parameters such as natural circulation driving force, average density difference of fluid in hot and cold sections, effective height difference of hot and cold sections, loop mass flow rate, flow channel cross-sectional area, local flow resistance coefficient, friction coefficient, and pipe length-to-diameter ratio.

[0389] And / or,

[0390] The two-phase heat transfer correlation model is constructed based on parameters such as Reynolds number, Prandtl number, correction factor for geometric density characteristics of integrated small reactor, convective heat transfer coefficient, nucleus boiling heat transfer coefficient, inhibition factor and enhancement factor;

[0391] And / or,

[0392] The emergency cooling water natural injection model is constructed based on parameters such as flow coefficient, injection port cross-sectional area, height difference between water tank level and core inlet, cooling water density, and pressure drop caused by local core resistance.

[0393] And / or,

[0394] The mathematical model includes a coefficient matrix, a system of equations, and initial conditions;

[0395] And / or,

[0396] The first simulation results include at least one of the following: temperature field, pressure, flow rate, and neutron flux distribution;

[0397] And / or,

[0398] The mathematical model also includes the neutron dynamics model;

[0399] Neutron dynamics models include point-pile dynamics models and spatial partitioning analysis models;

[0400] Among them, the point-pile dynamics model is used to adjust the steady-state power of the integrated small reactor and to simulate the global transient of the core of the integrated small reactor.

[0401] The spatial partitioning analysis model is used to analyze the impact of local power distribution variations of integrated small modular reactors on the safety margin of integrated small modular reactors.

[0402] And / or,

[0403] The mathematical model also includes a finite volume method multilayer heat conduction model, which is used to simulate the multilayer heat conduction behavior of fuel rods, pressure vessel walls and heat exchange tubes in an integrated small reactor.

[0404] And / or,

[0405] The mathematical model also includes a thermal stress coupling model, which is used to calculate the thermal stress and structural strength margin caused by cyclic temperature changes under preset operating conditions.

[0406] And / or,

[0407] The mathematical model also includes a sensor feedback correction model, which is used to correct the temperature data in the mathematical model other than the sensor feedback correction model based on the surface temperature measurement data of the sensor.

[0408] In one feasible approach, simulation solution layer 2 includes:

[0409] The coupled calculation module 21 is used to perform iterative coupled calculations on the mathematical model in each calculation time step to obtain a set of coupled equations;

[0410] The first result acquisition module 22 is used to obtain the first simulation result corresponding to each physical field based on the coupled equation set;

[0411] And / or,

[0412] Simulation solution layer 2 includes:

[0413] Simulation duration acquisition module 23 is used to acquire simulation duration;

[0414] The second result acquisition module 24 is used to take the currently obtained simulation result as the first simulation result in response to the simulation duration reaching the preset simulation period and / or the corresponding simulation result satisfying the preset convergence condition.

[0415] And / or,

[0416] Simulation solution layer 2 also includes:

[0417] Model correction module 25 is used to correct the coefficient matrix and initial conditions of the mathematical model based on the first simulation results;

[0418] And / or,

[0419] Simulation solution layer 2 includes:

[0420] The target result acquisition module 26 is used to assign independent computing nodes to the mathematical model corresponding to each integrated mini-heap using the MPI distributed computing framework, so as to obtain the target simulation results corresponding to each integrated mini-heap.

[0421] Optionally, the simulation system also includes:

[0422] Data interface layer 3 is used to acquire several actual measurement data; and to revise the mathematical model based on the several actual measurement data.

[0423] In one feasible solution, the data interface layer 3 is also used to remove the corresponding actual measurement data from a plurality of actual measurement data in response to the actual measurement data not belonging to the first preset range;

[0424] And / or,

[0425] Based on the preset prediction model, the prediction data is obtained;

[0426] Obtain the difference between the actual measured data and the predicted data;

[0427] In response to a difference greater than a preset threshold, the corresponding actual measurement data is removed from a number of actual measurement data.

[0428] In this embodiment, a multiphysics mathematical model dedicated to integrated small modular reactors is introduced, and a dedicated model library is added, including the natural circulation driving force model, the two-phase heat transfer correlation model, and the emergency cooling water natural injection model, to accurately reproduce the coupled thermal-hydraulic characteristics under the integrated small modular reactor layout, ensuring the accuracy and reliability of the simulation results.

[0429] Example 4

[0430] Corresponding to the aforementioned embodiment of the method for predicting the operating status of an integrated small modular reactor, this embodiment provides a system for predicting the operating status of an integrated small modular reactor, the system comprising:

[0431] The application function layer is used to acquire several actual measurement data; based on the several actual measurement data and the target simulation results, it predicts the preset operating parameters;

[0432] The target simulation results are obtained based on the aforementioned integrated small reactor simulation system.

[0433] In one feasible approach, the application functional layer is also used to determine the operational deviation state of the integrated small reactor based on several actual measurement data and target simulation results.

[0434] In this embodiment, the key operating parameters of the integrated small modular reactor are dynamically predicted based on several actual measurement data and target simulation results, which helps operators to identify operational risks in a timely manner and ensures the safety and reliability of the integrated small modular reactor.

[0435] The working principle of the integrated small-scale reactor operation status prediction system in this embodiment is explained below with specific examples:

[0436] By adopting an overall technical framework consisting of a physical modeling layer, a simulation solution layer, a data interface layer, and an application function layer, this approach addresses the problems of insufficient adaptability, poor real-time performance, and limited scalability of traditional simulation and prediction platforms in small integrated reactor applications. As a result, it has broad applicability in various application scenarios such as design verification, operation monitoring, accident analysis, operator training, and remote operation and maintenance.

[0437] Compared to traditional large pressurized water reactor simulation and prediction systems, integrated small modular reactors (SMRs) differ significantly in physical structure, operation mode, and safety assurance mechanisms. The characteristics of integrated SMRs are as follows:

[0438] The integrated layout results in a high degree of coupling between the reactor core, steam generator, pressurizer, and cooling circuit, making it difficult to directly map using traditional distributed node models;

[0439] Small modular reactors generally employ natural circulation and passive safety systems, while traditional simulation systems are mostly designed for forced circulation and active safety features.

[0440] During large-scale deployment, small-scale reactors are expected to be built in a multi-module parallel manner, which requires both precise modeling of individual reactors and consideration of coupled simulation across reactor units;

[0441] Since the application of small modular reactors may be targeted at different countries and regions, low-cost, lightweight, and remotely usable simulation tools are needed.

[0442] In view of the characteristics of the integrated small modular reactor mentioned above, the overall scheme of the prediction system proposed in this embodiment has the following technical ideas:

[0443] Compactly coupled physical modeling is employed to accommodate the integrated layout of small heaps;

[0444] A dedicated flow and heat transfer model for natural circulation is introduced to ensure accurate simulation under passive operating conditions;

[0445] A real-time multiphysics solver was built, which can complete the transient response calculation of mini-heaps in seconds under multi-threaded and GPU environments;

[0446] Establish a digital twin interface to connect the simulation system with power plant operation data to achieve dynamic correction;

[0447] It provides modular expansion capabilities, allowing for flexible configuration of simulation operations under single-stack, multi-stack, and different operating conditions;

[0448] Expand application layer functionality to cover purposes such as incident emergency response, operation and maintenance analysis, training and education, and public communication.

[0449] like Figure 12 As shown, the prediction system in this embodiment consists of the following four layers:

[0450] Physical Modeling Layer 1: Used to model various physical processes of the reactor system, including neutron dynamics, thermal hydraulics, heat conduction, and thermal stress. Specialized model libraries are included to address the natural circulation and passive safety characteristics of small modular reactors (SMRs), such as pressurizer pressure fluctuation models, natural circulation thermosiphon models, and emergency cooling water gravity injection models.

[0451] Simulation Solution Layer 2: Contains numerical solution algorithms for transient equations, employing parallel computing, adaptive meshing, and dynamic step size techniques to ensure real-time performance and stability. It includes two built-in modes: steady-state mode for initial state calculation and transient mode for accident or disturbance simulation.

[0452] Data Interface Layer 3: This layer interfaces with real small modular reactor (SMR) operation data via sensor interfaces, ensuring consistency between the model and actual measurements. It also provides database access: fuel parameter database, material property library, control logic parameter library, etc.

[0453] Application functional layer 4 implements the following functions: online operation prediction and status monitoring, continuously providing predictions of temperature field, flow field, and power distribution during reactor operation; accident emergency simulation and drills, supporting simulations of design basis accidents and beyond design basis accidents; operator training and public education; intuitive 3D visualization and VR interaction capabilities; operation and maintenance support and predictive maintenance, including online digital twins, supporting remote operation and maintenance and data-driven predictive maintenance; multi-reactor parallel simulation and grid adaptation, with a distributed parallel computing approach in the hardware architecture, where each reactor module corresponds to an independent high-performance computing node, performing refined numerical solutions for in-reactor neutronics, thermal hydraulics, etc., in parallel; a unified system bus interface in the software architecture for sharing key coupling parameters between different computing nodes, including steam pressure and flow rate, secondary loop load distribution, etc.; visualization and human-machine interaction, focusing on real-time visualization and user-friendly interaction of operating information.

[0454] The physical modeling layer includes neutron dynamics model, thermal-hydraulic model, thermal structure and heat transfer model, and control system model.

[0455] The simulation solution layer covers multiphysics equation coupling strategies, numerical calculation schemes, real-time performance guarantee mechanisms, parallel computing architectures, fault tolerance and robustness mechanisms, and other related content.

[0456] The data interface layer mainly includes the following functional modules: online data acquisition module, industry standard protocol adaptation module, parameter database and model library, data preprocessing and anomaly detection module, feedback correction and digital twin interface module, and scalable cloud interface and remote data access module.

[0457] Through the above-described hierarchical structure design, the prediction system of this embodiment can not only accurately reflect the multi-physics coupling behavior of the integrated small stack, but also ensure real-time performance and interactivity, making it suitable for various scenarios such as operation prediction, accident drills, digital twins, and teaching and training.

[0458] The data transfer between the physical modeling layer, simulation solution layer, data interface layer and application function layer adopts a two-way closed-loop feedback structure, including: using simulation results to correct the initial boundary conditions and physical property data of the physical model; using key operating parameters acquired in real time to update the simulation input; and using control commands generated by the application function layer to change the model control variables and operating conditions, thereby realizing a fully coupled closed loop between the physical field and the control system.

[0459] The mathematical model established in the physical modeling layer 1 includes a coefficient matrix, a system of equations, and initial conditions. These coefficient matrix, equations, and initial conditions are then passed to the simulation solution layer 2.

[0460] Simulation solution layer 2 receives the coefficient matrix, equation set and initial conditions generated by the physical modeling layer, solves them using numerical calculation methods, obtains the first simulation results such as temperature field, pressure, flow rate and neutron flux distribution, and outputs them to data interface layer 3.

[0461] The data interface layer 3 is located between the simulation solution layer 2 and the application function layer 4. It standardizes the data of the first simulation result, merges it with the real-time data, and outputs it to the application function layer 4.

[0462] Application functional layer 4 receives the standardized first simulation results and real-time data, analyzes and processes them to form user decisions or control commands, and the control commands can feed back values ​​to the mathematical model to update the parameters in the mathematical model.

[0463] For the system embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs.

[0464] Example 5

[0465] Figure 13This is a schematic diagram of the structure of an electronic device according to an example embodiment of the present disclosure. The electronic device includes a memory, a processor, and a computer program stored in the memory and used to run on the processor. When the processor executes the computer program, it implements the simulation method of the integrated small stack or the prediction method of the operating state of the integrated small stack as described in any of the above embodiments. Figure 13 The electronic device 90 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0466] like Figure 13 As shown, the electronic device 90 can be manifested as a general-purpose computing device, such as a server device. The components of the electronic device 90 may include, but are not limited to: at least one processor 91, at least one memory 92, and a bus 93 connecting different system components (including memory 92 and processor 91).

[0467] Bus 93 includes a data bus, an address bus, and a control bus.

[0468] The memory 92 may include volatile memory, such as random access memory (RAM) 921 and / or cache memory 922, and may further include read-only memory (ROM) 923.

[0469] The memory 92 may also include a program tool 925 (or utility) having a set (at least one) program module 924, such program module 924 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0470] The processor 91 executes various functional applications and data processing by running computer programs stored in the memory 92, such as the simulation method of the integrated small stack or the prediction method of the operating state of the integrated small stack provided in any of the above embodiments.

[0471] Electronic device 90 can also communicate with one or more external devices 94 (e.g., keyboard, pointing device, etc.). This communication can be performed through input / output (I / O) interface 95. Furthermore, electronic device 90 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public network, such as the Internet) via network adapter 96. As shown, network adapter 96 communicates with other modules of electronic device 90 via bus 93. It should be understood that, although not shown in the figure, other hardware and / or software modules can be used in conjunction with electronic device 90, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID (disk array) systems, tape drives, and data backup storage systems.

[0472] It should be noted that although several units / modules or sub-units / modules of the electronic device have been mentioned in the detailed description above, this division is merely exemplary and not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more units / modules described above can be embodied in one unit / module. Conversely, the features and functions of one unit / module described above can be further divided and embodied by multiple units / modules.

[0473] Example 6

[0474] This disclosure also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the simulation method for an integrated small stack or the prediction method for the operating state of an integrated small stack provided in any of the above embodiments.

[0475] The readable storage medium may be more specifically adopted, including but not limited to: portable disk, hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0476] Example 7

[0477] This disclosure also provides a computer program product, including a computer program that, when executed by a processor, implements the simulation method for an integrated small stack or the prediction method for the operating state of an integrated small stack as described above.

[0478] The program code for executing the computer program product of this disclosure can be written in any combination of one or more programming languages, and the program code can be executed entirely on a user device, partially on a user device, as a stand-alone software package, partially on a user device and partially on a remote device, or entirely on a remote device.

[0479] While specific embodiments of this disclosure have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of this disclosure is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of this disclosure, but all such changes and modifications fall within the scope of protection of this disclosure.

Claims

1. A simulation method for an integrated small-scale reactor, characterized in that, The simulation method includes: Based on the design and operating parameters of the integrated small reactor, a mathematical model of several physical fields of the integrated small reactor is established. The mathematical models include a natural circulation driving force model, a two-phase heat transfer correlation model, and an emergency cooling water natural injection model. The natural circulation driving force model is used to simulate the natural circulation intensity of the integrated small reactor based on the fluid state of the integrated small reactor; The two-phase flow heat transfer correlation model is used to simulate the two-phase flow heat transfer coefficient of the integrated small reactor. The emergency cooling water natural injection model is used to simulate the natural injection state of the cooling water tank of the integrated small reactor under accident conditions. The mathematical model also includes a neutron dynamics model, a thermal-hydraulic model, a thermal structure and heat transfer model, and a control system model; The neutron dynamics model, the thermal-hydraulic model, the thermal structure and heat transfer model, and the control system model achieve fully coupled closed-loop operation through parameter transfer and feedback mechanisms; The output of the neutron dynamics model is input as a heat source to the thermal-hydraulic model and the thermal-structure and heat transfer model; the output of the thermal-hydraulic model is provided as a fluid boundary condition to the thermal-structure and heat transfer model and fed back to the neutron dynamics model as a density; the fuel temperature output by the thermal-structure and heat transfer model is fed back to the neutron dynamics model; the control system model issues control commands based on monitoring signals from the neutron dynamics model and the thermal-hydraulic model to change the reactivity input of the neutron dynamics model and the flow or pressure boundary conditions of the thermal-hydraulic model. Based on the mathematical model, simulation calculations are performed on each physical field to obtain the first simulation result corresponding to each physical field. Based on the first simulation result, the target simulation result corresponding to the integrated small reactor is obtained; The calculation formula corresponding to the natural cycle driving force model is as follows: ； ； in, This represents the driving force of natural circulation (Pa). This represents the acceleration due to gravity (m / s²). H represents the average density difference of the fluid between the cold and hot sections (kg / m³), and H represents the effective height difference between the cold and hot sections (m). The value represents the loop mass flow rate (kg / s), and A represents the cross-sectional area of ​​the flow channel (m²). The sum of local flow resistance coefficients is represented by f, the friction coefficient is represented by L / D, and the length-to-diameter ratio of the pipe is represented by L / D. The calculation formula corresponding to the two-phase heat transfer correlation model is as follows: Modified Dittus–Boelter: ; The revised Chen model: ; Where Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number. To account for the correction factor of small stack geometry / power density characteristics, The two-phase heat transfer coefficient (W / m²K) The convective heat transfer coefficient is... Where is the nucleus boiling heat transfer coefficient, S is the inhibition factor, and F is the enhancement factor; First, the convective heat transfer coefficient adapted for small reactor operation is calculated using the modified Dittus-Boelter. Then the convective heat transfer coefficient The nucleus boiling heat transfer coefficient h is input into the modified Chen model. nb By superimposing these values, the heat transfer coefficient of the two-phase flow region is obtained, which is closer to the actual situation of the small pile. ; The calculation formula corresponding to the emergency cooling water natural injection model is as follows: ； in, Mass flow rate (kg / s) injected into the reactor core. For flow coefficient, This represents the cross-sectional area of ​​the injection port (m²). The height difference (m) between the water tank level and the reactor core inlet. The density of cooling water (kg / m³) The pressure drop (Pa) is caused by the local drag of the reactor core, and t represents time.

2. The simulation method for the integrated small reactor as described in claim 1, characterized in that, The natural circulation driving force model is constructed based on parameters such as natural circulation driving force, average fluid density difference between hot and cold sections, effective height difference between hot and cold sections, loop mass flow rate, flow channel cross-sectional area, local flow resistance coefficient, friction coefficient, and pipe length-to-diameter ratio. And / or, The two-phase heat transfer correlation model is constructed based on parameters such as Reynolds number, Prandtl number, correction factor for the geometric density characteristics of the integrated small reactor, convective heat transfer coefficient, nucleus boiling heat transfer coefficient, inhibition factor, and enhancement factor. And / or, The emergency cooling water natural injection model is constructed based on parameters such as flow coefficient, injection port cross-sectional area, height difference between water tank level and core inlet, cooling water density, and pressure drop caused by local core resistance. And / or, The mathematical model includes a coefficient matrix, a system of equations, and initial conditions; And / or, The first simulation results include at least one of the following: temperature field, pressure, flow rate, and neutron flux distribution; And / or, The neutron dynamics model includes a point-pile dynamics model and a spatial partitioning analysis model; The point-pile dynamics model is used to adjust the steady-state power of the integrated small reactor and to simulate the global transients of the core of the integrated small reactor. The spatial partitioning analysis model is used to analyze the impact of local power distribution changes of the integrated small reactor on the safety margin of the integrated small reactor. And / or, The mathematical model also includes a finite volume method multilayer heat conduction model, which is used to simulate the multilayer heat conduction behavior of the fuel rods, pressure vessel walls and heat exchange tubes of the integrated small reactor. And / or, The mathematical model also includes a thermal stress coupling model, which is used to calculate the thermal stress and structural strength margin caused by cyclic temperature changes under preset operating conditions. And / or, The mathematical model also includes a sensor feedback correction model, which is used to correct the temperature data in the mathematical model other than the sensor feedback correction model based on the surface temperature measurement data of the sensor.

3. The simulation method for the integrated small reactor as described in claim 1, characterized in that, The step of performing simulation calculations on each physical field based on the mathematical model to obtain the first simulation result corresponding to each physical field includes: Within each computation time step, the mathematical model is iteratively coupled to obtain a set of coupled equations; Based on the set of coupled equations, the first simulation result corresponding to each physical field is obtained; And / or, The step of performing simulation calculations on each physical field based on the mathematical model to obtain the first simulation result corresponding to each physical field includes: Obtain the simulation duration; In response to the simulation duration reaching a preset simulation period and / or the corresponding simulation result satisfying a preset convergence condition, the currently obtained simulation result is taken as the first simulation result. And / or, After the step of performing simulation calculations on each physical field based on the mathematical model to obtain the first simulation result corresponding to each physical field, the method further includes: Based on the first simulation results, the coefficient matrix and initial conditions of the mathematical model are corrected; And / or, The step of obtaining the target simulation result corresponding to the integrated small reactor based on the first simulation result includes: Using the MPI distributed computing framework, independent computing nodes are allocated to the mathematical model corresponding to each integrated mini-relay to obtain the target simulation results corresponding to each integrated mini-relay.

4. The simulation method for an integrated small modular reactor as described in any one of claims 1-3, characterized in that, The simulation method further includes: Obtain several actual measurement data; The mathematical model is modified based on several of the actual measurement data.

5. The simulation method for the integrated small-scale reactor as described in claim 4, characterized in that, Before the step of correcting the mathematical model based on several of the actual measurement data, the method further includes: In response to the actual measurement data not falling within the first preset range, the corresponding actual measurement data is removed from the plurality of actual measurement data; And / or, Based on the preset prediction model, the prediction data is obtained; Obtain the difference between the actual measurement data and the predicted data; In response to the difference being greater than a preset threshold, the corresponding actual measurement data is removed from a plurality of actual measurement data.

6. A method for predicting the operating status of an integrated small modular reactor, characterized in that, The prediction method includes: Obtain several actual measurement data; Based on several actual measurement data and target simulation results, the preset operating parameters are predicted. The target simulation results are obtained based on the simulation method of the integrated small reactor as described in any one of claims 1-5.

7. The method for predicting the operating status of an integrated small modular reactor as described in claim 6, characterized in that, The prediction method further includes: Based on several actual measurement data and the target simulation results, the operational deviation state of the integrated small reactor is determined.

8. An integrated simulation system for small modular reactors, characterized in that, The simulation system includes: The physical modeling layer is used to establish mathematical models of several physical fields of the integrated mini-relay based on the design and operating parameters of the integrated mini-relay. The mathematical models include a natural circulation driving force model, a two-phase heat transfer correlation model, and an emergency cooling water natural injection model. The natural circulation driving force model is used to simulate the natural circulation intensity of the integrated small reactor based on the fluid state of the integrated small reactor; The two-phase flow heat transfer correlation model is used to simulate the two-phase flow heat transfer coefficient of the integrated small reactor. The emergency cooling water natural injection model is used to simulate the natural injection state of the cooling water tank of the integrated small reactor under accident conditions. The mathematical model also includes a neutron dynamics model, a thermal-hydraulic model, a thermal structure and heat transfer model, and a control system model; The neutron dynamics model, the thermal-hydraulic model, the thermal structure and heat transfer model, and the control system model achieve fully coupled closed-loop operation through parameter transfer and feedback mechanisms; The output of the neutron dynamics model is input as a heat source to the thermal-hydraulic model and the thermal-structure and heat transfer model; the output of the thermal-hydraulic model is provided as a fluid boundary condition to the thermal-structure and heat transfer model and fed back to the neutron dynamics model as a density; the fuel temperature output by the thermal-structure and heat transfer model is fed back to the neutron dynamics model; the control system model issues control commands based on monitoring signals from the neutron dynamics model and the thermal-hydraulic model to change the reactivity input of the neutron dynamics model and the flow or pressure boundary conditions of the thermal-hydraulic model. The simulation solution layer is used to perform simulation calculations on each physical field based on the mathematical model to obtain a first simulation result corresponding to each physical field; and based on the first simulation result, to obtain the target simulation result corresponding to the integrated small reactor. The calculation formula corresponding to the natural cycle driving force model is as follows: ； ； in, This represents the driving force of natural circulation (Pa). This represents the acceleration due to gravity (m / s²). H represents the average density difference of the fluid between the cold and hot sections (kg / m³), and H represents the effective height difference between the cold and hot sections (m). The value represents the loop mass flow rate (kg / s), and A represents the cross-sectional area of ​​the flow channel (m²). The sum of local flow resistance coefficients is represented by f, the friction coefficient is represented by L / D, and the length-to-diameter ratio of the pipe is represented by L / D. The calculation formula corresponding to the two-phase heat transfer correlation model is as follows: Modified Dittus–Boelter: ; The revised Chen model: ; Where Nu is the Nusselt number, Re is the Reynolds number, and Pr is the Prandtl number. To account for the correction factor of small stack geometry / power density characteristics, The two-phase heat transfer coefficient (W / m²K) The convective heat transfer coefficient is... Where is the nucleus boiling heat transfer coefficient, S is the inhibition factor, and F is the enhancement factor; First, the convective heat transfer coefficient adapted for small reactor operation is calculated using the modified Dittus-Boelter. Then the convective heat transfer coefficient The nucleus boiling heat transfer coefficient h is input into the modified Chen model. nb By superimposing these values, the heat transfer coefficient of the two-phase flow region is obtained, which is closer to the actual situation of the small pile. ; The calculation formula corresponding to the emergency cooling water natural injection model is as follows: ； in, Mass flow rate (kg / s) injected into the reactor core. For flow coefficient, This represents the cross-sectional area of ​​the injection port (m²). The height difference (m) between the water tank level and the reactor core inlet. The density of cooling water (kg / m³) The pressure drop (Pa) is caused by the local drag of the reactor core, and t represents time.

9. A predictive system for the operating status of an integrated small modular reactor, characterized in that, The prediction system includes: The application function layer is used to acquire several actual measurement data; based on the several actual measurement data and the target simulation results, it predicts the preset operating parameters; The target simulation results are obtained based on the simulation system of the integrated small reactor described in claim 8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and for running on the processor, characterized in that, When the processor executes the computer program, it implements the simulation method of the integrated small stack as described in any one of claims 1-5, or the prediction method of the operating state of the integrated small stack as described in claim 6 or 7.

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