Method for constructing high-fidelity multi-physics data mapping plate fuel effective temperature model

Abstract

The present application belongs to the technical field of plate fuel temperature model, and particularly relates to a plate fuel effective temperature model construction method based on high-fidelity multi-physical field data mapping, which comprises the steps of establishing a fine three-dimensional geometric model, grid division and multi-physical field domain decomposition, setting thermal hydraulic boundary conditions, multi-physical field coupling calculation, and constructing an effective temperature model based on the interpolation idea. Based on the Cardinal framework of the MOOSE platform, a customized coupling is established between the continuous energy neutron transport solver and the solid heat conduction module, the moderator feedback is isolated by adopting the frozen fluid attribute strategy, a high-resolution intra-plate temperature field is generated for the plate fuel grid, and the Doppler reactivity is accurately evaluated. The interpolation type effective temperature model introduced in the present application quantifies the spatial self-shielding effect by introducing a dimensionless parameter γ, and taking the U3Si2-Al dispersed fuel in the standard MFR range as an example, the multi-scale verification from a single plate to a five-plate subassembly proves that the model has good universality.

Description

Technical Field

[0001] This invention belongs to the technical field of plate fuel temperature model, and specifically relates to a method for constructing an effective temperature model of plate fuel based on high-fidelity multiphysics data mapping. Background Technology

[0002] The Doppler effect in nuclear fuel is one of the key physical mechanisms underlying the safety of nuclear reactors. Its essence stems from the thermal motion of atomic nuclei in the fuel: as the fuel temperature increases, the thermal motion of uranium nuclei intensifies, leading to a broadening of the absorption cross-section within the neutron resonance energy region. Thus, with increased power, more neutrons are resonantly absorbed, introducing a transient negative reactive feedback. This mechanism is crucial for maintaining stable operation and safety under abnormal reactor accidents.

[0003] To accurately quantify this effect, existing literature has conducted extensive and in-depth research, but most of these studies focus on traditional rod-shaped fuel elements. With the continuous development of reactor design, plate-shaped fuel elements, due to their unique geometry and excellent heat transfer performance, have gradually become the ideal fuel form for reactors with high power density and high safety requirements. However, research results on rod-shaped fuel cannot be directly applied to plate-shaped fuel, mainly for the following two reasons: First, compared with rod-shaped fuel, which has a drastic radial temperature difference, plate-shaped fuel has a very small temperature difference at rated power. Although the temperature difference is small, under the strong resonant self-shielding effect, neutrons are mainly absorbed at the fuel surface. This means that an effective temperature assessment deviation of only 2-5K can significantly disturb the resonant cross section and cause serious error accumulation during transient processes such as reactive introduction accidents (RIA). Second, traditional multiphysics coupling methods rely heavily on lumped parameters. This simplification eliminates the crucial spatial resolution and related physical self-shielding weights, failing to meet the requirements of high-fidelity safety assessments for accurate feedback.

[0004] Therefore, there is an urgent need to construct a high-precision effective temperature model suitable for plate-shaped fuel elements. Summary of the Invention

[0005] This invention first constructs a high-fidelity numerical model of plate-shaped fuel based on the design parameters of the JRR-3M reactor, and implements a rigorous three-dimensional multiphysics coupling strategy using the Cardinal framework. Subsequently, the theoretical method for Doppler feedback evaluation and the physical interpretation of the novel effective temperature model constructed based on the interpolation principle of this invention are systematically defined. This model, by introducing a calibrable parameter γ, achieves a seamless transition between the limits of the Rowlands model and the Chabert-Santamarina model. Calibration is performed using the neutron resonance characteristics of U3Si2-Al dispersed fuel within the standard MFR range as an example. The results show that a specific value of γ of -0.969 can provide sufficiently accurate Doppler reactivity predictions within the studied MFR range, demonstrating the universality of this effective temperature model.

[0006] The technical solution adopted in this invention is: a method for constructing a high-fidelity multiphysics data mapping plate fuel effective temperature model, comprising the following steps:

[0007] Step 1. Based on the actual design parameters of the JRR-3M research reactor, establish a detailed three-dimensional computational domain geometric model that includes a single fuel plate and its adjacent coolant channels;

[0008] Step 2. Mesh Generation and Multiphysics Domain Decomposition: Considering the high aspect ratio geometry of the plate-shaped fuel element and the computational requirements of nuclear-thermal coupling, the computational domain is decomposed into a solid domain and a fluid domain, and mesh discretization is performed separately for each:

[0009] Solid domain mesh: The heat transfer equations of the fuel core, cladding and support structure are solved using the MOOSE finite element method to generate a mesh containing several HEX8 linear hexahedral elements, and the mesh is divided into three solid subdomains: fuel region, cladding region and support structure region.

[0010] Fluid region mesh: The flow and convective heat transfer of the coolant channels are solved by the NekRS spectral element method. The mesh contains 78,300 hexahedral elements. The corresponding mesh is represented as HEX27 second-order elements in the Exodus exchange format. After being converted to the native NekRS .re2 format by the exo2nek tool, NekRS applies high-order GLL quadrature nodes inside each element for spectral element solution.

[0011] Neutronics Mesh: The OpenMC Monte Carlo neutron transport calculation covers the entire computational domain and is uniformly divided into four material subdomains, which include three solid subdomains in the solid domain mesh and the coolant subdomain in the fluid domain mesh;

[0012] Step 3. Based on the rated operating conditions of the JRR-3M research reactor, set precise thermal-hydraulic boundary conditions;

[0013] Step 4. Coupling Strategy and Numerical Computation Method: Multiphysics simulation is coordinated using the Cardinal framework, which encapsulates OpenMC as the core physics engine. Simultaneously, Bison and NekRS are used to implement thermo-hydraulic feedback. Solid-state heat transfer is represented by the steady-state heat conduction equation. ,in It is the scalar equivalent thermal conductivity. It is a solid temperature gradient. The volumetric heat source is represented; a pseudo-transient interaction strategy is adopted to couple with the inherent transient turbulence solved by NekRS.

[0014] Step 5. Constructing an effective temperature model for plate-shaped fuel based on interpolation:

[0015] Based on the known Rowlands plate fuel model And Chabert-Santamarina model In the formula The space average temperature of the fuel core centerline plane, The space average temperature of the outer surface of the fuel core, To determine the volume average temperature, a dimensionless, calibrable parameter γ is introduced, making the parameter γ such that... and Linear interpolation between

[0016]

[0017] Will and Substituting the expression into the above equation, we derive its analytical form as a weighted synthesis of surface temperature, center temperature, and volume average temperature, which is the constructed effective temperature model for plate-shaped fuel:

[0018] .

[0019] Furthermore, in the constructed effective temperature model for plate-shaped fuels, the γ-ray neutron resonance characteristics of U3Si2-Al dispersed fuels within the standard MFR range were calibrated. -0.969, at which point the effective temperature model for plate-shaped fuel is constructed as follows: The MFR is the ratio of the atomic number density of the moderator to that of the fuel.

[0020] Moreover, in the constructed effective temperature model for plate fuel, when γ=0, it conforms to the Rowlands plate fuel model; when γ=1, it conforms to the Chabert-Santamarina model.

[0021] Furthermore, the actual design parameters of the JRR-3M research reactor used in step 1 include: coolant material: light water; coolant density: 999.63 kg / m³ 3 Average coolant temperature: 311.15 K; operating pressure: 0.152 MPa; core material: U3Si2-Al; fuel enrichment: 20%; U3Si2 volume fraction: 45%; fuel core height: 750 mm; fuel core length: 61.6 mm; fuel core width: 0.76 mm; fuel density: 6975 kg / m³ 3 Support body thickness: 4.8mm; Support body width: 3.8mm; Support body height: 770mm; Support body material: Al plate; Sheath material: 6061-Al; Sheath height: 770mm; Sheath length: 66.6mm; Sheath width: 1.52mm; Sheath density: 2700kg / m³ 3 .

[0022] Furthermore, in step 2, a mesh containing 71,700 HEX8 linear hexahedral elements is generated in the solid domain mesh; the mesh is divided into three material subdomains: a fuel region containing 24,300 elements, a cladding region containing 2,790 elements, and a support structure region containing 19,500 elements.

[0023] Furthermore, in step 2, a mesh containing 71,700 HEX8 linear hexahedral elements is generated in the solid domain mesh; the mesh is divided into three material subdomains: a fuel region containing 24,300 elements, a cladding region containing 2,790 elements, and a support structure region containing 19,500 elements.

[0024] Furthermore, the thermal-hydraulic boundary conditions used in step 3 include: inlet temperature 308.15 K; inlet velocity 7.5 m / s; total coolant flow rate 0.6667 m³ / s; outlet pressure 0.152 MPa; core pressure drop 57.99 kPa; average wall heat flux density 359 kW / m²; and maximum wall surface temperature under normal conditions <100°C.

[0025] It also includes methods for sub-component-scale verification and model extrapolation feasibility assessment of the constructed effective temperature model for plate-shaped fuel. The specific steps are as follows:

[0026] Based on the JRR-3M research reactor model constructed in steps 1 to 3, a representative multi-plate sub-assembly model containing five fuel plates and their adjacent coolant channels was constructed. Multiphysics simulation was performed using a fully coupled Cardinal framework. At a rated assembly power of 200kW, it was verified whether the deviation of the power of each single plate from the theoretical average value was less than 0.05%, whether the maximum fuel temperature of all fuel plates was consistent, and whether the one-dimensional temperature distribution within the sub-assembly exhibited strict periodicity.

[0027] Treating the five-plate sub-assembly as a representative three-dimensional macroscopic computing node, local thermal parameters are extracted. , , The effective temperature of a single local fuel was evaluated based on the effective temperature model of the plate-shaped fuel constructed in step 5. The reactivity of the lumped node is compared with that of the high-fidelity 3D mapping benchmark to verify whether the reactivity deviation between the lumped model and the high-fidelity 3D mapping benchmark is within the range of the 2σ statistical uncertainty calculated by Monte Carlo.

[0028] Compared with existing technologies, the advantages of this solution are as follows:

[0029] 1. For the core structure design of the JRR-3M reactor, the Cardinal multiphysics framework based on MOOSE forms the computational foundation. To strictly isolate radial Doppler reactive feedback, a customized high-fidelity coupling framework was established between the continuous energy neutron transport solver (OpenMC) and the solid-state heat transfer module (MOOSE / Bison). This customized architecture, employing controlled convective heat transfer boundaries, successfully generated a high-resolution intraplate temperature field for the plate-shaped fuel grid and achieved effective multiplication factor control. A precise assessment.

[0030] 2. The effective temperature model of traditional rod-shaped fuels (e.g.) was evaluated. , , , Theoretical limitations when applied to plate-like geometries. To overcome these limitations, a plate-like fuel effective temperature model based on interpolation is proposed:

[0031]

[0032] This model introduces a dimensionless parameter with a clear physical meaning to quantify the spatial self-shielding effect. It achieves a seamless transition between the limits of the Rowlands model and the Chabert-Santamarina model, combining the advantages of both.

[0033] 3. To improve the universality of this model and make the effective temperature model with a fixed γ value applicable under different MFR conditions, numerical results show that the constant γ value strategy maintains high accuracy (mean absolute error of 9 pcm), while the MFR-specific γ value scheme only provides a slight improvement in accuracy. At the same time, the constant γ value strategy significantly simplifies the model structure. The γ value was calibrated for the neutron resonance characteristics of U3Si2-Al dispersed fuels within the standard MFR range, and the optimal choice was determined to be a constant γ that provides sufficiently accurate Doppler reactivity predictions within the studied MFR range. At this point, the model meets the accuracy requirements for Doppler reactivity calculation under different MFR conditions.

[0034] 4. To verify the macroscopic robustness of the general formula, the proposed model (γ=-0.969) was systematically evaluated at the five-plate sub-assembly scale using highly convergent Monte Carlo parameters. The reactive predictions generated by this interpolation model showed a negligible deviation of only 7 pcm compared to the full three-dimensional high-fidelity benchmark. This deviation falls within the tightened 1σ Monte Carlo standard uncertainty (approximately 7 pcm), statistically demonstrating the model's excellent ability to extrapolate from single-plate analysis to transient applications at the sub-assembly level. Attached Figure Description

[0035] Figure 1 A schematic diagram of a single fuel plate and fuel assembly model constructed based on the actual design parameters of the JRR-3M research reactor;

[0036] Figure 2 For standard fuel plate grid configuration;

[0037] Figure 3 A schematic diagram illustrating the coupling strategy and numerical computation method using OpenMC, MOOSE, and NekRS;

[0038] Figure 4 Fuel plate temperature distribution at a rated power of 20MW;

[0039] Figure 5 This is the radial X-axis temperature distribution curve of the fuel plate under rated power;

[0040] Figure 6 Radial X-axis temperature distribution of fuel plates under different power levels;

[0041] Figure 7 For The relative error curve of the reference effective temperature model;

[0042] Figure 8 fuel temperature T and The fitted relationship curve;

[0043] Figure 9 A comparison chart of reactivity errors for various effective temperature models;

[0044] Figure 10 The Doppler response error is compared in eight different operating condition conversion cases, where the blue bars represent the varying γ parameter and the red bars represent the constant γ parameter.

[0045] Figure 11 A schematic diagram and geometric dimensions of the representative five-board component cross-section used for model extrapolation verification;

[0046] Figure 12 A schematic diagram of the radial temperature distribution of a representative five-plate assembly. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. However, the scope of the present invention is not limited to the following embodiments.

[0048] Step 1. Based on the actual design parameters of the JRR-3M research reactor, establish a detailed three-dimensional geometric model of a single fuel plate.

[0049] The JRR-3M reactor uses U3Si2-Al dispersed fuel (20% enrichment). Table 1 summarizes the key geometric parameters and thermohydraulic characteristics in the validated reactor design specifications. This framework utilizes high-fidelity fluid property modules provided by the Cardinal framework, which have been benchmarked using the NIST REFPROP database. By using these modules, coolant properties—including density, specific heat capacity, and thermal conductivity—are dynamically evaluated at each grid node as a function of temperature and pressure.

[0050] To establish the correlation mechanism between the multidimensional temperature field and Doppler broadening, the focus is on forced convection cooling under the rated full-core 20MW power condition. Under these operating conditions, the high chord-to-diameter ratio of the plate geometry induces specific multidimensional thermal gradients. Explicitly analyzing these local gradients through three-dimensional spatial modeling is a necessary prerequisite for accurately capturing the relevant spatial self-shielding effects. The single-plate modeling parameters are shown in Table 1, and the constructed single fuel plate and fuel assembly models are as follows. Figure 1 As shown.

[0051] Table 1. Single-board modeling parameters. Parameter settings strictly follow the JRR-3M design specifications.

[0052]

[0053] A high-fidelity 3D single-board model was established based on the design parameters in Table 1.

[0054] Step 2. Mesh Generation and Multiphysics Domain Decomposition: Considering the high aspect ratio geometry of the plate-shaped fuel element and the computational requirements of nuclear-thermal coupling, the computational domain is decomposed into a solid domain and a fluid domain, and mesh discretization is performed separately for each:

[0055] Solid domain mesh: The heat transfer equations of the fuel core, cladding and support structure are solved using the MOOSE finite element method, generating a mesh containing 71,700 HEX8 linear hexahedral elements, which are divided into three material subdomains: fuel region: 24,300 elements, cladding region: 27,900 elements, and support structure region: 19,500 elements.

[0056] Fluid region mesh: The coolant channels were solved using the NekRS spectral element method to determine flow and convective heat transfer. The mesh contains 78,300 hexahedral elements, represented as HEX27 second-order elements (corresponding to 676,362 nodes) in the Exodus exchange format. After being converted to the native NekRS .re2 format using the exo2nek tool, NekRS applied high-order GLL quadrature nodes within each element for spectral element solution.

[0057] Neutronics mesh: OpenMC Monte Carlo neutron transport calculations cover the entire computational domain and are uniformly divided into four material subdomains (a total of 150,000 elements), including the three solid subdomains mentioned above and the coolant subdomain (78,300 elements).

[0058] To accurately capture conjugate heat transfer (CHT) phenomena under extremely high aspect ratio geometries, separate meshing strategies (such as...) were employed for the solid and fluid domains. Figure 2 (As shown). The solid domain (Bison) is discretized using linear hexahedral (HEX8) elements, while the adjacent coolant channels are directly analyzed by the spectral CFD solver NekRS.

[0059] To ensure spatial convergence, a grid sensitivity analysis was conducted, evaluating three scaled-down grid levels. Since the peak temperature of the solid component directly determines the magnitude of the Doppler feedback, it was used as the core indicator for evaluating the convergence of the coupled system, as shown in Table 2.

[0060] Table 2. Convergence Study of Multiphysics Coupled Framework Mesh

[0061]

[0062] The relative error is calculated based on the highest fuel temperature compared to a fine-mesh reference.

[0063] The analysis results show that all refinement levels exhibit excellent macroscopic convergence. However, accurately resolving the steep temperature gradient across the fuel pellet thickness direction (along the X-axis) is crucial for capturing spatial self-shielding and Doppler feedback effects. Coarse meshes are considered insufficient because they may flatten local parabolic temperature distributions due to inadequate radial discretization. Therefore, a standard mesh is chosen as the optimal configuration.

[0064] Step 3. Based on the rated operating conditions of the JRR-3M research reactor, set precise thermal-hydraulic boundary conditions:

[0065] Table 3 summarizes the rated thermal-hydraulic boundary conditions for the single-plate model based on the JRR-3M reactor design specifications. A zero-gradient pressure condition was applied at the outlet, along with a uniform inlet velocity of 7.5 m / s and an inlet temperature of 308.15 K.

[0066] To accurately characterize the fluid flow and heat transfer state within the narrow rectangular channel, dimensionless parameters were evaluated before performing three-dimensional high-fidelity modeling. Based on the operating parameters in Table 3, the Reynolds number reached Re = 4.58 × 10⁻⁶. 4 This indicates that the flow is in a fully developed turbulent state (Re>10). 4 Furthermore, the Prandtl number Pr≈4.85 and the channel length-to-diameter ratio (L / D_h=175) ensure fully developed hydraulic conditions.

[0067] Table 3 Thermal-hydraulic parameters for single-plate modeling

[0068]

[0069] Step 4. Coupling Strategy and Numerical Computation Methods:

[0070] Multiphysics simulations are coordinated using the Cardinal framework, which encapsulates OpenMC as the core physics engine and utilizes Bison and NekRS for thermo-hydraulic feedback. A single-stack hierarchical structure is employed. Figure 3 In this architecture, solid-state heat transfer is described by the steady-state heat conduction equation (Equation 2.2). However, to couple with the inherent transient turbulence solved by NekRS, a pseudo-transient interaction strategy is employed:

[0071] Formula (2.2)

[0072] in, It is the scalar equivalent thermal conductivity. It is a solid temperature gradient. Represents a volumetric heat source.

[0073] like Figure 3 In the CHT sub-loop shown, the thermohydraulic loop is iterated N times in each global neutron step to obtain a converged solid temperature field. In each iteration, NekRS performs a series of transient Navier-Stokes steps (M fluid steps) to explicitly solve for the turbulent boundary layer and provides the time-averaged wall temperature to Bison. The fundamental purpose of deploying this high-fidelity CFD solver is not to evaluate coolant reactivity, but to eliminate empirical heat transfer correlations to obtain a highly accurate first-principles solid temperature field.

[0074] To precisely utilize this fuel temperature gradient while isolating the Doppler effect, an artificial "neutron freeze" strategy was employed. Although NekRS calculated the true 3D fluid enthalpy rise, the coolant properties fed back to OpenMC were intentionally constrained to nominal inlet conditions. Specifically, within the neutron model, the coolant temperature and density were kept constant at 308.15 K along the entire axial length. By neglecting this minute macroscopic density variation, this coupling mechanism prevented moderator reactivity noise from interfering with resonant absorption. Thus, Keff's convergence was entirely driven by a high-fidelity solid-state temperature redistribution.

[0075] The numerical model was then calculated and verified in various aspects. The relevant numerical verification process is as follows:

[0076] (1) Calculation of nuclear thermal coupling of plate-shaped fuel elements based on Cardinal:

[0077] Using the Cardinal neutron physics-thermal coupling framework, the steady-state temperature distribution of the fuel in the JRR-3M single-plate reactor was calculated under the operating condition of a core rated power of 20 MW (corresponding to an average heating power of 40 kW per plate). Figure 4 As shown in the figure. The simulation results show that the coupled calculation successfully obtained a convergent and physically reasonable temperature field. Under the efficient convective cooling driven by a flow rate of 7.5 m / s, the fuel plate temperature stabilized rapidly, with the highest temperature at the centerline reaching 310.69 K. Compared with the inlet coolant temperature of 308.15 K, the overall absolute temperature rise is approximately 2.5 K.

[0078] like Figure 5 The radial temperature distribution of the fuel core along the X-axis was further quantitatively extracted, as shown. This distribution exhibits a distinct parabolic shape, confirming that the high-fidelity spatial mapping strategy correctly captured the thermal gradient within the plate.

[0079] Table 4 Comparison and verification of JRR-3M average fuel plate thermal-hydraulic parameter codes (under full core power of 20 MW)

[0080]

[0081] To verify the physical validity of the Cardinal framework's thermal-hydraulic results, Table 4 provides cross-references with published JRR-3M fuel plate analysis results, including the three-dimensional CFD simulation by Gong et al. (2015) and the COOLOD-N2 safety analysis by Albati et al. (2014). Due to significant differences in boundary conditions, a direct quantitative comparison among the three is not possible. Specifically, this embodiment simulates the nominal average fuel plate condition, while Gong et al. used an extreme power peak factor to simulate the hypothetical thermal channel, resulting in a significantly increased temperature rise of approximately 51 K. Albati et al., using a lower inlet velocity and empirical correlations, obtained a moderate temperature rise of approximately 23 K.

[0082] Despite the aforementioned differences, all three analyses consistently demonstrate that the fuel plate operates within the subcooled forced convection range with sufficient safety margin. The temperature rise of approximately 2.5 K predicted by this model is physically consistent with its nominal average power boundary conditions and high inlet velocity, thus providing a reliable thermohydraulic baseline for subsequent Doppler reactivity analysis.

[0083] (2) Effective Doppler temperature assessment under the same MFR conditions is a systematic assessment:

[0084] The robustness of the effective Doppler temperature model was demonstrated by establishing a two-level simulation matrix containing nine power levels (from 20 kW to 2 MW for extreme conditions on a single board).

[0085] The first level (20kW to 200kW) represents actual steady-state operation and expected high-power transients within the safety margin of the supercooled single phase. For high-enrichment plate reactors, eliminating systematic biases in the temperature distribution is crucial, as Doppler broadening is the primary mechanism for transient negative reactivity feedback.

[0086] The second level (400 kW to 2 MW) serves as a rigorous theoretical numerical stress test to evaluate the performance of the proposed interpolation parameter (γ) under artificially amplified spatial temperature gradients. It should be noted that beyond 400 kW, the cladding temperature exceeds the local saturation point, physically marking the onset of nucleate boiling (ONB). Therefore, a single-phase CFD model lacking two-phase latent heat transport artificially exacerbates the radial thermal gradient. By pushing the solver into these artificially imposed over-design baseline conditions, the mathematical stability of the spatially weighted model can be rigorously verified under conditions of maximizing intra-plate temperature deviations.

[0087] like Figure 6The figure reveals the radial temperature distribution along the minor axis of the fuel pellet at different power levels. As the power of a single pellet increases from 20 kW to 2 MW, the internal temperature gradient of the fuel pellet exhibits a significant nonlinear increase. Under low power conditions, the temperature profile is relatively flat, with a limited temperature difference between the center and the surface; however, under high power conditions, the temperature profile evolves into a typical steep parabolic shape, indicating the formation of a severe temperature gradient within the fuel pellet, with the central region becoming a distinct hotspot.

[0088] Step 5. Constructing an effective temperature model for plate-shaped fuel based on interpolation.

[0089] First, let's clarify the spatial extraction method for input temperature: and These are defined as the spatial average temperatures of the fuel core centerline plane and its outer surface, respectively. Specifically, The temperature was obtained by integrating the temperature over a two-dimensional plane at half the thickness of the fuel core (in the X-axis direction). This represents the average temperature of the two two-dimensional interfaces between the fuel core and the cladding. Assuming the coolant temperature is axially uniform, these planar average values ​​accurately represent the representative radial thermal state of the fuel plates, which can be used for subsequent Doppler feedback assessments.

[0090] (1) First, point out the four existing traditional effective Doppler temperature models used for comparison ( , T GDTL T NEA The following is a list of examples:

[0091] (Existing Model 1) Rowlands Slab Fuel Model

[0092] Rowlands' effective temperature model for plate-shaped fuels assumes a parabolic internal temperature distribution, using surface temperature... and center temperature We get the weighted average:

[0093]

[0094] Although the model is based on the parabolic temperature distribution assumption, it has high accuracy for plate-shaped fuels, and the weighting coefficients have been rigorously derived theoretically.

[0095] (Existing Model 2) Chabert-Santamarina Model

[0096] This model is an extension of the Rowlands model, which does not require the strict assumption of a parabolic temperature distribution.

[0097]

[0098] In the formula: This is the volume average temperature. The theoretical basis of this model is more complete, and it has good applicability to plate-shaped fuels.

[0099] (Existing Model 3) Goltsev Volume Integral Model

[0100] Considering the flat structure of plate-shaped fuels, the volume integral method proposed by Goltsev is adopted as the baseline model:

[0101]

[0102] In the formula: = This is the flux weighting function. This model avoids the problem of geometric dimensionality sensitivity and is suitable as a benchmark for comparison.

[0103] (Existing Model 4) Neutron Equivalent Temperature Model

[0104] Based on the neutron equivalence principle, using a temperature weighting factor Chip surface temperature With center temperature Coupling to construct a method for reducing the order of temperature field characterization:

[0105]

[0106] (2) Calculation and comparison of four existing traditional effective Doppler temperature models:

[0107] To quantitatively evaluate the prediction accuracy of the classical effective Doppler temperature model, the surface temperature of the fuel plate was extracted based on the fine temperature field under various operating conditions. ) and core temperature ( ), and calculate the volume average temperature ( Subsequently, the corresponding effective Doppler temperatures were calculated using four existing traditional effective Doppler temperature models. As a benchmark, the temperature distribution field of the full fuel plate after Cardinal convergence was accurately fed back to the corresponding grid in OpenMC for neutronics calculations, obtaining high-fidelity results. As a reference solution, the relevant calculation results are summarized in Table 5, which provides support for comparing the calculation accuracy and Doppler feedback characteristics of different models.

[0108] Table 5 Effective Doppler Temperatures under Different Operating Conditions

[0109]

[0110] Note: As a benchmark for effective temperature, its value is obtained through high-fidelity volume integration, providing a neutral reference and avoiding deviations caused by extreme values ​​such as surface or center temperatures.

[0111] Analysis of Table 5 shows that:

[0112] 1. Differences between models: The calculation results of different models vary under various operating conditions. Under low power conditions, the calculation results of each model are similar, with the maximum deviation not exceeding 1K. As the power increases, the differences between models gradually widen.

[0113] 2. Performance of the reference temperature model: According to Figure 7 As shown, with Based on this, the relative errors of other models show a linear growth trend with increasing power. The model exhibits good stability under all operating conditions, with its calculated values ​​falling within the prediction range of other models and showing the smallest relative deviation.

[0114] 3. Model performance: The model deviates little from the benchmark under low power conditions, but its calculation results are generally lower than other models under high power conditions.

[0115] Therefore, as the input power increases... The baseline model exhibits high accuracy and robustness under various operating conditions, while The model slightly underestimates the effective temperature at high power. This provides a basis for subsequent more accurate nuclear thermal coupling calculations and safety analyses.

[0116] To verify the prediction accuracy of different effective temperatures, the calculation results of four existing traditional effective Doppler temperature models were used as single parameters input to the OpenMC fuel plate temperature calculation, and compared with the high-precision results obtained by using accurate temperature field mapping. Numerical solutions were compared (see Table 7), and the prediction errors of Doppler reactivity for each model were quantitatively analyzed (see Table 5). Although the four traditional effective Doppler temperature models can capture the basic influence of temperature on Doppler reactivity well, their equivalent performance under high power conditions is somewhat inadequate.

[0117] In all OpenMC critical calculations, simulations were performed under radial total internal reflection boundary conditions, incorporating a history of 90 million active neutrons (25,000 particles per generation; 400 inactive generations, 3,600 active generations). The continuous energy cross-section varying with temperature was rigorously handled using an on-the-fly stochastic interpolation method. Therefore, The statistical error was strictly limited to about 9 pcm, thus ensuring that any neutronics deviations observed between effective Doppler models were statistically significant.

[0118] Table 6 shows the calculated effective Doppler temperatures under different operating conditions. numerical values

[0119]

[0120] Table 7 Evaluation of the definition of effective Doppler temperature

[0121]

[0122] Doppler reactivity is defined as: .

[0123] Based on the above shortcomings, a better effective temperature model for plate-shaped fuel still needs to be proposed.

[0124] (3) The effective temperature model of plate fuel proposed in this method based on the interpolation idea:

[0125] Due to the influence of multidimensional heat conduction, the temperature distribution of plate-shaped fuels often deviates from the ideal parabolic distribution assumed by the classical Rowlands model. Furthermore, although the Chabert-Santamarina (CS) model introduces volume-average temperature (... This is used to correct the bias, but its fixed mathematical coefficients lack the flexibility to adapt to different plate geometries and flow scenarios.

[0126] To overcome these limitations, a dimensionless calibrable parameter γ is introduced, and a generalized effective temperature model is proposed. This parameter is in the ideal parabolic limit ( ) and deviation correction state ( Linear interpolation between )

[0127] Formula 3

[0128] Will and Substituting the expression into Formula 3, we derive its analytical form as surface temperature ( ), core temperature ( ) and volume average temperature ( Weighted composition of )

[0129] Formula 4

[0130] Physically, γ acts as a spatial shape factor. When γ=0, the model rigorously reproduces the classical Rowlands parabolic weighting. As γ deviates from zero, it dynamically rebalances the neutronological contributions between local thermal peaks and the bulk mean temperature. For thin-plate fuels with strong spatial self-shielding characteristics, this single parameter γ provides a semi-empirical framework for rigorously quantifying the competing physical effects between geometric thermal conduction and resonant neutron absorption.

[0131] (4) Verify the effectiveness of the plate fuel effective temperature model proposed in this method based on the interpolation idea.

[0132] To calibrate the key parameter γ in the interpolation model, a method of objective function optimization is used for parameter back-calculation. The specific process is as follows: First, the fuel temperature is established through numerical simulation. and The baseline relationship was determined, and the following empirical expression was obtained through fitting. The linear fitting process is as follows: Figure 8 As shown:

[0133] Formula 5

[0134] Based on known operating condition standards Under the premise of [condition], the corresponding "ideal" fuel temperature value can be derived by reverse calculation according to Formula 5. The ideal γ parameter is solved by the Nelder-Mead simplex method with unconstrained nonlinear optimization. To ensure the robustness of the algorithm and eliminate the possibility of convergence to a local minimum, a multi-starting point global search strategy is implemented. Nine initial guesses with uniform intervals of 0.5 in the range of -2.0 to 2.0 are systematically evaluated.

[0135] This method minimizes the root mean square error (RMSE) between the "ideal" effective temperature and the effective temperature predicted by the interpolation model by varying the γ parameter. The mathematical formulation of the optimization problem is to find the ideal parameter γ that minimizes the objective function RMSE(γ).

[0136] Formula 6

[0137] In Formula 6: n is the total number of typical operating conditions used for optimization; This is the "ideal" fuel temperature for the i-th operating condition obtained by reverse calculation.

[0138] During the computation, optimizations starting from all nine points consistently converged to the same global optimum. This behavior verifies that the objective function possesses strict convexity within the evaluation parameter space, thus mathematically guaranteeing the reliability of the obtained γ parameter. The computational results show that when the parameter γ takes a value of -1.224, the interpolation model can accurately describe the Doppler effect of plate fuel under different operating conditions.

[0139] The reliability of the effective temperature model was verified by comparing the Doppler reactivity in the operating condition transformation. Compared with the exact solution, the custom interpolated plate fuel temperature model showed a significant reduction in error when calculating Doppler reactivity. Table 8 shows the systematic evaluation of the interpolated temperature model.

[0140] Table 8 Evaluation of Interpolation Temperature Model Results

[0141]

[0142] Table 8 summarizes the performance of the proposed interpolated effective temperature model under eight operating conditions. For conditions 1 to 7, the reactive prediction error remained at an extremely low level, strictly limited to between 1 and 13 pcm. Considering the statistical uncertainty of approximately 9 pcm inherent in Monte Carlo simulations, these deviations indicate that the model's predictions have extremely high accuracy, with only a very weak positive bias. This demonstrates that the model retains strong robustness even with increased power and steeper temperature gradients.

[0143] However, under the extreme temperature gradient of condition 8, the prediction error reverses to -14 pcm. This sign reversal indicates that the interpolation weights ( The model begins to over-penalize spatial self-screen contributions. This shift clearly defines the effective boundary of the current single-phase model and further highlights the necessity of introducing multiphase flow CFD solvers to accurately capture extreme transient physical processes such as RIA.

[0144] Figure 9 The figure shows a comparison of errors among various effective temperature models. Compared with other effective models, this custom interpolation model demonstrates good predictive ability and stability.

[0145] In summary, the interpolation temperature model formula 7 with γ=-1.224 integrates the advantages of two typical effective temperature models, inheriting the physical rationality of the temperature difference in the Rowlands model while also possessing the theoretical perfection of the Chabert-Santamarina model.

[0146] Formula 7

[0147] (5) Study on effective temperature interpolation coefficient γ under different MFR conditions

[0148] To confirm the applicability of the interpolated effective temperature model in dynamic core environments, the following core assumptions are proposed: There exists an ideal universal constant γ that can produce highly accurate Doppler reactivity predictions under a wide range of MFR conditions.

[0149] MFR is defined as the ratio of the atomic number density of the moderator to that of the fuel, and its calculation formula is as follows:

[0150]

[0151] In the formula: The density of water is the only controlled variable, and all other parameters are constants.

[0152] To verify the applicability of the fixed-γ effective temperature model under different MFR conditions, five representative MFR conditions—15, 20, 29.5 (rated condition), 40, and 50—were selected to rigorously validate the applicability of the fixed-γ model. Physically, this specific range is designed to cover the full spectrum of actual and transient conditions in water-cooled plate reactors. The upper bound (MFR=50) corresponds to the cold zero-power condition, where the coolant density is at its maximum; while the lower bound (MFR=15) represents a severely undermoderated scenario caused by a large amount of coolant cavitation or high temperatures (e.g., a reduction in water density of approximately 50%).

[0153] First, to assess the sensitivity of γ to MFR, optimization was performed independently for each MFR condition, yielding locally optimal interpolation parameter γ values ​​of -0.914, -0.981, -1.224, -0.841, and -0.884. These values ​​fluctuated within a narrow range of -0.841 to -1.224, without exhibiting a monotonically changing trend with MFR. This finding strongly supports the applicability of a constant γ value under different MFR conditions. Furthermore, as MFR increases, The increasing trend confirms that all studied operating conditions are within the reactor's undermoderated region, ensuring the physical rationality of the analysis.

[0154] Based on this, data from all MFR operating conditions were integrated and globally optimized to determine the optimal constant coefficient γ = -0.969. To scientifically evaluate the reliability of the "MFR-specific γ" and "constant γ" schemes, the predicted Doppler reactivity was quantitatively compared with the precisely calculated benchmark value. Figure 10 The study presents a comparison of Doppler responsiveness errors in eight different operating condition conversion cases.

[0155] Furthermore, the evaluation results shown in Table 9 indicate that although the "constant γ" scheme is slightly inferior in terms of indicators such as the mean absolute error of Doppler reactivity, the difference between the two is within an acceptable range for engineering. Moreover, the scheme is more practical for engineering use because of its simple model structure and the fact that it does not require adjustment with MFR.

[0156] Table 9 Evaluation of Two γ Value Schemes

[0157]

[0158] Within the MFR range examined for the JRR-3M geometry, the optimal universal constant γ = -0.969 was determined. Substituting this into the interpolation framework, a generalized effective temperature model applicable to different MFR scenarios is obtained, as shown in Equation 8:

[0159] Formula 8

[0160] (6) The method for verifying the effective temperature model of the constructed plate fuel at the sub-component scale and assessing the feasibility of model extrapolation is as follows:

[0161] Based on the JRR-3M research reactor model constructed in steps 1 to 3, a representative multi-plate sub-assembly model containing five fuel plates and their adjacent coolant channels was constructed. Multiphysics simulation was performed using a fully coupled Cardinal framework. At a rated assembly power of 200kW, it was verified whether the deviation of the power of each single plate from the theoretical average value was less than 0.05%, whether the maximum fuel temperature of all fuel plates was consistent, and whether the one-dimensional temperature distribution within the sub-assembly exhibited strict periodicity.

[0162] Treating the five-plate sub-assembly as a representative three-dimensional macroscopic computing node, local thermal parameters T̅ are extracted. , The effective temperature of a single local fuel was evaluated based on the effective temperature model of the plate-shaped fuel constructed in step 5. The reactivity of the lumped node is compared with that of the high-fidelity 3D mapping benchmark to verify whether the reactivity deviation between the lumped model and the high-fidelity 3D mapping benchmark is within the range of the 2σ statistical uncertainty calculated by Monte Carlo.

[0163] Figure 11 The representative five-plate sub-module cross-sectional diagrams and geometric dimensions used in the model extrapolation verification demonstrate that, at a rated module power of 200 kW, the inter-plate neutron physics-thermal coupling produces a highly uniform power distribution. To suppress statistical noise in the sub-module-scale calculations, the number of particles per active generation was increased to 50,000 (compared to 25,000 per plate), achieving a total of 180 million effective histories and obtaining a highly convergent statistical uncertainty σ≈7 pcm. As summarized in Table 10, the deviation of each plate's power from the theoretical average is less than 0.05%, resulting in almost identical maximum fuel temperatures across all plates.

[0164] Table 10 Neutron physics and thermo-hydraulic parameters of a representative five-plate module under 200kW rated coupling conditions

[0165]

[0166] Therefore, the one-dimensional temperature distribution of the entire sub-component exhibits strict periodicity, such as... Figure 12As shown, the dramatic radial temperature gradient—characterized by a steep parabolic shape within the fuel core—is identical across all plates. This confirms that the primary source of the spatial self-shielding differences is almost entirely the intra-plate radial gradient, rather than inter-plate variations.

[0167] Treating the five-plate sub-assembly as a representative three-dimensional macroscopic computing node, local thermal parameters are extracted. , , The effective temperature of a single local fuel was evaluated using the plate-shaped fuel effective temperature model constructed in step 5. ( K). This lumped-node reactivity is directly compared to a high-fidelity 3D mapping benchmark that explicitly discretizes each 0.76mm thick fuel plate into 15 radial sublayers to strictly preserve the accurate radial temperature gradient (K). K vs. K).

[0168] Verification results show that the reactive deviation between the constructed lumped model and the three-dimensional mapping benchmark is within the range of the 2σ statistical uncertainty of Monte Carlo calculations. This confirms that the constructed effective temperature model for plate-shaped fuel can be extrapolated from the single-plate scale to subassemblies and even the whole-core node simulator without introducing significant spatial error accumulation. The physical basis for the feasibility of model extrapolation lies in the fact that the radial heat transfer of plate-shaped fuel is locally confined within each plate. The main source of spatial self-shielding differences comes almost entirely from the radial gradient within the plate rather than the inter-plate variation. Therefore, the approximation error is physically isolated within specific computational nodes.

[0169] As shown in Table 11, the general model predicts the following when evaluating at the sub-component scale: The value is 1.53516. Compared with the high-fidelity three-dimensional benchmark, the obtained reactivity deviation is only 7 pcm, which strictly falls within the 1σ statistical uncertainty range of the Monte Carlo simulation (σ ≈ 7 pcm).

[0170] The key point is that both the rated operating condition optimization model (deviation 10 pcm, Equation 7) and the generalized universal model (deviation 7 pcm, Equation 8) produced statistically indistinguishable and highly accurate results. This confirms that the constant γ = -0.969 is not only an empirical fitting value, but also captures the underlying physical mechanism: the spatial self-shielding weight of the plate-like fuel is dominated by its geometry and inherent resonance characteristics, and remains highly decoupled from the moderate shift in the neutron spectrum caused by the MFR variation.

[0171] Table 11 Reactivity Validation of Specific (Equation 7) and General (Equation 8) Effective Temperature Models at the Five-Plate Assembly Scale

[0172]

[0173] In summary, the embodiments of the present invention are summarized as follows:

[0174] First, the Cardinal multiphysics framework based on MOOSE forms the computational foundation. To rigorously isolate radial Doppler reactive feedback, a customized high-fidelity coupling framework was established between the continuous energy neutron transport solver (OpenMC) and the solid-state heat conduction module (MOOSE / Bison). This customized architecture, employing controlled convection heat transfer boundaries, successfully generated a high-resolution intraplate temperature field for the plate-shaped fuel grid and enabled the computation of... This design allows for precise evaluation of the radial Doppler effect in the temperature field, providing a clean physical benchmark for the subsequent construction of an effective temperature model.

[0175] Secondly, it systematically reveals the effective temperature model of traditional rod-shaped fuels (such as...) , , , The inherent biases and their physical origins when applied to plate geometries—namely, the spatial inverse correlation between neutron flux spatial depression and temperature peaks—are significantly enhanced in thin plate geometries. To overcome these limitations, a novel interpolation effective temperature model is proposed. This general model achieves a seamless transition between the limits of the Rowlands and Chabert-Santamarina models by introducing a dimensionless parameter γ with well-defined physical meaning for quantifying spatial self-shielding effects.

[0176] Third, to improve the model's universality, the applicability of the fixed γ effective temperature model under MFR conditions was verified. Using unconstrained nonlinear optimization techniques based on the Nelder-Mead simplex algorithm, the ideal γ parameters under different MFR conditions were solved. Analysis showed a correlation between MFR and the ideal γ value. Based on this finding, two engineering application strategies were evaluated: MFR-specific γ value and constant γ value. Numerical results showed that the constant γ value strategy maintained high accuracy (mean absolute error of 9 pcm), while the MFR-specific γ value scheme only provided a slight improvement in accuracy. Meanwhile, the constant γ value strategy significantly simplified the model structure. After comprehensive consideration, the constant γ = −0.969 scheme, which can provide sufficiently accurate Doppler reactivity predictions within the studied MFR range, was determined to be the optimal choice.

[0177] To verify the macroscopic robustness of this general formula, a systematic evaluation was conducted at the five-plate sub-assembly scale using highly convergent Monte Carlo parameters based on the proposed model (γ=-0.969). The evaluation results show that the reactive predictions generated by the interpolation model deviate by only 7 pcm from the full three-dimensional high-fidelity benchmark, falling within the Monte Carlo 1σ statistical uncertainty range, indicating that this deviation is not statistically significant. This deviation is within the tightened 1σ Monte Carlo standard uncertainty range (approximately 7 pcm), statistically confirming the model's excellent ability to extrapolate from single-plate analysis to transient applications at the sub-assembly level.

[0178] Despite the model's excellent robustness, certain limitations of the current framework must be acknowledged. Because the optimized parameters (γ = −0.969) are specifically calibrated for the neutron resonance characteristics of U3Si2-Al dispersed fuels within the standard MFR range, recalibration of γ is necessary when applying this formula to other advanced fuel types (such as monolithic U-Mo alloys) or extremely undermoderated loss-of-water accident (LOCA) scenarios.

[0179] In summary, the effective temperature model for plate fuel proposed in this invention, based on the interpolation concept, is grounded in a clear physical mechanism, uses high-fidelity multi-physics coupling calculation as a calibration method, and employs multi-scale verification as a reliability guarantee. It provides an effective temperature processing method that combines accuracy and engineering practicality for refined neutronics analysis and safety evaluation of plate fuel reactors.

Claims

1. A method for constructing a high-fidelity multiphysics data mapping model of the effective temperature of plate-shaped fuel, characterized in that... Includes the following steps: Step 1. Based on the actual design parameters of the JRR-3M research reactor, establish a detailed three-dimensional computational domain geometric model that includes a single fuel plate and its adjacent coolant channels; Step 2. Mesh Generation and Multiphysics Domain Decomposition: Considering the high aspect ratio geometry of the plate-shaped fuel element and the computational requirements of nuclear-thermal coupling, the computational domain is decomposed into a solid domain and a fluid domain, and mesh discretization is performed separately for each: Solid domain mesh: The heat transfer equations of the fuel core, cladding and support structure are solved using the MOOSE finite element method to generate a mesh containing several HEX8 linear hexahedral elements, and the mesh is divided into three solid subdomains: fuel region, cladding region and support structure region. Fluid region mesh: The flow and convective heat transfer of the coolant channels are solved by the NekRS spectral element method. The mesh contains 78,300 hexahedral elements. The corresponding mesh is represented as HEX27 second-order elements in the Exodus exchange format. After being converted to the native NekRS .re2 format by the exo2nek tool, NekRS applies high-order GLL quadrature nodes inside each element for spectral element solution. Neutronics Mesh: The OpenMC Monte Carlo neutron transport calculation covers the entire computational domain and is uniformly divided into four material subdomains, which include three solid subdomains in the solid domain mesh and the coolant subdomain in the fluid domain mesh; Step 3. Based on the rated operating conditions of the JRR-3M research reactor, set precise thermal-hydraulic boundary conditions; Step 4. Coupling Strategy and Numerical Computation Method: Multiphysics simulation is coordinated using the Cardinal framework, which encapsulates OpenMC as the core physics engine. Simultaneously, Bison and NekRS are used to implement thermo-hydraulic feedback. Solid-state heat transfer is represented by the steady-state heat conduction equation. ,in It is the scalar equivalent thermal conductivity. It is a solid temperature gradient. The volumetric heat source is represented; a pseudo-transient interaction strategy is adopted to couple with the inherent transient turbulence solved by NekRS. Step 5. Constructing an effective temperature model for plate-shaped fuel based on interpolation: Based on the known Rowlands plate fuel model And Chabert-Santamarina model In the formula The space average temperature of the fuel core centerline plane, The space average temperature of the outer surface of the fuel core, To determine the volume average temperature, a dimensionless, calibrable parameter γ is introduced, making the parameter γ such that... and Linear interpolation between Substituting the expressions of and into the above equation, the analytical form of the solution is derived as a weighted combination of the surface temperature, the center temperature, and the volume average temperature, i.e., the effective temperature model of the plate-shaped fuel constructed: 。 2. The method for constructing a high-fidelity multiphysics data mapping plate fuel effective temperature model according to claim 1, characterized in that: In the constructed effective temperature model for plate-shaped fuels, the γ-ray neutron resonance characteristics of U3Si2-Al dispersed fuels within the standard MFR range were calibrated. -0.969, at which point the effective temperature model for plate-shaped fuel is constructed as follows: The MFR is the ratio of the atomic number density of the moderator to that of the fuel.

3. The method for constructing a high-fidelity multiphysics data mapping plate fuel effective temperature model according to claim 1, characterized in that: In the constructed effective temperature model for plate fuel, when γ=0, it conforms to the Rowlands plate fuel model; when γ=1, it conforms to the Chabert-Santamarina model.

4. The method for constructing a high-fidelity multiphysics data mapping plate fuel effective temperature model according to claim 1, characterized in that: The actual design parameters of the JRR-3M research reactor used in Step 1 include: coolant material: light water; coolant density: 999.63 kg / m³ 3 Average coolant temperature: 311.15 K; operating pressure: 0.152 MPa; core material: U3Si2-Al; fuel enrichment: 20%; U3Si2 volume fraction: 45%; fuel core height: 750 mm; fuel core length: 61.6 mm; fuel core width: 0.76 mm; fuel density: 6975 kg / m³ 3 Support body thickness: 4.8mm; Support body width: 3.8mm; Support body height: 770mm; Support body material: Al plate; Sheath material: 6061-Al; Sheath height: 770mm; Sheath length: 66.6mm; Sheath width: 1.52mm; Sheath density: 2700kg / m³ 3 .

5. The method for constructing a high-fidelity multiphysics data mapping plate fuel effective temperature model according to claim 1, characterized in that: In step 2, a mesh containing 71,700 HEX8 linear hexahedral elements is generated in the solid domain mesh; the mesh is divided into three material subdomains: the fuel region containing 24,300 elements, the cladding region containing 2,790 elements, and the support structure region containing 19,500 elements.

6. The method for constructing a high-fidelity multiphysics data mapping plate fuel effective temperature model according to claim 5, characterized in that: The fluid region mesh in step 2 is a mesh containing 78,300 hexahedral elements, which corresponds to 676,362 nodes when represented as HEX27 second-order elements in the Exodus exchange format; the four material subdomains of the neutronics mesh contain a total of 150,000 elements.

7. The method for constructing a high-fidelity multiphysics data mapping plate fuel effective temperature model according to claim 1, characterized in that: The thermal-hydraulic boundary conditions used in step 3 include: inlet temperature 308.15 K; inlet velocity 7.5 m / s; total coolant flow rate 0.6667 m³ / s; outlet pressure 0.152 MPa; core pressure drop 57.99 kPa; average wall heat flux density 359 kW / m²; and maximum wall surface temperature under normal conditions <100°C.

8. The method for constructing a high-fidelity multiphysics data mapping plate fuel effective temperature model according to claim 1, characterized in that... It also includes methods for sub-component-scale verification and model extrapolation feasibility assessment of the constructed effective temperature model for plate-shaped fuel. The specific steps are as follows: Based on the JRR-3M research reactor model constructed in steps 1 to 3, a representative multi-plate sub-assembly model containing five fuel plates and their adjacent coolant channels was constructed. Multiphysics simulation was performed using a fully coupled Cardinal framework. At a rated assembly power of 200kW, it was verified whether the deviation of the power of each single plate from the theoretical average value was less than 0.05%, whether the maximum fuel temperature of all fuel plates was consistent, and whether the one-dimensional temperature distribution within the sub-assembly exhibited strict periodicity. Treating the five-plate sub-assembly as a representative three-dimensional macroscopic computing node, local thermal parameters are extracted. , , The effective temperature of a single local fuel was evaluated based on the effective temperature model of the plate-shaped fuel constructed in step 5. ; The reactivity of the lumped node is compared with that of the high-fidelity 3D mapping benchmark to verify whether the reactivity deviation between the lumped model and the high-fidelity 3D mapping benchmark is within the range of the 2σ statistical uncertainty calculated by Monte Carlo.

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