Method, device and equipment for calculating equivalent thermal conductivity of dispersed fuel pellets

Abstract

The application discloses a kind of coated particle dispersion type fuel pellet equivalent thermal conductivity calculation method, device and equipment, belong to reactor fuel design technical field.Method includes: based on numerical simulation method obtains the equivalent thermal conductivity of fuel pellet under limit filling rate and actual filling rate;According to the distribution mode of fuel particles in matrix material, three typical distribution models of extremely adverse distribution, extremely ideal distribution and uniform distribution are constructed;According to the equivalent thermal conductivity of fuel pellet under limit filling rate and actual filling rate, and the equivalent thermal conductivity of three typical distribution models is calculated respectively according to the thermal conductivity of matrix material;According to the equivalent thermal conductivity of three typical distribution models, the equivalent thermal conductivity meeting the requirement of confidence interval is calculated.The method is suitable for the calculation of the equivalent thermal conductivity of any coated particle dispersion type fuel pellet, and the calculation process is simple, efficient, to ensure that the equivalent thermal conductivity obtained by calculation is above a certain confidence level.

Description

Technical Field

[0001] This invention belongs to the field of reactor fuel design technology, specifically relating to a method, apparatus, and electronic equipment for calculating the equivalent thermal conductivity of coated particle-dispersed fuel pellets. Background Technology

[0002] The large amount of fission products and radioactivity generated during nuclear power generation poses a potential hazard to reactor operation, and nuclear power plant design must provide comprehensive measures to ensure its safe operation.

[0003] Safety goals for nuclear power plant design are constantly being upgraded. Therefore, the development of new fuels capable of withstanding severe accidents has become a key focus of conventional unit retrofitting and advanced reactor development, with coated particulate fuel being one of the most representative new types. This type of fuel disperses a large number of multi-layered coated fuel particles within a matrix material. The multi-layered coating structure of the fuel particles themselves has excellent fission product containment capacity, while the matrix material possesses good radiation stability, corrosion resistance, and high-temperature resistance, thus significantly improving the safety performance of this new type of fuel.

[0004] While using coated particulate fuel is beneficial for the safe operation of reactors, its complex structure also brings great difficulties to the analysis of thermal conductivity. In particular, a large number of tiny fuel particles are randomly dispersed within the matrix material (tens of thousands of particles can be dispersed within a single pellet), which are both independent of each other and influence each other within a certain range, resulting in extremely complex heat transfer paths and mechanisms within the pellet.

[0005] Most existing studies use equivalent thermal conductivity models or numerical simulations of solid-solid composite materials to calculate the equivalent thermal conductivity. However, existing models and methods still have the following limitations:

[0006] insufficient:

[0007] Firstly, most existing equivalent thermal conductivity models for composite materials are based on specific material systems and do not consider the heating of particles, making it impossible to effectively calculate the equivalent thermal conductivity of dispersed fuels coated with particles.

[0008] Secondly, when using numerical simulation for direct modeling and solving, the presence of a large number of small particles results in a huge number of model meshes. At the same time, the impact of random particle distribution on thermal conductivity requires a large amount of sampling modeling and numerical simulation, which is difficult to meet design requirements.

[0009] Finally, there is a lack of experimental research on the thermal conductivity of coated particle-dispersed fuels. The models and methods currently used lack reliability verification and uncertainty analysis for their calculation results. Calculation results that are too conservative or not conservative enough are not conducive to the research and design of reactor types. Summary of the Invention

[0010] The technical problem to be solved by this invention is to address the above-mentioned shortcomings of the prior art by providing a method, apparatus, and electronic device for calculating the equivalent thermal conductivity of coated particulate fuel pellets. This method is applicable to the calculation of the equivalent thermal conductivity of any coated particulate fuel pellet, and the calculation process is simple and efficient. By effectively considering the influence of the fuel pellets' own heat generation and random distribution on the macroscopic thermal conductivity of the pellet, the calculated equivalent thermal conductivity is guaranteed to be above a certain confidence level.

[0011] In a first aspect, the present invention provides a method for calculating the equivalent thermal conductivity of a coated particle-dispersed fuel pellet, comprising: obtaining the equivalent thermal conductivity of the fuel pellet under a limiting fill rate and an actual fill rate based on a numerical simulation method; constructing three typical distribution models—extremely poor distribution, extremely ideal distribution, and uniform distribution—based on the distribution mode of the fuel particles in the matrix material; calculating the equivalent thermal conductivity of the three typical distribution models based on the equivalent thermal conductivity of the fuel pellet under the limiting fill rate and the actual fill rate, and the thermal conductivity of the matrix material, wherein the equivalent thermal conductivity of the extremely poor distribution model is equivalent to the lower limit of the equivalent thermal conductivity of the fuel pellet, the equivalent thermal conductivity of the extremely ideal distribution model is equivalent to the upper limit of the equivalent thermal conductivity of the fuel pellet, and the equivalent thermal conductivity of the uniform distribution model is equivalent to the average value of the equivalent thermal conductivity of the fuel pellet; and calculating the equivalent thermal conductivity that satisfies the confidence interval requirement based on the equivalent thermal conductivity of the three typical distribution models, as the conservative thermal conductivity of the fuel pellet.

[0012] Preferably, before obtaining the equivalent thermal conductivity of the fuel pellets at the limit fill rate and the actual fill rate based on the numerical simulation method, the calculation method of the equivalent thermal conductivity further includes: obtaining the thermal conductivity analytical equation of the simplified pellet corresponding to the fuel pellet, wherein the simplified pellet has the same geometric dimensions as the fuel pellet and a uniformly distributed volumetric heat source inside; determining the analytical equation of the highest temperature, the adverse region and the ideal region of particle distribution based on the mathematical characteristics of the thermal conductivity analytical equation, wherein the adverse region is the region within the highest temperature and a first preset range centered on the highest temperature, and the ideal region is the region outside the adverse region.

[0013] Preferably, obtaining the thermal conductivity analytical equation of the simplified fuel pellet specifically includes: simplifying the fuel pellet to obtain a simplified pellet with a uniform medium material and uniform physical property parameters; and deriving the thermal conductivity analytical equation of the simplified pellet based on the thermal conductivity differential equation in the corresponding coordinate system according to the structure of the simplified pellet.

[0014] Preferably, obtaining the equivalent thermal conductivity of the fuel pellets at the limiting fill rate and the actual fill rate based on the numerical simulation method specifically includes: constructing geometric models of the fuel pellets at the limiting fill rate and the actual fill rate, respectively; calculating the temperature distribution of the geometric models of the fuel pellets at the limiting fill rate and the actual fill rate based on the numerical simulation method; and obtaining the equivalent thermal conductivity of the fuel pellets at the limiting fill rate and the actual fill rate based on the highest temperature in the temperature distribution.

[0015] Preferably, the step of constructing geometric models of fuel pellets at the limit fill rate and the actual fill rate respectively includes: setting the regular arrangement of fuel pellet particles at the limit fill rate and the actual fill rate respectively; extracting a local model of the fuel pellet based on the cell structure of the regular arrangement of particles, and separately modeling the composition structure of the fuel particles and the matrix material in the local model to obtain the geometric models of the fuel pellets at the limit fill rate and the actual fill rate, wherein the local model contains several fuel particles with a 1 / 4 symmetric structure.

[0016] Preferably, obtaining the equivalent thermal conductivity of the fuel pellets at the extreme fill rate and the actual fill rate based on the highest temperature in the temperature distribution specifically includes: substituting the highest temperature in the temperature distribution of the fuel pellet geometric model at the extreme fill rate and the actual fill rate into the simplified analytical equation for the highest temperature of the pellet, respectively, to obtain the equivalent thermal conductivity of the fuel pellets at the extreme fill rate and the actual fill rate.

[0017] Preferably, the construction of the three typical distribution models—extremely harsh distribution, extremely ideal distribution, and uniform distribution—specifically includes: setting the fuel particles to be uniformly distributed within the matrix material at the actual filling rate to construct a uniform distribution model; setting the fuel particles to be distributed in the harsh region at the limit filling rate, with the ideal region as the matrix material to construct an extremely harsh distribution model; and setting the fuel particles to be distributed in the ideal region at the limit filling rate, with the harsh region as the matrix material to construct an extremely ideal distribution model.

[0018] Preferably, the step of calculating the equivalent thermal conductivity of three typical distribution models based on the equivalent thermal conductivity of the fuel pellets at the limit fill rate and the actual fill rate, as well as the thermal conductivity of the matrix material, specifically includes: determining the size of the harsh / ideal region based on the number of fuel particles filled; calculating the hot spot temperature of the extremely harsh distribution model / extremely ideal distribution model based on the size of the harsh / ideal region and the thermal conductivity analytical equation of the simplified pellet corresponding to the harsh / ideal region; setting the equivalent thermal conductivity of the extremely harsh / extremely ideal distribution model and obtaining the highest temperature of the simplified pellet based on this setting; calculating the equivalent thermal conductivity of the extremely harsh / extremely ideal distribution model based on the equality relationship between the hot spot temperature of the extremely harsh / extremely ideal distribution model and the highest temperature of the simplified pellet, wherein the equivalent thermal conductivity of the extremely harsh / extremely ideal distribution model is related to the equivalent thermal conductivity of the fuel pellets at the limit fill rate, the thermal conductivity of the matrix material, and the fill rate; and determining the equivalent thermal conductivity of the uniform distribution model as the equivalent thermal conductivity of the fuel pellets at the actual fill rate.

[0019] Preferably, the step of calculating the equivalent thermal conductivity that meets the confidence interval requirement based on the equivalent thermal conductivity of the three typical distribution models specifically includes: treating the equivalent thermal conductivity of the fuel pellet as a continuous random variable taking values ​​within a second preset range and following a normal distribution; defining the center position and value range of the probability distribution curve using the equivalent thermal conductivity of the three typical distribution models respectively, and calculating the mathematical expectation and standard deviation of the probability distribution curve; and calculating the equivalent thermal conductivity that meets the confidence interval requirement based on the mathematical expectation and standard deviation, which serves as the conservative thermal conductivity of the fuel pellet.

[0020] Preferably, the mathematical expectation μ satisfies:

[0021] Or, μ = k E-uniform The standard deviation σ satisfies:

[0022]

[0023] Where, k E-best k is the equivalent thermal conductivity of the perfectly ideal distribution model. E-worst k is the equivalent thermal conductivity of the extremely poor distribution model. E-uniform is the equivalent thermal conductivity of the uniformly distributed model.

[0024] Secondly, the present invention provides a device for calculating the equivalent thermal conductivity of a coated particle-dispersed fuel pellet, comprising: an acquisition module for acquiring the equivalent thermal conductivity of the fuel pellet at both the limit fill rate and the actual fill rate using numerical simulation methods; a construction module for constructing three typical distribution models—extremely harsh distribution, extremely ideal distribution, and uniform distribution—based on the distribution pattern of fuel particles within the matrix material; and a first calculation module connected to the acquisition module and the construction module for calculating the equivalent thermal conductivity of the three typical distribution models based on the equivalent thermal conductivity of the fuel pellet at both the limit fill rate and the actual fill rate, as well as the thermal conductivity of the matrix material, respectively. The equivalent thermal conductivity of the extremely harsh distribution model is equivalent to the lower limit of the equivalent thermal conductivity of the fuel pellet, the equivalent thermal conductivity of the extremely ideal distribution model is equivalent to the upper limit of the equivalent thermal conductivity of the fuel pellet, and the equivalent thermal conductivity of the uniform distribution model is equivalent to the average equivalent thermal conductivity of the fuel pellet. The second calculation module, connected to the first calculation module, is used to calculate the equivalent thermal conductivity that meets the confidence interval requirements based on the equivalent thermal conductivity of three typical distribution models, so as to serve as the conservative thermal conductivity of the fuel pellet.

[0025] Thirdly, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to implement the method for calculating the equivalent thermal conductivity of coated particulate fuel pellets as described in the first aspect.

[0026] The present invention provides a method, apparatus, and electronic device for calculating the equivalent thermal conductivity of coated particle-dispersed fuel pellets. Based on three special arrangement models of fuel pellets (extremely poor distribution model, extremely ideal distribution model, and uniform distribution model), the particle arrangement and thermal conductivity of these three models are predictable. Therefore, it avoids extensive calculations required to address the uncertainty in the thermal conductivity of fuel pellets caused by random particle distribution. It effectively considers the heat generated by the fuel particles themselves and the impact of random distribution on the macroscopic thermal conductivity of the fuel pellets, ensuring that the calculated equivalent thermal conductivity is above a certain confidence level. By limiting the value of the equivalent thermal conductivity of the fuel pellets through the limiting distribution model, calculation results that meet the design confidence requirements are obtained. This appropriately reduces the conservatism of the calculation while ensuring sufficient reliability, thereby improving economic efficiency. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating a method for calculating the equivalent thermal conductivity of a coated particulate dispersion fuel pellet according to Embodiment 1 of the present invention.

[0028] Figure 2 This is a flowchart illustrating a method for calculating the equivalent thermal conductivity of a coated particulate dispersion fuel pellet according to Embodiment 2 of the present invention.

[0029] Figure 3 It is a three-layer coated fuel (TRistructural ISOtropic, TRISO).

[0030] Schematic diagram of particle structure;

[0031] Figure 4 This is a schematic diagram of a typical fuel pellet structure;

[0032] Figure 5(a) is a schematic diagram of heat conduction of a micro-element in cylindrical coordinates;

[0033] Figure 5(b) is a schematic diagram of heat conduction of a micro-element in cylindrical coordinates;

[0034] Figure 6 This is a schematic diagram of a partial model of a fuel pellet (40% fill rate, simple cubic arrangement);

[0035] Figure 7 This is a schematic diagram of a partial model of a fuel pellet (74% fill rate, face-centered cubic arrangement);

[0036] Figure 8 This is a schematic diagram of the structure of a device for calculating the equivalent thermal conductivity of a coated particulate dispersed fuel pellet according to Embodiment 3 of the present invention.

[0037] Among them: 1- Fuel core (such as UO2); 2- Loose pyrolytic carbon buffer layer; 3- Inner dense pyrolytic carbon layer (IPyC layer); 4- Silicon carbide layer (SiC layer); 5- Outer dense pyrolytic carbon layer (OPyC layer); 6- TRISO particles; 7- Matrix material. Detailed Implementation

[0038] To enable those skilled in the art to better understand the technical solution of the present invention, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0039] It is understood that the specific embodiments and accompanying drawings described herein are merely for explaining the invention and are not intended to limit the invention.

[0040] It is understood that, without conflict, the various embodiments and features in the embodiments of the present invention can be combined with each other.

[0041] It is understood that, for ease of description, only the parts related to the present invention are shown in the accompanying drawings, while the parts unrelated to the present invention are not shown in the drawings.

[0042] It is understood that each unit or module involved in the embodiments of the present invention may correspond to only one entity structure, or may be composed of multiple entity structures, or multiple units or modules may be integrated into one entity structure.

[0043] It is understood that, without conflict, the functions and steps marked in the flowcharts and block diagrams of this invention may occur in a different order than that marked in the accompanying drawings.

[0044] It is understood that the flowcharts and block diagrams of this invention illustrate the possible architecture, functions, and operations of systems, apparatuses, devices, and methods according to various embodiments of this invention. Each block in the flowchart or block diagram may represent a unit, module, program segment, or code, containing executable instructions for implementing the specified function. Furthermore, each block or combination of blocks in the block diagram and flowchart can be implemented using a hardware-based system to achieve the specified function, or using a combination of hardware and computer instructions.

[0045] It is understood that the units and modules involved in the embodiments of the present invention can be implemented by software or by hardware. For example, the units and modules can be located in a processor.

[0046] This embodiment provides a method for calculating the equivalent thermal conductivity of a coated particle-dispersed fuel pellet, including: obtaining the equivalent thermal conductivity of the fuel pellet at the limit fill rate and the actual fill rate based on numerical simulation; constructing three typical distribution models—extremely poor distribution, extremely ideal distribution, and uniform distribution—based on the distribution mode of fuel particles in the matrix material; calculating the equivalent thermal conductivity of the three typical distribution models based on the equivalent thermal conductivity of the fuel pellet at the limit fill rate and the actual fill rate, as well as the thermal conductivity of the matrix material, wherein the equivalent thermal conductivity of the extremely poor distribution model is equivalent to the lower limit of the equivalent thermal conductivity of the fuel pellet, the equivalent thermal conductivity of the extremely ideal distribution model is equivalent to the upper limit of the equivalent thermal conductivity of the fuel pellet, and the equivalent thermal conductivity of the uniform distribution model is equivalent to the average equivalent thermal conductivity of the fuel pellet; and calculating the equivalent thermal conductivity that satisfies the confidence interval requirement based on the equivalent thermal conductivity of the three typical distribution models, which is used as the conservative thermal conductivity of the fuel pellet.

[0047] The method for calculating the equivalent thermal conductivity of coated particle-dispersed fuel pellets in this embodiment has the advantages of high applicability, simple solution, and high computational efficiency. It effectively considers the influence of the fuel particle's own heat generation and random distribution on the pellet's thermal conductivity, avoiding complex uncertainty analysis calculations. The in-core fuel hotspot temperature (i.e., the highest temperature of the fuel particle at the hottest location in the reactor core) calculated based on the equivalent thermal conductivity obtained in this embodiment meets the confidence requirements of engineering design, and further reduces conservatism, improving the economic efficiency of reactor design.

[0048] Example 1:

[0049] like Figure 1 As shown in the figure, this embodiment provides a method for calculating the equivalent thermal conductivity of coated particulate dispersed fuel pellets, including:

[0050] Step 101: Obtain the equivalent thermal conductivity of fuel pellets at the limit fill rate and the actual fill rate using numerical simulation methods.

[0051] In this embodiment, the fuel pellets currently used in reactors generally have a fuel particle volume to total pellet volume ratio (i.e., fill factor) of less than 40%, meaning the actual fill factor is less than or equal to 40%. These fuel particles disperse in the matrix material in many ways, including unpredictable random arrangements and predictable regular arrangements. For random arrangements, the maximum volume percentage (i.e., the limit fill factor) of fuel particles that can fill a given matrix material can reach approximately 60.1% to 63.7%. For regular arrangements, the limit fill factor achievable by fuel particles arranged in a certain manner varies slightly; for example, the limit fill factor for a simple cubic arrangement can reach 52.4%, for a body-centered cubic arrangement it can reach 60%, and for a face-centered cubic arrangement it can reach 74%. In order to obtain the actual thermal conductivity of fuel pellets as basic data, this embodiment uses numerical simulation to perform numerical simulations on the geometric model of the fuel pellets with regularly arranged particles (examples are the three-dimensional model of the limit fill rate and the three-dimensional model of the actual fill rate). Specifically, by performing detailed modeling of the fuel core, the coating layer structure and the matrix material, the equivalent thermal conductivity of the fuel pellets under the limit fill rate and the actual fill rate is simulated respectively.

[0052] Optionally, the equivalent thermal conductivity of the fuel pellets at the limiting fill rate and the actual fill rate is obtained based on numerical simulation methods, specifically including steps 1011-1013:

[0053] Step 1011: Construct geometric models of fuel pellets under extreme fill ratio and actual fill ratio, respectively.

[0054] Specifically, constructing geometric models of fuel pellets at the limit fill rate and the actual fill rate includes: setting the regular particle arrangement of fuel pellets at the limit fill rate and the actual fill rate respectively; extracting local models of fuel pellets based on the cell structure of the regular particle arrangement, and separately modeling the composition structure of fuel particles and matrix materials in the local models to obtain geometric models of fuel pellets at the limit fill rate and the actual fill rate, wherein the local models contain several fuel particles with 1 / 4 symmetric structures.

[0055] In this embodiment, for fuel pellets with regularly arranged particles, the particles are uniformly distributed at a certain spacing within the matrix material. Therefore, the specific arrangement has no impact on the macroscopic thermal conductivity. Setting the regularly arranged particle arrangement includes: for fuel pellets with an actual fill rate, any arrangement can be selected, as long as it meets the actual fill rate requirement; for fuel pellets with a maximum fill rate, either a face-centered cubic arrangement or a close-packed hexagonal arrangement with the highest fill rate can be selected. The construction of the local pellet model includes: based on the cell structure of the regularly arranged fuel particles, a local model of the actual fuel pellet is extracted, ensuring that its radial dimensions are consistent with the actual pellet, and its height and width are equal to half the size of the cell. Therefore, the local model contains several fuel particles with a 1 / 4 symmetric structure. The local model includes the detailed structure of the fuel particles and the matrix material. The core and coating structure of the fuel particles from the inside out are modeled separately. It should be noted that the local model is a symmetric model extracted from the cell structure; other sizes can be used for modeling, and it is not limited to the size example in this embodiment. The local model in this embodiment contains several fuel particles with a 1 / 4 symmetric structure. The model is the simplest and requires the fewest meshes. Therefore, it consumes less computational resources and can improve the calculation speed of the equivalent thermal conductivity.

[0056] Step 1012: Calculate the temperature distribution of the fuel pellet geometric model under the limit fill rate and the actual fill rate using numerical simulation methods.

[0057] In this embodiment, the geometric model of the fuel pellet is imported into mesh generation software to complete mesh generation, defining the materials and corresponding boundary conditions for different regions, completing preliminary preprocessing to form a simulated pellet model. The simulated pellet model is then imported into CFD (Computational Fluid Dynamics) software, where a volumetric heat source is set in the core region of the pellet, and isothermal boundaries are set on the outer side of the pellet to simulate the actual operation of fuel within the reactor. Assuming the fuel pellet is an isotropic material, heat conduction along the height direction is ignored, and only radial heat conduction is considered. Other sections of the simulated pellet model are set as symmetrical boundaries. Appropriate materials are set in different regions of the simulated pellet model. The CFD software can automatically call up physical property parameters based on key parameters such as material, temperature, burnup, and neutron flux to calculate the temperature distribution of the fuel pellet geometric model at the limiting fill rate and the actual fill rate.

[0058] Step 1013: Obtain the equivalent thermal conductivity of the fuel pellets at the limit fill rate and the actual fill rate based on the highest temperature in the temperature distribution.

[0059] In this embodiment, all fuel particles are uniformly distributed within the matrix material. At this time, the fuel particles must be arranged in a certain regular manner. Therefore, the equivalent thermal conductivity can be directly obtained based on the numerical simulation results.

[0060] Specifically, obtaining the equivalent thermal conductivity of fuel pellets at the limiting fill rate and the actual fill rate based on the highest temperature in the temperature distribution includes: substituting the highest temperature in the temperature distribution of the fuel pellet geometric model at the limiting fill rate and the actual fill rate into the analytical equation for the highest temperature of the simplified pellet, respectively, to obtain the equivalent thermal conductivity of the fuel pellet at the limiting fill rate and the actual fill rate. The simplified pellet has the same geometric dimensions as the fuel pellet and a uniformly distributed volumetric heat source inside.

[0061] For example, cylindrical fuel pellets, based on the analytical equation of the highest temperature.

[0062]

[0063] The highest temperature t of the fuel pellets at the actual fill rate was obtained using numerical simulation. peak1 The equivalent thermal conductivity of the fuel pellets at the actual fill rate was obtained:

[0064]

[0065] Similarly, the highest temperature t of the fuel pellet with the ultimate fill rate was obtained by numerical simulation. peak2 The equivalent thermal conductivity of the fuel pellets under extreme filling conditions can be obtained as follows:

[0066]

[0067] Among them, t max f1 is the analytical equation for calculating the highest temperature in the core region, where φ is the highest temperature. s A heat source that is uniformly distributed within a unit volume, W / m 3 r2 is the outer diameter of the cylinder / sphere / cylindrical body, t2 is the outer wall temperature of the cylinder / sphere / cylindrical body, and k is the thermal conductivity. E-uniform f1 represents the equivalent thermal conductivity of the fuel pellets at the actual fill rate (i.e., the equivalent thermal conductivity of the uniform distribution model), f2 is the formula for calculating the equivalent thermal conductivity of the fuel pellets based on the highest temperature of TRISO (TRistructural ISOtropic, three-dimensional isotropic fuel particles), and k represents the equivalent thermal conductivity of the fuel pellets at the actual fill rate. Extreme The equivalent thermal conductivity of the fuel pellet under extreme filling conditions.

[0068] Optionally, before step 101: obtaining the equivalent thermal conductivity of the fuel pellets at the limit fill rate and the actual fill rate based on the numerical simulation method, the method for calculating the equivalent thermal conductivity of the coated particle-dispersed fuel pellets further includes: obtaining the thermal conductivity analytical equation of the simplified pellet corresponding to the fuel pellet, wherein the geometric dimensions of the simplified pellet are consistent with those of the fuel pellet, and the volumetric heat source is uniformly distributed inside; determining the analytical equation of the highest temperature, the adverse region and the ideal region of particle distribution based on the mathematical characteristics of the thermal conductivity analytical equation, wherein the adverse region is the region within the highest temperature and a first preset range centered on the highest temperature, and the ideal region is the region outside the adverse region.

[0069] Specifically, obtaining the thermal conductivity analytical equation of the simplified fuel pellet includes: simplifying the fuel pellet to obtain a simplified pellet with a uniform medium material and uniform physical property parameters; and deriving the thermal conductivity analytical equation of the simplified pellet based on the thermal conductivity differential equation in the corresponding coordinate system according to the structure of the simplified pellet.

[0070] In this embodiment, firstly, the fuel pellet is simplified: based on the geometric structure of the actual fuel pellet, the large number of fuel particles dispersed inside the pellet are simplified, and it is treated only as a simplified pellet with a uniform medium material and uniform physical property parameters. The temperature distribution inside this simplified pellet can be solved by analytical equations derived directly from theory. The simplified pellet has the same geometric dimensions as the actual pellet, and a uniformly distributed volumetric heat source inside. The thermal conductivity of the simplified pellet can characterize the macroscopic thermal conductivity of the actual fuel pellet, i.e., it is the equivalent thermal conductivity of the actual fuel pellet. Secondly, the analytical equations for the simplified pellet are derived: based on the structural characteristics of the simplified pellet, the analytical equations for thermal conductivity are directly derived from the thermal conductivity differential equations in different coordinate systems.

[0071] For example, the differential equation for heat conduction in cylindrical coordinates (r, θ, z) is:

[0072]

[0073] spherical coordinate system The differential equation for heat conduction is: In the formula: τ is time, in seconds; t is temperature, in K; k is thermal conductivity, in W / (m·K); ρ is density, in kg / m³. 3 c represents heat capacity, measured in J / (kg·K). This is based on the following assumptions:

[0074] (1) Considering the steady-state problem, the temperature change over time term is zero:

[0075]

[0076] (2) Consider a one-dimensional problem, focusing only on the radial temperature change:

[0077]

[0078]

[0079] (3) Considering that the thermal conductivity is constant within a small temperature difference range:

[0080] k = constant.

[0081] By combining the above equations, we can obtain the analytical equations for heat conduction under different specific structures:

[0082] Cylinder:

[0083]

[0084] Cylindrical body:

[0085]

[0086] Sphere:

[0087]

[0088] In the formula: r1 is the inner diameter of the cylinder, in meters (m); r2 is the outer diameter of the cylinder / sphere, in meters (m); t2 is the outer wall temperature of the cylinder / sphere, in Kelvin (K); φ s This represents a heat source that is uniformly distributed within a unit volume, with units of W / m². 3 .

[0089] Furthermore, the analytical process for determining the analytical equation for the highest temperature, and the analysis of the harsh and ideal regions of particle distribution, based on the mathematical characteristics of the thermal conductivity analytical equation, is as follows: The thermal conductivity analytical equation derived based on a specific structure has specific mathematical characteristics: given an outer diameter r2 and an outer wall temperature t2, the analytical equations for both cylinders and spheres are parabolic, meaning the temperature distribution follows a parabolic pattern, monotonically decreasing with increasing radius. The highest temperature occurs at the vertex of the parabola, i.e., the center of the cylinder / sphere. For a cylindrical body, when the inner diameter is infinitely small, its thermal conductivity is infinitely close to that of a cylinder; therefore, its temperature distribution is also close to that of a cylinder, and the highest temperature occurs on the inner wall of the cylinder. The analytical equations for the highest temperature under different specific structures are as follows:

[0090] Cylinder:

[0091]

[0092] Cylindrical body:

[0093]

[0094] Sphere:

[0095]

[0096] Based on the method of equal calculated maximum temperature, the hot spot temperature of the actual fuel pellet is calculated by simplifying the maximum temperature obtained from the pellet solution.

[0097] Thermal conductivity analysis: Based on the mathematical characteristics of the derived thermal conductivity analytical equation, the temperature distribution pattern can be obtained. The highest temperature and its vicinity (such as the area within the first preset range centered on the highest temperature) belong to the high-temperature zone of the fuel pellet. When fuel particles are distributed in this zone, the effect of particle heat dissipation is poor, and the local temperature is high. Therefore, this zone is considered a poor particle distribution zone. The area relative to the poor zone is the ideal particle distribution zone. When particles are distributed in the ideal zone, the effect of particle heat dissipation is good, and the local temperature is low.

[0098] Step 102: Based on the distribution pattern of fuel particles in the matrix material, construct three typical distribution models: extremely poor distribution, extremely ideal distribution, and uniform distribution.

[0099] In this embodiment, both the extremely poor distribution model and the extremely ideal distribution model have a limit filling rate, which are two extreme distribution models under the limit filling rate. The constructed uniform distribution model has an actual filling rate and is a distribution model with regularly arranged particles.

[0100] Specifically, three typical distribution models are constructed: extremely harsh distribution, extremely ideal distribution, and uniform distribution. The models include: setting the fuel particles to be uniformly distributed in the matrix material with the actual filling rate to construct a uniform distribution model; setting the fuel particles to be distributed in the harsh area with the limit filling rate and the ideal area as the matrix material to construct an extremely harsh distribution model; and setting the fuel particles to be distributed in the ideal area with the limit filling rate and the harsh area as the matrix material to construct an extremely ideal distribution model.

[0101] In this embodiment, for the uniform distribution model, all fuel particles are uniformly distributed within the matrix material. For the extremely poor distribution model, it is assumed that all fuel particles are densely distributed in the poor particle distribution region (region A) of the fuel pellet, while the corresponding ideal particle distribution region is the fuel-free region (region B). In this case, the heat conduction performance of the heating particles is the worst, therefore the equivalent thermal conductivity calculated by this model is the smallest, lower than that of the case where all other particles are randomly distributed. Region A of the pellet has a limiting fill rate ψ. Extreme The equivalent thermal conductivity k is obtained by numerical simulation method. Extreme Region B of the pellet is a fuel-free region, and its thermal conductivity can be directly selected from the thermal conductivity k of the matrix material. MatrixFor the ideal distribution model, it is assumed that all fuel particles are densely distributed in the ideal particle distribution region (region A) of the fuel pellet, while the corresponding poorly distributed region is the fuel-free region (region B). In this case, the heat-conducting particles exhibit the best outward heat conduction performance, thus the equivalent thermal conductivity calculated by this model is the largest, greater than that of the case where all other particles are randomly distributed. Region A of the pellet has a limiting fill ratio ψ. Extreme The equivalent thermal conductivity k is obtained by numerical simulation method. Extreme Region B of the pellet is a fuel-free region, and its thermal conductivity can be directly selected from the thermal conductivity k of the matrix material. Matrix .

[0102] Step 103: Based on the equivalent thermal conductivity of the fuel pellets under the limit filling rate and the actual filling rate, as well as the thermal conductivity of the matrix material, calculate the equivalent thermal conductivity of three typical distribution models. The equivalent thermal conductivity of the extremely poor distribution model is equivalent to the lower limit of the equivalent thermal conductivity of the fuel pellets, the equivalent thermal conductivity of the extremely ideal distribution model is equivalent to the upper limit of the equivalent thermal conductivity of the fuel pellets, and the equivalent thermal conductivity of the uniform distribution model is equivalent to the average value of the equivalent thermal conductivity of the fuel pellets.

[0103] Specifically, based on the equivalent thermal conductivity of fuel pellets at both the limit fill rate and the actual fill rate, as well as the thermal conductivity of the matrix material, the equivalent thermal conductivity of three typical distribution models is calculated. This includes: determining the size of the harsh / ideal region based on the number of fuel particles; calculating the hot spot temperature of the extremely harsh / ideal distribution model based on the size of the harsh / ideal region and the thermal conductivity analytical equation of the simplified pellet corresponding to the harsh / ideal region; setting the equivalent thermal conductivity of the extremely harsh / ideal distribution model and obtaining the highest temperature of the simplified pellet based on this setting; calculating the equivalent thermal conductivity of the extremely harsh / ideal distribution model based on the equality relationship between the hot spot temperature and the highest temperature of the simplified pellet, where the equivalent thermal conductivity of the extremely harsh / ideal distribution model is related to the equivalent thermal conductivity of the fuel pellet at the limit fill rate, the thermal conductivity of the matrix material, and the fill rate; and determining the equivalent thermal conductivity of the uniform distribution model as the equivalent thermal conductivity of the fuel pellet at the actual fill rate.

[0104] In this embodiment, for the extremely poor distribution model, all fuel particles are densely distributed in the poor particle distribution region (region A) of the fuel pellet, while the corresponding ideal particle distribution region is the fuel-free region (region B). The size of region A is determined based on the fact that the number of fuel particles filling region A is consistent with the number of fuel particles in the pellet.

[0105] r A =f3(r2,ψ Regular ,ψ Extreme ),

[0106] In the formula: r A ψ is the dimension of area A; Regular ψ represents the actual fill rate of the fuel pellets. Extreme f3 is the limit fill rate, and f3 is the formula for calculating the size of the limit fill region in the extremely poor distribution model. The form of this equation is different for different shaped core blocks. Example 2 illustrates the specific equation for a cylindrical core block.

[0107] The temperature distributions of regions A and B are calculated using the thermal conductivity analytical formula for a specific structure, ultimately yielding the hotspot temperatures of the extreme distribution model:

[0108]

[0109] Based on the equivalent simple core, assume that the equivalent thermal conductivity corresponding to the extremely poor distribution model is k. E-worst Therefore, the highest temperature of the simple core based on this thermal conductivity is:

[0110]

[0111] The principle of ensuring equal maximum temperatures:

[0112] t max =t peak ,

[0113] Therefore, we can conclude that:

[0114]

[0115] k E-worst =f5(ψ Regular ,ψ Extreme ,k Extreme ,k Matrix ).

[0116] Among them, t peak f4 is the hotspot temperature, f5 is the formula for calculating the highest temperature in the extreme distribution model of fuel pellets, and f6 is the formula for calculating the equivalent thermal conductivity in the extreme distribution model of fuel pellets. The equations differ depending on the shape of the pellet; Example 2 illustrates the specific equation for a cylindrical pellet. t2 is the outer wall temperature, kJ / m³. Matrix φ is the thermal conductivity of the base material. s For a heat source that is uniformly distributed within a unit volume, k E-worst ψ is the equivalent thermal conductivity of the extremely poor distribution model. Regular ψ represents the actual fill rate. Extreme k represents the limit fill rate. Extreme The equivalent thermal conductivity of the fuel pellet under extreme filling conditions.

[0117] Therefore, for fuel pellets under extreme distribution conditions, the calculation of their equivalent thermal conductivity only requires certain parameters such as the actual filling rate, the extreme filling rate, and the equivalent thermal conductivity of the fuel and the matrix material under the extreme filling rate.

[0118] For the ideal distribution model, all fuel particles are densely distributed in the ideal particle distribution region (region A) of the fuel pellet, while the corresponding poor particle distribution region is the fuel-free region (region B). The size of region A is determined based on the consistency between the number of fuel particles filling region A and the number of fuel particles in the pellet.

[0119] r A =f6(r2,ψ) Regular ,ψ Extreme ),

[0120] In the formula: r A ψ is the dimension of area A; Regular This represents the actual fill rate of the fuel pellets.

[0121] The temperature distributions of regions A and B are calculated using the thermal conductivity analytical formula for a specific structure, ultimately yielding the hotspot temperatures of the extreme distribution model:

[0122]

[0123] Based on the equivalent simple core, assume that the equivalent thermal conductivity corresponding to the perfectly ideal distribution model is k. E-best Therefore, the highest temperature of the simple core based on this thermal conductivity is:

[0124]

[0125] The principle of ensuring equal maximum temperatures:

[0126] t max =t peak ,

[0127] Therefore, we can conclude that:

[0128]

[0129] k E-best =f8(ψ Regular ,ψ Extreme ,k Extreme ,k Matrix ).

[0130] Wherein, f6 is the formula for calculating the limit filling region size of the ideal distribution model, f7 is the formula for calculating the maximum temperature of the ideal distribution model of the fuel pellet, and f8 is the formula for calculating the equivalent thermal conductivity of the ideal distribution model of the fuel pellet. The equations have different forms for different shaped pellets. Example 2 illustrates the specific equations for a cylindrical pellet.E-best It is the equivalent thermal conductivity of the ideal distribution model.

[0131] For the uniform distribution model, its equivalent thermal conductivity is the equivalent thermal conductivity of the fuel pellets under the actual fill rate.

[0132] Step 104: Calculate the equivalent thermal conductivity that meets the confidence interval requirement based on the equivalent thermal conductivity of the three typical distribution models, and use it as the conservative thermal conductivity of the fuel pellet.

[0133] In this embodiment, since the lower limit of the equivalent thermal conductivity obtained in step 103 is the equivalent thermal conductivity of the extremely poor distribution model, the upper limit of the equivalent thermal conductivity is the equivalent thermal conductivity of the extremely ideal distribution model, and the average value of the equivalent thermal conductivity is the equivalent thermal conductivity of the uniform distribution model, the probability distribution of the equivalent thermal conductivity can be obtained based on the results of step 103, and the corresponding equivalent thermal conductivity can be obtained according to the confidence interval requirements.

[0134] Specifically, the calculation of the equivalent thermal conductivity that meets the confidence interval requirement based on the equivalent thermal conductivity of three typical distribution models includes: treating the equivalent thermal conductivity of the fuel pellet as a continuous random variable taking values ​​within a second preset range and following a normal distribution; defining the center position and value range of the probability distribution curve using the equivalent thermal conductivity of the three typical distribution models respectively, and calculating the mathematical expectation and standard deviation of the probability distribution curve; and calculating the equivalent thermal conductivity that meets the confidence interval requirement based on the mathematical expectation and standard deviation, which serves as the conservative thermal conductivity of the fuel pellet.

[0135] Wherein, the mathematical expectation μ satisfies:

[0136] Or, μ = k E-uniform The standard deviation σ satisfies:

[0137]

[0138] Where, k E-best k is the equivalent thermal conductivity of the perfectly ideal distribution model. E-worst k is the equivalent thermal conductivity of the extremely poor distribution model. E-uniform is the equivalent thermal conductivity of the uniformly distributed model.

[0139] In this embodiment, if the different arrangements of the coated fuel particles within the pellet are considered as a random experiment, with each sample corresponding to a specific arrangement, the equivalent thermal conductivity corresponding to this specific arrangement can be treated as a continuous random variable within a certain range, following a normal distribution:

[0140] K~(μ,σ 2 ).

[0141] Based on the actual manufacturing process of fuel pellets, the distribution of fuel particles within the matrix material tends to be uniform. Therefore, the equivalent thermal conductivity calculated by the uniform distribution model has the highest probability of occurrence.

[0142] μ = k E-uniform .

[0143] Meanwhile, the limiting distribution model of fuel particles represents a very special case of fuel pellets, and the equivalent thermal conductivity calculated by it has the minimum probability of occurrence. The thermal conductivity of the pellets corresponding to any particle arrangement will fall between the calculation results of the extremely poor distribution model and the extremely ideal distribution model. According to the 3σ principle of normal distribution, we can obtain:

[0144] μ-3σ=k E-worst ,

[0145] μ+3σ=k E-best .

[0146] Choose any two of the three constant equations above and solve them simultaneously to obtain the expected value μ and standard deviation σ of the probability distribution. For example, calculate the equivalent thermal conductivity using the adverse distribution model and the ideal distribution model:

[0147]

[0148]

[0149] If the design requires a confidence level of 95%, the table can be consulted to obtain:

[0150] P(K>(μ-1.7σ))=95.54%.

[0151] Therefore, the conservative thermal conductivity that meets the confidence level requirement is:

[0152] k e =μ-1.7σ.

[0153] This embodiment of the method for calculating the equivalent thermal conductivity of coated particle-dispersed fuel pellets employs numerical simulation to analyze specially arranged fuel pellets with regular patterns. Detailed modeling is performed on local pellets truncated based on their cellular structure. The temperature distribution of the pellets under actual and extreme filler ratios is calculated, and the equivalent thermal conductivity of the pellets at the two filler ratios is obtained based on the highest temperature. Specifically, based on the actual geometric structure of the fuel pellets, they are treated as simplified pellets with uniform medium and properties. The corresponding analytical thermal conductivity equation is directly derived through the thermal conductivity differential equation. The highest temperature and the harsh and ideal regions of particle distribution are determined based on the mathematical properties of the analytical equation. Subsequently, based on different distribution patterns of fuel particles within the matrix material, three typical distribution models—uniform distribution, extremely harsh distribution, and extremely ideal distribution—are proposed. The equivalent thermal conductivity of the three typical distribution models is calculated based on the equivalent thermal conductivity obtained from existing numerical simulation methods and the thermal conductivity of the matrix material. Considering the impact of random particle dispersion within the matrix material on the macroscopic thermal conductivity of the fuel pellet, the equivalent thermal conductivity of the fuel pellet is treated as a continuous random variable taking values ​​within a certain range, following a normal distribution. The center position and value range of the probability density curve are defined using the equivalent thermal conductivity of three typical distribution models. Therefore, the equivalent thermal conductivity meeting a certain confidence level can be calculated based on the "three standard deviation principle." Since the particle arrangement and thermal conductivity of the three models (extremely poor distribution model, extremely ideal distribution model, and uniform distribution model) are predictable, a large amount of calculation for the uncertainty of fuel pellet thermal conductivity caused by random particle distribution is avoided. This effectively considers the heat generation of the fuel particles themselves and the impact of random distribution on the macroscopic thermal conductivity of the fuel pellet, ensuring that the calculated equivalent thermal conductivity is above a certain confidence level. By limiting the value of the equivalent thermal conductivity of the fuel pellet using the limiting distribution model, calculation results meeting the design confidence level requirements are obtained. This allows for an appropriate reduction in computational conservatism while ensuring sufficient reliability, thereby improving economic efficiency. Furthermore, the local model in this embodiment contains several fuel particles with a 1 / 4 symmetric structure. The model is the simplest and requires the fewest meshes. Therefore, it consumes less computational resources and can improve the calculation speed of the equivalent thermal conductivity.

[0154] Example 2:

[0155] This embodiment employs a combination of theoretical analysis, probabilistic analysis, and numerical simulation to analyze the macroscopic thermal conductivity characteristics of typical fuel pellets and provides a method for calculating the equivalent thermal conductivity of such typical fuel pellets. Figure 2As shown. The calculation method in this embodiment can effectively consider the impact of fuel particle heat generation and random distribution on the thermal conductivity of the fuel pellets, avoiding complex uncertainty analysis calculations. The in-pile fuel hot spot temperature (i.e., the highest temperature of the fuel particle at the hottest location in the pile) calculated based on this thermal conductivity can meet the confidence requirements of engineering design, and further reduce conservatism, thereby improving the economic efficiency of the reactor design.

[0156] Taking a typical fuel pellet (40% fill rate) widely used in high-temperature gas-cooled reactors as an example, this embodiment will be described in further detail. The fuel particles used in this embodiment are 6-TRISO (TRistructural ISOtropic, three-dimensional isotropic fuel particles). These particles consist of a multi-layered coating structure composed of a 1-fuel particle and sequentially coated layers of 2-Buffer, 3-IPyC, 4-SiC, and 5-OPyC. Figure 3 As shown, a large number of 6-TRISO particles are randomly dispersed within the matrix material, and are processed into a typical cylindrical fuel pellet, such as... Figure 4 As shown.

[0157] This embodiment provides a method for calculating the equivalent thermal conductivity of coated particulate fuel pellets. The specific implementation steps are as follows:

[0158] S1, analytical derivation of equivalent fuel pellets.

[0159] (1) Fuel pellet simplification:

[0160] Based on the simplified geometry of the actual fuel pellet, the large number of 6-TRISO particles dispersed inside the pellet are ignored. It is treated as a simplified pellet with a homogeneous medium and uniform physical properties. The temperature distribution within this simplified pellet can be solved using analytical equations derived directly from theory. The typical fuel pellet in this embodiment is simplified into a cylinder with a uniformly distributed volumetric heat source, ensuring that the simplified pellet's geometric dimensions are consistent with the actual pellet. The thermal conductivity of the simplified pellet characterizes the macroscopic thermal conductivity of the actual fuel pellet, i.e., it is the equivalent thermal conductivity of the actual fuel pellet.

[0161] (2) Derivation of analytical equations:

[0162] Based on the simplified core structure, the analytical equation for heat conduction of a cylinder with a uniform internal heat source is derived from the differential equation for heat conduction in cylindrical coordinates, as shown in Figure 5.

[0163] In cylindrical coordinates, the heat introduced into a infinitesimal element per unit time is equal to the sum of the heat introduced from the three directions (r, θ, z):

[0164]

[0165] in,

[0166]

[0167]

[0168]

[0169] The net heat introduced into the infinitesimal element is:

[0170]

[0171] The amount of heat generated by the heat source within the infinitesimal element per unit time is:

[0172] dφ s =φ s ·(dr·rdθ·dz),

[0173] The change in thermodynamic energy within a unit time interval is:

[0174]

[0175] In the formula, t is the temperature, in °C; ρ is the density, in kg / m³. 3 c is the specific heat capacity, in J / (kg·K); τ is time, in seconds; k is the thermal conductivity, in W / (m·K); φ s This represents a heat source that is uniformly distributed within a unit volume, with units of W / m². 3 .

[0176] According to the energy conservation equation:

[0177] dφ+dφ s =dU,

[0178] We can obtain:

[0179]

[0180] Eliminating the infinitesimal volume term, the transformation (dr·rdθ·dz) yields:

[0181]

[0182] Consider the steady-state problem:

[0183]

[0184] Consider a one-dimensional problem, focusing only on the radial temperature variation:

[0185]

[0186] Considering that the thermal conductivity is constant within a small temperature difference range:

[0187] k = constant

[0188] Substituting the values, we obtain the differential equation for heat conduction of a cylinder containing a uniformly distributed internal heat source:

[0189]

[0190] Given the outer wall temperature, the analytical equation for heat conduction can be obtained by integration:

[0191]

[0192] In the formula, r2 is the diameter of the fuel pellet in meters (m); t2 is the temperature of the outer wall of the fuel pellet in K.

[0193] (3) Equivalent processing method:

[0194] Based on the mathematical characteristics of the derived heat conduction analytical equation, given the outer diameter and outer wall temperature, the temperature exhibits a parabolic distribution, monotonically decreasing as the radius increases. The highest temperature occurs at the vertex of the parabola, i.e., the center of the cylinder (r = 0). Therefore, the highest temperature can be obtained as follows:

[0195]

[0196] The hot spot temperature of the actual fuel pellet will be calculated by simplifying the solution based on the maximum temperature of the pellet, using the method of equal maximum temperature.

[0197] (4) Thermal conductivity analysis:

[0198] Based on the mathematical characteristics of the derived heat conduction analytical equation, the temperature distribution pattern can be obtained. The highest temperature occurs at the center of the cylinder, therefore this location and its vicinity belong to the high-temperature zone of the fuel pellet. When fuel particles are distributed in the central region of the cylindrical fuel pellet, the outward dissipation of heat from the particles is poor, resulting in locally high temperatures; this region is considered a poorly distributed region. Conversely, when fuel particles are distributed in the peripheral region of the cylindrical fuel pellet, the outward dissipation of heat from the particles is good, resulting in locally low temperatures; this region is considered an ideally distributed region.

[0199] S2, numerical simulation of actual fuel pellets.

[0200] For fuel pellets with uniformly distributed fuel particles, the particles are distributed within the matrix material in a certain manner (simple cubic, body-centered cubic, face-centered cubic, etc.) and at a certain spacing. The specific arrangement of these particles has no impact on the macroscopic thermal conductivity of the pellet. For fuel pellets with such predictable structures, numerical simulations based on detailed modeling can realistically reflect the thermal conductivity of the pellet.

[0201] (1) Particle arrangement settings:

[0202] For fuel pellets with an actual fill rate of 40%, any arrangement can be chosen. This embodiment selects a simple cubic arrangement for modeling and calculation, such as... Figure 6 As shown. For fuel pellets with a limit to the fill rate, to obtain the maximum fill rate of 74%, either a face-centered cubic (FCC) arrangement or a close-packed hexagonal (HPC) arrangement can be selected. This embodiment selects the FCC arrangement for modeling and calculation, as shown below. Figure 7 As shown.

[0203] (2) Construction of local model of the core block:

[0204] A local model of an actual fuel pellet is extracted based on a cell structure with regularly arranged particles, ensuring that its radial dimension is consistent with the actual pellet, and its height and width are both equal to half the size of a unit cell. Therefore, the local model contains several fuel particles with a 1 / 4 symmetric structure, such as... Figure 6 , Figure 7 As shown, the 1-fuel core, 2-buffer layer, 3-IPyC layer, 4-SiC layer, 5-OPyC layer, and 7-matrix material of the 6-TRI SO particles are all modeled in detail individually.

[0205] (3) Model mesh generation:

[0206] The geometric model is imported into the mesh generation software to complete the mesh generation. The materials of different regions are defined, the corresponding boundary conditions are defined, and the preliminary preprocessing is completed to form the simulated core block model.

[0207] (4) Numerical simulation settings:

[0208] The simulated pellet model was imported into CFD software, a volumetric heat source was set in the pellet core region, and an isothermal boundary was set on the outside of the pellet to simulate the actual operation of fuel in the reactor.

[0209] Assuming the fuel pellets are isotropic materials, thermal conduction along the height direction is ignored and only radial thermal conduction is considered. Other cross sections of the simulated pellet model are set as symmetrical boundaries.

[0210] By setting corresponding materials in different regions of the simulated chip, the CFD software can automatically call up physical property parameters based on key parameters such as material, temperature, burnup, and neutron flux.

[0211] S3, equivalent treatment of typical distribution models.

[0212] (1) Uniform distribution model:

[0213] All 6-TRISO particles are uniformly distributed within the matrix material, and the equivalent thermal conductivity can be calculated using numerical simulation results. According to the analytical equation for thermal conductivity of the core, it can be known that...

[0214]

[0215] Therefore, at a 40% fill ratio, the equivalent thermal conductivity of the uniformly distributed model based on the highest temperature of the fuel pellets is:

[0216]

[0217] Similarly, the equivalent thermal conductivity of the fuel pellet at the limiting fill ratio is:

[0218]

[0219] In the formula: t peak1 The highest temperature of a 40% filler fuel pellet, in K; t peak2 The highest temperature of a 74% filler fuel pellet, expressed in Kelvin (K).

[0220] (2) Extremely severe distribution model:

[0221] All 6-TRISO particles are distributed with maximum density in the central region (Area A) of the cylindrical core, i.e., the harsh region, giving this region a maximum fill rate ψ. Extreme The equivalent thermal conductivity is k Extreme The outer region of the pellet is the fuel-free region (region B), and the thermal conductivity of this region is directly selected from the thermal conductivity k of the matrix material. Matrix Because all the heat-generating particles are densely dispersed in the harsh area, the fuel pellet has the worst thermal conductivity, resulting in the smallest equivalent thermal conductivity, which is smaller than that of the case where all other particles are randomly distributed.

[0222] Based on the number of particles filled, there can definitely be

[0223]

[0224]

[0225] In the formula r A ψ is the radius of region A, in meters; Regular This represents the actual fill rate of the fuel pellets.

[0226] Calculate the highest temperature in region A based on the analytical equation for heat conduction of a cylinder containing an internal heat source.

[0227]

[0228] Calculate the highest temperature in region B based on the analytical equation for heat conduction of a cylindrical body excluding internal heat sources.

[0229]

[0230] In the formula, t1 is the inner wall temperature of zone B, in K; Q s The linear power density of the fuel pellet is expressed in W / m.

[0231] By combining the temperature distributions of the two regions, the thermal conductivity temperature difference of the extremely poor distribution model can be obtained.

[0232]

[0233] Based on the equivalent simplified core, we assume that the equivalent thermal conductivity corresponding to the adverse distribution model is k. E-worst Therefore, the simplified maximum temperature of the core based on this thermal conductivity is:

[0234] The highest temperature of the simplified core based on the equivalent thermal conductivity analytical equation.

[0235]

[0236] To ensure that the maximum temperatures are equal, we have:

[0237] t peak =t max ,

[0238] Therefore, we can obtain

[0239]

[0240] Therefore, the equivalent thermal conductivity of the limiting distribution model can be solved based on the equivalent thermal conductivity of the fuel pellets at the limiting fill ratio, the thermal conductivity of the matrix material, and the actual fill ratio.

[0241]

[0242] (3) Perfectly ideal distribution model:

[0243] In contrast to the worst-case distribution model, the ideal region is defined as the area where all 6-TRISO particles are distributed at maximum density in the outer region (region A) of the cylindrical core, resulting in a limiting fill rate ψ. Extreme The equivalent thermal conductivity is k Extreme The central region of the fuel pellet is the fuel-free zone (Zone B). Since there is no internal heat source, the temperature distribution within Zone B is uniform and equal to the temperature of the inner wall of Zone A, which it contacts. Because all heat-generating particles are densely dispersed in this ideal region, the fuel pellet exhibits the best thermal conductivity, resulting in the highest equivalent thermal conductivity, greater than that of the case where all other particles are randomly distributed.

[0244] Based on the number of particles filled, there can definitely be

[0245]

[0246]

[0247] In the formula r A This is the inner diameter of area A, in meters.

[0248] Calculate the highest temperature in region A using the analytical equation for heat conduction of a cylindrical body containing an internal heat source:

[0249]

[0250] Based on the equivalent simple core, assume that the equivalent thermal conductivity corresponding to the perfectly ideal distribution model is k. E-best Therefore, the highest temperature of the simple core based on this thermal conductivity is

[0251]

[0252] To ensure that the maximum temperatures are equal, we have:

[0253] t peak =t max ,

[0254] Therefore, we can obtain

[0255]

[0256] Therefore, the equivalent thermal conductivity of the perfectly ideal distribution model can be obtained as follows:

[0257]

[0258] S4, the probability distribution model of fuel pellets.

[0259] If we treat the different arrangements of coated fuel particles within the pellet as a random experiment, with each sample corresponding to a specific arrangement, the equivalent thermal conductivity corresponding to this specific arrangement can be treated as a continuous random variable within a certain range, following a normal distribution:

[0260] K~(μ,σ 2 ),

[0261] Based on the actual manufacturing process of fuel pellets, the distribution of fuel particles within the matrix material tends to be uniform. Therefore, the equivalent thermal conductivity calculated by the uniform distribution model has the highest probability of occurrence.

[0262] μ = k E-uniform ,

[0263] Meanwhile, the limiting distribution model of fuel particles represents a very special case of fuel pellets, where the calculated equivalent thermal conductivity has the lowest probability of occurrence. The thermal conductivity of the pellets corresponding to any particle arrangement will fall between the results calculated by the extremely poor distribution model and the extremely ideal distribution model. Based on the 3σ principle of normal distribution, we can obtain...

[0264] μ-3σ=k E-worst ,

[0265] μ+3σ=k E-best ,

[0266] Choosing any two of the three constant equations above, and solving them simultaneously, we can obtain the expected value μ and standard deviation P of the probability distribution. For example, we can calculate the equivalent thermal conductivity using the adverse distribution model and the ideal distribution model.

[0267]

[0268]

[0269] If the design requires a confidence level of 95%, the table can be consulted to obtain:

[0270] P(K>(μ-1.7σ))=95.54%,

[0271] Therefore, the conservative thermal conductivity that meets the confidence level requirement is:

[0272] k e = k-1.7σ.

[0273] The features and advantages of this embodiment are as follows: by homogenizing, the complex structure of the coated particulate dispersed fuel pellet is transformed into a simplified pellet with a uniform medium material and uniform physical properties. Based on this simplified pellet and the calculation method proposed in this embodiment, the equivalent thermal conductivity and corresponding hot spot temperature of the fuel pellet can be calculated quickly.

[0274] Example 3:

[0275] like Figure 8As shown, this embodiment provides a device for calculating the equivalent thermal conductivity of a coated particle-dispersed fuel pellet, including: an acquisition module 31, used to acquire the equivalent thermal conductivity of the fuel pellet under the limit fill rate and the actual fill rate based on a numerical simulation method; a construction module 32, used to construct three typical distribution models—extremely poor distribution, extremely ideal distribution, and uniform distribution—based on the distribution mode of the fuel particles in the matrix material; and a first calculation module 33, connected to the acquisition module 31 and the construction module 32, used to calculate the equivalent thermal conductivity of the three typical distribution models based on the equivalent thermal conductivity of the fuel pellet under the limit fill rate and the actual fill rate, and the thermal conductivity of the matrix material, respectively. The equivalent thermal conductivity of the extremely poor distribution model is equivalent to the lower limit of the equivalent thermal conductivity of the fuel pellet, the equivalent thermal conductivity of the extremely ideal distribution model is equivalent to the upper limit of the equivalent thermal conductivity of the fuel pellet, and the equivalent thermal conductivity of the uniform distribution model is equivalent to the average equivalent thermal conductivity of the fuel pellet. The second calculation module 34 is connected to the first calculation module 33 and is used to calculate the equivalent thermal conductivity that meets the confidence interval requirements based on the equivalent thermal conductivity of three typical distribution models, so as to serve as the conservative thermal conductivity of the fuel pellet.

[0276] Optionally, the computing device further includes a determination module. The determination module is used to obtain the thermal conductivity analytical equation for a simplified fuel pellet corresponding to the fuel pellet, wherein the simplified pellet has the same geometric dimensions as the fuel pellet and a uniformly distributed volumetric heat source inside. It is also used to determine the analytical equation for the highest temperature, the harsh region and the ideal region of particle distribution based on the mathematical characteristics of the thermal conductivity analytical equation. The harsh region is the area within the highest temperature and a first preset range centered on the highest temperature, and the ideal region is the area outside the harsh region. Specifically, the determination module is used to simplify the fuel pellet to obtain a simplified pellet with a uniform medium material and uniform physical property parameters. It is also used to derive the thermal conductivity analytical equation for the simplified pellet based on the thermal conductivity differential equation in the corresponding coordinate system, according to the structure of the simplified pellet.

[0277] Optionally, the acquisition module is used to construct geometric models of fuel pellets under the limit fill rate and the actual fill rate, respectively, and to calculate the temperature distribution of the geometric models of fuel pellets under the limit fill rate and the actual fill rate based on numerical simulation methods, and to obtain the equivalent thermal conductivity of fuel pellets under the limit fill rate and the actual fill rate based on the highest temperature in the temperature distribution.

[0278] Optionally, the acquisition module is also used to set the particle regularity arrangement of fuel pellets under the limit fill rate and the actual fill rate respectively, and to extract the local model of the fuel pellet based on the cell structure of the particle regularity arrangement, and to separately model the composition structure of the fuel particles and the matrix material in the local model to obtain the geometric model of the fuel pellet under the limit fill rate and the actual fill rate, wherein the local model contains several fuel particles with 1 / 4 symmetry structure.

[0279] Optionally, the acquisition module is also used to substitute the highest temperature in the temperature distribution of the fuel pellet geometric model under the limiting fill rate and the actual fill rate into the simplified analytical equation of the highest temperature of the pellet, respectively, to obtain the equivalent thermal conductivity of the fuel pellet under the limiting fill rate and the actual fill rate.

[0280] Optionally, the construction module is used to set the fuel particles to be uniformly distributed in the matrix material at the actual filling rate to construct a uniform distribution model, and to set the fuel particles to be distributed in the harsh area at the limit filling rate and the ideal area as the matrix material to construct an extremely harsh distribution model, and to set the fuel particles to be distributed in the ideal area at the limit filling rate and the harsh area as the matrix material to construct an extremely ideal distribution model.

[0281] Optionally, the first calculation module is used to determine the size of the harsh / ideal region based on the number of fuel particles filled, and to calculate the hot spot temperature of the extremely harsh distribution model / extremely ideal distribution model based on the size of the harsh / ideal region and the thermal conductivity analytical equation of the simplified pellet corresponding to the harsh / ideal region. It is also used to set the equivalent thermal conductivity of the extremely harsh / extremely ideal distribution model, and to obtain the maximum temperature of the simplified pellet based on this setting. Furthermore, it is used to calculate the equivalent thermal conductivity of the extremely harsh / extremely ideal distribution model based on the equality relationship between the hot spot temperature of the extremely harsh / extremely ideal distribution model and the maximum temperature of the simplified pellet. The equivalent thermal conductivity of the extremely harsh / extremely ideal distribution model is related to the equivalent thermal conductivity of the fuel pellet at the limit fill rate, the thermal conductivity of the matrix material, and the fill rate. It is used to determine that the equivalent thermal conductivity of the uniform distribution model is the equivalent thermal conductivity of the fuel pellet at the actual fill rate.

[0282] Optionally, the second calculation module is used to treat the equivalent thermal conductivity of the fuel pellet as a continuous random variable taking values ​​within a second preset range, following a normal distribution. It uses the equivalent thermal conductivity of three typical distribution models to define the center position and value range of the probability distribution curve, calculates the mathematical expectation and standard deviation of the probability distribution curve, and calculates the equivalent thermal conductivity that meets the confidence interval requirement based on the mathematical expectation and standard deviation, as the conservative thermal conductivity of the fuel pellet. Wherein, the mathematical expectation μ satisfies:

[0283] Or, μ = k E-uniform ,

[0284] The standard deviation σ satisfies:

[0285]

[0286] Where, k E-best k is the equivalent thermal conductivity of the perfectly ideal distribution model.E-worst k is the equivalent thermal conductivity of the extremely poor distribution model. E-uniform is the equivalent thermal conductivity of the uniformly distributed model.

[0287] Example 4:

[0288] This embodiment provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor is configured to run the computer program to implement the method for calculating the equivalent thermal conductivity of coated particulate fuel pellets as described in Embodiment 1.

[0289] It is understood that the above embodiments are merely exemplary implementations used to illustrate the principles of the present invention, and the present invention is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A method for calculating the equivalent thermal conductivity of coated particulate dispersion fuel pellets, characterized in that, include: The equivalent thermal conductivity of fuel pellets under extreme and actual fill rates was obtained using numerical simulation methods. Based on the distribution of fuel particles within the matrix material, three typical distribution models are constructed: extremely poor distribution, extremely ideal distribution, and uniform distribution. Based on the equivalent thermal conductivity of fuel pellets under extreme and actual fill rates, as well as the thermal conductivity of the matrix material, the equivalent thermal conductivity of three typical distribution models is calculated. The equivalent thermal conductivity of the extremely poor distribution model is equivalent to the lower limit of the equivalent thermal conductivity of the fuel pellets, the equivalent thermal conductivity of the extremely ideal distribution model is equivalent to the upper limit of the equivalent thermal conductivity of the fuel pellets, and the equivalent thermal conductivity of the uniform distribution model is equivalent to the average equivalent thermal conductivity of the fuel pellets. The equivalent thermal conductivity that meets the confidence interval requirement is calculated based on the equivalent thermal conductivity of three typical distribution models, and is used as the conservative thermal conductivity of the fuel pellet. The construction of three typical distribution models—extremely adverse distribution, extremely ideal distribution, and uniform distribution—specifically includes: The fuel particles are set to be uniformly distributed within the matrix material at the actual filling rate in order to construct a uniform distribution model; The fuel particles are set to be distributed in the harsh region with a limit filling rate, and the ideal region is used as the matrix material to construct an extremely harsh distribution model. The harsh region is the region with the highest temperature and the first preset range centered on the highest temperature, and the ideal region is the region outside the harsh region. The fuel particles are set to be distributed in the ideal region with the limit of the filling rate, and the harsh region is used as the matrix material to construct an extremely ideal distribution model.

2. The calculation method according to claim 1, characterized in that, Before obtaining the equivalent thermal conductivity of the fuel pellets at the limiting fill rate and the actual fill rate using the numerical simulation method, the method further includes: Obtain the thermal conductivity analytical equation for the simplified pellet corresponding to the fuel pellet, wherein the simplified pellet has the same geometric dimensions as the fuel pellet and a uniformly distributed volumetric heat source inside; The analytical equation for the highest temperature, the harsh region and the ideal region of particle distribution are determined based on the mathematical properties of the thermal conductivity analytical equation.

3. The calculation method according to claim 2, characterized in that, The process of obtaining the simplified thermal conductivity analytical equation for the fuel pellet specifically includes: The fuel pellets are simplified to obtain simplified pellets with uniform medium material and uniform physical property parameters; Based on the simplified core structure, the simplified core's analytical thermal conductivity equation is derived from the thermal conductivity differential equation in the corresponding coordinate system.

4. The calculation method according to claim 2, characterized in that, The method for obtaining the equivalent thermal conductivity of fuel pellets at both the limiting and actual fill rates using numerical simulation specifically includes: Geometric models of fuel pellets were constructed under both the limit fill rate and the actual fill rate. The temperature distribution of the fuel pellet geometric model under the limit fill rate and the actual fill rate was calculated using numerical simulation methods. The equivalent thermal conductivity of fuel pellets at the limit fill rate and the actual fill rate is obtained based on the highest temperature in the temperature distribution.

5. The calculation method according to claim 4, characterized in that, The construction of geometric models for fuel pellets at both the limit fill rate and the actual fill rate includes: Set the particle arrangement of fuel pellets under the extreme fill rate and the actual fill rate respectively; A local model of the fuel pellet is extracted based on the cell structure of regularly arranged particles, and the composition structure of the fuel particles and the matrix material in the local model are modeled separately to obtain the geometric model of the fuel pellet under the limit filling rate and the actual filling rate. The local model contains several fuel particles with 1 / 4 symmetry structure.

6. The calculation method according to claim 4, characterized in that, The method of obtaining the equivalent thermal conductivity of fuel pellets at the extreme fill rate and the actual fill rate based on the highest temperature in the temperature distribution specifically includes: By substituting the highest temperature in the temperature distribution of the fuel pellet geometric model under the limiting fill rate and the actual fill rate into the simplified analytical equation for the highest temperature of the pellet, the equivalent thermal conductivity of the fuel pellet under the limiting fill rate and the actual fill rate is obtained.

7. The calculation method according to claim 1, characterized in that, The equivalent thermal conductivity of the fuel pellets at the limiting and actual fill rates, as well as the thermal conductivity of the matrix material, is calculated for three typical distribution models. Specifically, this includes: The size of the harsh / ideal area is determined based on the number of fuel particles filled. Based on the dimensions of the harsh / ideal regions and the thermal conductivity analytical equations of the simplified core blocks corresponding to the harsh / ideal regions, the hot spot temperatures of the extremely harsh distribution model / extremely ideal distribution model are calculated. Set the equivalent thermal conductivity of the extremely poor distribution model / extremely ideal distribution model, and obtain the highest temperature of the simplified core based on this setting; Based on the relationship between the hot spot temperature and the maximum temperature of the simplified pellet in the extreme distribution model / extreme ideal distribution model, the equivalent thermal conductivity of the extreme distribution model / extreme ideal distribution model is calculated. The equivalent thermal conductivity of the extreme distribution model / extreme ideal distribution model is related to the equivalent thermal conductivity of the fuel pellet with the limit fill rate, the thermal conductivity of the matrix material, and the fill rate. The equivalent thermal conductivity of the uniformly distributed model is determined to be the equivalent thermal conductivity of the fuel pellets under the actual filling rate.

8. The calculation method according to claim 1, characterized in that, The calculation of the equivalent thermal conductivity that satisfies the confidence interval requirement based on the equivalent thermal conductivity of three typical distribution models specifically includes: The equivalent thermal conductivity of the fuel pellet is treated as a continuous random variable taking values ​​within a second preset range and following a normal distribution; The equivalent thermal conductivity of three typical distribution models is used to define the center position and range of the probability distribution curve, and the mathematical expectation and standard deviation of the probability distribution curve are calculated. The equivalent thermal conductivity that meets the confidence interval requirement is calculated based on the mathematical expectation and standard deviation, and is used as the conservative thermal conductivity of the fuel pellet.

9. The calculation method according to claim 8, characterized in that, Mathematical expectation μ satisfy: ,or, , Standard deviation σ satisfy: ， in, The equivalent thermal conductivity is for a perfectly ideal distribution model. The equivalent thermal conductivity is given by the extremely poor distribution model. is the equivalent thermal conductivity of the uniformly distributed model.

10. A device for calculating the equivalent thermal conductivity of coated particulate dispersed fuel pellets, characterized in that, include: The acquisition module is used to obtain the equivalent thermal conductivity of fuel pellets at the limiting fill rate and the actual fill rate based on numerical simulation methods. The building block is used to construct three typical distribution models—extremely poor distribution, extremely ideal distribution, and uniform distribution—based on the distribution pattern of fuel particles within the matrix material. The first calculation module, connected to the acquisition module and the construction module, is used to calculate the equivalent thermal conductivity of three typical distribution models based on the equivalent thermal conductivity of the fuel pellets under the extreme fill rate and the actual fill rate, as well as the thermal conductivity of the matrix material. Specifically, the equivalent thermal conductivity of the extremely poor distribution model is equivalent to the lower limit of the equivalent thermal conductivity of the fuel pellets; the equivalent thermal conductivity of the extremely ideal distribution model is equivalent to the upper limit of the equivalent thermal conductivity of the fuel pellets; and the equivalent thermal conductivity of the uniform distribution model is equivalent to the average equivalent thermal conductivity of the fuel pellets. The second calculation module, connected to the first calculation module, is used to calculate the equivalent thermal conductivity that meets the confidence interval requirements based on the equivalent thermal conductivity of three typical distribution models, as the conservative thermal conductivity of the fuel pellet. The construction module is used to set the fuel particles to be uniformly distributed in the matrix material at the actual filling rate to construct a uniform distribution model. It is also used to set the fuel particles to be distributed in the harsh region at the limit filling rate, with the ideal region as the matrix material to construct an extremely harsh distribution model. Furthermore, it is used to set the fuel particles to be distributed in the ideal region at the limit filling rate, with the harsh region as the matrix material to construct an extremely ideal distribution model. The harsh region is the region within the first preset range centered on the highest temperature, and the ideal region is the region outside the harsh region.

11. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to implement the method for calculating the equivalent thermal conductivity of coated particulate fuel pellets as described in any one of claims 1-9.

Images