Nuclear heat propulsion fuel element, method and system for optimizing parameters of coated particles of nuclear heat propulsion fuel element and computer readable medium

Abstract

The invention discloses a nuclear heat propulsion fuel element, a coated particle parameter optimization method and system thereof and a computer readable medium, and relates to the technical field of nuclear heat propulsion fuel elements. The method comprises the following steps: constructing a fuel element matrix model with height and cross section geometry; a coated particle model is defined, the coated particle model comprises a UO2 core and a coating layer, the radius of the UO2 core is a fixed value, and the thickness of the coating layer is adjustable; based on the hexagonal close-packed arrangement principle, two-dimensional particle center coordinate distribution is generated in the cross section of a base body, three-dimensional arrangement is formed through stacking in the height direction, and adjacent particles are not overlapped; a plurality of coolant channels are arranged in the base body, and any two channels are not overlapped; screening effective particles; and calculating the volume fraction of the UO2 phase, if the volume fraction is lower than a target value, reducing the thickness of the coating layer, and rearranging the particles until the volume fraction reaches or exceeds the target value. According to the method, the key parameters, especially the thickness of the coating layer, of the coated fuel particles can be reasonably determined while the high UO2 volume fraction is ensured.

Description

Technical Field

[0001] This invention relates to the field of nuclear thermal propulsion fuel element technology, and in particular to a nuclear thermal propulsion fuel element and a method, system and computer-readable medium for optimizing the parameters of its coated particles. Background Technology

[0002] Ceramic fuel, a typical form of solid fuel for nuclear thermal propulsion, typically involves directly dispersing UO2 fuel particles with a diameter of several hundred micrometers within a refractory metal (such as tungsten) matrix, and then preparing composite fuel elements through processes such as sintering. During sintering, UO2 particles are prone to interconnection, aggregation, and even large-area agglomeration. This not only causes uneven distribution of fuel particles, leading to the emergence of localized hot spots, but may also damage the structural integrity of the fuel element, threatening reactor operational safety.

[0003] Considering the chemical and thermophysical incompatibility between UO2 particles and the metal matrix, researchers have proposed pre-coating the surface of UO2 particles with a metal coating layer that is the same as or compatible with the metal matrix. This coating layer has been proven to have multiple advantages: First, it can effectively isolate UO2 particles, preventing them from directly contacting, agglomerating, or even fusing during high-temperature sintering, thereby promoting uniform distribution; second, as a key structure and protective layer on the surface of fuel particles, it can significantly enhance the containment capacity of gaseous fission products and hydrogen isotopes; third, metal coating layers prepared by methods such as chemical vapor deposition often form columnar crystal structures with fewer transverse grain boundaries, which helps to suppress the diffusion and retention of hydrogen at the grain boundaries; in addition, the coating layer can also reduce the chemical reactivity of UO2 with the high-temperature hydrogen environment, reducing fuel corrosion and mass loss.

[0004] However, the introduction of a coating layer inevitably increases the volume fraction of non-fissile materials, thereby reducing the effective volume fraction of the UO2 phase. For nuclear thermal propulsion systems, a high thrust-to-weight ratio requires fuel elements to have high energy density, small volume, and light mass, typically requiring a UO2 volume fraction of approximately 60 vol%. In other words, while the coating layer can improve compatibility and safety, it contradicts the goal of high loading rate. How to rationally determine the coating layer thickness to achieve the target UO2 volume fraction while ensuring structural reliability has become a critical problem that urgently needs to be solved. Summary of the Invention

[0005] One objective of this invention is to provide a method for optimizing the parameters of coated fuel particles in nuclear thermal propulsion fuel elements, thereby achieving the rational determination of key parameters of coated fuel particles, especially the coating layer thickness, while ensuring a high UO2 volume fraction.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] A method for optimizing the coating particle parameters of nuclear thermal propulsion fuel elements includes the following steps:

[0008] S1. Construct a fuel element substrate model with height and cross-sectional geometry;

[0009] S2. Define a coated particle model, wherein the coated particle comprises a UO2 core and a coating layer covering its surface, wherein the radius of the UO2 core is a constant and the thickness of the coating layer is adjustable;

[0010] S3. Based on the principle of hexagonal close-packing, a two-dimensional particle center coordinate distribution is generated in the cross-section of the matrix, and the particles are stacked along the height direction to form a three-dimensional arrangement, so that adjacent particles do not overlap.

[0011] S4. Multiple coolant channels (e.g., circular coolant channels) are arranged in the matrix, and no two channels overlap.

[0012] S5. Screen effective particles, remove particles that are not completely contained in the matrix, and particles that geometrically overlap with any coolant channel;

[0013] S6. Calculate the volume fraction of the UO2 phase based on the effective number of particles and geometric parameters; if the volume fraction is lower than the target UO2 volume fraction, reduce the coating layer thickness and return to step S3 to rearrange until the UO2 volume fraction reaches or exceeds the target value.

[0014] The geometric parameters include the UO2 core radius, the geometric dimensions of the fuel element substrate, and the arrangement parameters of the coolant channels.

[0015] Furthermore, the cross-sectional geometry is a regular polygon with the number of sides selected from any integer of 4, 6, or 8; or, the cross-sectional geometry is a circle.

[0016] Furthermore, multiple layers of particles are stacked along the height of the matrix, and the center-to-center distance between any two adjacent particles in the same layer is not less than twice the radius of the coated particles.

[0017] Furthermore, multiple layers of particles are stacked along the height of the matrix, with the vertical spacing between the centers of adjacent layers of particles not less than [missing information]. The radius of the coated particles is times that of the coated particles.

[0018] Furthermore, the matrix has a regular hexagonal cross-section, and the particle centers are confined to a circle with the matrix center as the center and a radius of [missing information]. Within the circular region, where Lhexa is the side length of the regular hexagon, and the circular region is completely contained within the regular hexagon.

[0019] Furthermore, the target UO2 volume fraction is not less than 60 vol% (e.g., 60 vol%, 61 vol%, or higher).

[0020] Another object of the present invention is to provide a system for optimizing the coating particle parameters of nuclear thermal propulsion fuel elements, the system comprising:

[0021] The matrix modeling module is configured to build fuel element matrix models with height and cross-sectional geometry;

[0022] The particle definition module is configured to define a coated particle model that includes a UO2 core and a coating layer, wherein the radius of the UO2 core is a fixed value and the thickness of the coating layer is adjustable;

[0023] The arrangement generation module is configured to generate two-dimensional particle center distribution within the cross-section of the substrate based on the hexagonal close-packing principle, and stack them along the height direction to form a three-dimensional arrangement, ensuring that adjacent particles do not overlap.

[0024] The channel arrangement module is configured to arrange multiple coolant channels (e.g., circular coolant channels) in the substrate, such that no two channels overlap.

[0025] The particle screening module is configured to remove particles that are not completely contained within the matrix, as well as particles that geometrically overlap with any coolant channel;

[0026] The volume fraction calculation module is configured to calculate the volume fraction of the UO2 phase based on the effective number of particles and geometric parameters.

[0027] The parameter optimization module is configured to reduce the coating layer thickness and trigger the arrangement generation module to rearrange the particles when the volume fraction is lower than the target UO2 volume fraction, until the UO2 volume fraction reaches or exceeds the target value.

[0028] The present invention also provides a computer-readable medium storing a program for optimizing the coating particle parameters of a nuclear thermal propulsion fuel element. When the program for optimizing the coating particle parameters of the nuclear thermal propulsion fuel element is run, the steps in the aforementioned method can be implemented.

[0029] The present invention also provides a nuclear thermal propulsion fuel element comprising coated particles, the coated particles comprising a UO2 core and a coating layer covering its surface, the parameters of the coated particles being obtained by the method described above.

[0030] This invention can efficiently evaluate the impact of coating thickness and coating particle diameter on the UO2 volume fraction in nuclear thermal propulsion fuel elements. Under the constraints of no overlap between particles and no geometric interference with coolant channels, a UO2 volume fraction of not less than 60 vol% can be achieved through parameter adjustment. This method does not rely on physical prototyping and repeated sintering experiments, which can significantly shorten the design cycle, reduce computational resource consumption, and improve fuel element design efficiency. Attached Figure Description

[0031] Figure 1 The diagram shows the structure of the tungsten-coated particles and the fuel element embedded in the porous hexagonal tungsten matrix in the embodiment; the left diagram shows the structure of the tungsten-coated particles; the right diagram shows the structure of the fuel element embedded in the porous hexagonal tungsten matrix.

[0032] Figure 2 This is a schematic diagram showing the trend of UO2 volume fraction as a function of tungsten (W) coating thickness and fuel particle diameter in the embodiments.

[0033] Figure 3 This is a three-dimensional structural diagram of a porous hexagonal prism-shaped fuel element with 61 cooling channels in the embodiment;

[0034] Figure 4 This is a flowchart illustrating the steps for determining the diameter of the coated particles and the thickness of the coating layer in the embodiment.

[0035] Figure 5 The orthogonal view of the particle packing structure (particle distribution) generated based on the hexagonal dense stacking algorithm in the embodiment. Figure 1 This corresponds to the case where the radius of the coated particles is 500 μm;

[0036] Figure 6 This is a top view of the particle packing structure (particle distribution) generated based on the hexagonal dense stacking algorithm in the embodiment. Figure 1 This corresponds to the case where the radius of the coated particles is 500 μm;

[0037] Figure 7 The particle packing structure (particle distribution) generated by the hexagonal dense stacking algorithm in the embodiment is orthogonal. Figure 2 This corresponds to the case where the radius of the coated particles is 250 μm;

[0038] Figure 8 This is a top view of the particle packing structure (particle distribution) generated based on the hexagonal dense stacking algorithm in the embodiment. Figure 2 This corresponds to the case where the radius of the coated particles is 250 μm;

[0039] Figure 9 This is a schematic diagram illustrating the calculation process for determining the diameter of the coated particles and the thickness of the coating layer in the embodiment. Detailed Implementation

[0040] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0041] Traditional dispersed fuels typically use various sintering techniques to directly disperse UO2 powder within a metal matrix to form composite fuel pellets. However, this method can lead to contact, aggregation, and even agglomeration between UO2 particles, resulting in uneven distribution, localized hot spots, severely impairing fuel performance, reducing the structural integrity of fuel elements, and causing significant fuel loss.

[0042] The design and application of coatings are key measures to improve the safety and economy of fuel elements. By coating UO2 particles, uniform distribution of fuel particles can be achieved, preventing the evaporation of UO2 on the cermet surface at high temperatures and reducing fuel loss. However, the introduction of coatings occupies substrate space, thereby reducing fuel loading capacity.

[0043] Therefore, this embodiment designs different porous prismatic fuel elements, determining the appropriate coating thickness while ensuring a high fuel loading to improve the criticality of nuclear thermal propulsion reactors. Nuclear thermal propulsion tungsten-based fuels typically require a UO2 loading of around 60 vol%, and the coating thickness, coating particle diameter, and prismatic matrix geometry all significantly affect the UO2 loading. However, an effective method is currently lacking to determine the optimal coating thickness.

[0044] The specific objective of this embodiment is to determine a suitable coating thickness and coating particle size under given hexagonal prism matrix geometric parameters to meet the requirements of 60 vol% UO2 loading for nuclear thermal propulsion.

[0045] This embodiment uses tungsten (W)-based fuel for nuclear thermal propulsion as an example, wherein the UO2 particles are coated with tungsten material of the same composition as the matrix to form W-coated particles. Figure 1 A schematic diagram of the tungsten-coated particles and their fuel element structure embedded in a porous hexagonal tungsten matrix is ​​shown.

[0046] Figure 2 The curves showing the relationship between UO2 volume fraction and tungsten coating thickness and coated particle diameter are presented. The results indicate that, under fixed matrix geometry, UO2 loading (volume fraction) decreases with increasing coating thickness, requiring parameter co-optimization to meet criticality requirements.

[0047] This embodiment refers to the typical nuclear thermal propulsion fuel configuration proposed by Argonne National Laboratory in the United States, and selects a porous hexagonal prism fuel element with 61 coolant channels as the research object. The channel arrangement is as follows: Figure 3 As shown.

[0048] In this embodiment, the diameter of the coated fuel particles and the thickness of the coating layer are determined through the following process (see...). Figure 4 ):

[0049] S1. Construct a hexagonal prism matrix model of the fuel element and set the following geometric parameters (unit: μm):

[0050] Cooling channel diameter d_coolant = 1.7 × 10 3 μm (i.e., 1.7e3μm), from r_coolant=d_coolant / 2 (i.e., The radius of the coolant channel, r_coolant, is obtained.

[0051] The height of the hexagonal prism base is LB = 0.2 × 10⁻⁶. 4 μm (i.e. 0.2e4μm);

[0052] The cross-section of the hexagonal prism is a regular hexagon, and the length of opposite sides (i.e., the distance between opposite sides) is dB = 27.3 × 10⁻⁶. 3 μm (i.e., 27.3e3μm), by (That is, Lhexa = dB / sqrt(3)) to obtain the side length Lhexa.

[0053] S2. Define a coated particle model, which includes a UO2 core and a uniform coating layer covering its surface. The UO2 core has a preset radius (fixed value), while the thickness of the coating layer is adjustable; together, they determine the radius of the coated particle. Details are as follows:

[0054] Construct a model of the coated particles and set their radius and coating thickness.

[0055] The core radius of the coated particles is r_OPyC = 260 μm;

[0056] Coating thickness t_coat = 5 μm;

[0057] Therefore, the radius of the coated particle is obtained as r_circle = r_OPyC + t_coat.

[0058] S3. Based on the principle of hexagonal close-packing, a two-dimensional distribution of particle center coordinates is generated within the cross-section of the matrix (such as a plane perpendicular to its height direction), and these particles are stacked along the height direction to form a three-dimensional arrangement, ensuring that the distance between the centers of any adjacent particles is not less than the diameter of the coated particles. Specifically:

[0059] S3-1. Generate a two-dimensional particle arrangement (structure) with a hexagonal close-packed structure.

[0060] Within the cross-section of a hexagonal prism, a hexagonal close-packed two-dimensional mesh is constructed with the diameter of the coated particles as the spacing. The mesh covers the entire hexagonal region, and the initial arrangement contains enough particles to ensure complete filling. Subsequently, geometric trimming is used to retain particles located inside the matrix that do not interfere with coolant channels. For example, along the diagonal direction of the hexagonal cross-section (approximately 2Lhexa), the number of particles that can be accommodated in a single row can be initially estimated based on the diameter of the coated particles, 2r_circle: n_circle = fix(Lhexa*2 / (r_circle*2)) + 1; that is, ;in This indicates rounding down. However, the actual arrangement does not rely on this estimate. Instead, it uses a hexagonal close-packed two-dimensional mesh covering the entire hexagonal region, and retains particles located inside the matrix that do not interfere with the coolant channels through geometric trimming to ensure the integrity and robustness of the filling.

[0061] Based on the cross-sectional dimensions of the hexagonal prism and the diameter of the coating particles, the arrangement range of a single layer of particles is determined. The first layer of particles is arranged according to the hexagonal close-packing principle, defined as an odd-numbered layer, and its particle center coordinate set is denoted as the first coordinate set and stored in matrix A. The second layer of particles is embedded into the recessed positions formed by the first layer of particles according to the hexagonal close-packing rule, defined as an even-numbered layer, and its particle center coordinate set is denoted as the second coordinate set and stored in matrix B. During the arrangement process, it is ensured that the distance between any two particle centers in the same layer is not less than the diameter of the coating particle (i.e., ≥2r_circle) to ensure that there is no overlap between particles (e.g., no intersection, no tangency).

[0062] This step, based on the matrix model of step S1 and the coated particle model of step S2, is used to simulate the actual fuel element structure in which fuel particles are densely packed within the matrix.

[0063] S3-2. Stack multiple layers along the height direction to construct a three-dimensional particle distribution.

[0064] Based on the two-dimensional coordinates of the odd and even layers generated in step S3-1, the particles are stacked alternately along the height direction of the hexagonal prism matrix (where adjacent layers are offset so that the upper particles are above the gaps between the lower particles) to form a three-dimensional hexagonal close-packed structure. The three-dimensional positions of all particles are integrated into a coordinate set and saved to the E matrix.

[0065] The total number of stacked layers is determined based on the matrix height LB and the minimum safe spacing between layers. Considering the particle radius is r_circle, the center-to-center spacing between adjacent layers (i.e., the vertical distance between the centers of adjacent particles) is set to be no less than [value missing]. r_circle, then the total number of layers is initially estimated as follows:

[0066] n_circle_h=fix((LB-r_circle*2) / (r_circle*sqrt(3)))+2;

[0067] Right now, ;in This indicates rounding down to the nearest integer.

[0068] The z-coordinates of the centers of the particles in each layer generated initially cover the matrix height range (0 < z < LB). Subsequently, invalid particles that cause geometric interference due to proximity to the upper and lower bottom surfaces or coolant channels are removed in step S5.

[0069] This step expands the two-dimensional arrangement into a three-dimensional structure, accurately reflecting the spatial layout of particles in the fuel element, and providing input for the geometric interference judgment in the subsequent step S5.

[0070] S4. Arrange multiple circular coolant channels within the substrate (the channels penetrate the substrate along its height), each channel having the same preset radius, and the distance between the centers of any two channels being no less than the channel diameter (≥2r_coolant). This step defines the spatial distribution of the coolant channels.

[0071] Specifically, the coolant channels are uniformly distributed according to a pre-defined multi-level honeycomb symmetry rule. Starting from a central channel as the origin, concentric hexagonal rings expand outwards layer by layer, with each ring containing 6k channels (k=1,2,3,4), ultimately forming an arrangement of 61 channels (1 + 6 + 12 + 18 + 24 = 61). The center coordinates of all channels are generated according to this rule and saved to the H matrix. This arrangement ensures that the center-to-center distance between any two channels is not less than 2r_coolant, avoiding geometric overlap and providing clear geometric constraints for subsequent particle arrangement.

[0072] S5. Screen effective particles and remove particles located outside the matrix boundary (i.e., particles not completely contained within the matrix) and particles that spatially interfere with any coolant channel (e.g., geometrically overlap).

[0073] The condition for determining spatial interference is that the distance from the particle center to the channel center is less than the sum of the radius r_circle of the encapsulated particle and the radius r_coolant of the channel.

[0074] Specifically, for each particle, first determine whether it is completely located inside the hexagonal prism matrix (including the cross-sectional boundary and height range); if the following condition is met, store the particle coordinates (x, y) in matrix G; otherwise, discard the particle: (That is, E(1,i)^2+E(2,i)^2≤(Lhexa / sqrt(3))^2, where E(1,i) and E(2,i) represent the x and y coordinates of the i-th particle, respectively); To simplify the hexagonal boundary judgment, this embodiment adopts a conservative circular enclosing region with a radius of . This ensures that all retained particles are kept away from the matrix boundary to avoid geometric interference during arrangement.

[0075] Secondly, determine whether it overlaps with any coolant channel; if the following condition is met, store the particle coordinates in the I matrix, otherwise discard the particle: the distance between the particle center and the channel center is ≥ r_coolant + r_circle.

[0076] The particle is retained as a valid particle for subsequent modeling and volume fraction calculation only if both conditions are met.

[0077] This step ensures that the fuel particle arrangement conforms to actual physical constraints and avoids geometric interference, thereby truly reflecting the microstructure of the fuel element and ensuring the accuracy of the volume fraction calculation.

[0078] S6. Based on the effective particle count, UO2 core radius, matrix geometry, and coolant channel arrangement parameters, calculate the volume fraction of the UO2 phase in the fuel element; if the volume fraction is lower than the preset target value, reduce the coating thickness while keeping the core size unchanged, thereby reducing the diameter of the coated particles, and return to step S3 to rearrange the particles until the UO2 volume fraction reaches or exceeds the target value.

[0079] S6-1. Calculate the volume fraction of UO2.

[0080] The total volume of the matrix (vol_hexa_cermet) is:

[0081] vol_hexa_cermet = (6*(sqrt(3) / 4*Lhexa^2)-lieshu_H*π*r_coolant^2)*LB;

[0082] Right now, ;

[0083] The total volume of the UO2 phase (vol_UO2) is:

[0084] vol_UO2 = 4 / 3*π*r_OPyC³ *lieshu_I;

[0085] Right now, ;

[0086] The volume fraction of UO2 (vol_calculate) is then:

[0087] vol_calculate = vol_UO2 / vol_hexa_cermet;

[0088] Right now, ;

[0089] Where, lieshu_H represents the number of columns in the coolant channel position matrix H, i.e., the number of coolant channels (total); lieshu_I represents the number of columns in the effective particle position matrix I, i.e., the total number of particles that satisfy all geometric constraints (total number of effective particles).

[0090] S6-2. If the UO2 volume fraction does not reach the preset target value (e.g., 60 vol%), keep the UO2 core radius unchanged, reduce the coating layer thickness to reduce the diameter of the coated particles, and return to step S3 to regenerate the particle arrangement until the loading rate requirement is met.

[0091] Through the aforementioned steps of matrix modeling, particle definition, arrangement generation, channel layout, particle screening, volume fraction calculation, and parameter optimization, this embodiment provides a systematic design method for nuclear thermal propulsion fuel elements to optimize key parameters of the coated particles. This method can reasonably determine the coating thickness and coated particle diameter while ensuring a high UO2 volume fraction (not less than 60 vol%). Through iterative adjustments, it satisfies reactor criticality requirements while also considering the structural integrity and operational safety of the fuel element.

[0092] Figures 5 to 8 The orthogonal view and top view of the particle packing structure generated using the hexagonal close-packing algorithm are shown. Figure 5 and Figure 6 For the case where the radius of the coated particles is 500 μm, Figure 7 and Figure 8 This algorithm is designed for a coated particle radius of 250 μm. It can generate a corresponding three-dimensional arrangement structure based on the set coated particle geometry (coated particle diameter, coating layer thickness) and calculate its filling rate (i.e., volume fraction) using UO2 core parameters.

[0093] The following simulation test is conducted based on a set of initial parameters to verify the effectiveness of the proposed method.

[0094] (1) Parameters of the hexagonal prism base model:

[0095] Coolant channel radius r_coolant = 0.85 × 10 3 μm (i.e., 0.85e3μm), the side length of the hexagonal cross-section Lhexa = 15.76 × 10 3μm (i.e., 15.76e3μm), matrix height LB = 0.2 × 10 4 μm (i.e. 0.2e4μm).

[0096] (2) Parameters of the coated particle model:

[0097] The radius of the coated particle is r_circle = r_OPyC + t_coat = 265μm; where r_OPyC is the core radius of UO2 and t_coat is the coating thickness.

[0098] (3) Two-dimensional particle arrangement:

[0099] The initial estimate is that the number of particles that can be filled along the diagonal of the hexagon is n_circle=60; based on the hexagonal close-packing rule, in the initial grid covering the entire cross-section, the odd-numbered layers and even-numbered layers each contain 3780 particles, that is, lieshu_A (number of particles in the odd-numbered layers) = lishu_B (number of particles in the even-numbered layers) = 3780;

[0100] (4) Three-dimensional stacking:

[0101] Alternately stack odd and even layers along the height direction to generate a total number of layers n_circle_h=5; the initial total number of three-dimensional particles Lishu_E=18900.

[0102] (5) Coolant passage layout:

[0103] Multiple circular coolant channels are arranged within the substrate, with the center-to-center distance between any two channels not less than 1.7 × 10⁻⁶. 3 μm (i.e. 1.7e3μm) (i.e. ≥2r_coolant) to ensure no channel overlap.

[0104] (6) Screening of effective particles:

[0105] First, remove particles located outside the boundary of the hexagonal prism matrix. Store the coordinates of particles whose positions are inside the hexagonal prism in the E matrix into the G matrix. Keep 13290 particles located inside the matrix, that is, the number of particles that meet the conditions is lieshu_G=13290.

[0106] Further, particles that spatially interfere with any coolant channel are removed (i.e., the distance from the particle center to the channel center is < r_coolant + r_circle). The coordinates of particles whose positions in the G matrix are outside the coolant channel are stored in the I matrix, and finally 8460 effective fuel particles are obtained, that is, the number of particles that meet the conditions is lieshu_I = 8460.

[0107] (7) Calculation of UO2 volume fraction.

[0108] The effective total volume of the substrate (excluding coolant channels) is vol_hexa_cermet = 1.01×10 12 μm 3 (i.e., 1.01e12μm) 3 );

[0109] The total volume of the UO2 phase is vol_UO 2 = 6.19×10 11 μm 3 (i.e., 6.19e11μm) 3 );

[0110] The calculated volume fraction of UO2 is vol_calculate = 0.61 (i.e., 61%).

[0111] The corresponding UO2 core radius is 260 μm, the coating layer thickness is 5 μm, and the coating particle radius is 265 μm.

[0112] The above method can be executed automatically by a computer program, and its calculation process is as follows: Figure 9 As shown.

[0113] Using the above method, the diameter of the coated particles and the thickness of the coating layer in the hexagonal prism fuel element for nuclear thermal propulsion can be determined efficiently, achieving synergistic optimization of high loading rate and structural safety while ensuring that the UO2 volume fraction is not less than 60 vol%.

[0114] This embodiment uses a refractory metal (tungsten) as the matrix, UO2 as the core, and tungsten metal of the same type as the matrix as the coating layer. However, the method is also applicable to other refractory metals (such as zirconium, niobium, tantalum, titanium, molybdenum, vanadium, chromium) or their alloys as the matrix or coating material.

[0115] The hexagonal close-packing algorithm used in this embodiment is not only applicable to hexagonal prism geometry, but can also be extended to fuel elements with other cross-sectional shapes such as cylindrical, square prism, and octagonal prisms by adjusting boundary constraints and packing direction (or adjusting geometric parameters and packing rules). Furthermore, the particle coordinates can be stored using any suitable data organization method such as arrays, linked lists, or graph structures; the parameter optimization process can also be replaced by an automatic search strategy based on machine learning to further improve design efficiency.

[0116] Compared to the problem of hot spots easily formed by particle aggregation in traditional dispersed fuels, this method, through geometric modeling and parameter iteration, ensures that the UO2 loading meets the critical requirements while maintaining the integrity of the coating, providing a feasible fuel design path for high power density nuclear thermal propulsion systems.

[0117] Furthermore, this embodiment also provides a system for performing the above method, the system comprising:

[0118] The matrix modeling module is used to construct a fuel element matrix model with a preset height and cross-sectional geometry;

[0119] The particle definition module is used to define a coated particle model that includes a UO2 core and a coating layer, wherein the UO2 core has a fixed radius and the coating layer has an adjustable thickness.

[0120] The arrangement generation module is used to generate a two-dimensional distribution of particle center coordinates within the cross-section of the substrate based on the hexagonal close-packing principle, stack them along the height direction to form a three-dimensional arrangement, and ensure that the distance between the centers of any adjacent particles is not less than the diameter of the coated particles (i.e., no overlap occurs between any adjacent particles).

[0121] The channel arrangement module is used to arrange multiple circular coolant channels in the substrate. Each channel has the same preset radius, and the center-to-center distance between any two channels is not less than the channel diameter.

[0122] The particle screening module is used to remove particles located outside the matrix boundary (i.e., particles not completely contained within the matrix) and particles that spatially interfere with any coolant channel (e.g., geometrically overlap). The spatial interference determination condition is: the distance from the particle center to the channel center is less than the sum of the radius of the encapsulated particle and the radius of the channel.

[0123] The volume fraction calculation module is used to calculate the volume fraction of the UO2 phase based on the effective number of particles, core radius, matrix geometry and coolant channel arrangement parameters.

[0124] The parameter optimization module is used to reduce the coating layer thickness when the volume fraction is lower than the target UO2 volume fraction, and to trigger the arrangement generation module to rearrange the particles until the UO2 volume fraction reaches or exceeds the target UO2 volume fraction.

[0125] Furthermore, this embodiment also provides a computer-readable storage medium storing a program for optimizing the coating particle parameters of nuclear thermal propulsion fuel elements. When the program is loaded and executed by a processor (such as a CPU, GPU, or dedicated computing unit), the method described above can be implemented.

[0126] The computer-readable storage media include, but are not limited to, non-transitory storage media such as ROM, RAM, disk, optical disk, flash memory, solid-state drive (SSD), USB flash drive, and cloud storage devices. This program can be deployed on standalone workstations, server clusters, or cloud computing platforms for the automated design of nuclear thermal propulsion fuel element structures with high UO2 loading rates.

[0127] By solidifying the method of this embodiment into an executable program and storing it in the aforementioned medium, standardization, efficiency, and reusability of fuel element parameter design can be achieved, significantly improving the design efficiency of nuclear fuel engineering.

[0128] This invention is not limited to the above embodiments. Those skilled in the art will understand that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of this invention. The scope of this invention is defined by the claims and their equivalents.

Claims

1. A method for optimizing the coating particle parameters of nuclear thermal propulsion fuel elements, characterized in that, Includes the following steps: S1. Construct a fuel element substrate model with height and cross-sectional geometry; S2. Define a coated particle model, wherein the coated particle comprises a UO2 core and a coating layer covering its surface, wherein the radius of the UO2 core is a constant and the thickness of the coating layer is adjustable; S3. Based on the principle of hexagonal close-packing, a two-dimensional particle center coordinate distribution is generated in the cross-section of the matrix, and the particles are stacked along the height direction to form a three-dimensional arrangement, so that adjacent particles do not overlap. S4. Multiple coolant channels are arranged in the matrix, and no two channels overlap. S5. Screen effective particles, remove particles that are not completely contained in the matrix, and particles that geometrically overlap with any coolant channel; S6. Calculate the volume fraction of the UO2 phase based on the effective number of particles and geometric parameters; if the volume fraction is lower than the target UO2 volume fraction, reduce the coating layer thickness and return to step S3 to rearrange until the UO2 volume fraction reaches or exceeds the target value.

2. The method according to claim 1, characterized in that, The cross-sectional geometry is a regular polygon with the number of sides selected from any integer of 4, 6, or 8; or, the cross-sectional geometry is a circle.

3. The method according to claim 1, characterized in that, Multiple layers of particles are stacked along the height of the matrix, and the center-to-center distance between any two adjacent particles in the same layer is not less than twice the radius of the coated particles.

4. The method according to claim 1, characterized in that, Multiple layers of particles are stacked along the height of the matrix, with the vertical spacing between the centers of adjacent layers of particles not less than [value missing]. The radius of the coated particles is times that of the coated particles.

5. The method according to claim 1, characterized in that, The matrix has a regular hexagonal cross-section, and the particle centers are confined to a circle with the matrix center as the center and a radius of [missing information]. Within the circular region, where Lhexa is the side length of the regular hexagon, and the circular region is completely contained within the regular hexagon.

6. The method according to claim 1, characterized in that, The target UO2 volume fraction is not less than 60 vol%.

7. A system for optimizing the coating particle parameters of nuclear thermal propulsion fuel elements, characterized in that, include: The matrix modeling module is configured to build fuel element matrix models with height and cross-sectional geometry; The particle definition module is configured to define a coated particle model that includes a UO2 core and a coating layer, wherein the radius of the UO2 core is a fixed value and the thickness of the coating layer is adjustable; The arrangement generation module is configured to generate two-dimensional particle center distribution within the cross-section of the substrate based on the hexagonal close-packing principle, and stack them along the height direction to form a three-dimensional arrangement, ensuring that adjacent particles do not overlap. The channel arrangement module is configured to arrange multiple coolant channels in the substrate so that no two channels overlap. The particle screening module is configured to remove particles that are not completely contained within the matrix, as well as particles that geometrically overlap with any coolant channel; The volume fraction calculation module is configured to calculate the volume fraction of the UO2 phase based on the effective number of particles and geometric parameters. The parameter optimization module is configured to reduce the coating layer thickness and trigger the arrangement generation module to rearrange the particles when the volume fraction is lower than the target UO2 volume fraction, until the UO2 volume fraction reaches or exceeds the target value.

8. A computer-readable medium storing a program for optimizing the coating particle parameters of a nuclear thermal propulsion fuel element, wherein the program, when run, is used to perform the steps of the method according to any one of claims 1-6.

9. A nuclear thermal propulsion fuel element, comprising coated particles, said coated particles comprising a UO2 core and a coating layer covering its surface, characterized in that: The parameters of the coated particles are obtained using the method described in any one of claims 1-6.

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