A method and device for modeling neutronics of high packing rate dispersion particles

Abstract

The application provides a neutron equivalent modeling method and device for high filling rate dispersion particles, and the method comprises the following steps: calculating the maximum outer radius of the equivalent particles; under the premise of keeping the core diameter of the particles unchanged, calculating the maximum compression ratio of the cladding layer of the particles; according to the set compression ratio, calculating the filling rate of the equivalent fuel element after the size of the cladding layer of the particles is compressed, wherein the set compression ratio is less than or equal to the maximum compression ratio; adjusting the density of the cladding layer material and the density of the matrix material to ensure the conservation of nucleon number of the cladding layer and the matrix material before and after the equivalent; and using a traditional modeling method to perform geometric modeling and neutron calculation on the equivalent fuel element. The application can effectively avoid the filling rate limitation of the random sequence increasing method, meet the modeling demand of random distribution of high filling rate dispersion particles, and realize reactivity equivalence and ensure the neutron calculation accuracy.

Description

Technical Field

[0001] This invention specifically relates to a neutronics equivalent modeling method and apparatus for highly filled dispersed particles. Background Technology

[0002] High-temperature gas-cooled reactors (HTGRs) are internationally recognized as a generation four reactor type with inherently high safety. Their coated particle fuel possesses significant advantages, including high-temperature resistance and strong containment capacity for radioactive fission products, which is a major guarantee of the HTGR's high safety. Coated particles consist of a core and a cladding layer surrounding the core. These particles are dispersed within the matrix material, forming spherical or cylindrical fuel elements. The coated particles can be either fuel particles or poison particles. The core can be fuel, combustible poison, or other materials with strong self-shielding effects, while the cladding layer can be materials such as carbon or silicon carbide. The dual inhomogeneity of this type of fuel system presents certain challenges to neutronics calculations.

[0003] To simulate the dispersed distribution of particles in a matrix, various particle arrangement models have been developed, such as regular arrangement models, random grid perturbation models, random sequence addition models, and Metropolis models. Among these, the random sequence addition method is the most widely used and is one of the models that most closely approximates a true random distribution. This method can achieve a maximum fill ratio of 38%. When the fill ratio approaches the theoretical upper limit of 38%, the probability of rejection and the overall modeling time increase significantly to an unacceptable level. Therefore, theoretically, it is impossible to perform neutronics modeling on coated particle dispersed fuels with a fill ratio greater than 38% by directly using the above methods.

[0004] With the development of small modular high-temperature gas-cooled reactors, in order to reduce core size and increase core fuel loading, the particle filling rate in fuel elements has gradually increased, reaching as high as 40%-70%, which significantly exceeds the application range of random sequence addition methods. Therefore, it is necessary to invent a random distribution modeling method for dispersed particles to meet the neutronics calculation requirements of coated particle dispersed fuel systems with high filling rates. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the aforementioned shortcomings in the prior art by providing a neutronics equivalent modeling method for highly filled dispersed particles, expanding the application scope of the random sequence addition method, and solving the problem of modeling the random distribution of particles under high filling ratios. A corresponding apparatus for implementing this method is also provided.

[0006] The technical solution adopted to solve the technical problem of this invention is:

[0007] This invention provides a neutron equivalence modeling method for highly packed dispersed particles, comprising:

[0008] 1) Calculate the maximum outer radius of the equivalent particles based on the maximum allowable filling rate and the actual filling rate of the fuel element;

[0009] 2) Keeping the core diameter of the particle unchanged, calculate the maximum compression ratio of the coating layer of the particle based on the equivalent maximum outer radius of the particle;

[0010] 3) Based on the set compression ratio, after compressing the particle coating size, calculate the equivalent filling rate of the fuel element, wherein the set compression ratio is less than or equal to the maximum compression ratio.

[0011] 4) Adjust the density of the coating material according to the set compression ratio, and adjust the density of the matrix material according to the actual filling rate of the fuel element and the equivalent filling rate of the fuel element, so as to ensure the conservation of nucleon number of the coating and matrix materials before and after equivalence.

[0012] 5) Use traditional modeling methods to perform geometric modeling and neutronics calculations on the equivalent fuel element.

[0013] Optionally, the equivalent maximum outer radius R of the particle outer,max The result obtained using formula (1) is:

[0014]

[0015] Among them, R outer,0 PF represents the outer radius of the actual particle. max PF0 is the maximum allowable fill rate of the fuel element, and PF0 is the actual fill rate of the fuel element.

[0016] Optionally, the maximum compression ratio F of the coating layer of the particles max The result obtained using formula (2) is:

[0017]

[0018] Among them, R kernel Let be the radius of the particle's core.

[0019] Optionally, the equivalent fill ratio PF of the fuel element is calculated using equation (3):

[0020]

[0021] Among them, R outer The equivalent outer radius of the particle is calculated using equation (4):

[0022]

[0023] Where F is the set compression ratio.

[0024] Optionally, the density of the coating material can be adjusted using equation (5):

[0025] ρ coat =ρ coat,0 / F (5)

[0026] Adjust the density of the matrix material using formula (6):

[0027]

[0028] Where, ρ coat,0 ρ is the actual density of the coating material. coat The equivalent density of the coating material;

[0029] ρ matrix,0 ρ is the actual density of the matrix material. matrix The equivalent density of the matrix material.

[0030] The present invention also provides a neutronics equivalent modeling device for high-fill-rate dispersed particles, comprising:

[0031] The first calculation module is used to calculate the equivalent maximum outer radius of the particles based on the maximum allowable filling rate and the actual filling rate of the fuel element.

[0032] The second calculation module is used to calculate the maximum compression ratio of the particle's coating layer based on the equivalent maximum outer radius of the particle obtained by the first calculation module, while keeping the core diameter of the particle unchanged.

[0033] An interactive module is used to display the maximum compression ratio of the particle coating layer calculated by the second calculation module, and to receive a set compression ratio input by the user, wherein the set compression ratio is less than or equal to the maximum compression ratio.

[0034] The third calculation module is used to calculate the equivalent filling rate of the fuel element after compressing the particle coating size according to the compression ratio set by the user input.

[0035] The adjustment module is used to adjust the density of the coating material according to the set compression ratio, and to adjust the density of the matrix material according to the actual filling rate of the fuel element and the equivalent filling rate of the fuel element, so as to ensure the conservation of the nucleon number of the coating and matrix materials before and after equivalence.

[0036] The modeling module is used to perform geometric modeling and neutronics calculations on the equivalent fuel element using traditional modeling methods.

[0037] Optionally, the first calculation module is used to calculate the equivalent maximum outer radius R of the particle according to equation (1). outer,max :

[0038]

[0039] Among them, R outer,0 PF represents the outer radius of the actual particle. max PF0 is the maximum allowable fill rate of the fuel element, and PF0 is the actual fill rate of the fuel element.

[0040] Optionally, the second calculation module is used to calculate the maximum compression ratio F of the coating layer of the particle according to equation (2). max :

[0041]

[0042] Among them, R kernel Let be the radius of the particle's core.

[0043] Optionally, the third calculation module is used to calculate the equivalent outer radius R of the particle according to equation (4). outer :

[0044]

[0045] Where F is the set compression ratio;

[0046] Furthermore, the third calculation module is also used to calculate the equivalent fill rate PF of the fuel element according to equation (3):

[0047]

[0048] Optionally, the adjustment module uses formula (5) to adjust the density of the coating material:

[0049] ρ coat =ρ coat,0 / F (5)

[0050] The adjustment module uses formula (6) to adjust the density of the matrix material:

[0051]

[0052] Where, ρ coat,0 ρ is the actual density of the coating material. coat The equivalent density of the coating material;

[0053] ρ matrix,0 ρ is the actual density of the matrix material. mayrix The equivalent density of the matrix material.

[0054] This invention addresses the bottleneck of neutronics calculation software being unable to model coated particle dispersed fuel with a fill rate greater than 38%. By constructing an equivalent particle model, it can directly utilize existing particle distribution modeling techniques, breaking through the 38% limit on the fill rate of the random sequence addition method, and meeting the requirements for random distribution modeling of dispersed particles under high fill rates.

[0055] This invention reduces the volumetric filling rate by compressing the coating layer to decrease the size of the coated particles while maintaining the core size of the particles with strong resonant self-shielding effects. Simultaneously, it alters the density of both the coating layer and the matrix material, ensuring the conservation of nucleon numbers for all materials before and after equivalence, thus maintaining unchanged neutronics properties. Compared to compressing the particle size as a whole, the method proposed in this invention offers higher neutronics calculation accuracy.

[0056] Therefore, the equivalent neutronics modeling method of the present invention can effectively avoid the fill rate limitation of the random sequence addition method, meet the modeling requirements of random distribution of high fill rate dispersed particles, and achieve reactive equivalence, thus ensuring the accuracy of neutronics calculation. Attached Figure Description

[0057] Figure 1 The flowchart shows the neutron equivalence modeling method for high-fill-rate dispersed particles of the present invention.

[0058] Figure 2 This is a schematic diagram of the particle structure;

[0059] Figure 3 This is a schematic diagram of the fuel element. Detailed Implementation

[0060] The technical solutions of the invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without creative effort are within the scope of the invention.

[0061] In the description of this invention, it should be noted that the use of terms such as "above" to indicate orientation or positional relationship is based on the orientation or positional relationship shown in the accompanying drawings and is only for the purpose of facilitating and simplifying the description. It does not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0062] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0063] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connection," "setting," "installation," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0064] This invention provides a neutron equivalence modeling method for highly packed dispersed particles, comprising:

[0065] 1) Calculate the maximum outer radius of the equivalent particles based on the maximum allowable filling rate and the actual filling rate of the fuel element;

[0066] 2) Keeping the core diameter of the particle unchanged, calculate the maximum compression ratio of the coating layer of the particle based on the equivalent maximum outer radius of the particle;

[0067] 3) Based on the set compression ratio, after compressing the particle coating size, calculate the equivalent filling rate of the fuel element, wherein the set compression ratio is less than or equal to the maximum compression ratio.

[0068] 4) Adjust the density of the coating material according to the set compression ratio, and adjust the density of the matrix material according to the actual filling rate of the fuel element and the equivalent filling rate of the fuel element, so as to ensure the conservation of nucleon number of the coating and matrix materials before and after equivalence.

[0069] 5) Use traditional modeling methods to perform geometric modeling and neutronics calculations on the equivalent fuel element.

[0070] The present invention also provides a neutronics equivalent modeling device for high-fill-rate dispersed particles, comprising:

[0071] The first calculation module is used to calculate the equivalent maximum outer radius of the particles based on the maximum allowable filling rate and the actual filling rate of the fuel element.

[0072] The second calculation module is used to calculate the maximum compression ratio of the particle's coating layer based on the equivalent maximum outer radius of the particle obtained by the first calculation module, while keeping the core diameter of the particle unchanged.

[0073] An interactive module is used to display the maximum compression ratio of the particle coating layer calculated by the second calculation module, and to receive a set compression ratio input by the user, wherein the set compression ratio is less than or equal to the maximum compression ratio.

[0074] The third calculation module is used to calculate the equivalent filling rate of the fuel element after compressing the particle coating size according to the compression ratio set by the user input.

[0075] The adjustment module is used to adjust the density of the coating material according to the set compression ratio, and to adjust the density of the matrix material according to the actual filling rate of the fuel element and the equivalent filling rate of the fuel element, so as to ensure the conservation of the nucleon number of the coating and matrix materials before and after equivalence.

[0076] The modeling module is used to perform geometric modeling and neutronics calculations on the equivalent fuel element using traditional modeling methods.

[0077] High fill rate refers to a particulate fill rate of more than 38% in the fuel element.

[0078] Example 1:

[0079] like Figure 1 As shown, this embodiment provides a neutronics equivalent modeling method for highly packed dispersed particles, including:

[0080] 1) Calculate the maximum outer radius of the equivalent particles based on the maximum allowable filling rate and the actual filling rate of the fuel element;

[0081] 2) Keeping the core diameter of the particle unchanged, calculate the maximum compression ratio of the coating layer of the particle based on the equivalent maximum outer radius of the particle;

[0082] 3) Based on the set compression ratio, after compressing the particle coating size, calculate the equivalent filling rate of the fuel element, wherein the set compression ratio is less than or equal to the maximum compression ratio.

[0083] 4) Adjust the density of the coating material according to the set compression ratio, and adjust the density of the matrix material according to the actual filling rate of the fuel element and the equivalent filling rate of the fuel element, so as to ensure the conservation of nucleon number of the coating and matrix materials before and after equivalence.

[0084] 5) Use traditional modeling methods to perform geometric modeling and neutronics calculations on the equivalent fuel element.

[0085] This invention addresses the bottleneck of neutronics calculation software being unable to model coated particle dispersed fuel with a fill rate greater than 38%. By constructing an equivalent particle model, it can directly utilize existing particle distribution modeling techniques, breaking through the 38% limit on the fill rate of the random sequence addition method, and meeting the requirements for random distribution modeling of dispersed particles under high fill rates.

[0086] This invention reduces the volumetric filling rate by compressing the coating layer to decrease the size of the coated particles while maintaining the core size of the particles with strong resonant self-shielding effects. Simultaneously, it alters the density of both the coating layer and the matrix material, ensuring the conservation of nucleon numbers for all materials before and after equivalence, thus maintaining unchanged neutronics properties. Compared to compressing the particle size as a whole, the method proposed in this invention offers higher neutronics calculation accuracy.

[0087] Therefore, the equivalent neutronics modeling method of the present invention can effectively avoid the fill rate limitation of the random sequence addition method, meet the modeling requirements of random distribution of high fill rate dispersed particles, and achieve reactive equivalence, thus ensuring the accuracy of neutronics calculation.

[0088] In this embodiment, the equivalent maximum outer radius R of the particle outer,max The result obtained using formula (1) is:

[0089]

[0090] Among them, R outer,0 PF represents the outer radius of the actual particle. max PF0 is the maximum allowable fill rate of the fuel element, and PF0 is the actual fill rate of the fuel element.

[0091] In this embodiment, the maximum compression ratio F of the particle's coating layer is... max The result obtained using formula (2) is:

[0092]

[0093] Among them, R kernel Let be the radius of the particle's core.

[0094] In this embodiment, the equivalent fill rate PF of the fuel element is calculated using equation (3):

[0095]

[0096] Among them, R outer The equivalent outer radius of the particle is calculated using equation (4):

[0097]

[0098] Where F is the set compression ratio.

[0099] In this embodiment, equation (5) is used to adjust the density of the coating material:

[0100] ρ coat =ρ coat,0 / F (5)

[0101] Adjust the density of the matrix material using formula (6):

[0102]

[0103] Where, ρ coat,0 ρ is the actual density of the coating material. coat The equivalent density of the coating material;

[0104] ρ matrix,0 ρ is the actual density of the matrix material. matrix The equivalent density of the matrix material.

[0105] Example 2

[0106] This embodiment uses a typical TIRSO fuel prism assembly as an example to describe how the present invention can be applied to the neutron physics analysis of a high-fill-rate dispersed fuel system.

[0107] The structure of TIRSO particles 3 in this embodiment is as follows: Figure 2 As shown, it includes a core 1 and a covering layer 2. Its dimensions are shown in Table 1. Figure 3 As shown, TIRSO particles 3 are dispersed in the matrix 4, forming fuel pellets. The particle filling rate in the fuel pellets is 40%, exceeding the theoretical upper limit of 38% for the random sequence addition method. Therefore, this method cannot be directly used for modeling and calculating the random distribution of particles.

[0108] The particle model was equivalently processed using the method of this invention to reduce the filling rate. Based on the particle size and actual filling rate, the maximum compression ratio corresponding to the maximum filling rate of 38% was calculated to be 94% using formulas (1) and (2). Then, compression ratios of 90%, 85%, and 80% were selected, and the outer radius of each coating layer after compression was calculated using formula (4). The corresponding equivalent filling rate was calculated using formula (3), and the results are shown in Table 1. Then, the equivalent density of the coating layer and the matrix material after compression was calculated using formulas (5) and (6). Neutronics calculations were performed using the above equivalent particle model with regular arrangement and random distribution, respectively.

[0109] Table 1 Particle size before and after compression

[0110]

[0111]

[0112] To further demonstrate the neutron equivalence of the method of the present invention, neutron calculation results of particles compressed as a whole at the same compression ratio are used for comparison. This method simultaneously alters the size and density of the core and coating layers, as well as the density of the matrix material.

[0113] k of various models infThe calculation results are shown in Table 2. The random standard deviation of a single Monte Carlo calculation is approximately 0.00009. Since the regular arrangement model can simulate a particle distribution with a 40% fill rate, the influence of the compressed equivalent particle model on reactivity is first examined using the regular arrangement model. The calculation results show that the reactivity calculation results of the equivalent particle model under different compression ratios are basically consistent with the calculation results of the original particle model. Then, the compressed equivalent particle model is applied to perform random distribution modeling calculations, and the results are compared with those of the particle model with a core-coated layer compressed proportionally. The calculation results of the equivalent particle model under different compression ratios obtained using the method provided by this invention are basically consistent, and the neutron reactivity before and after compression is equivalent; however, the method of proportional compression of the core-coated layer will introduce significant reactivity errors, and the smaller the compression ratio, the greater the reactivity deviation. The comparison results show that using the method of this invention to construct the equivalent particle model can overcome the fill rate limitation of the random sequence addition method while ensuring the accuracy of neutron calculations.

[0114] Table 2 Calculation results for fuel pellets with a 40% fill rate

[0115]

[0116]

[0117] Example 3

[0118] This embodiment uses a typical spherical fuel element as an example, with TIRSO particles dispersed in the central spherical fuel region. The particle size is the same as in Example 2, and the fill rate is set to 50%, which exceeds the theoretical upper limit of 38% for the random sequence addition method. Therefore, this method cannot be directly used to model and calculate the random distribution of particles.

[0119] The particle model was equivalently processed using the method of this invention to reduce the filling rate. Based on the particle size and actual filling rate, the maximum compression ratio corresponding to the maximum filling rate of 38% was calculated to be 71.4% using formulas (1) and (2). Then, compression ratios of 65%, 60%, and 50% were selected, and the outer radius of each coating layer after compression was calculated using formula (4). The corresponding equivalent filling rate was calculated using formula (3). Then, the equivalent density of the coating layer and matrix material after compression was calculated using formulas (5) and (6). Neutronics calculations were performed using the above equivalent particle model with regular arrangement and random distribution, respectively, and compared with the overall proportional compression model of the core coating layer.

[0120] k of various models infThe calculation results are shown in Table 3. The random standard deviation of a single Monte Carlo calculation is approximately 0.00009. Since the regular arrangement model can simulate a particle distribution with a 50% fill rate, the influence of the compressed equivalent particle model on reactivity is first examined using the regular arrangement model. The calculation results show that the reactivity calculation results of the equivalent particle model under different compression ratios are basically consistent with the calculation results of the original particle model. Then, the compressed equivalent particle model is applied to perform random distribution modeling calculations, and the results are compared with those of the particle model with a core-coated layer compressed proportionally. The calculation results of the equivalent particle model under different compression ratios obtained using the method provided by this invention are basically consistent, and the neutron reactivity is equivalent before and after compression; however, the method of proportional compression of the core-coated layer will introduce significant reactivity errors, and the smaller the compression ratio, the greater the reactivity deviation. The comparison results show that using the method of this invention to construct the equivalent particle model can overcome the fill rate limitation of the random sequence addition method while ensuring the accuracy of neutron calculations.

[0121] Table 3 Calculation results for fuel balls with 50% fill rate

[0122]

[0123] Example 4:

[0124] The present invention also provides an apparatus for implementing the neutron equivalence modeling method for high-fill-rate dispersed particles of Example 1, comprising:

[0125] The first calculation module is used to calculate the equivalent maximum outer radius of the particles based on the maximum allowable filling rate and the actual filling rate of the fuel element.

[0126] The second calculation module is used to calculate the maximum compression ratio of the particle's coating layer based on the equivalent maximum outer radius of the particle obtained by the first calculation module, while keeping the core diameter of the particle unchanged.

[0127] An interactive module is used to display the maximum compression ratio of the particle coating layer calculated by the second calculation module, and to receive a set compression ratio input by the user, wherein the set compression ratio is less than or equal to the maximum compression ratio.

[0128] The third calculation module is used to calculate the equivalent filling rate of the fuel element after compressing the particle coating size according to the compression ratio set by the user input.

[0129] The adjustment module is used to adjust the density of the coating material according to the set compression ratio, and to adjust the density of the matrix material according to the actual filling rate of the fuel element and the equivalent filling rate of the fuel element, so as to ensure the conservation of the nucleon number of the coating and matrix materials before and after equivalence.

[0130] The modeling module is used to perform geometric modeling and neutronics calculations on the equivalent fuel element using traditional modeling methods.

[0131] In this embodiment, the first calculation module is used to calculate the equivalent maximum outer radius R of the particle according to equation (1). outer,max :

[0132]

[0133] Among them, R outer,0 PF represents the outer radius of the actual particle. max PF0 is the maximum allowable fill rate of the fuel element, and PF0 is the actual fill rate of the fuel element.

[0134] In this embodiment, the second calculation module is used to calculate the maximum compression ratio F of the coating layer of the particle according to equation (2). max :

[0135]

[0136] Among them, R kernel Let be the radius of the particle's core.

[0137] In this embodiment, the third calculation module is used to calculate the equivalent outer radius R of the particle according to equation (4). outer :

[0138]

[0139] Where F is the set compression ratio;

[0140] Furthermore, the third calculation module is also used to calculate the equivalent fill rate PF of the fuel element according to equation (3):

[0141]

[0142] In this embodiment, the adjustment module uses formula (5) to adjust the density of the coating material:

[0143] ρ coat =ρ coat,0 / F (5)

[0144] The adjustment module uses formula (6) to adjust the density of the matrix material:

[0145]

[0146] Where, ρ coat,0 ρ is the actual density of the coating material. coat The equivalent density of the coating material;

[0147] ρ matrix,0 ρ is the actual density of the matrix material.mayrix The equivalent density of the matrix material.

[0148] 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 neutronics equivalent modeling method for highly packed dispersed particles, characterized in that, include: 1) Calculate the maximum outer radius of the equivalent particles based on the maximum allowable filling rate and the actual filling rate of the fuel element; 2) Keeping the core diameter of the particle unchanged, calculate the maximum compression ratio of the coating layer of the particle based on the equivalent maximum outer radius of the particle; 3) Based on the set compression ratio, after compressing the particle coating size, calculate the equivalent filling rate of the fuel element, wherein the set compression ratio is less than or equal to the maximum compression ratio. 4) Adjust the density of the coating material according to the set compression ratio, and adjust the density of the matrix material according to the actual filling rate of the fuel element and the equivalent filling rate of the fuel element, so as to ensure the conservation of nucleon number of the coating and matrix materials before and after equivalence. 5) Use traditional modeling methods to perform geometric modeling and neutronics calculations on the equivalent fuel element; High filling rate refers to a particle filling rate of more than 38% in the fuel element.

2. The neutronics equivalent modeling method for high-fill-rate dispersed particles according to claim 1, characterized in that, The maximum outer radius R of the particle after equivalent outer,max The result obtained using formula (1) is: Among them, R outer,0 PF represents the outer radius of the actual particle. max PF0 is the maximum allowable fill rate of the fuel element, and PF0 is the actual fill rate of the fuel element.

3. The neutronics equivalent modeling method for high-fill-rate dispersed particles according to claim 2, characterized in that, The maximum compression ratio F of the coating layer of the particle max The result obtained using formula (2) is: Among them, R kernel Let be the radius of the particle's core.

4. The neutronics equivalent modeling method for high-fill-rate dispersed particles according to claim 3, characterized in that, The equivalent fill rate PF of the fuel element is calculated using equation (3): Among them, R outer The equivalent outer radius of the particle is calculated using equation (4): Where F is the set compression ratio.

5. The neutronics equivalent modeling method for high-fill-rate dispersed particles according to claim 4, characterized in that, Adjust the density of the coating material using formula (5): r coat =ρ coat,0 / F (5) Adjust the density of the matrix material using formula (6): Where, ρ coat,0 ρ is the actual density of the coating material. coat The equivalent density of the coating material; ρ matrix,0 ρ is the actual density of the matrix material. matrix The equivalent density of the matrix material.

6. A neutronics equivalent modeling device for highly packed dispersed particles, characterized in that, include: The first calculation module is used to calculate the equivalent maximum outer radius of the particles based on the maximum allowable filling rate and the actual filling rate of the fuel element. The second calculation module is used to calculate the maximum compression ratio of the particle's coating layer based on the equivalent maximum outer radius of the particle obtained by the first calculation module, while keeping the core diameter of the particle unchanged. An interactive module is used to display the maximum compression ratio of the particle coating layer calculated by the second calculation module, and to receive a set compression ratio input by the user, wherein the set compression ratio is less than or equal to the maximum compression ratio. The third calculation module is used to calculate the equivalent filling rate of the fuel element after compressing the particle coating size according to the compression ratio set by the user input. The adjustment module is used to adjust the density of the coating material according to the set compression ratio, and to adjust the density of the matrix material according to the actual filling rate of the fuel element and the equivalent filling rate of the fuel element, so as to ensure the conservation of the nucleon number of the coating and matrix materials before and after equivalence. The modeling module is used to perform geometric modeling and neutronics calculations on the equivalent fuel element using traditional modeling methods. High filling rate refers to a particle filling rate of more than 38% in the fuel element.

7. The neutronics equivalent modeling device for high-fill-rate dispersed particles according to claim 6, characterized in that, The first calculation module is used to calculate the equivalent maximum outer radius R of the particle according to equation (1). outer,max : Among them, R outer,0 PF represents the outer radius of the actual particle. max PF0 is the maximum allowable fill rate of the fuel element, and PF0 is the actual fill rate of the fuel element.

8. The neutronics equivalent modeling device for high-fill-rate dispersed particles according to claim 7, characterized in that, The second calculation module is used to calculate the maximum compression ratio F of the coating layer of the particle according to equation (2). max : Among them, R kernel Let be the radius of the particle's core.

9. The neutronics equivalent modeling device for high-fill-rate dispersed particles according to claim 8, characterized in that, The third calculation module is used to calculate the equivalent outer radius R of the particles according to equation (4). outer : Where F is the set compression ratio; Furthermore, the third calculation module is also used to calculate the equivalent fill rate PF of the fuel element according to equation (3):

10. The neutronics equivalent modeling device for high-fill-rate dispersed particles according to claim 9, characterized in that, The adjustment module uses formula (5) to adjust the density of the coating material: r coat =ρ coat,0 / F (5) The adjustment module uses formula (6) to adjust the density of the matrix material: Where, ρ coat,0 ρ is the actual density of the coating material. coat The equivalent density of the coating material; ρ matrix,0 ρ is the actual density of the matrix material. matrix The equivalent density of the matrix material.

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