Calculation method and device for maximum temperature of dispersion type fuel element and verification method

Abstract

The invention discloses a calculation method and device for the maximum temperature of a dispersion type fuel element and a verification method, and the method comprises the steps: S1, carrying out the region division of the fuel element, and forming a first region and a second region; s2, according to the probability distribution of the coated fuel particles in the first area and the second area, correcting the initial volume ratio eta of the coated fuel particles in the first area and the second area, and respectively determining the corrected volume ratio eta z of the coated fuel particles in the first area and the second area after modification; and S3, calculating the temperature tmaxr = 0 at the center of the second region according to the corrected volume ratio eta z of the coated fuel particles of the first region and the second region and the radiuses of the outer boundaries of the first region and the second region, so as to obtain the highest temperature tmax of the fuel element. According to the method and the device, the more accurate highest temperature tmax of the fuel element can be determined under the condition corresponding to the probability distribution, so that the corresponding engineering requirements are met.

Description

Technical Field

[0001] The invention belongs to the field of nuclear technology, and in particular relates to a calculation method, a device and a verification method for the maximum temperature of a dispersed fuel element. Background Art

[0002] Dispersed fuel elements used in high temperature gas-cooled reactors. Dispersed fuel elements are a type of dispersed fuel, consisting of coated fuel particles and a graphite matrix. The matrix graphite is used to moderate neutrons and conduct fission heat, and to withstand external pressure, impact, corrosion and wear. Coated fuel particles are used for nuclear reactions.

[0003] The calculation process of the maximum temperature of the dispersed fuel element can be to determine the maximum temperature of the dispersed fuel element according to the outer boundary temperature of the dispersed fuel element and the change from the outer boundary of the fuel element to the center temperature of the fuel element. The determined maximum temperature of the dispersed fuel element can be used in subsequent corresponding engineering requirements.

[0004] In the prior art, when calculating the maximum temperature of a dispersed fuel element, it is assumed that the temperature change from the outer boundary of the fuel element to the center of the fuel element is uniform. However, in actual dispersed fuel elements, there are local high temperatures, and the temperature change from the outer boundary of the fuel element to the center of the fuel element is not uniform. Therefore, there is a large deviation between the maximum temperature of the dispersed fuel element determined in the prior art and the actual maximum temperature of the dispersed fuel element, which is difficult to meet the corresponding engineering requirements. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method, device and system for calculating the maximum temperature of a dispersed fuel element in view of the above-mentioned deficiencies in the prior art. By using this method, the local high temperature of the dispersed fuel element caused by the random distribution of coated fuel particles can be reflected, thereby determining a more accurate maximum temperature of the dispersed fuel element to meet corresponding engineering requirements.

[0006] In a first aspect, the present invention provides a method for calculating the maximum temperature of a dispersed fuel element, comprising:

[0007] S1. Divide the fuel element into regions to form a first region and a second region; the first region and the second region are distributed sequentially from the outer boundary of the fuel element to the center of the fuel element;

[0008] S2. According to the probability distribution of the coated fuel particles in the first region and the second region, the initial volume proportion η of the coated fuel particles in the first region and the second region is corrected, and the modified volume proportion η of the coated fuel particles in the first region and the second region is determined respectively. z ;

[0009] S3. According to the modified volume ratio η of the coated fuel particles in the first region and the second region z , and the radii of the outer boundaries of the first and second regions, calculate the temperature t at the center of the second region max | r＝0 , to obtain the maximum temperature t of the fuel element max .

[0010] In some embodiments, step S1 specifically includes:

[0011] The coated fuel particles are densely packed inside the fuel element, and then the fuel element is divided, and the area corresponding to the blank area of ​​the coated fuel particles connected to the outer boundary of the fuel element is set as the first area, and the area corresponding to the center of the fuel element and the dense area of ​​the coated fuel particles is set as the second area;

[0012] The first area and the second area are concentric, the second area is spherical, and the first area is surrounded by the outside of the second area and is in the shape of a circular sphere.

[0013] In some embodiments, step S2 specifically includes:

[0014] S21. Obtain the target standard score corresponding to the target significance level α in the standard normal distribution table

[0015] S22. According to the target standard score and the initial volume proportion ξ of the coated fuel particles, respectively determine the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 .

[0016] In some embodiments, step S22 specifically includes:

[0017] According to the following formula (1), the modified volume fraction η of the coated fuel particles in the first region is determined: z1 ,

[0018]

[0019] Among them, η is the initial volume proportion of the coated fuel particles, ξ is the volume proportion of the spheres when they are stacked together in a limited space in the most densely packed manner, is the target standard score, N is the number of coated fuel particles contained in the fuel element;

[0020] According to the following formula (2), the modified volume proportion η of the coated fuel particles in the second region is determined: z2 ,

[0021]

[0022] Among them, ξ is the initial volume proportion of the coated fuel particles, ξ is the volume proportion of the spheres when they are stacked together in a limited space in the most densely packed manner, is the target standard score, and N is the number of coated fuel particles contained in the fuel element.

[0023] In some embodiments, step S3 specifically includes:

[0024] S31. Obtaining the temperature t1 of the outer boundary of the first region;

[0025] S32. According to the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 , respectively determining a regional temperature increment of the first region and a regional temperature increment of the second region;

[0026] S33. Calculate the temperature t at the center of the second region based on the temperature t1 of the outer boundary of the first region and the regional temperature increment of the first region and the regional temperature increment of the second region. max | r＝0 .

[0027] In some embodiments, step S32 specifically includes:

[0028] S321. Make the coated fuel particles densely packed inside the first region, and divide the first region into two regions: the outer region is the region in the first region connected to the outer boundary of the fuel element and corresponding to the blank region of the coated fuel particles, which is set as the first matrix region D1; the inner region is the region in the first region corresponding to the dense region of the coated fuel particles, which is set as the first particle region D2, and

[0029] The coated fuel particles are densely packed inside the second region, and the second region is divided, the region corresponding to the blank region of the coated fuel particles in the second region is set as the second matrix region D3, and the region corresponding to the dense region of the coated fuel particles in the second region is set as the second particle region D4;

[0030] S322. According to the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 , respectively determine the radius of the first matrix region D1, the radius of the first particle region D2, the radius of the second matrix region D3 and the radius of the second particle region D4;

[0031] S323. According to the radius of the first matrix region D1, the radius of the first particle region D2, the radius of the second matrix region D3 and the radius of the second particle region D4, respectively determine the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3 and the temperature increment t5 of the second particle region D4;

[0032] Step S33 specifically includes:

[0033] The temperature t1 at the outer boundary of the first region, the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3 and the temperature increment t5 of the second particle region D4 are summed to obtain the temperature t at the center of the second region. max | r＝0 .

[0034] In some embodiments, step S323 specifically includes:

[0035] The temperature increment t2 of the first matrix region D1 from the outer boundary of the first matrix region D1 to the outer boundary of the first particle region D2 is determined according to the following formula (3):

[0036]

[0037] Wherein, Q is the total power of the dispersed fuel element, λ1 is the thermal conductivity of the first matrix region D1, r1 is the radius of the outer boundary of the first matrix region D1, and r2 is the radius of the outer boundary of the first particle region D2;

[0038] The temperature increment t3 of the first particle region D2 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (4):

[0039]

[0040] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ2 is the thermal conductivity of the first particle region D2, r2 is the radius of the outer boundary of the first particle region D2, and r3 is the radius of the outer boundary of the second matrix region D3;

[0041] The temperature increment t4 of the second matrix region D3 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (5):

[0042]

[0043] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ3 is the thermal conductivity of the second matrix region D3, r3 is the radius of the outer boundary of the second matrix region D3, and r4 is the radius of the outer boundary of the second particle region D4;

[0044] The temperature increment t5 of the second particle region D4 from the outer boundary of the second particle region D4 to the center of the second particle region D4 is determined according to the following formula (6):

[0045]

[0046] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ4 is the thermal conductivity of the second particle region D4, and r4 is the radius of the outer boundary of the second particle region D4.

[0047] In some embodiments, step S321 specifically includes:

[0048] Performing iterative division of the second matrix region D3 and the second particle region D4 by dense packing of coated fuel particles, so as to divide the fuel element into 2n regions;

[0049] The temperature t1 at the outer boundary of the first region and the temperature increments of the 2n regions are summed to obtain the temperature t at the center of the second region. max | r＝0 .

[0050] In some embodiments, the method further comprises:

[0051] According to the standard score in the correction factor, the probability P that the possible temperature is not higher than the calculated maximum temperature is determined according to the following formula (7):

[0052]

[0053] Among them, α is the target significance level, is the target standard score, is the cumulative probability density function, n is 1 / 2 of the 2n regions divided by the fuel element, and n is an integer greater than or equal to 2.

[0054] In a second aspect, the present invention further provides an engineering verification method for a dispersed fuel element, comprising:

[0055] According to the calculation method described in any one of the above items, the maximum temperature t of the fuel element is obtained. max ;

[0056] According to the maximum temperature t max Conduct engineering verification on dispersed fuel elements to determine whether the dispersed fuel elements are qualified.

[0057] In a third aspect, the present invention further provides a device for calculating the maximum temperature of a dispersed fuel element, the device comprising:

[0058] A division module, configured to divide the fuel element into regions to form a first region and a second region; the first region and the second region are distributed sequentially from the outer boundary of the fuel element to the center of the fuel element;

[0059] A correction module is connected to the division module, and is configured to correct the initial volume proportion η of the coated fuel particles in the first region and the second region according to the probability distribution of the coated fuel particles in the first region and the second region, and respectively determine the modified volume proportion η of the coated fuel particles in the first region and the second region. z ;

[0060] The obtaining module is connected to the correction module, which is configured to obtain the corrected volume proportion η of the coated fuel particles in the first region and the second region according to the corrected volume proportion η z , and the radii of the outer boundaries of the first and second regions, calculate the temperature t at the center of the second region max | r＝0 , to obtain the maximum temperature t of the fuel element max .

[0061] The method for calculating the maximum temperature of the dispersed fuel element of the present invention determines the modified volume ratio η of the coated fuel particles in the first region and the second region by forming the first region and the second region. z Because the corrected volume fraction η z In the determination process, the probability distribution of the coated fuel particles in the first region and the second region is considered, which can characterize the aggregation or sparse distribution of the coated fuel particles in the fuel element. Therefore, the corrected volume proportion η of the coated fuel particles in the first region and the second region is determined. z , calculate the temperature at the center of the second region, which can reflect the local high temperature of the dispersed fuel element, that is, the non-uniformity of the temperature change from the outer boundary of the fuel element to the center of the fuel element. In this way, a more accurate maximum temperature t of the fuel element corresponding to this probability distribution can be determined. max to meet the corresponding engineering needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1A flow chart of a method for calculating the maximum temperature of a dispersed fuel element provided in an embodiment of the present invention;

[0063] Figure 2 A flowchart of an application example of a method for calculating the maximum temperature of a dispersed fuel element provided by an embodiment of the present invention;

[0064] Figure 3 A schematic diagram of the structure of a dispersed fuel element provided in an embodiment of the present invention;

[0065] Figure 4 A schematic diagram of the structure of a fuel element after being divided in a method for calculating the maximum temperature of a dispersed fuel element provided in an embodiment of the present invention;

[0066] Figure 5 A schematic diagram of the structure of a fuel element after being divided in another method for calculating the maximum temperature of a dispersed fuel element provided in an embodiment of the present invention;

[0067] Figure 6 A schematic diagram of the structure of a fuel element after being divided in another method for calculating the maximum temperature of a dispersed fuel element provided in an embodiment of the present invention;

[0068] Figure 7 A structural diagram of a device for calculating the maximum temperature of a dispersed fuel element provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0069] In order to make those skilled in the art better understand the technical scheme of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and Examples. It should be understood that the specific embodiments described herein are only intended to explain the application, rather than to limit the application. For those skilled in the art, the application can be implemented when some details in these specific details are not needed. The following description of the embodiments is only for providing a better understanding of the application by illustrating the examples of the application.

[0070] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "include..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0071] In the related art, when calculating the maximum temperature of a dispersed fuel element, it is considered that the temperature change from the outer boundary of the fuel element to the center of the fuel element is uniform, because the coated fuel particles are considered to be uniformly distributed in the graphite matrix. In reality, the coated fuel particles are randomly distributed in the graphite matrix, and the coated fuel particles may be locally aggregated or sparse, resulting in local high temperatures in the actual dispersed fuel element. Therefore, the temperature change from the outer boundary of the fuel element to the center of the fuel element is not uniform. It should be noted that the prior art believes that the temperature change from the outer boundary of the fuel element to the center of the fuel element is uniform, which can be a linear uniform change or a parabolic uniform change. That is, the prior art believes that the temperature distribution curve from the outer boundary of the fuel element to the center of the fuel element can be linear or parabolic.

[0072] If the coated fuel particles are evenly distributed in the graphite matrix, the calculated temperature of the dispersed fuel element has a large deviation from the actual maximum temperature of the dispersed fuel element, which is difficult to meet the corresponding engineering requirements. In addition, considering the situation that the coated fuel particles are evenly distributed in the graphite matrix, the calculated temperature of the dispersed fuel element has only a 50% probability of being higher than other situations, and it cannot cover all situations, making it difficult to meet various engineering requirements.

[0073] The inventors have found that when the coated fuel particles gather in the central area, the maximum temperature at this time is higher than when the coated fuel particles are uniformly distributed in the graphite matrix. Specifically, by dividing the fuel element into a first area and a second area (central area), and considering the probability distribution of the coated fuel particles in the first area and the second area, the volume proportion of the coated fuel particles in the first area and the second area is corrected, which can characterize the aggregation or sparse distribution of the coated fuel particles in the fuel element. Then, by determining the corrected volume proportion η of the coated fuel particles in the first area and the second area z , calculate the temperature at the center of the second region, which can reflect the local high temperature of the dispersed fuel element and the non-uniformity of the temperature change from the outer boundary of the fuel element to the center of the fuel element (non-linear uniform change or non-parabolic uniform change). In this way, a more accurate maximum temperature t of the fuel element corresponding to this probability distribution can be determined. max to meet the corresponding engineering needs.

[0074] Based on this, in order to solve the problems of the prior art, the present invention proposes a method and device for calculating the maximum temperature of a dispersed fuel element, which can determine the maximum temperature of a dispersed fuel element that is closer to actual engineering requirements to meet corresponding engineering requirements.

[0075] Embodiment 1:

[0076] like Figure 1 As shown, this embodiment provides a method for calculating the maximum temperature of a dispersed fuel element, including steps S1 to S3:

[0077] Step S1. Divide the fuel element into regions to form a first region and a second region; the first region and the second region are distributed sequentially from the outer boundary of the fuel element to the center of the fuel element.

[0078] Here, the fuel element is a dispersed fuel element, which is composed of coated fuel particles and a matrix (such as a graphite matrix). The matrix graphite is used to moderate neutrons and conduct fission heat, and withstand external pressure, impact, corrosion and wear. The coated fuel particles are used to carry out nuclear reactions.

[0079] In some embodiments, the fuel element is a sphere, that is, the overall shape of the matrix is ​​a sphere, and the shape of the coated fuel particles is also a sphere. The coated fuel particles are dispersed in the matrix. Figure 3 As shown, the fuel element 1 is a sphere, and the coated fuel particles 2 are dispersed in the matrix 3.

[0080] It should be noted that the coated fuel particles are randomly distributed in the graphite matrix, and the coated fuel particles may be locally aggregated or sparse in the fuel element.

[0081] The first region and the second region are distributed sequentially from the outer boundary of the fuel element to the center of the fuel element. In some embodiments, the second region includes the spherical center of the fuel element and forms a sphere in the fuel element with the spherical center of the fuel element as the center. The first region is a circular sphere in the fuel element surrounding the second region.

[0082] Of course, the shapes of the first region and the second region are not limited to the above examples. In some other embodiments, the divided second region can also be a cuboid, and the first region and the second region are co-centered, forming a surrounding body surrounding the second region in the fuel element.

[0083] Figure 4 A schematic diagram of the structure of a fuel element after being divided in a method for calculating the maximum temperature of a dispersed fuel element provided in an embodiment of the present invention is a cross-sectional structure diagram through the center of the fuel element sphere, such as Figure 4 As shown, the fuel element is divided into regions to form a first region D a and the second region D b .

[0084] During implementation, the coated fuel particles may be densely packed at the center of the fuel element to form the second region, and the second region may be formed at the periphery of the second region. Other division methods may also be used, for example, the fuel element may be divided into a preset proportion along the radial direction of the sphere to form the first region and the second region distributed in sequence from the outer boundary of the fuel element to the center of the fuel element.

[0085] Step S2. According to the probability distribution of the coated fuel particles in the first region and the second region, the initial volume proportion η of the coated fuel particles in the first region and the second region is corrected, and the corrected volume proportion η of the coated fuel particles in the first region and the second region after the correction is determined respectively. z .

[0086] Here, the probability distribution of the coated fuel particles in the first region and the second region represents the probability that the coated fuel particles may be locally aggregated or sparse in the fuel element. Specifically, on the assumption that the coated fuel particles in the fuel element are uniformly distributed in the group, the probability of a portion of the coated fuel particles migrating between the first region and the second region. In addition, the migration of the coated fuel particles between the first region and the second region may be from the first region to the second region, or from the second region to the first region.

[0087] It should also be noted that the number of partially coated fuel particles that migrate between the first region and the second region may be related to a target probability distribution. For example, the target standard score may be determined by querying a standard normal distribution table (Z table) with a target significance level α. According to the target standard score The number of migrated partially coated fuel particles corresponding to a target probability distribution is determined.

[0088] In some embodiments, considering that the coated fuel particles gather in the central area of ​​the fuel element, the temperature of the central area will increase, and according to the probability distribution of the coated fuel particles in the first area and the second area, the initial volume proportion η of the coated fuel particles in the first area and the second area is corrected, that is, considering that a part of the coated fuel particles migrate from the first area to the second area, the volume proportion of the coated fuel particles in the fuel element in the first area and the second area is respectively the modified volume proportion v of the coated fuel particles in the first area and the second area. z .

[0089] Step S3. Based on the modified volume proportion η of the coated fuel particles in the first region and the second region z , and the radii of the outer boundaries of the first and second regions, calculate the temperature t at the center of the second region max | r＝0, to obtain the maximum temperature t of the fuel element max .

[0090] Here, the temperature at the center of the second region is max | r＝0 , as the maximum temperature of the fuel element t max It is understandable that the aggregation of coated fuel particles in the central area is considered when calculating the maximum temperature of the dispersed fuel element because of the long heat conduction path, low thermal conductivity, symmetrical geometric structure and random distribution in the central area. These factors work together to make the central area more likely to become a local hot spot, thereby affecting the overall temperature distribution of the fuel element. By considering these factors, the maximum temperature of the fuel element can be more accurately predicted and controlled to ensure its safety and reliability.

[0091] During implementation, according to the modified volume ratio η of the coated fuel particles in the first region and the second region z , the number of coated fuel particles in the first region and the second region can be determined respectively; according to the radius of the outer boundaries of the first region and the second region, the temperature increment from the outer boundary of the first region to the outer boundary of the second region and the temperature increment from the outer boundary of the second region to the center of the second region can be determined; then by obtaining the temperature of the outer boundary of the first region and summing the temperature of the outer boundary of the first region, the temperature increment from the outer boundary of the first region to the outer boundary of the second region, and the temperature increment from the outer boundary of the second region to the center of the second region, the temperature t at the center of the second region can be determined. max | r＝0 .

[0092] In this embodiment, the modified volume proportion η of the coated fuel particles in the first region and the second region is determined by forming the first region and the second region. z Because the corrected volume fraction η z In the determination process, the probability distribution of the coated fuel particles in the first region and the second region is considered, which can characterize the aggregation or sparse distribution of the coated fuel particles in the fuel element. Therefore, the corrected volume proportion η of the coated fuel particles in the first region and the second region is determined. z , calculate the temperature at the center of the second region, which can reflect the local high temperature of the dispersed fuel element, that is, the non-uniformity of the temperature change from the outer boundary of the fuel element to the center of the fuel element. In this way, a more accurate maximum temperature t of the fuel element corresponding to this probability distribution can be determined. max to meet the corresponding engineering needs.

[0093] In some embodiments, step S1 specifically includes:

[0094] The coated fuel particles are densely packed inside the fuel element, and then the fuel element is divided, and the area corresponding to the outer boundary of the fuel element and the blank area of ​​the coated fuel particles is set as the first area, and the area corresponding to the center of the fuel element and the dense area of ​​the coated fuel particles is set as the second area; wherein the first area and the second area are concentric, the second area is spherical, and the first area is surrounded by the outside of the second area, and is a circular spherical shape.

[0095] Here, the densest packing means that the coated fuel particles (a kind of sphere) are stacked together in a limited space in a densest packing manner. For example, the densest packing can be face-centered cubic (FCC) or hexagonal close packing (HCP). The volume proportion ξ of the coated fuel particles corresponding to these two densest packing modes (i.e., the ratio of the volume of the coated fuel particles in the unit cell to the volume of the unit cell) is:

[0096]

[0097] like Figure 3 and Figure 4 As shown, the fuel element 1 is a sphere, and the coated fuel particles 2 are dispersed in the matrix 3. The coated fuel particles are densely packed inside the fuel element 1, and the fuel element 1 is divided to form a first region D. a and the second region D b Among them, the first area D a and the second region D b Concentric, second area D b The first area D is spherical. a Surrounded by the second area D b The outside is a round ball. The first area D a The outer boundary of the connected fuel element is the blank area of ​​the coated fuel particles, and the second area D b The center of the covering fuel element is a dense area of ​​coated fuel particles.

[0098] It should be noted that in this embodiment, the fuel element is divided according to the fact that the coated fuel particles are most densely packed inside the fuel element, so as to be used for the subsequent calculation of the actual number of coated fuel particles in the first area and the second area. The calculation of the actual number of coated fuel particles in the first area and the second area is specifically referred to the explanation of step S22.

[0099] It should also be noted that after the first region and the second region are formed, the radius of the outer boundary of the first region and the radius of the outer boundary of the second region can be determined for subsequent calculation of the maximum temperature of the dispersed fuel element.

[0100] In this embodiment, the fuel element is divided into a first area of ​​blank areas of coated fuel particles and a second area of ​​dense areas of coated fuel particles, thereby determining two areas in the fuel element to provide a basis for the subsequent probability distribution of coated fuel particles in the two areas.

[0101] In some embodiments, step S2 specifically includes steps S21 to S22:

[0102] Step S21. Obtain the target standard score corresponding to the target significance level α in the standard normal distribution table

[0103] Step S22. According to the target standard score and the initial volume proportion η of the coated fuel particles, respectively determine the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 .

[0104] Here, the standard normal distribution table (also called Z table) is used to measure the different Z values ​​(target standard scores) in the standard normal distribution. ) corresponding to the cumulative distribution function (CDF) values. The standard normal distribution is a special normal distribution with mean μ = 0 and standard deviation σ = 1. The standard normal distribution table provides Z values ​​from Z = -3.00 to Z = 3.00 and their corresponding cumulative probabilities.

[0105] The target significance level α is the significance level required by the corresponding engineering requirement. The target significance level α is also called the complementary value of the confidence level, which is used to determine the standard for rejecting the null hypothesis or accepting the alternative hypothesis in hypothesis testing or confidence interval estimation. For example, for a certain engineering requirement, the target significance level α = 0.05, that is, the 95% confidence level required by the corresponding engineering requirement. In this embodiment, the maximum temperature determined can cover 95% of the cases.

[0106] It is understandable that for a certain engineering requirement, the maximum temperature of the dispersed fuel element determined can cover various situations, but the maximum temperature of the dispersed fuel element determined is too high and has no practical application value; if the maximum temperature determined is low, the situations that can be covered are limited. Therefore, in actual engineering, it is necessary to determine the maximum temperature corresponding to the envelope probability according to the engineering requirements to meet the corresponding engineering requirements.

[0107] Target standard score It is the critical value corresponding to the target significance level α in the standard normal distribution. It is used to decide whether to reject the null hypothesis or calculate the upper and lower limits of the confidence interval in a two-sided hypothesis test or confidence interval estimation. The target standard score can be determined by looking up the standard normal distribution table. For example, α=0.05, α / 2=0.025, and the target standard score Z can be obtained by looking up the standard normal distribution table. 0.025 ≈2.

[0108] During implementation, the target standard score is A formula for the number of partially coated fuel particles migrating between the first region and the second region can be constructed to determine the number of partially coated fuel particles migrating between the first region and the second region. Then, the number of coated fuel particles in the first region and the second region when the partially coated fuel particles migrate is determined to determine the corrected volume fraction η of the coated fuel particles in the first region, respectively. z1 and the modified volume proportion η of the coated fuel particles in the second region z2 .

[0109] In this embodiment, the target standard score corresponding to the target significance level α is The acquisition of the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 The determination of can consider the probability distribution of the coated fuel particles in the first region and the second region under the target significance level required by the corresponding engineering requirements, which can characterize the aggregation or sparse distribution of the coated fuel particles in the fuel element, and provide a basis for the subsequent determination of the corrected volume proportion v of the coated fuel particles in the first region and the second region. z , calculate the temperature at the center of the second region, provide a basis for the local high temperature existing in the reactive diffuse fuel element, and the non-uniformity of the temperature change from the outer boundary of the fuel element to the center of the fuel element.

[0110] In some embodiments, step S22 specifically includes:

[0111] According to the following formula (1), the modified volume fraction η of the coated fuel particles in the first region is determined: z1 ,

[0112]

[0113] Among them, η is the initial volume proportion of the coated fuel particles, ξ is the volume proportion of the spheres when they are stacked together in a limited space in the most densely packed manner, is the target standard score, N is the number of coated fuel particles contained in the fuel element;

[0114] According to the following formula (2), the modified volume proportion η of the coated fuel particles in the second region is determined: z2 ,

[0115]

[0116] Among them, η is the initial volume proportion of the coated fuel particles, ξ is the volume proportion of the spheres when they are stacked together in a limited space in the most densely packed manner, is the target standard score, and N is the number of coated fuel particles contained in the fuel element.

[0117] Here, consider the envelope Under probability conditions, the number n of partially coated fuel particles migrating between the first region and the second region is determined according to the following formula (1-1): 移动 :

[0118]

[0119] Without considering the migration of some coated fuel particles between the first region and the second region (i.e., the coated fuel particles in the first region and the second region are uniformly distributed), the number N of coated fuel particles contained in the first region is Da , the number N of coated fuel particles contained in the second region Db , determined according to formula (1-2) and formula (1-3) in turn:

[0120]

[0121] After the coated fuel particles move from the first area to the second area, the envelope Under the probability condition, the number of coated fuel particles contained in the first region is N Da移动 , determined according to the following formula (1-4):

[0122]

[0123] After the coated fuel particles move from the first area to the second area, the envelope Under the probability condition, the number of coated fuel particles n contained in the second region is Db移动 , determined according to the following formula (1-5):

[0124]

[0125] Then, according to the following formula (1-6), the volume proportion of the coated fuel particles in the first region is corrected to obtain the corrected volume proportion η of the coated fuel particles in the first region: z1 :

[0126]

[0127] Wherein, the numerator in the above formula (1-6) is expressed as a part (N 移动 ) After the coated fuel particles gather from the first region to the second region, the volume of the coated fuel particles in the first region; the denominator in the above formula (1-6) represents the volume of the first region. It can be understood that the ratio of the two is the modified volume ratio η of the coated fuel particles in the first region z1 , and then simplified to obtain the corrected volume proportion η of the coated fuel particles in the first region z1 As shown in formula (1).

[0128] And, according to the following formula (1-7), the volume proportion of the coated fuel particles in the second region is corrected to obtain the corrected volume proportion η of the coated fuel particles in the second region: z2 :

[0129]

[0130] Wherein, the numerator in the above formula (1-7) is expressed as a part (N 移动 ) After the coated fuel particles gather from the first region to the second region, the volume of the coated fuel particles in the second region; the denominator in the above formula represents the volume of the second region. It can be understood that the ratio of the two is the modified volume ratio η of the coated fuel particles in the second region z2 , and then simplified to obtain the modified volume proportion η of the coated fuel particles in the second region z2 As shown in formula (2).

[0131] In this embodiment, the corrected volume proportion η of the coated fuel particles passing through the first region is z1 The determination of the modified volume proportion η of the coated fuel particles in the second region z2 After considering the probability distribution, consider the envelope Under the probability condition, a corresponding number of coated fuel particles migrate and gather from the first region to the second region, and the modified volume ratio v of the coated fuel particles in the first region and the second region is determined. z In this way, the local high temperature of the dispersed fuel element can be reflected, that is, the non-uniformity of the temperature change from the outer boundary of the fuel element to the center of the fuel element can be reflected, so as to calculate a more accurate temperature at the center of the second region.

[0132] In some embodiments, step S3 specifically includes steps S31 to S33:

[0133] Step S31. Obtaining the temperature t1 of the outer boundary of the first region;

[0134] Here, the temperature t1 of the outer boundary of the first region may be measured through experiments, determined through simulation calculations, or acquired through other methods.

[0135] Step S32. Based on the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 , determine the regional temperature increment of the first region and the regional temperature increment of the second region respectively.

[0136] Here, the regional temperature increment of the first region and the regional temperature increment of the second region can be determined by the uniform increase of the temperature of the first region and the uniform increase of the temperature of the second region. The first region and the second region can also be further divided to form a coated fuel particle blank area (matrix) and a coated fuel particle dense area in the first region, and a coated fuel particle blank area (matrix) and a coated fuel particle dense area in the second region. That is, the temperature of the first region is uniformly increased in sections, and the temperature of the second region is also uniformly increased in sections, and the regional temperature increment of the first region is determined by calculating the temperature increments of the coated fuel particle blank area (matrix) and the coated fuel particle dense area in the first region, and the regional temperature increment of the second region is determined by calculating the temperature increments of the coated fuel particle blank area (matrix) and the coated fuel particle dense area in the second region.

[0137] Step S33: Calculate the temperature t at the center of the second region based on the temperature t1 of the outer boundary of the first region, the regional temperature increment of the first region, and the regional temperature increment of the second region. max | r＝0 .

[0138] In implementation, the temperature t1 at the outer boundary of the first region, the regional temperature increment of the first region, and the regional temperature increment of the second region are summed, that is, the temperature t at the center of the second region can be calculated. max | r＝0

[0139] In this embodiment, the temperature t1 at the center of the second region is calculated by obtaining the temperature t1 of the outer boundary of the first region, determining the regional temperature increment of the first region and the regional temperature increment of the second region. max | r＝0 Because the corrected volume fraction η z In the determination process, the probability distribution of the coated fuel particles in the first region and the second region is considered, which can characterize the aggregation or sparse distribution of the coated fuel particles in the fuel element. Therefore, the corrected volume proportion η of the coated fuel particles in the first region and the second region is determined. z, respectively determine the regional temperature increment of the first region and the regional temperature increment of the second region, which can reflect the local high temperature of the dispersed fuel element, that is, the non-uniformity of the temperature change from the outer boundary of the fuel element to the center of the fuel element. In this way, a more accurate maximum temperature t of the fuel element corresponding to this probability distribution can be determined. max to meet the corresponding engineering needs.

[0140] In some embodiments, step S32 specifically includes steps S321 to S323:

[0141] Step S321. Make the coated fuel particles densely packed inside the first region, and divide the first region into two regions: the outer region is the region in the first region connected to the outer boundary of the fuel element and corresponding to the blank region of the coated fuel particles, which is set as the first matrix region D1; the inner region is the region in the first region corresponding to the dense region of the coated fuel particles, which is set as the first particle region D2, and

[0142] The coated fuel particles are densely packed inside the second region, and the second region is divided into the region corresponding to the blank region of coated fuel particles in the second region as the second matrix region D3, and the region corresponding to the dense region of coated fuel particles in the second region as the second particle region D4.

[0143] Here, if Figure 5 As shown, the first area D a The first matrix region D1 and the first particle region D2 are divided into a first matrix region D1 and a first particle region D2. b It is divided into a second matrix area D3 and a second particle area D4.

[0144] It can be understood that the present embodiment is achieved by further dividing the first region and the second region to form a blank region (matrix) of coated fuel particles and a dense region of coated fuel particles in the first region, and a blank region (matrix) of coated fuel particles and a dense region of coated fuel particles in the second region, that is, the temperature of the first region is increased in stages, and the temperature of the second region is also increased in stages, to determine the regional temperature increment of the first region and the regional temperature increment of the second region.

[0145] Step S322. Based on the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 , respectively determine the radius of the first matrix region D1, the radius of the first particle region D2, the radius of the second matrix region D3, and the radius of the second particle region D4.

[0146] It should be noted that the radius of the first matrix area D1, the radius of the first particle area D2, the radius of the second matrix area D3 and the radius of the second particle area D4 are respectively the radii of the outer boundaries of each area, that is, the radius of the outer boundary of the first matrix area D1, the radius of the outer boundary of the first particle area D2, the radius of the outer boundary of the second matrix area D3 and the radius of the outer boundary of the second particle area D4.

[0147] like Figure 5 As shown, the radius r1 of the first substrate region D1 can be measured through experiments or determined according to the design parameters of the fuel element.

[0148] According to the following formula (2-1) (the number of coated fuel particles uniformly distributed in the first region after the volume ratio is corrected is equal to the number of coated fuel particles most densely packed in the first particle region D2 in the first region after the volume ratio is corrected),

[0149]

[0150] The radius r2 of the first particle area D2 can be determined as:

[0151]

[0152] According to the following formula (2-3) (the number of coated fuel particles uniformly distributed in the fuel element when the volume fraction is not corrected is equal to the number of coated fuel particles most densely packed in the second region after the volume fraction is corrected),

[0153]

[0154] The radius r3 of the second base region D3 can be determined as:

[0155]

[0156] According to the following formula (2-5) (the number of coated fuel particles uniformly distributed in the second region after the volume ratio is corrected, and the number of coated fuel particles most densely packed in the second particle region D4 in the second region after the volume ratio is corrected is equal),

[0157]

[0158] The radius r4 of the second particle area D4 can be determined as:

[0159]

[0160] Step S323. Determine the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3 and the temperature increment t5 of the second particle region D4 according to the radius of the first matrix region D1, the radius of the first particle region D2, the radius of the second matrix region D3 and the radius of the second particle region D4 respectively.

[0161] Here, in each region, the heat conduction equation is as follows (3-1):

[0162]

[0163] Where Q is the heat generation rate per unit volume, λ is the heat transfer coefficient of each region, and r is the radius of each region (the radius of the outer boundary of each region).

[0164] First, the temperature distribution of each region is obtained by integrating and solving the heat conduction equation of each region; then, based on the fact that the temperature at the boundary of each region must be continuous and matching the boundary conditions of each region, the temperature at the outer boundary of each region can be solved. Then, based on the temperature of two adjacent regions at the outer boundary of each region, the temperature increment between the two adjacent regions is calculated, thereby determining the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3, and the temperature increment t5 of the second particle region D4.

[0165] Step S33 specifically includes:

[0166] The temperature t1 at the outer boundary of the first region, the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3 and the temperature increment t5 of the second particle region D4 are summed to obtain the temperature t at the center of the second region. max | r＝0 .

[0167] In this embodiment, by setting the first matrix region D1, the first particle region D2, the second matrix region D3, and the second particle region D4, determining the radius of the first matrix region D1, the radius of the first particle region D2, the radius of the second matrix region D3, and the radius of the second particle region D4, determining the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3, and the temperature increment t5 of the second particle region D4, the temperature t max | r＝0 The maximum temperature t of the fuel element, which can reflect the local high temperature of the dispersed fuel element and more accurately reflect the local high temperature of the dispersed fuel element, can be calculated. max to meet the corresponding engineering needs.

[0168] In some embodiments, step S323 specifically includes:

[0169] The temperature increment t2 of the first matrix region D1 from the outer boundary of the first matrix region D1 to the outer boundary of the first particle region D2 is determined according to the following formula (3):

[0170]

[0171] Wherein, Q is the total power of the dispersed fuel element, λ1 is the thermal conductivity of the first matrix region D1, r1 is the radius of the outer boundary of the first matrix region D1, and r2 is the radius of the outer boundary of the first particle region D2;

[0172] The temperature increment t3 of the first particle region D2 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (4):

[0173]

[0174] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ζ is the volume ratio of the spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ2 is the thermal conductivity of the first particle region D2, r2 is the radius of the outer boundary of the first particle region D2, and r3 is the radius of the outer boundary of the second matrix region D3;

[0175] The temperature increment t4 of the second matrix region D3 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (5):

[0176]

[0177] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ζ is the volume ratio of the spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ3 is the thermal conductivity of the second matrix region D3, r3 is the radius of the outer boundary of the second matrix region D3, and r4 is the radius of the outer boundary of the second particle region D4;

[0178] The temperature increment t5 of the second particle region D4 from the outer boundary of the second particle region D4 to the center of the second particle region D4 is determined according to the following formula (6):

[0179]

[0180] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ4 is the thermal conductivity of the second particle region D4, and r4 is the radius of the outer boundary of the second particle region D4.

[0181] It should be noted that the thermal conductivity coefficient λ1 of the first substrate region D1 is the same as the thermal conductivity coefficient λ3 of the second substrate region D3, and both are thermal conductivity coefficients of the corresponding substrate material (such as graphite). The thermal conductivity coefficient of the substrate material is an inherent property of the substrate material and can be measured experimentally, determined by simulation calculation, or obtained by other methods.

[0182] The thermal conductivity coefficient λ2 of the first particle region D2 is the same as the thermal conductivity coefficient λ4 of the second particle region D4, both of which are the thermal conductivity coefficients when the coated fuel particles are most densely arranged in the matrix. The thermal conductivity coefficient when the coated fuel particles are most densely arranged in the matrix is ​​an inherent property and can be measured by experiment, determined by simulation calculation, or obtained by other methods.

[0183] In this embodiment, the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3, and the temperature increment t5 of the second particle region D4 are used to determine the temperature increment of each region. Because the determined temperature increment can reflect the local high temperature existing in the dispersed fuel element, that is, the non-uniformity of the temperature change from the outer boundary of the fuel element to the center of the fuel element, it can provide a basis for calculating a more accurate maximum temperature of the dispersed fuel element. In addition, the calculation process of the maximum temperature of the dispersed fuel element is simplified.

[0184] In some embodiments, step S321 specifically includes steps S3211 to S3212:

[0185] Step S3211. Perform iterative division of the second matrix region D3 and the second particle region D4 by dense packing of coated fuel particles to divide the fuel element into 2n regions.

[0186] Step S3212: Based on the temperature t1 of the outer boundary of the first region and the temperature increments of the 2n regions, the temperature t at the center of the second region is obtained. max | r＝0 .

[0187] Here, if Figure 6As shown, the second matrix region D3 and the second particle region D4 are iteratively divided into the densest packing of the coated fuel particles, which is to pack the second matrix region D3 and the second particle region D4 again in the center of the second matrix region D3 and the second particle region D4. That is, the process similar to the fuel element being divided into the first region and the second region is repeated, and the second matrix region D3 and the second particle region D4 are divided into the first sub-region (D31+D32) and the second sub-region (D31+D32), and the volume proportion of the coated fuel particles in the first sub-region (D31+D32) and the second sub-region (D31+D32) is corrected, and then the temperature increment of the first sub-region and the temperature increment of the second sub-region are determined. The temperature of the outer boundary of the first region and the temperature increment of each region are summed to obtain the temperature t at the center of the second region. max | r＝0 .

[0188] It should also be noted that n will not increase infinitely, because the second particle region D4 may have been the densest packing and the migration of the coated fuel particles in the second particle region D4 can no longer occur, so iterative division can no longer be performed. In some embodiments, n is 2, 3, 4, or 5.

[0189] In this embodiment, the second particle area D4 is used to iteratively divide the densest packing of the coated fuel particles, and the temperature t max | r＝0 The probability distribution of the coated fuel particles in the fuel element can be iteratively considered to further improve the accuracy of the determined maximum temperature of the dispersed fuel element.

[0190] In some embodiments, the method further comprises:

[0191] Step S4. According to the standard score in the correction factor, the probability P that the possible temperature is not higher than the calculated maximum temperature is determined according to the following formula (7):

[0192]

[0193] Among them, α is the target significance level, is the target standard score, is the cumulative probability density function, n is 1 / 2 of the 2n regions divided by the fuel element, and n is an integer greater than or equal to 2.

[0194] here, The cumulative probability density function can be determined by looking up the standard normal distribution table (Z table). For example, for the target significance level α = 0.05, the target standard score Z 0.025≈2, by looking up the table φ(2) = 0.9772. If the fuel element is divided into the first matrix area D1, the first particle area D2, the second matrix area D3, and the second particle area D4, the probability P represents that the temperature that may occur during actual use is not higher than the calculated maximum temperature, which is 97.72%.

[0195] In addition, after the second matrix region D3 and the second particle region D4 are iteratively divided into the densest packing of the coated fuel particles, the probability that the temperature is not higher than the calculated maximum temperature is reduced.

[0196] The following is an example of the maximum temperature calculation and probability calculation of a fuel element. For example, the equivalent thermal conductivity λ1 of the graphite matrix is ​​20W / (m·K), and when the volume proportion of the coated particles is 10%, the volume proportion of the densest packing of the coated particles is The equivalent thermal conductivity of the dispersed fuel element is 10W / (m·K), the radius r1 of the dispersed fuel element is 0.1m, the outermost boundary temperature t1 of the dispersed fuel element is 500K, and the power Q of the dispersed fuel element is 100000. The number of coated particles in the dispersed fuel element is 100000. The calculated probability is 2 times the standard deviation When , the corresponding maximum temperature and the probability of its energy envelope are as follows:

[0197] Step 1: Calculate η according to formula (1) and formula (2). z1 and η z2 .

[0198]

[0199] Get η z1 =0.0998;

[0200]

[0201] Get η z2 =0.1016

[0202] Step 2: Obtain the radius r1 of the dispersed fuel element and calculate the radius of each area according to formula (2-2), formula (2-4) and formula (2-6).

[0203] r1=0.1m

[0204]

[0205] We get r2 = 0.0631

[0206]

[0207] We get r3 = 0.0513

[0208]

[0209] We get r4 = 0.0265

[0210] Step 3. Calculate the maximum temperature.

[0211] t max | r＝0 =568.66

[0212] Step 4. Calculate the probability.

[0213] P=φ(2)=0.9772

[0214] Under the conditions of the fuel element in this example, it can be calculated through the above steps that the probability that the temperature that may occur during actual use is not higher than 569.26K is 97.72%.

[0215] In this embodiment, by determining the probability P that the possible temperature is not higher than the calculated maximum temperature, a determined maximum temperature and the probability that the maximum temperature can be enveloped are given to meet corresponding engineering requirements.

[0216] Embodiment 2:

[0217] The specific implementation process of the above method is described below in conjunction with specific application examples.

[0218] Dispersed fuel elements used in high temperature gas-cooled reactors. Dispersed fuel elements are a type of dispersed fuel, consisting of randomly distributed coated fuel particles and a graphite matrix. The matrix graphite is used to moderate neutrons and conduct fission heat, and withstand external pressure, impact, corrosion and wear.

[0219] Since the coated fuel particles are randomly distributed in the graphite matrix, the coated fuel particles may be locally aggregated or sparse. When the coated fuel particles are aggregated together, it may cause local high temperature of the dispersed fuel element, which is higher than the case where the coated fuel particles are uniformly distributed in the graphite matrix.

[0220] At present, when calculating the fuel temperature, the situation that the coated fuel particles are evenly distributed in the graphite matrix is ​​considered. At this time, the temperature obtained has only a 50% probability of being higher than other situations, and cannot cover all situations. It cannot meet engineering needs.

[0221] Therefore, a method for calculating the maximum temperature and probability of a dispersed fuel element is invented, which can be used to quickly calculate the maximum temperature of a dispersed fuel element and obtain the corresponding probability.

[0222] like Figure 2 As shown, the above-mentioned purpose of the present invention can be achieved by adopting the following technical solutions:

[0223] The spheres are stacked together in a limited space in the most densely packed manner, and their volume proportion ξ is:

[0224]

[0225] It is known that the outer radius of the dispersed fuel element is r1, the total power is Q, and the temperature of the outer boundary surface is t1. The dispersed fuel element contains N coated fuel particles, and the volume proportion of the coated fuel particles is η.

[0226] Step 1: Calculate the correction factor η considering the probability distribution z1 and η z2 .

[0227] Specifically, Figure 5 Assume that the coated fuel particles are densely packed inside the fuel element, divide the fuel element into a first region (D1+D2) and a second region (D3+D4), and calculate the volume proportion η of the coated fuel particles in the outer region in the D1 and D2 regions z1 , and the volume proportion of the coated fuel particles in the D3 and D4 regions η z2 .

[0228] According to the following formula (1-6) and formula (1-7), calculate η z1 and η z2 , η z1 and η z2 is the correction factor considering the probability distribution. Wherein, formula (1-6) is as follows:

[0229]

[0230] The numerator in formula (1-6) is: After considering the aggregation of the enveloped fuel particles from the D1 and D2 regions to the D3 and D4 regions, D1 and Under probability conditions, a portion of the volume of the fuel particles enclosed in the D2 region.

[0231] The denominator in formula (1-6) is: the total volume of areas D1 and D2.

[0232] It can be understood that if the distribution is uniform, the number of coated fuel particles contained in each region is related to the volume of the region. In the case of uniform distribution, the number of coated fuel particles contained in regions D3 and D4 is determined according to formula (1-3) as shown below:

[0233]

[0234] In addition, under uniform distribution, the number of coated fuel particles contained in the D1 and D2 regions is determined according to formula (1-2):

[0235]

[0236] Consider the envelope Under probability conditions, as shown in the following formula (1-1), a portion of the coated fuel particles gather from regions D1 and D2 to regions D3 and D4.

[0237]

[0238] Then, after the coated fuel particles move from the D1 and D2 regions to the D3 and D4 regions, consider the envelope Under the probability condition, the number of coated fuel particles contained in the D3 and D4 regions is determined according to the following formula (1-5):

[0239]

[0240] After the coated fuel particles move from the D1 and D2 regions to the D3 and D4 regions, the envelope Under the probability condition, the number of coated fuel particles contained in the D3 and D4 regions is determined according to the following formula (1-4):

[0241]

[0242] η z1 After considering the probability distribution, consider the envelope In the probability case, after a part of the coated fuel particles gather in the D3 and D4 regions, the volume proportion of the coated fuel particles in the D1 and D2 regions.

[0243] Simplifying formula (1-6) yields the following formula (1):

[0244]

[0245] In addition, formula (1-7) is as follows:

[0246]

[0247] The numerator in formula (1-7) is: Consider the envelope Under probability conditions, the volume of the coated fuel particles in regions D3 and D4 after a portion of the coated fuel particles gather from regions D1 and D2 to regions D3 and D4.

[0248] The denominator in formula (1-7) is: the total volume of areas D3 and D4.

[0249] η z2 After considering the probability distribution, consider the envelope Under probability conditions, after a part of the coated fuel particles gather in the D3 and D4 regions, the volume proportion of the coated fuel particles in the D3 and D4 regions.

[0250] Simplifying formula (1-7) yields the following formula (2):

[0251]

[0252] in, is the z standard score.

[0253] Step 2: Assume that the dispersed fuel element is divided into four regions and calculate the radius of each region.

[0254] Specifically, assuming that the coated fuel particles are densely packed inside the outer region (D2), and assuming that the coated fuel particles are densely packed inside the inner region (D4), the dispersed fuel element is divided into 4 regions, and the radius of each region is calculated, as shown in the figure. From the outside to the inside, they are numbered sequentially as D1, D2, D3, and D4, and all variable subscripts in the subsequent regions correspond to 1, 2, 3, and 4, respectively.

[0255] r1, r2, r3, and r4 correspond to the radii of the outer boundaries of each area respectively.

[0256] r1=r1(known parameters of fuel element)

[0257] According to the following formula (2-1) (the number of coated fuel particles uniformly distributed in the first region after the volume ratio is corrected is equal to the number of coated fuel particles most densely packed in the first particle region D2 in the first region after the volume ratio is corrected),

[0258]

[0259] The radius r2 of the first particle area D2 can be determined as:

[0260]

[0261] According to the following formula (2-3) (the number of coated fuel particles uniformly distributed in the fuel element when the volume fraction is not corrected is equal to the number of coated fuel particles most densely packed in the second region after the volume fraction is corrected),

[0262]

[0263] The radius r3 of the second base region D3 can be determined as:

[0264]

[0265] According to the following formula (2-5) (the number of coated fuel particles uniformly distributed in the second region after the volume ratio is corrected, and the number of coated fuel particles most densely packed in the second particle region D4 in the second region after the volume ratio is corrected is equal),

[0266]

[0267] The radius r4 of the second particle area D4 can be determined as:

[0268]

[0269] Assume that the outermost hollow spherical area of ​​the D1 layer does not contain coated fuel particles and has a thermal conductivity coefficient of λ1; the outer hollow spherical area of ​​the D2 layer contains coated fuel particles and has a thermal conductivity coefficient of λ2; the central hollow spherical area of ​​the D3 layer does not contain coated fuel particles and has a thermal conductivity coefficient of λ3; the central spherical area of ​​the D4 layer contains coated fuel particles and has a thermal conductivity coefficient of λ4.

[0270] Step 3, calculate the maximum temperature.

[0271] t1=t1

[0272] The temperature increment t2 of the first matrix region D1 from the outer boundary of the first matrix region D1 to the outer boundary of the first particle region D2 is determined according to the following formula (3):

[0273]

[0274] Wherein, Q is the total power of the dispersed fuel element, λ1 is the thermal conductivity of the first matrix region D1, r1 is the radius of the outer boundary of the first matrix region D1, and r2 is the radius of the outer boundary of the first particle region D2;

[0275] The temperature increment t3 of the first particle region D2 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (4):

[0276]

[0277] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ζ is the volume ratio of the spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ2 is the thermal conductivity of the first particle region D2, r2 is the radius of the outer boundary of the first particle region D2, and r3 is the radius of the outer boundary of the second matrix region D3;

[0278] The temperature increment t4 of the second matrix region D3 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (5):

[0279]

[0280] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ3 is the thermal conductivity of the second matrix region D3, r3 is the radius of the outer boundary of the second matrix region D3, and r4 is the radius of the outer boundary of the second particle region D4;

[0281] The temperature increment t5 of the second particle region D4 from the outer boundary of the second particle region D4 to the center of the second particle region D4 is determined according to the following formula (6):

[0282]

[0283] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ4 is the thermal conductivity of the second particle region D4, and r4 is the radius of the outer boundary of the second particle region D4.

[0284] T max =t1+t2+t3+t4+t5

[0285] As shown in the following formula (4-1), the maximum temperature expression is:

[0286]

[0287] Step 4, calculate the probability. The probability that the temperature that may occur during actual use is not higher than the calculated temperature is as shown in the following formula (7):

[0288]

[0289] in, It is the cumulative probability density function, and the specific value can be obtained by looking up the standard normal distribution table.

[0290] For example, the equivalent thermal conductivity of the graphite matrix is ​​20W / (m·K), the equivalent thermal conductivity of the dispersed fuel element when the coated particles account for 10% by volume is 15W / (m·K), and the densest packing volume of the coated particles accounts for The equivalent thermal conductivity of the dispersed fuel element is 10 W / (m·K), the radius of the dispersed fuel element is 0.1 m, the outermost boundary temperature of the dispersed fuel element is 500 K, and the power of the dispersed fuel element is 1000 W. The number of coated particles contained in the dispersed fuel element is 100,000.

[0291] Calculate the maximum temperature when the probability is 2 times the standard deviation.

[0292] Step 1: Calculate η according to formula (1) and formula (2). z1 and η z2 .

[0293]

[0294] Get η z1 =0.0998;

[0295]

[0296] Get η z2 =0.1016

[0297] Step 2: Obtain the radius r1 of the dispersed fuel element and calculate the radius of each area according to formula (2-2), formula (2-4) and formula (2-6).

[0298] r1=0.1m

[0299]

[0300] We get r2 = 0.0631

[0301]

[0302] We get r3 = 0.0513

[0303]

[0304] We get r4 = 0.0265

[0305] Step 3. Calculate the maximum temperature.

[0306] t max | r＝0 =568.66

[0307] Step 4. Calculate the probability.

[0308] P=φ(2)=0.9772

[0309] Under the conditions of Example 1, it can be calculated through the above steps that the probability that the temperature that may occur during actual use is not higher than 569.26K is 97.72%.

[0310] For example, the equivalent thermal conductivity of the graphite matrix is ​​20W / (m·K), the equivalent thermal conductivity of the dispersed fuel element when the coated particles account for 30% by volume is 12W / (m·K), and the densest packing volume of the coated particles accounts for The equivalent thermal conductivity of the dispersed fuel element is 10W / (m·K). The radius of the dispersed fuel element is 70mm, the outermost boundary temperature of the dispersed fuel element is 1000K, and the power of the dispersed fuel element is 700W. The number of coated particles contained in the dispersed fuel element is 500,000.

[0311] Calculate the maximum temperature when the probability is 3 times the standard deviation.

[0312] Step 1: Calculate η z1 and η z2 .

[0313] η z1 =0.2989

[0314] η z2 =0.3015

[0315] Step 2: Calculate the radius of each area.

[0316] r1=0.07

[0317] r2=0.0605

[0318] r3=0.0518

[0319] r4=0.0384

[0320] Step 3. Calculate the maximum temperature.

[0321] t max | r＝0 =1053.85

[0322] Step 4. Calculate the probability.

[0323] P=φ(3)=0.9987

[0324] Under the conditions of Example 2, it can be calculated through the above steps that the probability that the temperature that may occur during actual use is not higher than 1053.85K is 99.87%.

[0325] In this embodiment, through the above calculation steps, the maximum temperature of the dispersed fuel element can be quickly calculated and the corresponding probability can be obtained. The present invention takes into account the influence of the random distribution of the coated fuel particles in the dispersed fuel element, and can select a suitable probability value according to actual needs to quickly calculate the maximum temperature of the dispersed fuel element.

[0326] Embodiment 3:

[0327] The present invention also provides an engineering verification method for a dispersed fuel element, comprising:

[0328] According to the calculation method described in any one of the above items, the maximum temperature t of the fuel element is obtained. max ;

[0329] According to the maximum temperature t max Conduct engineering verification on dispersed fuel elements to determine whether the dispersed fuel elements are qualified.

[0330] In this embodiment, the maximum temperature of the fuel element is obtained, and the dispersed fuel element is engineered for verification based on the maximum temperature. Because the probability distribution of the coated fuel particles is taken into account in the process of determining the maximum temperature to characterize the aggregation of the coated fuel particles in the fuel element, the maximum temperature corresponding to the probability distribution is determined for engineering verification, which can better meet the needs of the engineering verification.

[0331] Embodiment 4:

[0332] like Figure 7 As shown, the present invention also provides a device for calculating the maximum temperature of a dispersed fuel element, the device 100 comprising:

[0333] A dividing module 11 is configured to divide the fuel element into regions to form a first region and a second region; the first region and the second region are distributed sequentially from the outer boundary of the fuel element to the center of the fuel element;

[0334] The correction module 12 is connected to the division module 11 and is configured to correct the initial volume proportion η of the coated fuel particles in the first region and the second region according to the probability distribution of the coated fuel particles in the first region and the second region, and respectively determine the modified volume proportion η of the coated fuel particles in the first region and the second region. z ;

[0335] The obtaining module 13 is connected to the correction module 12, which is configured to obtain the corrected volume proportion η of the coated fuel particles in the first region and the second region according to the corrected volume proportion η z , and the radii of the outer boundaries of the first and second regions, calculate the temperature t at the center of the second region max | r＝0 , to obtain the maximum temperature t of the fuel element max .

[0336] In some embodiments, the dividing module 11 is further used to make the coated fuel particles densely packed inside the fuel element, and then divide the fuel element, setting the area corresponding to the outer boundary of the fuel element and the blank area of ​​the coated fuel particles as the first area, and setting the area corresponding to the center of the fuel element and the dense area of ​​the coated fuel particles as the second area;

[0337] The first area and the second area are concentric, the second area is spherical, and the first area is surrounded by the outside of the second area and is in the shape of a circular sphere.

[0338] In some embodiments, the correction module 12 includes:

[0339] The first acquisition unit is used to obtain the target standard score corresponding to the target significance level α in the standard normal distribution table.

[0340] The first determining unit is connected to the first obtaining unit and is used to determine the target standard score. and the initial volume proportion η of the coated fuel particles, respectively determine the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 .

[0341] In some embodiments, the first determination unit is further configured to determine the modified volume fraction η of the coated fuel particles in the first region according to the following formula (1): z1 ,

[0342]

[0343] Among them, ξ is the initial volume proportion of the coated fuel particles, ξ is the volume proportion of the spheres when they are stacked together in a limited space in the most densely packed manner, is the target standard score, N is the number of coated fuel particles contained in the fuel element;

[0344] According to the following formula (2), the modified volume proportion η of the coated fuel particles in the second region is determined: z2 ,

[0345]

[0346] Among them, η is the initial volume proportion of the coated fuel particles, ξ is the volume proportion of the spheres when they are stacked together in a limited space in the most densely packed manner, is the target standard score, and N is the number of coated fuel particles contained in the fuel element.

[0347] In some embodiments, obtaining module 13 includes:

[0348] A second acquisition unit, used to acquire a temperature t1 of an outer boundary of the first region;

[0349] The second determining unit is connected to the second obtaining unit and is used to determine the corrected volume proportion η of the coated fuel particles in the first region according to the corrected volume proportion η of the coated fuel particles in the first region. z1 and the modified volume proportion η of the coated fuel particles in the second region z2 , respectively determining a regional temperature increment of the first region and a regional temperature increment of the second region;

[0350] A calculation unit connected to the second determination unit is used to calculate the temperature t at the center of the second area according to the temperature t1 of the outer boundary of the first area and the regional temperature increment of the first area and the regional temperature increment of the second area. max | r＝0 .

[0351] In some embodiments, the second determining unit includes:

[0352] The dividing subunit is used to make the coated fuel particles densely packed inside the first area, and divide the first area into two inner and outer areas: the outer area is the area in the first area connected to the outer boundary of the fuel element and corresponding to the blank area of ​​the coated fuel particles, which is set as the first matrix area D1; the inner area is the area in the first area corresponding to the dense area of ​​the coated fuel particles, which is set as the first particle area D2, and

[0353] The coated fuel particles are densely packed inside the second region, and the second region is divided, the region corresponding to the blank region of the coated fuel particles in the second region is set as the second matrix region D3, and the region corresponding to the dense region of the coated fuel particles in the second region is set as the second particle region D4;

[0354] The first determining subunit is connected to the dividing subunit and is used to determine the corrected volume proportion η of the coated fuel particles in the first region according to the modified volume proportion η z1 and the modified volume proportion η of the coated fuel particles in the second region z2 , respectively determine the radius of the first matrix region D1, the radius of the first particle region D2, the radius of the second matrix region D3 and the radius of the second particle region D4;

[0355] a second determining subunit, connected to the first determining subunit, for determining a temperature increment t2 of the first substrate region D1, a temperature increment t3 of the first particle region D2, a temperature increment t4 of the second substrate region D3, and a temperature increment t5 of the second particle region D4, respectively, according to a radius of the first substrate region D1, a radius of the first particle region D2, a radius of the second substrate region D3, and a radius of the second particle region D4;

[0356] The calculation unit is further used to sum the temperature t1 of the outer boundary of the first region, the temperature increment t2 of the first substrate region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second substrate region D3 and the temperature increment t5 of the second particle region D4 to obtain the temperature t max | r＝0 .

[0357] In some embodiments, the second determining subunit is further used to determine the temperature increment t2 of the first substrate region D1 from the outer boundary of the first substrate region D1 to the outer boundary of the first particle region D2 according to the following formula (3):

[0358]

[0359] Wherein, Q is the total power of the dispersed fuel element, λ1 is the thermal conductivity of the first matrix region D1, r1 is the radius of the outer boundary of the first matrix region D1, and r2 is the radius of the outer boundary of the first particle region D2;

[0360] The temperature increment t3 of the first particle region D2 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (4):

[0361]

[0362] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ2 is the thermal conductivity of the first particle region D2, r2 is the radius of the outer boundary of the first particle region D2, and r3 is the radius of the outer boundary of the second matrix region D3;

[0363] The temperature increment t4 of the second matrix region D3 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (5):

[0364]

[0365] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ3 is the thermal conductivity of the second matrix region D3, r3 is the radius of the outer boundary of the second matrix region D3, and r4 is the radius of the outer boundary of the second particle region D4;

[0366] The temperature increment t5 of the second particle region D4 from the outer boundary of the second particle region D4 to the center of the second particle region D4 is determined according to the following formula (6):

[0367]

[0368] Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ζ is the volume ratio of the spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ4 is the thermal conductivity of the second particle region D4, and r4 is the radius of the outer boundary of the second particle region D4.

[0369] In some embodiments, the division subunit is further used to perform iterative division of the second matrix region D3 and the second particle region D4 by the densest packing of coated fuel particles, so as to divide the fuel element into 2n regions;

[0370] The temperature t1 at the outer boundary of the first region and the temperature increments of the 2n regions are summed to obtain the temperature t at the center of the second region. max | r＝0 .

[0371] In some embodiments, the method further comprises:

[0372] The determination module is connected to the division subunit and is used to determine the probability P that the possible temperature is not higher than the calculated maximum temperature according to the standard score in the correction factor and the following formula (7):

[0373]

[0374] Among them, α is the target significance level, is the target standard score, is the cumulative probability density function, n is 1 / 2 of the 2n regions divided by the fuel element, and n is an integer greater than or equal to 2.

[0375] It should be noted that this embodiment is a corresponding device of the method for calculating the maximum temperature of the dispersed fuel element in the above-mentioned embodiment 1. The method in embodiment 1 can be implemented by using this device. The specific implementation method can refer to the description in the method for calculating the maximum temperature of the dispersed fuel element, and this embodiment will not be repeated here.

[0376] It should be clear that the present application is not limited to the specific configuration and processing described above and shown in the figures. For the sake of simplicity, a detailed description of the known method is omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present application is not limited to the specific steps described and shown, and those skilled in the art can make various changes, modifications and additions, or change the order between the steps after understanding the spirit of the present application.

[0377] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware or a combination thereof. When implemented in hardware, it can be, for example, an electronic circuit, an application specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present application are programs or code segments that are used to perform the required tasks. The program or code segment can be stored in a machine-readable medium, or transmitted on a transmission medium or a communication link by a data signal carried in a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, optical fiber media, radio frequency (RF) links, etc. The code segment can be downloaded via a computer network such as the Internet, an intranet, etc.

[0378] The above are only specific implementation methods of the present application. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, modules and units described above can refer to the corresponding processes in the aforementioned method embodiments, and will not be repeated here. It should be understood that the protection scope of the present application is not limited to this. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in this application, and these modifications or replacements should be included in the protection scope of this application.

Claims

1. A method for calculating the maximum temperature of a dispersed fuel element, characterized in that: include: S1. Divide the fuel element into regions to form a first region and a second region; the first region and the second region are distributed sequentially from the outer boundary of the fuel element to the center of the fuel element; S2. According to the probability distribution of the coated fuel particles in the first region and the second region, the initial volume proportion η of the coated fuel particles in the first region and the second region is corrected, and the modified volume proportion η of the coated fuel particles in the first region and the second region is determined respectively. z ; S3. According to the modified volume ratio η of the coated fuel particles in the first region and the second region z , and the radii of the outer boundaries of the first and second regions, calculate the temperature t at the center of the second region max | r＝0 , to obtain the maximum temperature t of the fuel element max .

2. The method for calculating the maximum temperature of a dispersed fuel element according to claim 1, characterized in that: Step S1 specifically includes: The coated fuel particles are densely packed inside the fuel element, and then the fuel element is divided, and the area corresponding to the blank area of ​​the coated fuel particles connected to the outer boundary of the fuel element is set as the first area, and the area corresponding to the center of the fuel element and the dense area of ​​the coated fuel particles is set as the second area; The first area and the second area are concentric, the second area is spherical, and the first area is surrounded by the outside of the second area and is in the shape of a circular sphere.

3. The method for calculating the maximum temperature of a dispersed fuel element according to claim 1, characterized in that: Step S2 specifically includes: S21. Obtain the target standard score corresponding to the target significance level α in the standard normal distribution table S22. According to the target standard score and the initial volume proportion η of the coated fuel particles, respectively determine the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 .

4. The method for calculating the maximum temperature of a dispersed fuel element according to claim 3, characterized in that: Step S22 specifically includes: According to the following formula (1), the modified volume fraction η of the coated fuel particles in the first region is determined: z1 , Among them, η is the initial volume proportion of the coated fuel particles, ξ is the volume proportion of the spheres when they are stacked together in a limited space in the most densely packed manner, is the target standard score, N is the number of coated fuel particles contained in the fuel element; According to the following formula (2), the modified volume proportion η of the coated fuel particles in the second region is determined: z2 , Among them, η is the initial volume proportion of the coated fuel particles, ξ is the volume proportion of the spheres when they are stacked together in a limited space in the most densely packed manner, is the target standard score, and N is the number of coated fuel particles contained in the fuel element.

5. The method for calculating the maximum temperature of a dispersed fuel element according to claim 1, characterized in that: Step S3 specifically includes: S31. Obtaining the temperature t1 of the outer boundary of the first region; S32. According to the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 , respectively determining a regional temperature increment of the first region and a regional temperature increment of the second region; S33. Calculate the temperature t at the center of the second region based on the temperature t1 of the outer boundary of the first region and the regional temperature increment of the first region and the regional temperature increment of the second region. max | r＝0 .

6. The method for calculating the maximum temperature of a dispersed fuel element according to claim 5, characterized in that: Step S32 specifically includes: S321. Make the coated fuel particles densely packed inside the first region, and divide the first region into two regions: the outer region is the region in the first region connected to the outer boundary of the fuel element and corresponding to the blank region of the coated fuel particles, which is set as the first matrix region D1; the inner region is the region in the first region corresponding to the dense region of the coated fuel particles, which is set as the first particle region D2, and The coated fuel particles are densely packed inside the second region, and the second region is divided, the region corresponding to the blank region of the coated fuel particles in the second region is set as the second matrix region D3, and the region corresponding to the dense region of the coated fuel particles in the second region is set as the second particle region D4; S322. According to the modified volume proportion η of the coated fuel particles in the first region z1 and the modified volume proportion η of the coated fuel particles in the second region z2 , respectively determine the radius of the first matrix region D1, the radius of the first particle region D2, the radius of the second matrix region D3 and the radius of the second particle region D4; S323. According to the radius of the first matrix region D1, the radius of the first particle region D2, the radius of the second matrix region D3 and the radius of the second particle region D4, respectively determine the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3 and the temperature increment t5 of the second particle region D4; Step S33 specifically includes: The temperature t1 at the outer boundary of the first region, the temperature increment t2 of the first matrix region D1, the temperature increment t3 of the first particle region D2, the temperature increment t4 of the second matrix region D3 and the temperature increment t5 of the second particle region D4 are summed to obtain the temperature t at the center of the second region. max | r＝0 .

7. The method for calculating the maximum temperature of a dispersed fuel element according to claim 6, characterized in that: Step S323 specifically includes: The temperature increment t2 of the first matrix region D1 from the outer boundary of the first matrix region D1 to the outer boundary of the first particle region D2 is determined according to the following formula (3): Wherein, Q is the total power of the dispersed fuel element, λ1 is the thermal conductivity of the first matrix region D1, r1 is the radius of the outer boundary of the first matrix region D1, and r2 is the radius of the outer boundary of the first particle region D2; The temperature increment t3 of the first particle region D2 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (4): Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ2 is the thermal conductivity of the first particle region D2, r2 is the radius of the outer boundary of the first particle region D2, and r3 is the radius of the outer boundary of the second matrix region D3; The temperature increment t4 of the second matrix region D3 from the outer boundary of the first particle region D2 to the outer boundary of the second matrix region D3 is determined according to the following formula (5): Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ3 is the thermal conductivity of the second matrix region D3, r3 is the radius of the outer boundary of the second matrix region D3, and r4 is the radius of the outer boundary of the second particle region D4; The temperature increment t5 of the second particle region D4 from the outer boundary of the second particle region D4 to the center of the second particle region D4 is determined according to the following formula (6): Among them, Q is the total power of the dispersed fuel element, N is the number of coated fuel particles contained in the fuel element, and ξ is the volume ratio of spheres when they are stacked together in a limited space in the most densely packed manner. is the target standard score, λ4 is the thermal conductivity of the second particle region D4, and r4 is the radius of the outer boundary of the second particle region D4.

8. The method for calculating the maximum temperature of a dispersed fuel element according to claim 6, characterized in that: Step S321 specifically includes: Performing iterative division of the densest packing of coated fuel particles on the second matrix region D3 and the second particle region D4, so as to divide the fuel element into 2n regions; The temperature t1 at the outer boundary of the first region and the temperature increments of the 2n regions are summed to obtain the temperature t at the center of the second region. max | r＝0 .

9. The method for calculating the maximum temperature of a dispersed fuel element according to claim 8, characterized in that: The method further comprises: According to the standard score in the correction factor, the probability P that the possible temperature is not higher than the calculated maximum temperature is determined according to the following formula (7): Among them, α is the target significance level, is the target standard score, is the cumulative probability density function, n is 1 / 2 of the 2n regions divided by the fuel element, and n is an integer greater than or equal to 2.

10. An engineering verification method for a dispersed fuel element, characterized in that: include: According to the calculation method according to any one of claims 1 to 8, the maximum temperature t of the fuel element is obtained. max ; According to the maximum temperature t max Conduct engineering verification on dispersed fuel elements to determine whether the dispersed fuel elements are qualified.

11. A device for calculating the maximum temperature of a dispersed fuel element, characterized in that: The device comprises: A division module, configured to divide the fuel element into regions to form a first region and a second region; the first region and the second region are distributed sequentially from the outer boundary of the fuel element to the center of the fuel element; A correction module is connected to the division module, and is configured to correct the initial volume proportion η of the coated fuel particles in the first region and the second region according to the probability distribution of the coated fuel particles in the first region and the second region, and respectively determine the modified volume proportion η of the coated fuel particles in the first region and the second region. z ; The obtaining module is connected to the correction module, which is configured to obtain the corrected volume proportion η of the coated fuel particles in the first region and the second region according to the corrected volume proportion η z , and the radii of the outer boundaries of the first and second regions, calculate the temperature t at the center of the second region max | r＝0 , to obtain the maximum temperature t of the fuel element max .

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