A method of modeling random distribution of triso fuel particles in an fcm fuel element

Abstract

The application discloses a modeling method of random distribution of TRISO fuel particles in FCM fuel elements, comprising the following steps: 1) setting the geometric parameters of the FCM fuel element; 2) layering the FCM fuel element to obtain N' layer FCM fuel element sub-regions, and calculating the number of TRISO fuel particles in each layer FCM fuel element sub-region; 3) setting a coordinate system and calculating the random distribution coordinates of the TRISO fuel particles in the X and Y directions in each layer FCM fuel element sub-region; 4) calculating the random distribution coordinates of the TRISO fuel particles in the Z direction in each layer FCM fuel element sub-region; 5) creating a geometric model of the FCM fuel element according to the random distribution coordinates, and using the difference set in Boolean operation to distinguish the FCM fuel element and the TRISO fuel particles, and the modeling is completed. The application realizes full three-dimensional modeling of the FCM fuel element, retains the complete five-layer structure of the TRISO fuel particles, and ensures the simulation effect of the in-pile behavior of the FCM fuel element.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of fuel particle random distribution modeling, and particularly relates to a modeling method of TRISO fuel particle random distribution in FCM fuel element. BACKGROUND

[0002] Full ceramic microencapsulation (FCM) fuel has excellent thermal performance and radiation resistance, and is an important research direction of new generation of fuel concept accident tolerant fuel (ATF). As a kind of dispersion fuel element, FCM fuel element is composed of a matrix and a large number of three-layer structure isotropic (TRISO) fuel particles. Specifically, the TRISO fuel particles formed by the fuel core, the buffer layer of loose pyrolytic carbon, the inner pyrolytic carbon (IPyC) layer, the silicon carbide (CVD-SiC) layer and the outer pyrolytic carbon (OPyC) layer are randomly dispersed in the matrix from the inside to the outside. Therefore, it is necessary to establish a TRISO fuel particle random distribution model in the FCM fuel element, so as to better simulate the behavior of the FCM fuel element in the nuclear reactor.

[0003] The existing modeling methods of FCM fuel element all have certain limitations. Most of the methods cannot simulate the overall structure of the FCM fuel element and the random distribution of the TRISO fuel particles in it. Although some methods can realize the full three-dimensional modeling of the FCM fuel element, the filling efficiency of the TRISO fuel particles is not high.

[0004] Therefore, it is still an urgent problem to be solved in this field to efficiently establish a performance analysis model of the FCM fuel element which can fully simulate the fuel behavior. SUMMARY

[0005] The purpose of the present application is to provide a modeling method of TRISO fuel particle random distribution in FCM fuel element, which comprises the following steps:

[0006] 1) setting the geometric parameters of the FCM fuel element;

[0007] The geometric parameters of the FCM fuel element include the filling rate of the TRISO fuel particles in the FCM fuel element, the size of the FCM fuel element, the width of the fuel-free area in the FCM fuel element, and the radius of each layer of the TRISO fuel particles.

[0008] The TRISO fuel particles include five layers, namely the core, the loose pyrolytic carbon layer, the inner pyrolytic carbon layer, the silicon carbide layer and the outer pyrolytic carbon layer.

[0009] 2) layering the FCM fuel element to obtain N' layers of FCM fuel element sub-regions, and calculating the number of TRISO fuel particles in each layer of FCM fuel element sub-region;

[0010] The number of layers N' of an FCM fuel element is as follows:

[0011] N′=floor(H / (2*r)) (1)

[0012] Where: floor() represents the floor function; r represents the radius of the TRISO fuel particle; H represents the height of the FCM fuel element.

[0013] The steps for calculating the number of TRISO fuel particles in each FCM fuel element sub-region include:

[0014] 2.1) Calculate the total number of TRISO fuel particles N in the FCM fuel element, that is:

[0015]

[0016] Wherein, round() represents the rounding function; V1 represents the volume of the FCM fuel element; V2 represents the volume of a TRISO fuel particle; F represents the filling rate of the TRISO fuel particles in the FCM fuel element; R represents the radius of the FCM fuel element; r represents the radius of the TRISO fuel particle; H represents the height of the FCM fuel element;

[0017] 2.2) Calculate the layer height h of each FCM fuel element sub-region, that is:

[0018] The calculation formula for the layer height of FCM fuel elements is:

[0019] h=H / N′ (3)

[0020] 2.3) Calculate the number n of TRISO fuel particles in the k-th FCM fuel element sub-region k ,Right now:

[0021] n k =n′+n″ k (4)

[0022] Where k = 1, 2, ..., N'; n' represents the basic number of TRISO fuel particles in each FCM fuel element sub-region; n" k represents the random number of TRISO fuel particles in the sub-region of the k-th layer FCM fuel element;

[0023] The basic number n′ of TRISO fuel particles in each FCM fuel element sub-region is as follows:

[0024] n′=floor(N / N′) (5)

[0025] where N' is the number of the layers of the FCM fuel element.

[0026] the random number n" of the TRISO fuel particles in each layer of the FCM fuel element sub-region k is determined by the number of the remaining TRISO fuel particles;

[0027] The step of determining the random number of the TRISO fuel particles in each layer includes:

[0028] a) calculating the number of the remaining TRISO fuel particles m, i.e.:

[0029] m = N - n' * N' (6)

[0030] b) inserting the remaining TRISO fuel particles randomly and without repetition into each layer of the FCM fuel element sub-region, the step including:

[0031] b.a) setting the initial value of the random number of the TRISO fuel particles in each layer of the FCM fuel element sub-region as 0;

[0032] directly generating a random sequence τ containing m integers between 1 and N' using the randperm(N', m) expression, 1≤τ i ≤N'; i = 1, 2, …, m; τ i is the i-th element in the random sequence τ;

[0033] b.b) adding 1 to the random number of the TRISO fuel particles in the τ i layer of the FCM fuel element sub-region.

[0034] 3) setting a coordinate system and calculating the random distribution coordinates of the TRISO fuel particles in the X and Y directions in each layer of the FCM fuel element sub-region.

[0035] The step of calculating the random distribution coordinates of the TRISO fuel particles in the X and Y directions in each layer of the FCM fuel element sub-region includes:

[0036] 3.1) randomly generating the X and Y coordinates of the TRISO fuel particles in the k-th layer of the FCM fuel element sub-region; the initial value of k is 1;

[0037] The X and Y coordinates of the sphere center of the i-th TRISO fuel particle in the k-th layer of the FCM fuel element sub-region are as follows:

[0038] x k = unifrnd(-(R - d - r), (R - d - r), [1 n k ]) (7)

[0039]

[0040] where 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer; x k represents the spherical X coordinate of the kth TRISO fuel particle in the kth FCM fuel element sub-region, which is a row vector; row vector x ki represents the spherical X coordinate of the ith TRISO fuel particle in the kth FCM fuel element sub-region; represents the spherical Y coordinate of the ith TRISO fuel particle in the kth FCM fuel element sub-region; unifrnd() represents a function of generating a random number matrix; d is the width of the unfueled region;

[0041] 3.2) Determine the direction of the resultant force on each TRISO fuel particle in the kth FCM fuel element sub-region, and calculate the total elastic potential energy of all TRISO fuel particles in the kth FCM fuel element sub-region;

[0042] The total elastic potential energy U of all TRISO fuel particles in the kth FCM fuel element sub-region is k as follows:

[0043]

[0044] where 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer;

[0045] where the elastic potential energy of the ith TRISO fuel particle in the kth FCM fuel element sub-region is as follows:

[0046]

[0047] where 1≤i≤n k , 1≤j≤n k , i≠j, and i and j are both integers;

[0048] where the depth of the ith TRISO fuel particle embedded in the jth TRISO fuel particle in the kth FCM fuel element sub-region is as follows:

[0049]

[0050] where 1≤i≤n k , 1≤j≤n k , i≠j, and i and j are both integers; represents the spherical Y coordinate of the jth TRISO fuel particle in the kth FCM fuel element sub-region; x kiXk,j,i represents the spherical center X coordinate of the jth TRISO fuel particle in the kth layer; abs() represents the absolute value function; and sqrt() represents the square root function.

[0051] Embedded depth between the ith TRISO fuel particle in the kth FCM fuel element sub-region and the side wall of the kth FCM fuel element As shown below:

[0052]

[0053] wherein 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer.

[0054] 3.3) determining whether the total elastic potential energy is lower than a set threshold value, if yes, outputting the X coordinate and Y coordinate of the TRISO fuel particle in the kth FCM fuel element sub-region, and entering step 4), otherwise updating the corresponding X coordinate and Y coordinate according to the direction of the resultant force suffered by each TRISO fuel particle in the kth FCM fuel element sub-region, and returning to step 3.2);

[0055] 3.4) determining whether the layer number k is less than N', if yes, setting k=k+1, and returning to step

[0056] 3.1), otherwise, outputting the random distribution coordinates of the TRISO fuel particles in the X and Y directions in each FCM fuel element sub-region.

[0057] 4) calculating the random distribution coordinates of the TRISO fuel particles in the Z direction in each FCM fuel element sub-region;

[0058] The step of calculating the random distribution coordinates of the TRISO fuel particles in the Z direction in each FCM fuel element sub-region includes:

[0059] 4.1) setting the upper limit value of the free interval of the TRISO fuel particle in the first FCM fuel element sub-region as (H-r), and the lower limit value of the free interval of the TRISO fuel particle in the N' th FCM fuel element sub-region as r;

[0060] 4.2) calculating the upper limit value of the free interval of the TRISO fuel particle in each FCM fuel element sub-region except the first layer, which includes:

[0061] determining whether the TRISO fuel particles in each FCM fuel element sub-region above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle;

[0062] if no, setting the upper limit value of the free interval of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the FCM fuel element sub-region in the previous layer.

[0063] If yes, calculate the Z coordinate of the current TRISO fuel particle when it is tangent to each TRISO fuel particle that obstructs its vertical upward movement along the Z direction, and take the minimum value;

[0064] Determine whether the minimum value is less than the Z coordinate value of the center circle plane of the FCM fuel element sub-region of the layer above the layer where the current TRISO fuel particle is located. If yes, set the upper limit value of the free interval of the current TRISO fuel particle as the minimum value. Otherwise, set the upper limit value of the free interval of the current TRISO fuel particle as the Z coordinate value of the center circle plane of the FCM fuel element sub-region of the layer above the layer where the current TRISO fuel particle is located;

[0065] The criterion for determining whether the TRISO fuel particles in each layer of the FCM fuel element sub-region above the current TRISO fuel particle obstruct the vertical upward movement of the current TRISO fuel particle is:

[0066] Determine whether formula (13) is true. If yes, the TRISO fuel particles in each layer of the FCM fuel element sub-region above the current TRISO fuel particle obstruct the vertical upward movement of the current TRISO fuel particle;

[0067]

[0068] wherein 2≤k1≤N′ and k1 is an integer, 1≤l<k and l is an integer; 1≤i≤n k and i is an integer, 1≤i′≤n l and i is an integer; represents the X coordinate of the spherical center of the i′th TRISO fuel particle in the lth layer; represents the Y coordinate of the spherical center of the i′th TRISO fuel particle in the lth layer;

[0069] 4.3) Calculate the lower limit value of the free interval of the TRISO fuel particles in the FCM fuel element sub-region of each layer except the N′th layer, which includes the following steps:

[0070] Determine whether the TRISO fuel particles in each layer of the FCM fuel element sub-region below the current TRISO fuel particle obstruct the vertical downward movement of the current TRISO fuel particle;

[0071] If no, set the lower limit value of the free interval of the current TRISO fuel particle as the Z coordinate value of the center circle plane of the FCM fuel element sub-region of the layer below the layer where the current TRISO fuel particle is located;

[0072] If yes, calculate the Z coordinate of the current TRISO fuel particle when it is tangent to each TRISO fuel particle that obstructs its vertical downward movement along the Z direction, and take the maximum value;

[0073] determining whether the maximum value is greater than the Z coordinate value of the center circle plane of the next layer FCM fuel element sub-region of the layer in which the current TRISO fuel particle is located, and if yes, setting the lower limit value of the free interval of the current TRISO fuel particle as the maximum value, otherwise, setting the lower limit value of the free interval of the current TRISO fuel particle as the Z coordinate value of the center circle plane of the next layer FCM fuel element sub-region;

[0074] The criterion for determining whether the TRISO fuel particles in each layer FCM fuel element sub-region below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle is:

[0075] determining whether formula (14) is established, and if yes, the TRISO fuel particles in each layer FCM fuel element sub-region below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle;

[0076]

[0077] wherein 1≤k2≤(N'-1) and k2 is an integer; 1≤i≤n k and i is an integer, 1≤i'≤n l and i is an integer; represents the X coordinate of the spherical center of the i'th TRISO fuel particle in the k+1 layer; represents the Y coordinate of the spherical center of the i'th TRISO fuel particle in the k+1 layer.

[0078] 4.4) Within the free interval range of the TRISO fuel particles in each layer FCM fuel element sub-region, the Z coordinate of the TRISO fuel particle is randomly determined by using the unifrnd() function.

[0079] 5) According to the randomly distributed coordinates, a geometric model of the FCM fuel element is created, and the difference set in Boolean operation is used to distinguish the FCM fuel element and the TRISO fuel particle, and the modeling is completed.

[0080] The technical effect of the present application is self-evident. The present application realizes the random distribution of the three-dimensional TRISO fuel particle spherical center coordinates by combining two-dimensional random and one-dimensional random, which not only completes the full three-dimensional modeling of the FCM fuel element, but also makes the filling efficiency of the TRISO fuel particle higher, and is suitable for all FCM fuel elements involving TRISO fuel particles dispersed in the matrix in the nuclear reactor.

[0081] The present application realizes the full three-dimensional modeling of the FCM fuel element, and retains the complete five-layer structure of the TRISO fuel particle, so as to ensure the simulation effect of the in-pile behavior of the FCM fuel element.

[0082] The application is widely applicable to the establishment of FCM fuel element models of various filling rates and has higher filling efficiency, and can efficiently complete the establishment of FCM fuel element models of TRISO fuel particles with a filling rate of more than 35%.

[0083] The application can realize the uniform axial distribution of TRISO fuel particles in the FCM fuel element model at a low filling rate through layering and setting a Z-direction free interval, and can better simulate the real distribution state of the TRISO fuel particles in the FCM fuel element.

[0084] The application realizes the random distribution of three-dimensional TRISO fuel particle spherical core coordinates in a two-dimensional random and one-dimensional random combined manner, is independent of the model, is innovative in method, and can give FCM fuel element models of different filling rates and different geometric sizes through parameterized modeling.

[0085] The random distribution modeling method of TRISO fuel particles in the FCM fuel element proposed in the application is applicable to the modeling of the FCM fuel of the nuclear reactor, but the ideas and methods mentioned in the application are also applicable to all FCM fuel elements in which TRISO fuel particles are dispersed in the matrix in the nuclear reactor. BRIEF DESCRIPTION OF DRAWINGS

[0086] Fig. 1 A flow chart of the random distribution modeling method of TRISO fuel particles in the FCM fuel element;

[0087] Fig. 2 A schematic diagram of the random distribution of TRISO fuel particles in the FCM fuel element;

[0088] Fig. 3 A cross-sectional view of the FCM fuel element.

[0089] In the figure, 1 is a TRISO fuel particle, 2 is a cross-sectional local enlargement of the FCM fuel element, 3 is a fuel-free zone, and 4 is a matrix. DETAILED DESCRIPTION

[0090] The application will be further described below in conjunction with examples, but should not be understood as limiting the above-mentioned subject matter of the application to the following examples. According to ordinary technical knowledge and conventional means in the art, various substitutions and changes can be made without departing from the above-mentioned technical ideas of the application, and all should be included in the protection scope of the application.

[0091] Example 1

[0092] Referring to Figs. 1-3 A random distribution modeling method of TRISO fuel particles in a FCM fuel element includes the following steps:

[0093] 1) Set the geometric parameters of the FCM fuel element composed of TRISO fuel particles 1 and matrix 4; the local enlarged view of the FCM fuel element cross section is shown as No. 2 in the figure. Fig. 2

[0094] The geometric parameters of the FCM fuel element include the filling rate of TRISO fuel particles 1 in the FCM fuel element, the size of the FCM fuel element, the width of the fuel-free area 3 in the FCM fuel element, and the radius of each layer of the TRISO fuel particles;

[0095] The TRISO fuel particles include five layers, namely the core, the loose pyrolytic carbon layer, the inner dense pyrolytic carbon layer, the silicon carbide layer, and the outer dense pyrolytic carbon layer.

[0096] 2) Stratify the FCM fuel element to obtain N' layers of FCM fuel element sub-regions, and calculate the number of TRISO fuel particles in each layer of FCM fuel element sub-region;

[0097] The stratification number N' of the FCM fuel element is as follows:

[0098] N' = floor (H / (2*r)) (1)

[0099] Wherein: floor() represents the floor function; r represents the radius of the TRISO fuel particles; H represents the height of the FCM fuel element.

[0100] The step of calculating the number of TRISO fuel particles in each layer of FCM fuel element sub-region includes:

[0101] 2.1) Calculate the total number N of TRISO fuel particles in the FCM fuel element, that is:

[0102]

[0103] Wherein, round() represents the rounding function; V1 represents the volume of the FCM fuel element; V2 represents the volume of one TRISO fuel particle; F represents the filling rate of TRISO fuel particles in the FCM fuel element; R represents the radius of the FCM fuel element; r represents the radius of the TRISO fuel particles; H represents the height of the FCM fuel element;

[0104] 2.2) Calculate the layer height h of each layer of FCM fuel element sub-region, that is:

[0105] The calculation formula of the layer height of the stratification of the FCM fuel element is:

[0106] h = H / N' (3)

[0107] 2.3) Calculate the number n of TRISO fuel particles in the kth layer of FCM fuel element sub-region​k i.e.

[0108] n k = n' + n" k (4)

[0109] wherein k = 1, 2, …, N'; n' represents the base number of TRISO fuel particles in each FCM fuel element sub-region; n" k represents the random number of TRISO fuel particles in the k-th FCM fuel element sub-region;

[0110] wherein the base number n' of TRISO fuel particles in each FCM fuel element sub-region is as follows:

[0111] n' = floor(N / N') (5)

[0112] wherein N' is the number of sub-regions of FCM fuel elements.

[0113] The random number n" of TRISO fuel particles in each FCM fuel element sub-region k is determined by the number of remaining TRISO fuel particles;

[0114] The step of determining the random number of TRISO fuel particles in each layer includes:

[0115] a) calculating the number of remaining TRISO fuel particles m, i.e.

[0116] m = N - n' * N' (6)

[0117] b) randomly and non-repetitively inserting the remaining TRISO fuel particles into each FCM fuel element sub-region, which includes:

[0118] b.a) setting the initial value of the random number of TRISO fuel particles in each FCM fuel element sub-region to 0;

[0119] directly generating a random sequence of m integers between 1 and N' using the randperm(v', m) expression, 1≤τ i ≤N'; i = 1, 2, …, m; τ i is the i-th element in the random sequence τ;

[0120] b.b) adding 1 to the random number of TRISO fuel particles in the τ i -th FCM fuel element sub-region.

[0121] 3) setting a coordinate system and calculating the random distribution coordinates of TRISO fuel particles in each FCM fuel element sub-region in the X and Y directions.

[0122] The step of calculating the random distribution coordinates of the TRISO fuel particles in the X and Y directions in each layer FCM fuel element sub-region includes:

[0123] 3.1) Randomly generate the X and Y coordinates of the TRISO fuel particles in the kth layer FCM fuel element sub-region; the initial value of k is 1;

[0124] The X and Y coordinates of the sphere center of the ith TRISO fuel particle in the kth layer FCM fuel element sub-region are as follows:

[0125] x k = unifrnd(-(R-d-r), (R-d-r), [1 n k ]) (7)

[0126]

[0127] wherein 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer; x k represents the X coordinate of the sphere center of the kth layer TRISO fuel particle, which is a row vector; the row vector x ki represents the X coordinate of the sphere center of the ith TRISO fuel particle in the kth layer FCM fuel element sub-region; represents the Y coordinate of the sphere center of the ith TRISO fuel particle in the kth layer; unifrnd() represents a function for generating a random number matrix; d is the width of the unfueled region;

[0128] 3.2) Determine the direction of the resultant force on each TRISO fuel particle in the kth layer FCM fuel element sub-region, and calculate the total elastic potential energy of all TRISO fuel particles in the kth layer FCM fuel element sub-region;

[0129] The total elastic potential energy U k of all TRISO fuel particles in the kth layer FCM fuel element sub-region is as follows:

[0130]

[0131] wherein 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer;

[0132] wherein the elastic potential energy of the ith TRISO fuel particle in the kth layer FCM fuel element sub-region is as follows:

[0133]

[0134] wherein 1≤i≤n​k , 1≤j≤n k , i≠j, and i, j are integers;

[0135] wherein the depth of the i-th TRISO fuel particle in the k-th layer FCM fuel element sub-region embedded into the j-th TRISO fuel particle as follows:

[0136]

[0137] wherein 1≤i≤n k , 1≤j≤n k , i≠j, and i, j are integers; represents the Y-coordinate of the center of the k-th layer j-th TRISO fuel particle; x ki represents the X-coordinate of the center of the k-th layer j-th TRISO fuel particle; abs() represents the absolute value function; sqrt() represents the square root function;

[0138] the depth of the i-th TRISO fuel particle in the k-th layer FCM fuel element sub-region embedded into the side wall of the k-th layer FCM fuel element as follows:

[0139]

[0140] wherein 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer.

[0141] 3.3) judging whether the total elastic potential energy is lower than a set threshold value, if yes, outputting the X-coordinate and Y-coordinate of the TRISO fuel particle in the k-th layer FCM fuel element sub-region, and entering step 4), otherwise updating the corresponding X-coordinate and Y-coordinate according to the direction of the resultant force suffered by each TRISO fuel particle in the k-th layer FCM fuel element sub-region, and returning to step 3.2);

[0142] 3.4) judging whether the layer number k is less than N', if yes, setting k=k+1, and returning to step 3.1), otherwise outputting the random distribution coordinates of the TRISO fuel particles in the X and Y directions in each layer FCM fuel element sub-region.

[0143] 4) calculating the random distribution coordinates of the TRISO fuel particles in the Z direction in each layer FCM fuel element sub-region;

[0144] The step of calculating the random distribution coordinates of the TRISO fuel particles in the Z direction in each layer FCM fuel element sub-region comprises:

[0145] 4.1) Set the upper limit of free space of TRISO fuel particles in the first layer FCM fuel element sub-region as (H-r), and the lower limit of free space of TRISO fuel particles in the N'th layer FCM fuel element sub-region as r;

[0146] 4.2) Calculate the upper limit of free space of TRISO fuel particles in the FCM fuel element sub-region of other layers except the first layer, the steps include:

[0147] Determine whether the TRISO fuel particles in each layer FCM fuel element sub-region above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle;

[0148] If not, set the upper limit of free space of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the last layer FCM fuel element sub-region;

[0149] If yes, calculate the Z coordinate when the movement of the current TRISO fuel particle along the Z direction is tangent to the TRISO fuel particles that hinder its vertical upward movement, and take the minimum value;

[0150] Determine whether the minimum value is less than the Z coordinate value of the central circular plane of the last layer FCM fuel element sub-region of the layer where the current TRISO fuel particle is located, if yes, set the upper limit of free space of the current TRISO fuel particle as the minimum value, otherwise, set the upper limit of free space of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the last layer FCM fuel element sub-region;

[0151] The criterion for determining whether the TRISO fuel particles in each layer FCM fuel element sub-region above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle is:

[0152] Determine whether formula (13) is true, if yes, the TRISO fuel particles in each layer FCM fuel element sub-region above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle;

[0153]

[0154] wherein, 2≤k1≤N' and k1 is an integer, 1≤l<k and l is an integer; 1≤i≤n k and i is an integer, 1≤i'≤n l and i is an integer; represents the X coordinate of the spherical center of the i'th TRISO fuel particle in the l'th layer; represents the Y coordinate of the spherical center of the i'th TRISO fuel particle in the l'th layer;

[0155] 4.3) Calculate the lower limit of the free space of the TRISO fuel particles in the FCM fuel element sub-region other than the N' layer, the steps include:

[0156] Determine whether the TRISO fuel particles in the FCM fuel element sub-region below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle;

[0157] If not, set the lower limit of the free space of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the next layer FCM fuel element sub-region;

[0158] If yes, calculate the Z coordinate when the movement of the current TRISO fuel particle along the Z direction is tangent to the TRISO fuel particles hindering its vertical downward movement, and take the maximum value;

[0159] Determine whether the maximum value is greater than the Z coordinate value of the central circular plane of the next layer FCM fuel element sub-region of the layer where the current TRISO fuel particle is located, if yes, set the lower limit of the free space of the current TRISO fuel particle as the maximum value, otherwise, set the lower limit of the free space of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the next layer FCM fuel element sub-region;

[0160] The criterion for determining whether the TRISO fuel particles in the FCM fuel element sub-region below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle is:

[0161] Determine whether formula (14) is true, if yes, the TRISO fuel particles in the FCM fuel element sub-region below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle;

[0162]

[0163] wherein, 1≤k2≤(N'-1) and k2 is an integer; 1≤i≤n k and i is an integer, 1≤i'≤n l and i is an integer; represents the X coordinate of the spherical center of the i'th TRISO fuel particle in the k+1 layer; represents the Y coordinate of the spherical center of the i'th TRISO fuel particle in the k+1 layer.

[0164] 4.4) In the free space range of the TRISO fuel particles in each layer FCM fuel element sub-region, the Z coordinate of the TRISO fuel particle is randomly determined by using the unifrnd() function.

[0165] 5) Create the geometric model of FCM fuel element according to random distribution coordinates, and use the difference set in Boolean operation to distinguish FCM fuel element and TRISO fuel particle, and end the modeling.

[0166] Example 2:

[0167] A modeling method of random distribution of TRISO fuel particles in FCM fuel element, which realizes the random distribution of three-dimensional TRISO fuel particle spherical core coordinates by the combination of two-dimensional random and one-dimensional random, can complete the full three-dimensional modeling of FCM fuel element under different fuel-free zone widths, and is suitable for all FCM fuel elements involving TRISO fuel particles dispersed in the matrix in nuclear reactors; in addition, compared with the existing full three-dimensional modeling method, the filling efficiency of TRISO fuel particles is higher, and the five-layer structure of TRISO fuel particles is not simplified to ensure the simulation effect of the in-pile behavior of FCM fuel element.

[0168] The method is specifically implemented as follows:

[0169] Step 1: Set the geometric parameters.

[0170] Set the filling rate of TRISO fuel particles in FCM fuel element; set the size of FCM fuel element, set the fuel-free zone width, set the radius of each layer of TRISO fuel particles; when modeling TRISO fuel particles, the five-layer structure of TRISO fuel particles is not simplified, and the five-layer structure is respectively the core, the buffer pyrolytic carbon layer, the inner pyrolytic carbon layer, the silicon carbide layer and the outer pyrolytic carbon layer, so as to ensure the simulation effect of the in-pile behavior of FCM fuel element.

[0171] Step 2: Layer the FCM fuel element, and calculate the number of TRISO fuel particles in each layer.

[0172] The total number of TRISO fuel particles in the FCM fuel element is calculated according to the parameters set in step 1 by using the round() function in MATLAB language, which can round the number in the parentheses to the nearest integer. At the same time, the FCM fuel element is layered according to the size of the FCM fuel element and the outer diameter of the outermost layer of the TRISO fuel particle, and the number of layers is determined by using the floor() function in MATLAB language, which can round down the number in the parentheses to the nearest integer. Then the layer height is calculated by the height of the FCM fuel element and the number of layers. Finally, the number of TRISO fuel particles in each layer is determined by adding the base number and the random number, wherein the base number is calculated by using the floor() function according to the total number of TRISO fuel particles and the number of layers, and the random number is determined by using the randperm(p, q) function in MATLAB language, where p ≥ q, which can randomly generate q random integers between 1 and p.

[0173] The total number of TRISO fuel particles is calculated by the formula:

[0174]

[0175] In the formula:

[0176] N represents the total number of TRISO fuel particles in the FCM fuel element;

[0177] round() is a rounding function in MATLAB language, which can round the number in the parentheses to the nearest integer;

[0178] V1 represents the volume of the FCM fuel element;

[0179] V2 represents the volume of a TRISO fuel particle;

[0180] F represents the filling rate of TRISO fuel particles in the FCM fuel element, i.e. the ratio of the sum of the volumes of all TRISO fuel particles to the volume of the FCM fuel element;

[0181] R represents the radius of the FCM fuel element;

[0182] r represents the radius of the TRISO fuel particle;

[0183] H represents the height of the FCM fuel element;

[0184] The number of layers of the FCM fuel element is calculated by the formula:

[0185] N' = floor(H / (2*r)) (2)

[0186] In the formula:

[0187] N'—N' represents the number of layers of the FCM fuel element layering;

[0188] floor()—the floor function in MATLAB language, which can round down the number in the parentheses to the nearest integer;

[0189] The calculation formula of the layer height of the FCM fuel element layering is:

[0190] h=H / N' (3)

[0191] In the formula:

[0192] h—h represents the layer height of the FCM fuel element layering;

[0193] The calculation formula of the number of TRISO fuel particles in each layer is:

[0194] n k =n'+n" k (4)

[0195] In the formula:

[0196] n k —n k represents the number of TRISO fuel particles in the kth layer;

[0197] n'—n' represents the base number of TRISO fuel particles in each layer;

[0198] n" k —n" k represents the random number of TRISO fuel particles in the kth layer;

[0199] The calculation formula of the base number of TRISO fuel particles in each layer is:

[0200] n'=floor(N / N') (5)

[0201] The calculation of the random number of TRISO fuel particles in each layer is as follows: Since n'≤N / N', after removing the base number of TRISO fuel particles in each layer, the total number of TRISO fuel particles still remains, and the number of remaining TRISO fuel particles is less than or equal to N'. Considering the randomness of the distribution of TRISO fuel particles, the remaining TRISO fuel particles will be randomly and repeatedly inserted into each layer of the FCM fuel element.

[0202] The calculation formula of the number of remaining TRISO fuel particles is:

[0203] m=N-n'*N' (6)

[0204] In the formula: m represents the number of remaining TRISO fuel particles;

[0205] The remaining TRISO fuel particles will be inserted into the layers of the FCM fuel element randomly and non-repetitively, specifically according to the following method: m integers are randomly generated between 1 and N' using the randperm(N', m) expression, and the m integers are corresponded to the layer numbers of the FCM fuel element from top to bottom numbered from 1 to N', and the random number of TRISO fuel particles in these layers is 1, and the random number of TRISO fuel particles in the remaining layers is 0. For example: assuming that there is a number τ in the m integers, 1≤τ≤N' and τ is an integer, then the random number of TRISO fuel particles in the τth layer from top to bottom is 1.

[0206] Step 3: Calculate the random distribution coordinates of TRISO fuel particles in each layer in the X and Y directions.

[0207] It is assumed that the Z-direction positions of TRISO fuel particles in the same layer are all on the central circular plane of the layer, then taking this plane as the research object, the side surface of the FCM fuel element can be abstracted as a large circular container, and the TRISO fuel particles can be abstracted as small elastic circular cakes. This method uses the idea of simulation, and believes that when these small elastic circular cakes are congested in the closed large circular container, they will move to their respective equilibrium positions in a very short time according to the elastic force they receive, so that the deformation they receive is minimized. This method can achieve high efficiency of filling, and easily realize a FCM fuel element model with higher TRISO fuel particle filling rate.

[0208] Specifically, for each layer of the FCM fuel element, the first step is to randomly generate a number of XY coordinates equal to the number of TRISO fuel particles corresponding to the layer, representing the XY coordinates of the centers of the TRISO fuel particles. The second step is to perform a force analysis to calculate the magnitude and direction of the force received by the small circular cake corresponding to each TRISO fuel particle, and to calculate the sum of the elastic potential energy of all small circular cakes in the layer at this time, i.e. the total elastic potential energy, by the elastic potential energy formula. The third step is to determine whether the total elastic potential energy is lower than the set threshold value, if yes, it is considered that the XY coordinate set meeting the condition is found, and the loop is exited; otherwise, the fourth step is performed. The fourth step is to determine the moving direction of the small circular cake by the direction of the force received by the small circular cake, and to move to the new XY coordinates in the direction of the force to obtain the new XY coordinates, and then return to the second step.

[0209] The XY coordinates of the centers of the TRISO fuel particles are mainly realized by the unifrnd() function in MATLAB language, which can generate a random number matrix in a specified range, such as unifrnd(a, b, [p q]) which generates a random number matrix of p rows and q columns in the range [a, b]. Specifically, the formula for randomly generating the XY coordinates of the centers of the TRISO fuel particles is:

[0210] x kunifrnd(-(R-d-r), (R-d-r), [1 n k ]) (7)

[0211]

[0212] wherein:

[0213] 1≤k≤N′ and k is an integer, 1≤i≤n k and i is an integer;

[0214] x k — x k represents the spherical center X coordinate of the kth layer TRISO fuel particle, and is a row vector; represents the spherical center Y coordinate of the ith TRISO fuel particle in the kth layer;

[0215] represents the spherical center X coordinate of the ith TRISO fuel particle in the kth layer;

[0216] unifrnd() - a function in MATLAB language, which can generate a random number matrix in a specified range;

[0217] The elastic potential energy of the small pie includes the extrusion elastic potential energy between small pies and the extrusion elastic potential energy between small pies and large annular rings, which are calculated according to the embedding depth between different small pies and the embedding depth of small pies and large annular rings respectively;

[0218] Preferably, the calculation formula of the embedding depth between the ith and jth small pies in the kth layer is:

[0219]

[0220] wherein:

[0221] 1≤k≤N′ and k is an integer;

[0222] 1≤i≤n k , 1≤j≤n k , i≠j, and i, j are both integers;

[0223] represents the embedding depth between the ith and jth small pies in the kth layer; represents the spherical center Y coordinate of the jth TRISO fuel particle in the kth layer;

[0224] represents the spherical center X coordinate of the jth TRISO fuel particle in the kth layer;

[0225] abs() - an absolute value function in MATLAB language, which can calculate the absolute value of the number in the parentheses;

[0226] sqrt() - square root function in MATLAB language, which can square the numbers in the parentheses;

[0227] The calculation formula of the embedding depth between the kth layer and the ith small pie and the large ring is:

[0228]

[0229] In the formula:

[0230] 1≤k≤N′ and k is an integer, 1≤i≤n k And i is an integer;

[0231] Indicates the embedding depth between the kth layer and the ith small pie and the large ring;

[0232] The calculation formula of the elastic potential energy of the kth layer and the ith small pie is:

[0233]

[0234] In the formula:

[0235] 1≤k≤N′ and k is an integer;

[0236] 1≤i≤n k , 1≤j≤n k , i≠j, and i, j are integers;

[0237] Indicates the elastic potential energy of the kth layer and the ith small pie;

[0238] Preferably, the calculation formula of the total elastic potential energy of the kth layer is:

[0239]

[0240] In the formula:

[0241] 1≤k≤N′ and k is an integer, 1≤i≤n k And i is an integer;

[0242] U k - U k Indicates the total elastic potential energy of the kth layer;

[0243] The set threshold value of the total elastic potential energy is 10 -7 here.

[0244] Step 4: Calculate the Z-direction random distribution coordinates of each layer TRISO fuel particle.

[0245] The X, Y direction random distribution coordinates of each layer of TRISO fuel particles have been determined according to step 3, i.e. it has been ensured that the TRISO fuel particles in each layer do not overlap. It is worth noting that step 3 also preliminarily sets the Z direction positions of the TRISO fuel particles in the same layer on the central circular plane of the layer. It is convenient to calculate the Z direction free interval of each TRISO fuel particle from top to bottom to meet the condition that neither overlaps with other TRISO fuel particles nor exceeds the FCM fuel element boundary, and then randomly determine the Z coordinate using the unifrnd() function in MATLAB language.

[0246] The upper limit value of the free interval of the first layer of TRISO fuel particles from top to bottom is (H-r), and the lower limit value of the free interval of the last layer is r.

[0247] The calculation method of the upper limit value of the free interval of the TRISO fuel particles in other layers except the first layer is as follows: first, determine whether there are TRISO fuel particles above the TRISO fuel particle that hinder its vertical upward movement, i.e. whether it affects the upper limit value of its free interval. If so, calculate the Z coordinate when the TRISO fuel particle moves along the Z direction and is tangent to each TRISO fuel particle that hinders its vertical upward movement, take the minimum value, and compare it with the Z coordinate value of the central circular plane of the layer above the TRISO fuel particle, and the upper limit value of the free interval of the TRISO fuel particle is the smaller one; if not, the upper limit value of the free interval of the TRISO fuel particle is the Z coordinate value of the central circular plane of the layer above it.

[0248] The calculation method of the lower limit value of the free interval of the TRISO fuel particles in other layers except the last layer is as follows: first, determine whether there are TRISO fuel particles below the TRISO fuel particle that hinder its vertical downward movement, i.e. whether it affects the lower limit value of its free interval. If so, calculate the Z coordinate when the TRISO fuel particle moves along the Z direction and is tangent to each TRISO fuel particle that hinders its vertical downward movement, take the maximum value, and compare it with the Z coordinate value of the central circular plane of the layer below the TRISO fuel particle, and the lower limit value of the free interval of the TRISO fuel particle is the larger one; if not, the upper limit value of the free interval of the TRISO fuel particle is the Z coordinate value of the central circular plane of the layer below it.

[0249] The formula for determining whether there are TRISO fuel particles affecting the upper limit value of the free interval of the i th TRISO fuel particle in the k th layer is:

[0250]

[0251] In the formula:

[0252] 2≤k≤N′ and k is an integer, 1≤l<k and l is an integer;

[0253] 1≤i≤n k and i is an integer, 1≤i'≤n l and i is an integer;

[0254] represents the X-coordinate of the spherical center of the i'th TRISO fuel particle in the lth layer;

[0255] represents the Y-coordinate of the spherical center of the i'th TRISO fuel particle in the lth layer;

[0256] The formula for determining whether a TRISO fuel particle affects the lower limit value of the free interval of the i'th TRISO fuel particle in the kth layer is:

[0257]

[0258] In the formula:

[0259] 1≤k≤(N'-1) and k is an integer;

[0260] 1≤i≤n k and i is an integer, 1≤i'≤n l and i is an integer;

[0261] represents the X-coordinate of the spherical center of the i'th TRISO fuel particle in the k+1th layer;

[0262] represents the Y-coordinate of the spherical center of the i'th TRISO fuel particle in the k+1th layer;

[0263] Step 5: Create the geometry of the FCM fuel element, use the difference set in Boolean operation to distinguish the FCM fuel element and the TRISO fuel particle, and end the modeling.

[0264] Example 3:

[0265] A modeling method for the random distribution of TRISO fuel particles in an FCM fuel element, comprising the following steps:

[0266] 1) Set the geometric parameters of the FCM fuel element;

[0267] 2) Layer the FCM fuel element to obtain N' FCM fuel element sub-regions, and calculate the number of TRISO fuel particles in each layer of FCM fuel element sub-region;

[0268] 3) Set up a coordinate system and calculate the random distribution coordinates of TRISO fuel particles in the X and Y directions in each layer of FCM fuel element sub-region.

[0269] 4) Calculate the random distribution coordinates of TRISO fuel particles in the Z direction in each layer FCM fuel element sub-area;

[0270] 5) Create a geometric model of the FCM fuel element according to the random distribution coordinates, and distinguish the FCM fuel element and the TRISO fuel particles by using the difference set in Boolean operation, and the modeling is completed.

[0271] Example 4:

[0272] A modeling method of random distribution of TRISO fuel particles in a FCM fuel element, the main content of which is seen in Example 3, wherein the geometric parameters of the FCM fuel element include the filling rate of TRISO fuel particles in the FCM fuel element, the size of the FCM fuel element, the width of the fuel-free area in the FCM fuel element, and the radius of each layer of TRISO fuel particles.

[0273] The TRISO fuel particles include five layers, namely the core, the loose pyrolytic carbon layer, the inner dense pyrolytic carbon layer, the silicon carbide layer and the outer dense pyrolytic carbon layer.

[0274] Example 5:

[0275] A modeling method of random distribution of TRISO fuel particles in a FCM fuel element, the main content of which is seen in Example 3, wherein the number of layers N' of the FCM fuel element is as follows:

[0276] N' = floor(H / (2*r)) (1)

[0277] In the formula, floor() represents the floor function; r represents the radius of the TRISO fuel particles; and H represents the height of the FCM fuel element.

[0278] Example 6:

[0279] A modeling method of random distribution of TRISO fuel particles in a FCM fuel element, the main content of which is seen in Example 3, wherein the step of calculating the number of TRISO fuel particles in each layer FCM fuel element sub-area includes:

[0280] 1) Calculate the total number N of TRISO fuel particles in the FCM fuel element, that is:

[0281]

[0282] In the formula, round() represents the rounding function; V1 represents the volume of the FCM fuel element; V2 represents the volume of a TRISO fuel particle; F represents the filling rate of TRISO fuel particles in the FCM fuel element; R represents the radius of the FCM fuel element; r represents the radius of the TRISO fuel particles; and H represents the height of the FCM fuel element.

[0283] 2) Calculate the layer height h of each FCM fuel element sub-region, that is:

[0284] The calculation formula for the layer height of FCM fuel elements is:

[0285] h=H / N′ (3)

[0286] 3) Calculate the number n of TRISO fuel particles in the k-th layer FCM fuel element sub-region k ,Right now:

[0287] n k =n′+n″ k (4)

[0288] Where k = 1, 2, ..., N'; n' represents the basic number of TRISO fuel particles in each FCM fuel element sub-region; n" k represents the random number of TRISO fuel particles in the sub-region of the k-th layer FCM fuel element;

[0289] The basic number n′ of TRISO fuel particles in each FCM fuel element sub-region is as follows:

[0290] n′=floor(N / N′) (5)

[0291] Where N' is the number of layers of the FCM fuel element.

[0292] Example 7:

[0293] A modeling method for the random distribution of TRISO fuel particles in FCM fuel elements, the main content of which is shown in Example 3, wherein the random number n" of TRISO fuel particles in each sub-region of the FCM fuel element is k The value of is determined by the number of remaining TRISO fuel particles;

[0294] The steps for determining the random number of TRISO fuel particles per layer include:

[0295] 1) Calculate the number of remaining TRISO fuel particles m, that is:

[0296] m=Nn′*N′ (6)

[0297] 2) randomly and non-repeatedly inserting the remaining TRISO fuel particles into the FCM fuel element sub-regions of each layer, the steps comprising:

[0298] 2.1) Set the initial value of the random number of TRISO fuel particles in each FCM fuel element sub-region to 0;

[0299] A random sequence τ of m integers between 1 and N' is generated directly by the randperm(N', m) expression, 1≤τ i ≤N'; i = 1, 2, …, m; τ i is the i-th element in the random sequence τ;

[0300] 2.2) Increment the random number of TRISO fuel particles in the i-th sub-region of the k-th layer FCM fuel element by 1. i

[0301] Example 8:

[0302] A modeling method for random distribution of TRISO fuel particles in a FCM fuel element, the main content of which is seen in Example 3, wherein the step of calculating the random distribution coordinates of TRISO fuel particles in the X and Y directions in each sub-region of each layer FCM fuel element comprises:

[0303] 1) Randomly generate the X and Y coordinates of TRISO fuel particles in the k-th layer FCM fuel element sub-region; k is initially 1;

[0304] 2) Determine the direction of the resultant force on each TRISO fuel particle in the k-th layer FCM fuel element sub-region, and calculate the total elastic potential energy of all TRISO fuel particles in the k-th layer FCM fuel element sub-region;

[0305] 3) Determine whether the total elastic potential energy is lower than the set threshold value, if yes, output the X and Y coordinates of TRISO fuel particles in the k-th layer FCM fuel element sub-region, and go to step 4), otherwise, update the corresponding X and Y coordinates according to the direction of the resultant force on each TRISO fuel particle in the k-th layer FCM fuel element sub-region, and return to step 2);

[0306] 4) Determine whether the layer number k < N' is true, if yes, let k = k + 1, and return to step 1), otherwise, output the random distribution coordinates of TRISO fuel particles in the X and Y directions in each layer FCM fuel element sub-region.

[0307] Example 9:

[0308] A modeling method for random distribution of TRISO fuel particles in a FCM fuel element, the main content of which is seen in Example 3, wherein the X and Y coordinates of the ball center of the i-th TRISO fuel particle in the k-th layer FCM fuel element sub-region are as follows:

[0309] x k = unifrnd(-(R-d-r), (R-d-r), [1 n k ]) (7)

[0310] ​

[0311] where 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer; x k represents the spherical center X coordinate of the kth layer TRISO fuel particle, and is a row vector; row vector represents the spherical center X coordinate of the ith TRISO fuel particle in the kth layer FCM fuel element sub-region; represents the spherical center Y coordinate of the ith TRISO fuel particle in the kth layer; unifrnd() represents a function of generating a random number matrix; d is the width of the unfueled region;

[0312] Example 10:

[0313] A modeling method of random distribution of TRISO fuel particles in a FCM fuel element, the main content of which is seen in Example 3, wherein the total elastic potential energy U of all TRISO fuel particles in the kth layer FCM fuel element sub-region k is as follows:

[0314]

[0315] where 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer;

[0316] where the elastic potential energy of the ith TRISO fuel particle in the kth layer FCM fuel element sub-region is as follows:

[0317]

[0318] where 1≤i≤n k , 1≤j≤n k , i≠j, and i and j are both integers;

[0319] where the depth of the ith TRISO fuel particle embedded in the jth TRISO fuel particle in the kth layer FCM fuel element sub-region is as follows:

[0320]

[0321] where 1≤i≤n k , 1≤j≤n k , i≠j, and i and j are both integers; represents the spherical center Y coordinate of the jth TRISO fuel particle in the kth layer; x kiXk j represents the spherical center X coordinate of the jth TRISO fuel particle in the kth layer; abs() represents the absolute value function; and sqrt() represents the square root function.

[0322] Embedded depth between the ith TRISO fuel particle in the kth FCM fuel element sub-region and the side wall of the kth FCM fuel element As shown below:

[0323]

[0324] wherein 1≤k≤N' and k is an integer, 1≤i≤n k and i is an integer.

[0325] Example 11:

[0326] A modeling method of random distribution of TRISO fuel particles in an FCM fuel element, the main content of which is shown in Example 3, wherein the step of calculating the random distribution coordinates of TRISO fuel particles in the Z direction in each layer FCM fuel element sub-region includes:

[0327] 1) Set the upper limit value of the free interval of the TRISO fuel particles in the first layer FCM fuel element sub-region as (H-r), and the lower limit value of the free interval of the TRISO fuel particles in the N' layer FCM fuel element sub-region as r;

[0328] 2) Calculate the upper limit value of the free interval of the TRISO fuel particles in the FCM fuel element sub-region of other layers except the first layer, which includes:

[0329] Determine whether the TRISO fuel particles in each layer FCM fuel element sub-region above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle;

[0330] If not, set the upper limit value of the free interval of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the last layer FCM fuel element sub-region;

[0331] If yes, calculate the Z coordinate value when the movement of the current TRISO fuel particle along the Z direction is tangent to each TRISO fuel particle that hinders the vertical upward movement of the current TRISO fuel particle, and take the minimum value;

[0332] Determine whether the minimum value is less than the Z coordinate value of the central circular plane of the last layer FCM fuel element sub-region in the layer where the current TRISO fuel particle is located, if yes, set the upper limit value of the free interval of the current TRISO fuel particle as the minimum value, otherwise, set the upper limit value of the free interval of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the last layer FCM fuel element sub-region;

[0333] 3) calculating the lower limit of the free space of the TRISO fuel particles in the FCM fuel element sub-region other than the N' layer, the steps comprising:

[0334] determining whether the TRISO fuel particles in each layer FCM fuel element sub-region above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle;

[0335] if not, setting the lower limit of the free space of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the next layer FCM fuel element sub-region;

[0336] if yes, calculating the Z coordinate when the movement of the current TRISO fuel particle along the Z direction is tangent to the TRISO fuel particles that hinder its vertical downward movement, and taking the maximum value;

[0337] determining whether the maximum value is greater than the Z coordinate value of the central circular plane of the next layer FCM fuel element sub-region in the layer where the current TRISO fuel particle is located, if yes, setting the lower limit of the free space of the current TRISO fuel particle as the maximum value, otherwise, setting the lower limit of the free space of the current TRISO fuel particle as the Z coordinate value of the central circular plane of the next layer FCM fuel element sub-region;

[0338] 4) within the free space range of the TRISO fuel particles in each layer FCM fuel element sub-region, the Z coordinate of the TRISO fuel particle is randomly determined using the unifrnd() function.

[0339] Example 12:

[0340] A modeling method for the random distribution of TRISO fuel particles in an FCM fuel element, the main content of which is seen in Example 3, wherein the criterion for determining whether the TRISO fuel particles in each layer FCM fuel element sub-region above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle is:

[0341] determining whether formula (13) is true, if yes, the TRISO fuel particles in each layer FCM fuel element sub-region above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle;

[0342]

[0343] wherein 2≤k1≤N' and k1 is an integer, 1≤l<k and l is an integer; 1≤i≤n k and i is an integer, 1≤i'≤n l and i is an integer; denotes the X coordinate of the center of the lth layer i'th TRISO fuel particle; Yk+i′ represents the spherical center Y coordinate of the i'th TRISO fuel particle in the k+1th layer;

[0344] The criterion for judging whether the TRISO fuel particles in the sub-regions of the FCM fuel elements in the layers below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle is:

[0345] If formula (14) is true, the TRISO fuel particles in the sub-regions of the FCM fuel elements in the layers below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle.

[0346]

[0347] wherein 1≤k2≤(N'-1) and k2 is an integer; 1≤i≤n k and i is an integer, 1≤i'≤n l and i is an integer; Xk+i′ represents the spherical center X coordinate of the i'th TRISO fuel particle in the k+1th layer; Yk+i′ represents the spherical center Y coordinate of the i'th TRISO fuel particle in the k+1th layer.

Claims

1. A modeling method for the random distribution of TRISO fuel particles in FCM fuel elements, characterized in that: The following steps are involved: 1) Setting the geometric parameters of the FCM fuel element; 2) Layering the FCM fuel element to obtain N′ layers of FCM fuel element sub-regions, and calculating the number of TRISO fuel particles in each layer of FCM fuel element sub-region; 3) Setting up a coordinate system and calculating the random distribution coordinates of TRISO fuel particles in the sub-regions of each layer of FCM fuel elements in the X and Y directions; 4) Calculate the random distribution coordinates of TRISO fuel particles in the Z direction within the sub-regions of each layer of FCM fuel elements; 5) Create a geometric model of the FCM fuel element based on the randomly distributed coordinates, and use the difference in Boolean operations to distinguish between the FCM fuel element and the TRISO fuel particles. The modeling is completed. The steps for calculating the number of TRISO fuel particles in each FCM fuel element sub-region include: 2.1) Calculate the total number of TRISO fuel particles N in the FCM fuel element, that is: Wherein, round( ) represents the rounding function; V1 represents the volume of the FCM fuel element; V2 represents the volume of a TRISO fuel particle; F represents the filling rate of the TRISO fuel particles in the FCM fuel element; R represents the radius of the FCM fuel element; r represents the radius of the TRISO fuel particle; H represents the height of the FCM fuel element; 2.2) Calculate the layer height h of each FCM fuel element sub-region, that is: The calculation formula for the layer height of FCM fuel elements is: h=H / N′ (3) 2.3) Calculate the number n of TRISO fuel particles in the k-th FCM fuel element sub-region k ,Right now: n k =n′+n″ k (4) Where k = 1, 2, ..., N'; n' represents the basic number of TRISO fuel particles in each FCM fuel element sub-region; n" k represents the random number of TRISO fuel particles in the sub-region of the k-th layer FCM fuel element; The basic number n′ of TRISO fuel particles in each FCM fuel element sub-region is as follows: n′=floor(N / N′) (5) Where N′ is the number of layers of the FCM fuel element; The steps of calculating the random distribution coordinates of TRISO fuel particles in the Z direction within the sub-regions of each layer of FCM fuel elements include: 4.1) The upper limit of the free range of TRISO fuel particles in the first layer of FCM fuel element sub-region is set to (Hr), and the lower limit of the free range of TRISO fuel particles in the N′th layer of FCM fuel element sub-region is set to r; 4.2) Calculating the upper limit of the free range of TRISO fuel particles in the FCM fuel element sub-regions of all layers except the first layer, the steps include: Determine whether the TRISO fuel particles in the FCM fuel element sub-regions above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle; If not, then set the upper limit of the current TRISO fuel particle free range to the Z coordinate value of the center circle plane of the FCM fuel element sub-region in the previous layer; If so, calculate the Z coordinate when the current TRISO fuel particle moving in the Z direction is exactly tangent to each TRISO fuel particle that hinders its vertical upward movement, and take the minimum value; Determine whether the minimum value is less than the Z coordinate value of the center circle plane of the FCM fuel element sub-region of the previous layer where the current TRISO fuel particle is located. If so, set the upper limit value of the free range of the current TRISO fuel particle to the minimum value; otherwise, set the upper limit value of the free range of the current TRISO fuel particle to the Z coordinate value of the center circle plane of the FCM fuel element sub-region of the previous layer; 4.3) Calculating the lower limit of the free range of TRISO fuel particles in the FCM fuel element sub-regions of all layers except the N′ layer, the steps include: Determine whether the TRISO fuel particles in the FCM fuel element sub-regions below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle; If not, then set the lower limit of the current TRISO fuel particle free range to the Z coordinate value of the center circle plane of the next layer of FCM fuel element sub-region; If so, calculate the Z coordinate when the current TRISO fuel particle moving in the Z direction is exactly tangent to each TRISO fuel particle that hinders its vertical downward movement, and take the maximum value; Determine whether the maximum value is greater than the Z coordinate value of the center circle plane of the FCM fuel element sub-region of the next layer where the current TRISO fuel particle is located. If so, set the lower limit value of the free range of the current TRISO fuel particle to the maximum value; otherwise, set the lower limit value of the free range of the current TRISO fuel particle to the Z coordinate value of the center circle plane of the FCM fuel element sub-region of the next layer; 4.4) Within the free range of TRISO fuel particles in each FCM fuel element sub-region, the Z coordinate of the TRISO fuel particles is randomly determined using the unifrnd() function.

2. The modeling method for random distribution of TRISO fuel particles in an FCM fuel element according to claim 1, characterized in that: The geometric parameters of the FCM fuel element include the filling rate of TRISO fuel particles in the FCM fuel element, the size of the FCM fuel element, the width of the fuel-free zone in the FCM fuel element, and the radius of each layer of TRISO fuel particles; The TRISO fuel particles include five layers, namely a core, a loose pyrolytic carbon layer, an inner dense pyrolytic carbon layer, a silicon carbide layer and an outer dense pyrolytic carbon layer.

3. The modeling method for random distribution of TRISO fuel particles in an FCM fuel element according to claim 1, characterized in that: The number of layers N' of an FCM fuel element is as follows: N′=floor(H / (2*r)) (1) Where: floor( ) represents the floor function; r represents the radius of the TRISO fuel particle; H represents the height of the FCM fuel element.

4. The modeling method for random distribution of TRISO fuel particles in an FCM fuel element according to claim 1, characterized in that: The random number b″ ​​of TRISO fuel particles in each FCM fuel element sub-region k The value of is determined by the number of remaining TRISO fuel particles; The steps for determining the random number of TRISO fuel particles per layer include: 1) Calculate the number of remaining TRISO fuel particles m, that is: n=Nn′*N′ (6) 2) randomly and non-repeatedly inserting the remaining TRISO fuel particles into the FCM fuel element sub-regions of each layer, the steps comprising: 2.1) Set the initial value of the random number of TRISO fuel particles in each FCM fuel element sub-region to 0; Use the randperm(N′,m) expression to directly randomly generate a random sequence τ containing m integers between 1 and N′, 1≤τ i ≤N′;i=1,2,…,m;τ i is the i-th element in the random sequence τ; 2.2) Let τ i The random number of TRISO fuel particles in the FCM fuel element sub-region of the layer is increased by 1.

5. The modeling method for random distribution of TRISO fuel particles in an FCM fuel element according to claim 1, characterized in that: The steps of calculating the random distribution coordinates of TRISO fuel particles in the sub-regions of each layer of FCM fuel elements in the X and Y directions include: 1) Randomly generate the X and Y coordinates of the TRISO fuel particles in the k-th layer of the FCM fuel element sub-region; the initial value of k is 1; 2) Determine the direction of the resultant force acting on each TRISO fuel particle within the k-th layer FCM fuel element sub-region, and calculate the total elastic potential energy of all TRISO fuel particles within the k-th layer FCM fuel element sub-region; 3) Determine whether the total elastic potential energy is lower than a set threshold. If so, output the X and Y coordinates of the TRISO fuel particles in the k-th layer FCM fuel element sub-region and proceed to step 4). Otherwise, update the corresponding X and Y coordinates of each TRISO fuel particle in the k-th layer FCM fuel element sub-region according to the direction of the resultant force acting on the TRISO fuel particle, and return to step 2). 4) Determine whether the number of layers k < N′ holds true. If so, set k = k + 1 and return to step 1). Otherwise, output the randomly distributed coordinates of the TRISO fuel particles in the sub-regions of the FCM fuel elements in each layer in the X and Y directions.

6. The modeling method for random distribution of TRISO fuel particles in an FCM fuel element according to claim 5, characterized in that: The X-coordinate and Y-coordinate of the center of the i-th TRISO fuel particle in the k-th FCM fuel element sub-region are as follows: x k =unifrnd(-(R-d-r),(R-d-r),[1 n k ]) (7) Where 1≤k≤N′ and k is an integer, 1≤i≤n k And i is an integer; x k represents the X coordinate of the center of the k-th TRISO fuel particle, which is a row vector; x ki represents the X coordinate of the center of the i-th TRISO fuel particle in the k-th FCM fuel element sub-region; represents the Y coordinate of the center of the i-th TRISO fuel particle in the k-th layer; unifrnd() represents the function of generating a random number matrix; d is the width of the fuel-free zone.

7. The modeling method for random distribution of TRISO fuel particles in an FCM fuel element according to claim 5, characterized in that: The total elastic potential energy U of all TRISO fuel particles in the k-th layer FCM fuel element sub-region k As shown below: Where 1≤k≤N′ and k is an integer, 1≤i≤n k and i is an integer; The elastic potential energy of the i-th TRISO fuel particle in the k-th FCM fuel element sub-region is As shown below: Where, 1≤i≤n k , 1≤j≤n k , i≠j, and i and j are both integers; The depth of the i-th TRISO fuel particle embedded in the j-th TRISO fuel particle in the k-th FCM fuel element sub-region is As shown below: Where, 1≤i≤n k , 1≤j≤n k , i≠j, and i and j are both integers; represents the Y coordinate of the center of the jth TRISO fuel particle in the kth layer; x ki represents the X coordinate of the center of the j-th TRISO fuel particle in the k-th layer; abs() represents the absolute value function; sqrt() represents the square root function; The embedding depth between the i-th TRISO fuel particle in the k-th FCM fuel element sub-region and the side wall of the k-th FCM fuel element As shown below: Where 1≤k≤N′ and k is an integer, 1≤i≤n k And i is an integer.

8. The modeling method for random distribution of TRISO fuel particles in an FCM fuel element according to claim 1, characterized in that: The criteria for determining whether the TRISO fuel particles in the FCM fuel element sub-regions above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle are: Determine whether formula (13) is valid. If so, the TRISO fuel particles in the FCM fuel element sub-regions above the current TRISO fuel particle hinder the vertical upward movement of the current TRISO fuel particle. where \(2\leq k_1\leq N'\) and \(k_1\) is an integer, \(1\leq l < k\) and \(l\) is an integer; \(1\leq i\leq n\) k and \(i\) is an integer, \(1\leq i'\leq n\) l and \(i\) is an integer; represents the X coordinate of the center of the \(i'\)-th TRISO fuel particle in the \(l\)-th layer; represents the Y coordinate of the center of the \(i'\)-th TRISO fuel particle in the \(l\)-th layer; The criteria for determining whether the TRISO fuel particles in the FCM fuel element sub-regions below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle are: Determine whether formula (14) is valid. If so, the TRISO fuel particles in the FCM fuel element sub-regions below the current TRISO fuel particle hinder the vertical downward movement of the current TRISO fuel particle. Where, 1≤k2≤(N′-1) and k2 is an integer; 1≤i≤n k And i is an integer, 1≤i′≤n l and i is an integer; represents the X coordinate of the center of the i′th TRISO fuel particle in the k+1th layer; represents the Y coordinate of the center of the i′th TRISO fuel particle in the k+1th layer.

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