Method for neutron transport calculation or resonance calculation for dispersion fuel

Abstract

This invention relates to a method for neutron transport calculation or resonance calculation for dispersed fuels. The method is characterized by correcting the matrix chord length probability and average chord length used in related calculations based on the true chord length probability distribution and true average chord length of the matrix, and pre-constructing an interpolation table or fitting formula for solving the true average chord length correction factor using dimensionless parameters. The method for solving the true chord length probability distribution and true average chord length of the matrix includes the following steps: setting the geometric shape of a random medium region according to the fuel type; generating a random distribution of particle positions within the given random medium region according to a given filling rate; randomly selecting particle surfaces to isotropically emit neutrons outwards, or uniformly and isotropically emitting neutrons from the matrix, and calculating the distance to the next particle; statistically analyzing the chord lengths of all neutrons passing through the matrix, thereby obtaining the true chord length probability distribution and true average chord length of the matrix.

Description

Technical Field

[0001] This invention relates to a method for calculating neutron transport or resonance for dispersed fuels, particularly a method for calculating the chord length of a random medium in the field of nuclear reactor physics calculations. Background Technology

[0002] Dispersed fuel elements in nuclear reactors reduce the risk of radioactive leakage by randomly dispersing various types of coated particles within a matrix, and are therefore widely used in advanced nuclear reactors. Common dispersed fuels include: spherical or cylindrical fuel elements composed of three-layer coated isotropic (TRISO) fuel particles dispersed in a graphite matrix used in high-temperature gas-cooled reactors; fully ceramic micro-encapsulated (FCM) fuel used in advanced pressurized water reactors; plate-shaped dispersed fuels used in some research reactors or special-purpose reactors; and various geometric forms of dispersed fuels used in other new types of reactors such as space reactors.

[0003] Dispersed fuels differ from traditional nuclear fuel elements. Due to the presence of randomly distributed coating particles within the fuel, they exhibit dual inhomogeneity, which poses challenges to neutron transport calculations based on Monte Carlo and deterministic methods.

[0004] Deterministic computational methods for stochastic media mainly include the Hébert method and the Sanchez method, as well as a series of methods related to stochastic media resonance processing, such as the analytical calculation method for the Dankov factor of fuel in high-temperature gas-cooled reactors. The implementation of these methods requires the direct or indirect use of the matrix chord length probability distribution and the matrix mean chord length. Furthermore, the matrix chord length probability distribution is also needed in the Monte Carlo chord length sampling (CLS) method for stochastic media.

[0005] Therefore, the chord length probability distribution is an important foundation for deterministic computational methods in stochastic media and Monte Carlo chord length sampling methods. In publicly available literature on stochastic media physics computation, the matrix chord length probability and average chord length, based on theoretical approximations, are commonly used.

[0006] During neutron transport in a random medium, the matrix chord length includes three cases: ① the distance from a neutron entering the random medium region from another region to the next particle surface along the flight direction; ② the distance from a neutron exiting from one particle surface to another particle surface along the flight direction; ③ the distance from a neutron colliding in the matrix to the next particle surface along the flight direction.

[0007] In existing deterministic computational procedures for random media, the chord length l of the random medium matrix is ​​assumed to follow the following exponential distribution:

[0008]

[0009] Where l is the theoretical average chord length of the matrix:

[0010]

[0011] Where ρ is the particle filling rate and r is the particle radius.

[0012] When considering multiple particle types, the average chord length of the matrix is:

[0013]

[0014] Where, ρ i Let r be the filling rate of the i-th type of particles. i Let be the radius of the i-th type of particle.

[0015] Some literature has statistically analyzed the probability distribution of the true chord length, but its conclusion is that it fits well with the exponential distribution. Therefore, the chord length probability distribution described in formulas (1), (2), and (3) above is still used in existing calculation procedures. Some literature has also attempted to use the true mean chord length in the Monte Carlo chord length sampling method, but the process of statistically analyzing the true mean chord length is approximate.

[0016] Through research, the inventors discovered that the difference between the matrix chord length probability distribution described in the above formulas (1), (2), and (3) and the actual chord length distribution will cause a non-negligible calculation deviation in the neutron transport calculation results. Therefore, they proposed to correct the matrix chord length probability distribution and the average chord length.

[0017] Therefore, it is hoped that the theoretically approximate matrix chord length probability distribution and average chord length can be corrected in neutron transport calculations or resonance calculations for dispersed fuels, so as to improve the accuracy of deterministic calculation methods for random media and Monte Carlo chord length sampling methods. Summary of the Invention

[0018] To address the aforementioned technical problems, this application provides a method for neutron transport calculation or resonance calculation of dispersed fuels. The method is characterized by correcting the matrix chord length probability and average chord length used in the relevant calculations based on the true chord length probability distribution and the true average chord length of the matrix. The method for solving for the true chord length probability distribution and the true average chord length of the matrix includes the following steps:

[0019] Set the geometry of the random medium region according to the fuel type;

[0020] A random distribution of particle positions is generated within a given random medium region according to a given filling rate;

[0021] The distance to the next particle is calculated by randomly selecting the surface of a particle to emit neutrons isotropically to the outside, or by uniformly and isotropically emitting neutrons from the matrix. When the ray encounters the boundary of a random medium region, sampling is performed according to isotropic reflection or specular reflection.

[0022] The true string length probability distribution and true average string length of the matrix are obtained by statistically analyzing the string lengths of all neutrons passing through it.

[0023] In this way, a high-fidelity random medium model is constructed by randomly generating particle coordinate positions, and then the probability density distribution of the true chord length of the matrix and the true average chord length are statistically analyzed by random ray tracing.

[0024] Preferably, the random distribution of particle positions is generated within a given random medium region according to a given fill rate using the Random Sequence Addition (RSA) method. However, the present invention is not limited to generating a random distribution of particle positions using the RSA method.

[0025] Preferably, in the step of generating a random distribution of particle positions within a given random medium region according to a given filling rate, the random number seed is changed to generate multiple sets of particle position distributions in order to reduce statistical fluctuations in particle positions.

[0026] Preferably, the neutron transport calculation or resonance calculation method requires the use of deterministic calculation methods of string length probability distribution or Monte Carlo string length sampling methods.

[0027] In deterministic calculation methods for random media or Monte Carlo chord length sampling methods, this invention proposes two ways to modify the relevant calculation processes of the original methods based on the true chord length probability distribution and the true average chord length of the matrix.

[0028] In a preferred embodiment of the neutron transport calculation or resonance calculation method according to the present invention, the theoretical approximate average chord length used in the relevant calculation process is directly replaced by the actual average chord length of the matrix. In this case, the corrected chord length probability density distribution is:

[0029]

[0030] in, This represents the true average chord length.

[0031] In another preferred embodiment of the neutron transport calculation or resonance calculation method according to the present invention, the theoretical approximate chord length probability distribution and theoretical approximate average chord length used in the correlation calculation process are replaced by piecewise functions that approximate the true chord length probability distribution and the true average chord length of the matrix. Similarly, the theoretical approximate chord length probability distribution and theoretical approximate average chord length used in the correlation calculation process can also be replaced by rational function expansions that approximate the true chord length probability distribution and the true average chord length of the matrix.

[0032] Preferably, the piecewise function is a different function on both sides of the critical chord length and is continuous at the critical chord length. The integral of the piecewise function over the chord length from 0 to +∞ is equal to 1, and the integral of the product of the piecewise function and the chord length over the chord length from 0 to +∞ is equal to the true average chord length of the matrix.

[0033] For example, in a preferred embodiment of the neutron transport calculation or resonance calculation method according to the present invention, the piecewise function is from 0 to the critical chord length l. c The interval is a quadratic function, and the critical chord length l is... c The function is exponential up to +∞. That is, we can assume that l∈(0,l) c ) satisfies a quadratic function distribution, l∈(l c The expression ,∞) satisfies an exponential distribution.

[0034]

[0035] Piecewise functions should satisfy the following relationship:

[0036] f1(l c )=f2(l c (6)

[0037]

[0038]

[0039] Figure 1 This is a comparison diagram of the true chord length probability distribution and the theoretical chord length probability distribution of the matrix in the neutron transport calculation or resonance calculation method for dispersed fuels according to the present invention. A schematic diagram of the true chord length probability distribution of the matrix is ​​given. It can be seen that there is a certain difference between the matrix chord length l and the exponential distribution given by formula (1), especially in (0, l). c The differences are large within the interval (0, l), but large within (0, l). c Within the interval of ), quadratic functions can be used to fit it well.

[0040] To improve the usability of the chord length correction method, interpolation tables or fitting equations can be pre-constructed. These tables or equations can use parameters such as particle radius, random medium region size, and filling rate as independent variables, and parameters such as the true average chord length and critical chord length as dependent variables. However, to broaden the applicability of the interpolation tables or fitting equations, the applicant further proposes pre-constructing interpolation tables or fitting equations for solving the true average chord length using dimensionless parameters. The independent variables of these tables or equations include dimensionless parameters constructed from particle radius, random medium region size, and filling rate, while the dependent variables include dimensionless parameters constructed from the true average chord length and critical chord length. In a preferred embodiment of the neutron transport calculation or resonance calculation method according to the present invention, the dimensionless parameters include the random medium size ratio and the filling rate, wherein the random medium size ratio h is the ratio of the random medium region size L to the particle radius r, as shown in the following equation:

[0041]

[0042] Here, L is used to measure the macroscopic size of the random medium region. For example, when the random medium region is a sphere or a one-dimensional cylinder, L can represent the radius or diameter; when the random medium region is a cube, L can represent its side length. When the size of the random medium region differs in different dimensions, the size ratio h of multiple dimensions can be defined separately. x h y h z .

[0043] The dimensionless parameters also include an average chord length correction factor and a critical chord length factor, wherein the average chord length correction factor α is the ratio of the actual average chord length to the theoretical average chord length, as shown in the following formula:

[0044]

[0045] The critical chord length factor β is the ratio of the critical chord length to the particle radius, representing the critical chord length l. c The ratio to the particle radius r is shown in the following formula:

[0046]

[0047] Using the above dimensionless parameters, construct an interpolation table or fitting equation: the independent variables are the fill rate ρ and the random medium size ratio h, and the dependent variables are the average chord length correction factor α and the critical chord length factor β.

[0048] By pre-setting different fill ratios ρ and random medium size ratios h, and solving for the true chord length probability distribution and true average chord length of the matrix using the method described above, the corresponding average chord length correction factor α and critical chord length factor β are obtained, resulting in the two-dimensional interpolation table shown below:

[0049]

[0050] Or we can obtain the following fitting function relationship:

[0051] α=f a (ρ,h) (12)

[0052] β=f b (ρ,h) (13)

[0053] In neutron transport calculations in random media, based on the actual input parameters, the corresponding mean chord length correction factor α0 and critical chord length factor β0 are calculated by looking up the interpolation table or solving the fitting equation, thereby calculating the true mean chord length and critical chord length of the matrix:

[0054]

[0055] l c =rβ0 (15)

[0056] It should be understood that, in addition to the dimensionless parameters mentioned above, other dimensionless parameters can be constructed based on this idea as alternatives without affecting the implementation of this invention. For example, the definition of the critical chord length factor β can be changed to the ratio of the critical chord length to the true average chord length, etc. Attached Figure Description

[0057] Embodiments of the present invention are illustrated below with reference to the accompanying drawings. In the drawings:

[0058] Figure 1 This is a comparison diagram of the true chord length probability distribution and the theoretical chord length probability distribution of the matrix in the neutron transport calculation or resonance calculation method for dispersed fuels according to the present invention;

[0059] Figure 2 The flowchart schematically illustrates the steps for random medium chord length correction in the neutron transport calculation or resonance calculation method for dispersed fuels according to the present invention. Detailed Implementation

[0060] The following section uses fuel spheres from a high-temperature gas-cooled reactor as the calculation object and provides an application example using the true mean chord length correction. The standard design parameters are: random dielectric region radius 2.5 cm, TRISO particle radius 0.046 cm, filling ratio 7%, and corresponding random dielectric size ratio of 54.35.

[0061] Step 1: Calculate the true mean chord length of the matrix.

[0062] First, the RSA method is used to randomly and uniformly generate a particle position distribution with a given filling rate within a sphere of a given radius.

[0063] Then, neutrons are randomly selected from the surface of a particle and emitted isotropically to the outside, or neutrons are emitted uniformly and isotropically from the matrix, and the distance to the next particle is calculated; when the ray encounters a boundary, sampling is performed according to isotropic reflection or specular reflection.

[0064] Finally, the matrix chord lengths through which all neutrons passed were counted to obtain the true average matrix chord length. Calculate the true mean chord length With the theoretical average chord length The ratio of α to β is the mean chord length correction factor α.

[0065] Step 2: Generate the average chord length correction factor interpolation table

[0066] Repeat step 1 by changing the fill ratio ρ and the random medium size ratio h respectively. For simplicity, set parameters ρ and h to 0.5 times, 1 times, and 2 times the standard design parameters respectively, and calculate the corresponding average chord length correction factor α to obtain the following two-dimensional interpolation table:

[0067]

[0068] Step 3: Correction of matrix mean chord length

[0069] In the calculation of random media, the theoretical average chord length is first calculated based on the actual filling ratio and particle radius. Based on the actual fill ratio and size ratio, the mean chord length correction factor α0 is obtained through interpolation. Then, the true matrix mean chord length is calculated using the mean chord length correction factor. Finally, the matrix chord length probability distribution given by formula (4) is used to perform random medium transport calculations or resonance calculations.

[0070] Figure 2 The above steps 1-3 of the random medium chord length correction are illustrated in flowchart form.

[0071] The preferred embodiments of the present invention have been described above, but the spirit and scope of the present invention are not limited to the specific contents disclosed herein. Those skilled in the art can make many more implementations and applications based on the teachings of the present invention, including any combination of the various technical features of the above embodiments. These implementations and applications are all within the spirit and scope of the present invention. The spirit and scope of the present invention are not limited by the specific embodiments, but by the claims.

Claims

1. A method for calculating neutron transport or resonance in dispersed fuels, characterized in that, The matrix chord length probability and average chord length used in the relevant calculations are corrected based on the true chord length probability distribution and the true average chord length of the matrix. The method for solving the true chord length probability distribution and the true average chord length of the matrix includes the following steps: Set the geometry of the random medium region according to the fuel type; A random distribution of particle positions is generated within a given random medium region according to a given filling rate; The distance to the next particle is calculated by randomly selecting the surface of a particle to emit neutrons isotropically to the outside, or by uniformly and isotropically emitting neutrons from the matrix. When the ray encounters the boundary of a random medium region, sampling is performed according to isotropic reflection or specular reflection. The true string length probability distribution and true average string length of the matrix are obtained by statistically analyzing the string lengths of all neutrons passing through it.

2. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 1, characterized in that, By using a random sequence addition method, a random distribution of particle positions is generated within a given random medium region according to a given filling rate.

3. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 1, characterized in that, In the step of generating a random distribution of particle positions within a given random medium region according to a given filling rate, the random number seed is changed to generate multiple sets of particle position distributions.

4. The method for neutron transport calculation or resonance calculation of dispersed fuels according to any one of claims 1 to 3, characterized in that, The neutron transport calculation or resonance calculation method requires the use of deterministic calculation methods or Monte Carlo methods based on the chord length probability distribution.

5. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 4, characterized in that, The actual average chord length of the matrix is ​​directly replaced by the theoretical approximate average chord length used in the relevant calculation process.

6. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 5, characterized in that, The theoretical approximate chord length probability distribution and theoretical approximate average chord length used in the relevant calculation process are replaced by a piecewise function of the true chord length probability distribution and the true average chord length that approximates the matrix.

7. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 5, characterized in that, The theoretical approximate chord length probability distribution and theoretical approximate average chord length used in the relevant calculation process are replaced by rational function expansions that approximate the true chord length probability distribution and the true average chord length of the matrix.

8. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 6, characterized in that, The piecewise function is a different function on both sides of the critical chord length and is continuous at the critical chord length. The integral of the piecewise function over the chord length from 0 to +∞ is equal to 1. The integral of the product of the piecewise function and the chord length over the chord length from 0 to +∞ is equal to the true average chord length of the matrix.

9. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 8, characterized in that, The piecewise function is a quadratic function between 0 and the critical chord length, and an exponential function between the critical chord length and +∞.

10. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 5, characterized in that, An interpolation table or fitting formula for solving the true average chord length is constructed in advance using dimensionless parameters. The independent variables of the interpolation table or fitting equation include dimensionless parameters constructed from particle radius, random medium region size, and filling rate, while the dependent variables include dimensionless parameters constructed from true average chord length and critical chord length.

11. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 10, characterized in that, The dimensionless parameters include the random medium size ratio and the filling rate, wherein the random medium size ratio is the ratio of the random medium region size to the particle radius.

12. The method for neutron transport calculation or resonance calculation of dispersed fuels according to claim 10, characterized in that, The dimensionless parameters include the average chord length correction factor and the critical chord length factor, wherein the average chord length correction factor is the ratio of the true average chord length to the theoretical average chord length, and the critical chord length factor is the ratio of the critical chord length to the particle radius.

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