JP7349379B2 - Fuel rod output analysis method, analysis device, and fuel rod output analysis program - Google Patents

Description

The present disclosure relates to a fuel rod output analysis method, an analysis device, and a fuel rod output analysis program.

BACKGROUND ART Analyzers that perform analysis of a reactor core loaded with fuel assemblies are conventionally known (for example, see Patent Document 1). The analysis device calculates the nuclear constant of the fuel assembly, which is the input data for the core calculation, by calculating the nuclear constant of the fuel assembly, and performs the core calculation based on the calculated nuclear constant. Characteristics are being calculated.

Japanese Patent Application Publication No. 2016-156739

In Patent Document 1, in order to suppress an increase in calculation load without deteriorating calculation accuracy, in nuclear constant calculation, a large number of energy groups are group-reduced to a small number of groups, and neutron transport calculations based on the small number of groups are performed. is running.

By the way, as a reactor core, for example, there is a fast reactor that generates a nuclear fission reaction using fast neutrons. A fast reactor has a shielding material placed around the fuel assembly to be loaded. When using a shielding material containing magnesium oxide (MgO), which is composed of light nuclei with high neutron moderating ability, as a fast reactor shielding material, the shielding material slows down and reflects neutrons, so the reflected neutrons This becomes a thermal neutron, and the fuel rods of the fuel assembly that are close to the shielding material are susceptible to nuclear fission reactions. When analyzing such a core, it is necessary to accurately consider the behavior of the fuel rods in the fuel assembly near the shielding material, but when performing core analysis using multiple energy groups, it is generally Due to the handling of nuclear constants and nuclear properties in the low-energy region (<100 eV) where the influence is small, the analysis results were not numerically stable, and it was sometimes difficult to accurately simulate the behavior of the fuel rods.

Therefore, the present disclosure provides a fuel rod that can stably and accurately analyze the local output of the fuel rod even when a shielding material containing light nuclides is placed around the fuel assembly in a fast reactor. The object of the present invention is to provide an output analysis method, an analysis device, and a fuel rod output analysis program.

A fuel rod output analysis method of the present disclosure is a fuel rod output analysis method executed in an analysis device that analyzes the local output of a fuel rod of a fuel assembly loaded in a fast reactor using an analytical model. The analytical model includes the fuel assembly and a shielding material provided around the fuel assembly, and calculates the nuclear constant of the fuel assembly to determine the Calculating a shape function of a fuel assembly and group reduction of the shape function to a few groups smaller than many groups; and performing core calculations of the fast reactor to determine boundaries regarding neutron flux in the energy groups of the multiple groups. calculating a condition and group reducing the boundary condition to the minority group; calculating a homogeneous neutron flux of the fuel assembly based on the boundary condition after the group reduction; and after the group reduction. and calculating the local power of the fuel rod based on the shape function of the fuel rod and the homogeneous neutron flux.

An analysis device of the present disclosure includes a processing unit that uses an analysis model to analyze the local power of a fuel rod of a fuel assembly loaded in a fast reactor, wherein the analysis model includes the fuel assembly, The model includes a shielding material provided around the fuel assembly, and the processing unit calculates the nuclear constant of the fuel assembly and determines the shape of the fuel assembly in multiple energy groups. calculating a function and group-reducing the shape function to a few groups smaller than the many groups; and calculating a core calculation of the fast reactor to calculate a boundary condition regarding neutron flux in the energy group of the multiple groups; a step of group-reducing the boundary conditions to the minority group; a step of calculating a homogeneous neutron flux of the fuel assembly based on the boundary conditions after group reduction; and a step of group-reducing the shape function after group reduction. calculating the local power of the fuel rod based on the homogeneous neutron flux.

The fuel rod output analysis program of the present disclosure is a fuel rod output analysis program that causes an analysis device to analyze the local output of a fuel rod of a fuel assembly loaded in a fast reactor using an analytical model. The model includes the fuel assembly and a shielding material provided around the fuel assembly, and calculates the nuclear constant of the fuel assembly to determine the fuel in multiple energy groups. Calculating the shape function of the aggregate and group-reducing the shape function to a few groups smaller than the many groups, and calculating the core of the fast reactor to determine the boundary conditions regarding the neutron flux in the energy group of the multiple groups. calculating the homogeneous neutron flux of the fuel assembly based on the boundary conditions after the group reduction, and calculating the homogeneous neutron flux of the fuel assembly after the group reduction. calculating the local power of the fuel rod based on the shape function and the homogeneous neutron flux.

According to the present disclosure, even when a shielding material containing light nuclides is arranged around a fuel assembly in a fast reactor, the local output of a fuel rod can be stably and precisely analyzed.

FIG. 1 is a diagram of an analysis model used in the analysis apparatus of this embodiment. FIG. 2 is an explanatory diagram regarding the mesh set in the analytical model. FIG. 3 is a schematic configuration diagram schematically showing the analysis device according to this embodiment. FIG. 4 is an explanatory diagram regarding calculation of local power of a fuel rod. FIG. 5 is a flowchart regarding a method for analyzing fuel rod output according to this embodiment.

Embodiments according to the present disclosure will be described in detail below based on the drawings. Note that the present invention is not limited to this embodiment. Furthermore, the constituent elements in the embodiments described below include those that can be easily replaced by those skilled in the art, or those that are substantially the same. Furthermore, the constituent elements described below can be combined as appropriate, and if there are multiple embodiments, it is also possible to combine each embodiment.

[This embodiment]
In the fuel rod output analysis method and analysis device according to the present embodiment, the fuel assembly loaded in the fast reactor is calculated by dividing the calculation into two stages: nuclear constant calculation, which is the first stage, and core calculation, which is the second stage. The local power output of the fuel rods in the body is being evaluated. Note that the fast reactor is not particularly limited, and may be applied to, for example, a fast breeder reactor or a dedicated furnace. First, prior to explaining the analysis of fuel rod output, an analytical model of a fast reactor to be analyzed will be explained with reference to FIGS. 1 and 2.

FIG. 1 is a diagram of an analysis model used in the analysis apparatus of this embodiment. FIG. 2 is an explanatory diagram regarding the mesh set in the analytical model. As shown in FIG. 1, the analytical model is an example of an analytical model, and is a model that simply simulates the core 5 of a fast reactor. The analytical model M includes a plurality of fuel assemblies 6 and a shielding material 7 provided around the fuel assemblies 6.

Each fuel assembly 6 accommodates a plurality of fuel rods (not shown) bundled together. As shown in FIG. 1, the fuel assembly 6 has a hexagonal cross section. In the fuel assembly 6, an inner fuel, an outer fuel, a blanket fuel, and a shielding material are arranged from the center toward the outside. The analytical model M shown in FIG. 1 is a model in which a shielding material 7 having a hexagonal cross section is provided around the fuel assembly 6.

Further, as shown in FIGS. 1 and 2, a mesh 9 for dividing the internal space of the fuel assembly 6 is set in the fuel assembly 6 of this analytical model M. Since the fuel assembly 6 has a hexagonal cross section, the mesh 9 has a triangular shape that can be filled into the inside of the fuel assembly 6.

The shielding material 7 is a shielding material containing magnesium oxide (MgO). The shielding material 7 containing magnesium oxide (MgO) decelerates and reflects fast neutrons in the fast reactor. The reflected fast neutrons are decelerated to a lower energy region.

Next, the analysis device 10 will be explained with reference to FIG. FIG. 3 is a schematic configuration diagram schematically showing the analysis device according to this embodiment. The analysis device 10 includes a processing unit 11 that can execute various programs to perform analysis processing, a storage unit 12 that stores various programs and data, an input unit 13 that includes an input device such as a keyboard, a monitor, etc. The output unit 14 includes an output device. Note that the analysis device 10 may be configured as a single device, as an integrated device with a core analysis device 20 described later, or as a plurality of devices in which a calculation device, a data server, etc. are combined. Good, but not particularly limited.

The storage unit 12 stores various programs such as a nuclear constant calculation code C1 used to calculate nuclear constants, a core calculation code C2 used to calculate nuclear properties, and an analysis for analyzing local power of fuel rods. A program (a fuel rod output analysis program) P1 and the like are stored.

The nuclear constant calculation code C1 uses the specification data regarding the fuel assembly 6 and the micro cross section obtained from the cross section library as input values, and performs resonance calculation, neutron transport calculation, combustion calculation, and the like based on this micro cross section. We perform various calculations such as aggregate (nuclear constant) calculations. The specification data includes, for example, the radius of the fuel rod, the gap between the fuel rods, the fuel composition, the fuel temperature, and the coolant temperature.

The nuclear constant calculation code C1 uses a hexagonal geometric shape, which is a cross section of the fuel assembly 6 taken along a plane perpendicular to the axial direction, as a two-dimensional analysis target area, and can calculate the nuclear constant in this analysis target area. It is a code. Note that the nuclear constant is an input value used in the core calculation code C2, and the nuclear constant includes an absorption cross section, a removal cross section, a production cross section, and the like. That is, the nuclear constants, which are input values for core calculations, are generated by performing aggregate calculations using the nuclear constant calculation code C1.

The core calculation code C2 performs core calculations by dividing the fuel assembly 6 into multiple parts in the axial direction and setting the calculated nuclear constants for each fuel node (not shown) that has a triangular prism-shaped small volume. . The plurality of fuel nodes represent the reactor core 5, and the core calculation code C2 is a code that can evaluate nuclear characteristics in the core such as power distribution, effective multiplication factor, and reactivity coefficient by performing core calculations. It has become.

Next, a fuel rod output analysis method for calculating the local output of a fuel rod will be described with reference to FIGS. 4 and 5. FIG. 4 is an explanatory diagram regarding calculation of local power of a fuel rod. FIG. 5 is a flowchart regarding a method for analyzing fuel rod output according to this embodiment.

As shown in Fig. 4, the local power of the fuel rods in the fuel assembly loaded in the fast reactor is determined by the shape function F regarding the distribution of the fuel rod power in the assembly and the homogeneous neutron flux φ in the core 5 of the fast reactor. The local power P of the fuel rod is calculated by the product. Here, when calculating the local power P of a fuel rod in a fast reactor, the energy of neutrons is divided into a plurality of energy groups. Then, by adding up the fuel rod outputs calculated for each energy group, the local output P of the fuel rods is calculated.

Hereinafter, with reference to FIG. 5, a fuel rod output analysis method for calculating the local output of a fuel rod will be specifically described. First, the processing unit 11 calculates the nuclear constant of the fuel assembly 6 using the nuclear constant calculation code C1, and calculates the shape function F ^g (x, y) of the fuel assembly 6 in the multiple energy group g. The shape function is group-reduced to a shape function F (=FF ^G (x, y)) in a minority group G (g∈G) which is smaller than the multiple groups (step S1). Here, the number of energy groups in the multi-group is, for example, 70 groups, and the number of energy groups in the minority group is, for example, 7 groups.

Next, the processing unit 11 performs core calculation of the reactor core 5 using the core calculation code C2, calculates boundary conditions regarding neutron flux in multiple energy groups, and group-reduces the boundary conditions to a small number of groups. (Step S2). ^The _boundary conditions calculated in ^step _S2 are, ^as _shown in FIG. neutron flows (J ₁ ^net , J ₂ ^net , J ₃ ^net ) at the edges. In step S2, boundary conditions are calculated for each energy group. Then, in step S2, the boundary conditions calculated for each of the multiple energy groups are group-reduced to a small number of energy groups. Note that in FIG. 2, the position coordinates of each vertex of the mesh 9 are illustrated.

Subsequently, the processing unit 11 calculates the homogeneous neutron flux of the fuel assembly 6 from, for example, equation (1) based on the boundary conditions after group contraction (step S3).
φ ^G (x, y)=c ₁ ^G + c ₂ ^G x + c ₃ ^G y + c ₄ ^G x ² + c ₅ ^G xy + c ₆ ^G y ² ... (1)
φ ^G (x, y): Neutron flux at coordinates x, y c _n ^G (n=1 to 6): Energy G group, coefficients of n items x, y: Coordinates within the assembly

Then, the processing unit 11 processes each energy group G based on the shape function F (=FF ^G (x, y)) after group contraction and the homogeneous neutron flux φ (=φ ^G (x, y)). By calculating the output of the fuel rods and adding up the outputs of the fuel rods calculated for each energy group G, the local output P of the fuel rods is calculated from equation (2) (step S4).
P (x, y) = Σ {FF ^G (x, y)・Σ _f φ ^G (x, y)} ... (2)
Σ _f : Nuclear constant (fission cross section)
φ ^G (x, y): Homogeneous neutron flux

Next, the analysis results of the local power P of the fuel rod will be explained. The analysis results include the difference when comparing the local output of the reference solution and the conventional fuel rod that has not been group-reduced, and the difference between the reference solution and the local output P of the fuel rod of the present disclosure that has been group-reduced. It uses the difference in time.

Moreover, the above analysis results are the results of calculating the fuel rod power distribution of the fuel assembly 6 adjacent to the shielding material 7 containing magnesium oxide (MgO). The local power P of the fuel rod of the present disclosure that has been group-reduced has a maximum difference from the reference solution of about 20% to about 5% compared to the local power P of a conventional fuel rod that has not been group-reduced. , results were obtained in which the standard deviation of the differences was reduced from about 3% to about 1%.

In other words, the minority group is set such that the local power P of the fuel rod calculated after group contraction reduces the difference with respect to the reference solution.

Note that the method of dividing into minority groups is not particularly limited to the above method of division. A large number of energy groups may be divided into a small number of groups according to the division method described below.

As example 1 of how to divide a small number of groups, we draw typical cross-sectional area data for a fast reactor (the horizontal axis is energy and the vertical axis is cross-sectional area), and while considering the size of the cross-sectional area, 70 groups are drawn. The energy groups may be divided into predetermined groups so that the number of groups becomes a predetermined number.

In addition, as a second example of how to divide into small groups, 70 energy groups are divided into small groups with a plurality of patterns by round robin. On the other hand, a large number of core systems for verification will be created to cover the range of neutron spectra expected in fast reactor core design. For each small group of patterns, in each core system, the local power P of the fuel rod is evaluated using the analysis method described above, and the pattern of the small group of groups that reduces the difference from the reference solution in a wider core system is determined as one. Select only one item.

In addition, as a creation example 3 of how to divide a minority group, it is not limited to a minority group of one pattern as in creation example 2, but it is possible to select from among multiple patterns according to the conditions of the neutron spectrum in the reactor core system. You may switch to a smaller group that provides an appropriate pattern.

In addition, as an example 4 of how to divide a minority group, we performed a calculation of a single non-homogeneous aggregate (nuclear constant) simulating the typical neutron spectrum conditions of a fast reactor, and The aggregate average neutron flux φ _avg (g) and aggregate surface neutron flux φ _suf (g) for each aggregate are calculated. The ensemble average neutron flux φ _avg (g) and the ensemble surface neutron flux φ _suf (g) are group-reduced to the G-th group (g∈G) after reduction, and a set that is the ratio of the two is obtained. The field discontinuity factor DF(G) (=φ _suf (g)/φ _avg (g)) is calculated. For each energy group G of the small group after reduction, the number of groups and group structure after reduction are determined so that the aggregate discontinuity factor DF(G) is equal to or less than a predetermined threshold value DF(Limit). decide. In this case, the homogenization error increases as DF deviates from 1, so in creation example 4, the group structure can be determined so as to alleviate the homogenization error.

As described above, the fuel rod output analysis method, analysis device 10, and fuel rod output analysis program P1 described in this embodiment are understood as follows, for example.

The fuel rod output analysis method according to the first aspect is performed in a fuel rod analysis device 10 that analyzes the local power P of a fuel rod of a fuel assembly 6 loaded in a fast reactor using an analysis model M. In the output analysis method, the analysis model M includes the fuel assembly 6 and a shielding material 7 provided around the fuel assembly 6, and the nuclear constant of the fuel assembly 6 is Step S1 of performing calculation to calculate the shape function F of the fuel assembly 6 in the multiple energy groups, and group-reducing the shape function F to a smaller number of groups than the multiple groups; step S2 of performing calculation to calculate the boundary condition regarding the neutron flux in the energy group of the multi-group, and group-reducing the boundary condition to the minority group; and based on the boundary condition after the group reduction, Step S3 of calculating the homogeneous neutron flux φ of the fuel assembly 6; Step S4 of calculating the local output P of the fuel rod based on the shape function F after group contraction and the homogeneous neutron flux φ; , is provided.

According to this configuration, even if the shielding material 7 is arranged around the fuel assembly 6 in the fast reactor, the local power P of the fuel rod can be analyzed stably and accurately.

As a second aspect, the minority group is configured such that the local output of the fuel rod calculated based on the shape function after group contraction and the homogeneous neutron flux has a difference with respect to a reference solution within a predetermined range. Thus, the multiple energy groups are divided into the few energy groups.

According to this configuration, it is possible to perform group contraction by dividing a large number of energy groups into a small number of groups so that the difference falls within a predetermined range.

As a third aspect, the number of energy groups in the multiple groups is 70 groups, and the number of energy groups in the minority group is 7 groups.

According to this configuration, group contraction can be performed by dividing a large number of energy groups into a small number of groups having an appropriate number of groups.

As a fourth aspect, the shielding material includes magnesium oxide (MgO).

According to this configuration, even if the shielding material 7 contains magnesium oxide, the local power P of the fuel rod can be analyzed stably and accurately.

An analysis device 10 according to a fifth aspect includes a processing unit 11 that analyzes a local power P of a fuel rod of a fuel assembly 6 loaded in a fast reactor using an analysis model M. The model M includes the fuel assembly 6 and a shielding material 7 provided around the fuel assembly 6, and the processing section 11 calculates the nuclear constant of the fuel assembly 6. Step S1 of calculating the shape function F of the fuel assembly 6 in multiple energy groups, and group-reducing the shape function F to a few groups smaller than the multiple groups, and performing core calculation of the fast reactor. Step S2 of calculating the boundary conditions regarding the neutron flux in the multiple energy groups and group reduction of the boundary conditions to the minority groups, and based on the boundary conditions after the group reduction, step S3 of calculating the homogeneous neutron flux φ of the body 6; and step S4 of calculating the local power P of the fuel rod based on the shape function F after group contraction and the homogeneous neutron flux φ. Execute.

According to this configuration, even if the shielding material 7 is arranged around the fuel assembly 6 in the fast reactor, the local power P of the fuel rod can be analyzed stably and accurately.

The fuel rod output analysis program P1 according to the sixth aspect causes an analysis device 10 that analyzes the local output of the fuel rods of the fuel assembly 6 loaded in the fast reactor to be executed using the analysis model M. In the analysis program P1, the analysis model M includes the fuel assembly 6 and a shielding material 7 provided around the fuel assembly 6, and the nuclear constant of the fuel assembly 6 is Step S1 of performing calculation to calculate the shape function F of the fuel assembly 6 in the multiple energy groups, and group-reducing the shape function F to a smaller number of groups than the multiple groups; step S2 of performing calculation to calculate the boundary condition regarding the neutron flux in the energy group of the multi-group, and group-reducing the boundary condition to the minority group; and based on the boundary condition after the group reduction, Step S3 of calculating the homogeneous neutron flux φ of the fuel assembly 6; Step S4 of calculating the local output P of the fuel rod based on the shape function F after group contraction and the homogeneous neutron flux φ; , is executed.

According to this configuration, even if the shielding material 7 is arranged around the fuel assembly 6 in the fast reactor, the local power P of the fuel rod can be analyzed stably and accurately.

5 Reactor core 6 Fuel assembly 7 Shielding material 9 Mesh 10 Analysis device 11 Processing section 12 Storage section 13 Input section 14 Output section M Analysis model C1 Nuclear constant calculation code C2 Core calculation code P1 Analysis program

Claims (6)

In a fuel rod output analysis method executed in an analysis device that analyzes the local output of a fuel rod of a fuel assembly loaded in a fast reactor using an analytical model,
The analytical model is a model including the fuel assembly and a shielding material provided around the fuel assembly,
calculating a nuclear constant of the fuel assembly to calculate a shape function of the fuel assembly in multiple energy groups, and group-reducing the shape function to a smaller number of groups than the multiple groups;
performing core calculations of the fast reactor to calculate boundary conditions regarding neutron flux in the multiple energy groups, and group reduction of the boundary conditions to the minority groups;
calculating a homogeneous neutron flux of the fuel assembly based on the boundary condition after group contraction;
calculating the local output of the fuel rod based on the shape function after group contraction and the homogeneous neutron flux ,
In the step of group reduction to the minority group,
The nuclear constant calculation for the single non-homogeneous fuel assembly that simulates the neutron spectrum of the fast reactor is performed, and the assembly average neutron flux and assembly surface neutron flux for each of the multiple energy groups are calculated. death,
The aggregate average neutron flux and the aggregate surface neutron flux are group-reduced to the reduced group, respectively, and the aggregate is the ratio of the aggregate average neutron flux and the aggregate surface neutron flux. Calculate the discrete factor,
For each energy group of the minority group after contraction, the fuel rod output that determines the number of groups of the minority group after contraction is determined such that the aggregate discontinuity factor is less than or equal to a predetermined threshold. analysis method. The small group is selected from the large group so that the local output of the fuel rod calculated based on the shape function after group contraction and the homogeneous neutron flux has a difference with respect to a reference solution within a predetermined range. 2. The fuel rod output analysis method according to claim 1, wherein the energy group is divided into the small number groups. 3. The fuel rod output analysis method according to claim 1, wherein the number of energy groups in the multiple energy groups is 70 groups, and the number of energy groups in the minority energy groups is 7 groups. The method for analyzing fuel rod output according to any one of claims 1 to 3, wherein the shielding material contains magnesium oxide (MgO). In an analysis device including a processing unit that analyzes the local power of a fuel rod of a fuel assembly loaded into a fast reactor using an analytical model,
The analytical model is a model including the fuel assembly and a shielding material provided around the fuel assembly,
The processing unit includes:
calculating a nuclear constant of the fuel assembly to calculate a shape function of the fuel assembly in multiple energy groups, and group-reducing the shape function to a smaller number of groups than the multiple groups;
performing core calculations of the fast reactor to calculate boundary conditions regarding neutron flux in the multiple energy groups, and group reduction of the boundary conditions to the minority groups;
calculating a homogeneous neutron flux of the fuel assembly based on the boundary condition after group contraction;
calculating the local power of the fuel rod based on the shape function after group contraction and the homogeneous neutron flux ;
In the step of group reduction to the minority group,
The nuclear constant calculation for the single non-homogeneous fuel assembly that simulates the neutron spectrum of the fast reactor is performed, and the assembly average neutron flux and assembly surface neutron flux for each of the multiple energy groups are calculated. death,
The aggregate average neutron flux and the aggregate surface neutron flux are group-reduced to the reduced group, respectively, and the aggregate is the ratio of the aggregate average neutron flux and the aggregate surface neutron flux. Calculate the discrete factor,
An analysis device that determines the number of groups in the minority group after contraction so that the aggregate discontinuity factor for each energy group in the minority group after contraction is equal to or less than a predetermined threshold. In a fuel rod output analysis program that runs an analysis device that analyzes the local output of the fuel rods of a fuel assembly loaded in a fast reactor using an analytical model,
The analytical model is a model including the fuel assembly and a shielding material provided around the fuel assembly,
calculating a nuclear constant of the fuel assembly to calculate a shape function of the fuel assembly in multiple energy groups, and group-reducing the shape function to a smaller number of groups than the multiple groups;
performing core calculations of the fast reactor to calculate boundary conditions regarding neutron flux in the multiple energy groups, and group reduction of the boundary conditions to the minority groups;
calculating a homogeneous neutron flux of the fuel assembly based on the boundary condition after group contraction;
calculating the local output of the fuel rod based on the shape function after group contraction and the homogeneous neutron flux ;
In the step of group reduction to the minority group,
The nuclear constant calculation for the single non-homogeneous fuel assembly that simulates the neutron spectrum of the fast reactor is performed, and the assembly average neutron flux and assembly surface neutron flux for each of the multiple energy groups are calculated. death,
The aggregate average neutron flux and the aggregate surface neutron flux are group-reduced to the reduced group, respectively, and the aggregate is the ratio of the aggregate average neutron flux and the aggregate surface neutron flux. Calculate the discrete factor,
For each energy group of the minority group after contraction, the fuel rod output that determines the number of groups of the minority group after contraction is determined such that the aggregate discontinuity factor is less than or equal to a predetermined threshold. Analysis program.

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