JP6832248B2 - Resonance calculation method, analyzer and resonance calculation program - Google Patents

Description

The present invention divides the energy of neutrons in an analysis target region such as a fuel assembly into a plurality of energy groups, and obtains an effective cross-sectional area which is the average cross-sectional area of each divided energy group. It is about a calculation program.

Conventionally, there is known a resonance calculation program that divides neutron energy into a plurality of energy groups and obtains an effective cross section which is the average cross section of each divided energy group (see, for example, Patent Document 1). This resonance calculation program is incorporated in the nuclear constant calculation code (lattice calculation code), and the nuclear constant calculation code includes a transport calculation program, a nuclear constant calculation program, and the like in addition to the resonance calculation program. In this nuclear constant calculation code, the resonance calculation based on the equivalence principle is performed in the resonance calculation program in order to improve the calculation efficiency. Specifically, in the nuclear constant calculation code, the background cross-sectional area is calculated based on the input specification data in the resonance calculation program, and the calculated background cross-sectional area is used as an argument to be effective micro from the cross-sectional area library. The cross-sectional area is calculated. Further, in the nuclear constant calculation code, the neutron flux is calculated over a large number of groups based on the characteristic curve method using the calculated effective micro cross section in the transport calculation program. Then, in the nuclear constant calculation code, in the nuclear constant calculation program, the effective macro cross-sectional area of the multi-group of the fuel aggregate is reduced and homogenized by weighting the neutron flux of the multi-group of the fuel aggregate, and the homogenized macro. The nuclear constant is calculated.

Japanese Unexamined Patent Publication No. 2012-58071

However, in the conventional resonance calculation program, in the resonance calculation based on the equivalence principle, the analysis target region is treated as a calculation system having a simple geometric shape consisting of a fuel region and a non-fuel region. Here, the fuel cell of the fuel assembly to be the analysis target region is composed of a fuel pellet, a cladding tube, and a moderator such as light water. In the resonance calculation based on the equivalence principle, the circular region in the axial cross section of the fuel pellet is usually treated as a single fuel mass, that is, as a single fuel region. On the other hand, in the resonance calculation based on the equivalence principle, the cladding tube and moderator are homogenized and treated as a non-fuel region. In this case, in the conventional resonance calculation program, the distribution of the effective cross-sectional area in the radial direction of the circular region of the fuel pellet is accurately evaluated for an event such as a decrease or loss of moderator, that is, for a wide range of analysis conditions. Is difficult.

On the other hand, in resonance calculation, in order to improve the calculation accuracy, the analysis target area is treated as a calculation system with detailed geometric shapes, and the energy of neutrons is treated as a calculation system with detailed ultra-multigroup energy groups with many divisions. In some cases, it is handled and a super-multigroup calculation is performed to obtain the effective cross-sectional area. In this case, it is possible to accurately evaluate the effective cross section of the analysis target region, but the calculation load is high, and the calculation efficiency is significantly reduced as compared with the resonance calculation based on the equivalence principle.

Therefore, the present invention provides a resonance calculation method, an analysis device, and a resonance calculation program capable of calculating an effective cross-sectional area with good calculation accuracy while suppressing a decrease in calculation efficiency even under a wide range of analysis conditions. Is the subject.

The resonance calculation method of the present invention is a resonance calculation method in which the energy of neutrons in the analysis target region is divided into a plurality of energy groups and the effective cross-sectional area which is the average cross-sectional area of each divided energy group is obtained. Is treated as a calculation system having a simple geometric shape, and a plurality of the energy groups are treated as a calculation system to be a dense super-multi-group energy group with many divisions, and a super-multi-group neutron flux is included. The first resonance calculation step for calculating the multi-group data and the analysis target region are treated as a calculation system having a more detailed geometric shape than the first resonance calculation step, and compared with the first resonance calculation step. It is treated as a calculation system that becomes a coarse multi-group energy group with few divisions, and each group is classified into a plurality of subgroups using the super-multi-group data, and the super-many in each subgroup. A second resonance calculation that generates a subgroup cross-sectional area by reducing the ultra-multi-group cross-sectional area included in the group data, and calculates the effective cross-sectional area of the analysis target region using the subgroup cross-sectional area. It is characterized by having steps.

Further, the analyzer of the present invention divides the neutron energy in the analysis target region into a plurality of energy groups, and executes a resonance calculation for obtaining an effective cross-sectional area which is the average cross-sectional area of each divided energy group. In the analysis device provided, the calculation unit treats the analysis target region as a calculation system having a simple geometric shape, and calculates a plurality of the energy groups to be a dense super-multi-group energy group with many divisions. The first resonance calculation step for calculating the super-multi-group data including the super-multi-group neutron flux, which is treated as a system, and the calculation in which the analysis target region has a more detailed geometric shape than the first resonance calculation step. In addition to being treated as a system, it is also treated as a calculation system that is a multi-group energy group that is coarser with less division than the first resonance calculation step, and each group is treated as a plurality of subs using the super-multi-group data. By classifying into groups and reducing the super-multi-group cross-sectional area included in the super-multi-group data in each of the sub-groups, a sub-group cross-sectional area is generated, and the analysis is performed using the sub-group cross-sectional area. It is characterized by executing the second resonance calculation step of calculating the effective cross-sectional area of the target region.

Further, the resonance calculation program of the present invention divides the neutron energy in the analysis target region into a plurality of energy groups in the calculation unit of the analyzer, and obtains an effective cross-sectional area which is the average cross-sectional area of each divided energy group. In the resonance calculation program, the analysis target region is treated as a calculation system having a simple geometric shape, and a plurality of the energy groups are treated as a calculation system which is a dense super-multigroup energy group with many divisions. The first resonance calculation step for calculating the super-multi-group data including the super-multi-group neutron flux and the analysis target region are treated as a calculation system having a more detailed geometric shape than the first resonance calculation step. It is treated as a calculation system that becomes a multi-group energy group that is coarser and less divided than the first resonance calculation step, and each group is classified into a plurality of subgroups using the super-multi-group data. , The subgroup cross-sectional area is generated by reducing the super-multi-group cross-sectional area included in the super-multi-group data in each of the subgroups, and the subgroup cross-sectional area is used to generate the effect of the analysis target region. It is characterized by including a second resonance calculation step for calculating the cross-sectional area.

According to these configurations, in the first resonance calculation step, the neutron energy can be divided into super-multigroups for the analysis target region having a simple geometric shape, and the super-multigroup data can be calculated. Therefore, in the first resonance calculation step, since the analysis target region has a simple geometric shape, the calculation efficiency can be increased. On the other hand, since the calculated ultra-multigroup data has insufficient spatial accuracy, in the second resonance calculation step, the energy of neutrons is first applied to the analysis target region having a detailed geometric shape. The effective cross-sectional area of the analysis target region can be calculated by dividing into multiple energy groups, which are smaller than the resonance calculation step. Therefore, in the second resonance calculation step, since the energy group of neutrons is small, the calculation efficiency can be increased, and since the analysis target area has a detailed geometric shape, the calculated effective cutoff of the analysis target area The area can be assumed to be spatially accurate. From the above, it is possible to calculate an effective cross-sectional area with good calculation accuracy while suppressing a decrease in calculation efficiency even under a wide range of analysis conditions.

Further, in the first resonance calculation step, the analysis target region having a simple geometric shape is a region consisting of a fuel region and a non-fuel region, and the neutron escape probability in the analysis target region is a rational formula. Given by a polynomial rational equation including a coefficient, the first resonance calculation step includes a coefficient calculation step for calculating the rational equation coefficient so as to be the polynomial rational equation expressing the escape probability of neutrons in the analysis target region. It is preferable to have a super-multi-group data calculation step of performing a super-multi-group deceleration calculation using the rational coefficient calculated in the coefficient calculation step and calculating the super-multi-group data.

According to this configuration, since the neutron escape probability in the analysis target region can be taken into consideration, the ultra-multigroup data can be calculated accurately. The analysis target area is a fuel assembly having a fuel cell, and the fuel cell includes a fuel pellet, a cladding tube, and a moderator. At this time, the fuel pellets are set as the fuel region, and the cladding and moderator are homogenized and set as the non-fuel region. As a result, it can be handled as a calculation system having a simple geometric shape.

Further, in the second resonance calculation step, the analysis target area having a detailed geometric shape is a region simulating a fuel system, and the super-multigroup data is each energy group of neutrons forming a super-multigroup. The second resonance calculation step is based on the range of the super-multigroup cross-sectional area of each group of the multi-group energy groups using the super-multi-group data. Then, it is classified into subgroups divided into the neutron energy range, and the subgroup cross section is generated by reducing the supermultigroup cross section in the neutron energy range corresponding to the subgroup. A neutron flux calculation step for creating a cross-sectional area data including a subgroup cross-sectional area and a neutron flux calculation step for calculating a neutron flux corresponding to the subgroup in the analysis target region using the cross-sectional area data. It is preferable to have an effective cross-sectional area calculation step for calculating the effective cross-sectional area of the analysis target region with the calculated neutron flux corresponding to the subgroup as a weight.

According to this configuration, the cross-sectional area data of the subgroups is created using the super-multigroup data, and the subgroup cross-sectional area of each group is reduced by weighting the neutron flux corresponding to the subgroups. The effective cross-sectional area of the target area can be calculated accurately. The analysis target area is a fuel assembly having a fuel cell, and the fuel cell includes a fuel pellet, a cladding tube, and a moderator. At this time, the fuel pellet, the cladding tube, and the moderator can be set as the respective regions in the analysis target region. As a result, it can be handled as a calculation system having a detailed geometric shape.

Further, it is preferable that the energy range of the neutron corresponding to the range of the ultra-multigroup cross-sectional area of the subgroup is different.

According to this configuration, when dividing each group of the multi-group energy group into a plurality of subgroups, the range of the neutron energy is not considered, and the range of the super-multi-group cross-sectional area is considered. Can be divided into groups.

Further, the setting related to the classification of the subgroup is classified so as to be the range of the energy of the neutron corresponding to the range of the super-multi-group cross-sectional area using the super-multi-group cross-sectional area represented by the log scale as an index. Is preferably set.

According to this configuration, the range of neutron energy can be set based on the range of the ultra-multigroup cross-sectional area. Therefore, as an example, by setting the range of the ultra-multigroup cross-sectional area represented by the log scale to be evenly spaced, the range of neutron energy can be set to an appropriate range in which the calculation accuracy can be improved. Can be set as.

FIG. 1 is a schematic configuration diagram schematically showing an analysis device according to the present embodiment. FIG. 2 is an explanatory diagram schematically showing a core to be analyzed by the analyzer according to the present embodiment. FIG. 3 is a cross-sectional view of the fuel assembly to be analyzed when the fuel assembly is cut along a plane orthogonal to the axial direction. FIG. 4 is an explanatory diagram relating to the grid calculation code stored in the analyzer. FIG. 5 is an explanatory diagram showing an analysis target area divided into a plurality of detailed areas. FIG. 6 is an explanatory diagram showing an analysis target region in which a neutron path is drawn. FIG. 7 is an explanatory diagram relating to resonance calculation. FIG. 8 is an explanatory diagram relating to the setting of subgroups using a graph of the cross-sectional area that changes according to the neutron energy. FIG. 9 is a flowchart of the first resonance calculation step. FIG. 10 is a flowchart of the second resonance calculation step. FIG. 11 is an explanatory diagram relating to the number of neutron flux calculations corresponding to the resonance calculation method. FIG. 12 is a graph showing the calculation accuracy corresponding to the resonance calculation method.

Hereinafter, embodiments according to the present invention will be described in detail with reference to the drawings. The present invention is not limited to this embodiment. In addition, the components in the following embodiments include those that can be easily replaced by those skilled in the art, or those that are substantially the same. Further, the components described below can be appropriately combined, and when there are a plurality of embodiments, the respective embodiments can be combined.

[Embodiment]
The resonance calculation program according to this embodiment is incorporated in the core analysis program for evaluating the fuel assembly in the core. The core analysis program is stored in the analysis device, and when the core analysis program is executed in the analysis device, the neutron flux in the core is calculated and the distribution and behavior of neutrons that mediate the nuclear reaction in the core are predicted. Then, evaluate the nuclear characteristics in the core. Then, the core design is performed based on the analysis result obtained by this core analysis program. The core design is performed to replace the fuel loaded in the core in consideration of safety, combustion efficiency, fuel arrangement, and the like. First, the analyzer will be described with reference to FIG.

FIG. 1 is a schematic configuration diagram schematically showing an analysis device. As shown in FIG. 1, the analysis device 40 is an input unit 43 composed of a calculation unit 41 capable of executing various programs and performing calculations, a storage unit 42 for storing various programs and data, and an input device such as a keyboard. And an output unit 44 composed of an output device such as a monitor. The analysis device 40 may be composed of a single device or a plurality of devices in which a computing device, a data server, and the like are combined, and is not particularly limited.

The core analysis program P is stored in the storage unit 42 as various programs, and as data, the cross-sectional area library D1 that summarizes the cross-sectional areas and the nuclear constant data D2 that summarizes the nuclear constants that are a plurality of sets are stored. , Is remembered. Further, the core analysis program P includes a lattice calculation code C1 for calculating the nuclear constant and a core calculation code C2 for analyzing the nuclear characteristics in the core based on the nuclear constant.

Here, the core 5 to be analyzed by the core analysis program P will be described with reference to FIGS. 2 and 3. FIG. 2 is an explanatory view schematically showing a core to be analyzed by the analysis device according to the present embodiment, and FIG. 3 is a cross section of a fuel assembly to be an analysis target region at a plane orthogonal to the axial direction. It is a cross-sectional view of the time. As shown in FIG. 2, the reactor core 5 is stored, which is the target of the core design. The core 5 is composed of a plurality of fuel assemblies 6. The fuel is exchanged in units of 6 fuel assemblies.

As shown in FIG. 3, each fuel assembly 6 includes a fuel rod 9 composed of a plurality of fuel pellets 10 and a plurality of cladding tubes 11 covering each fuel pellet 10, and a grid (not shown) for bundling the plurality of cladding tubes 11. The inside of the fuel assembly 6 is filled with the moderator (coolant) 13, and a plurality of control rods 14 and the core instrumentation 15 in the furnace can be inserted. The fuel rods 9 are arranged with a plurality of fuel pellets 10 having a cylindrical shape arranged in an axial direction, and the outside thereof is covered with a cladding tube 11.

The fuel assembly 6 is formed in a rectangular cross section, and is composed of, for example, 17 × 17 cells 20. The control rods 14 are inserted into the 24 cells 20 of the 17 × 17 cells 20, and the inner core instrumentation 15 is inserted into the cell 20 at the center of the assembly. At this time, the cell 20 into which the control rod 14 is inserted is referred to as a control rod guide pipe, and the cell 20 into which the inner core instrumentation 15 is inserted is referred to as an instrumentation guide pipe. Further, fuel rods 9 are inserted into the other cells 20, respectively. When the fuel assembly 6 is used in a boiling water reactor (BWR), the outside of the fuel assembly 6 is covered with a channel box. On the other hand, when the fuel assembly 6 is used in a pressurized water reactor (PWR), the outside of the fuel assembly 6 is open. Then, in the case of BWR, there is an inter-aggregate gap 12 outside the channel box, and in the case of PWR, outside the fuel assembly 6.

Next, the grid calculation code C1 and the core calculation code C2 of the core analysis program P will be described.

The lattice calculation code C1 defines a two-dimensional analysis target region 30 (see FIG. 3) as a quadrangular geometric shape having a cross section obtained by cutting the fuel assembly 6 along a plane orthogonal to the axial direction, and nucleation in the analysis target region 30. It is a code that can calculate the number. The nuclear constant is input data used in the core calculation code C2, and the nuclear constant includes a diffusion coefficient, an absorption cross section, a removal cross section, a generation cross section, and the like. That is, the nuclear constant, which is the input data for the core calculation, is generated by performing the nuclear constant calculation using the grid calculation code C1.

The core calculation code C2 calculates the core by setting the calculated nuclear constants in the fuel nodes (not shown) which are divided into a plurality of fuel assemblies 6 in the axial direction and have a small volume in the shape of a rectangular parallelepiped. .. The multiple fuel nodes represent the core, and the core calculation code C2 is a code that can evaluate the nuclear characteristics in the core such as the critical boron concentration, output distribution, and reactivity coefficient by performing the core calculation. ing.

The analysis device 40 causes the calculation unit 41 to execute the core analysis program P stored in the storage unit 42 based on the input parameters input from the input unit 43. Then, the analysis device 40 calculates the nuclear constant in the analysis target region 30 of the fuel assembly 6 using the lattice calculation code C1, and sets the calculated nuclear constant in each fuel node using the core calculation code C2. Then, the core characteristics of the core 5 are evaluated by performing the core calculation. Then, the analysis device 40 outputs the analysis result by the core analysis program P to the output unit 44.

Next, the grid calculation code C1 will be specifically described with reference to FIG. FIG. 4 is an explanatory diagram relating to the grid calculation code stored in the analyzer. The lattice calculation code C1 of the present embodiment calculates the neutron flux in the fuel assembly 6, performs the combustion calculation, and performs the nuclear constant calculation.

The lattice calculation code C1 includes a resonance calculation program 51, a transport calculation program 52, a combustion calculation program 53, and a nuclear constant calculation program 54. Then, the lattice calculation code C1 is based on the specification data regarding the fuel assembly 6 input to the analysis device 40 and the cross-sectional area acquired from the cross-sectional area library D1 stored in the storage unit 42 of the analysis device 40. , Performs various calculations. The specification data includes, for example, the radius of the fuel rods, the gap between the aggregates, the fuel composition, the fuel temperature, the moderator temperature, and the like.

FIG. 5 is an explanatory diagram showing an analysis target area divided into a plurality of detailed areas. As shown in FIG. 5, the analysis target area 30 to be analyzed by the grid calculation code C1 is an arbitrary system, and is composed of a plurality of cell areas 31a and 31b corresponding to each cell 20. The cell regions 31a and 31b include, for example, a cell region 31a in which the fuel rods 10 are inserted and a cell region 31b in which the control rods 14 are inserted. The cell areas 31a and 31b are divided into a plurality of detail areas i. A part of the plurality of detailed regions i is a resonance region in which a resonance phenomenon occurs.

The resonance calculation program 51 is executed to obtain the effective cross-sectional area of each detailed region i in consideration of the resonance phenomenon. Here, the resonance phenomenon is a phenomenon in which the cross-sectional area dramatically increases when the energy of neutrons reaches a predetermined energy. In this resonance calculation program 51, the effective cross-sectional area of each detailed region i is obtained by performing the resonance calculation in two steps. Specifically, in the resonance calculation of the first stage, the neutron energy is divided into ultra-multigroup (ultra-detailed) energy groups of about 100,000 groups, and the analysis target region 30 is treated as a simple geometric shape. By performing fixed neutron source calculations, super-multi-group data including super-multi-group neutron bundles can be obtained. In the second-stage resonance calculation, the obtained super-multigroup data is used to reduce the number of neutron energy groups to be super-multigroups to a plurality (for example, 1 for each group of multigroups). The neutron flux corresponding to the energy group of the subgroup is calculated by dividing into subgroups of 3 to 10) per group, treating the analysis target region 30 as a detailed geometric shape, and performing a monochromatic fixed source calculation. Then, in the resonance calculation in the second stage, the neutron flux corresponding to the calculated energy group of the subgroup is used as a weight to reduce the cross-sectional area of the subgroup, for example, for each detailed region i in the analysis target region 30. Calculate the effective cross-sectional area. Then, the calculated effective cross-sectional area is stored in the cross-sectional area library D1.

The transport calculation program 52 uses the calculated effective cross-section to calculate the neutron flux of each detailed region in the fuel assembly 6 over a large number of groups based on the characteristic curve method. Here, FIG. 6 is an explanatory diagram showing an analysis target region in which a neutron path is drawn. As shown in FIG. 6, the transport calculation program 52 creates a plurality of neutron flight paths s on the analysis target region 30 divided into a plurality of detailed regions. Then, for each neutron flight path s created, the neutron transport equation is solved to calculate the neutron flux in each detailed region.

The combustion calculation program 53 executes a combustion calculation that tracks the generation and disappearance of nuclides in the core 5. The combustion calculation program 53 evaluates the time change of the atomic number density of each nuclide by solving the combustion equation, and gives an input condition for the multigroup neutron transport calculation at each combustion degree point. As a result, the fuel calculation program 53 tracks the combustion state (time change of combustion) by alternately performing the combustion calculation and the transportation calculation at predetermined sampling cycles.

The nuclear constant calculation program 54 reduces, homogenizes, and homogenizes the effective cross-sectional area of the multi-group in the fuel assembly 6 by weighting the neutron flux of the multi-group in the fuel assembly 6 obtained by the transport calculation program 52. Calculate the resulting nuclear constant.

Subsequently, the resonance calculation program 51 according to the present embodiment will be described in detail with reference to FIGS. 7 to 10. FIG. 7 is an explanatory diagram relating to resonance calculation. FIG. 8 is an explanatory diagram relating to the setting of subgroups using a graph of the cross-sectional area that changes according to the neutron energy. FIG. 9 is a flowchart of the first resonance calculation step. FIG. 10 is a flowchart of the second resonance calculation step. In this resonance calculation program 51, the first resonance calculation step S1 shown in FIGS. 7 and 9 and the second resonance calculation step S2 shown in FIGS. 7 and 10 are executed.

In the first resonance calculation step S1, the resonance calculation that combines the equivalence principle and the super-multigroup deceleration calculation is executed. Here, as shown in FIG. 7, in the first resonance calculation step S1, the analysis target region 30 is treated as a region having a simple geometric shape, and specifically, it is composed of a fuel region f and a non-fuel region nf. It is treated as two areas. The analysis target region 30 is a cell (fuel cell) 20 into which the fuel rod 10 is inserted, and the fuel cell 20 includes the fuel pellet 10, the cladding tube 11, and the moderator 13 as described above. .. At this time, the fuel pellet 10 is set as a circular fuel region f which is a shaft cross section of the fuel pellet 10, and the cladding tube 11 and the moderator 13 are homogenized and set as a non-fuel region nf. In the present embodiment, in the first resonance calculation step S1, in order to evaluate the distribution of the effective cross-sectional area in the radial direction of the circular fuel region f, the circular fuel region f is provided at a predetermined interval along the radial direction. By dividing each, it is divided into a plurality of annular regions i. Each annular region i is circular in the circumferential direction, and the plurality of annular regions i are arranged concentrically. On the other hand, when it is not necessary to evaluate the distribution of the effective cross-sectional area in the radial direction of the fuel region f, the fuel region f may be treated as a single region, and the analysis target region 30 is not the fuel region f. As long as it is treated as two regions including the fuel region nf, it is not particularly limited.

Next, the calculation formula used in the first resonance calculation step S1 will be described. The neutron flux in the fuel region f is represented by the following equation (1).

Further, the slowing-down cross-section regarding the deceleration of neutrons in the fuel region f is expressed by the following equation (2).

Then, the factor considering the self-shielding effect in the non-fuel region nf is expressed by the following equation (3).

By performing the super-multi-group deceleration calculation using these three equations, the super-multi-group neutron flux in the two-region system of the fuel region f and the non-fuel region nf is calculated.

In the first resonance calculation step S1, in order to reduce the calculation load, a simple calculation is performed by calculating the neutron flux of a super-multigroup that is spatially dependent in the radial direction. Further, since the spatial accuracy can be ensured in the second resonance calculation step S2, which will be described later, a simple calculation can be performed in the first resonance calculation step S1.

Further, in the first resonance calculation step S1, it is assumed that the macro cross section of the fuel region f and the scattered neutron source are spatially flat, and the neutron escape probability can be expressed by a polynomial rational expression. That is, the neutron escape probability ( _{Pi → nf} (E)) is gray between the blackbody in which the annular region i absorbs all neutrons and the whitebody in which the annular region i absorbs no neutrons. It is represented by the following equation (4), which is a polynomial rational expression including a _{first rational expression coefficient α n} and a second rational expression coefficient β _{n, which represents a range. In addition, li and m} defined in the equation (4) represent the average chord length with respect to the m term of the annular region i.

Then, in the first resonance calculation step S1, the neutron flux of a super-multi-group is obtained based on the polynomial rational equation derived as follows starting from the neutron transport equation for the annular region i in the multi-domain system. Here, the neutron transport equation is an integral transport equation, and when it is separated into the components of the fuel region f and the non-fuel region nf, it is expressed by the following equation (5).

Here, the reciprocity theorem expressed by the following equation (6) is applied.

Then, the first and second terms on the right side of the equation (5) become the following equations (7) and (8).

Here, assuming that the macro cross section of the fuel region f and the scattered neutron source are spatially flat as described above, Eq. (7) can be approximated as Eq. (9) below.

Further, when the equation (8) is arranged by using the equation (3), the equation (8) becomes the following equation (10).

Then, by substituting the equations (9) and (10) into the equation (5) and rearranging them, the following equation (11) is obtained.

Finally, by substituting the equation (4) into the equation (11) and rearranging, the following equation (12) is obtained. As described above, the neutron flux of the super-multigroup with respect to the annular region i of the fuel region f can be calculated by the equation (12). That is, the ultra-multigroup neutron flux calculated by Eq. (12) is treated as ultra-multigroup data.

Next, the second resonance calculation step S2 will be described. In the second resonance calculation step S2, the resonance calculation incorporating the subgroup method is executed. Here, as shown in FIG. 7, in the second resonance calculation step S2, the analysis target region 30 is treated as a region having a detailed geometric shape, and specifically, it is a region simulating the system of the fuel cell 20. ing. That is, the analysis target region 30 is set as a region of the fuel pellet 10, a region of the cladding tube 11, and a region of the moderator 13, respectively. In the present embodiment, similarly to the first resonance calculation step S1, in the second resonance calculation step S2, in order to evaluate the distribution of the effective cross-sectional area of the circular fuel pellet 10 in the radial direction, the circular fuel pellet is used. By dividing 10 at predetermined intervals along the radial direction, the 10 is divided into a plurality of annular regions i. On the other hand, when it is not necessary to evaluate the distribution of the effective cross-sectional area of the fuel pellet 10 in the radial direction, the fuel pellet 10 may be treated as a single region and is not particularly limited. Further, the fuel pellet 10, the cladding tube 11, and the moderator 13 may be divided at predetermined intervals along the circumferential direction, and the respective regions may be set. At this time, when considering the spatial dependence in the circumferential direction, the fixed source calculation of neutrons should be performed using the monochromatic method of characteristics (MOC), which is a two-dimensional fuel system. Just do it.

Next, the calculation formula used in the second resonance calculation step S2 will be described. In the second resonance calculation step S2, the calculation system is treated as a multi-group energy group having less division and coarseness than in the first resonance calculation step S1. For example, a multi-group structure having 172 groups is obtained. There is. In the second resonance calculation step S2, each group of the 172 groups is divided into a plurality of subgroups by using the super-multi-group cross-sectional area.

Here, in the graph shown in FIG. 8, the vertical axis thereof is a macro cross section, and is represented by a log scale. Further, in the graph shown in FIG. 8, the horizontal axis thereof is the energy of neutrons, and the energy range of one group in the multi-group structure (for example, 172 groups) is shown. As shown in FIG. 8, the subgroup is divided into neutron energy ranges based on the macro cross-section range of the fuel region f. Specifically, the space between the upper limit value and the lower limit value of the macro cross section represented by the log scale is divided at equal intervals according to the number of divisions of the subgroup, and corresponds to the range of the divided macro cross section. It divides the range of neutron energy. In this way, the setting related to the classification of subgroups sets the range of neutron energy by classifying using the cross-sectional area represented by the log scale as an index. Further, as shown in FIG. 8, a plurality of neutron energy ranges corresponding to the range of the cross-sectional area of the subgroup may be set to different ranges (discontinuous ranges).

The micro cross-sectional area (subgroup cross-sectional area) for each subgroup divided as described above is calculated by the following equation (13).

Further, the neutron source for each subgroup divided as described above is calculated by the following equation (14).

Then, in the second resonance calculation step S2, the monochromatic fixed source calculation is independently executed for each subgroup using the micro cross section and the neutron source for each subgroup as input values, and the neutron flux (sub) of each annular region i is executed. Group neutron flux) is calculated.

After that, the micro cross section for each subgroup is reduced with the neutron flux of each ring region i as a weight, and the effective cross section of the ring region i is calculated by the following equation (15).

Next, with reference to FIGS. 9 and 10, a series of flows of the analysis device 40 for calculating the effective cross-section by the resonance calculation program 51 will be described using the above calculation formula. In the first resonance calculation step S1 shown in FIG. 9, the coefficient calculation step S11 and the super multigroup data calculation step S12 are executed to calculate the super multigroup data.

In the coefficient calculation step S11, the rational expression coefficient is calculated so as to be a multinomial rational expression that approximates the neutron escape probability in the analysis target region 30. That is, in the coefficient calculation step S11, the neutron escape probability is represented by the polynomial rational expression shown in Eq. (4), and the first rational coefficient and the second rational coefficient expressing the neutron escape probability are expressed. calculate.

In the super-multi-group data calculation step S12, the super-multi-group deceleration calculation is performed using the calculated rational coefficient, and the super-multi-group data is calculated. That is, in the super multigroup data calculation step S12, the neutron flux of the super multigroup is calculated by using the equation (12).

In the second resonance calculation step S2 shown in FIG. 10, the cross-section data creation step S21, the neutron flux calculation step S22, and the effective cross-section calculation step S23 are executed to obtain the effective cross-section in the analysis target region. It is calculated.

In the cross-sectional area data creation step S21, as shown in FIG. 8, each group of the energy groups of the multi-group (for example, 172 groups) is subjected to the super-multi-group data based on the range of the super-multi-group cross-sectional area. Classify into subgroups divided into neutron energy ranges. Then, in the cross-sectional area data creation step S21, the subgroup cross-sectional area is generated by reducing the ultra-multi-group cross-sectional area within the range of the neutron energy corresponding to the subgroup, and the cross-sectional area including the subgroup cross-sectional area is generated. Create data. That is, in the cross-sectional area data creation step S21, the super-multi-group cross-sectional area is generated by reducing the super-multi-group cross-sectional area belonging to the sub-group by using the super-multi-group data as an input value and using the equation (13). Further, in the cross-sectional area data creation step S21, the neutron source in the subgroup is calculated by using the equation (14).

In the neutron flux calculation step S22, the micro cross section for each subgroup calculated by Eqs. (13) and (14) and the cross section data including the neutron source are used as input values, and each subgroup is independently monochromatic fixed source. Execute the calculation and calculate the neutron flux (subgroup neutron flux) of each annular region i.

In the effective cross-section calculation step S23, the effective cross-section of the analysis target region 30 is obtained by reducing the micro-cross-section for each subgroup with the neutron flux corresponding to the subgroup as a weight by using the equation (15). calculate.

Next, the calculation speed and the calculation accuracy by the resonance calculation of the present embodiment will be described with reference to FIGS. 11 and 12. FIG. 11 is an explanatory diagram relating to the number of neutron flux calculations corresponding to the resonance calculation method. FIG. 12 is a graph showing the calculation accuracy corresponding to the resonance calculation method.

As shown in FIG. 11, as the resonance calculation method, the number of neutron flux calculations by the monochromatic fixed source calculation was compared with respect to the resonance calculation based on the equivalence principle, the super-multigroup deceleration calculation, and the resonance calculation of the method of the present application. As a result, the number of calculations is about 1 to 20 times for the resonance calculation based on the equivalence principle, about 10,000 to 200,000 times for the ultra-multigroup deceleration calculation, and the resonance calculation of the method of the present application. The number of calculations was about 500-11,000. Therefore, it was shown that the calculation load of the resonance calculation of the method of the present application is reduced as compared with the super-multigroup deceleration calculation.

Further, as shown in FIG. 12, as the resonance calculation method, the resonance calculation based on the equivalence principle, the super-multigroup deceleration calculation, the resonance calculation of the present application method in which only the first resonance calculation is performed, and the first and second resonances are performed. Regarding the resonance calculation of the method of the present application in which the calculation was executed, the errors with respect to the true value were compared. In the graph shown in FIG. 12, the vertical axis thereof is an error with respect to the true value, and the horizontal axis thereof is a relative distance in the radial direction of the fuel region f. In the results shown in FIG. 12, the super-multigroup deceleration calculation and the resonance calculation of the method of the present application in which the first and second resonance calculations are performed have a small error with respect to the true value, and the resonance calculation based on the equivalence principle and the first resonance It was shown that the resonance calculation of the method of the present application in which only the calculation was performed has a large error with respect to the true value.

From the results shown in FIGS. 11 and 12, the resonance calculation of the present embodiment has a calculation load smaller than that of the ultra-multigroup deceleration calculation, and the calculation accuracy is almost the same as that of the ultra-multigroup deceleration calculation. It was confirmed that the calculation accuracy was high.

As described above, in the first resonance calculation step S1, the resonance calculation program 51 of the present embodiment divides the neutron energy into super-multigroups with respect to the analysis target region 30 having a simple geometric shape, and super Multi-group data can be calculated. Therefore, in the first resonance calculation step S1, the analysis target region 30 has a simple geometric shape, so that the calculation efficiency can be increased. On the other hand, since the calculated ultra-multigroup data has insufficient spatial accuracy, the energy of neutrons is applied to the analysis target region 30 having a detailed geometric shape in the second resonance calculation step S2. The effective cross-sectional area of the analysis target region 30 can be calculated by dividing into multiple energy groups smaller than the first resonance calculation step S1. Therefore, in the second resonance calculation step S2, the calculation efficiency can be increased because the energy group of neutrons is small, and the analysis target area 30 is calculated because the analysis target area 30 has a detailed geometric shape. The effective cross-sectional area of can be assumed to ensure spatial accuracy. From the above, it is possible to calculate an effective cross-sectional area with good calculation accuracy while suppressing a decrease in calculation efficiency even under a wide range of analysis conditions.

Further, in the first resonance calculation step S1, by executing the coefficient calculation step S11 and the super multigroup data calculation step S12, the neutron escape probability in the analysis target region 30 can be considered, so that the super multigroup data Can be calculated accurately.

Further, in the second resonance calculation step S2, by executing the cross-section data creation step S21, the neutron flux calculation step S22, and the effective cross-section calculation step S23, the neutron flux corresponding to the subgroup is used as a weight for each group. Since the cross-sectional area corresponding to the subgroup can be reduced, the effective cross-sectional area of the analysis target area 30 can be calculated accurately.

In addition, the setting related to the classification of subgroups can be set by classifying the neutron energy range corresponding to the range of the cross-sectional area using the cross-sectional area represented by the log scale as an index. Therefore, the range of neutron energy corresponding to the range of the cross-sectional area of the subgroup may be different (discontinuous). As a result, it is possible to divide into multiple subgroups by considering the range of cross-sectional area without considering the continuous range of neutron energy, and to improve the calculation accuracy of the range of neutron energy. It can be set as an appropriate range.

5 Core 6 Fuel assembly 9 Fuel rod 10 Fuel pellet 11 cladding tube 12 Moderator gap 13 Moderator 14 Control rod 15 In-core nuclear instrumentation 20 Cell 30 Analysis target area 31a, 31b Cell area 40 Analysis device 41 Calculation unit 42 Memory Part 43 Input part 44 Output part 51 Resonance calculation program 52 Transport calculation program 53 Combustion calculation program 54 Nuclear constant calculation program P Core analysis program D1 Cross-sectional area library D2 Nuclear constant data C1 Lattice calculation code s Neutron flight path i Circular region f Fuel Region nf non-fuel region

Claims (7)

In the resonance calculation method, the energy of neutrons in the analysis target region is divided into a plurality of energy groups, and the effective cross section, which is the average cross section of each divided energy group, is obtained.
The analysis target region is treated as a calculation system having a simple geometric shape, and a plurality of the energy groups are treated as a calculation system to be a dense super-multi-group energy group with many divisions, and the super-multi-group neutrons are treated. The first resonance calculation step to calculate the ultra-multigroup data including the flux, and
The analysis target region is treated as a calculation system having a detailed geometric shape as compared with the first resonance calculation step, and a multi-group energy group having less division and coarseness than the first resonance calculation step. Using the super-multi-group data, each group is classified into a plurality of subgroups, and the super-multi-group cross-sectional area included in the super-multi-group data is reduced in each sub-group. A resonance calculation method comprising: a second resonance calculation step of generating a subgroup cross-sectional area and calculating the effective cross-sectional area of the analysis target region by using the subgroup cross-sectional area. .. In the first resonance calculation step, the analysis target region having a simple geometric shape is a region including a fuel region and a non-fuel region.
The neutron escape probability in the analysis target region is given by a multinomial rational expression including a rational equation coefficient.
The first resonance calculation step is
A coefficient calculation step for calculating the rational expression coefficient so as to be the polynomial rational expression expressing the neutron escape probability in the analysis target region, and
The first aspect of claim 1 is characterized by having a super-multi-group data calculation step of performing a super-multi-group deceleration calculation using the rational coefficient calculated in the coefficient calculation step and calculating the super-multi-group data. The described resonance calculation method. In the second resonance calculation step, the analysis target region having a detailed geometric shape is a region simulating the fuel system.
The super-multi-group data includes the super-multi-group cross-sectional area corresponding to each energy group of neutrons to be super-multi-group.
The second resonance calculation step is
Each group of the multi-group energy group is classified into subgroups divided into the neutron energy range based on the range of the super-multi-group cross-sectional area using the super-multi-group data. In the cross-sectional area data creation step of creating subgroup cross-sectional area by reducing the super-multi-group cross-sectional area within the range of the neutron energy corresponding to, and creating cross-sectional area data including the subgroup cross-sectional area. ,
A neutron flux calculation step for calculating a neutron flux corresponding to the subgroup in the analysis target region using the cross-sectional area data, and a neutron flux calculation step.
The resonance calculation according to claim 1 or 2, further comprising an effective cross-section calculation step for calculating the effective cross-section of the analysis target region with the calculated neutron flux corresponding to the subgroup as a weight. Method. The resonance calculation method according to any one of claims 1 to 3, wherein the neutron energy range corresponding to the range of the super-multigroup cross-sectional area of the subgroup is different from each other. The settings related to the classification of the subgroups are set by classifying the neutrons into the energy range corresponding to the range of the supermultigroup cross-sectional area using the supermultigroup cross-sectional area represented by the log scale as an index. The resonance calculation method according to any one of claims 1 to 4, wherein the resonance calculation method is performed. In an analysis device equipped with a calculation unit that divides the neutron energy in the analysis target region into a plurality of energy groups and executes resonance calculation for obtaining an effective cross section which is the average cross section of each divided energy group.
The calculation unit
The analysis target region is treated as a calculation system having a simple geometric shape, and a plurality of the energy groups are treated as a calculation system to be a dense super-multi-group energy group with many divisions, and the super-multi-group neutrons are treated. The first resonance calculation step to calculate the ultra-multigroup data including the flux
The analysis target region is treated as a calculation system having a more detailed geometric shape than the first resonance calculation step, and a multi-group energy group having less division and coarser than the first resonance calculation step. Using the super-multi-group data, each group is classified into a plurality of subgroups, and the super-multi-group cross-sectional area included in the super-multi-group data is reduced in each sub-group. A second resonance calculation step of generating a subgroup cross-sectional area and calculating the effective cross-sectional area of the analysis target region by using the subgroup cross-sectional area is executed. .. In the resonance calculation program, the calculation unit of the analysis device divides the neutron energy in the analysis target region into a plurality of energy groups and obtains the effective cross-sectional area which is the average cross-sectional area of each divided energy group.
The analysis target region is treated as a calculation system having a simple geometric shape, and a plurality of the energy groups are treated as a calculation system to be a dense super-multi-group energy group with many divisions, and the super-multi-group neutrons are treated. The first resonance calculation step to calculate the ultra-multigroup data including the flux
The analysis target region is treated as a calculation system having a detailed geometric shape as compared with the first resonance calculation step, and a multi-group energy group having less division and coarseness than the first resonance calculation step. Using the super-multi-group data, each group is classified into a plurality of subgroups, and the super-multi-group cross-sectional area included in the super-multi-group data is reduced in each sub-group. A resonance calculation program comprising: a second resonance calculation step of generating a subgroup cross-sectional area and calculating the effective cross-sectional area of the analysis target region by using the subgroup cross-sectional area. ..

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