JPH11295472A - Method and device for calculating particle transportation, device for monitoring reactor core characteristic of reactor, and nuclear power station - Google Patents

Abstract

PROBLEM TO BE SOLVED: To greatly improve calculation speed in the correlation sampling Monte Carlo method by taking in virtual scattering in a transportation equation. SOLUTION: First, at the initial stage of combustion, a normal Monte Carlo calculation is executed, and sampling information is calculated while analyzing nuclear characteristics and is retained on a memory. In the Monte Carlo calculation, virtual scattering is used. Then, the degree of combustion is updated and the number density of each nuclide is calculated, and a new macro sectional area is calculated. More specifically, the weight of a neutron is adjusted from a current macro sectional area and a retained reference system macro sectional area, based on sampling information, thus solving nuclear characteristics and hence drastically reducing the analysis time of particle transportation by the correlation sampling Monte Carlo method. The method can also be applied the time-series calculation of the operation schedule calculation of the reactor.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and apparatus for evaluating and predicting power distribution and reactivity in a nuclear reactor core by numerical calculation.

[0002]

2. Description of the Related Art The Monte Carlo method is generally used as an analysis technique for solving transport problems of neutral particles and charged particles such as distribution of neutrons in a reactor core. The Monte Carlo method is a method of simulating (tracking) the behavior of each particle based on a probability distribution, and is called a statistical method. On the other hand, there is a method of obtaining a numerical solution by discretizing from a transport equation representing a particle density distribution in a spatial region, energy, a particle flight direction, and the like, and is called a deterministic method. In the deterministic method, to discretize the spatial domain,
In addition to the disadvantage of not being able to handle complex shapes well, discretization itself causes errors.

On the other hand, the Monte Carlo method has an excellent feature that any shape can be analyzed and that space and energy can be handled continuously. Therefore, it is often used as a correct answer for verifying a new analysis model or a new design. As described above, the Monte Carlo method can be said to be a method with high accuracy in principle, but has a drawback that it requires a long calculation time because it needs to track an enormous number of particles.

In the Monte Carlo method, no error due to discretization occurs, but there is always a statistical error, and this statistical error is inversely proportional to the square root of the number of neutrons to be tracked.
To increase the double precision, a calculation time of 100 times is required.

For the above reasons, the Monte Carlo method is not suitable for large-scale calculations. For example, in the core analysis of a nuclear reactor, the Monte Carlo method is used for static analysis of the individual fuel assemblies that compose the core. It is not normally used because it takes too much analysis computation time.

In order to overcome the above-mentioned disadvantages, various methods have been used to speed up the Monte Carlo method, but the method can be roughly divided into two methods. That is, a method for reducing the error itself and a method for improving the processing speed. In the former, a method called importance sampling method is typical, and in the latter, a method using a correlation sampling method is recently studied.

The correlation sampling method is described in "Monte Carlo
Principles and Neutron TransportProblems ", J. Spani
As described in Er and EM Gerbard, p. 129, when two cases are solved by the Monte Carlo method, analysis is performed using highly correlated sampling information. Here, the sampling information refers to the history of the behavior of each particle determined based on the probability distribution.

Originally, the correlation sampling method is a method for improving the accuracy of evaluating the difference when very similar cases are solved by the Monte Carlo method. In other words, if very similar cases are solved independently, the differences will be hidden in each other's statistical errors, so using highly correlated sampling information to offset the deviations due to the statistical errors,
It attempts to evaluate only the differences.

Therefore, the higher the correlation between the two, the better, and a method of analyzing two cases using exactly the same sampling information is used. Here, the calculation serving as a reference for calculating the sampling information is referred to as a reference calculation, and the calculation for analyzing a similar system using the same sampling information is referred to as a perturbation calculation.

In the perturbation calculation, a difference from the reference calculation is taken in by adjusting the existence probability of each particle, which is called a particle weight. That is, for each element of the sampling information of each particle, adjustment is performed by multiplying the ratio of the probability in the reference case and the probability of the perturbation case by the weight of the particle. This technique was used to improve the processing speed of the Monte Carlo method.
“Calculations of Reactivity Perturbations Using C
orrelated SamplingMonte Carlo ", A.Majumdar, Trans.
Am. Nucl. Soc. (1994), p. 203.

In this method, a plurality of perturbation calculations are simultaneously analyzed using exactly the same sampling information.
The calculation time has been shortened. In other words, in Monte Carlo calculation, a great deal of time is spent calculating the collision position of each particle and calculating the random number, but since the sampling information is shared by the correlation sampling method, these processes need not be performed in the perturbation calculation, The calculation time is shortened accordingly. As described above, according to the related art, the speed of the Monte Carlo method is increased by simultaneously solving a plurality of cases by the correlation sampling method.

[0012]

The above prior art has two problems. One is that the improvement in calculation speed is not large. Second, multiple calculations can be performed simultaneously, but not in chronological order.

The former problem is based on the following reasons. We have already mentioned that in order to adjust the particle weight, we need to find the ratio of probabilities between the reference system and the perturbation system. In the case of neutral particles, the probability of the interval between collisions is given by:

[0014]

(Equation 1)

S: Distance from the previous collision position p (s): Probability of collision at s Σ (s): Total collision cross-section at s Thus, in order to obtain the collision interval probability p, the collision position It is necessary to perform the integration of Σ between. Since the spatial distribution of 異 な る differs between calculation cases, it is necessary to find it in each of the reference case and the perturbation case, which imposes a heavy burden on calculation time. As described above, even if it is not necessary to calculate the collision position in the perturbation case, the probability itself needs to be evaluated, so that the calculation time cannot be significantly reduced.

The latter problem is based on the following reasons. In other words, when performing time-series calculations such as performing perturbation calculation after performing reference calculation, sampling information for reference calculation is temporarily stored in a memory or a storage medium such as a hard disk, and is reused when performing perturbation calculation. Must be possible. If this processing is possible, the correlation sampling method can be applied to time series processing that cannot be calculated simultaneously, such as combustion calculation in reactor core analysis, and the application range is greatly expanded.

However, as can be seen from equation (1), it is necessary to know the exact coordinates of each collision as sampling information, and the storage capacity is enormous. Taking the analysis of a fuel assembly of a nuclear reactor as an example, if the number of neutrons tracked is approximately 200,000 and the average number of collisions of each neutron is estimated to be 100 to obtain sufficient accuracy in analysis, sampling of 2 × 10 ⁷ Elements are required. Assuming that the coordinates of x, y, and z are represented by a 4-byte real number, an information amount of 240 MB is required only with the coordinate information. Further, in addition to the information on the energy and the angle of the particle, information on a detailed geometric shape for calculating the equation (Equation 1) is required, and it is difficult to apply the information to a large-scale calculation.

An object of the present invention is to make it possible to greatly improve the calculation speed in the correlation sampling Monte Carlo method.
An object of the present invention is to provide a calculation method, a device therefor, and the like, which enable time-series processing by greatly reducing the capacity required for storing sampling information.

[0019]

The above object is achieved by incorporating virtual scattering into the transport equation.

The virtual scattering is virtual scattering that does not change the energy and direction of particles before and after scattering, and is described in “Monte Carlo Principles and Neutron Transport”.
Problems ", J. Spanier and EM Gerbard, page 68, described as delta scattering. Applying this to the Monte Carlo method treats virtual scattering as a single collision, but does not change the energy or direction of the particles. Therefore, virtual scattering is a scattering that has no actual state, so it can be taken in any size, and the total collision cross section Σ ^* including virtual scattering depends on the location If you choose the magnitude of virtual scattering Σ _δ (s) so as not to

[0021]

[Number 2] ^{Σ * = Σ (s) +} Σ δ (s) ... ( Equation 2) sigma ^*: (not depending on location) total collision cross-section Σ δ _(s): may be a virtual scattering cross section . If the correlation sampling method is applied to the Monte Carlo method using virtual scattering, the collision probability in the equation (Equation 1) is as follows.

[0022]

P (s) = Σ (s) exp (−Σ ^* s) (Equation 3) That is, e which had to be evaluated by the equation (Equation 1)
The integral in xp can be expressed as a constant multiple of the distance between collisions. More importantly, in equation (2):
The reference calculation and perturbation calculation, as Σ ^* are the same Σ
_{If δ} (s) is selected, the exp term in equation (Equation 3) is equivalent in both calculations, so that adjustment of the particle weight is possible only with the total cross-sectional area Σ (s) at the collision position.

From the above, the above two problems can be solved by means of combining virtual scattering with the correlated sampling Monte Carlo method. That is, since the particle weight can be adjusted only by the cross-sectional area at the collision position, the perturbation calculation is greatly simplified and speeded up. Furthermore, it is not necessary to store the exact position of the collision, and instead, it is sufficient to store which cross-sectional area data the collision position belongs to.

Taking the analysis of a fuel assembly of a nuclear reactor as an example,
Since there are about 50 types of cross-sectional area data, it can be stored if it has 1 byte. Therefore, it is possible to store the coordinate data with 20 MB, which is 1/10 the capacity of the conventional example. Further, since it is not necessary to perform integral calculation based on the geometric shape, it is not necessary to hold the geometric shape data. From these points, the capacity required for storing the sampling information can be significantly reduced, and time-series processing in large-scale calculation can be performed.

[0025]

DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below with reference to the drawings.

In the first embodiment of the present invention, nuclear characteristics such as infinite multiplication factor and power distribution in a fuel assembly constituting a reactor core are analyzed while updating burnup. FIG. 1 is a flowchart illustrating the flow of the correlation sampling Monte Carlo calculation according to the present embodiment. First, normal Monte Carlo calculation is performed in the early stage of combustion, sampling information is calculated while analyzing nuclear characteristics, and the information is stored in a memory. The Monte Carlo calculation here uses virtual scattering. The used macro cross-sectional area is stored in the memory as a reference system macro cross-sectional area.

Next, the burnup is updated, the number density of each nuclide is calculated, and a new macro sectional area is calculated. In the normal calculation, the same Monte Carlo calculation as in the initial stage of combustion is performed here, but in the present invention, the correlation sampling calculation using virtual scattering is performed. That is, based on the sampling information, the neutron weight is adjusted from the current macro cross section (perturbation system macro cross section) and the retained reference system macro cross section, and the nuclear properties are analyzed. The operations of updating the burnup, creating the macro sectional area, and updating the burnup are repeated until the desired burnup is reached, but the same sampling information and the same reference macro sectional area are used.

FIG. 2 is a sectional view of the assembly used in this embodiment. The fuel assembly is composed of three different types of fuel, with enrichments of 0.7%, 1.3% and 1.7% by weight, respectively. In this embodiment, reflection conditions are used for the boundary of the aggregate and the vertical direction. The void ratio was 40%. FIG. 3 shows a comparison between a change in combustion at an infinite multiplication factor calculated by ordinary Monte Carlo calculation and that according to the present embodiment. In each calculation, 3 × 10 ⁵ per burnup
Neutrons were tracked. In addition, as a reference solution,
A case where doubled (6 × 10 ⁶ ) neutrons are traced is also shown.
As can be seen from the figure, the changes of the three infinite multiplication factors are almost the same, indicating that the present embodiment is effective in accuracy.

FIG. 4 shows the change in combustion of the relative output of the upper left fuel rod in FIG. Since the output is a local characteristic, the output is statistically larger than the infinite multiplication factor, which is the overall characteristic, and is an evaluation item that the Monte Carlo method is not good at. As can be seen from the figure, the Monte Carlo calculation usually fluctuates up and down with respect to the reference solution, and there is a part where the relative output that should increase with combustion decreases.

On the other hand, the tendency of the output by the correlation sampling method almost coincides with the reference solution, and it can be seen that a constant bias is applied as a value. Because this is calculated only from the sampling information at the beginning of combustion,
This is because the statistical error between the combustions is offset. The constant bias can be seen as trailing the statistical error at the beginning of combustion.

FIG. 5 shows the structure of the apparatus in this embodiment. Input information such as macro cross-sectional area information, cross-sectional area configuration, and geometric shape, which are basic information, is held on a magnetic disk.
The information used for the correlation sampling calculation, such as the sampling information and the reference system macro cross-sectional area, is read into the memory, and an area is previously secured in the memory, and is always held there. By doing so, the time for acquiring data can be minimized, and high-speed correlation sampling calculation can be performed.

Although the effect of shortening the calculation time in the present embodiment differs depending on the type of calculation, when the calculation is performed by a vector processing type computer, a speed improvement of about 70 times is seen in the Monte Carlo calculation part. In addition, when the calculation was performed using a normal engineering workstation, a speed improvement of about 10 times was observed.

According to the present embodiment, it is possible to greatly reduce the calculation time while maintaining the accuracy of the original Monte Carlo method. In addition, the time-series calculation which has not been performed conventionally stores the sampling information in the memory. Holding on showed that this was possible.

Next, a second embodiment according to the present invention will be described with reference to FIG.
It will be described based on. In the present embodiment, the calculation flow is as follows.
Same as the first embodiment, but the usage of the device is different.
All the sampling information is placed on the magnetic disk, and only a part of the sampling information is placed on the memory. The processor performs the correlation sampling calculation based on the sampling information in the memory, but after using all the sampling information in the memory, repeats the process of loading new sampling information from the magnetic disk into the memory and performing the calculation. .

As described above, by using the magnetic disk, the amount of memory used can be reduced, and correlation sampling for a large-scale system and with a computer having a small amount of memory can be performed. In addition, if the multi-shred processing is performed separately for the shred for performing the correlation sampling and the shred for reading the sampling data from the magnetic disk into the memory, the former mainly uses the processor,
Since the latter mainly uses the IO processing system, efficient processing with less waiting for the CPU is possible.

Next, a third embodiment according to the present invention will be described with reference to FIG.
It will be described based on. In this embodiment, the reference calculation and the perturbation calculation are completely independent calculations. However, the geometric shapes must be the same to perform the correlation sampling calculation. The sampling information and the reference system macro cross-sectional area calculated in the reference calculation are stored in the magnetic disk, and the reference calculation ends. As shown in FIG. 8, in the perturbation system calculation, the input and the sampling information regarding the cross-sectional area configuration stored on the magnetic disk and the reference system macro cross-sectional area are called out on a memory and calculated by the correlation sampling method. Geometry information is not required only by perturbation system calculation. In the present embodiment, the perturbation system calculation is a combustion calculation of one system, but a plurality of systems can be calculated sequentially. It is also possible to leave sampling information or the like on a memory without storing it once on a magnetic disk and use it as it is in perturbation calculation.

Next, a fourth embodiment according to the present invention will be described with reference to FIG.
It will be described based on. In this embodiment, n reference calculations are performed, and the respective sampling information and reference macro sectional area are stored on the magnetic disk. In the perturbation calculation, the correlation sampling calculation is performed using any or all of the sampling information and the reference macro sectional area. By increasing the amount of statistics in this way, it is possible to reduce statistical errors. Also, in this embodiment,
It is also possible to leave all sampling information and the like on a memory without storing it on a magnetic disk and use it as it is in perturbation calculation.

Next, a fifth embodiment according to the present invention will be described with reference to FIG.
0 will be described. In this embodiment, correlation sampling calculation of a plurality of perturbation systems is performed using m processors. However, since each processor shares one memory, it is called shared memory type parallel processing. Since the same sampling information can be shared between perturbation systems, this type of parallel processing is effective. However,
It is necessary to provide the cross-sectional area configuration depending on each system and the macro cross-sectional area information based on it. In this embodiment, as in the fourth embodiment, the sampling information and the reference system macro cross section machine data calculated from a plurality of reference calculations are shared by a plurality of perturbation calculations.

Next, a sixth embodiment according to the present invention will be described with reference to FIG.
1 will be described. In this embodiment, an independent perturbation calculation is performed by j × m processors. m
Since each processor shares one memory, there are j memories. The sampling information and the reference macro cross-sectional area obtained by the n individual reference calculations are arbitrarily distributed from the magnetic disk to the m memories. Each processor is directly connected to the sampling data stored in the shared memory, and to the sampling data stored in the non-shared memory.
Arbitrary sampling data can be accessed by communication via another processor. By distributing a plurality of processors, a plurality of memories, and a plurality of sampling data in this manner, a plurality of correlation sampling calculations can be executed at high speed.

Next, a sixth embodiment according to the present invention will be described with reference to FIG.
2 will be described. In this embodiment, the reference calculation and the k correlation sampling calculations are performed simultaneously. That is, when tracking individual neutrons, the weight of neutrons in each perturbation system is adjusted for each collision. This makes it possible to perform the correlation sampling calculation without holding the sampling information in the memory.

[0041]

According to the present invention, the time required for analyzing particle transport by the correlation sampling Monte Carlo method can be greatly reduced. In addition, the present invention can be applied to time-series calculations such as a reactor operation plan calculation. Since it is possible to provide an operation planning method and a device thereof for a reactor that simulates a transport equation without modeling, it is possible to accurately predict core characteristics such as power distribution and reactivity in a core, and Driving becomes easy.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a flow of a fuel assembly combustion characteristic analysis calculation according to an embodiment of the present invention.

FIG. 2 is a sectional view illustrating a configuration of a fuel assembly used in an example of the present invention.

FIG. 3 is a graph showing an infinite multiplication factor combustion change of a fuel assembly analyzed in an example of the present invention.

FIG. 4 is a graph showing a change in combustion of one fuel rod of a fuel assembly analyzed in an example of the present invention.

FIG. 5 is a configuration diagram of a computing device according to an embodiment of the present invention.

FIG. 6 is a configuration diagram of a computing device according to an embodiment of the present invention.

FIG. 7 is a flowchart illustrating a flow of a fuel assembly combustion characteristic analysis calculation according to an embodiment of the present invention.

FIG. 8 is a configuration diagram of a computing device according to an embodiment of the present invention.

FIG. 9 is a configuration diagram of a computing device according to an embodiment of the present invention.

FIG. 10 is a configuration diagram of a computing device according to an embodiment of the present invention.

FIG. 11 is a configuration diagram of a computing device according to an embodiment of the present invention.

FIG. 12 is a flowchart showing the flow of a fuel assembly combustion characteristic analysis calculation according to one embodiment of the present invention.

[Explanation of symbols]

11 ... Low enrichment fuel rod, 12 ... Medium enrichment fuel rod, 13 ...
High enrichment fuel rods, 14 ... channel box, 15 ... boundaries of the calculation area.

Continued on the front page (72) Inventor Hajio Aoyama 7-2-1, Omika-cho, Hitachi City, Ibaraki Prefecture Within Hitachi, Ltd. Electric Power & Electric Equipment Development Division

Claims (16)

[Claims] In a reference calculation for solving a transport equation of a particle by a Monte Carlo method, and in one or more perturbation calculations for solving a different system by a correlation sampling Monte Carlo method using sampling information of the reference calculation, sampling information in the reference calculation is accumulated. And performing a perturbation calculation based on the accumulated sampling information. 2. The method according to claim 1, wherein the sampling information in the reference calculation is stored in a memory. 3. The calculation method according to claim 1, wherein the sampling information in the reference calculation is recorded on a non-volatile storage medium such as a hard disk, and the sampling information is later loaded on a memory, and one or more of the sampling information is loaded based on the sampling information. Calculation method of particle transport that performs perturbation calculation. 4. The method according to claim 1, wherein a perturbation calculation is performed using sampling information of a plurality of reference calculations. 5. An apparatus for calculating particle transport, wherein calculations are performed based on claim 1. 6. In a reference calculation for solving a transport equation of a particle by a Monte Carlo method, and in one or more perturbation calculations for solving a different system by a correlation sampling Monte Carlo method using sampling information of the reference calculation, virtual scattering is applied to each transport equation. And calculating the perturbation calculation by adjusting the neutron weight at the time of the perturbation calculation based on the difference in the reaction cross section at the collision position of each particle between the reference calculation and the perturbation calculation. 7. The calculation method according to claim 6, wherein the generation position of each particle in the reference calculation, the particle energy at the time of generation, each collision position, the particle energy and angle at each collision or after the collision, and the particle of each space region. A particle transport calculation method for accumulating the reaction cross section of the above as sampling information and performing one or more perturbation calculations based on the accumulated sampling information. 8. The method according to claim 7, wherein the sampling information in the reference calculation is stored in a memory. 9. The calculation method according to claim 7, wherein the sampling information in the reference calculation is recorded on a non-volatile storage medium such as a hard disk, and the sampling information is loaded on a memory later, and one or more of the sampling information is stored based on the sampling information. Calculation method of particle transport that performs perturbation calculation. 10. The method according to claim 7, wherein a perturbation calculation is performed by using sampling information of a plurality of reference calculations. 11. An apparatus for calculating particle transport based on claim 7. 12. A fuel assembly according to claim 7, wherein in a fuel assembly calculation for evaluating a nuclear characteristic value of each region in the reactor core divided into multiple regions by a Monte Carlo method, calculation for a certain fuel assembly is performed. 7. A calculation method of particle transport which is used as a reference calculation in 7, and is performed as a perturbation calculation in a calculation of a fuel assembly having the same geometric shape and a different fuel enrichment distribution. 13. The fuel assembly calculation according to claim 7, wherein a nuclear characteristic value according to the burnup of each region in the reactor core divided into multiple regions is evaluated by a Monte Carlo method.
8. A method for calculating particle transport, wherein a calculation at a certain burning point is used as a reference calculation, and a calculation at several subsequent burning points is performed as a perturbation calculation according to claim 7. 14. A fuel assembly calculation method according to claim 7, wherein a nuclear characteristic value corresponding to a void fraction of each region in the reactor core divided into multiple regions is evaluated by a Monte Carlo method. A method of calculating particle transport, where the calculation at the void fraction is used as the reference calculation, and the perturbation calculation is performed in the calculations at other void fractions. 15. The power distribution and reactivity in the reactor core are evaluated based on the nuclear characteristic values of each region in the reactor core divided into multiple regions, and the fuel composition and control rods in the reactor are evaluated. 15. The reactor according to any one of claims 12 to 14, wherein the reactor core characteristic monitoring device used for drafting an insertion plan includes means for evaluating a nuclear characteristic value of each region. Core characteristic monitoring equipment. 16. Power distribution and reactivity in the reactor core are evaluated based on nuclear characteristic values in each region in the reactor core divided into multiple regions, and a core is designed based on the evaluation values. The nuclear power plant according to any one of claims 12 to 14, wherein the nuclear power plant is designed using the evaluated nuclear characteristic value.