JP3023185B2 - Reactor core performance calculator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an on-line core performance calculation apparatus for calculating the core performance of a nuclear reactor based on a three-dimensional physical model of the core, and more particularly to a coarse mesh 1.5 group neutron diffusion model as a three-dimensional physical model. The present invention relates to a reactor performance calculation device for a nuclear reactor using the same.

[0002]

2. Description of the Related Art In on-line core monitoring based on a three-dimensional physical model of a reactor, it is necessary to evaluate core performance in a short time on a process computer at a reactor site. It is common to use a coarse mesh diffusion model (also referred to as 1.5 group).

With respect to the conventional 1.5-group coarse mesh diffusion model, a representative PRESTO model (S. Borrensen, "AS
implified, Coarse-mesh, Three-Dimensional DiffusionS
cheme for Calculating the Gross Power Distribution
in a Boiling WaterReactor ”, Nuclear Science and
Technology, vol. 44, p37, 1971).

In the coarse mesh node method, a fuel assembly constituting a core is divided into a large number of fuel nodes, and it is approximated that the fuel composition in the nodes is homogeneous. The diffusion equation for the fast group in the neutron two-group scheme uses the usual notation,
It is expressed by the following equation.

[0005]

(Equation 1) Where the ratio of thermal neutron flux to fast neutron flux,

[0006]

(Equation 2) Is called a spectrum index.

Near the center of a node, f is approximated by an asymptotic spectral index equal to the node-averaged spectral index in an infinite lattice system.

[0008]

(Equation 3) In order to solve Equation 1 by a computer using the finite difference method, spatial discretization is required. For this reason, when Equation 1 is integrated with the node volume,

[0009]

(Equation 4) Here, B: node surface area n: surface normal vector V: node volume φ: Node average fast neutron flux f: Node average spectrum index. The first term on the left side of Equation 4 representing the neutron balance of the node is neutron leakage from the node surface due to neutron flow, the second term on the left side is neutron removal by absorption and deceleration, and the first term on the right side is fission. It represents the production of neutrons, that is, the reaction rate.

The neutron flow of the first term is represented by a finite difference approximation. The neutron flow at the boundary surface between the nodes i and j is calculated using the fast neutron flux φ _i at the center of the volume of the node.

[0011]

(Equation 5) Becomes Here, h is the radial width of the node. In the axial direction, h is replaced by the axial node width k.

Using equation 5, the three-dimensional difference equation is:

[0013]

(Equation 6) Here, 4j and 2k indicate radially and axially adjacent nodes, respectively. Also,

[0014]

(Equation 7) It is.

The fast neutron flux at the node average in Equation 6 is given by the weighted average of the fast neutron flux at the center of the volume between itself and the adjacent node.

[0016]

(Equation 8) The load factors a and b are adjustment factors determined by numerical experiments so as to reproduce the neutron flow between nodes by detailed calculation.

Similarly, the node-averaged spectrum index of Equation 6 is given by the weighted average of the asymptotic spectrum index between itself and the adjacent node.

[0018]

(Equation 9) Here, the load factors c and d are adjustment factors determined by numerical experiments so as to reproduce the node-averaged thermal neutron flux by the detailed calculation.

The power density of a node is given by the following equation.

[0020]

(Equation 10)

[0021]

The conventional modified group model described above requires (1) parameter adjustment for each core in order to include an adjustment factor in the model, which requires cost and time. Such a detailed calculation must be performed. (2) Since the fast neutron flux and the thermal neutron flux distribution in the node are not explicitly considered, even if the above-mentioned regulator is adjusted, the accuracy of the neutron flow and the reaction rate included in the neutron balance equation of the node is high. Absent. (3) The inhomogeneity of the composition of the substance in the node is not taken into account. There are problems such as.

In recent years, for the purpose of improving the core economy, a multi-fuel core initially loaded, a high burnup of fuel, or a MOX fuel core containing plutonium has been introduced.
In these fuel cores, since the asymptotic spectrum difference between the fuel nodes is large, the thermal neutron transfer between the nodes due to the spectral coupling between the fuel nodes is larger than in the conventional core. For this reason, in the conventional modified one-group model that does not explicitly consider the thermal neutron flux distribution in the node, the calculation accuracy of the node output deteriorates due to the above-described disadvantages.

An example of addressing the above problem (2) within the framework of the modified one-group model is described in M. Tsuiki et al., "A New Br
ief Diffusion Scheme for Three-Dimensional Calcula
tionof a BWR core ", Journal of Nuclear Science and
Technology, vol.13, p541, 1976. In this method, the weighting factor of Equation 9 representing the node-averaged spectral index is analytically represented by solving a one-dimensional diffusion problem to obtain a spectral index distribution in the node. The distribution of the spectral index in a one-dimensional node (0 ≦ x ≦ h) is represented by the following equation. Here, the values of the spectrum indexes at the node boundaries x = 0 and x = h are f (0) and f (h), respectively.

[0024]

[Equation 11] Here, k is the reciprocal of the diffusion distance of the heat group.

Thus, the node average spectrum index is represented by the following equation using the node constant.

[0026]

(Equation 12) However

[0027]

(Equation 13) Represents the difference between the spectral index and the asymptotic value at the node boundary.

The second term of the equation (12) represents the change of the node average spectrum index from the asymptotic value.
2 indicates that the node average spectrum index is represented by the sum of the asymptotic value of the spectrum index and the average of changes from the asymptotic value.

However, in this method, it is difficult to analytically determine the spectral index distribution in two or more dimensions. Therefore, the extension from the one-dimensional problem to the three-dimensional problem is performed by a simple analogy. Since the inhomogeneity of is not explicitly taken into account, the load factor still has an adjustment factor to be determined numerically. In addition, the influence of the distribution of the spectral index within the node on the neutron flow has been neglected.

Further, a so-called modern node method has been proposed as a method for improving the drawbacks of the conventional modified group method. This method is described in, for example, Toshikazu Takeda, “A New Power Distribution Calculation Method for Light Water Reactors”, Nuclear Power Industry, vol.3
3, p58, 1987. In the modern node method, for the above-mentioned disadvantage (2), the accuracy is improved by polynomial expansion of the neutron flux in the node. As for the defect (3), the neutron flux discontinuity factor is used to introduce the node heterogeneity effect.

However, the modern node method can be used only for models with two or more neutrons, and because it performs polynomial expansion, it takes too much calculation time as compared with the modified one-group method, and the on-line core calculation that requires speed is required. Not suitable for

The present invention has been made in view of the above points, and has a short calculation time suitable for on-line calculation and can accurately calculate the power distribution in the reactor core. It is intended to provide a device.

[0033]

According to the present invention, there is provided an on-line core performance calculation apparatus for calculating the core performance of a nuclear reactor based on a three-dimensional physical model of a core, as a means for achieving the above object. Using a 1.5-group neutron diffusion model and inputting core state parameters, the core 3D neutron that calculates and outputs the fast neutron flux distribution of the fuel node average and the asymptotic ratio of the thermal neutron flux to the fast neutron flux in the fuel node Diffusion calculator; this core 3
A thermal neutron flux distribution calculator in the fuel node for analytically obtaining the distribution of thermal neutron flux in the fuel node based on the output from the three-dimensional neutron diffusion calculator; and an output from the thermal neutron flux distribution calculator in the fuel node. A spectrum correction amount calculating device for calculating a spectrum correction amount for a fast neutron flow between fuel nodes and a reaction rate of the fuel node based on the coarse mesh method;
A core power distribution calculator for calculating a three-dimensional power distribution of the core based on each output from the three-dimensional neutron diffusion calculator;
Are provided, respectively.

[0034]

In the reactor core performance calculation apparatus according to the present invention, a coarse mesh 1.5
By using the group neutron diffusion model and using the fast neutron flux of the fuel node average and the asymptotic spectrum index of the node average to analytically represent the spatial distribution of the thermal neutron flux in the fuel node, the fuel node in the coarse mesh method Between the fast neutron flow and the average reaction rate of the fuel node. As a result, the distribution of the thermal neutron flux in the node is explicitly considered while maintaining the advantage of the modified one-group method on the calculation speed, and the power distribution in the core can be accurately calculated.

[0035]

An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 shows an example of an apparatus for calculating core performance of a nuclear reactor according to the present invention. The apparatus for calculating core performance of a nuclear reactor includes a core three-dimensional neutron diffusion calculator 1 and a thermal neutron in a fuel node. A flux distribution calculator 2, a spectrum correction amount calculator 3, and a core power distribution calculator 4 are provided, and a coarse mesh 1.5 is used as a three-dimensional physical model of the core.
Using the group neutron diffusion model, the core performance of the reactor is calculated online.

The core three-dimensional neutron diffusion calculator 1 calculates the node average fast neutron flux distribution in the core based on the modified one-group coarse mesh diffusion calculation by inputting the core state parameters 6 from the reactor core 5. Has become. The calculation results of the three-dimensional core neutron diffusion calculator 1 are output to the thermal neutron flux distribution calculator 2 in the fuel node and the power distribution calculator 4 in the core, respectively.

That is, the fuel node average fast neutron flux distribution 7 and the asymptotic ratio of the thermal neutron flux to the fast neutron flux in the fuel node, that is, the spectrum index 8, are calculated by the thermal neutron flux distribution calculator 2 in the fuel node. Given. The in-core power distribution calculator 4 is provided with the fast neutron flux distribution 7.

Thermal neutron flux distribution calculator 2 in fuel node
Is configured to analytically determine the distribution of the fast neutron flux in the fuel node based on the signal from the core three-dimensional neutron diffusion calculator 1, and the determined thermal neutron flux distribution 9 in the fuel node is: It is given to the spectrum correction amount calculation device 3. The spectrum correction amount calculation device 3 calculates a spectrum correction amount for the fast neutron flow between the fuel nodes and the average reaction rate of the nodes in the coarse mesh method. And
The calculation result 10 by the spectrum correction amount calculation device 3 is:
This is supplied to the in-core power distribution calculator 4 together with the fast neutron distribution 7.
A dimensional output distribution is calculated.

Next, the operation of the present embodiment will be described.
First, the basic concept of the present invention will be described. In the present invention, the influence of the distribution of the spectral index in the node is considered for the neutron flow in Equation 4 as the neutron balance equation of the node. In other words, the expression 1 as a diffusion equation is laterally integrated in a direction other than the direction of interest (referred to as the x direction) to make it one-dimensional. In such a one-dimensional system, focusing on the fact that the spectral index distribution in the node can be approximated by Expression 11, the following differential equation in the x- direction is obtained.

[0041]

[Equation 14] However

[0042]

(Equation 15) Is the buckling in the x-direction,

[0043]

(Equation 16) Is lateral buckling.

Solving Equation 14 gives the following equation for the neutron flow at x = 0.

[0045]

[Equation 17] The second term of Equation 17 represents the effect on the neutron flow of the distribution within the node of the spectral index, which has been neglected in Equation 5 as a conventional modified group equation.

Γ and θ are correction coefficients based on the distribution of the fast neutron flux in the node, and are represented by the following equations, respectively.

[0047]

(Equation 18)

[0048]

[Equation 19] The final finite difference equation in the present invention is expressed by

[0049]

(Equation 20) Becomes here,

[0050]

(Equation 21) Represents the effect on the neutron flux due to the change of the spectral index from the asymptotic value, and is expressed by the following equation.

[0051]

(Equation 22) Here, j represents a node adjacent in the radial direction, k represents a node adjacent in the axial direction, and δf _j is a change of a spectrum index at a node boundary.

[0052] Factor F _r, F _a are each represented by the following formula.

[0053]

(Equation 23)

[0054]

(Equation 24) Equation 22 indicates that when considering the in-node distribution of the spectrum index in the neutron flow, in the final difference equation, the node average of the change from the asymptotic value of the spectrum index must be added by a factor F. Is shown.
The value of F is 0.2 to 0.3 for normal fuel. In the conventional modified one-group method, since F = 1.0, when the change of the spectral index from the asymptotic value is large, the calculation accuracy deteriorates.

On the other hand, as for the node average output density, similarly to the conventional modified one-group method, the influence of the change of the spectrum index from the asymptotic value may be obtained simply by averaging the nodes. Is given by the following equation.

[0056]

(Equation 25) here,

[0057]

(Equation 26) Represents the influence on the power density due to the change of the spectrum index from the asymptotic value, and is given by the equation where F = 1.0 in Equation 22.

In the modified one-group method, it is extremely important to accurately evaluate the change of the node-averaged spectral index from the asymptotic value, or, similarly, the node-averaged spectral index. In the case of one-dimensional, the spectral index distribution in the node can be analytically represented, but in the case of two-dimensional or more, it is difficult to obtain analytically, and in the past it was only a simple analogy from the one-dimensional case. . For this reason, it has been difficult to accurately determine the node average spectrum index.

In the present invention, the thermal neutron flux distribution in the node is expanded using a general solution of the diffusion equation in a limited area in the core composed of the fuel node of interest and the surrounding fuel nodes. It is expressed with high accuracy. The expansion coefficient can be determined using the spectrum index of the center of the node and the node boundary. For simplicity, a method is first shown for the two-dimensional case, and then extended to three-dimensional.

The diffusion equation for the thermal neutron flux of a system in which each of the fuel nodes is homogenized is expressed by the following equation 27 using two groups of neutron diffusion models. Here, the first group is a high-speed group, and the second group is a heat group.

[0061]

[Equation 27] Here, k is the reciprocal of the diffusion distance of the heat group, and is defined by the following equation.

[0062]

[Equation 28] Here, Σ _{2 is the} average macroscopic removal cross-sectional area of the thermal neutron fuel segment, and D ₂ is the average diffusion coefficient of the thermal neutron fuel segment. The fast neutron flux can be assumed to be spatially constant in the fuel segment.

In the right side of Equation 27,

[0064]

(Equation 29) Denotes a thermal neutron flux without thermal neutron gradient, ie, in a homogenized infinite lattice system, and is called asymptotic thermal neutron flux. Equation 27 as a diffusion equation can be analytically solved under approximation of certain boundary conditions. In this method, the influence of the adjacent fuel node on the value of the thermal neutron flux in the ordinary LWR fuel decreases with the distance r from the boundary with the adjacent fuel node in the form of approximately exp (−κr), and becomes 1 / the fuel node width. By giving an asymptotic boundary condition using the fact that it becomes almost negligible at about 2, the thermal neutron flux and the asymptotic thermal neutron flux at the position (x, y) in the fuel assembly are given. Give the difference.

Consider a limited region in the core composed of four nodes adjacent to the fuel node of interest and four adjacent nodes from the diagonal position as shown in FIG. The difference between the thermal neutron flux distribution in the fuel node of interest and the asymptotic thermal neutron flux is analytically represented by an order by superposition of general solutions of the diffusion equation.

[0066]

[Equation 30]

[0067]

(Equation 31)

[0068]

(Equation 32) Here, the subscripts j = 1 and 4 represent four nodes radially adjacent to the fuel node 0 of interest as shown in FIG. 2, and the subscripts j = 5 and 8 denote the four fuel nodes adjacent from the diagonal position. Represent. The subscripts m and n represent two surface adjacent nodes that are adjacent to both the diagonally adjacent fuel node j and the target node 0. δf _j is a point on the boundary of fuel node 0 of interest in FIG.
The value of the change from the asymptotic spectrum of the spectrum at j) is shown.

Equation 31 is the value of the spectral change at the midpoint of the side of the fuel node, and Equation 32 is the value of the spectral change at the vertex of the node. Also, r _j is the length of the perpendicular drawn from the fuel rod (x, y) to the boundary with the adjacent fuel node j.

Equation 30 is a kind of analytically approximate solution of Equation 27, and has the following preferable properties. (1) At the center of the fuel node, the thermal neutron flux approaches an asymptotic value. That is, δφ approaches 0. (2) Asymptotic boundary values given by Expressions 31 and 32 are satisfied at the midpoint and the vertex of the side of the fuel node. (3) On the line connecting the centers of the two fuel nodes in surface contact (shown by the broken line in FIG. 1), the thermal neutron flux approaches Equation 11 of the one-dimensional diffusion equation on this line.

The distribution of the difference between the thermal neutron flux in the node and the asymptotic thermal neutron flux in the node obtained by the homogenization calculation obtained as described above is calculated by the thermal neutron flux distribution from the infinite system obtained by the inhomogeneous calculation. It has been confirmed by numerical experiments that it is in good agreement with the change in.

When calculating the change from the asymptotic value of the reaction rate of the node average, it is necessary to consider the heterogeneity of the substance in the node. As shown in the cross-sectional view of the fuel assembly in FIG. 3 described later in detail, the fissile material exists only in the in-channel region 15 of the fuel and does not exist in the water gap region 16. The node integration of the reaction rate change results in the integration of the thermal neutron flux change in the in-channel region 15.

[0073]

[Equation 33] here,

[0074]

(Equation 34) : In-channel mean thermal group fission cross section in infinite system

[0075]

(Equation 35) Is a correction factor for calculating the integral of the inhomogeneous inchannel response rate change using the in-channel average fission cross section.

Using Equation 33, Equation 20, Equation 25
Spectral correction term in

[0077]

[Equation 36] Is

[0078]

(37) It can be expressed as. here

[0079]

(38) Is the spectral index change of the in-channel average.

From the definition of the average sectional area,

[0081]

[Equation 39] Therefore, by substituting Expression 39 into Expression 37 and transforming it,

[0082]

(Equation 40) I can write Here, since the term enclosed by [] in Equation 40 is an amount close to 1 regardless of the fuel type, the spectral correction amount for the reaction rate is finally

[0083]

[Equation 41] Can be expressed using only the average cross-sectional area of the node and the in-channel average spectral index change amount.

The in-channel average spectral index change amount is obtained by integrating Expression 30 in the in-channel region.

[0085]

(Equation 42) Becomes Here, w is the water gap width. When the integration of Expression 42 is executed and arranged, the change of the spectrum index of the in-channel average is represented by the weighted average of the difference between the asymptotic spectrum index of the target node and the asymptotic spectrum index of the adjacent node as follows.

[0086]

[Equation 43] Becomes Here, j = 1 and 4 represent four nodes that are radially adjacent to each other, and j = 5 and 8 represent four nodes that are diagonally adjacent.

The weighting factors are

[0088]

[Equation 44]

[0089]

[Equation 45] Here, h is the width of the in-channel node.

[0090]

[Equation 46] When Equation 43 is extended to three dimensions,

[0091]

[Equation 47] Becomes Here, k = 1 and 2 represent two nodes adjacent to each other in the axial direction, and the axial load factor is represented by the following equation.

[0092]

[Equation 48] Equation 47 is an expression of a spectrum index when used for power density calculation. When used for the neutron flux calculation, as shown in Expression 22, it is necessary to multiply and add the factor F for each adjacent node.

Next, a calculation example of the in-core power distribution during the power operation according to the present invention will be shown in comparison with a calculation example by the two-dimensional three-group detailed heterogeneous diffusion calculation. For comparison, a case where the spectrum correction is set to 0 in the conventional method and the present invention is also shown.

The target fuel is a fuel assembly for a boiling water reactor shown in FIG. 3. This fuel assembly has fuel rods 12 arranged in a channel box 11 in 8 rows and 8 columns. Two water rods 13 are arranged in the center. In the figure, reference numeral 14 is a fuel node, and reference numeral 15
Denotes an in-channel region, reference numeral 16 denotes a water gap region, and reference numeral 17 denotes a control rod.

FIG. 4 is a diagram showing a fuel loading pattern in the core used for the calculation. Here, fuel type 1 is a low-enriched fuel having an average enrichment of 1.3 w / o, fuel type 2 is a medium-enriched fuel having an average enrichment of 2.4 w / o, and fuel type 3 is an average enrichment of 3.3 w / o. o Highly concentrated fuel. Each fuel type has a fuel rod enrichment distribution in the transverse direction of the assembly. Fuel types 2 and 3 also include gadolinia-filled fuel rods. The in-channel void fraction of the fuel is 40% for both fuel types 1, 2, and 3. A cross-shaped control rod is inserted in a fuel node surrounded by a thick square in the fuel loading pattern diagram of the core.

FIG. 5 and FIG. 6 are diagrams comparing the node average relative power distribution in the radial direction according to the present invention and the conventional method with the detailed diffusion calculation for the lower left quarter section of the core. Similarly, FIG. 7 is a comparison with a detailed calculation when the spectrum correction is set to 0 in the present invention.

From FIG. 7, when the spectrum correction is ignored, the root mean square error of the power distribution of the core average is 11.7%, and the maximum error reaches 35.2%. Further, from FIG. 6, in the case of the conventional method, the root mean square error of the power distribution of the core average is 3.7%, and the maximum error is 9.7%. On the other hand, the root mean square error of the output distribution in this method is 1.4%, the maximum error is also only 4.0%, and the error is about 1/10 compared to the case without the spectrum correction. Also, it is reduced to about 1/3 compared to the conventional method. As described above, the calculation accuracy of the power distribution according to the present invention is greatly improved as compared with the related art, and it can be said that it is sufficient for core operation management. In addition, the calculation time of the present invention is about 1/1000 of the detailed calculation, which is a calculation speed sufficient for online use.

[0098]

As described above, according to the present invention, the core 3
As a dimensional physical model, a coarse mesh 1.5 group neutron diffusion model is used, and the spectral correction amount is obtained by explicitly considering the thermal neutron flux distribution in the fuel node. Therefore, a short calculation time suitable for online calculation The power distribution in the core can be calculated with high accuracy.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an apparatus for calculating core performance of a nuclear reactor according to one embodiment of the present invention.

FIG. 2 is an explanatory diagram showing a calculation system according to the present invention.

FIG. 3 is a cross-sectional view showing a fuel assembly for a boiling water reactor used to show the effects of the present invention.

FIG. 4 is an explanatory diagram showing a fuel loading pattern in a reactor core used for a two-dimensional detailed diffusion calculation to show the effect of the present invention.

FIG. 5 is a diagram comparing the relative power distribution in the reactor core with the detailed calculation according to the method of the present invention.

FIG. 6 is a diagram comparing a relative power distribution in a reactor core with a detailed calculation according to a conventional method.

FIG. 7 is a diagram comparing the relative power distribution in the core in the case of a spectrum correction of 0 with a detailed calculation.

[Explanation of symbols]

 REFERENCE SIGNS LIST 1 core three-dimensional neutron diffusion calculator 2 thermal neutron flux distribution calculator in fuel node 3 spectrum correction calculator 4 core power distribution calculator 5 reactor core

Continuation of the front page (56) References JP-A-57-67897 (JP, A) JP-A-62-184392 (JP, A) JP-A-3-264896 (JP, A) Tsuiki M et al, "A new bridge" diffusion scheme for three-dimension cal-calculation of a BWR core "J. Nucl. Sci. Technol. , Vol. 13, No. 10, pp. 541-554 (1976) Iwamoto T et al, "Proc. Topical. Mtg. On Advances in Reactor or Physics," Charleston, p. 1-476 (1992) Iwamoto T et al, "New node diffusion and pin power cal calculation method based on modified on e-group scheme." p. 1.476-1. 487 (1992) (58) Field surveyed (Int. Cl. ⁷ , DB name) G21C 17/00 JICST file (JOIS)

Claims (1)

(57) [Claims] 1. An on-line core performance calculation apparatus for calculating the core performance of a nuclear reactor based on a three-dimensional physical model of a core, wherein a coarse mesh 1.5 group neutron diffusion model is used as the physical model, and a core state parameter is input. A three-dimensional neutron diffusion calculator for calculating and outputting the fuel node average fast neutron flux distribution and the asymptotic ratio of the thermal neutron flux to the fast neutron flux in the fuel node, and an output from the core three-dimensional neutron diffusion calculator , A thermal neutron flux distribution calculator in the fuel node for analytically obtaining the distribution of thermal neutron flux in the fuel node, and a fuel node in the coarse mesh method based on the output from the thermal neutron flux distribution calculator in the fuel node. A spectrum correction amount calculating device for obtaining a spectrum correction amount for the fast neutron flow between the fuel node and the reaction rate of the fuel node, A core power distribution calculator for calculating a three-dimensional power distribution of the core based on each output from the correction amount calculator and the core three-dimensional neutron diffusion calculator. apparatus.