CN111523233B - Neutron transport calculation method for three-dimensional pressurized water reactor core - Google Patents

Neutron transport calculation method for three-dimensional pressurized water reactor core Download PDF

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CN111523233B
CN111523233B CN202010327917.8A CN202010327917A CN111523233B CN 111523233 B CN111523233 B CN 111523233B CN 202010327917 A CN202010327917 A CN 202010327917A CN 111523233 B CN111523233 B CN 111523233B
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刘宙宇
张思凡
曹良志
吴宏春
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Xian Jiaotong University
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Abstract

The invention discloses a neutron transport calculation method for a three-dimensional pressurized water reactor core, which comprises the following steps of dividing a reactor to be calculated into two regions along the radial direction, wherein the two regions are a region with simpler geometric materials and a complex region; then, dividing grids in a simple area, establishing a neutron transport numerical model by using a discrete longitudinal marking method, dividing a flat source area in a complex area, and establishing the neutron transport numerical model by using a characteristic line method; performing coupling calculation through the region boundary until the result is converged, and finally obtaining the characteristic value and neutron flux information of the reactor core; the method combines the advantages of a characteristic line method and a discrete longitudinal marking method, can meet the requirement of finely constructing a complex area, can perform quick calculation on a simple area, simultaneously gives consideration to the precision and the efficiency, and saves the time and the money cost for the numerical simulation of the reactor.

Description

Neutron transport calculation method for three-dimensional pressurized water reactor core
Technical Field
The invention relates to the field of nuclear reactor core design and core safety calculation, in particular to a neutron transport calculation method for a three-dimensional pressurized water reactor core.
Background
The nuclear energy is used as a clean energy, has incomparable advantages compared with the traditional fossil energy, and can be used as a newly added energy for the subsequent development of China to mainly supply power. The physical calculation and analysis of the nuclear reactor obtains the internal operation state of the reactor through numerical simulation, and the method is basically used for solving a steady-state boltzmann neutron transport equation. The dominant methods include the discrete vertical notation method (Sn) and the characteristic line Method (MOC).
The Sn method disperses continuous angle directions to obtain neutron transport equations of a plurality of angles, solves the equation set to obtain neutron angular flux of each direction, and obtains neutron flux density distribution through numerical integration. The Sn method has clear physical meaning and high calculation speed, but has weak geometric processing capability. The MOC method utilizes mathematical transformation to convert a neutron transport equation into an equation on a certain characteristic line along a certain angle, and solves equations of all characteristic lines in an area to obtain the angular flux density in each direction. Because the characteristic line has no geometric limitation, the MOC method can process any geometric and accurate core simulation condition.
In high-fidelity calculation of the reactor, the Sn method cannot be used for finely simulating the state of each part of the reactor because the Sn method cannot process complex geometry. MOC methods are often applied to modeling of complex geometries. In order to obtain a high-precision result, a large number of grids and characteristic lines are needed, and if a full reactor is divided by using an MOC method, a large amount of computing resources are wasted by dividing fine grids at a simple geometric position of the reactor, and the time cost is increased.
As described above, in order to efficiently and accurately perform numerical simulation of a pressurized water reactor core, it is necessary to combine the discrete vertical marking method and the characteristic line method to make up for the deficiencies. The characteristic line method is applied to the calculation of complex geometric parts of the reactor core, the discrete vertical marking method is applied to the calculation of simple geometric parts, and the calculation resource waste caused by a large number of grids is avoided by the tight coupling of the calculation region boundaries, and meanwhile, the precision and the efficiency are considered.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a neutron transport calculation method for a three-dimensional pressurized water reactor core, which can be applied to the problem of a great amount of grid resources waste caused by the simulation of a full core by a traditional characteristic line method. Compared with the traditional method, the method adopts a close coupling mode of a characteristic line method and a discrete vertical scaling method, uses the characteristic line method at the part for calculating fine geometry and uses the discrete vertical scaling method at the part for calculating simple geometry, saves a large amount of calculation resources and provides favorable conditions for reactor design.
In order to achieve the purpose, the invention adopts the following technical scheme:
a neutron transport calculation method for a three-dimensional pressurized water reactor core comprises the following steps:
step 1: dividing the pressurized water reactor core into a simple region and a complex region along the radial direction based on the calculation requirement, the geometry of the pressurized water reactor core and the material distribution condition; the simple area comprises a moderator area and a reflecting layer area, and the complex area comprises a fuel area, a control rod and a guide pipe, a coaming and a grid, and a reactor core supporting structure;
step 2: respectively reading the geometric information, the material information and the boundary condition information of the two areas;
and step 3: dividing grids in the simple region in the step 1 based on the geometric information, the material information and the boundary condition information read in the step 2, and establishing a neutron transport numerical model in the simple region on the grids by using a discrete longitudinal marking method; dividing a flat source region in a complex region, and establishing a neutron transport numerical model in the complex region by using a characteristic line method;
and 4, step 4: respectively carrying out internal iterative computation on neutron transport numerical models of a simple region and a complex region, computing the distribution of source terms, neutron flux and flux moments of the two regions, communicating the boundary neutron angular flux densities of the two regions through the interface of the two regions, namely, coupling boundary conditions in the iterative process, wherein the boundary conditions are as shown in the formula (1) until the average neutron flux density in internal iteration is converged, and the internal iteration convergence conditions are as shown in the formula (2); the inner iteration convergence is regarded as finishing an outer iteration step;
Figure BDA0002463886720000031
Figure BDA0002463886720000032
in the formula:
n is the number of the inner iteration step;
moc-a characteristic line method to calculate regions, i.e., complex regions;
sn is a calculation area of a discrete vertical marking method, namely a simple area;
b-coupling boundary;
in-incident direction;
out-exit direction;
g is the energy group number of the transport model;
l is the number of the grid and the flat source region divided by the reactor core;
Figure BDA0002463886720000041
the nth internal iteration step is carried out, and the neutron angular flux density in the incident direction of the coupling boundary of the complex region of the reactor core is obtained;
Figure BDA0002463886720000042
the nth internal iteration step is carried out, and the neutron angular flux density in the exit direction of the reactor core simple region coupling boundary is obtained;
Figure BDA0002463886720000043
the nth internal iteration step is carried out, and the neutron angular flux density in the incident direction of the simple region coupling boundary of the reactor core is obtained;
Figure BDA0002463886720000044
the nth internal iteration step is carried out, and the neutron angular flux density in the exit direction of the coupling boundary of the complex region of the reactor core is obtained;
Figure BDA0002463886720000045
-in the nth internal iteration step, the average neutron flux density of the ith grid or flat source region of the gth group of the reactor core is an assumed initial value when n is 0;
Figure BDA0002463886720000046
-the average neutron flux density of the ith grid or flat source region of the ith group of reactor cores in the (n-1) th internal iteration step;
εin-an inner iteration convergence limit;
and 5: step 4, obtaining the characteristic value and the average neutron flux density of the first external iteration step by the calculation result, judging whether the convergence criterion (3) of the characteristic value and the convergence criterion (4) of the fission rate are met, if so, considering that the external iteration calculation result is converged, and if not, repeating the steps 4 to 5; the final calculation result comprises the effective value-added factors of the reactor core, namely the characteristic value k and the distribution of neutron flux density;
Figure BDA0002463886720000047
Figure BDA0002463886720000048
in the formula:
Figure BDA0002463886720000051
Figure BDA0002463886720000052
m is the number of the outer iteration step;
g is the total energy group number of the transport model;
l is the total number of grids and flat source regions divided by the reactor core;
k(m)-the characteristic value of the mth outer iteration step, when m is 0, is an assumed initial value;
k(m-1)-the characteristic value of the m-1 th iteration step;
εk-a feature value convergence limit;
Figure BDA0002463886720000053
-in the mth external iteration step, the average neutron flux density of the ith grid or flat source region of the gth group of the reactor core is an assumed initial value when n is 0;
Figure BDA0002463886720000054
-the m-1 external iteration step, the average neutron flux density of the ith grid or flat source region of the core group g;
Figure BDA0002463886720000055
-maximum value of the ratio of the m-th and m-1-th iteration results of fission sources of each grid or flat source region in the core;
Figure BDA0002463886720000056
-minimum of the ratio of the m-th and m-1-th iteration results of fission sources of each grid or flat source region in the core;
Figure BDA0002463886720000057
-the neutron production cross section of the g-th group;
εout-outer iteration convergence limit.
Compared with the prior art, the invention has the following outstanding advantages:
the invention combines the respective advantages of the characteristic line method and the discrete vertical scaling method, tightly couples the characteristic line method and the discrete vertical scaling method, adopts the characteristic line method when calculating the fine geometric part, and uses the discrete vertical scaling method when calculating the simple geometric part, thereby not only meeting the requirement of fine construction of a complex area, but also being capable of carrying out rapid calculation on the simple area, simultaneously considering the precision and the efficiency, and saving the time and the money cost for the numerical simulation of the reactor. The grid waste caused by the characteristic line method in the process of simulating the whole reactor core is avoided, a large amount of computing resources are saved, and favorable conditions are provided for reactor design.
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FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a cross-sectional view of a three-dimensional pressurized water reactor.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The method comprises the following specific steps of dividing a three-dimensional pressurized water reactor core to be simulated into two parts along the radial direction as shown in figure 1:
step 1: as shown in fig. 2, based on the calculation requirement, the geometry of the pressurized water reactor core and the material distribution, the pressurized water reactor core is divided into two regions, namely an outer simple heavy water light water region and an inner complex core region, in the radial direction, wherein the inner complex region comprises a fuel region, control rods and guide tubes, a surrounding plate and a grid, and a core support structure;
step 2: respectively reading the information of the geometry, the material, the boundary condition and the like of the two areas;
and step 3: based on the geometric information, the material information and the boundary condition information read in the step 2, dividing and calculating grids in a simple area, namely a heavy water and light water area by using a discrete longitudinal marking method, and establishing a neutron transport numerical model on the grids, such as an Sn method based on triangular blocks; a characteristic line Method (MOC) is used in a complex region, namely an inner core region, a flat source region is divided to establish a MOC neutron transport numerical model, such as a 2D/1D coupling method based on the MOC;
and 4, step 4: respectively carrying out internal iterative computation on neutron transport numerical models of a simple region and a complex region, computing the distribution of source terms, neutron flux and flux moments of the two regions, communicating the boundary neutron angular flux densities of the two regions through the interface of the two regions, namely, coupling boundary conditions in the iterative process, wherein the boundary conditions are as shown in the formula (1) until the average neutron flux density in internal iteration is converged, and the internal iteration convergence conditions are as shown in the formula (2); the inner iteration convergence is regarded as finishing an outer iteration step;
Figure BDA0002463886720000071
Figure BDA0002463886720000072
in the formula:
moc-a characteristic line method to calculate regions, i.e., complex regions;
sn is a calculation area of a discrete vertical marking method, namely a simple area;
b-coupling boundary;
in-incident direction;
out-exit direction;
g is the energy group number of the transport model;
l is the number of the grid and the flat source region divided by the reactor core;
Figure BDA0002463886720000073
the nth internal iteration step is carried out, and the neutron angular flux density in the incident direction of the coupling boundary of the complex region of the reactor core is obtained;
Figure BDA0002463886720000081
the nth internal iteration step is carried out, and the neutron angular flux density in the exit direction of the reactor core simple region coupling boundary is obtained;
Figure BDA0002463886720000082
the nth internal iteration step is carried out, and the neutron angular flux density in the incident direction of the simple region coupling boundary of the reactor core is obtained;
Figure BDA0002463886720000083
the nth internal iteration step is carried out, and the neutron angular flux density in the exit direction of the coupling boundary of the complex region of the reactor core is obtained;
Figure BDA0002463886720000084
-in the nth internal iteration step, the average neutron flux density of the ith grid or flat source region of the gth group of the reactor core is an assumed initial value when n is 0;
Figure BDA0002463886720000085
-the average neutron flux density of the ith grid or flat source region of the ith group of reactor cores in the (n-1) th internal iteration step;
εin-an inner iteration convergence limit;
and 5: step 4, obtaining the characteristic value and the average neutron flux density of the first external iteration step by the calculation result, judging whether the convergence criterion (3) of the characteristic value and the convergence criterion (4) of the fission rate are met, if so, considering that the external iteration calculation result is converged, and if not, repeating the steps 4 to 5; the final calculation result comprises the effective value-added factors of the reactor core, namely the characteristic value k and the distribution of neutron flux density;
Figure BDA0002463886720000086
Figure BDA0002463886720000087
in the formula:
Figure BDA0002463886720000091
Figure BDA0002463886720000092
m is the number of the outer iteration step;
g is the total energy group number of the transport model;
l is the total number of grids and flat source regions divided by the reactor core;
k(m)-the characteristic value of the mth outer iteration step, when m is 0, is an assumed initial value;
k(m-1)-the characteristic value of the m-1 th iteration step;
εk-a feature value convergence limit;
Figure BDA0002463886720000093
-in the mth external iteration step, the average neutron flux density of the ith grid or flat source region of the gth group of the reactor core is an assumed initial value when n is 0;
Figure BDA0002463886720000094
-the m-1 external iteration step, the average neutron flux density of the ith grid or flat source region of the core group g;
Figure BDA0002463886720000095
-maximum value of the ratio of the m-th and m-1-th iteration results of fission sources of each grid or flat source region in the core;
Figure BDA0002463886720000096
-minimum of the ratio of the m-th and m-1-th iteration results of fission sources of each grid or flat source region in the core;
Figure BDA0002463886720000097
-the neutron production cross section of the g-th group;
εout-outer iteration convergence limit.
Fig. 2 shows that a complex reactor core wraps a circle of heavy water and a circle of light water from inside to outside, when the reactor type is calculated, a characteristic line method is adopted in an internal complex reactor core region, and a separation vertical marking method is adopted in the rest parts.

Claims (1)

1. A neutron transport calculation method for a three-dimensional pressurized water reactor core is characterized by comprising the following steps: the method comprises the following steps:
step 1: dividing the pressurized water reactor core into a simple region and a complex region along the radial direction based on the calculation requirement, the geometry of the pressurized water reactor core and the material distribution condition; the simple area comprises a moderator area and a reflecting layer area, and the complex area comprises a fuel area, a control rod and a guide pipe, a coaming and a grid, and a reactor core supporting structure;
step 2: respectively reading the geometric information, the material information and the boundary condition information of the two areas;
and step 3: dividing grids in the simple region in the step 1 based on the geometric information, the material information and the boundary condition information read in the step 2, and establishing a neutron transport numerical model in the simple region on the grids by using a discrete longitudinal marking method; dividing a flat source region in a complex region, and establishing a neutron transport numerical model in the complex region by using a characteristic line method;
and 4, step 4: respectively carrying out internal iterative computation on neutron transport numerical models of a simple region and a complex region, computing the distribution of source terms, neutron flux and flux moments of the two regions, communicating the boundary neutron angular flux densities of the two regions through the interface of the two regions, namely, coupling boundary conditions in the iterative process, wherein the boundary conditions are as shown in the formula (1) until the average neutron flux density in internal iteration is converged, and the internal iteration convergence conditions are as shown in the formula (2); the inner iteration convergence is regarded as finishing an outer iteration step;
Figure FDA0002463886710000011
Figure FDA0002463886710000021
in the formula:
n is the number of the inner iteration step;
moc-a characteristic line method to calculate regions, i.e., complex regions;
sn is a calculation area of a discrete vertical marking method, namely a simple area;
b-coupling boundary;
in-incident direction;
out-exit direction;
g is the energy group number of the transport model;
l is the number of the grid and the flat source region divided by the reactor core;
Figure FDA0002463886710000022
-the nth internal iteration step, the neutron angular flux in the incident direction of the coupling boundary of the complex region of the reactor coreDensity;
Figure FDA0002463886710000023
the nth internal iteration step is carried out, and the neutron angular flux density in the exit direction of the reactor core simple region coupling boundary is obtained;
Figure FDA0002463886710000024
the nth internal iteration step is carried out, and the neutron angular flux density in the incident direction of the simple region coupling boundary of the reactor core is obtained;
Figure FDA0002463886710000025
the nth internal iteration step is carried out, and the neutron angular flux density in the exit direction of the coupling boundary of the complex region of the reactor core is obtained;
Figure FDA0002463886710000026
-in the nth internal iteration step, the average neutron flux density of the ith grid or flat source region of the gth group of the reactor core is an assumed initial value when n is 0;
Figure FDA0002463886710000027
-the average neutron flux density of the ith grid or flat source region of the ith group of reactor cores in the (n-1) th internal iteration step;
εin-an inner iteration convergence limit;
and 5: step 4, obtaining the characteristic value and the average neutron flux density of the first external iteration step by the calculation result, judging whether the convergence criterion (3) of the characteristic value and the convergence criterion (4) of the fission rate are met, if so, considering that the external iteration calculation result is converged, and if not, repeating the steps 4 to 5; the final calculation result comprises the effective value-added factors of the reactor core, namely the characteristic value k and the distribution of neutron flux density;
Figure FDA0002463886710000031
Figure FDA0002463886710000032
in the formula:
Figure FDA0002463886710000033
Figure FDA0002463886710000034
m is the number of the outer iteration step;
g is the total energy group number of the transport model;
l is the total number of grids and flat source regions divided by the reactor core;
k(m)-the characteristic value of the mth outer iteration step, when m is 0, is an assumed initial value;
k(m-1)-the characteristic value of the m-1 th iteration step;
εk-a feature value convergence limit;
Figure FDA0002463886710000041
-in the mth external iteration step, the average neutron flux density of the ith grid or flat source region of the gth group of the reactor core is an assumed initial value when n is 0;
Figure FDA0002463886710000042
-the m-1 external iteration step, the average neutron flux density of the ith grid or flat source region of the core group g;
Figure FDA0002463886710000043
-maximum value of the ratio of the m-th and m-1-th iteration results of fission sources of each grid or flat source region in the core;
Figure FDA0002463886710000044
-minimum of the ratio of the m-th and m-1-th iteration results of fission sources of each grid or flat source region in the core;
Figure FDA0002463886710000045
-the neutron production cross section of the g-th group;
εout-outer iteration convergence limit.
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