CN113254860B - Method for calculating neutron flux of reactor core grid cells - Google Patents

Method for calculating neutron flux of reactor core grid cells Download PDF

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CN113254860B
CN113254860B CN202110629007.XA CN202110629007A CN113254860B CN 113254860 B CN113254860 B CN 113254860B CN 202110629007 A CN202110629007 A CN 202110629007A CN 113254860 B CN113254860 B CN 113254860B
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庄坤
颜江涛
尚文
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention provides a method for calculating neutron flux of a reactor core grid element, which comprises the following steps: step 1, establishing a three-dimensional Quas i-d i ffus i on equation and neutron flux continuity conditions; step 2, defining an Edd i ngton factor tensor; and 3, establishing a numerical solving method of the Quas i-d i ffus i on equation. In practical application, considering that the off-diagonal element value of the Edd i ngton factor tensor is smaller than the diagonal element value by several orders of magnitude, neglecting the off-diagonal element term, and adopting the idea of transverse integration to obtain three mutually coupled one-dimensional Quas i-d i ffus i on transverse integration equations. The method solves the three-dimensional Quas i-d iffus i on equation by deducing, calculating and verifying the Edgton factor, determines a practical, efficient and accurate reactor core grid element neutron flux calculation method, can be applied to solving various complex or simple reactor types, effectively overcomes the accuracy problem of the traditional diffusion equation calculation and the efficiency problem of the transport equation, and has important significance and engineering practical value.

Description

Method for calculating neutron flux of reactor core grid cells
Technical Field
The invention belongs to the field of reactor physical neutron calculation, and particularly relates to a method for calculating neutron flux of a reactor core grid element.
Background
The distribution of neutron flux density in time, space and energy determines the characteristics of the nuclear reactor, and obtaining the distribution of neutron flux density by establishing a reasonable mathematical model is the primary task of neutron design in the reactor. The neutron transport theory can solve the problem well, however, due to the complexity of the neutron transport equation, solving the equation by either a determinism method or a non-determinism method is very complex and time-consuming. Therefore, in the case of fast or repeated acquisition of neutron flux density, such as core fuel management calculation and neutron dynamics calculation of a nuclear power plant, a neutron diffusion equation with diffusion approximation to a neutron transport equation is generally adopted. Along with the demands of nuclear energy in the aspects of space, ocean, environment and the like, more and more advanced novel reactors are proposed, such as liquid metal fast reactors, renewable boiling water reactors, molten salt reactors and the like, and the novel reactors are obviously different from the traditional pressurized water reactor: 1) more advanced fuel types, higher enrichment, more non-uniform core placement, all resulting in a core with a complex neutron spectrum, strong neutron flux anisotropy; 2) the fuel assembly geometry, the core arrangement are complex (for example, the heat pipe space reactor has both hexagonal fuel assemblies and cylindrical heat pipes), and the core structure geometry is complex (control drum structure in the space reactor, etc.); 3) the miniaturization and compactness design enables the reactor core to have larger leakage, violent change of neutron flux spatial distribution and stronger neutron anisotropy degree. The complex neutron energy spectrum and strong neutron anisotropy in the reactor core enable the precision of diffusion calculation to be low, and the diffusion approximation assumption is not applicable.
Technical scheme of prior art I
The current reactor core neutron calculation method comprises the following steps: 1) direct one-step non-uniform calculation; 2) carrying out homogenization calculation on the embedded assembly; 3) carrying out Pin-by-Pin transport calculation on the grid cell homogenized whole reactor core; 4) and (4) calculating the diffusion of the assembly homogenized core.
The core calculation 'one-step method' also comprises Monte Carlo calculation and deterministic theory calculation, the Monte Carlo method generally carries out full core fine description, no or few approximations such as a bounding wall reflecting layer, a positioning grid frame and the like are introduced, and the one-step method fine calculation is realized based on a multi-group constant library.
The embedded assembly uniform calculation adopts a multi-group section library to perform core transport calculation, and subsequent few-group neutron transport calculation is performed through an assembly section rehomogenization process in the calculation process.
The method comprises the following steps that (1) a two-step method calculation mode is adopted for the diffusion calculation of the assembly homogenized reactor core aiming at the non-uniform reactor core, and 1) an assembly homogenized few-group parameter (generally 2 groups) is obtained on the basis of seed transport calculation on the assembly level by utilizing an equivalent homogenization theory; 2) and performing diffusion calculation on the reactor core level based on the obtained few-group component sections to finally obtain the power distribution of the reactor core components, and then calculating the power distribution of grid cells in the components by adopting a fine power reconstruction method.
Different from the diffusion calculation of the assembly homogenized reactor core, the Pin-by-Pin transport calculation of the grid cell homogenized whole reactor core adopts the homogenization calculation on the grid cell layer to obtain the cross section of a few grid cell groups (6-8 groups), and in consideration of the fact that the reactor core after the grid cell homogenization still has strong heterogeneity, the subsequent reactor core calculation almost completely adopts a simplified spherical harmonic function SP3 transport method.
Disadvantages of the first prior art
Although the non-uniform one-step calculation and the embedded component calculation have higher calculation accuracy, the calculation efficiency is lower, and the non-uniform one-step calculation and the embedded component calculation cannot be applied to engineering practice at the current development level of computer hardware. At present, although the commonly adopted component homogenized core diffusion calculation method has higher calculation efficiency, details in the components are ignored, and for a complex energy spectrum reactor, the fine power reconstruction of the complex energy spectrum reactor has limitation on the prediction of the power and reactivity change of a grid cell layer, and particularly has strong neutron energy spectrum interference effect among the components for strong heterogeneous cores such as MOX fuel containing Pu, Gd-containing fuel, deep burnup fuel and the like.
The calculation of the Pin-by-Pin of the grid cell homogenized whole reactor core is a very potential calculation method, gets rid of assembly homogenization errors, can finely reflect the energy spectrum difference among grid cells and directly provides single-rod power. Because the core after the grid cells are homogenized still has strong heterogeneity, the related researches almost all adopt a Pin-by-Pin-SP3 simplified spherical harmonic function SP3 transportation method. The method converts a neutron transport equation into two coupled moment equations with the same mathematical form as a diffusion equation, and overcomes the defects of complex formula and large calculated amount of a spherical harmonic function (Pn) method. Nevertheless, the calculation of Pin-by-Pin-SP3 still requires a large calculation cost due to the coupling between the high-order matrix equations with a large amount of full core space grid. The calculation shows that the calculation time of the single-core primary pressurized water reactor whole core Pin-by-Pin-SP3 exceeds 24 hours, and the 100-core parallel calculation takes 20 minutes. The coupled solution of the high-low order matrix equation is a fundamental source of the calculation amount of the SP3 method, and although various acceleration techniques are introduced, it is difficult to further greatly improve the calculation efficiency due to theoretical limitations.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a method for calculating neutron flux of a reactor core grid element.
The invention adopts the following technical scheme:
a method for calculating neutron flux of a reactor core grid cell is characterized by comprising the following steps:
step 1, establishing a three-dimensional Quasi-diffusion equation and neutron flux continuity conditions;
step 2, similar P1 equation derivation, but without introducing neutron angular flux density angle first-order approximation, establishing a Quasi-diffusion equation consistent with the traditional diffusion equation in form, and the difference is in the expression mode of neutron leakage terms;
and 3, defining an Eaton factor tensor, wherein the expression of the Eaton factor tensor is as follows:
in practical application, considering that the off-diagonal element value of the aitton factor tensor is smaller than the diagonal element value by several orders of magnitude, the off-diagonal element term is usually ignored, and the idea of transverse integration is adopted to obtain three mutually coupled one-dimensional transverse integration equations:
Figure GDA0003481157590000031
wherein the content of the first and second substances,
Figure GDA0003481157590000032
is transverse integral flux, Q is a transverse source term, and L is a transverse leakage term;
and 4, establishing the reactor core Pin-by-Pin calculation method based on the Quasi-dispersion equation by taking the traditional mature neutron diffusion equation numerical solution as reference, improving and expanding the traditional mature neutron diffusion equation numerical solution on the basis, and considering the characteristics that the size of the reactor core Pin-by-Pin calculation grid is equivalent to the size of the grid cell and the grid size is huge.
Step 5, determining key parameters of an Eaton factor and a grid cell homogenization parameter to realize the calculation of reactor core Pin-by-Pin of the Quasi-dispersion equation;
s501, considering the energy spectrum interference effect between the components and the grid cells and the influence of the environmental effect on the neutron energy spectrum, and establishing a grid cell homogenization model capable of accurately reflecting the true energy spectrum of the homogenized material region;
s502, analyzing the characteristics of a key parameter Eaton factor, wherein the calculation needs to know the neutron angular flux density and the angular components of the neutron angular flux density in the x, y and z directions;
s503, regarding the Edison factor as a special grid cell homogenization parameter, and considering that the existing component program does not have the calculation function, performing secondary program development on the basis to enable the Edison factor to have the calculation function;
s504, acquiring conventional few-group parameters and an Edton factor of a homogenization area by using the established grid cell homogenization model and a component program with an Edton factor calculation function.
The further technical scheme is that the step 2 comprises the following steps: similar to the derivation of the P1 equation, integrating the neutron transport equation with continuous energy independent of time in Ω e [0,4 pi ] and multiplying by Ω and integrating in the full angle space to obtain the neutron standard flux equation and the neutron flux equation respectively, unlike the derivation of the P1 equation, in the derivation process of the neutron flux equation, the assumption that the neutron angular flux density is first-order approximated in the angle variable is not introduced, and the ebton factor is defined as follows:
Figure GDA0003481157590000041
Figure GDA0003481157590000042
wherein Ω is an angle; omegau，ΩvFor angles of various directions, ψ (r, Ε, Ω) is the neutron angular flux density, Φ (r, Ε) is the neutron flux density, Εu(r, Ε) denotes energy components in the u-direction,
Figure GDA0003481157590000043
respectively representing unit vectors in all directions;
the neutron flow is expressed as follows
Figure GDA0003481157590000044
Whereintr(r, E) is a neutron transport cross section, J (r)E) is the neutron flux density;
finally obtaining a three-dimensional Quasi-dispersion equation:
Figure GDA0003481157590000045
wherein, lambda is the reciprocal of the effective value-added coefficient, chi (E) is the fission energy spectrum, upsilon sigmaf(E') is a neutron production cross section, Σs(e '→ Ε) represent the scattering cross-sections from energy level Ε' to energy level Ε. Sigmat(r, Ε) is the sum of absorption and scattering cross-sections;
continuous conditions in the Quasi-dispersion approximation equation are based on the neutron angular flux Ψθ(r, Ε) is r at the two-media interface, the continuous function is derived, replaced by the following set of approximate conditions:
∫Ωn·ΩΨθ(r,Ω))Yn,m(m) (4)
wherein N is 0,1, N is continuous at the interface, Y isn,m(m) is a spherical harmonic function, n is an order, and m ═ n.
The continuous conditions of the Quasi-diffusion approximate equation, namely the continuous boundary conditions of the flow and the continuous flux conditions can be obtained through simplification
∫Ωn·ΩΦθ(r,Ω))Y0,0(Ω)＝n·Jθ (5)
Wherein phiθ(r, Ω) represents the neutron angular flux density of the g energy group, JθNeutron flux density representing g energy cluster:
∫Ωn·ΩΨθ(r,Ω)Y1.0(Ω)＝n·Εx,g(r)Φθ(r)
∫Ωn·ΩΨθ(r,Ω)Y1,-1(Ω)＝n·Εy,g(r)Φθ(r) (6)
∫Ωn·ΩΨθ(r,Ω)Y1,1(Ω)＝n·Εz,g(r)Φθ(r)
it is worth pointing out that in equation (3), if the Euton factor is 1/3 in each region, each energy group and each direction, then the Quasi-dispersion theory degenerates to diffusion theory, which means neutron flow isotropy, so when the Euton factor is not equal to 1/3, the neutron flow is anisotropic, the Euton factor makes the Quasi-dispersion approximation equation have some transport properties of neutron anisotropy, which is neglected in the conventional diffusion theory, and the Quasi-dispersion equation has similarity in form with the conventional diffusion equation, and the difference is mainly reflected in the equation leakage terms.
Further, in step 3, equation (3) is consistent with the mathematical form of the transverse integral equation obtained by the Quasi-diffusion equation (diffusion equation), and the difference is the leakage term expression mode.
Further, in step 4, a traditional nodal block expansion method NEM is adopted for calculation, the expansion order of related variables is properly reduced according to the characteristics that the size of a nodal block of the Pin-by-Pin geometry is close to that of a grid cell and the number of the nodal blocks is large, attention needs to be paid to the continuity condition of flux, and the continuity condition of a Quasi-diffusion equation considering a discontinuous factor in the advanced homogenization method is expressed as follows:
Figure GDA0003481157590000051
wherein
Figure GDA0003481157590000052
And
Figure GDA0003481157590000053
respectively is a discontinuous factor and a transverse integral surface flux of the surface in the u + direction of the m grid;
and then, adopting the same processing mode as the traditional NEM method to finally establish a Pin-by-Pin-QD core calculation method.
Further, S503 includes: regarding the Eaton factor as a special grid cell homogenization parameter, and obtaining the small group homogenization Eaton factor in the grid cell i region by utilizing the neutron angular flux obtained by grid cell homogenization calculation based on the general principle of equivalent homogenization
Figure GDA0003481157590000054
Figure GDA0003481157590000055
Wherein
Figure GDA0003481157590000061
And
Figure GDA0003481157590000062
respectively uniform Eatoton factors and conventional uniform sections in a grid cell i area;
due to the small optical thickness of the cells, the calculation of the cell with the total reflection boundary condition of the cell will generate a large error when different types of cells are adjacently arranged. The characteristic analysis of fuel assemblies in a reactor core and a large number of numerical results show that the section of a homogenized few groups is mainly a function of an assembly type, when the actual total core Quasi-dispersion is calculated, the grid calculation of an assembly level is usually carried out by adopting a total reflection boundary condition to obtain the angular flux density of non-uniform neutrons in the assemblies in a total formula, in addition, the real environment of the fuel assemblies in the actual reactor cannot be considered by the total reflection boundary condition, an infinite medium energy spectrum correction method considering the environmental effect is established by utilizing a leakage correction B1 model and a P1 model, the study of calculating the Eatoton factor by a Monte Carlo program SERPENT through a Monte Carlo program secondary development is carried out, and the homogenization calculation is carried out by utilizing the SERPENT.
The invention has the beneficial effects that:
considering the influence of the environmental effect in the complex energy spectrum reactor on the homogenization of the grid cells, establishing a method for calculating the neutron flux anisotropy key parameter Eatoton factor in the Quasi-dispersion method, and realizing effective treatment of the heterogeneity between the grid cells after homogenization. The method is developed and improved based on a mature neutron diffusion numerical method, meanwhile, the characteristics of large grid quantity and equivalent size to grid cells are considered, a quick-diffusion efficient and accurate calculation method is established, and the bottleneck of calculation efficiency of the traditional method is broken through.
At present, almost all component calculation programs do not have the function of calculating the Edton factor, the calculation of the Edton factor requires the neutron angular flux density and the components of the Edton factor in the x, y and z directions, and if the Edton factor is replaced, secondary development of the existing component programs is needed to realize the calculation.
A practical, efficient and accurate reactor core neutron flux calculation method is determined by deducing, calculating and verifying the Euton factor to solve the three-dimensional Quasi-diffusion equation, can be applied to solving various complex or simple reactor types, effectively overcomes the accuracy problem of the traditional diffusion equation calculation and the efficiency problem of the transport equation, and has important significance and engineering practical value.
Drawings
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a flow chart of the steps of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention are described below clearly and completely, and it is obvious that the described embodiments are some, not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Aiming at the problem that the calculation efficiency of the Pin-by-Pin-SP3 method is bottleneck and the calculation precision and the calculation efficiency cannot be simultaneously considered, the invention provides an accurate reactor core grid element neutron flux calculation method from a new angle and verifies the accurate reactor core grid element neutron flux calculation method, and the specific targets are as follows:
(1) aiming at the influence of the environmental effect of the complex energy spectrum reactor on the homogenization of the grid cells, a calculation method for effectively processing the key parameter of the Euton factor of neutron flux anisotropy among the grid cells is established.
(2) A processing mode of second-order tensor form leakage items and continuous conditions in the Quasi-dispersion is sought based on a mature neutron diffusion method, and the order of magnitude of the calculation efficiency is improved by establishing a Quasi-dispersion core calculation method through algorithm improvement.
As shown in fig. 1-2, the method for calculating neutron flux in core cells of the present invention includes the following steps:
1) establishment of three-dimensional Quasi-diffusion equation and neutron flux continuity condition processing
Similar to the derivation of the P1 equation, the neutron transport equation with continuous energy independent of time is integrated in omega E [0,4 pi ] and multiplied by omega and integrated in the full angle space, and the neutron flux equation and the equation for obtaining neutron flux are respectively obtained. It is worth noting that, unlike the derivation of the P1 equation, the derivation of the neutron flux equation herein does not introduce the assumption that the neutron angular flux density is a first order approximation in angular variation, and defines the eitton factor as follows:
Figure GDA0003481157590000071
wherein Ω is an angle; omegau，ΩvFor angles of various directions, ψ (r, Ε, Ω) is the neutron angular flux density, Φ (r, Ε) is the neutron flux density, Εu(r, Ε) denotes energy components in the u-direction,
Figure GDA0003481157590000072
each representing a unit vector of each direction.
The neutron flow expression is as follows:
Figure GDA0003481157590000073
wherein Ex(r,Ε)，Εy(r,Ε)，Εz(r, Ε) represents the vectors, Σ, of the oxetanon factor tensor mapped to the x, y, z directions, respectivelytr(r, E) is the neutron transport cross-section, J (r, Ε) is the neutron flux density.
Finally obtaining a three-dimensional Quasi-dispersion equation:
Figure GDA0003481157590000081
whereinλ is the reciprocal of the effective multiplication coefficient, χ (E) is the fission spectrum, upsilon Σf(E') is a neutron production cross section, Σs(e '→ Ε) represent the scattering cross-sections from energy level Ε' to energy level Ε. Sigmat(r, E) is the sum of absorption and scattering cross-sections, and phi (r, E ') represents the neutron flux density at energy E'.
Continuous conditions in the Quasi-dispersion approximation equation are based on the neutron angular flux Ψθ(r, Ε) is a continuous function of r at the interface between the two media, substituted with the following set of approximate conditions:
∫Ωn·ΩΨθ(r,Ω)Yn,m(Ω) (4)
wherein N is 0,1, N is continuous at the interface, Y isn,m(m) is the spherical harmonic, n is the order, m-n.
The continuous conditions of the Quasi-diffusion approximate equation, namely the continuous boundary conditions of the flow and the continuous flux conditions can be obtained through simplification
∫Ωn·ΩΦθ(r,Ω)Y0,0(Ω)＝n·Jθ (5)
Wherein phiθ(r, Ω) represents the neutron angular flux density of the g energy group, JθRepresents the neutron flux density of the g energy population.
∫Ωn·ΩΨθ(r,Ω)Y1.0(Ω)＝n·Εx,g(r)Φθ(r)
∫Ωn·ΩΨθ(r,Ω))Y1,-1(Ω)＝n·Εy,g(r)Φθ(r) (6)
∫Ωn·ΩΨθ(r,Ω)Y1,1(Ω)＝n·Εz,g(r)Φθ(r)
Wherein, Εx,g(r)Φθ(r)、Εy,g(r)Φθ(r)、Εz,gΦθ(r) represents the product of the Eatoton factor vector and the neutron flux density in the g-energy group mapped to the x, y, z direction.
It is to be noted that in equation (3), if the Ebutaton factor is 1/3 in each region, each energy group and each direction, the Quasi-dispersion theory degenerates to the diffusion theory, which means that the neutron flux is isotropic. The neutron flux is therefore anisotropic when the Euton factor is not equal to 1/3, which gives the Quasi-dispersion approximation equation some transport properties of neutron anisotropy, which are neglected in conventional diffusion theory. The Quasi-diffusion equation and the traditional diffusion equation have similarity in form, and the difference between the Quasi-diffusion equation and the traditional diffusion equation is mainly reflected in equation leakage terms. The invention adopts a node expansion method to establish a Quasi-diffusion core calculation method.
In practical applications, the off-diagonal element terms are usually ignored considering that the values of off-diagonal elements of the etton factor tensor are several orders of magnitude smaller than the values of the diagonal elements. And three mutually coupled one-dimensional transverse integral equations are obtained by adopting the transverse integral idea.
Figure GDA0003481157590000091
Wherein the content of the first and second substances,
Figure GDA0003481157590000092
for transverse fluence, Q is the transverse source term and L is the transverse leakage term.
Figure GDA0003481157590000093
Expressing the reciprocal of the transport section, ΕuugRepresents the u-th element of the Eaton factor vector that maps under the g-energy group to the u-direction.
Equation (3) is consistent with the mathematical form of the transverse integral equation obtained by the diffusion equation, except for the leakage term expression mode, the traditional node expansion method NEM can be adopted for calculation, the expansion order of the related variables is properly reduced according to the characteristics that the node size of the Pin-by-Pin geometry is similar to the grid cell and the number of the node sizes is large, and attention needs to be paid to the continuity condition of the flux. The continuity condition of the Quasi-diffusion equation considering the discontinuity factor in the advanced homogenization method is expressed as follows.
Figure GDA0003481157590000094
m denotes the mth segment, ΕuugRepresents the u-th element of the aiterton factor vector that maps under the g-energy group in the u-direction,
Figure GDA0003481157590000095
and
Figure GDA0003481157590000096
respectively, the discontinuity factor and the transverse plane flux of the surface in the u + direction of the m grid.
And then, the Pin-by-Pin-QD core calculation method can be finally established by adopting the same processing mode as the traditional NEM method, such as nonlinear iteration and the like.
2) Study on Euton's factor calculation method
The invention adopts a homogenization method to replace certain inhomogeneous medium with equivalent homogeneous medium spar in the grid cell scale for the medium with larger overall span and more complex fine distribution in the spatial domain energy scale, abandons the characteristic of microscopic local part on the premise of not influencing the macroscopic overall calculation precision, and utilizes corresponding equivalent grid cell homogenization parameters to perform reactor core Quasi-dispersion calculation so as to reduce the calculation requirement and improve the calculation speed.
Besides the traditional homogenization parameters, the Quasi-dispersion method also needs a key parameter, namely the Ebutaton factor, for describing the neutron flux anisotropy. The calculation precision of the Quasi-dispersion method for the heterogeneous medium depends on the accuracy of the Eduton factor to a great extent. The invention regards the Euton factor as a special grid cell homogenization parameter, and obtains the small group homogenization Euton factor in the grid cell i area by utilizing the neutron angular flux obtained by grid cell homogenization calculation based on the general principle of equivalent homogenization
Figure GDA0003481157590000101
Figure GDA0003481157590000102
Wherein omegau、ΩvPhi (r, Ε, omega) denotes the angular components of the u, v directions (u, v may denote the x, y, z directions) and the neutron angular flux density, respectively.
Figure GDA0003481157590000103
And
Figure GDA0003481157590000104
respectively, the homogenized Euton's factor and the conventional homogenized cross-section in the cell i-region.
Due to the small optical thickness of the cells, the calculation of the cell with the total reflection boundary condition of the cell will generate a large error when different types of cells are adjacently arranged. The characteristic analysis of the fuel assemblies in the reactor core and a large number of numerical results show that the sections of the homogenized few groups are mainly functions of the assembly types, and when the actual total reactor core Quasi-dispersion is calculated, the grid calculation of the assembly level is usually carried out by adopting the boundary condition of total reflection to obtain the angular flux density of the non-uniform neutrons in the assemblies in the total formula. In addition, the real environment of the fuel assembly in the actual reactor cannot be considered under the boundary condition of total reflection, and an infinite medium energy spectrum correction method considering the environmental effect is established by utilizing a leakage correction B1 model and a P1 model. The invention develops the research of calculating the Ebutaton factor by the Monte Carlo program SERPENT through the Monte Carlo program secondary development, and uses the SERPENT to carry out the homogenization calculation.
The method regards the Euton factor as similar to the traditional few-group parameter, and adopts a Monte Carlo method to realize the calculation of the Euton factor.
The Quasi-diffusion equation is applied to the neutron flux calculation of the reactor core grid cells based on the nonlinear iterative nodal expansion method for the first time, and the calculation efficiency and the calculation precision can be considered simultaneously. Compared with the existing neutron transport method, the method has higher calculation efficiency and higher calculation precision than the traditional neutron diffusion method.
The Quasi-dispersion calculation method can achieve the calculation accuracy equivalent to high-order transport, and can enable the calculation scale to be obviously reduced even in magnitude order. Firstly, the Eaton factor contained in the super equation avoids spherical harmonic function first-order myopia of angle variables, the spherical harmonic function first-order myopia can be regarded as a special type few-group parameter, and the Quasi-dispersion equation has the transport characteristic of describing neutron flux anisotropy and can be used for calculating a reactor core with strong heterogeneity after grid cells are homogenized. The calculation of the Eduton factor in the Quasi-dispersion equation requires the known neutron angular flux which is obviously the unknown quantity of the reactor core, which is a nonlinear problem, and more importantly, the conventional component program cannot calculate at present. The method regards the Euton factor as a special grid cell homogenization parameter, obtains neutron angular flux obtained by utilizing grid cell homogenization calculation based on the general principle of equivalent homogenization, and carries out calculation on the secondary development of a Monte Carlo program SERPENT.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (3)

1. A method for calculating neutron flux of a reactor core grid cell is characterized by comprising the following steps:
step 1, establishing a three-dimensional Quasi-diffusion equation and neutron flux continuity conditions;
step 2, similar P1 equation derivation, but without introducing neutron angular flux density angle first-order approximation, establishing a Quasi-diffusion equation consistent with the traditional diffusion equation in form, and the difference is in the expression mode of neutron leakage terms;
similar to the derivation of the P1 equation, integrating the neutron transport equation with continuous energy independent of time in Ω e [0,4 pi ] and multiplying by Ω and integrating in the full angle space to obtain the neutron standard flux equation and the neutron flux equation respectively, unlike the derivation of the P1 equation, in the derivation process of the neutron flux equation, the assumption that the neutron angular flux density is first-order approximated in the angle variable is not introduced, and the ebton factor is defined as follows:
Figure FDA0003497562800000011
wherein Ω is an angle; omegau，ΩvPhi (r, E) is neutron angular flux density, phi (r, E) is neutron flux density, E is angle of each directionu(r, E) represents an energy component in the u direction,
Figure FDA0003497562800000012
respectively representing unit vectors in all directions;
the neutron flow is expressed as follows
Figure FDA0003497562800000013
Wherein Ex(r,E)，Ey(r,E)，Ez(r, E) represents vectors, Σ, mapping the Ebutaton factor tensor into the x, y, z directions, respectivelytr(r, E) neutron transport cross-section, J (r, E) neutron flux density;
finally obtaining a three-dimensional Quasi-dispersion equation:
Figure FDA0003497562800000021
wherein, lambda is the reciprocal of the effective value-added coefficient, chi (E) is the fission energy spectrum, upsilon sigmaf(E') is a neutron generation cross section ∑s(E '→ E) shows a scattering cross section, Σ, scattered from the energy group E' to the energy group Et(r, E) is the sum of the absorption cross-section and the scattering cross-section, and phi (r, E ') represents the neutron flux density with energy E';
continuous conditions in the Quasi-dispersion approximation equation are based on the neutron angular flux Ψθ(r, E) is a continuous function of r at the interface between the two media, substituted with the following set of approximate conditions:
∫Ωn·ΩΨθ(r,Ω)Yn,m(m) (4)
wherein N is 0,1, N is continuous at the interface, Y isn,m(m) is a spherical harmonic function, n is an order, and m ═ n.
The continuous conditions of the Quasi-diffusion approximate equation, namely the continuous boundary conditions of the flow and the continuous flux conditions can be obtained through simplification
∫Ωn·ΩΦθ(r,Ω)Y0,0(Ω)＝n·Jθ (5)
Wherein phiθ(r, Ω) represents the neutron angular flux density of the g energy group, JθNeutron flux density representing g energy cluster:
Figure FDA0003497562800000022
wherein E isx,g(r)Φθ(r)、Ey,g(r)Φθ(r)、Ez,gΦθ(r) represents the product of the Eatoton factor vector and the neutron flux density in the g energy group mapped to the x, y, z direction;
in equation (3), if the ericton factor is 1/3 in each region, each energy group, and each direction, the Quasi-dispersion theory degenerates to diffusion theory, which means that the neutron flow is isotropic, so when the ericton factor is not equal to 1/3, the neutron flow is anisotropic;
and 3, defining an Eaton factor tensor, wherein the expression of the Eaton factor tensor is as follows:
neglecting non-diagonal element terms, adopting the idea of transverse integration to obtain three mutually coupled one-dimensional transverse integral equations:
Figure FDA0003497562800000023
Figure FDA0003497562800000031
representing the inverse of the transport cross-section, EuugRepresenting Aiding under g energy group mapped to u directionThe u-th element of the pause factor vector;
wherein the content of the first and second substances,
Figure FDA0003497562800000032
is transverse integral flux, Q is a transverse source term, and L is a transverse leakage term;
step 4, improving and expanding on the basis of a neutron diffusion equation numerical solution method for reference, and establishing a reactor core Pin-by-Pin calculation method based on a Quasi-diffusion equation by considering the characteristics that the size of a reactor core Pin-by-Pin calculation grid is the same as that of a grid cell and the size of the grid;
step 5, determining key parameters of an Eaton factor and a grid cell homogenization parameter to realize the calculation of reactor core Pin-by-Pin of the Quasi-dispersion equation;
s501, considering the energy spectrum interference effect between the components and the grid cells and the influence of the environmental effect on the neutron energy spectrum, and establishing a grid cell homogenization model capable of accurately reflecting the true energy spectrum of the homogenization material region;
s502, analyzing the characteristics of a key parameter Eaton factor, wherein the calculation needs to know the neutron angular flux density and the angular components of the neutron angular flux density in the x, y and z directions;
s503, regarding the Edison factor as a special grid cell homogenization parameter, and considering that the existing component program does not have the calculation function, performing secondary program development on the basis to enable the Edison factor to have the calculation function;
s504, acquiring few group parameters and Edton factors of a homogenization area by using the established grid cell homogenization model and a component program with an Edton factor calculation function.
2. The method for calculating the neutron flux in the core cell according to claim 1, wherein in the step 4, a nodal expansion method NEM is adopted for calculation, the expansion order of the relevant variables is reduced according to the characteristics that the sizes of the geometric nodes of the Pin-by-Pin are the same as the size of the cell and the number of the geometric nodes is large, attention needs to be paid to the continuity condition of the flux, and the continuity condition of the Quasi-dispersion equation considering the discontinuity factor in the advanced homogenization method is expressed as follows:
Figure FDA0003497562800000033
wherein
Figure FDA0003497562800000034
And
Figure FDA0003497562800000035
respectively is a discontinuous factor and a transverse integral surface flux of the surface in the u + direction of the m grid;
and then, adopting the same processing mode as the NEM method to finally establish a Pin-by-Pin-QD core calculation method.
3. The method for calculating neutron flux in core cells according to claim 1, wherein S503 comprises: regarding the Eaton factor as a special grid cell homogenization parameter, and obtaining the small group homogenization Eaton factor in the grid cell i region by utilizing neutron angular flux obtained by grid cell homogenization calculation based on the principle of equivalent homogenization
Figure FDA0003497562800000036
Figure FDA0003497562800000041
Figure FDA0003497562800000042
Wherein omegau、Ωvψ (r, E, Ω) represents angular components in the u and v directions and neutron angular flux density, respectively,
Figure FDA0003497562800000043
and
Figure FDA0003497562800000044
respectively uniform Eatoton factors and uniform sections in a grid cell i area;
the method comprises the steps of adopting a total reflection boundary condition to carry out grid calculation on an assembly level to obtain the angular flux density of non-uniform neutrons in an assembly in a total formula, in addition, the total reflection boundary condition cannot consider the real environment of a fuel assembly in an actual reactor, establishing an infinite medium energy spectrum correction method considering the environmental effect by utilizing a leakage correction B1 model and a P1 model, carrying out research on calculating the Euton factor by a Monte Carlo program SERPENT through a Monte Carlo program secondary development, and carrying out homogenization calculation by utilizing the SERPENT.
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