Improved sub-grid method for handling environmental effects in pressurized water reactor core physics calculations

Abstract

The application discloses an improved sub-grid method for processing environmental effects in a pressurized water reactor core physical calculation. After obtaining a sub-grid homogenization few-group constant library, a thermal calculation is first performed according to input core design parameters to obtain a current operation state of the core. Then, a sub-grid two-dimensional calculation is performed, including a sub-grid core two-dimensional calculation and a sub-grid single-component two-dimensional calculation, to obtain a component homogenization few-group constant considering a component environment and a component homogenization few-group constant without considering the component environment. Afterwards, the two kinds of component homogenization few-group constants considering and without considering the environment are used for a few-group constant correction calculation. Finally, a three-dimensional full-core diffusion calculation is performed by using the corrected few-group constant, and an axial leakage calculation is performed through iteration of the three-dimensional calculation and the two-dimensional calculation, and the physical analysis of the reactor core is completed after iteration convergence. The method adopts a self-consistent correction mode for each type of few-group constant, and the correction mode is more in line with the physical meaning of the few-group constant.

Description

Technical Field

[0001] This invention relates to the field of pressurized water reactor core physics calculation technology, and more specifically to an improved subgrid method for handling environmental effects in pressurized water reactor core physics calculation. Background Technology

[0002] In commercial pressurized water reactor (PWR) cores, core performance analysis requires precise coupled analysis of physical fields such as neutronics, thermal hydraulics, and nuclide burnup. Currently, the mainstream method in industry is still the "two-step method": first, under fully symmetric boundary conditions of a single component, the homogenization minority group constant of the component is obtained through component calculations; then, neutron diffusion calculations and nuclear-thermal coupling calculations are performed within the three-dimensional full core under coarse mesh conditions. However, the total internal reflection boundary assumption in the component calculations often differs from the actual environment of the component in the core, introducing errors into the calculated homogenization minority group constant, a phenomenon known as the environmental effect.

[0003] Currently, the main methods for handling environmental effects both domestically and internationally are as follows: 1. BN theory correction method: This technique corrects the neutron non-leakage probability by calculating the core's geometric curvature, thus obtaining a critical energy spectrum that considers leakage. Although this method has been applied in both deterministic and probabilistic methods, it is not theoretically rigorous and is only applicable to cores in a critical state, with limited effectiveness in handling environmental effects. 2. Boundary condition error correction method: This method uses embedded homogenization or Colorset component calculation methods to perform component calculations under the condition of considering the actual environment of the components. It requires treating the same component under different environments as different types of components, resulting in a large number of component types and a large computational burden. It is mainly used for experimental pressurized water reactors with simple operating conditions and has not yet been applied in commercial pressurized water reactors. 3. Re-homogenization method: In the French nuclear physics calculation program SCIENCE, a numerical method is used to write the neutron flux density as a two-dimensional expansion of an indivisible half-analytic function. This technique is incompatible with the minority group energy group of the basis functions due to the multi-group flux calculated by the non-homogeneous components, requiring approximation, which introduces bias. 4. The subgrid method first adds subgrid homogenization calculations to the assembly calculation to obtain the subgrid homogenization minority group constant. Then, in the core calculation, under the subgrid, the correction term for the assembly homogenization minority group constant due to environmental effects is obtained under both conditions, considering and not considering the environment. This technique has been applied to the CMS5 software developed by Studsvik in the United States. However, it uses simple addition and subtraction forms to correct different types of minority group constants such as nuclear reaction cross section, diffusion coefficient, and discontinuity factor.

[0004] Σ 3D =Σ LATTICE +(Σ 2D -Σ SA )

[0005] D3D =D LATTICE +(D 2D -D SA )

[0006] f 3D =f LATTICE +(f 2D -f SA )

[0007] Among them, the LATTCIE term is the component homogenization minority group constant given by the component calculation under the single component fully symmetric boundary condition; the 2D and SA terms are the component homogenization minority group constants under the two conditions of considering and not considering the environment, respectively; the 3D term represents the component homogenization minority group constant used in the core three-dimensional diffusion calculation; Σ represents the nuclear reaction cross section; D represents the diffusion coefficient; and f represents the discontinuity factor.

[0008] The above simple addition and subtraction form does not take into account the physical properties of different types of minority group constants, which is theoretically inconsistent and the correction effect needs to be improved. Summary of the Invention

[0009] To overcome the shortcomings of the above-mentioned subgrid methods in terms of both theory and effectiveness, this invention proposes an improved subgrid method for handling environmental effects in the physical calculation of pressurized water reactor cores. This method adopts a self-consistent correction method for each type of minority group constant, which is more consistent with the physical meaning of the minority group constant itself.

[0010] The improved subgrid method with new correction techniques can improve the calculation accuracy of square and hexagonal fuel assemblies and reflector assemblies, as well as the calculation accuracy of rod-shaped, plate-shaped, ring-shaped, and sleeve-shaped fuel assemblies. It can also improve the calculation accuracy of power levels, boron concentration, control rod insertion and removal, and core multi-cycle history tracking during core design and core operating condition simulation.

[0011] To achieve the above objectives, the present invention employs the following calculation scheme:

[0012] An improved subgrid method for handling environmental effects in the physical calculations of pressurized water reactor cores includes the following steps:

[0013] Step 1: Obtain the sub-mesh homogenization minority group constant: In the component calculation, for each type of component, the sub-mesh homogenization calculation is completed to obtain the homogenization minority group constant of each sub-mesh in the component;

[0014] Step 2: Perform parameterized calculations on the sub-grid homogenization minority group constants to obtain a library of sub-grid homogenization minority group constants that characterizes the quantitative functional relationship between the sub-grid homogenization minority group constants and the component state parameters. The component state parameters include the component burn-out depth, boron concentration, fuel temperature, and moderator temperature.

[0015] Step 3: Obtain the core state through thermal calculations. Based on the subgrid homogenization minority group constant library from Step 2, complete the two-dimensional subgrid calculation, including two-dimensional core calculation and two-dimensional single-module calculation. Obtain the module homogenization minority group parameters considering the module environment through the two-dimensional core calculation, and obtain the module homogenization minority group parameters without considering the module environment through the two-dimensional single-module calculation.

[0016] Step 4: Since the physical meaning of the nuclear reaction cross section is the probability of a neutron reacting with an atomic nucleus, according to the principle of probability superposition, the nuclear reaction cross section satisfies the summation relationship. Therefore, the nuclear reaction cross section parameters are corrected using formula (4).

[0017] Σ 3D =Σ LATTICE +(Σ 2D -Σ SA (4)

[0018] Where, Σ 3D This represents the homogenized nuclear reaction cross section (cm) used in the three-dimensional diffusion calculation of the reactor core. -1 ;Σ LATTICE This represents the homogenized nuclear reaction cross section (cm) of the component calculated under fully symmetric boundary conditions for a single component. -1 ;Σ 2D This represents the homogenized nuclear reaction cross section of the component, taking environmental conditions into account, in cm. -1 ;Σ SA This indicates the homogenized nuclear reaction cross section of the components without considering environmental conditions / cm. -1 ;

[0019] Step 5: Since the diffusion coefficient represents the efficiency of neutron diffusion from a high-concentration region to a low-concentration region, its value satisfies a one-third reciprocal relationship with the total macroscopic cross-section in the nuclear reaction cross section:

[0020]

[0021] Where: D represents the diffusion coefficient, ∑ t Represents the total macroscopic cross-section of the nuclear reaction / cm -1 ;

[0022] Therefore, the diffusion coefficient is corrected using formula (6), which can ensure the theoretical consistency between the diffusion coefficient and the nuclear reaction cross section.

[0023]

[0024] Among them, D 3D D represents the component homogenization diffusion coefficient used in the three-dimensional diffusion calculation of the reactor core, expressed as D / cm. LATTICE D represents the homogenization diffusion coefficient (cm) of the module calculated under fully symmetric boundary conditions for a single module; 2DD represents the homogenization diffusion coefficient of the component considering environmental conditions (in cm). SA This represents the homogenization diffusion coefficient of the component without considering environmental conditions ( / cm).

[0025] Step 6: The discontinuity factor f is the ratio of the neutron flux density obtained from non-uniform calculation to that obtained from uniform calculation:

[0026]

[0027] Where φ het φ represents the neutron surface flux density obtained from non-uniform calculations. hom This represents the neutron surface flux density obtained through uniform calculation;

[0028] Since the value of the discontinuity factor is generally around 1.0, it is easier to use a multiplication correction method to achieve a discontinuity factor that is closer to the real environment. Therefore, formula (8) is used to correct the discontinuity factor:

[0029]

[0030] Among them, f 3D This represents the component homogenization discontinuity factor used in the three-dimensional diffusion calculation of the reactor core; f LATTICE f represents the homogenization discontinuity factor of the component calculated under the fully symmetric boundary conditions of a single component; 2D This represents the component homogenization discontinuity factor considering environmental conditions; f SA This indicates that the component homogenization discontinuity factor has not taken into account environmental conditions.

[0031] Step 7: After obtaining the corrected component homogenization minority group constants in steps 4-6, perform three-dimensional whole-core neutron diffusion calculations using the corrected component homogenization minority group constants.

[0032] Step 8: Considering that the core calculation and single-assembly calculation in Step 3 are only performed in two dimensions, it is necessary to further modify the component homogenization minority group constant based on the results of the three-dimensional neutron diffusion calculation and the leakage correction theory to consider the influence of axial leakage on the axial motion of neutrons. After the iterative process between the three-dimensional diffusion calculation and the two-dimensional diffusion calculation, the improved subgrid method core calculation can be completed after convergence. The calculation results of effective multiplication coefficient, radial and axial power distribution, critical boron concentration, moderator temperature coefficient, fuel temperature coefficient, and control rod value are obtained, and the core physical analysis is completed.

[0033] Since the effective multiplication coefficient is a lumped parameter, the convergence criterion for the iterative process is that the difference between two consecutive solutions to the effective multiplication coefficient is less than 10. -6 .

[0034] Compared with the prior art, the present invention has the following advantages:

[0035] (1) The correction to the diffusion coefficient is more in line with its physical definition and maintains its theoretical consistency with the nuclear reaction cross section.

[0036] (2) The correction of the discontinuity factor is more in line with the physical definition of the parameter itself, and the correction effect is theoretically guaranteed.

[0037] (3) It has strong technical versatility and can be used to calculate the core of square and hexagonal components, as well as the core of fuel in the form of plates, rods, rings and tubular tubes. Attached Figure Description

[0038] Figure 1 The flowchart shows the calculation process for the minority group constant in subgrid homogenization.

[0039] Figure 2 The flowchart shows the parameterization calculation process for the minority group constant in subgrid homogenization.

[0040] Figure 3 A flowchart for core calculation using the improved subgrid method. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0042] This invention provides an improved subgrid method for handling environmental effects in the physical calculation of pressurized water reactor cores. The specific implementation steps are as follows:

[0043] Step 1: Obtain the sub-mesh homogenization minority group constant: In the component calculation, for each type of component, the sub-mesh homogenization calculation is completed to obtain the homogenization minority group constant of each sub-mesh in the component.

[0044] The calculation process for obtaining the minority group constant of submesh homogenization is as follows: Figure 1 As shown: First, the component design parameters must be input. Then, after resonance calculation, transport calculation and fundamental mode correction calculation, the flux distribution within the component is obtained. This flux distribution is used as the weight to perform sub-mesh homogenization calculation, thereby obtaining the sub-mesh homogenization minority group constant.

[0045] The solution for the subgrid homogenization minority group constant is shown in Equations (1), (2), and (3):

[0046]

[0047]

[0048]

[0049] Where A represents the component; het represents the result of non-uniform computation; hom represents the result of uniform computation; V i This represents the volume of the i-th subgrid in cm³. 3 ; This represents the neutron flux density of the h-th group at position r within the component, expressed as (cm²). 2 ·s) -1 ; This represents the non-uniform macroscopic cross section x at position r, group h (x represents the total cross section t, absorption cross section a, fission cross section f, and scattering cross section s) / cm. -1 ; Represents the uniform macroscopic x-section / cm of the i-th subgrid and the g-th group. -1 ; This represents the diffusion coefficient of the g-th group in the i-th subgrid, expressed in cm. Let represent the discontinuity factor of the s-th face of the g-th group in the i-th subgrid; This represents the non-uniform surface flux of the s-th face in the g-th group of the i-th subgrid / (cm) 2 ·s) -1 ; This represents the uniform surface flux (cm) of the s-th face in the g-th group of the i-th subgrid. 2 ·s) -1 .

[0050] Step 2: Perform parameterized calculations on the sub-grid homogenization minority group constants to obtain a library of sub-grid homogenization minority group constants that characterizes the quantitative functional relationship between the sub-grid homogenization minority group constants and the component state parameters. The component state parameters include the component burn-out depth, boron concentration, fuel temperature, and moderator temperature.

[0051] The calculation process is as follows Figure 2 As shown: The sub-mesh homogenization minority group constants obtained in step 1 are used as input to perform sub-mesh homogenization minority group constant parameterization calculation, thereby obtaining the sub-mesh homogenization minority group constant library.

[0052] Step 3: In the core calculation using the improved subgrid method, such as... Figure 3 As shown, the core design parameters must first be input, and then the core state is obtained through thermal calculations. Based on the subgrid homogenization minority group constant library obtained in step 2, subgrid two-dimensional calculations are completed. These subgrid two-dimensional calculations include two-dimensional core calculations and two-dimensional single-assembly calculations. The two-dimensional core calculations obtain the assembly homogenization minority group parameters considering the assembly environment, while the two-dimensional single-assembly calculations obtain the assembly homogenization minority group parameters not considering the assembly environment. These component homogenization minority group parameters, considering and not considering the assembly environment, are used for the minority group constant correction calculations in steps 4-6.

[0053] Two-dimensional core computation involves performing diffusion calculations across the entire core, with the boundary conditions between modules being true boundaries. This yields the flux of each subgrid within the two-dimensional full-core area and the net neutron flux at the boundaries. Two-dimensional single-module computation, on the other hand, performs diffusion calculations within a module, with the module's boundary conditions being total reflection boundaries. This yields the flux of each subgrid within the module and the net neutron flux at the boundaries.

[0054] Step 4: Since the physical meaning of the nuclear reaction cross section is the probability of a neutron reacting with an atomic nucleus, according to the principle of probability superposition, the nuclear reaction cross section satisfies an additive relationship. Therefore, the parameters of the nuclear reaction cross section are corrected using formula (4).

[0055] Σ 3D =Σ LATTICE +(Σ 2D -Σ SA (4)

[0056] Where, Σ 3D This represents the homogenized nuclear reaction cross section (cm) used in the three-dimensional diffusion calculation of the reactor core. -1 ;Σ LATTICE This represents the homogenized nuclear reaction cross section (cm) of the component calculated under fully symmetric boundary conditions for a single component. -1 ;Σ 2D This represents the homogenized nuclear reaction cross section of the component, taking environmental conditions into account, in cm. -1 ;Σ SA This indicates the homogenized nuclear reaction cross section of the components without considering environmental conditions / cm. -1 .

[0057] Step 5: Since the diffusion coefficient represents the efficiency of neutron diffusion from a high-concentration region to a low-concentration region, its value satisfies a one-third reciprocal relationship with the total macroscopic cross-section in the nuclear reaction cross section:

[0058]

[0059] Where: D represents the diffusion coefficient, ∑ t Represents the total macroscopic cross-section of the nuclear reaction / cm -1 .

[0060] Therefore, the diffusion coefficient can be corrected using formula (6) to ensure the theoretical consistency between the diffusion coefficient and the nuclear reaction cross section.

[0061]

[0062] Among them, D 3D D represents the component homogenization diffusion coefficient used in the three-dimensional diffusion calculation of the reactor core, expressed as D / cm. LATTICE D represents the homogenization diffusion coefficient (cm) of the module calculated under fully symmetric boundary conditions for a single module;2D D represents the homogenization diffusion coefficient of the component considering environmental conditions (in cm). SA This represents the component homogenization diffusion coefficient / cm without considering environmental conditions.

[0063] Step 6: For the discontinuity factor f, it is defined as the ratio of the neutron surface flux density obtained by non-uniform calculation to the neutron flux density obtained by uniform calculation:

[0064]

[0065] Where φ het φ represents the neutron surface flux density obtained from non-uniform calculations. hom This represents the neutron flux density obtained through uniform calculation.

[0066] Since the value of the discontinuity factor is generally around 1.0, it is easier to use a multiplication correction method to achieve a discontinuity factor that is closer to the real environment. Therefore, formula (8) is used to correct the discontinuity factor:

[0067]

[0068] Among them, f 3D This represents the component homogenization discontinuity factor used in the three-dimensional diffusion calculation of the reactor core; f LATTICE f represents the homogenization discontinuity factor of the component calculated under the fully symmetric boundary conditions of a single component; 2D This represents the component homogenization discontinuity factor considering environmental conditions; f SA This indicates that the component homogenization discontinuity factor has not taken into account environmental conditions.

[0069] Step 7: Obtain the corrected component homogenization minority group constant Σ after steps 4-6. 3D D 3D f 3D Subsequently, three-dimensional whole-core diffusion calculations were performed using the modified component homogenization minority group constant.

[0070] Step 8: Considering that the core calculations and single-assembly calculations in Step 3 are only performed in two dimensions, it is necessary to further modify the assembly homogenization minority group constant based on the results of the three-dimensional full-core diffusion calculation and the leakage correction theory, in order to account for the influence of axial leakage on neutron axial motion. After iterative processes between the three-dimensional full-core diffusion calculation and the two-dimensional diffusion calculation, the convergence criterion for the iteration is that the difference between two consecutive solutions of the effective multiplication coefficient is less than 10. -6 After convergence, the improved subgrid method core calculation can be completed, obtaining the calculation results of effective multiplication factor, radial and axial power distribution, critical boron concentration, moderator temperature coefficient, fuel temperature coefficient, and control rod value, thus completing the core physical analysis. Axial leakage calculation is shown in formula (9):

[0071]

[0072] Where: leak represents the equivalent of leakage; sid represents the boundary; out represents outflow; h represents the submesh height in cm; This represents the boundary outflow neutron flux density (cm²) of the m-th surface in the z-direction of the subgrid at position (x, y). 2 ·s) -1 ;φ g (x,y) represents the neutron flux density of the g-th energy group at position (x,y) / (cm²). 2 ·s) -1 ;∑ leak,g (z) represents the leakage equivalent cross section (cm) of the g-th energy group in the z-direction. -1 .

Claims

1. An improved subgrid method for handling environmental effects in the physical calculation of pressurized water reactor cores, characterized by: Includes the following steps: Step 1: Obtain the sub-mesh homogenization minority group constant: In the component calculation, for each type of component, the sub-mesh homogenization calculation is completed to obtain the homogenization minority group constant of each sub-mesh in the component; Step 2: Perform parameterized calculations on the sub-grid homogenization minority group constants to obtain a library of sub-grid homogenization minority group constants that characterizes the quantitative functional relationship between the sub-grid homogenization minority group constants and the component state parameters. The component state parameters include the component burn-out depth, boron concentration, fuel temperature, and moderator temperature. Step 3: Obtain the core state through thermal calculations. Based on the subgrid homogenization minority group constant library from Step 2, complete the two-dimensional subgrid calculation, including two-dimensional core calculation and two-dimensional single-module calculation. Obtain the module homogenization minority group parameters considering the module environment through the two-dimensional core calculation, and obtain the module homogenization minority group parameters without considering the module environment through the two-dimensional single-module calculation. Step 4: Since the physical meaning of the nuclear reaction cross section is the probability of a neutron reacting with an atomic nucleus, according to the principle of probability superposition, the nuclear reaction cross section satisfies the summation relationship. Therefore, the nuclear reaction cross section parameters are corrected using formula (4). S 3D =S LATTICE +(S 2D -S SA ) (4) Where, Σ 3D This represents the homogenized nuclear reaction cross section (cm) used in the three-dimensional diffusion calculation of the reactor core. -1 ;Σ LATTICE This represents the homogenized nuclear reaction cross section (cm) of the component calculated under fully symmetric boundary conditions for a single component. -1 ;Σ 2D This represents the homogenized nuclear reaction cross section of the component, taking environmental conditions into account, in cm. -1 ;Σ SA This indicates the homogenized nuclear reaction cross section of the components without considering environmental conditions / cm. -1 ; Step 5: Since the diffusion coefficient represents the efficiency of neutron diffusion from a high-concentration region to a low-concentration region, its value satisfies a one-third reciprocal relationship with the total macroscopic cross-section in the nuclear reaction cross section: Where: D represents the diffusion coefficient, ∑ t Represents the total macroscopic cross-section of the nuclear reaction / cm -1 ; Therefore, the diffusion coefficient is corrected using formula (6), which can ensure the theoretical consistency between the diffusion coefficient and the nuclear reaction cross section. Among them, D 3D D represents the component homogenization diffusion coefficient used in the three-dimensional diffusion calculation of the reactor core, expressed as D / cm. LATTICE D represents the homogenization diffusion coefficient (cm) of the module calculated under fully symmetric boundary conditions for a single module; 2D D represents the homogenization diffusion coefficient of the component considering environmental conditions (in cm). SA This represents the homogenization diffusion coefficient of the component without considering environmental conditions ( / cm). Step 6: The discontinuity factor f is the ratio of the neutron flux density obtained from non-uniform calculation to that obtained from uniform calculation: Where φ het φ represents the neutron surface flux density obtained from non-uniform calculations. hom This represents the neutron surface flux density obtained through uniform calculation; Since the discontinuity factor is around 1.0, it is easier to use a multiplicative correction method to achieve a discontinuity factor that is closer to the real environment. Therefore, formula (8) is used to correct the discontinuity factor: Among them, f 3D This represents the component homogenization discontinuity factor used in the three-dimensional diffusion calculation of the reactor core; f LATTICE f represents the homogenization discontinuity factor of the component calculated under the fully symmetric boundary conditions of a single component; 2D This represents the component homogenization discontinuity factor considering environmental conditions; f SA This indicates that the component homogenization discontinuity factor has not taken into account environmental conditions. Step 7: After obtaining the corrected component homogenization minority group constants in steps 4-6, perform three-dimensional whole-core neutron diffusion calculations using the corrected component homogenization minority group constants. Step 8: Considering that the core calculation and single-assembly calculation in Step 3 are only performed in two dimensions, it is necessary to further modify the component homogenization minority group constant based on the results of the three-dimensional neutron diffusion calculation and the leakage correction theory to consider the influence of axial leakage on the axial motion of neutrons. After the iterative process between the three-dimensional diffusion calculation and the two-dimensional diffusion calculation, the improved subgrid method core calculation is completed after convergence. The calculation results of effective multiplication coefficient, radial and axial power distribution, critical boron concentration, moderator temperature coefficient, fuel temperature coefficient, and control rod value are obtained, and the core physical analysis is completed.

2. The improved subgrid method for handling environmental effects in the physical calculation of pressurized water reactor core according to claim 1, characterized in that: Since the effective multiplication coefficient is a lumped parameter, the convergence criterion for the iterative process is that the difference between two consecutive solutions to the effective multiplication coefficient is less than 10. -6 .

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