A method for calculating nuclear fuel multi-group data considering resonant upscattering effects

Abstract

A method for calculating multi-group data of nuclear fuel considering resonance upscattering effects includes: 1. For nuclides in the nuclear fuel with resonant scattering cross-sections, a nuclear data processing program generates a resonance upscattering correction factor table for their total cross-section, fission cross-section, and absorption cross-section; 2. A fuel assembly calculation program performs resonance calculations to obtain the average multi-group cross-section of the nuclides, and interpolates the average multi-group cross-section in a traditional multi-group cross-section table that does not consider resonance upscattering to obtain the corresponding dilution cross-section; 3. Using the dilution cross-section, interpolation in the resonance upscattering correction factor table yields a correction factor, which is used to correct the average multi-group cross-section, resulting in a nuclear fuel multi-group cross-section considering resonance upscattering effects. This method solves the problem that fuel assembly calculation programs using ultrafine group methods for resonance calculations cannot consider resonance upscattering effects, providing accurate multi-group data for neutron transport calculations and improving the calculation accuracy of nuclear reactor safety parameters such as the effective multiplication coefficient and fuel temperature coefficient.

Description

Technical Field

[0001] This invention relates to the fields of nuclear reactor physics calculation and nuclear data calculation technology, specifically to a method for calculating nuclear fuel multi-group data considering resonant upscattering effects. Background Technology

[0002] The core physics design of nuclear reactors relies on numerical simulations and calculations. Multi-group neutron transport calculations are a crucial component of this process, simulating neutron migration within the reactor to determine its distribution. This is fundamental for calculating safety parameters such as the effective multiplication coefficient and fuel temperature coefficient. Multi-group transport calculations require multi-group data as basic input parameters, including the total multi-group cross section, fission cross section, absorption cross section, and scattering matrix. The multi-group data used in neutron transport calculations is typically generated by nuclear data processing programs. Traditional programs use an asymptotic scattering model to approximate the weighted energy spectrum, which is then used to calculate the multi-group data. The asymptotic scattering model assumes that the target nucleus is stationary in the laboratory coordinate system and that its scattering cross section is constant, meaning that neutrons only lose energy upon collision. However, in reality, heavy nuclides like U-238 in nuclear fuel are in a state of thermal vibration, and their scattering cross section varies drastically with energy. Neutrons colliding with such target nuclei have a high probability of gaining energy, a phenomenon known as resonant upscattering. For the reasons mentioned above, the weighted energy spectrum calculated based on the asymptotic scattering model deviates significantly from the actual energy spectrum, affecting the accuracy of multi-group data and consequently the accuracy of neutron transport calculations.

[0003] Although nuclear data processing programs both domestically and internationally have developed the ability to handle resonance upscattering effects in recent years, generating multi-group data that takes resonance upscattering effects into account, current advanced fuel assembly calculation programs use the ultrafine group method for resonance calculations. The multi-group cross-sections are calculated based on the actual geometry, fuel composition, and temperature of the fuel assembly. The ultrafine group method uses asymptotic scattering models to solve the neutron moderation equations, which also cannot take resonance upscattering effects into account. Therefore, the multi-group cross-sections that take resonance upscattering effects into account generated by nuclear data processing programs cannot be used for transport calculations in assembly programs.

[0004] In summary, current fuel assembly calculation programs using the ultrafine group method for resonance calculations cannot provide multi-group data that considers the resonance upscattering effect for neutron transport calculations. This results in large calculation errors for parameters such as the reactor effective multiplication factor and fuel temperature coefficient, affecting nuclear reactor safety. Therefore, it is necessary to invent a nuclear fuel multi-group data calculation method that considers the resonance upscattering effect, generating the accurate multi-group cross-sections required for neutron transport calculations. This would improve the calculation accuracy of safety parameters such as the reactor effective multiplication factor and fuel temperature coefficient, thereby enhancing nuclear reactor safety. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a method for calculating multi-group data of nuclear fuel considering resonant upscattering effects. For heavy nuclides in nuclear fuel whose scattering cross-sections exhibit resonance, a nuclear data processing program generates a resonant upscattering correction factor table with dilution cross-section as the independent variable, based on the total cross-section, fission cross-section, and absorption cross-section of the nuclear fuel. After obtaining the average multi-group fission cross-section, total cross-section, and absorption cross-section of the heavy nuclide through resonance calculations in the fuel assembly calculation program, the corresponding dilution cross-section is obtained by interpolation from a traditional resonance cross-section table that does not consider resonant upscattering. The obtained dilution cross-section is then used to interpolate in the resonant upscattering correction factor table to obtain a correction factor, which is used to correct the average multi-group cross-section obtained from the resonance calculation, thus obtaining a multi-group cross-section of nuclear fuel considering resonant upscattering effects. This method solves the problem that fuel assembly calculation programs using the ultrafine group method for resonance calculations cannot consider resonant upscattering effects, providing accurate multi-group data for subsequent neutron transport calculations, improving the calculation accuracy of core safety parameters such as the effective multiplication coefficient and fuel temperature coefficient of nuclear reactors, and thereby improving the safety of nuclear reactors.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for calculating nuclear fuel multi-group data considering resonant on-scattering effects includes the following steps:

[0008] Step 1: For a homogeneous material composed of moderation nuclides and resonance nuclides, establish the neutron moderation equation:

[0009]

[0010] In the formula:

[0011] i—Nucleolabel;

[0012] Σ t,i (E) — The total cross section of nuclide i at energy E, provided by the nuclear data processing program;

[0013] Σ s,i (E') — The scattering cross section of nuclide i at energy E′, provided by the nuclear data processing program;

[0014] φ(E') — neutron weighted energy spectrum at energy E

[0015] φ(E) — is the neutron weighted energy spectrum at energy E′;

[0016] P i (E′→E) represents the probability that a neutron with incident energy E′ will change its energy to E after a scattering reaction with nuclide i. For moderated nuclides, which are lightweight and have no resonance in their scattering cross section, a gradual scattering model that does not consider upscattering is used to calculate P. i(E′→E); For resonance nuclides, P needs to be calculated using both the asymptotic scattering model and a scattering model that considers the resonance upscattering effect. i (E′→E), thus two weighted energy spectra can be obtained;

[0017] Step 2: For the overall reaction, fission reaction, and absorption reaction, use the two weighted energy spectra calculated in Step 1 to generate multi-group cross-section tables for several typical dilution cross-sections; for each dilution cross-section, use formula (2) to calculate the resonance upscattering correction factor, and obtain a resonance upscattering correction factor table with the dilution cross-section as the independent variable:

[0018]

[0019] In the formula:

[0020] f k,x,g (σ0) — The resonance on-scattering correction factor of the g-th energy group for the x-reaction type of nuclide k when the dilution cross section is σ0;

[0021] —The cross section of the g-th energy group of the x-reaction type of nuclide k, calculated based on the weighted energy spectrum considering the resonant upscattering effect when the dilution cross section is σ0;

[0022] —The cross section of the g-th energy group of the x-reaction type of nuclide k, calculated based on the weighted energy spectrum of the asymptotic scattering model when the dilution cross section is σ0;

[0023] σ0—Dilution cross section, reflecting the influence of nuclear fuel composition, geometry, and temperature on multiple cross sections, is preset by the user and provided to the nuclear data processing program;

[0024] Step 3: Perform resonance calculations using a fuel assembly calculation program that uses the ultra-fine group method to obtain the average multigroup cross section of the nuclear fuel, including: average total multigroup cross section, average multigroup fission cross section, and average multigroup absorption cross section. The multigroup cross section obtained at this time does not take into account the resonance upscattering effect.

[0025] Step 4: Using the average multigroup cross section obtained in Step 3, back-interpolate the multigroup cross section table calculated in Step 2 based on the asymptotic scattering model to obtain the dilution cross section σ corresponding to the multigroup cross section. 0,k,x,g Then, using this diluted cross section, the resonant upscattering correction factor f(σ) is obtained by interpolation in the resonant upscattering correction factor table obtained in step 2. 0,k,x,g );

[0026] Step 5: Using the resonant upscattering correction factor obtained in Step 4, the average multigroup cross section obtained in Step 3 is corrected using Formula (3) to account for the influence of resonant upscattering on the average multigroup cross section:

[0027]

[0028] In the formula:

[0029] σ k,x,g —The average multigroup cross section of the g-th energy group of the x-reaction type of nuclide k after considering the resonant upscattering effect;

[0030] —The average multigroup cross section of the g-th energy group of the x-reaction type of nuclide k obtained by resonance calculation;

[0031] Step 6: Use the average multigroup cross section obtained in Step 5 to perform neutron transport calculations.

[0032] Compared with existing technologies, it has the following advantages:

[0033] 1. The method of this invention employs a resonant upscattering correction factor to correct the multi-group cross-section obtained based on the ultrafine group method, considering the influence of resonant upscattering on the multi-group data. Compared with existing methods that use weighted energy spectra obtained by asymptotic scattering models to calculate multi-group cross-sections, this method can improve the calculation accuracy of multi-group data, which helps to improve the calculation accuracy of nuclear reactor effective multiplication coefficient, fuel temperature coefficient, etc., thereby improving the safety of nuclear reactors.

[0034] 2. The method of this invention only requires correction of the average multigroup cross section obtained from the resonance calculation using a correction factor after the resonance calculation. Compared with methods used domestically and internationally that statistically consider the scattering effect on resonance based on the Doppler rejection correction method using Monte Carlo programs, this method has high computational efficiency and is highly practical in the engineering design of nuclear reactors. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention.

[0036] Figure 2 This is the calculation result of the fuel for a single grid cell after the method of the present invention is implemented in the fuel assembly calculation program LOCUST.

[0037] Figure 3 , Figure 4 The present invention describes how, after the method is implemented in the component calculation program LOCUST, the homogenized minority cross section of the component after considering the resonance upscattering effect is provided to the matching core calculation program SPARK. This is used to calculate the boron concentration change curves during the third and fourth cycles of a CNP1000 pressurized water reactor in operation in China. Detailed Implementation

[0038] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0039] This invention is a method for calculating nuclear fuel multi-group data considering the resonant upscattering effect. Based on a nuclear data processing program, a resonant upscattering correction factor is generated to correct the average multi-group cross-section obtained from the resonant calculation. This fully considers the impact of the resonant upscattering effect on neutron transport calculations, thereby improving the accuracy of nuclear reactor core safety parameter calculations. The specific steps are as follows:

[0040] Step 1: For a homogeneous material composed of moderation nuclides and resonance nuclides, establish the neutron moderation equation:

[0041]

[0042] In the formula:

[0043] i—Nucleolabel;

[0044] Σ t,i (E) — The total cross section of nuclide i at energy E, provided by the nuclear data processing program;

[0045] Σ s,i (E') — The scattering cross section of nuclide i at energy E′, provided by the nuclear data processing program;

[0046] φ(E') — neutron weighted energy spectrum at energy E

[0047] φ(E) — is the neutron weighted energy spectrum at energy E′;

[0048] P i (E′→E) represents the probability that a neutron with incident energy E′ will change its energy to E after a scattering reaction with nuclide i. For moderated nuclides, which are lightweight and have no resonance in their scattering cross section, a gradual scattering model that does not consider upscattering is used to calculate P. i (E′→E); For resonance nuclides, P needs to be calculated using both the asymptotic scattering model and a scattering model that considers the resonance upscattering effect. i (E′→E), thus two weighted energy spectra can be obtained;

[0049] Step 2: For the overall reaction, fission reaction, and absorption reaction, use the two weighted energy spectra calculated in Step 1 to generate multi-group cross-section tables for several typical dilution cross-sections; for each dilution cross-section, use formula (2) to calculate the resonance upscattering correction factor, and obtain a resonance upscattering correction factor table with the dilution cross-section as the independent variable:

[0050]

[0051] In the formula:

[0052] f k,x,g (σ0) — The resonance on-scattering correction factor of the g-th energy group for the x-reaction type of nuclide k when the dilution cross section is σ0;

[0053] —The cross section of the g-th energy group of the x-reaction type of nuclide k, calculated based on the weighted energy spectrum considering the resonant upscattering effect when the dilution cross section is σ0;

[0054] —The cross section of the g-th energy group of the x-reaction type of nuclide k, calculated based on the weighted energy spectrum of the asymptotic scattering model when the dilution cross section is σ0;

[0055] σ0—Dilution cross section, reflecting the influence of nuclear fuel composition, geometry, and temperature on multiple cross sections, is preset by the user and provided to the nuclear data processing program;

[0056] Step 3: Perform resonance calculations using a fuel assembly calculation program that uses the ultra-fine group method to obtain the average multigroup cross section of the nuclear fuel, including: average total multigroup cross section, average multigroup fission cross section, and average multigroup absorption cross section. The multigroup cross section obtained at this time does not take into account the resonance upscattering effect.

[0057] Step 4: Using the average multigroup cross section obtained in Step 3, back-interpolate the multigroup cross section table calculated in Step 2 based on the asymptotic scattering model to obtain the dilution cross section σ corresponding to the multigroup cross section. 0,k,x,g Then, using this diluted cross section, the resonant upscattering correction factor f(σ) is obtained by interpolation in the resonant upscattering correction factor table obtained in step 2. 0,k,x,g );

[0058] Step 5: Using the resonant upscattering correction factor obtained in Step 4, the average multigroup cross section obtained in Step 3 is corrected using Formula (3) to account for the influence of resonant upscattering on the average multigroup cross section:

[0059]

[0060] In the formula:

[0061] σ k,x,g —The average multigroup cross section of the g-th energy group of the x-reaction type of nuclide k after considering the resonant upscattering effect;

[0062] —The average multigroup cross section of the g-th energy group of the x-reaction type of nuclide k obtained by resonance calculation;

[0063] Step 6: Use the average multigroup cross section obtained in Step 5 to perform neutron transport calculations.

[0064] The nuclear data processing program used in step 1 is not limited; any nuclear data processing program with resonance upscattering effect processing capabilities is acceptable, such as NECP-Atlas developed by Xi'an Jiaotong University and FRENDY developed by the Japan Atomic Energy Agency. The prepared resonance elastic scattering correction factor can be of a high order, and the resonance upscattering correction energy range for each nuclide is unrestricted. Figure 2 , Figure 3 , Figure 4 The energy range corrected in the calculation results shown is 4 eV to 200 eV; the version of the evaluation kernel database used to make the correction factor is not limited, such as ENDF / B-VII.0, VII.1, VIII.0 in the United States, CENDL-3.2 in China, etc.

[0065] The average multi-group cross section obtained from resonance calculation can be corrected using the method of this invention in component calculation programs using the ultra-fine group method and the one-step calculation program of the whole core. Such calculation programs include the LOCUST program and NECP-X program developed by Xi'an Jiaotong University, the SCALE program of the United States, the GALAXY program of Japan, and the MPACT program of the United States.

[0066] After implementing the method of this invention into the component calculation program LOCUST developed by Xi'an Jiaotong University, it was tested on the Mosteller UOX fuel benchmark problem (single-gate problem), such as... Figure 2 As shown in the table, HZP represents hot zero power (temperature 600K), HFP represents hot full power (temperature 900K), and FTC represents the Doppler fuel temperature coefficient. The table shows that the resonant upscattering effect is weak at hot zero power; at hot full power, compared to the original results, the eigenvalue decreases by 75–128 pcm, and the Doppler fuel temperature coefficient becomes more negative by 10.3%–11.9%, indicating that the system's negative feedback capability is stronger after considering the resonant upscattering effect.

[0067] The homogenized few-group cross section of the component, obtained by considering the resonant upscattering effect in LOCUST calculations, is then constantized and provided to the supporting core program SPARK for calculations of commercial pressurized water reactors. Taking the boron concentration change curves of the third and fourth cycles of a CNP1000 pressurized water reactor operating in China as an example, ... Figure 3 , Figure 4 As shown in the figure, the boron concentration calculated by the core program under full-power operation is 10-14 ppm lower than the original result, and is closer to the measured value. The original core program calculation results without considering the resonance upscattering effect were generally about 40 ppm higher than the measured value. This invention improves the accuracy of reactor core physics design, thereby improving the safety of nuclear reactors.

Claims

1. A method for calculating nuclear fuel multi-group data considering resonant upscattering effects, characterized in that: Includes the following steps: Step 1: For a homogeneous material composed of moderation nuclides and resonance nuclides, establish the neutron moderation equation: Official (1) In the formula: i —Nucleoside label; —nuclide i In energy E The total cross-section at that location is provided by the nuclear data processing program; —nuclide i In energy The scattering cross section at that location is provided by the nuclear data processing program; —for energy E Neutron weighted energy spectrum at the location —for energy Neutron weighted energy spectrum at the location; —where the incident energy is Neutrons and nuclides i The probability of energy becoming E after a scattering reaction is calculated using a gradual scattering model that does not consider upscattering, for slowed nuclides that are light in mass and have no resonance in the scattering cross section. ; For resonance nuclides, calculations must be performed using both the asymptotic scattering model and a scattering model that considers the resonance upscattering effect. Therefore, two weighted energy spectra can be obtained; Step 2: For the overall reaction, fission reaction, and absorption reaction, use the two weighted energy spectra calculated in Step 1 to generate multi-group cross-section tables for several typical dilution cross-sections; for each dilution cross-section, use formula (2) to calculate the resonance upscattering correction factor, and obtain a resonance upscattering correction factor table with the dilution cross-section as the independent variable: Official (2) In the formula: —Dilution cross section is At that time, nuclides k of x Reaction type g The resonant scattering correction factor of the energy group; —Dilution cross section is At that time, nuclides were calculated based on weighted energy spectra that take into account resonance scattering effects. k of x Reaction type g The cross section of the energy group; —Dilution cross section is At that time, nuclides calculated based on weighted energy spectra using asymptotic scattering models k of x Reaction type g The cross section of the energy group; —Dilution cross section, which reflects the influence of nuclear fuel composition, geometry and temperature on multiple cross sections, is preset by the user and provided to the nuclear data processing program; Step 3: Perform resonance calculations using a fuel assembly calculation program that uses the ultra-fine group method to obtain the average multigroup cross section of the nuclear fuel, including: average total multigroup cross section, average multigroup fission cross section, and average multigroup absorption cross section. The multigroup cross section obtained at this time does not take into account the resonance upscattering effect. Step 4: Using the average multigroup cross section obtained in Step 3, back-interpolate the multigroup cross section table calculated in Step 2 based on the asymptotic scattering model to obtain the diluted cross section corresponding to the multigroup cross section. Then, the resonance upscattering correction factor is obtained by interpolation using the diluted cross section in the resonance upscattering correction factor table obtained in step 2. ; Step 5: Using the resonant upscattering correction factor obtained in Step 4, the average multigroup cross section obtained in Step 3 is corrected using Formula (3) to account for the influence of resonant upscattering on the average multigroup cross section: Official (3) In the formula: —Considering resonance upscattering effects, nuclides k of x Reaction type g The average multigroup cross section of the energy group; —Nucite obtained by resonance calculation k of x Reaction type g The average multigroup cross section of the energy group; Step 6: Use the average multigroup cross section obtained in Step 5 to perform neutron transport calculations.

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