Hyperfine group rapid calculation method for single group reaction cross section in Monte Carlo burn-up calculation

Abstract

The invention discloses a hyperfine group rapid calculation method for a single group reaction section in Monte Carlo burnup calculation. The hyperfine group rapid calculation method comprises the following steps: (a) calculating each nuclide in each burnup region to generate a hyperfine group section; (b) carrying out Monte Carlo neutron transport calculation on each burnup region to obtain hyperfine group flux, wherein an energy group structure is matched with a hyperfine group cross section; and (c) using the hyperfine group flux as a weight spectrum, and merging hyperfine group sections into single group reaction sections for burn-up calculation and calling. When the hyperfine group cross section of each type of nuclide is calculated, a new background cross section algorithm is adopted, and only the single group absorption cross section of one type of nuclide needs to be calculated for each burnup area; according to the method, the calculation amount of Monte Carlo neutron transport is not additionally increased, the calculation of the hyperfine group flux and the background cross section of each burnup region is completed in a neutron transport process, and compared with a traditional reaction rate-flux ratio method for calculating the burnup cross section, the reaction rate counting time in the Monte Carlo neutron transport process is remarkably shortened, and the calculation efficiency is improved. The calculation speed can be increased in magnitude, and the method can be used for solving the calculation speed bottleneck problem that in Monte Carlo burnup calculation, burnup section calculation consumes much time.

Description

Technical Field

[0001] The present application relates to the field of nuclear energy utilization, and in particular to a method for fast calculation of a single-group reaction cross section in a Monte Carlo burnup calculation. Background Art

[0002] The burnup cross section in the Monte Carlo burnup calculation is usually obtained by the reaction rate flux ratio method in the Monte Carlo neutron transport calculation process, that is, each reaction rate of each nuclide in each burnup zone and the volume average flux of each burnup zone are calculated separately, and then the burnup cross section of each nuclide is obtained by dividing the reaction rate by the flux. The reaction rate calculation requires that each time a collision with the target nucleus occurs during the neutron transport process, the microscopic reaction cross section of the corresponding collision target nucleus is queried, and the neutron track length and the microscopic reaction cross section are multiplied and accumulated. The essence of this time-consuming process is that the emission energy of the neutron after each collision is different, so each time it is necessary to query the microscopic cross section of the corresponding nuclide according to the emission energy, and in order to achieve better convergence, the number of collisions must be quite large, resulting in a sharp increase in calculation time.

[0003] As the burnup area increases, for example, from research reactors to million-kilowatt nuclear power plant reactors, the burnup area will increase in magnitude. For large burnup systems, Monte Carlo burnup calculations are difficult to obtain good convergence results within a reasonable time even on supercomputers. Therefore, the time-consuming calculation of the burnup cross section in Monte Carlo burnup calculations is a bottleneck problem that needs to be solved urgently in this field. Summary of the invention

[0004] In view of this, the purpose of the present invention is to provide a method for fast calculation of a single group reaction cross section in a Monte Carlo burnup calculation, so as to solve the serious time-consuming problem of Monte Carlo burnup cross section calculation for the above-mentioned large-scale burnup system. The present invention avoids in principle the problem of significant increase in calculation time consumption in the reaction rate flux ratio method of traditional burnup cross section calculation when the reaction rate count increases with the increase of the burnup zone and nuclides.

[0005] The present invention provides a method for fast calculation of a single group reaction cross section in a Monte Carlo burnup calculation, which is characterized by comprising the following steps:

[0006] (a) Calculate and generate the hyperfine group cross section for each nuclide in each burnup region;

[0007] (b) For each burnup region, a Monte Carlo neutron transport calculation is performed to obtain the hyperfine group flux, and the energy group structure matches the hyperfine group cross section;

[0008] (c) The hyperfine group flux is used as the weight spectrum, and the hyperfine group cross sections are merged into a single group reaction cross section for fuel consumption calculation.

[0009] Further, step (a) comprises the following steps:

[0010] (a1) The neutron continuous energy cross section of the ENDF original database of each nuclide is converted into a hyperfine group cross section data GENDF format database after resonance reconstruction, Doppler broadening and thermal scattering processing;

[0011] (a2) For fissile nuclides and nuclides with resonance capture reactions, multiple sets of hyperfine group cross section databases with different background cross sections are prepared;

[0012] (a3) For other nuclides with lower atomic density generated by nuclear reactions, such as fission products, the background cross section is taken as infinite, and only one set of hyperfine group cross section database needs to be prepared.

[0013] Further, step (b) comprises the following steps:

[0014] (b1) Setting up the Monte Carlo neutron transport calculation to count the neutron flux in all burnup zones;

[0015] (b2) Setting the energy group structure of neutron flux counting to match the hyperfine group cross section;

[0016] (b3) For each burnup time step, a full-system Monte Carlo neutron transport calculation is performed to obtain the hyperfine group flux of all burnup zones.

[0017] Further, step (c) comprises the following steps:

[0018] (c1) The merging method of single group reaction cross sections adopts formula (1),

[0019]

[0020] in, is a single group microscopic cross section, the cross section type can be (n, γ), (n, f), (n, α), (n, p), (n, 2n), etc., the unit is barn; E is the neutron energy, the unit is MeV; σ(E) is the continuous energy microscopic cross section, the unit is barn; φ(E) is the energy-related neutron flux, the unit is n / (cm 2 ·s); N is the number of hyperfine energy groups; σ i is the i-th group microscopic cross section of the hyperfine group cross section, in barn; φ i is the neutron flux of the i-th group of the hyperfine group flux, in units of n / (cm 2 s);

[0021] (c2) For fissile nuclides and nuclides with resonance capture reactions, their hyperfine group cross sections have multiple sets of databases based on different background cross sections. The background cross section is calculated according to formula (2):

[0022]

[0023] Among them, σ 0，i Background cross section of nuclide i; N i The atomic density of nuclide i; the number of nuclides M; σ p，j The potential scattering cross section of nuclide j; The average chord length of the burnup zone; α is the Bell factor; γ is the Dankov factor;

[0024] The numerator in the above formula is fixed for a fixed burnup cell. The material and geometry are fixed. Therefore, for each nuclide in the cell, the numerator in the above formula is fixed and is a constant, namely: 0，i N i = C. The density of nuclide i is obtained by burnup calculation. Therefore, in principle, only one additional background cross section of a resonant nuclide needs to be calculated to obtain the constant value of the numerator in the above formula. The background cross section of each nuclide can then be obtained by simply dividing the constant by the nuclide atomic density.

[0025] Based on the calculated background cross section, multiple sets of databases with different background cross sections are interpolated to obtain the hyperfine group cross section that takes into account the resonant self-screen and the spatial self-screen. This is brought into step (c1) to complete the calculation of the single group reaction cross section of the fissile nuclides and the nuclides with resonant capture reactions.

[0026] (c3) For other nuclides with lower atomic density generated by nuclear reactions, such as fission products, the hyperfine group cross sections under the infinite dilution assumption obtained in step (a3) ​​are brought into step (c1) to complete the calculation of single group reaction cross sections for all nuclides, thus forming a complete set of burnup calculation cross sections for use in burnup calculations.

[0027] Beneficial effects of the present invention:

[0028] In principle, the problem of significant increase in calculation time consumption of reaction rate counts with the increase of burnup zone and nuclides in the reaction rate flux ratio method of traditional burnup cross section calculation is avoided. The technical solution of the present invention does not increase the Monte Carlo neutron transport calculation amount, and completes the calculation of the hyperfine group flux and background cross section of each burnup zone in one neutron transport process. Compared with the traditional reaction rate flux ratio method for calculating the burnup cross section, the reaction rate counting time consumption in the Monte Carlo neutron transport process is significantly reduced, and the calculation speed can be improved by an order of magnitude, which can be used to solve the calculation speed bottleneck problem of serious time consumption of burnup cross section calculation in Monte Carlo burnup calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart of a method for fast calculation of a single group reaction cross section in a Monte Carlo burnup calculation of the present invention;

[0030] Figure 2 This is a schematic diagram of the grid cell geometry in the embodiment of the present application;

[0031] In the figure, 1. Model boundary; 2. Fuel core; 3. Gap between fuel and cladding; 4. Cladding; 5. Moderator. DETAILED DESCRIPTION

[0032] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0033] The present invention provides a method for fast calculation of a single group reaction cross section in a Monte Carlo burnup calculation, which is characterized by comprising the following steps:

[0034] (a) Calculate and generate the hyperfine group cross section for each nuclide in each burnup region;

[0035] (b) For each burnup region, a Monte Carlo neutron transport calculation is performed to obtain the hyperfine group flux, and the energy group structure matches the hyperfine group cross section;

[0036] (c) The hyperfine group flux is used as the weight spectrum, and the hyperfine group cross sections are merged into a single group reaction cross section for fuel consumption calculation.

[0037] Further, step (a) comprises the following steps:

[0038] (a1) The neutron continuous energy cross section of the ENDF original database of each nuclide is converted into a hyperfine group cross section data GENDF format database after resonance reconstruction, Doppler broadening and thermal scattering processing;

[0039] (a2) For fissile nuclides and nuclides with resonance capture reactions, multiple sets of hyperfine group cross section databases with different background cross sections are prepared;

[0040] (a3) For other nuclides with lower atomic density generated by nuclear reactions, such as fission products, the background cross section is taken as infinite, and only one set of hyperfine group cross section database needs to be prepared.

[0041] Further, step (b) comprises the following steps:

[0042] (b1) Setting up the Monte Carlo neutron transport calculation to count the neutron flux in all burnup zones;

[0043] (b2) Setting the energy group structure of neutron flux counting to match the hyperfine group cross section;

[0044] (b3) For each burnup time step, a full-system Monte Carlo neutron transport calculation is performed to obtain the hyperfine group flux of all burnup zones.

[0045] Further, step (c) comprises the following steps:

[0046] (c1) The merging method of single group reaction cross sections adopts formula (1),

[0047]

[0048] in, is a single group microscopic cross section, the cross section type can be (n, γ), (n, f), (n, α), (n, p), (n, 2n), etc., the unit is barn; E is the neutron energy, the unit is MeV; σ(E) is the continuous energy microscopic cross section, the unit is barn; φ(E) is the energy-related neutron flux, the unit is n / (cm 2 ·s); N is the number of hyperfine energy groups; σ i is the i-th group microscopic cross section of the hyperfine group cross section, in barn; φ i is the neutron flux of the i-th group of the hyperfine group flux, in units of n / (cm 2 s);

[0049] (c2) For fissile nuclides and nuclides with resonance capture reactions, their hyperfine group cross sections have multiple sets of databases based on different background cross sections. The background cross section is calculated according to formula (2):

[0050]

[0051] Among them, σ 0，i Background cross section of nuclide i; N i The atomic density of nuclide i; the number of nuclides M; σ p，j The potential scattering cross section of nuclide j; The average chord length of the burnup zone; α is the Bell factor; γ is the Dankov factor;

[0052] The numerator in the above formula is fixed for a fixed burnup cell. The material and geometry are fixed. Therefore, for each nuclide in the cell, the numerator in the above formula is fixed and is a constant, namely: 0，j N i = C. The density of nuclide i is obtained by burnup calculation. Therefore, in principle, only one additional background cross section of a resonant nuclide needs to be calculated to obtain the constant value of the numerator in the above formula. The background cross section of each nuclide can then be obtained by simply dividing the constant by the nuclide atomic density.

[0053] Based on the calculated background cross section, multiple sets of databases with different background cross sections are interpolated to obtain the hyperfine group cross section that takes into account the resonant self-screen and the spatial self-screen. This is brought into step (c1) to complete the calculation of the single group reaction cross section of the fissile nuclides and the nuclides with resonant capture reactions.

[0054] (c3) For other nuclides with lower atomic density generated by nuclear reactions, such as fission products, the hyperfine group cross sections under the infinite dilution assumption obtained in step (a3) ​​are brought into step (c1) to complete the calculation of single group reaction cross sections for all nuclides, thus forming a complete set of burnup calculation cross sections for use in burnup calculations.

[0055] Example 1

[0056] Figure 1 This is a flow chart of a method for fast calculation of single group reaction cross section in Monte Carlo burnup calculation of the present invention. In order to focus on the calculation of burnup cross section, a simple geometric single grid element benchmark problem is selected for acceleration performance verification. The benchmark problem used is the Westinghouse PWR grid element benchmark problem, such as Figure 2 As shown, it includes four regions: fuel core, air gap, fuel cladding and surrounding moderator. The fuel core is UO2 with an enrichment of 9.75%, and the burnup depth is expected to reach a high burnup depth of 100MWd / kgU. Both radial and axial boundary conditions are reflection boundaries. Figure 2 The model boundaries 1 are all total reflection boundaries.

[0057] The detailed material composition information is shown in Table 1.

[0058] Table 1 Materials and geometric descriptions of the basic grid element questions

[0059]

[0060]

[0061] The comparison between the calculated radiation capture cross section and fission cross section of the main actinide nuclides and the corresponding cross sections obtained by the traditional reaction rate counting method is shown in Table 2. The nuclides selected for calculation are the resonant nuclides with a relatively large atomic density in the material, and the comparison parameters are the radiation capture cross section and fission cross section related to the background cross section.

[0062] Table 2 Comparison of capture cross section and fission cross section of U and Pu

[0063]

[0064] Here, relative error = (ultrafine group method result - reaction rate counting result) / reaction rate counting result × 100%.

[0065] It can be seen that among the important resonant nuclides in this embodiment, the relative deviations of the calculation results of the two methods are within 0.3% except for the fission cross section of Pu-240 which is -1.4%. The comparison results show that the cross section values ​​calculated by the hyperfine group method are in good agreement with the cross section values ​​obtained by the traditional reaction rate counting method, which verifies the validity of the calculation results of the hyperfine group method.

[0066] Table 3 shows the comparison of the computational time and acceleration of the Westinghouse PWR grid element model using the hyperfine group method and the traditional reaction rate counting method.

[0067] Table 3 Acceleration of the hyperfine group method

[0068]

[0069] From this we can see that eff Taking the calculation time of "+1 group flux counting" as the basis, adding a 50,000 group flux counting only increases the calculation time by 11%; while the traditional reaction rate counting method increases the time for calculating the reaction rate of 234 nuclides by nearly 30 times. For this embodiment, the calculation time of the burnup cross section by the ultrafine group method is increased by 27.4 times compared with the traditional reaction rate counting method. It can be seen that this method significantly reduces the calculation time of the burnup cross section.

[0070] The present invention is described in detail above in combination with specific implementation methods and exemplary examples. The above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments; the above description cannot be understood as limiting the present invention. Those skilled in the art understand that, without departing from the spirit and scope of the present invention, the technical solution of the present invention and its implementation methods may be subjected to a variety of equivalent substitutions, modifications or improvements, all of which fall within the scope of the present invention; the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A method for fast calculation of single-group reaction cross sections in Monte Carlo burnup calculations, characterized in that: The following steps are involved: (a) Calculate and generate the hyperfine group cross section for each nuclide in each burnup region; (b) For each burnup region, a Monte Carlo neutron transport calculation is performed to obtain the hyperfine group flux, and the energy group structure matches the hyperfine group cross section; (c) The hyperfine group flux is used as a weight spectrum, and the hyperfine group cross sections are merged into a single group reaction cross section for fuel consumption calculation.

2. The method for fast calculation of single-group reaction cross sections in Monte Carlo burnup calculation according to claim 1, characterized in that: The step (a) comprises the following steps: (a1) The neutron continuous energy cross section of the ENDF original database of each nuclide is converted into a hyperfine group cross section data GENDF format database after resonance reconstruction, Doppler broadening and thermal scattering processing; (a2) For fissile nuclides and nuclides with resonance capture reactions, multiple sets of hyperfine group cross section databases with different background cross sections are prepared; (a3) For other nuclides with lower atomic density such as fission products produced by nuclear reactions, the background cross section is taken to be infinite.

3. The method for fast calculation of single group reaction cross section in Monte Carlo burnup calculation according to claim 1, characterized in that: The step (b) comprises the following steps: (b1) Setting up the Monte Carlo neutron transport calculation to count the neutron flux in all burnup zones; (b2) Setting the energy group structure of neutron flux counting to match the hyperfine group cross section; (b3) For each burnup time step, a full-system Monte Carlo neutron transport calculation is performed to obtain the hyperfine group flux of all burnup zones.

4. The method for fast calculation of single group reaction cross section in Monte Carlo burnup calculation according to claim 1, characterized in that: The step (c) comprises the following steps: (c1) The merging method of single group reaction cross sections adopts formula (1), in, is a single group microscopic cross section, the cross section type can be (n, γ), (n, f), (n, α), (n, p), (n, 2n), etc., the unit is barn; E is the neutron energy, the unit is MeV; σ(E) is the continuous energy microscopic cross section, the unit is barn; φ(E) is the energy-related neutron flux, the unit is n / (cm 2 ·s); N is the number of hyperfine energy groups; σ i is the i-th group microscopic cross section of the hyperfine group cross section, in barn; φ i is the neutron flux of the i-th group of the hyperfine group flux, in units of n / (cm 2 s); (c2) For fissile nuclides and nuclides with resonance capture reactions, their hyperfine group cross sections have multiple sets of databases based on different background cross sections. The background cross section is calculated according to formula (2): Among them, σ 0，i Background cross section of nuclide i; N i The atomic density of nuclide i; the number of nuclides M; σ p，j The potential scattering cross section of nuclide j; The average chord length of the burnup zone; α is the Bell factor; γ is the Dankov factor; Based on the calculated background cross section, multiple sets of databases with different background cross sections are interpolated and brought into step (c1) to complete the calculation of single-group reaction cross sections of fissile nuclides and nuclides with resonance capture reactions; (c3) For other nuclides with lower atomic density generated by nuclear reactions, such as fission products, the hyperfine group cross sections under the infinite dilution assumption obtained in step (a3) ​​are brought into step (c1) to complete the calculation of single group reaction cross sections for all nuclides, thus forming a complete set of burnup calculation cross sections for use in burnup calculations.

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