A method for accelerating the calculation of few-group cross sections for two-dimensional complex geometry assemblies

Abstract

The application relates to an acceleration method applied to two-dimensional complex geometry component few-group cross section calculation. In the two-dimensional geometry component few-group cross section calculation, 1968-group resonance calculation is performed on all nuclides, thereby obtaining 1968-group microscopic cross sections; then, the neutron transport equation is solved for each region in the two-dimensional component calculation, thereby obtaining the neutron flux distribution of each region in 1968 groups; subsequently, the obtained 1968-group microscopic cross sections are grouped into 81 groups for each region, and then the two-dimensional 81-group neutron transport equation is solved to obtain an accurate energy spectrum; finally, the regions and energy groups are merged to obtain the few-group cross section for the reactor core. The purpose of the method is to reduce the number of energy groups in the transport calculation, thereby greatly reducing the two-dimensional transport calculation time, greatly shortening the calculation time in the two-dimensional few-group cross section calculation under the premise of ensuring no loss of accuracy, and improving the overall calculation efficiency of the two-dimensional complex geometry component cross section calculation.

Description

Technical Field

[0001] This invention relates to the fields of nuclear reactor core design and nuclear reactor physics calculations, and is an accelerated method for calculating the few-group cross-sections of two-dimensional complex geometric components. Background Technology

[0002] The design of advanced nuclear reactors relies heavily on efficient and accurate numerical simulations. In existing two-step calculation strategies, the accuracy of few-group cross-section calculations plays a crucial role. Faced with the complexity of the energy spectrum and structure in advanced nuclear reactor design, the calculation methods and models for few-group cross-sections have evolved towards greater refinement. For example, the US MC... 2 Advanced reactor physics calculation software, such as REBUS and APOLLO3 (France), employs the characteristic line method in its few-group cross-section calculation modules to accommodate structural complexity. Simultaneously, they utilize an energy group structure of approximately 2000 groups to ensure the accuracy of obtaining the effective self-shield cross-section. Based on this, neutron transport equations are calculated to obtain the neutron energy spectrum for the component problem, and the cross-section is then grouped to the minimum required group.

[0003] However, it should be noted that under the current computational strategy, component computation requires approximately 2000 neutron transport calculations. As the problem becomes more complex and the flat-source region for characteristic line calculations becomes more finely divided, completing the computation takes an extremely long time and consumes enormous computational resources. Currently, some research institutions are attempting to improve computational efficiency through CPU parallelism and heterogeneous parallelism, but these methods do not fundamentally reduce the overall computation time and resources required.

[0004] Therefore, it is essential to invent an accelerated method for calculating the few-group cross-sections of two-dimensional complex geometric components, which can reduce the consumption of computing resources and significantly reduce the calculation time while ensuring the accuracy of calculation. This would be beneficial for the physical calculations and core design of advanced nuclear reactors. Summary of the Invention

[0005] An accelerated method for calculating the few-group cross-section of a two-dimensional complex geometric component is characterized by compressing the microscopic cross-section of group 1968 to group 81 using the neutron flux of a single region, and finally performing neutron transport calculations for group 81 coupled across all regions of the two-dimensional component, comprising the following steps:

[0006] Step 1: First, perform resonance calculations on the few-group cross sections of each two-dimensional component in the reactor to obtain the 1968 group micro-cross sections of each nuclide in each region of each two-dimensional component in the reactor.

[0007]

[0008] σ k,g,i,r —The energy interval of the i-nuclide in the r region is ΔEg The microscopic cross-section within the membrane is measured in cm. 2 ;k represents the cross-section type, including the i-nucleus with an energy interval of ΔE in the r region. g The total cross section σ inside t,g,i,r Absorption cross section σ a,g,i,r Fission cross section σ f,g,i,r scattering cross section σ s,g,i,r ;

[0009] φ r (E) — Neutron flux density with energy E at region r, in cm⁻¹ -2 ·s -1 ;

[0010] σ k,i,r (E) — Microscopic cross-section of nuclide i at energy E at region r, in cm 2 ;

[0011] ΔE g —Energy interval;

[0012] E – Neutron energy;

[0013] Step 2: Solve the neutron transport equations for individual regions in the two-dimensional reactor assembly to obtain the approximate 1968 group neutron flux density for each region;

[0014]

[0015] Σ t =Nσ t

[0016] Σ s =Nσ s

[0017] φ 1968 — Neutron flux density of group 1968 in each region, in cm³ -2 ·s -1 ;

[0018] Σ t —Total macroscopic cross-section, in cm -1 ;

[0019] Σ s — Macroscopic scattering cross section, in cm -1 ;

[0020] N – Nucleus density, measured in cm³ -3 ;

[0021] S—Source term;

[0022] σ t—Total microscopic cross-section, in cm 2 ;

[0023] σ s —Microscopic scattering cross section, in cm 2 ;

[0024] Ω — The direction of neutron motion is Ω;

[0025] Ω′ — The direction of neutron motion is Ω′;

[0026] E′ — The energy of a neutron is E′;

[0027] Step 3: For each region in the two-dimensional reactor assembly, the 1986 group micro-sections obtained in Step 1 are subjected to energy group compression. The compression process is based on the idea of ​​reaction rate conservation. The cross-sections are compressed using the approximate 1968 group neutron flux density of each region obtained in Step 2 as the weight, and finally the 81 group micro-sections of each nuclide in each region are obtained.

[0028]

[0029] σ k,81,i,r —Microscopic cross-section of nuclide i in region r, group 81, unit cm 2 k represents the cross-section type; including the total cross-section σ of 81 groups of nuclide i within region r. t,81,i,r 81 group absorption cross section σ a,81,i,r Group 81 fission cross section σ f,81,i,r Group 81 scattering cross section σ s,81,i,r ;

[0030] φ r,1968 — Neutron flux density of group 1968 at region r, in cm⁻¹ -2 ·s -1 ;

[0031] σ 1968,i,r —A microscopic cross-section of nuclide i in group 1968 at region r, in cm. 2 ;

[0032] ΔE g —Energy interval;

[0033] Step 4: Calculate the neutron transport equations for all regions coupled in each two-dimensional component of the entire reactor to obtain the accurate 81-group neutron flux density;

[0034]

[0035] Σ t,r =Nσ t,r

[0036] Σs,r =Nσ s,r

[0037] φ r,81 — Neutron flux density of group 81 within region r, in cm³ -2 ·s -1 ;

[0038] Σ t,r —The macroscopic total cross-section of region r, in cm -1 ;

[0039] Σ s,r — Macroscopic scattering cross section of region r, in cm -1 ;

[0040] σ t,r —Total microscopic cross section of region r, in cm 2 ;

[0041] σ s,r —Microscopic scattering cross section of region r, in cm 2 ;

[0042] Step 5: The 81 group micro-sections obtained in Step 3 are finally merged using the accurate 81 group neutron flux density obtained in Step 4 as the weight, to obtain the small group section used for reactor core calculation.

[0043] Compared with the prior art, the present invention has the following outstanding advantages:

[0044] 1. In this method, a two-dimensional few-group section calculation process with 1968 group resonance and 81 group transport is adopted, which avoids the problem of low calculation efficiency of 1968 group transport in the calculation of two-dimensional reactor components, improves the calculation efficiency of few-group sections, greatly reduces the time of reactor physical design calculation, and provides a new idea for efficient reactor calculation and analysis.

[0045] 2. In this method, the neutron transport equation is first solved for each region in each two-dimensional component of the reactor to obtain the neutron flux. Then, based on the idea of ​​reaction rate conservation, the energy groups are merged with the higher-order moments of the neutron flux in a single region as weights, which ensures the accuracy of the final few-group cross-section calculation and guarantees the accuracy of the reactor physics design calculation. Attached Figure Description

[0046] Figure 1 This is a flowchart of the accelerated method of the present invention applied to the calculation of few-group cross sections of two-dimensional complex geometric components.

[0047] Figure 2 This is a schematic diagram of a two-dimensional irradiation channel assembly. Detailed Implementation

[0048] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0049] for Figure 2 The two-dimensional irradiation channel assembly shown is used to model and calculate this complex two-dimensional geometric assembly using the present invention. The steps are as follows:

[0050] Step 1: First, for Figure 2 Resonance calculations of few-group sections were performed on the fuel, water, stainless steel, air gap, and aluminum regions of the irradiation channel assembly to obtain 1968 group microsections of each nuclide in each region of the assembly.

[0051]

[0052] σ k,g,i,r —The energy interval of the i-nuclide in the r region is ΔE g The microscopic cross-section within the membrane is measured in cm. 2 ;k represents the cross-section type, including the i-nucleus with an energy interval of ΔE in the r region. g The total cross section σ inside t,g,i,r Absorption cross section σ a,g,i,r Fission cross section σ f,g,i,r scattering cross section σ s,g,i,r ;

[0053] φ r (E) — Neutron flux density with energy E at region r, in cm⁻¹ -2 ·s -1 ;

[0054] σ k,i,r (E) — Microscopic cross-section of nuclide i at energy E at region r, in cm 2 ;

[0055] ΔE g —Energy interval;

[0056] E – Neutron energy;

[0057] Step 2: Solve the neutron transport equations for each region in the component individually to obtain the approximate 1968 group neutron flux density for each region;

[0058]

[0059] Σ t =Nσ t

[0060] Σ s =Nσ s

[0061] φ 1968— Neutron flux density of group 1968 in each region, in cm³ -2 ·s -1 ;

[0062] Σ t —Total macroscopic cross-section, in cm -1 ;

[0063] Σ s — Macroscopic scattering cross section, in cm -1 ;

[0064] N – Nucleus density, measured in cm³ -3 ;

[0065] S—Source term;

[0066] σ t —Total microscopic cross-section, in cm 2 ;

[0067] σ s —Microscopic scattering cross section, in cm 2 ;

[0068] Ω — The direction of neutron motion is Ω;

[0069] Ω′ — The direction of neutron motion is Ω′;

[0070] E′ — The energy of a neutron is E′;

[0071] Step 3: For each region in the component, the 1986 group micro-sections obtained in Step 1 are subjected to energy group compression. The compression process is based on the idea of ​​reaction rate conservation. The cross-sections are compressed using the approximate 1968 group neutron flux density of each region obtained in Step 2 as the weight, and finally the 81 group micro-sections of each nuclide in each region are obtained.

[0072]

[0073] σ k,81,i,r —Microscopic cross-section of nuclide i in region r, group 81, unit cm 2 k represents the cross-section type; including the total cross-section σ of 81 groups of nuclide i within region r. t,81,i,r 81 group absorption cross section σ a,81,i,r Group 81 fission cross section σ f,81,i,r Group 81 scattering cross section σ s,81,i,r ;

[0074] φ r,1968 — Neutron flux density of group 1968 at region r, in cm⁻¹ -2 ·s -1 ;

[0075] σ 1968,i,r —A microscopic cross-section of nuclide i in group 1968 at region r, in cm. 2 ;

[0076] ΔE g —Energy interval;

[0077] Step 4: Calculate the neutron transport equations for all regions coupled in the entire irradiation channel assembly to obtain the accurate 81 group neutron flux density.

[0078]

[0079] Σ t,r =Nσ t,r

[0080] Σ s,r =Nσ s,r

[0081] φ r,81 — Neutron flux density of group 81 within region r, in cm³ -2 ·s -1 ;

[0082] Σ t,r —The macroscopic total cross-section of region r, in cm -1 ;

[0083] Σ s,r — Macroscopic scattering cross section of region r, in cm -1 ;

[0084] σ t,r —Total microscopic cross section of region r, in cm 2 ;

[0085] σ s,r —Microscopic scattering cross section of region r, in cm 2 ;

[0086] Step 5: The 81-group micro-sections obtained in Step 3 are finally merged using the accurate 81-group neutron flux density obtained in Step 4 as the weight, to obtain the irradiation pore assembly minority group section used for reactor core calculation.

[0087] Table 1 Comparison of overall computation time before and after using the acceleration method of the present invention.

[0088] Before acceleration 341 0.84910 After acceleration 10 0.84677

[0089] The results are shown in Table 1: Before and after acceleration, the transport computation time of this two-dimensional complex geometric component was significantly reduced from 341 minutes to 10 minutes, and the final k infThe result deviates from the initial value by less than 300 pcm, demonstrating high computational accuracy.

[0090] This invention significantly reduces the transport calculation time in few-group cross-section calculations under two-dimensional geometry while ensuring the accuracy of the calculation results. It provides a new approach to reducing the calculation time for two-dimensional few-group cross-sections and reactor physics design, playing a significant role in overall core design and core calculations.

Claims

1. An accelerated method for calculating the few-group cross-sections of complex two-dimensional geometric components, characterized in that, The microscopic cross-section of group 1968 was compressed to group 81 using the neutron flux of a single region. Finally, neutron transport calculations were performed on group 81, which is coupled to all regions in the two-dimensional component. The steps included: Step 1: First, perform resonance calculations on the few-group cross sections of each two-dimensional component in the reactor to obtain the 1968 group micro-cross sections of each nuclide in each region of each two-dimensional component in the reactor. （1） —— i Nuclide in r The regional energy interval is The micro-section within, in units of ; k For cross-section types, including i Nuclide in r The regional energy interval is Total cross section inside Absorption cross section Fission cross section scattering cross section ; —In the region r The energy is E neutron flux density, in units of ; —In the region r Nuclide i In energy E The micro-section at the location, in units of ; —Energy interval; ——Neutron energy; Step 2: Solve the neutron transport equations for individual regions in the two-dimensional reactor assembly to obtain the approximate 1968 group neutron flux density for each region; （2） — Neutron flux density of group 1968 in each region, in units ; —Total macroscopic cross-section, unit: ; —Macroscopic scattering cross section, in units of ; —Nuclear density, in units of ; —Source item; —Total microscopic cross-section, in units of ; —Microscopic scattering cross section, in units of ; —The direction of neutron motion is ; —The direction of neutron motion is ; —The energy of a neutron is ; Step 3: For each region in the two-dimensional reactor assembly, the 1968 group micro-sections obtained in Step 1 are subjected to energy group compression. The compression process is based on the idea of ​​reaction rate conservation. The cross-sections are compressed using the approximate 1968 group neutron flux density of each region obtained in Step 2 as the weight, and finally the 81 group micro-sections of each nuclide in each region are obtained. （3） —Nucleotides i In the region r The 81 groups of micro-sections within, unit , k For cross-section types; Including nuclides i In the region r The total cross section of group 81 within 81 group absorption cross section Group 81 fission cross section Group 81 scattering cross section ; —In the region r Neutron flux density at group 1968, in units of ; —In the region r Nuclide i The 1968 group of micro-sections, in units of ; —Energy interval; Step 4: Calculate the neutron transport equations for all regions coupled in each two-dimensional component of the entire reactor to obtain the accurate 81-group neutron flux density; （4） --area r Neutron flux density of inner group 81, in units ; --area r The macroscopic total cross section, in units of ; --area r Macroscopic scattering cross section, in units of ; --area r Microscopic total cross section, unit: ; --area r Microscopic scattering cross section, in units of ; Step 5: The 81 group micro-sections obtained in Step 3 are finally merged using the accurate 81 group neutron flux density obtained in Step 4 as the weight, to obtain the small group section used for reactor core calculation.

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