Accelerated scanning method for neutron transport calculation of characteristic line based on penetration probability
By using a feature line neutron transport calculation method based on penetration probability, the entire core feature line is directly scanned, solving the problem of high computational cost under complex geometric problems and achieving efficient and economical neutron transport calculation.
Patent Information
- Application Number
- CN202511102101.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-07
- Publication Date
- 2025-11-21
AI Technical Summary
In nuclear reactor core design and safety analysis, the use of the method of characteristics to calculate complex geometric problems results in large computational loads, long processing times, and increased costs.
A feature line neutron transport calculation method based on penetration probability is adopted to directly scan the entire core feature line and calculate the outgoing boundary angle flux through the incident boundary angle flux and penetration probability, avoiding multiple segment-by-segment calculations until the incident boundary angle flux converges.
It improves computational efficiency, reduces computational costs, maintains computational accuracy, and enhances the scalability of the characteristic line method.
Smart Images
Figure CN120998557A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of nuclear reactor core design and safety technology, and specifically to an accelerated scanning method based on characteristic line neutron transport calculation using penetration probability. Background Technology
[0002] In the field of nuclear reactor engineering, physical analysis and calculations revolve around solving the Boltzmann neutron transport equation, which is a crucial aspect of nuclear reactor core design and safety. The method of characteristics (MOC) has strong geometric applicability, can solve complex non-uniform geometric problems, and can perform calculations with high resolution and accuracy, making it an important method for solving steady-state neutron transport equations.
[0003] However, when using MOC to calculate geometrically complex and highly anisotropic core problems, it often requires feature lines with close angles and fine widths, as well as a dense geometric mesh. Therefore, in neutron transport calculations, on the one hand, the increased number of core feature lines leads to a higher computational cost for feature line scanning; on the other hand, mesh refinement results in core feature lines containing more feature segments, further increasing the computational cost of scanning each segment. Thus, increasing the number of feature line scans when using MOC to calculate complex geometric core problems incurs significant time and economic costs. Summary of the Invention
[0004] To overcome the problems existing in the prior art, the present invention aims to propose an accelerated scanning method for neutron transport calculation based on the penetration probability of the feature line. The present invention directly scans the entire core feature line, and obtains the outgoing boundary angle flux from the incident boundary angle flux and the penetration probability of the core feature line. After boundary condition reflection processing, the incident boundary angle flux in the other direction of the point is obtained from the outgoing boundary angle flux. The outgoing boundary angle flux is calculated again from the incident boundary angle flux using the corresponding penetration probability coefficient. The above process is repeated until the incident boundary angle flux in all directions of the boundary point converges. This avoids multiple segment-by-segment calculations of the feature line before convergence, reduces the amount of computation, and improves the computational efficiency of the feature line method.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] An accelerated scanning method based on characteristic line neutron transport calculation using penetration probability includes the following steps:
[0007] Step 1: Based on the geometric and material information of the reactor core, establish the feature line information, and divide each feature line into N feature line segments according to the geometric grid;
[0008] Step 2: Based on the characteristic line segment information, directly establish the penetration probability coefficients from the incident boundary angular flux to the exit boundary angular flux along each characteristic line, i.e., a and b in formulas (1) and (2). iseg ;
[0009]
[0010]
[0011] In the formula:
[0012] a—Penetration probability coefficient of core characteristic line;
[0013] b iseg —The penetration probability coefficient of the i-th segment of the core feature line;
[0014] Q iseg —The source term of the flat source region grid that the iege segment of the core feature line passes through;
[0015] Σ t,iseg —The total cross section of the iege segment of the core feature line that passes through the flat source region grid;
[0016] s iseg —The length of the i-th segment of the core feature line;
[0017] Σ t,j —The total cross section of the j-th feature line segment in the core feature line that passes through the flat source region grid;
[0018] s j —The length of the j-th feature line segment in the core feature line;
[0019] N—The number of feature segments contained in the entire core feature line;
[0020] iseg—the characteristic line segment of the iseg segment;
[0021] j—the j-th characteristic line segment;
[0022] Step 3: Scan the entire feature line in all directions and use the penetration probability coefficient to determine the incident boundary angular flux from the core feature line. The outgoing boundary angular flux of the core feature line can be directly calculated using formula (3).
[0023] In the formula:
[0024] —Ejection boundary angle flux of the core feature line;
[0025] —Incident boundary angle flux along the core feature line;
[0026] in—incident direction;
[0027] out—direction of emission;
[0028] b—boundary value;
[0029] After the boundary condition reflection processing of the geometric region, the incident boundary angle flux in the other direction of the boundary point is obtained from the outgoing boundary angle flux of the core feature line. The outgoing boundary angle flux is calculated from the incident boundary angle flux again using the corresponding penetration probability coefficient. The above process is repeated until the incident boundary angle flux in all directions of the boundary point converges.
[0030] Step 4: Based on the convergent incident boundary angular flux, for each feature line in all directions at the boundary point, perform only one segment-by-segment scan of the feature line to calculate the incident angular flux of each feature line segment in the core feature line. and the flux of the exit angle Once flux information on the fine grid is obtained, the scan is complete.
[0031] The derivation processes of formulas (1), (2), and (3) are as follows:
[0032] 1) Based on the neutron transport characteristic line method, after discretizing the transport equation by angle and energy, the emission angular flux of the characteristic line segment along the characteristic line direction under one angle and one energy group is:
[0033]
[0034] In the formula:
[0035] —Emission angle flux of the i-th segment of the core feature line;
[0036] —Incident angle flux of the i-th segment of the core feature line;
[0037] Q iseg —The source term of the flat source region grid that the iege segment of the core feature line passes through;
[0038] Σ t,iseg —The total cross section of the iege segment of the core feature line that passes through the flat source region grid;
[0039] s iseg —The length of the i-th segment of the core feature line;
[0040] in—incident direction;
[0041] out—direction of emission;
[0042] iseg—the characteristic line segment of the iseg segment;
[0043] 2) If the entire core feature line contains N feature line segments, and the outgoing angular flux of the previous feature line segment is equal to the incoming angular flux of the next feature line segment, then the outgoing angular flux of each feature line segment can be obtained sequentially from the incident boundary angular flux according to formula (4):
[0044]
[0045] …
[0046]
[0047] …
[0048]
[0049] After sorting, we get:
[0050]
[0051] In the formula:
[0052] —Incident angle flux of the first characteristic line segment in the core characteristic line;
[0053] —The emission angle flux of the Nth characteristic line segment in the core characteristic line;
[0054]
[0055]
[0056] In summary, we obtain the calculation formulas (1) and (2) for the penetration probability coefficient.
[0057] 3) Since the incident boundary angular flux and the incident angular flux of the first characteristic line segment are equal, the exit boundary angular flux and the exit angular flux of the Nth characteristic line segment are equal, that is:
[0058]
[0059] Substituting into formula (5) and rearranging, we get:
[0060]
[0061] In summary, we obtain the calculation formula (3) for directly calculating the outgoing boundary angular flux of the core feature line from the incident boundary angular flux using the penetration probability coefficient.
[0062] Compared with the prior art, the present invention has the following outstanding advantages:
[0063] This invention obtains the outgoing boundary angular flux directly by scanning the entire core feature line. Compared with the usual scanning method that scans each feature line segment in the core feature line, it avoids multiple segment-by-segment calculations before the incident boundary angular flux converges.
[0064] The accelerated feature line scanning method proposed in this invention overcomes the shortcomings of the neutron transport feature line method in calculating reactor cores, such as low computational efficiency of feature line scanning. It effectively reduces computational costs, balances efficiency and accuracy, and improves the scalability of the neutron transport feature line method. Attached Figure Description
[0065] Figure 1 This is a flowchart of the method of the present invention;
[0066] Figure 2 This is a schematic diagram of the entire core feature line described in this invention;
[0067] Figure 3 This is a schematic diagram of each feature line segment and one of the feature line segments in the entire core feature line described in this invention;
[0068] Figure 4 This is a radial geometry diagram of the calculation examples that have been applied and verified in this invention. Detailed Implementation
[0069] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0070] This invention proposes an accelerated scanning method based on characteristic line neutron transport calculation using penetration probability, the flowchart of which is shown below. Figure 1 The specific steps are as follows:
[0071] Step 1: Based on the reactor core geometry and material information, establish characteristic line information, and divide each characteristic line into N characteristic line segments according to the geometric mesh. For example... Figure 2 The image shows a core feature line with a generated angle of 45°, divided into 11 feature line segments. The feature line segments contained in the core feature line are as follows: Figure 3 As shown.
[0072] Step 2: Based on the feature line segment information, directly establish the penetration probability coefficient from the incident boundary angular flux to the exit boundary angular flux along each feature line. Specifically, this is applied to... Figure 2 , Figure 3 The problem shown can be solved by obtaining the penetration probability coefficients along the core characteristic line, i.e., a and b in formulas (1) and (2). iseg ;
[0073]
[0074]
[0075] In the formula:
[0076] a—Penetration probability coefficient of core characteristic line;
[0077] b iseg —The penetration probability coefficient of the i-th segment of the core feature line;
[0078] Q iseg —The source term of the flat source region grid that the iege segment of the core feature line passes through;
[0079] Σ t,iseg —The total cross section of the iege segment of the core feature line that passes through the flat source region grid;
[0080] s iseg —The length of the i-th segment of the core feature line;
[0081] Σ t,j —The total cross section of the j-th feature line segment in the core feature line that passes through the flat source region grid;
[0082] s j —The length of the j-th feature line segment in the core feature line;
[0083] iseg—the characteristic line segment of the iseg segment;
[0084] j—the j-th characteristic line segment.
[0085] Step 3: Scan Figure 2 The entire feature line of the problem shown is obtained by using the penetration probability coefficient to measure the incident boundary angular flux from the core feature line. The outgoing boundary angular flux of the core feature line can be directly calculated using formula (3).
[0086] In the formula:
[0087] —Ejection boundary angle flux of the core feature line;
[0088] —Incident boundary angle flux along the core feature line;
[0089] in—incident direction;
[0090] out—direction of emission;
[0091] iseg—the characteristic line segment of the iseg segment;
[0092] b—boundary value.
[0093] After boundary condition reflection processing, the incident boundary angle flux in the other direction of the boundary point is obtained from the outgoing boundary angle flux of the core feature line. The outgoing boundary angle flux is then calculated from the incident boundary angle flux again using the corresponding penetration probability coefficient. The above process is repeated until the incident boundary angle flux in all directions of the boundary point converges.
[0094] Step 4: Based on the converged incident boundary angle flux, perform only one segment-by-segment feature line scan to calculate the incident and exit angle flux of the 11 feature line segments in the core feature line, obtain flux information on the fine grid, and the scan ends.
[0095] Figure 4 The diagram shows a schematic of the radial geometry of a core test case used for application verification of the method described in this invention. This problem is the C5G7 neutron transport calculation benchmark problem commonly used in the nuclear reactor physics industry for verifying core physics calculation programs.
[0096] The test case underwent feature line scanning calculations. The feature line scanning calculation conditions were: an argument of 8, a polar angle of 3, and a width of 0.03 cm within one octant (0-90°). A total of 5 radial MOC scans were performed. Using the method described in this invention, 4 scans were accelerated, followed by one scan of each feature line segment in the core feature line. The total scan calculation time consumed was 147.3 s. In contrast, performing 5 scans of each feature line segment in the core feature line consumed 207.1 s. Therefore, the accelerated feature line scanning method described in this invention saves approximately 60 s of calculation time, and the final calculation accuracy is consistent with that of the non-accelerated scan calculation, verifying the practical effect of this invention.
[0097] This invention accelerates characteristic line scanning calculations, facilitating more economical, efficient, and accurate neutron transport calculations. Particularly for solving geometrically complex and anisotropic problems, accelerating characteristic line scanning calculations effectively saves computational and time costs while achieving higher accuracy.
Claims
1. A method for accelerating scanning based on characteristic line neutron transport calculation using penetration probability, characterized in that: Before the flux at the incident boundary angle converges, multiple segment-by-segment scans of the feature line are replaced by multiple fast scans of the entire feature line, including the following steps: Step 1: Based on the geometric and material information of the reactor core, establish the feature line information, and divide each feature line into N feature line segments according to the geometric grid; Step 2: Based on the characteristic line segment information, directly establish the penetration probability coefficients from the incident boundary angular flux to the exit boundary angular flux along each characteristic line, i.e., a and b in formulas (1) and (2). iseg ; In the formula: a—Penetration probability coefficient of core characteristic line; b iseg —The penetration probability coefficient of the i-th segment of the core feature line; Q iseg —The source term of the flat source region grid that the iege segment of the core feature line passes through; Σ t,iseg —The total cross section of the iege segment of the core feature line that passes through the flat source region grid; s iseg —The length of the i-th segment of the core feature line; Σ t,j —The total cross section of the j-th feature line segment in the core feature line that passes through the flat source region grid; s j —The length of the j-th feature line segment in the core feature line; N—The number of feature segments contained in the entire core feature line; iseg—the characteristic line segment of the iseg segment; j—the j-th characteristic line segment; Step 3: Scan the entire feature line in all directions and use the penetration probability coefficient to determine the incident boundary angular flux from the core feature line. The angular flux emitted from the core feature line exiting the boundary is directly calculated using formula (3). In the formula: —Ejection boundary angle flux of the core feature line; —Incident boundary angle flux along the core feature line; in—incident direction; out—direction of emission; b—boundary value; After the boundary condition reflection processing of the geometric region, the incident boundary angle flux in the other direction of the boundary point is obtained from the outgoing boundary angle flux of the core feature line. The outgoing boundary angle flux is calculated from the incident boundary angle flux again using the corresponding penetration probability coefficient. The above process is repeated until the incident boundary angle flux in all directions of the boundary point converges. Step 4: Based on the convergent incident boundary angular flux, for each feature line in all directions at the boundary point, perform only one segment-by-segment scan of the feature line to calculate the incident angular flux of each feature line segment in the core feature line. and the flux of the exit angle Once flux information on the fine grid is obtained, the scan is complete.
2. The accelerated scanning method for characteristic line neutron transport calculation based on penetration probability according to claim 1, characterized in that: The derivation processes of formulas (1), (2), and (3) are as follows: 1) Based on the neutron transport characteristic line method, after discretizing the transport equation by angle and energy, the emission angular flux of the characteristic line segment along the characteristic line direction under one angle and one energy group is: In the formula: —Emission angle flux of the i-th segment of the core feature line; —Incident angle flux of the i-th segment of the core feature line; Q iseg —The source term of the flat source region grid that the iege segment of the core feature line passes through; Σ t,iseg —The total cross section of the iege segment of the core feature line that passes through the flat source region grid; s iseg —The length of the i-th segment of the core feature line; in—incident direction; out—direction of emission; iseg—the characteristic line segment of the iseg segment; 2) If the entire core feature line contains N feature line segments, and the outgoing angular flux of the previous feature line segment is equal to the incoming angular flux of the next feature line segment, then the outgoing angular flux of each feature line segment can be obtained sequentially from the incident boundary angular flux according to formula (4): After sorting, we get: In the formula: —Incident angle flux of the first characteristic line segment in the core characteristic line; —The emission angle flux of the Nth characteristic line segment in the core characteristic line; In summary, we obtain the calculation formulas (1) and (2) for the penetration probability coefficient. 3) Since the incident boundary angular flux and the incident angular flux of the first characteristic line segment are equal, the exit boundary angular flux and the exit angular flux of the Nth characteristic line segment are equal, that is: Substituting into formula (5) and rearranging, we get: In summary, we obtain the calculation formula (3) for directly calculating the outgoing boundary angular flux of the core feature line from the incident boundary angular flux using the penetration probability coefficient.