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CN114840959A - Method for manufacturing high-precision complex energy spectrum micro-stack multi-group cross section - Google Patents

Method for manufacturing high-precision complex energy spectrum micro-stack multi-group cross section Download PDF

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CN114840959A
CN114840959A CN202210449729.1A CN202210449729A CN114840959A CN 114840959 A CN114840959 A CN 114840959A CN 202210449729 A CN202210449729 A CN 202210449729A CN 114840959 A CN114840959 A CN 114840959A
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吴逸炜
郭辉
刘利民
冯快源
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Shanghai Jiao Tong University
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Abstract

本发明涉及一种高精度复杂能谱微堆多群截面制作方法，包括如下步骤：步骤1：针对所需计算的组件或堆芯进行建模，基于ACE格式截面数据，进行连续能量蒙特卡罗输运计算；步骤2：追踪指定均匀化区域内不同入射角度区间的中子；步骤3：根据步骤2，统计不同散射出射角度余弦区间内的散射事件数目，计算散射出射角余弦在各区间内的概率，确定散射角度分布；步骤4：根据步骤2和步骤3，计算得到多群数据；步骤5：根据步骤2和步骤4，制作多群数据库。本发明通过追踪统计中子入射角度，解决了所有截面的计算问题，降低现有方法中采用的近似与误差对微堆多群截面数据的影响，提高微堆多群截面数据精度。

Figure 202210449729

The invention relates to a method for fabricating multi-group cross-sections of high-precision complex energy spectrum micro-stacks, comprising the following steps: Step 1: Modeling components or cores to be calculated, and performing continuous energy Monte Carlo based on ACE format cross-section data Transport calculation; Step 2: Track neutrons in different incident angle intervals in the specified homogenization area; Step 3: According to Step 2, count the number of scattering events in the cosine interval of different scattering and outgoing angles, and calculate the cosine of scattering outgoing angle in each interval The probability of , determine the scattering angle distribution; Step 4: According to Step 2 and Step 3, calculate and obtain multi-group data; Step 5: According to Step 2 and Step 4, make a multi-group database. The invention solves the calculation problem of all sections by tracking and counting the neutron incident angles, reduces the influence of the approximation and error adopted in the existing method on the micro-stack multi-group section data, and improves the micro-stack multi-group section data accuracy.

Figure 202210449729

Description

一种高精度复杂能谱微堆多群截面制作方法A high-precision complex energy spectrum microstack multi-group cross-section fabrication method

技术领域technical field

本发明属于粒子输运计算领域，具体涉及一种基于蒙特卡罗方法的复杂能谱微堆多群截面制作方法。The invention belongs to the field of particle transport calculation, and in particular relates to a method for manufacturing a multi-group cross section of a complex energy spectrum micro-stack based on a Monte Carlo method.

背景技术Background technique

为快速、高效获取反应堆参数，“两步法”计算成为反应堆工程中的主要方法。“两步法”的第一步是对堆芯内各结构材料进行中子输运计算，生成均匀化多群截面；第二步是基于第一步生成的多群截面进行堆芯多群计算，获取堆芯物理量。In order to obtain reactor parameters quickly and efficiently, the "two-step" calculation has become the main method in reactor engineering. The first step of the "two-step method" is to calculate the neutron transport of each structural material in the core to generate a homogenized multi-group cross section; the second step is to calculate the core multi-group based on the multi-group cross section generated in the first step. , to obtain the physical quantities of the core.

反应堆物理计算的主要方法有蒙特卡罗方法与确定论方法。微型反应堆几何复杂，非均匀性强，确定论方法处理时采用大量近似与修正，其对微堆计算的适用性与可靠性有待验证。蒙特卡罗方法对复杂几何的强大处理能力适用于微堆模型的精细表征，成为复杂能谱微堆多群截面生成的有效手段。The main methods of reactor physics calculation are Monte Carlo method and deterministic method. The micro-reactor has complex geometry and strong non-uniformity. A large number of approximations and corrections are used in the processing of the deterministic method, and its applicability and reliability to the micro-reactor calculation need to be verified. The powerful processing ability of the Monte Carlo method for complex geometry is suitable for the fine characterization of the micro-stack model, and it becomes an effective means for generating multi-group cross-sections of the complex energy-spectrum micro-stack.

目前，蒙特卡罗方法生成多群截面过程中通常采用通量可分离性近似。通量可分离性近似，即中子通量的能量相关性与角度相关性相互独立。基于上述近似，使用指定均匀化区域内的标通量而非角通量加权平均计算多群截面。但上述近似在均匀化区域非均匀性强或均匀化空间材料不连续情况下将对群常数精度造成较大影响。Currently, the flux separability approximation is usually used in the Monte Carlo method to generate multi-group cross-sections. The flux separability is approximated, that is, the energy dependence of the neutron flux is independent of the angle dependence. Based on the above approximation, the multi-cluster cross-sections are calculated using the weighted average of the scalar fluxes within the specified homogenization region rather than the angular fluxes. However, the above approximation will have a great impact on the accuracy of the group constant when the homogenization region is highly non-uniform or the homogenized space material is discontinuous.

目前，多群截面生成方法针对散射各向异性的处理主要采用Pn方法。Pn方法即将散射截面关于中子出射角度余弦勒让德展开，而后拟合计算各阶散射矩阵，形成多群散射截面数据。但上述方法将产生多项式截断误差，该截断误差可能导致拟合的散射截面关于散射角余弦分布函数出现负值，这在物理上是不可能的。针对散射截面关于角余弦的分布函数值为负的点，目前的多群截面生成方法将上述点函数值指定为0，这将影响多群常数精度。At present, the multi-group cross-section generation method mainly adopts the Pn method to deal with scattering anisotropy. The Pn method expands the scattering cross section with respect to the cosine Legendre of the neutron exit angle, and then fits and calculates the scattering matrices of each order to form multi-group scattering cross section data. However, the above method will generate a polynomial truncation error, which may lead to a negative value of the fitted scattering cross section with respect to the cosine distribution function of the scattering angle, which is physically impossible. For points where the distribution function value of the scattering cross section with respect to the angular cosine is negative, the current multigroup cross section generation method assigns the above point function value to 0, which will affect the multigroup constant accuracy.

微堆多群截面制作中，由于微堆结构的非对称型以及并区导致的非均匀性或不连续性，通量可分近似及Pn方法表征各项异性散射的截断误差不可忽略。因此，需要开发一种可以获取高精度微堆多群截面数据的方法。In the fabrication of multi-group cross sections of microstacks, the truncation error of the flux separable approximation and the Pn method to characterize anisotropic scattering cannot be ignored due to the asymmetric type of the microstack structure and the non-uniformity or discontinuity caused by the parallel region. Therefore, it is necessary to develop a method that can acquire multi-group cross-section data of microstacks with high precision.

发明内容SUMMARY OF THE INVENTION

为解决上述现有技术存在的技术问题，本发明提供一种基于蒙特卡罗方法制作高精度微堆多群数据库的方法，该数据库的制作方法是在连续能量蒙特卡罗计算结果处理中统计指定多群空间区域不同中子入射角度区间的多群参数，并通过统计不同中子散射角度区间内的散射事件表征各向异性散射，计算得到多群数据，制作多群数据库。统计不同中子入射角度区间降低了通量可分近似对群常数的影响，统计学方法表征各向异性散射消除了传统Pn方法截断误差导致分布函数值为负对多群常数的影响。多群空间区域不同中子入射角度划分的区间适用于所有截面。In order to solve the technical problems existing in the above-mentioned prior art, the present invention provides a method for making a high-precision micro-stack multi-group database based on a Monte Carlo method. Multi-group parameters of different neutron incident angle intervals in multi-group space area, and anisotropic scattering is characterized by counting scattering events in different neutron scattering angle intervals, and multi-group data is obtained by calculation, and multi-group database is made. Statistical analysis of different neutron incident angle intervals reduces the influence of the flux separable approximation on the group constant, and the statistical method to characterize anisotropic scattering eliminates the influence of the negative distribution function value on the multigroup constant caused by the truncation error of the traditional Pn method. The interval divided by different neutron incidence angles in the multi-group space region is applicable to all sections.

本发明采取如下技术方案：The present invention adopts following technical scheme:

具体的，一种高精度复杂能谱微堆多群截面制作方法，其特征在于：包括如下步骤：Specifically, a method for fabricating multi-group cross-sections of a high-precision complex energy spectrum micro-stack is characterized by comprising the following steps:

步骤1：针对所需计算的组件或堆芯进行建模，基于ACE格式截面数据，进行连续能量蒙特卡罗输运计算；Step 1: Model the components or cores to be calculated, and perform continuous energy Monte Carlo transport calculations based on ACE format cross-section data;

步骤2：追踪指定均匀化区域内不同入射角度区间的中子；Step 2: Track neutrons in different incident angle intervals in the specified homogenization area;

步骤3：根据步骤2，统计不同散射出射角度余弦区间内的散射事件数目，计算散射出射角余弦在各区间内的概率，确定散射角度分布；Step 3: According to Step 2, count the number of scattering events in the cosine interval of different scattering exit angles, calculate the probability of scattering exit angle cosine in each interval, and determine the scattering angle distribution;

步骤4：根据步骤2和步骤3，计算得到多群数据；Step 4: According to Step 2 and Step 3, calculate the multi-group data;

步骤5：根据步骤2和步骤4，制作多群数据库。Step 5: According to Step 2 and Step 4, make a multi-group database.

更进一步地，go a step further,

所述步骤2包括：根据步骤1所述计算，追踪指定均匀化区域内不同入射角度区间的中子，将z、n、Ωn、g、r、E、ΔE、V作为指定入射角度区间的中子通量的筛选数据，经过蒙特卡罗输运计算，输出W、T、i、li参数，通过公式(1)计算指定入射角度区间的中子通量；将z、x、Ωn、g、ΔE、V、r、E作为中子在指定均匀化区域内的各类反应率的筛选数据，经过蒙特卡罗输运计算，输出W、i、wi、Ag参数，通过公式(2)计算所述中子在指定均匀化区域内的各类反应率。The step 2 includes: according to the calculation described in step 1, tracking neutrons in different incident angle intervals in the specified homogenization area, and taking z, n, Ω n , g, r, E, ΔE, and V as the neutrons in the specified incident angle interval. The screening data of neutron flux, through Monte Carlo transport calculation, output W, T, i , li parameters, and calculate the neutron flux in the specified incident angle range by formula (1); g, ΔE, V, r, and E are used as the screening data for various reaction rates of neutrons in the designated homogenization area. After Monte Carlo transport calculation, the parameters of W, i, wi, and Ag are output. Through formula (2) Calculate the various reaction rates of the neutrons in the specified homogenization region.

Figure BDA0003618124970000031
Figure BDA0003618124970000031

Figure BDA0003618124970000032
Figure BDA0003618124970000032

其中：in:

Figure BDA0003618124970000033
---能群g范围内，入射角度在Ωn区间的中子在均匀化空间z内的通量
Figure BDA0003618124970000033
---In the range of energy group g, the flux of neutrons with incident angle in the interval Ω n in the homogenization space z

Figure BDA0003618124970000034
---入射角度在Ωn区间的中子在能群g与均匀化空间z内产生的x类型反应率
Figure BDA0003618124970000034
---The reaction rate of type x produced in the energy group g and the homogenization space z of the neutron with the incident angle in the Ω n interval

z---均匀化空间变化z---homogenize the spatial variation

n---入射角离散区间编号n---incidence angle discrete interval number

Ωn---第n个中子入射角度离散区间Ω n --- discrete interval of the nth neutron incident angle

g---能群编号g---energy group number

r---空间位置r---spatial position

E---中子能量E---neutron energy

ΔE---能群g的能量上下界ΔE---energy upper and lower bounds of energy group g

V---均匀化空间z的体积V---the volume of the homogenized space z

W---初始中子总权重W---Initial neutron total weight

T---所有中子在均匀化空间体积内的轨迹集合T---set of trajectories of all neutrons in the homogenized space volume

i---事件编号i---event number

li---中子第i个轨迹的长度li---the length of the ith trajectory of the neutron

x---反应类型x---reaction type

wi---中子发生反应事件i前的权重wi---the weight of the neutron before the reaction event i

Ag---中子能量在能群g内的所有反应事件的总集合Ag---the total set of all reaction events with neutron energy in energy group g

所述步骤3包括：在步骤2的多群参数统计中，离散散射出射角度余弦，统计不同散射出射角度余弦区间内的散射事件数目，通过公式(3)计算散射出射角余弦在各区间内的概率，确定散射角度分布，经过蒙特卡罗输运计算，通过公式(4)确定散射截面。The step 3 includes: in the multi-group parameter statistics in step 2, the scattering outgoing angle cosine is discrete, the number of scattering events in different scattering outgoing angle cosine intervals is counted, and the scattering outgoing angle cosine in each interval is calculated by formula (3). Probability, determine the scattering angle distribution, through Monte Carlo transport calculation, determine the scattering cross section by formula (4).

Figure BDA0003618124970000041
Figure BDA0003618124970000041

Figure BDA0003618124970000042
Figure BDA0003618124970000042

其中：in:

Figure BDA0003618124970000043
---入射角度在Ωn区间内的中子，散射反应出射角余弦为μ的概率，满足关系式
Figure BDA0003618124970000044
Figure BDA0003618124970000043
--- For neutrons whose incident angle is in the interval of Ω n , the probability of scattering reaction exit angle cosine is μ, which satisfies the relation
Figure BDA0003618124970000044

Figure BDA0003618124970000045
---入射角度在Ωn区间，能量为E的中子在r处，散射反应出射角余弦为μ的散射反应宏观截面
Figure BDA0003618124970000045
---The incident angle is in the Ω n interval, the neutron with energy E is at r, and the scattering reaction macroscopic cross-section with the cosine of the scattering reaction exit angle μ

μ---散射反应出射角余弦μ---scattering reaction exit angle cosine

Δμn---第n个散射角余弦离散区间的区间长度Δμn---the interval length of the nth scattering angle cosine discrete interval

Wμ---散射出射角余弦为μ的中子权重Wμ---neutron weight with cosine of scattering exit angle μ

wμ---散射出射角余弦为μ的事件数wμ---the number of events with the cosine of the scattering exit angle μ

Figure BDA0003618124970000051
---入射角度在Ωn区间，能量为E的中子在r处的散射反应宏观截面
Figure BDA0003618124970000051
---The incident angle is in the interval of Ω n , the macroscopic cross section of the scattering reaction of the neutron with energy E at r

所述步骤4包括：基于步骤2和步骤3中得到的中子通量、反应率与散射角分布，通过蒙特卡罗输运计算获得参数

Figure BDA0003618124970000052
fg'→g(μ)，利用公式(5)计算多群散射矩阵，利用公式(6)计算其他多群截面。The step 4 includes: based on the neutron flux, reaction rate and scattering angle distribution obtained in steps 2 and 3, obtaining parameters through Monte Carlo transport calculation
Figure BDA0003618124970000052
f g'→g (μ), use formula (5) to calculate the multigroup scattering matrix, and use formula (6) to calculate other multigroup cross sections.

Figure BDA0003618124970000053
Figure BDA0003618124970000053

Figure BDA0003618124970000054
Figure BDA0003618124970000054

其中：in:

s---散射反应s---scattering reaction

g'---能群编号g'---energy group number

Figure BDA0003618124970000055
---入射角度在Ωn区间，出射角余弦为μ，能群g’与能群g之间的多群散射矩阵。
Figure BDA0003618124970000055
---The incident angle is in the Ω n interval, the cosine of the exit angle is μ, and the multi-group scattering matrix between the energy group g' and the energy group g.

fg'→g(μ)---出射角余弦为μ的散射反应将中子能量由g’转移至能群g的概率f g'→g (μ)---Probability that a scattering reaction with exit angle cosine μ transfers neutron energy from g' to energy group g

Figure BDA0003618124970000056
---能群g与均匀化空间z内，入射角度在Ωn区间的中子产生的x类型反应宏观截面
Figure BDA0003618124970000056
---In the energy group g and the homogenization space z, the x-type reaction macro-section produced by the neutron with the incident angle in the Ω n interval

Figure BDA0003618124970000057
---入射角在Ωn区间，能群g’散射反应截面
Figure BDA0003618124970000057
---The incident angle is in the Ω n interval, the energy group g' scattering reaction cross section

所述步骤5包括：根据步骤2与步骤4，制作生成高精度复杂能谱微堆多群数据库。The step 5 includes: according to the steps 2 and 4, creating and generating a high-precision complex energy spectrum micro-stack multi-group database.

步骤4中所述参数

Figure BDA0003618124970000061
fg'→g(μ)通过公式(7)和公式(8)确定，Parameters described in step 4
Figure BDA0003618124970000061
f g'→g (μ) is determined by Equation (7) and Equation (8),

Figure BDA0003618124970000062
Figure BDA0003618124970000062

Figure BDA0003618124970000063
Figure BDA0003618124970000063

更进一步地，所述步骤1中所述建模使用体素构造法；使用所述体素构造法建立目标堆芯三维精细模型，使用真实边界条件进行全堆连续能量蒙特卡罗输运计算。Further, the modeling in step 1 uses a voxel construction method; the voxel construction method is used to establish a three-dimensional fine model of the target core, and the full-stack continuous energy Monte Carlo transport calculation is performed using the real boundary conditions.

更进一步地，所述计算，包含燃料与结构物。Further, the calculation includes fuel and structure.

更进一步地，go a step further,

所述步骤2，根据步骤1所述计算，包含燃料与结构物的所有所需均匀化空间内的反应率与中子通量。The step 2, calculated according to the step 1, includes the reaction rates and neutron fluxes in all the required homogenization spaces of the fuel and the structure.

所述步骤3，根据步骤1所述计算，包含燃料与结构物的所有所需均匀化空间内的散射事件。The step 3, calculated according to the step 1, includes all scattering events in the required homogenization space of the fuel and the structure.

所述步骤4，基于步骤2和步骤3中得到的中子通量、反应率与散射角分布，计算包含燃料与结构物的所有所需均匀化空间的多群截面数据。In step 4, based on the neutron fluxes, reaction rates and scattering angle distributions obtained in steps 2 and 3, multi-group cross-sectional data including all required homogenization spaces for fuel and structures are calculated.

更进一步地，所述步骤5中所述根据步骤2与步骤4，制作生成高精度复杂能谱微堆多群数据库，包括所述步骤2中的中子入射角度离散方式与所述步骤4计算得到的多群截面数据，制作生成高精度复杂能谱微堆多群数据库。Further, according to step 2 and step 4, the multi-group database of high-precision complex energy spectrum micro-stacks is produced and generated in step 5, including the discrete method of neutron incident angle in step 2 and the calculation in step 4. The obtained multi-group cross-section data is produced to generate a high-precision complex energy spectrum micro-stack multi-group database.

更进一步地，所述步骤2中所述追踪指定均匀化区域内不同入射角度区间的中子，包括针对指定均匀化空间，离散若干个中子入射角度区间，计算过程中对入射到均匀化区域内的中子进行追踪，依据入射角度进行筛选，确定不同入射角区间的中子，并分别统计不同入射角区间内的中子在均匀化区域内的行为，计算上述中子在指定均匀化空间内的中子通量与反应率。Further, in the step 2, the tracking of neutrons in different incidence angle intervals in the specified homogenization area includes discretizing several neutron incidence angle intervals for the specified homogenization space, and in the calculation process, the incidence of the neutrons in the homogenization area is calculated. The neutrons are tracked and screened according to the incident angle to determine the neutrons in different incident angle intervals, and the behavior of neutrons in the different incident angle intervals in the homogenization area is calculated separately, and the above neutrons are calculated in the specified homogenization space. Neutron flux and reaction rate in

更进一步地，所述步骤3包括针对指定均匀化空间，离散若干个中子入射角度区间，分别追踪不同入射角区间的中子，统计中子在指定均匀化空间内的散射事件。Further, the step 3 includes discretizing several neutron incident angle intervals for a specified homogenization space, respectively tracking neutrons in different incident angle intervals, and counting neutron scattering events in the specified homogenization space.

更进一步地，所述步骤4中，基于步骤2和步骤3中得到的中子通量、反应率与散射角分布，针对所有均匀化空间，所有入射角区间生成多群截面数据。Further, in the step 4, based on the neutron flux, the reaction rate and the scattering angle distribution obtained in the step 2 and the step 3, for all the homogenized spaces and all the incident angle intervals, multiple groups of cross-sectional data are generated.

本发明的优点在于：The advantages of the present invention are:

本发明多群空间区域通过中子入射角度的划分、中子入射角度的追踪，入射角区间生成多群截面数据适用于所有截面。The multi-group space region of the present invention generates multi-group section data in the incident angle interval through the division of the neutron incident angle and the tracking of the neutron incident angle, which is applicable to all sections.

本发明生成多群截面时采用真实堆芯边界条件，消除了边界条件对多群截面数据精度的影响。The present invention adopts real core boundary conditions when generating multi-group cross-sections, and eliminates the influence of boundary conditions on the accuracy of multi-group cross-section data.

本发明在连续能量蒙特卡罗计算中统计入射方向相关的能群中子通量，有效降低了通量可分近似对产生的多群截面数据精度的影响。The present invention counts the energy group neutron fluxes related to the incident direction in the continuous energy Monte Carlo calculation, thereby effectively reducing the influence of the flux separable approximation on the accuracy of the generated multi-group cross-section data.

本发明采用统计学方法表征各向异性散射，消除了Pn方法截断误差导致散射截面分布函数出现负值对群常数精度的影响。The invention adopts the statistical method to characterize the anisotropic scattering, and eliminates the influence on the precision of the group constant caused by the truncation error of the Pn method and the negative value of the distribution function of the scattering cross section.

附图说明Description of drawings

图1为一种高精度复杂能谱微堆多群截面制作流程图。Figure 1 is a flow chart of the fabrication of a multi-group cross-section of a high-precision complex energy spectrum microstack.

具体实施方式Detailed ways

下面结合附图对本发明的技术方案进行更详细的说明，本发明包括但不仅限于下述实施例。The technical solutions of the present invention will be described in more detail below with reference to the accompanying drawings. The present invention includes but is not limited to the following embodiments.

如附图1所示，本发明的一种高精度复杂能谱微堆多群截面制作方法，步骤如下：As shown in accompanying drawing 1, a kind of high-precision complex energy spectrum micro-stack multi-group cross-section manufacturing method of the present invention, the steps are as follows:

步骤1：针对所需计算的组件或堆芯进行建模，基于ACE格式截面数据，进行连续能量蒙特卡罗输运计算；Step 1: Model the components or cores to be calculated, and perform continuous energy Monte Carlo transport calculations based on ACE format cross-section data;

步骤2：追踪指定均匀化区域内不同入射角度区间的中子；Step 2: Track neutrons in different incident angle intervals in the specified homogenization area;

步骤3：根据步骤2，统计不同散射出射角度余弦区间内的散射事件数目，计算散射出射角余弦在各区间内的概率，确定散射角度分布；Step 3: According to Step 2, count the number of scattering events in the cosine interval of different scattering exit angles, calculate the probability of scattering exit angle cosine in each interval, and determine the scattering angle distribution;

步骤4：根据步骤2和步骤3，计算得到多群数据；Step 4: According to Step 2 and Step 3, calculate the multi-group data;

步骤5：根据步骤2和步骤4，制作多群数据库。Step 5: According to Step 2 and Step 4, make a multi-group database.

其中，步骤1具体如下：针对所需计算的组件或堆芯，进行精细几何建模。针对模型几何的精确建模主要使用体素构造法(CSG)进行。体素构造法将复杂实体视作由若干基本实体，如球面、柱面、平面等，通过布尔运算构造生成，该方法能够严格精确表征反应堆几何结构。基于评价核数据库，如ENDF数据库，加工处理得到的ACE格式截面数据文件。依据加工得到的ACE格式截面数据文件，设置真实堆芯边界条件，进行全堆连续能量蒙特卡罗中子输运计算。Among them, step 1 is specifically as follows: perform fine geometric modeling for the components or cores to be calculated. Accurate modeling of model geometry is primarily performed using voxel construction (CSG). The voxel construction method regards complex entities as several basic entities, such as spheres, cylinders, planes, etc., which are constructed through Boolean operations. This method can strictly and accurately characterize the reactor geometry. Based on the evaluation core database, such as the ENDF database, the ACE format cross-section data file obtained by processing is processed. Based on the processed ACE format cross-section data file, the boundary conditions of the real core are set, and the full-stack continuous energy Monte Carlo neutron transport calculation is carried out.

步骤2具体如下：根据步骤1所述计算，追踪指定均匀化区域内不同入射角度区间的中子。具体地，针对指定均匀化空间，将中子入射极角与幅角划分成若干区间(即离散若干个中子入射角度区间)，计算过程中对入射到均匀化区域内的中子进行追踪，依据入射角度进行筛选，确定不同入射角区间的中子，并分别统计不同入射角区间内的中子在均匀化区域内的行为，将参数z、n、Ωn、g、r、E、ΔE、V作为指定入射角度区间的中子通量的筛选参数，经过蒙特卡罗输运计算筛选出W、T、i、li参数，通过公式(1)统计指定入射角度区间的中子通量；将参数z、x、Ωn、g、ΔE、V、r、E作为中子在指定均匀化区域内的各类反应率的筛选参数，经过蒙特卡罗输运计算筛选出W、i、wi、Ag参数，通过公式(2)计算所述中子在指定均匀化区域内的各类反应率，所述蒙特卡罗输运计算可以使用多种方法，如迹径长度计数利用公式(1)统计中子通量。不同入射角度区间的中子于指定均匀化区域内的各类反应率通过公式(2)统计，所述各类反应率包括总反应率、吸收率、散射反应率、裂变反应率、裂变份额等。步骤2根据步骤1所述计算，包含燃料与结构物的所有所需均匀化空间内的反应率与中子通量。Step 2 is specifically as follows: according to the calculation described in step 1, track neutrons in different incident angle intervals in the specified homogenization area. Specifically, for the specified homogenization space, the neutron incident polar angle and the argument are divided into several intervals (that is, discrete several neutron incident angle intervals), and the neutrons incident into the homogenization area are tracked during the calculation process, Screen according to the incident angle, determine the neutrons in different incident angle intervals, and count the behavior of neutrons in different incident angle intervals in the homogenization area respectively. , V are used as the screening parameters for the neutron flux in the specified incidence angle range, and the W, T, i, and li parameters are screened out through Monte Carlo transport calculation, and the neutron flux in the specified incidence angle range is calculated by formula (1); The parameters z, x, Ω n , g, ΔE, V, r, and E are used as the screening parameters for various reaction rates of neutrons in the specified homogenization region, and W, i, wi are screened out through Monte Carlo transport calculation. , Ag parameter, calculate the various reaction rates of the neutron in the specified homogenization area by formula (2), the Monte Carlo transport calculation can use various methods, such as track length counting using formula (1) Statistical neutron flux. The various reaction rates of neutrons in different incident angle ranges in the specified homogenization area are calculated by formula (2). The various reaction rates include total reaction rate, absorption rate, scattering reaction rate, fission reaction rate, fission share, etc. . Step 2 calculates the reaction rates and neutron fluxes in all desired homogenization spaces including fuel and structures as described in step 1.

Figure BDA0003618124970000091
Figure BDA0003618124970000091

Figure BDA0003618124970000092
Figure BDA0003618124970000092

Figure BDA0003618124970000093
---能群g范围内，入射角度在Ωn区间的中子在均匀化空间z内的通量
Figure BDA0003618124970000093
---In the range of energy group g, the flux of neutrons with incident angle in the interval Ω n in the homogenization space z

Figure BDA0003618124970000094
---入射角度在Ωn区间的中子在能群g与均匀化空间z内产生的x类型反应率
Figure BDA0003618124970000094
---The reaction rate of type x produced in the energy group g and the homogenization space z of the neutron with the incident angle in the Ω n interval

z---均匀化空间变化z---homogenize the spatial variation

n---入射角离散区间编号n---incidence angle discrete interval number

Ωn---第n个中子入射角度离散区间Ω n --- discrete interval of the nth neutron incident angle

g---能群编号g---energy group number

r---空间位置r---spatial position

E---中子能量E---neutron energy

ΔE---能群g的能量上下界ΔE---energy upper and lower bounds of energy group g

V---均匀化空间z的体积V---the volume of the homogenized space z

W---初始中子总权重W---Initial neutron total weight

T---所有中子在均匀化空间体积内的轨迹集合T---set of trajectories of all neutrons in the homogenized space volume

i---事件编号i---event number

li---中子第i个轨迹的长度li---the length of the ith trajectory of the neutron

x---反应类型x---reaction type

wi---中子发生反应事件i前的权重wi---the weight of the neutron before the reaction event i

Ag---中子能量在能群g内的所有反应事件的总集合Ag---the total set of all reaction events with neutron energy in energy group g

步骤3具体如下：在步骤2的多群参数统计中，针对散射截面，通过统计学方法表征各向异性散射。散射的各向异性(即不同值的散射截面)由公式(4)确定，统计学方法将中子散射反应的出射角度余弦离散为若干个中子入射角度区间，在计算中追踪并统计散射反应后不同散射入射角度或出射角度余弦区间内中子的散射事件数目，将各散射角度余弦区间内的散射事件频率视作散射反应出射角余弦在各区间内的概率，利用公式(3)计算散射截面关于散射出射角度余弦的概率密度分布函数，确定散射角度分布，经过蒙特卡罗输运计算，通过公式(4)统计中子在指定均匀化空间内的散射事件，以直方分布形式表示各项异性散射，确定散射截面。步骤3，根据步骤1所述计算，包含燃料与结构物的所有所需均匀化空间内的散射事件。其中，统计学方法表征各向异性散射就是求出散射出射角分布，在每个出射角度上散射截面值不同。Step 3 is as follows: in the multi-group parameter statistics in step 2, for the scattering cross section, the anisotropic scattering is characterized by a statistical method. The anisotropy of scattering (that is, the scattering cross-section of different values) is determined by formula (4). The statistical method discretizes the cosine of the exit angle of the neutron scattering reaction into several neutron incident angle intervals, and the scattering reaction is tracked and counted in the calculation. The number of neutron scattering events in the cosine interval of different scattering incident angles or exit angles, the frequency of scattering events in the cosine interval of each scattering angle is regarded as the probability of the scattering reaction in the cosine of the exit angle in each interval, and formula (3) is used to calculate the scattering The probability density distribution function of the cross section with respect to the cosine of the scattering exit angle is used to determine the scattering angle distribution. After the Monte Carlo transport calculation, the neutron scattering events in the specified homogenization space are calculated by formula (4), and the items are expressed in the form of histogram distribution. Anisotropic scattering, to determine the scattering cross section. Step 3, according to the calculation described in step 1, including the scattering events in all desired homogenization spaces of the fuel and the structure. Among them, the statistical method to characterize anisotropic scattering is to obtain the distribution of the scattering exit angle, and the scattering cross section value is different at each exit angle.

Figure BDA0003618124970000101
Figure BDA0003618124970000101

Figure BDA0003618124970000102
Figure BDA0003618124970000102

其中：in:

Figure BDA0003618124970000103
---入射角度在Ωn区间内的中子，散射反应出射角余弦为μ的概率，满足关系式
Figure BDA0003618124970000104
Figure BDA0003618124970000103
--- For neutrons whose incident angle is in the interval of Ω n , the probability of scattering reaction exit angle cosine is μ, which satisfies the relation
Figure BDA0003618124970000104

Figure BDA0003618124970000111
---入射角度在Ωn区间，能量为E的中子在r处，散射反应出射角余弦为μ的散射反应宏观截面
Figure BDA0003618124970000111
---The incident angle is in the Ω n interval, the neutron with energy E is at r, and the scattering reaction macroscopic cross-section with the cosine of the scattering reaction exit angle μ

μ---散射反应出射角余弦μ---scattering reaction exit angle cosine

Δμn---第n个散射角余弦离散区间的区间长度Δμn---the interval length of the nth scattering angle cosine discrete interval

Wμ---散射出射角余弦为μ的中子权重Wμ---neutron weight with cosine of scattering exit angle μ

wμ---散射出射角余弦为μ的事件数wμ---the number of events with the cosine of the scattering exit angle μ

Figure BDA0003618124970000112
---入射角度在Ωn区间，能量为E的中子在r处的散射反应宏观截面
Figure BDA0003618124970000112
---The incident angle is in the interval of Ω n , the macroscopic cross section of the scattering reaction of the neutron with energy E at r

步骤4具体如下：基于步骤2和步骤3中得到的中子通量、反应率与散射角分布，通过蒙特卡罗输运计算获得参数

Figure BDA0003618124970000113
fg'→g(μ)，通过公式(5)计算多群散射矩阵，即多群截面中的散射反应截面，通过公式(6)计算其他多群截面。所述步骤4中，基于步骤2和步骤3中得到的中子通量、反应率与散射角分布，计算包含燃料与结构物的所有所需均匀化空间的多群截面数据。所述步骤4中，基于步骤2和步骤3中得到的中子通量、反应率与散射角分布，针对所有均匀化空间，所有入射角区间生成多群截面数据。Step 4 is as follows: Based on the neutron flux, reaction rate and scattering angle distribution obtained in steps 2 and 3, parameters are obtained by Monte Carlo transport calculation
Figure BDA0003618124970000113
f g'→g (μ), the multi-group scattering matrix is calculated by formula (5), that is, the scattering reaction cross-section in the multi-group cross-section, and the other multi-group cross-sections are calculated by formula (6). In the step 4, based on the neutron flux, reaction rate and scattering angle distribution obtained in the step 2 and step 3, the multi-group cross-sectional data including all the required homogenization spaces of the fuel and the structure are calculated. In the step 4, based on the neutron flux, the reaction rate and the scattering angle distribution obtained in the step 2 and the step 3, for all the homogenization spaces and all the incident angle intervals, multiple groups of cross-sectional data are generated.

Figure BDA0003618124970000114
Figure BDA0003618124970000114

Figure BDA0003618124970000115
Figure BDA0003618124970000115

其中：in:

s---散射反应s---scattering reaction

g'---能群编号g'---energy group number

Figure BDA0003618124970000116
---入射角度在Ωn区间，出射角余弦为μ，能群g’与能群g之间的多群散射矩阵，即散射反应截面。
Figure BDA0003618124970000116
---The incident angle is in the Ω n interval, the cosine of the exit angle is μ, and the multi-group scattering matrix between the energy group g' and the energy group g is the scattering reaction cross section.

fg'→g(μ)---出射角余弦为μ的散射反应将中子能量由g’转移至能群g的概率f g'→g (μ)---Probability that a scattering reaction with exit angle cosine μ transfers neutron energy from g' to energy group g

Figure BDA0003618124970000121
---能群g与均匀化空间z内，入射角度在Ωn区间的中子产生的x类型反应宏观截面
Figure BDA0003618124970000121
---In the energy group g and the homogenization space z, the x-type reaction macro-section produced by the neutron with the incident angle in the Ω n interval

Figure BDA0003618124970000122
---入射角在Ωn区间，能群g’散射反应截面
Figure BDA0003618124970000122
---The incident angle is in the Ω n interval, the energy group g' scattering reaction cross section

其中所述参数

Figure BDA0003618124970000128
fg'→g(μ)通过公式(7)和公式(8)确定，where the parameters
Figure BDA0003618124970000128
f g'→g (μ) is determined by Equation (7) and Equation (8),

Figure BDA0003618124970000123
Figure BDA0003618124970000123

Figure BDA0003618124970000124
Figure BDA0003618124970000124

其中，

Figure BDA0003618124970000125
同其他截面，fg'→g(μ)为群间转移概率，蒙卡方法实现群间转移概率的计算，即通过统计由g’能群反应后变为g能群的中子数占总反应中子数的比便可得到，其中反应截面
Figure BDA0003618124970000126
如下：in,
Figure BDA0003618124970000125
As with other sections, f g'→g (μ) is the inter-group transition probability, and the Mon-card method realizes the calculation of the inter-group transition probability, that is, the number of neutrons that change from the g' energy group to the g energy group after the reaction accounts for the total number of neutrons. The ratio of the number of neutrons in the reaction can be obtained, where the reaction cross section
Figure BDA0003618124970000126
as follows:

Figure BDA0003618124970000127
Figure BDA0003618124970000127

步骤5具体如下：根据步骤2中的中子入射角度离散方式与所述步骤4计算得到的多群截面数据，制作生成高精度复杂能谱微堆多群数据库。步骤4中计算得到的多群截面数据是针对所有步骤2中离散的入射中子角度区间的多群截面数据，在数据加工制作时，将产生能群数×入射角度离散区间数目的数据。Step 5 is specifically as follows: according to the neutron incident angle dispersion method in step 2 and the multi-group cross-section data calculated in step 4, a high-precision complex energy spectrum micro-stack multi-group database is generated. The multi-group cross-section data calculated in step 4 is the multi-group cross-section data for all the discrete incident neutron angle intervals in step 2. During data processing, data of the number of energy groups × the number of discrete intervals of incident angle will be generated.

本发明能够使用更少的能群数目达到相同的精度，提高了堆芯多群计算的效率。The invention can achieve the same precision by using fewer energy groups, and improve the efficiency of multi-group calculation in the core.

本发明能够通过一次全堆计算得出包含燃料与结构物的所有目标堆芯所需的空间均匀化区域截面。The invention can obtain the space homogenization area cross section required by all target cores including fuel and structures through one full-stack calculation.

本发明不仅局限于上述具体实施方式，本领域一般技术人员根据实施例和附图公开内容，可以采用其它多种具体实施方式实施本发明，因此，凡是采用本发明的设计结构和思路，做一些简单的变换或更改的设计，都落入本发明保护的范围。The present invention is not limited to the above-mentioned specific embodiments. Those skilled in the art can use other various specific embodiments to implement the present invention according to the disclosed contents of the embodiments and the accompanying drawings. Simple transformations or modified designs fall within the protection scope of the present invention.

Claims (10)

1. A method for manufacturing a high-precision complex energy spectrum micro-stack multi-group cross section is characterized by comprising the following steps: the method comprises the following steps:
step 1: modeling is carried out aiming at the components or reactor cores required to be calculated, and continuous energy Monte Carlo transportation calculation is carried out based on ACE format section data;
step 2: tracking neutrons in different incidence angle intervals in the designated homogenization area;
and step 3: according to the step 2, counting the number of scattering events in different scattering emergence angle cosine intervals, calculating the probability of the scattering emergence angle cosine in each interval, and determining the scattering angle distribution;
and 4, step 4: calculating to obtain a plurality of groups of data according to the step 2 and the step 3;
and 5: according to step 2 and step 4, a multi-group database is created.
2. The method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 1, wherein the method comprises the following steps:
the step 2 comprises the following steps: tracking neutrons in different incidence angle intervals in the designated homogenization area according to the calculation in the step 1, and converting z, n and omega into n and omega n G, r, E and delta E, V are used as screening data of neutron flux in a specified incidence angle interval, parameters of W, T, i and li are output through Monte Carlo transport calculation, and specified incidence is calculated through a formula (1)Neutron flux in an angular interval; will z, x, omega n And g, delta E, V, r and E are used as screening data of various reaction rates of neutrons in the designated homogenization area, parameters of W, i, wi and Ag are output through Monte Carlo transport calculation, and the various reaction rates of the neutrons in the designated homogenization area are calculated through a formula (2).
Figure FDA0003618124960000011
Figure FDA0003618124960000012
Wherein:
Figure FDA0003618124960000021
in the range of energy group g, the angle of incidence is Ω n Flux of interval neutrons in homogenization space z
Figure FDA0003618124960000022
Angle of incidence at Ω n X-type reactivity of interval neutrons generated in energy group g and homogenization space z
z-uniform spatial variation
n-discrete interval numbering of incident angles
Ω n -discrete interval of n-th neutron incidence angle
g- -energy group numbering
r- -spatial position
E- -neutron energy
Delta E- -upper and lower energy boundaries of energy group g
V- -volume of the homogenization space z
W- -initial neutron Total weight
T- -set of trajectories of all neutrons within a homogenized spatial volume
i- -event numbering
li- -length of the ith trajectory of a neutron
x- - -reaction type
wi- -weight before neutron Generation reaction event i
Ag- -the aggregate of all reaction events with neutron energies within an energy cluster g
The step 3 comprises the following steps: in the multi-group parameter statistics of the step 2, cosine of the scattering emergence angle is dispersed, the number of scattering events in cosine intervals of different scattering emergence angles is counted, the probability of the cosine of the scattering emergence angle in each interval is calculated through a formula (3), the scattering angle distribution is determined, and the scattering cross section is determined through a formula (4) through Monte Carlo transport calculation.
Figure FDA0003618124960000031
Figure FDA0003618124960000032
Wherein:
Figure FDA0003618124960000033
angle of incidence at Ω n The probability that the cosine of the scattering reaction exit angle of the neutrons in the interval is mu satisfies the relational expression
Figure FDA0003618124960000034
Figure FDA0003618124960000035
Angle of incidence at Ω n Interval, where E energy neutrons are at r, scattering reaction exit angle cosine is μ
Mu-scattering reaction exit angle cosine
Delta mu n-interval length of n scattering angle cosine discrete interval
Weight of neutron with W mu- - -cosine of scattering exit angle mu
Number of events w mu-cosine of the scattering exit angle mu
Figure FDA0003618124960000036
Angle of incidence at Ω n Macroscopic section of scattering reaction of neutrons of energy E at r
The step 4 comprises the following steps: obtaining parameters through Monte Carlo transport calculation based on the neutron flux, the reactivity and the scattering angle distribution obtained in the step 2 and the step 3
Figure FDA0003618124960000037
f g'→g (μ), the multi-cluster scattering matrix is calculated using equation (5), and the other multi-cluster cross-sections are calculated using equation (6).
Figure FDA0003618124960000038
Figure FDA0003618124960000039
Wherein:
s- -scattering reaction
g' - - - -energy group number
Figure FDA0003618124960000041
Angle of incidence at Ω n Interval, cosine of exit angle μ, multiple group scattering matrix between energy group g' and energy group g.
f g'→g Probability of neutron energy transfer from g' to g of the energy cluster by scattering reaction with (mu) - - -exit angle cosine mu
Figure FDA0003618124960000042
Energy group g and homogenization spacez, the incident angle is omega n Interval neutron-producing x-type reaction macroscopic cross-section
Figure FDA0003618124960000043
Angle of incidence at Ω n Interval, energy group g' scattering reaction cross section
The step 5 comprises the following steps: and (4) according to the step 2 and the step 4, manufacturing and generating a high-precision complex energy spectrum micro-stack multi-group database.
3. The method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 2, wherein the method comprises the following steps:
parameters described in step 4
Figure FDA0003618124960000044
f g'→g (μ) is determined by formula (7) and formula (8),
Figure FDA0003618124960000045
Figure FDA0003618124960000046
4. the method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 2, wherein the method comprises the following steps: the modeling in the step 1 uses a voxel construction method; and establishing a three-dimensional fine model of the target core by using the voxel construction method, and performing full-stack continuous energy Monte Carlo transportation calculation by using a real boundary condition.
5. The method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 2, wherein the method comprises the following steps: the calculations include fuel and structure.
6. The method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 5, wherein the method comprises the following steps:
and step 2, calculating according to the step 1, and including the reaction rate and the neutron flux in all required homogenization spaces of the fuel and the structure.
And step 3, calculating according to the step 1, and including scattering events in all required homogenization spaces of the fuel and the structure.
And 4, calculating multi-group section data of all required homogenization spaces containing the fuel and the structure based on the neutron flux, the reaction rate and the scattering angle distribution obtained in the step 2 and the step 3.
7. The method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 2, wherein the method comprises the following steps: and in the step 5, according to the step 2 and the step 4, a high-precision complex energy spectrum micro-stack multi-group database is manufactured and generated, wherein the high-precision complex energy spectrum micro-stack multi-group database comprises the neutron incident angle discrete mode in the step 2 and the multi-group section data obtained by calculation in the step 4.
8. The method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 2, wherein the method comprises the following steps: the step 2 of tracking neutrons in different incident angle intervals in the designated homogenization area includes dispersing a plurality of neutron incident angle intervals for the designated homogenization space, tracking neutrons incident into the homogenization area in the calculation process, screening according to incident angles, determining neutrons in different incident angle intervals, respectively counting behaviors of the neutrons in the different incident angle intervals in the homogenization area, and calculating neutron flux and reaction rate of the neutrons in the designated homogenization space.
9. The method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 2, wherein the method comprises the following steps: and 3, dispersing a plurality of neutron incidence angle intervals aiming at the designated homogenization space, respectively tracking neutrons in different incidence angle intervals, and counting scattering events of the neutrons in the designated homogenization space.
10. The method for manufacturing the multi-group cross section of the high-precision complex spectrum micro-stack according to claim 2, wherein the method comprises the following steps: in the step 4, based on the neutron flux, the reaction rate and the scattering angle distribution obtained in the steps 2 and 3, multiple groups of section data are generated for all the uniformization spaces and all the incidence angle intervals.
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