线性源近似的中子输运方程特征线解法

基于非结构网格的中子输运方程特征线解法已成为堆芯设计程序中组件输运计算的标准方法之一。但现有的大部分特征线法程序均是基于平源近似的步特征线法模型开发的,平源近似是特征线法中除角度变量直接离散外又一基本假定。本工作提出一种基于线性源近似的中子输运方程特征线解法,并提出相关负中子源分布的修正方法。采用自行研制的数值计算软件PEACH,对OECD/NEAC5G7-MOX2D基准问题和自定义沸水堆小堆芯问题进行检验。数值计算结果表明,本工作提出的线性源近似特征线法模型在相同计算精度的前提下,占用更少的系统内存和运行时间。     

Reduction of the Spatial Discretization Error in the Method of Characteristics using the Diamond-difference Scheme

In this paper, the diamond-difference (DD) scheme, which is commonly used in discrete-ordinate codes, is applied to the method of characteristics (MOC) to reduce the spatial discretization error of the flat flux approximation. Smaller spatial discretization error allows coarser background mesh division, which leads to smaller computational burden. Some theoretical considerations on the DD scheme are discussed to clarify the strength of this method. An absorption cross section weighted DD scheme (AWDD), which utilizes macroscopic absorption cross section to set the weight, is also discussed. The DD and AWDD schemes are implemented to AEGIS, which is a lattice physics code based on MOC. Then the AEGIS code is applied to two different benchmark problems whose spatial discretization errors are large. The calculation results indicate that from the viewpoint of spatial discretization error, the AWDD scheme is superior to the conventional MOC in which the step characteristics approximation is commonly used. Since incorporation of the AWDD scheme to current MOC codes is very simple, it will be a good candidate of spatial discretization method for MOC codes.     

一维特征线法中子输运程序开发及验证

为探讨两维/一维综合法堆芯分析方法,本文基于特征线法研制了一维中子输运程序--PEACH-1D.不同于通常的平源近似特征线方法,PEACH-1D可对子区的中子源项作线性近似;程序运用指数函数插值表和渐近源外推技术来加速计算过程.相关数值结果表明,PEACH-1D具有很高的计算精度和效率,线性源近似的特征线法具备处理较粗网格的能力,值得推广.     

采用边界流响应矩阵的组件等效计算方法研究

由于反应堆堆芯存在大量重复结构,本文研究采用边界流响应矩阵的组件等效方法处理这些复杂结构。为使组件表面入射流J⁺与表面出射流J^-的耦合关系为线性关系,将组件的裂变截面除以堆芯的k_eff,将堆芯物理计算的本征值问题转化为一固定源问题,这样只需得到J⁺与J^-之间的线性耦合系数即可确定二者的耦合关系。然后通过在全堆芯范围内进行迭代,求出堆芯的k_eff及各组件的表面流,进而得到堆芯各处的通量分布形状。采用二维S_N程序SN2D,对C5G7基准题的等效误差进行计算分析。结果表明：在不进行能群和角度归并的情况下,采用该方法可得到较为精确的k_eff及组件功率,但栅元功率分布仍存在一定误差,需在进一步研究中加以解决。     

一种栅元等效均匀化计算的改进方法及其验证

传统的栅元等效均匀化计算方法一般采用体积-通量权重法,保证了在反射边界条件下各群通量和反应率的守恒,但该方法在边界入射流较强时有一定误差。本文提出了一种改进的等效均匀化方法,该方法以栅元边界入射流与出射流之间的响应等效作为理论基础,认为不需要保证等效前后的平均通量守恒,而应保证入射流与出射流以及各群反应率之间的响应关系守恒。和原有均匀化方法相比,改进方法几乎不增加任何计算量。对带反射层的平板问题及C5G7MOX基准例题分别进行测试计算,结果表明,改进的栅元等效均匀化方法对特征值和棒功率分布的计算精度有明显的改善作用。     

Use of the surface harmonics method forcalculation of 2D C5G7 MOX benchmark

The C5G7 MOX benchmark specifying a sixteen-assembly core with asurrounding water reflector was proposed as a basis to measure current transport code abilities in the treatment of reactor core problems without spatial homogenization. Seven-group cross sections for all materials were used as initial information. Just that fact allows to test an accuracy of solving the neutron transport equation excluding additional errors connected with preparing the group cross sections. In this paper, Surface Harmonics Method (SHM) is applied to calculation of the two-dimensional configuration of this benchmark. Different approximations of SHM were applied, both with and without spatial homogenization. Additionally, this fact allowed evaluating the effect of spatial homogenization of cells. Comparisons were carried out for k_eff and pin powers both with the reference results and between the results calculated by different SHM approximations.