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。     

全堆芯三维时空动力学中子输运程序SAAFCGSN应用研究

当前为了应对新型先进小堆技术的发展,反应堆物理数值计算程序对三维全堆芯输运计算的要求不断提高。本文基于MOOSE平台开发了全堆芯三维时空动力学中子输运程序SAAFCGSN,该程序基于有限元方法实现空间变量离散,基于残差形式实现堆芯稳态、瞬态中子输运方程以及缓发中子先驱核方程的求解,采用JFNK方法避免直接求解Jacobin矩阵,从而提高计算速度,降低内存占用。为了检验程序的瞬态计算能力,本文使用经济发展与合作组织核能机构（OECD/NEA）C5G7-TD系列基准题验证了程序的可靠性,并与高保真确定论中子输运程序及蒙特卡罗程序模拟结果进行比较分析。研究表明,SAAFCGSN程序计算精度较高,可以有效处理控制棒尖齿效应,并得到详细的三维堆芯中子注量率分布,满足先进小堆的稳态及瞬态中子学计算需求。     

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.     

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。     

超级等效方法研究

在广义等效理论(GET)和超级均匀化方法(SPH)的基础上,提出同时满足反应率、界面流和组件特征值守恒,且不显式使用等效因子的超级等效方法(SPE)。在蒙特卡罗组件均匀化中应用SPE,将该方法植入蒙特卡罗组件均匀化程序MCMC,并通过C5G7基准题进行验证。验证分析表明:SPE等效均匀化群常数堆芯计算精度更高,适应性更广。     

SN2D程序在C5G7基准例题上的验证与分析

C5G7基准例题因其具有强烈非均匀性、组件能谱差异大等特点,常用来检验软件计算有效性。在对栅元进行不同的几何等效和对原有的栅元等效均匀化方法进行改进的情况下,采用二维离散纵标法输运计算程序SN2D对C5G7基准例题进行了分析计算,给出了各种计算条件下k_eff和功率分布的计算误差。结果表明,SN2D程序可应用于C5G7基准例题的求解。计算结果可为求解类似问题时计算程序及条件的选择提供直接参考。     

粗网节块法中非全反射边界条件下节块等效均匀化参数的计算

现有组件均匀化方法在组件能谱差异显著、堆芯非均匀性强烈的情况下应用效果不佳,本文提出采用Colorset均匀化方法来代替目前使用的单组件全反射边界均匀化方法,并阐述了非全反射边界条件下粗网格等效均匀化参数的计算原理、计算方法以及在C5G7-MOX 二维问题上的应用结果.     

Two-dimensional c5g7 mox fuel assembly benchmark calculations using the FEM-PN code EVENT

This paper discusses the application of the general-purpose finite-element-sphericalharmonics code EVENT to the solution of the two-dimensional version of the C5G7 benchmark. This benchmark has been devised to provide a point of comparison against which to evaluate the capabilities of transport codes to treat reactor core problems without spatial homogenization. Using the reference results for the eigenvalue and pin power distribution for the problem (obtained with Monte Carlo), a detailed analysis was conducted with respect to space-angle resolution and its effect on eigenvalue percentage error. The comparisons indicate that EVENT is capable of dealing with the geometrical complexity of the problem, and that its underlying methodology is capable of producing accurate solutions. The numerical exercise also provided valuable pointers for the computational effort required for the solution of detailed geometrical configurations.     

一步法输运计算程序KuaFu开发与验证

为了拓展一步法输运计算方法在结构复杂先进反应堆中的应用,基于构建实体几何理论及二维/一维耦合方法,采用C++、Python混合编程开发了一步法输运计算程序KuaFu,并应用粗网有限差分方法(CMFD)、大规模并行技术对二维/一维耦合方法进行加速。通过C5G7基准题对几何建模的可视化功能、并行功能及计算精度进行评估,获得计算结果与蒙特卡罗程序(MCNP)的相对误差。计算结果表明,程序具有较好的可视化功能和用户友好性;KuaFu程序与MCNP参考解符合较好,计算精度良好。     

Benchmark on deterministic 2-D MOX fuel assembly transport calculationswithout spatial homogenization

An important issue of deterministic transport methods for whole core calculations concerns the accuracy of homogenization techniques. A direct calculation for whole core heterogeneous geometries was not feasible in the past due to the limited capability of computers. With modern computational abilities, direct whole core heterogeneous calculations are becoming feasible. This paper explores a recent OECD/NEA benchmark problem proposed to test the accuracy of modern deterministic transport methods when applied to reactor core problems without spatial homogenization.

For this work a two-dimensional configuration was investigated and an accurate Monte Carlo reference solution was obtained. Twenty participants submitted solutions for the two-dimensional configuration and all of the participant solutions were compared to a reference Monte Carlo solution. Overall all the results submitted by the participants agreed well with the reference solution. A majority of the participants obtained solutions that were more than acceptable for typical reactor calculations and the remaining errors in the participant solutions can be attributed to the high order space-angle approximation necessary to solve this particular benchmark problem. It is important to note that the high order space-angle approximation needed for this benchmark is not necessary typical for all such whole-core heterogeneous problems.     

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.     

基于最小二乘的线性源特征线方法研究

特征线方法一般采用平源近似来求解,平源近似需要大量较小的网格才能获得精确的结果,从而会消耗较多内存,影响计算效率。相比平源近似,线性源可在网格较少的情况下得到较精确的数值结果。本文提出一种基于最小二乘的线性源特征线方法,并通过计算压水堆栅元及C5G7基准题等算例,对该方法进行了分析。数值结果表明,基于最小二乘的线性源特征线方法能在网格较少的情况下提供稳定、精确的数值结果。     

Results on the DECD/NEA C5G7-MOX benchmark obtainedwith the discrete ordinates code dort

The well-known multigroup Discrete Ordinates code DORT has been employed to perform calculations on the DECD/NEA C5G7-MOX benchmark. The participants were required to supply the effective multiplication factor as well as the pin power distribution of the problem specification. We show our submitted results to be well consistent with the reference solution, which was produced by Monte-Carlo calculations. Furthermore, we point out some improvements being made on the computational procedure, which give rise to an additional gain in accuracy.     

γ全谱法测定空气吸收剂量率的M-C法应用

γ辐射场剂量的测量可以通过γ剂量率仪或谱-剂量转换的方法来实现。其中一种谱-剂量转换方法为γ全谱法（G（E）函数）,即通过建立能谱转换函数G（E）,把测得的能谱直接换算成剂量,G（E）函数的系数可通过标准源刻度获得,但标准源及其能量分布会受实际条件限制。我们采用蒙特卡罗方法,在0.1–2.5 MeV能量范围内较均匀地选择了11个能量点,用MCNP5软件模拟了不同尺寸NaI（Tl）晶体的响应能谱,并把它们作为标准谱求解得到了G（E）函数;最后利用该G（E）函数计算各模拟能谱的剂量,并与理论计算值进行比较,平均误差<4%。     

Optimal Feedback Control of a Nuclear Reactor as a Distributed Parameter System

The analytical treatment of a distributed reactor having spatially dependent parameters is presented. Both the modal expansion method and the function space method are applied successfully to obtain the optimal feedback system for the terminal cost problem. The explicitly posed control obtained by means of the function space method is particularly convenient for machine computation. A numerical example is presented to show the characteristics of the synthesized optimal feedback system.