围板和反射层的等效均匀化常数的计算

应用Ｓｍｉｔｈ的一般等效均匀化理论推导了围板和反射层的等效均匀化常数的计算公式，并编制了计算软件。利用该软件计算了Ｚｉｏｎ－１ｃｏｒｅ及秦山压水堆的图板、反射层等效均匀化常数，并将它们应用到堆芯扩散计算中。数值结果表明，这样计算的图板和反射层的等效均匀化常数能很好地改善堆芯功率分布的计算精度，尤其是堆芯周围组件的功率分布。     

堆芯Pin-by-pin超级均匀化因子计算方法研究

随着科学研究的不断深入、计算条件和对设计计算精度要求的不断提高,全堆芯Pin-by-pin计算已成为了下一代堆芯数值计算方法研究热点。超级均匀化方法作为全堆芯Pin-by-pin计算的均匀化方法主流方法之一被广泛使用。针对燃料组件采用传统超级均匀化方法,对存在中子泄漏的反射层组件采用空间泄漏相关的超级均匀化方法,产生了包含超级均匀化因子在内的等效均匀化常数。基于三维C5G7基准题,分析了此等效均匀化常数计算方式在非均匀性较强、中子泄漏较大反应堆堆芯的中子学计算精度。数值结果表明:与传统组件均匀化计算方法相比,应用了超级均匀化方法的堆芯Pin-by-pin计算的计算精度更高。     

基于连续能量蒙特卡罗方法的均匀化群常数计算

两步法反应堆物理计算流程中,组件均匀化群常数显著影响堆芯计算精度。相比确定论方法,连续能量蒙特卡罗方法均匀化精确描述各种几何构型栅格,避免繁琐共振自屏计算,保留更多连续能量信息,不仅产生的群常数更精确,而且普适性也更强。作为实现连续能量蒙特卡罗组件均匀化的第一步,本文应用径迹长度方法统计计算一般群截面和群常数,提出并使用散射事件方法获得不能直接应用确定论方法计算群间散射截面和高阶勒让德系数,应用P1截面计算扩散系数。为还原两步法计算流程中组件在堆芯的临界状态,本文应用BN理论对均匀化群常数进行泄漏修正。在4种类型组件和简化压水堆堆芯上数值验证蒙特卡罗均匀化群常数。验证结果表明:连续能量蒙特卡罗方法组件均匀化群常数具有良好几何适应性,显著提高堆芯计算精度。     

蒙特卡罗均匀化与多群蒙特卡罗输运研究

基于蒙特卡罗方法(MCNP)进行组件均匀化产生少群常数继而进行堆芯计算,是MCNP应用于堆芯物理分析的一种可行方案。研究MCNP统计产生少群截面以及等效均匀化理论应用于多群蒙特卡罗计算的方法,并进行数值验证。结果表明,本文提出的利用MCNP模拟产生等效均匀化少群常数的方法是可行的,在保证预定精度的条件下提高了效率。     

一般等效均匀化理论在节块格林函数方法中的应用

本文介绍了一般等效均匀化理论（Ｇ．Ｅ．Ｔ）及其在格林函数方法中的应用，并改编了二维节块格林函数方法程序（ＮＧＦＭ）。为了验证程序的正确性，对ＨＥＮＲＹ－ＷＯＲＬＥＹ沸水堆基准题作了计算。结果表明，在节块方法中采用一般等效均匀化理论可以有效地提高计算精度，极大地改善由于组件均匀化引起的误差。     

等效均匀化方法在连续能量蒙特卡罗均匀化群常数上的应用

连续能量蒙特卡罗方法均匀化群常数直接用于堆芯均匀计算,不能与非均匀计算保持反应率和界面流守恒,需进一步处理使其满足等效均匀化原理。本工作研究广义均匀化理论（GET）和超级均匀化方法（SPH）在蒙特卡罗均匀化中的应用,并数值验证简化压水堆堆芯和C5G7基准题。研究表明,GET和SPH的应用提高了蒙特卡罗均匀化群常数堆芯扩散计算的精度,可作为蒙特卡罗等效均匀化方法。     

环形燃料超临界水冷堆中子学计算方法研究

基于先进组件程序HELIOS和堆芯节块法程序SIXTUS,研发了超临界水冷堆（SCWR）的中子学计算程序FENNEL-N,并通过与蒙特卡罗程序对比分析了其用于环形燃料超临界水冷堆计算的精度。组件验证结果表明：制作多群数据库的压水堆能谱与超临界水冷堆能谱的差异是导致计算误差的主要原因。堆芯验证结果表明：传统的组件均匀化方法在计算超临界水冷堆时会引入较大误差。应用FENNEL-N程序对组件均匀化方法进行了研究,结果表明,采用优化的组件参数少群结构能减少堆芯能谱变化对精度的影响,采用超组件模型计算组件参数可考虑反射层对组件参数的影响。采用新的组件均匀化方法后,FENNEL-N的计算精度满足了预概念设计需求。     

处理轴向三维非均匀效应的单组件均匀化模型

传统以两维单组件模型为基础的均匀化理论及后续的改进均匀化理论产生的粗网均匀化参数无法直接体现轻水堆(LWR)堆芯轴向所存在的非均匀性。本文提出了以单组件逐棒模型为基础的三维均匀化方法,为堆芯计算提供粗网均匀化参数,在维持堆芯粗网计算模型的前提下实现对三维效应的处理。基准数值实验表明,本文提出的方法具有较好的精度表现,适用于堆芯轴向三维非均匀性的处理。     

基于连续能量蒙特卡罗的快中子反应堆均匀化截面计算方法研究

快堆确定论两步法通常由组件均匀化截面计算和堆芯扩散/输运计算共同组成,已广泛应用于快堆工程设计与分析领域。基于连续能量精细几何的蒙特卡罗均匀化截面计算方法可为先进快堆提供高精度均匀化群常数。本文简要综述了蒙特卡罗生成的均匀化截面与堆芯扩散/输运计算结合的发展现状与技术趋势。介绍了蒙特卡罗体积通量均匀化方法和超级均匀化等效修正方法,提出了蒙特卡罗通量矩均匀化方法。以MET-1000金属燃料快堆数值对标为例,针对堆芯扩散计算,对控制棒使用超级均匀化等效修正方法,将堆芯扩散计算的控制棒价值高估从13.5%减小到0.35%,并提高了功率分布预测精度;针对堆芯输运计算,定量解析了误差原因,提出了蒙特卡罗通量矩均匀化方法,可减小MET-1000堆芯输运计算的反应性误差698 pcm。本文中适用于快堆扩散及堆芯输运计算的蒙特卡罗均匀化截面生成方法针对先进非均匀布置快堆、小型快堆等新型堆芯,与不同堆芯求解器的结合有待进一步发展与验证。同时,蒙特卡罗生成快堆均匀化截面还有许多问题需要深入研究,如不连续因子修正、基模修正、历史效应处理方法等。     

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。     

压水堆堆芯pin-by-pin计算环境效应处理模型研究

栅格非均匀计算过程中采用的全反射边界条件近似带来的中子射流效应和中子能谱干涉效应等环境效应对栅元均匀化常数具有较大影响。为在全堆芯pin by pin计算中处理环境效应带来的影响,本文从两个方面进行了计算分析。首先,基于棋盘式多组件问题对栅元均匀化群常数相对误差及各能群栅元不连续因子相对重要性进行了分析,可发现在等效均匀化常数中,热群不连续因子对全堆芯pin by pin计算精度的影响最重要;其次,基于最小二乘法建立了热群栅元不连续因子和堆芯中子学特征量之间的多项式函数关系,利用参数化技术提出了热群常数堆芯在线计算方法,其中堆芯中子学特征量包括扩散系数、移出截面、中子源项、归一化中子通量密度等。采用C5G7基准题和KAIST基准题进行了数值验证,计算结果表明,热群常数堆芯在线计算方法能有效降低全堆芯pin by pin计算特征值和棒功率相对误差,对处于不同燃料组件交界面附近的栅元,计算精度提升尤为显著。     

An effective homogenization method for heterogeneous assemblies

An effective homogenization method has been developed for heterogeneous assemblies such as fuel assemblies with and without control blades in BWR and control-rod channels in FBR. Effective homogenized cross sections are calculated so as to preserve the integrated reaction rates in a heterogeneous assembly in each group by iteratively changing the cross section used in homogeneous super-cell calculations in a model composed of the heterogeneous assembly and a fuel region. The method has been applied to the rod-worth calculation for pin rods in the fast critical assembly ZPPR-10 and to the power-density calculation of a test BWR core.     

Reconstruction method of homogenized cross sections

The reconstruction method of homogenized cross sections in the direct response matrix method has been developed. In this reconstruction method, homogenized cross sections, which take into consideration the influences of neighboring fuel assemblies, can be reconstructed with the response relationship of incoming neutron partial currents and neutron production rates. Calculations for heterogeneous multi fuel assembly systems were done to verify the developed method. The thermal energy group fuel assembly cell-averaged homogenized cross sections reconstructed by this method agreed with those evaluated by the direct calculation of the whole system using the Monte Carlo method within 0.2%. The effect using the reconstructed fuel assembly cell-averaged homogenized cross sections in a conventional core analysis code using cross sections homogenized in a fuel assembly cell was also investigated. The results obtained showed that the analysis accuracy of k-infinity can be improved by using the cross sections reconstructed by the method. Because almost no influences on the analysis accuracy could be found related to the divided numbers of the surfaces and the angles, and the response relationship with neutron production rates of fuel rods or a fuel assembly cell-averaged neutron production rate, this reconstruction method is applicable to a conventional core analysis code using homogenized cross sections in a fuel assembly cell.     

气冷快堆燃料组件均匀化初步研究

气冷快堆是第4代核能系统候选方案之一,具有高温多用途、能增殖等优点。本工作以一气冷快堆的设计方案为研究对象,针对单组件模型和全堆芯模型,采用MCNP耦合ORIGEN的方法,计算了有关临界、燃耗过程的几个重要物理特性,比较了采用精细化结构和组件均匀化方法在计算精度、计算时间等的差别,说明了采用组件均匀化方法进行气冷快堆全堆燃耗计算的必要性和可行性。     

Two-Dimensional Baffle/Reflector Constants for Nodal Code in PWR Core Design

Currently nodal codes are widely used in three-dimensional core calculation. For nodal calculations, in addition to fuel assembly homogenization constants, baffle/reflector homogenization constants (B/R constants) have to be generated. Due to the complexity of its geometrical structure, the baffle/reflector region is usually represented by the two regions, which are called flat edges and corner edges. B/R constants are generated using an equivalent one-dimensional model for each region. However, errors of 3–4% appear for fuel assemblies along core corner when one-dimensional B/R constants are used. Therefore, in order to improve the accuracy of power distribution calculation based on the nodal method, B/R constants need to be calculated by modeling the geometrical configuration of the baffle/reflector region in greater detail. For this purpose, a method of calculating two-dimensional B/R constants that reflects the geometrical configuration has been developed, in which the geometrical configuration ouside the core is treated explicitly using a two-group fine-mesh diffusion code. The two-dimensional B/R constants thus obtained have reproduced assembly power from heterogeneous calculation within 0.5%, error regardless of fuel loading patterns.     

Reconstruction of cell homogenized macroscopic cross sections for analyzing fast and thermal coupled cores using the SRAC system

A fast and thermal neutron coupled core adopts blanket fuel assemblies with zirconium hydrides in the core for negative coolant void reactivity. Conventional neutronics calculation methods have been developed for analysis of a fast core or thermal core, in which the coarse-group macroscopic cross sections of fuel assemblies are prepared without including the effect of the surrounding fuel assemblies. However, such methods are not adequate for analyzing fast and thermal neutron coupled cores where the intra-assembly and inter-assembly heterogeneity effects must be precisely taken into account. Recently, a concept of reconstruction of cell homogenized macroscopic cross sections has been proposed to take into account effects of inter-assembly heterogeneities on macroscopic cross sections used in the reactor core analysis and successfully applied based on a Monte Carlo method. In the present study, a reconstruction method of cell homogenized coarse-group macroscopic cross section for analyzing fast and thermal coupled cores is developed based on a deterministic neutronics calculation code system, SRAC. Three types of fixed source calculations for unit assembly cell geometry are performed independently of the specific core layouts and their results are combined with the results of core analysis to produce cell homogenized coarse-group macroscopic cross sections. Numerical results show that the heterogeneity effects can be adequately reflected in the reconstructed macroscopic cross sections with the proposed method. When the number of energy groups is small, the proposed method gives poor results in the transitional energy groups from resonance to thermal energy. Therefore, it is necessary to increase the number of energy groups in this energy range.     

On the use of the Serpent Monte Carlo code for few-group cross section generation

Serpent is a recently developed 3D continuous-energy Monte Carlo (MC) reactor physics burnup calculation code. Serpent is specifically designed for lattice physics applications including generation of homogenized few-group constants for full-core core simulators.     

High-order cross-section homogenization method

A high-order cross-section homogenization method based on boundary condition perturbation theory is developed to improve the accuracy of nodal methods for coarse-mesh eigenvalue calculations. The method expands the homogenized parameters such as the cross-sections and the neutron flux discontinuity factor in terms of the node surface current-to-flux ratio. The expansion coefficients are evaluated during the nodal calculations using additional precomputed homogenization parameters. As a result, it is possible to correct (update) the homogenized parameters to arbitrary order of accuracy for the effect of reactor core environment (fuel assembly neutron leakage) with very little computational effort in the core calculation. The reconstructed fine-mesh flux (fuel-pin power) is a natural byproduct of the new method. A benchmark problem typical of a BWR core is analyzed in one dimension, monoenergetic diffusion theory by modifying a nodal method based on a bilinear, flat as well as a fine-mesh intranodal flux shape. The homogenized parameters are first computed using exact (fine-mesh) albedos and compared to those determined from a fine-mesh core calculation. Two nodal (coarse-mesh) examples are given to show how well this approach works as a higher-order perturbation method is utilized. The paper concludes by showing that this method succeeds in giving excellent results for cores that may be difficult to model using standard nodal methods.     

全陶瓷微密封燃料有效多群截面计算方法研究

全陶瓷微密封（FCM）燃料是一种弥散颗粒燃料。由于弥散颗粒燃料存在双重非均匀性,传统的确定论方法及蒙特卡罗方法皆难以处理这种双重非均匀效应以获得有效多群截面。本文基于超细群方法建立FCM燃料的有效多群截面计算方法。为描述燃料棒内TRISO颗粒的非均匀性,在共振能量段,通过采用超细群方法求解包含TRISO颗粒的一维球模型得到超细群缺陷因子,通过超细群缺陷因子修正所有核素的超细群截面即可将颗粒和基质均匀化。由于TRISO颗粒在热能区也存在较强的自屏效应,在热能区,利用穿透概率及碰撞概率等价得到多群缺陷因子,通过多群缺陷因子修正所有核素的多群截面将燃料和基质均匀化。均匀化后的FCM燃料组件即可视为普通压水堆燃料组件进行共振计算。利用丹可夫修正因子等价得到FCM燃料组件各燃料棒的等效一维棒模型,对一维棒模型求解超细群慢化方程从而得到共振能量段的有效自屏截面。数值结果表明,该方法能有效处理FCM燃料的双重非均匀性,得到精确的有效自屏截面。