蒙特卡罗模拟CFETR中子输运计算中的全局减方差方法应用及对比

在具有全局特性的蒙特卡罗输运精细计算的问题中,传统的MCNP(Monte Carlo N Particle Transport Code)局部减方差方法很难得到理想的计算结果,全局减方差方法(Global Variance Reduction,GVR)则是一种有效的解决方法。针对中国聚变工程试验反应堆(Chinese Fusion Engineering Testing Reactor,CFETR)的中子输运过程中减小全局方差的问题,将多种形式的GVR方法应用到柱状CFETR中子学模型的计算中。依据不同的中子分布信息,在算例中应用和对比了6种不同形式的GVR权窗,并对不同GVR方法的品质因子(FOMG)、标准差(σ)和有效计数率(Scoring)进行了分析。与AN(MCNPanalog method)相比,GVR方法的FOMG有很大的增长,误差在空间的分布也更加平缓,且具有更高的Scoring。在前人提出的全局减方差的基础上,在计算中应用一些新的GVR形式(能量、径迹数等),计算结果表明,基于中子通量的GVR方法的全局计算效率较AN提高了6.43倍。此外,基于中子能量的全局减方差方法也是一种可行的GVR应用形式,其与AN比较,计算效率提高了5.11倍。综上,基于中子通量的GVR方法具有最佳的全局减方差效果。     

全局减方差方法在乏燃料干式贮存容器屏蔽计算中的应用

开发了基于离散纵标(S_N)方法的蒙特卡罗(MC)全局减方差方法，针对乏燃料干式贮存容器，分别建立了中子源及光子源MC直接计算模型、S_N计算模型及全局减方差方法计算模型，并进行了计算精度和效率的比较。数值结果表明，全局减方差方法计算结果与无偏的MC及S_N计算结果相比吻合良好。其中S_N计算的次级光子剂量率与全局减方差方法计算的偏差较大，这主要是由于MC计算和S_N计算时的数据库差异导致的。和无偏的MC结果相比，全局减方差方法计算的中子及次级光子输运计算收敛效率提高了近2个数量级，初级光子输运计算收敛效率提高了1~2个数量级。     

Shielding Design and Analysis of Fusion–Fission Hybrid Energy Reactor Blanket

A preliminary design of fusion–fission hybrid energy reactor (FFHER) has been proposed by Institute of Nuclear Physics and Chemistry based on current fusion science and well-developed fission technology. In FFHER, shield blocks provide nuclear shielding and thermal shielding for internal and external blanket components. The hybrid of fusion core and fission blanket makes the spectra rather complex. Therefore, it is necessary to make detail shielding design and carry out radiation analysis according to the blanket structure and material property. In this study, a shielding design of combining several different material shield blocks has been proposed. The shielding analysis is performed by Monte Carlo (MC) method. For the radiation deep-penetration problem, the flux and statistical relative error of forward MC estimate are applied to get an optimal weight window for global variance reduction (GVR). The spatial distribution of neutron and gamma flux have been assessed along the shield block depth. Power deposited and dose rate distributions have also been simulated and analysed. Neutron irradiation damage has been studied to evaluate the material damage. Based on the configuration analysis, nuclear analysis and GVR method, an optimal FFHER blanket shielding design has been obtained.     

全局减方差方法的HBR-2基准题应用

对于深穿透类型的屏蔽问题，在合理的时间内计算得到可信的结果对于蒙特卡罗(MC)方法是一个巨大的挑战。基于离散纵标(S_N)方法的局部和全局减方差方法能有效降低MC计算深穿透问题的计数误差。本文基于HBR-2基准题比较了全局减方差方法和局部减方差方法的计算效率。结果表明，对于HBR-2基准题，局部和全局减方差方法均取得了较好的结果。全局减方差方法1次计算即可同时优化辐照监督管和堆外探测器的计数，因此实际应用更加方便和高效。     

Global variance reduction method for global Monte Carlo particle transport simulations of CFETR

It can be difficult to calculate some under-sampled regions in global Monte Carlo radiation transport calculations. The global variance reduction(GVR) method is a useful solution to the problem of variance reduction everywhere in a phase space. In this research, a GVR procedure was developed and applied to the Chinese Fusion Engineering Testing Reactor(CFETR). A cylindrical CFETR model was utilized for comparing various implementations of the GVR method to find the optimum.It was found that the flux-based GVR method could ensure more reliable statistical results, achieving an efficiency being 7.43 times that of the analog case. A mesh tally of the scalar neutron flux was chosen for the GVR method to simulate global neutron transport in the CFETR model.Particles distributed uniformly in the system were sampled adequately through ten iterations of GVR weight window.All voxels were scored, and the average relative error was 2.4% in the ultimate step of the GVR iteration.     

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

The pin-by-pin fine-mesh core calculation method is considered as a candidate next-generation core calculation method for BWR. In this study, the diffusion and simplified P3 (SP3) theories are applied to the BWR pin-by-pin fine-mesh calculation. The performances of the diffusion and SP3 theories for cell-homogeneous pin-by-pin fine-mesh calculation for BWR are evaluated through comparison with a cell-heterogeneous detailed transport calculation by the method of characteristics (MOC). Two-dimensional, 2 × 2 multi-assemblies geometry is used to compare the prediction accuracies of the diffusion and SP3 theories. The 2 × 2 multi-assemblies geometry consists of 9 × 9 UO₂ fuel assemblies that have two different enrichment splittings. To minimize the cell-homogenization error, the SPH method is applied for the pin-by-pin fine-mesh calculation. The SPH method is a technique that reproduces a result of heterogeneous calculation using that of homogeneous calculation. The calculation results indicated that the diffusion theory shows a discrepancy larger than that of the SP3 theory on the pin-wise fission rate distribution. In contrast to the diffusion theory, the SP3 theory shows a much better accuracy on the pin-wise fission rate distribution. The computation time using the SP3 theory is about 1.5 times longer than that using the diffusion theory. The BWR core analysis consists of various calculations, e.g., the cross section interpolation, neutron flux calculation, thermal hydraulic calculation, and burn-up calculation. The function of the calculation time for the neutron flux calculation is usually less than half in the typical BWR core analysis. Therefore, the difference in the calculation time between the diffusion and SP3 theories would have no significant impact on the calculation time of the BWR core analysis. For these reasons, the SP3 theory is more suitable than the diffusion theory and is expected to have sufficient accuracy for the 2 × 2 multi-assemblies geometry used in this study, which simulates a typical situation of the actual BWR core.     

用于求解细网SP3中子输运方程的两节块方法的精度与效率分析

采用两节块方法求解细网3阶简化球谐函数（SP3）中子输运方程，该方法只对零阶角通量密度的拉普拉斯算子进行节块法处理，对应的零阶通量密度采用2阶展开，横向泄漏采用零阶近似；以此方法开发了适用于细网全堆输运计算的CORCA-PIN程序，该程序同时集成了细网有限差分方法。验证算例采用KAIST 3A基准问题及扩展三维问题。数值结果表明，采用栅元1×1划分的两节块法具有可接受的计算精度，而计算时间只有相同精度的细网有限差分方法的11%。因此，本文提出的两节块方法适用于细网SP3中子输运方程计算。      

基于离散纵标法与蒙特卡罗方法的三维耦合程序开发

辐射屏蔽设计是核装置工程设计的核心内容之一。单一的离散纵标法(比如SN)或蒙特卡罗方法(MC)在大型核装置屏蔽计算分析方面均存在一定限制。为了满足大型复杂核装置精确辐射屏蔽计算要求,本文实现了三维SN-MC耦合方法,并发展了相应的三维耦合程序系统。该程序结合了SN方法解决深穿透问题的优势和MC方法模拟复杂几何的长处,克服两种方法的缺点,为保证屏蔽系统优化设计的质量提供有力的技术支持。采用接口程序和MC自定义源抽样程序将SN计算得到的粒子角注量率转换为MC计算所需的源粒子信息,为下一步MC计算提供源项,实现三维SN-MC耦合输运计算。采用MC、SN、SN-MC耦合三种方法对直角坐标系和圆柱坐标系下的测试例题进行了计算比较分析。计算结果吻合良好,初步证明了所开发的三维SN-MC耦合程序的正确性。     

六角形轻水堆组件中子通量密度分布的计算

介绍利用穿透概率法求解二维六角形轻水堆燃料组件中子通量密度分布。子区内中子源及通量密度在空间上采用二次分布 ,子区表面通量密度在空间上采用平通量密度分布 ,在方向上采用简化 6P1近似。根据提出的模型 ,编制了TPHEX D程序 ,并对一些轻水堆六角形组件问题作了计算 ,计算结果与MC结果进行了比较 ,符合良好。本程序可用于六角形轻水堆燃料组件计算。     

Advanced PWR Core Calculation Based on Multi-group Nodal-transport Method in Three-dimensional Pin-by-Pin Geometry

A parallel production code, SCOPE2, has been developed for advanced calculations in the reactor core design of PWRs. In SCOPE2, the multi-group diffusion and/or SP3 transport equations are solved by the Red/Black iterative method within the framework of the finite difference method or the advanced nodal method without non-linear iterations. The effects due to pin-cell homogenization are taken into account by using the SPH factors.

In this paper, calculation methods needed for fast computation are derived including efficient response matrix formulation of the nodal-SP3 method, an analytic solution of the flux moments in the nodal-SP3 transport equations, and coarse-group coarse-mesh diffusion acceleration method. It was found that the present pin-by-pin nodal-SP3 method was more accurate than the finite difference SP3 method with a small additional computational cost in the same meshing scheme.

Tracking calculations of a commercial PWR plant by SCOPE2 revealed that the present model accurately predicted the power distribution and critical boron concentration. A set of depletion calculations in a typical design scheme can be completed within a few hours running on a PC-cluster (16 processors) for the full-core geometry of a 3-loop PWR with 340×3407times;26 meshes based on the 9-group pin-by-pin nodal-SP3 method.     

氟盐冷却高温堆精细中子通量密度分布计算方法研究

氟盐冷却高温堆(FHR)作为第4代核能系统,对安全性和经济性更加注重。FHR全空间中子通量密度的精细分布数据对于材料构件的辐照损伤计算、放射性源项分析以及辐射屏蔽设计等均有重要意义。针对这一需求,本文采用离散纵标(SN)方法为蒙特卡罗(MC)方法偏倚计算提供所需的源偏倚和权窗参数,使蒙特卡罗粒子均匀地分布于整个计算模型空间,从而有效降低中子通量密度分布计算的统计误差。在该方法的基础上,编写了耦合程序SN2MCNP,并使用该程序对FHR全空间的中子通量密度分布进行了精细计算。经对比验证,在同样的计算时间和统计方法的要求下,单独使用MCNP计算的结果中,只有30.1%的相对误差达到要求(10%),而使用SN2MCNP的计算结果中则有99.6%的相对误差达到要求(10%)。     

基于蒙特卡罗-离散纵标双向耦合方法的堆坑粒子注量率计算

为有效解决大型复杂核设施屏蔽计算问题,研究了三维蒙特卡罗(MC)-离散纵标（S_N）双向耦合方法,通过自主开发接口程序实现MC粒子概率分布与S_N角通量密度之间的相互转换,实现MC-S_N双向耦合计算。将基于MC-S_N双向耦合方法的程序用于某反应堆堆坑底部粒子注量率计算。利用MC程序建立堆芯及堆坑处的精细模型进行计算,三维S_N程序用于堆芯下表面与压力容器底面之间区域的计算。通过MC-S_N-MC两步耦合计算,给出堆坑通道及小室内的中子和光子注量率。三维MC-S_N双向耦合方法计算结果与单一MCNP程序结果吻合较好,初步验证了该方法是解决大型复杂核装置屏蔽问题的有效工具。     

二维六角形轻水堆燃料组件中子通量分布的计算

介绍利用穿透概率法求解二维六解形几何多群中子积分输运方程。子区内中子源及通量采用线性分布,子区表面通量在方向上采用简化６Ｐ１近似。根据提出的模型,编制了ＴＰＨＥＸ－Ｂ程序,并对一些轻水堆六解形组件问题做了计算,计算结果与ＭＣ结果进行了比较,符合良好。本程序可用于六解形轻水堆燃料组件计算。     

ADS次临界系统中子时空动力学计算与瞬态分析

加速器驱动次临界反应堆(ADS)中子时空动力学计算需要考虑外中子源和空间分布的影响,比临界系统中子动力学计算要复杂得多。本文将改进准静态(IQS)近似与蒙特卡罗(MC)方法相结合,对于带外源的ADS次临界系统中子时空动力学过程,形状函数、动力学参数由MCNPX程序计算得到,幅度函数与集总参数热工反馈模型进行耦合计算,并开发了IQS/MC计算程序可视化操作界面。针对CIADS靶堆耦合系统参考方案物理模型,对引入束流瞬变及无保护失流工况过程进行瞬态模拟计算分析,给出了堆芯相对功率、燃料温度及冷却剂出口温度随时间的变化曲线。同时,将中子注量率进行分群计算,得到了堆芯分能群的相对中子注量率网格分布随时间的变化,模拟结果与理论分析一致。     

A new approach for calculating non-uniform lattices

A new method is proposed for calculating non-uniform LWR lattices. The method is based on some reasonable assumptions. A new fine-mesh algorithm is derived for the global reactor calculation. The balance equation can be considered as the generalization of the finite-difference form of the diffusion equation. Its coefficients are response matrix elements instead of the traditional homogenized macroscopic cross-sections. As not only cell boundary quantities but also cell-averaged reaction rates (including average flux) are connected with each other by response matrices, on solving the balance equation not only is the fine-mesh flux distribution obtained but also the effective cell parameters. The response matrix elements are obtained from cylindricalized cell transport calculations. In the proposed method several transport problems with different boundary conditions are to be solved for each cell type. The cell transport calculations and the global reactor calculation are coupled in a consistent manner.     

基于蒙特卡罗-离散纵标双向耦合方法的快中子注量基准分析

蒙特卡罗（MC）-离散纵标（S_N）双向耦合方法是解决大型复杂核装置屏蔽问题的有效方法。本文针对三维MC-S_N双向耦合方法在大型压水堆核电站屏蔽计算中的应用,进行了基准验证分析。基于美国核管会（NRC）发布的NUREG/CR-6115压水堆基准模型,采用自主开发的三维MC-S_N双向耦合屏蔽计算分析方法,利用MCNP4C精确计算堆芯到热屏蔽精细模型以及位于压力容器内部计算区域的精确模型,三维S N 程序TORT用于进行热屏蔽到第2下降区外表面间的计算。通过自主研发的接口程序实现MC粒子概率分布与S_N角通量密度间的相互转换,实现MC和S_N 双向耦合计算。三维MC-S_N双向耦合方法计算结果与基准报告提供的MCNP、DORT结果符合良好,初步验证了该方法解决大型复杂核装置屏蔽问题的可行性。     

用于换料方案快速评价的低阶谐波结合线性扰动展开法——理论模型

为解决核电厂装料方案优化搜索过程计算最大和耗时的难题,提出了用于装料方案快速评价的谐波结合线性扰动法.在该方法中,由核燃料倒换所引起的堆芯中子注量率空间分布变化,被区分为局部扰动和全局宏观倾斜两种效应,并分别采用扰动基函数和参考堆芯装载方案的低阶谐波基函数来近似表达.再通过剩余权重方法,将原本大规模矩阵特征值问题的求解转换成有关展开系数的小规模矩阵特征值问题求解,从而实现对堆芯装载方案的快速评价.     

Adjoint Sensitivity and Uncertainty Analyses in Monte Carlo Forward Calculations

The adjoint-weighted perturbation (AWP) method, in which the required adjoint flux is estimated in the course of Monte Carlo (MC) forward calculations, has recently been proposed as an alternative to the conventional MC perturbation techniques, such as the correlated sampling and differential operator sampling (DOS) methods. The equivalence of the first-order AWP method and first-order DOS method with the fission source perturbation taken into account is proven. An algorithm for the AWP calculations is implemented in the Seoul National University MC code McCARD and applied to the sensitivity and uncertainty analyses of the Godiva and Bigten criticalities.     

Application of global variance reduction method to calculate a high-resolution fast neutron flux distribution for TMSR-SF1

The solid fuel thorium molten salt reactor(TMSR-SF1) is a 10-MWth fluoride-cooled pebble bed reactor. As a new reactor concept, one of the major limiting factors to reactor lifetime is radiation-induced material damage. The fast neutron flux(E 0.1 MeV) can be used to assess possible radiation damage. Hence, a method for calculating high-resolution fast neutron flux distribution of the full-scale TMSR-SF1 reactor is required. In this study,a two-step subsection approach based on MCNP5 involving a global variance reduction method, referred to as forward-weighted consistent adjoint-driven importance sampling, was implemented to provide fast neutron flux distribution throughout the TMSR-SF1 facility. In addition,instead of using the general source specification cards, the user-provided SOURCE subroutine in MCNP5 source code was employed to implement a source biasing technique specialized for TMSR-SF1. In contrast to the one-step analog approach, the two-step subsection approach eliminates zero-scored mesh tally cells and obtains tally results with extremely uniform and low relative uncertainties.Furthermore, the maximum fast neutron fluxes of the main components in TMSR-SF1 are provided, which can be used for radiation damage assessment of the structural materials.     

插棒法空间效应修正因子计算中MC方法的应用

研究了MC方法在插棒法空间效应修正因子计算中的应用。用MCNP／4B计算了脉冲堆稳态堆芯第一循环插棒前后探测器位置的中子注量率,得到了探测器位置的空问因子。设计了修正空间效应的方法,并用该方法测量了脉冲堆所有控制棒的积分价值,结果令人满意。