Improvement of Monte Carlo Lattice Burnup Calculation Performance with the Correlated Sampling Method

For next generation reactor designs, which are attempting wide variations of assembly configurations, the flexibility Monte Carlo method holds is attractive, but still costly for repetitive design study works. This paper presents an advanced correlated sampling (ACS) method which was developed to speed up Monte Carlo lattice burnup calculations. The ACS method is the combination of the correlated sampling method and a pseudo-scattering technique. All burnup steps are considered as consecutive perturbed problems using the same neutron collision history, which is pre-calculated based on a selected unperturbed problem. Since neutron weights can be adjusted on every collision point, rather than along paths between them, the perturbed calculation is very fast and the neutron collision history is light enough to be stored in memory or physical storage, which is an indispensable feature for consecutive perturbed calculations. The presented theory shows that the ACS method has good potential to work for a wide range of neutron absorption variations, the dominant perturbation in the lattice burnup. In an example calculation on a BWR lattice, the ACS calculation results of 600,000 neutrons/step agree well with the independent Monte Carlo runs of 20,000,000 neutrons/step within 0.1%dk/k in terms of k_? throughout 95 steps (~50GWd/t). Average calculation time of neutron tracking with the former method is 3.4 s/step with 600,000 neutron histories on a single processor of an Alpha21164-600 MHz, and the speed-up factor against the Monte Carlo calculation turns out to be about 100.     

Improvement of Correlated Sampling Monte Carlo Methods for Reactivity Calculations

Two correlated Monte Carlo methods, the similar flight path and the identical flight path methods, have been improved to evaluate up to the second order change of the reactivity perturbation. Secondary fission neutrons produced by neutrons having passed through perturbed regions in both unperturbed and perturbed systems are followed in a way to have a strong correlation between secondary neutrons in both the systems. These techniques are incorporated into the general purpose Monte Carlo code MORSE, so as to be able to estimate also the statistical error of the calculated reactivity change.

The control rod worths measured in the FCA V-3 assembly are analyzed with the present techniques, which are shown to predict the measured values within the standard deviations. The identical flight path method has revealed itself more useful than the similar flight path method for the analysis of the control rod worth.     

改进弦长抽样方法开发及在弥散燃料蒙特卡罗模拟的应用

弥散型燃料广泛应用于高温气冷堆、事故容忍燃料、实验研究堆及核动力舰船等,是重要的燃料类型之一。弦长抽样(CLS)方法可简化弥散燃料几何建模,提高计算效率,然而传统CLS方法只能描述单种颗粒的填充,同时在高体积填充率时误差较大。针对CLS方法的两大问题,本文在自主化堆用蒙特卡罗程序RMC中开发了改进CLS方法,并应用于全陶瓷微胶囊封装燃料棒算例及含毒物颗粒的高温堆燃料球算例。计算结果表明,改进CLS方法可解决多种颗粒混合填充的问题,并且可保证体积填充率的准确性,为弥散燃料的临界及燃耗计算提供了高效、精确的方法。     

Development of Improved Chord-length Sampling Method and Its Application in Monte Carlo Simulation of Dispersion Fuel

Dispersion fuel is widely used in high-temperature gas-cooled reactor (HTGR), accident tolerant fuel, experimental research reactor, naval nuclear power plant and so on. The chord-length sampling (CLS) method can simplify the geometry modeling of dispersion fuel, which can improve the efficiency. However, traditional CLS can only handle the packing of single particle, and has large error when the packing fraction is high. Aiming to solve these two problems, the improve CLS method was developed in reactor Monte Carlo code RMC, and applied to the fully ceramic micro-encapsulated fuel pin case and HTGR fuel pebble with mixed fuel and poison particles. Results show that the proposed method can handle mixed particles with multiple types, and preserve the accuracy of packing fraction, which provide precise and high efficiency for the critical and burnup calculations.     

基于中子首次裂变的MC/S_N耦合输运算法

外源驱动次临界系统是一类广泛存在且重要的核能系统。固有的射线效应和存在空间局部源,使得离散纵标(SN)法难以精确计算该类系统内的中子注量率。虽然蒙特卡罗(MC)方法可有效地模拟局部源问题,但存在计算效率较低的不足。因此,单一的SN方法或MC方法难以兼顾计算精度和效率。为充分发挥两种方法的优点,提出了以中子首次裂变为耦合点的MC/SN耦合算法。首先,采用MC方法模拟源中子在发生裂变反应之前的输运过程,并统计出首次裂变中子源;其次,采用SN方法求解对应于首次裂变中子源的输运方程;最后叠加两种方法计算的中子注量率,得到最终结果。算例表明,该耦合算法可有效地模拟外源驱动次临界系统的中子输运过程。     

Improvement of fission source distribution by correlated sampling method in Monte Carlo perturbation calculations

To increase the accuracy of Monte Carlo perturbation calculations, the main issue is to estimate the variations of fission source distribution in perturbed systems. For estimating the difference between effective multiplication factors in unperturbed and perturbed systems, this study proposes combining the fission matrix method and the correlated sampling method, and applying the weight window technique for stabilizing the weight fluctuation of fission sources in perturbed systems. By applying the proposed method to the Smart and User-frIendly Monte Carlo Particle Transport Code (SUIT) Monte Carlo code, perturbation calculations are carried out for GODIVA and for simplified STACY problems. The results thus estimated show good agreement compared with those of reference calculations, demonstrating that the proposed method can effectively estimate variations of fission source distribution in perturbed systems for improving the accuracy of Monte Carlo correlated sampling method, especially for large variations.     

蒙特卡罗共轭输运法计算反应堆压力容器快中子注量率

为了保证压力容器（RPV）在核电厂寿期内的安全,通过理论方法准确评估其受到的快中子积分注量率非常重要。本文提出了一种应用共轭输运理论解决深穿透问题的计算方法,并将该方法的计算结果与基准题HBR-2给出的实测值及确定论方法的结果进行了比较。结果表明：本文计算结果与基准题给出的实测数据吻合良好,大多反应率计算相对误差小于10%,最大相对误差不超过35%;70%以上的计算结果准确性优于确定论方法,表明本文提出的解决蒙特卡罗深穿透问题的方法是有效且准确的。     

Improvement of Neutron Source Introduction Method for Absolute Measurements of Low Reactor Power

The neutron source introduction method was applied to absolute measurements of low reactor power at the Static Experiment Critical Facility STACY. To obtain the effective neutron source intensity more accurately, which is a key parameter for the source introduction method, the neutron source is newly defined as fission neutrons from the first fission reaction caused by neutrons emitted from the external neutron source. To obtain the newly defined effective neutron source intensity, the probability that a neutron from the external neutron source causes a fission reaction is calculated using the Monte Carlo code MCNP. This calculation took into consideration the three-dimensional complicated core structures. Furthermore, the fission reaction distribution, fundamental mode forward and adjoint flux distribution in a critical state were calculated using the three-dimensional transport code THREEDANT. Following the principle of the neutron source introduction method, an external neutron source was inserted near the STACY core tank and the reactor power was measured. The reactor powers by the neutron source introduction method were in good agreement with the ones from the analyses of the FP activity generated by high power operation.     

New Sampling Method in Continuous Energy Monte Carlo Calculation for Pebble Bed Reactors

A pebble bed reactor generally has double heterogeneity consisting of two kinds of spherical fuel element. In the core, there exist many fuel balls piled up randomly in a high packing fraction. And each fuel ball contains a lot of small fuel particles which are also distributed randomly. In this study, to realize precise neutron transport calculation of such reactors with the continuous energy Monte Carlo method, a new sampling method has been developed. The new method has been implemented in the general purpose Monte Carlo code MCNP to develop a modified version MCNP-BALL. This method was validated by calculating inventory of spherical fuel elements arranged successively by sampling during transport calculation and also by performing criticality calculations in ordered packing models. From the results, it was confirmed that the inventory of spherical fuel elements could be reproduced using MCNP-BALL within a sufficient accuracy of 0.2%. And the comparison of criticality calculations in ordered packing models between MCNP-BALL and the reference method shows excellent agreement in neutron spectrum as well as multiplication factor.

MCNP-BALL enables us to analyze pebble bed type cores such as PROTEUS precisely with the continuous energy Monte Carlo method.     

基于改进多区delta-tracking方法的蒙特卡罗中子输运跟踪与临界计算验证

传统蒙特卡罗程序进行中子输运跟踪时,当中子穿越不同材料边界时需频繁大量地计算中子到材料边界的距离,若中子平均自由程大于局部模型的宏观尺寸,则大量的距离计算会显著降低中子输运跟踪效率。为弥补传统中子输运跟踪方法带来的潜在效率降低的缺陷,本文提出了改进多区delta-tracking中子输运跟踪方法,通过引入虚截面来对模型进行多区的虚拟均匀化处理,进而在中子输运跟踪时可不考虑材料边界穿越问题,理论上可提高中子输运跟踪效率。将改进多区delta-tracking中子输运跟踪方法在多功能辐射输运模拟仿真平台MOSRT系统中进行了程序实现。利用基准题和全堆芯模型开展了临界计算验证,证明了本文方法及程序的正确性和有效性。     

基于蒙特卡罗抽样的简化核电站SBO事故的风险指引安全裕度分析

风险指引的安全裕度是近十年来核电行业提出的新的安全理念。本文研究风险指引的安全裕度的计算框架和蒙特卡罗抽样方法下的风险指引的安全裕度定量化技术,并重点研究蒙特卡罗抽样方法下的核电站全厂断电（SBO）事故下的风险指引的安全裕度定量化技术。借鉴蒙特卡罗抽样次数估算方法和基于蒙特卡罗的可靠度计算方法,根据蒙特卡罗抽样方法下的风险指引的安全裕度的不确定度计算方法以及蒙特卡罗抽样次数的估算流程,计算得出在绝对误差小于001或相对误差小于5%时,两种不同误差方法选择时SBO事故的风险指引的安全裕度计算的抽样次数,并分别完成两个抽样次数下核燃料包壳失效概率均值和标准差定量化计算。计算结果表明,不同的抽样方法、不同的正态分布对核燃料包壳失效概率均值和标准差均有显著影响。     

Vectorization of Continuous Energy Monte Carlo Method for Neutron Transport Calculation

The vectorization method was studied to achieve a high efficiency for the precise physics model used in the continuous energy Monte Carlo method. The collision analysis task was reconstructed on the basis of the event based algorithm, and the stack-driven zone-selection method was applied to the vectorization of random walk simulation. These methods were installed into the vectorized continuous energy MVP code for general purpose uses. Performance of the present method was evaluated by comparison with conventional scalar codes VIM and MCNP for two typical problems. The MVP code achieved a vectorization ratio of more than 95% and a computation speed faster by a factor of 8–22 on the FACOM VP-2600 vector supercomputer compared with the conventional scalar codes.     

用于核素在线瞬发伽马数据测量的热中子源设计

基于MCNP程序建立了西安脉冲堆热中子源设计的蒙特卡罗深穿透耦合屏蔽计算方法;采用MCNP临界源模型计算了热柱方腔前表面的中子、伽马平面源的参数,并与实验值进行了对比,给出了平面源的修正系数;基于中子、伽马等效平面源,采用新型硼铝复合材料以及铅、铋等材料,优化设计了热中子束流滤束装置,给出了热中子束流滤束装置的升级改造方案,得到热中子通量密度较原设计方案提高3倍、中子伽马通量密度比值大于10的平行热中子束,且束流外侧区域的中子、伽马本底剂量率接近0.025 mSv/h的辐射防护标准。     

Analysis of a multigroup stylized CANDU half-core benchmark

An 8-group cross section library is provided to augment a previously published 2-group 3D stylized half-core Canadian deuterium uranium (CANDU) reactor benchmark problem. Reference eigenvalues and selected pin and bundle fission rates are also included. This benchmark is intended to provide computational reactor physicists and methods developers with a stylized model problem in more than two energy groups that is realistic with respect to the underlying physics. In addition to transport theory code verification, the 8-group energy structure provides reactor physicist with an ideal problem for examining cross section homogenization and collapsing effects in a full-core environment. To this end, additional 2-, 4- and 47-group full-core Monte Carlo benchmark solutions are compared to analyze homogenization-free transport approximations incurred as a result of energy group condensation.     

基于抽样方法的特征值不确定度分析

核数据是反应堆物理计算的基础数据,研究其不确定度对反应堆物理计算引入的不确定度,对提高反应堆的安全性和经济性具有重要意义。本文基于抽样理论研究了反应堆物理计算不确定度分析的方法,研发了不确定度分析程序UNICORN。基于ENDF/B-Ⅶ.1评价数据库,使用NJOY程序开发了多群协方差数据库。采用UNICORN程序和多群协方差数据库对三哩岛燃料棒和基准题RB31的k∞进行了不确定度分析,得到核数据库中各分反应道截面的不确定度对k∞造成的不确定度。结果表明:238 U(n,γ)截面对三哩岛燃料棒k∞造成的不确定度最大,相对不确定度达0.4%左右;协方差数据库的不同来源会对不确定度分析结果造成一定影响。     

Neutronics shielding analysis for the end plug of a tandem mirror fusion reactor

A neutronics analysis using the Monte Carlo method is carried out for the end-plug penetration and magnet system of a tandem mirror fusion reactor. Detailed penetration and the magnets' three-dimensional configurations are modeled. A method of position dependent angular source biasing is developed to adequately sample the DT fusion source in the central cell region and obtain flux contributions at the penetration components.To assure cryogenic stability, the barrier cylindrical solenoid is identified as needing substantial shielding of about 1 m of a steel-lead-boron-carbide-water mixture. Heating rates there would require a thermal-hydraulic design similar to that in the central cell blanket region. The transition coils, however, need a minimal 0.2 m thickness shield. The leakage neutron flux at the direct converters is estimated at 1.3×10¹⁵ n/(m²·s), two orders of magnitude lower than that reported at the neutral beam injectors for tokamaks around 10¹⁷ n/(m²·s) for a 1 MW/m² 14 MeV neutron wall loading. This result is obtained through a coupling between the nuclear and plasma physics designs in which hydrogen ions rather than deuterium atoms are used for energy injection at the end plug, to avoid creating a neutron source there. This lower and controllable radiation leakage problem is perceived as a potential major advantage of tandem mirrors compared to tokamaks and laser reactor systems.     

Calculation of Electron Swarm Parameters of SF6/N2 in a Uniform Field Using an Improved Monte Carlo Collision Simulation Method

The electron swarm parameters of SF6/N2 are calculated in the present study using an improved Monte Carlo collision simulation method （MCS）. And some improved sampling techniques are also adopted. The simulation results show that the improved simulation method can provide more accurate results.     

节块法与蒙特卡罗方法耦合计算研究

普通节块法无法在计算中获得不同组件内精细中子通量密度分布的信息。本文提出一种利用入射角通量将节块法与蒙特卡罗方法相耦合的方法(节块-蒙卡入射角通量耦合方法),并编制了计算程序进行验证。结果表明:本文计算结果与参考值相符,节块-蒙卡入射角通量耦合方法适用于局部特定位置精细中子通量密度等参数的计算,计算效率高,计算结果准确。     

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。