基于中子扩散方程的JFNK方法研究

将中子扩散方程采用有限差分法离散成广义特征值问题,采用JFNK方法进行求解,同时采用LRA基准题和无限平板基准题对JFNK方法进行了验证,并基于单棒例题对JFNK方法的微扰量、预处理矩阵等关键技术进行了研究,结果表明:JFNK方法求解中子扩散方程具有良好的精度和收敛效率;在差分构造雅阁比向量时,微扰量在10~(-5)附近时与解析构造雅阁比向量的效果相当;采用中子扩散方程对应的完整雅阁比矩阵作为预处理矩阵的加速效果更好;源迭代次数超过一定值后,源迭代计算结果作为初值带来的加速效果逐渐减弱。     

采用JFNK方法求解三维中子扩散方程

采用有限差分方法将三维中子扩散方程离散为大型稀疏矩阵的广义特征值问题,并应用JFNK(Jacobian-Free Newton-Krylov)非线性求解方法对该问题进行求解,得到有效增殖因子(k_(eff))和功率分布。数值结果表明,JFNK方法求解三维中子扩散方程具有良好的计算精度。     

基于非线性预处理JFNK的中子-热工联立求解

利用Jacobian-free Newton-Krylov(JFNK)方法联立求解中子-热工耦合问题,采用非线性预处理方式,以避免求解非线性残差,使得JFNK具有可以充分利用原有的中子-热工计算程序,易于实现"黑箱"耦合的特点。对非线性预处理的相关性质进行分析,同时对非线性预处理与线性预处理的区别与联系以及计算效率进行理论分析。以二维简化中子-热工耦合模型作为算例,对比非线性预处理/线性预处理JFNK方法、传统耦合求解方法的计算效率。结果表明:非线性预处理/线性预处理JFNK方法的计算效率比传统方法具有明显优势,线性预处理的计算效率高于非线性预处理。     

模块式高温气冷堆三维中子动力学计算分析

模块式高温气冷堆是国际上公认的安全性好、发电效率高、用途广的先进堆型。本文研究开发了三维圆柱几何堆芯多群中子动力学改进准静态方法模拟计算程序。对给定的模块式高温气冷堆堆芯物理模型进行了模拟计算。初始状态下,该程序计算结果与中子扩散程序CITATION吻合很好。动态情况下,模拟了堆芯反应性、堆芯相对功率以及堆内r,z网格上各群点中子注量率三维分布随时间的变化,计算结果与理论分析一致。     

三维多群六角形几何中子扩散程序开发

本文基于解析基函数展开方法求解中子扩散方程的原理,利用满足中子扩散方程的解析基函数,将节块内的各群中子注量率近似展开。为提高该方法的计算精度,节块间耦合条件采用面中子注量率和面中子净流连续。节块间耦合条件的选取需利用源迭代法来求解中子扩散方程。源迭代中的内迭代选用加速的高斯 塞德尔方法,外迭代采用Lyusternik-Wagner外推加速收敛技术。针对中子注量率收敛慢、有效增殖因数收敛快、内迭代方程组系数矩阵更新耗时的特点,采用一种新的加速方法--一次外迭代多次内迭代的方法。基于以上理论模型,发展了三维多群六角形几何中子扩散程序HANDF-D,对三维二群vver440基准题、高通量堆临界实验2、三维四群热堆问题、三维七群快堆问题计算的结果表明,该方法能准确快速地给出堆芯有效增殖因数和功率。     

基于COMSOL Multiphysics的中子扩散问题求解以及气冷微堆应用分析

基于三维有限元程序COMSOL Multiphysics的“系数形式偏微分方程接口”开发了中子扩散方程的求解模型，利用COMSOL Multiphysics的特征值和瞬态求解器分别对稳态和瞬态中子扩散方程进行了求解。通过与二维的2D-TWIGL基准题(包括稳态和瞬态工况)以及三维的3D IAEA PWR基准题的计算结果进行对比，验证了所开发中子扩散方程求解模型的正确性。针对气冷微堆堆芯进行建模，采用蒙特卡罗程序RMC生成双群和25群的群常数，利用该中子扩散求解模型开展了气冷微堆堆芯临界计算，结果分别与连续能量和多群蒙特卡罗计算参考值进行对比。结果表明：得到的有效增殖因数以及三维功率分布总体上能与对应的多群蒙特卡罗参考值较好吻合。与连续能量蒙特卡罗参考值相比，采用25能群的结果较双群划分方式更为准确。对于气冷微堆堆型，能群结构划分方式对结果精度的影响显著。采用精细能群划分能改善计算精度，但会使得求解所需资源和时间大幅上升。     

基于CITATION-ORIGEN2球床堆平衡态计算程序的实现

基于确定论中子扩散软件CITATION和点燃耗软件ORIGEN2,编写了球床堆分析程序COBBLE,以实现指定燃料球加载策略下的球床堆平衡态燃耗计算。COBBLE程序采用谱区能谱修正方法,通过迭代求解得到球床堆堆芯平衡态参数。本文选取简化的球床模块高温气冷堆(PBMR)堆芯进行建模,计算其功率分布及燃耗分布,并使用基于蒙特卡罗方法的球床堆燃耗计算程序PBRE进行了验证与分析。结果表明,COBBLE程序适用于球床堆的平衡态燃耗计算。     

基于MOOSE开发的中子扩散问题求解程序

基于MOOSE平台，开发了用JFNK方法求解中子扩散本征值、瞬态问题的程序。在程序中实现了反照率边界条件和真空边界条件的设置。通过基准题TWIGL对程序进行了验证，发现对于本征值和瞬态问题，模拟解和参考解都是一致的。程序中采用全隐式Newton法求解中子本征值问题，并与经典幂迭代法进行了对比，发现Newton法能极大减少非线性步的步数，大幅加快收敛速度。采用全空间时空动力学对中子瞬态问题进行求解，可精确跟踪空间中任何一点在瞬态过程中的变化，时间项处理采用向后欧拉差分，时间步长为0.01 s和0.05 s的计算结果和采用0.001 s为时间步长的参考解吻合得很好，说明程序在较大的时间步长下也能保证问题的收敛性和精度。     

高温气冷堆中子时空动力学实时仿真计算

本文研究开发了三维圆柱几何堆芯多群中子时空动力学改进准静态方法模拟计算程序。对给定的模块式高温气冷堆模型进行了模拟计算。在初始状态下,该程序的计算结果与中子扩散程序CITATION的计算结果吻合很好。在动态情况下,模拟了堆芯反应性、堆内各能群中子平均注量率和堆芯相对功率等物理量随时间的变化。计算结果与理论分析一致,在一定精度下,可达到实时仿真计算的要求。     

高温气冷堆全耦合系统直接联立求解的方法研究和程序开发

反应堆耦合计算是对现有反应堆各领域数值技术的融合、集成和提升,完整的反应堆核电站系统同时具有多种耦合机制,是一个超大规模非线性强耦合系统,以JFNK/NK为代表的直接联立方法是极具潜力的发展方向。本文在综述国内外反应堆耦合计算研究的基础上,介绍了清华大学核能与新能源技术研究院在高温气冷堆核电站全耦合直接联立求解方法及程序开发方面的研究工作。针对高温气冷堆多物理、多尺度、多部件、多回路、多模块的耦合特点,首次提出了非线性消去直接联立方法等关键技术,研发可以描述多层级耦合结构的统一耦合平台框架,已形成多个中间版本的程序。     

Core Burnup Calculation of Plutonium Burning Inert-Matrix Fueled High Temperature Gas Cooled Reactor

For the efficient reduction of excess plutonium amount, Japan Atomic Energy Research Institute (JAERI, now Japan Atomic Energy Agency) has studied a concept of rock-like oxide (ROX) fuel as a kind of inert matrix fuel (IMF). In the JAERI study, ROX fuel is burnt in existing light water reactors (LWRs), while in this study, pebble bed type high temperature gas cooled reactor (HTGR) is studied, mainly because of its high neutron economy and softer neutron spectrum than LWRs. Here, PuO₂-yttria stabilized zirconia (YSZ: (Zr,Y)O_2-x) particles are dispersed in graphite matrix. In the ROX fueled LWR study, it was necessary to improve fuel temperature reactivity coefficients by adding such additives as ²³⁸U and Er. Here in HTGR, although the negative temperature coefficient is much larger than that in LWR without any improvements, temperature coefficient was improved as large as possible to the level of UO₂ HTGR case by adding Er in the fuel. Burnup calculations on PuO_2-YSZ fueled HTGR, by simulating the continuous refueling of fuel pebbles with the batch fuel loading, showed almost complete transmutation for ²³⁹Pu and more than 80% for the total plutonium. As the maximum power density of the fuel pebble obtained by the core burnup calculation was very large in comparison with the UO₂ HTGR, the maximum temperature in YSZ fuel particle was also evaluated. Despite the low thermal conductivity of YSZ, the evaluated YSZ temperature was well below the melting point, thanks to the high thermal conductivity of graphite and small YSZ particle size. Here, the high power density in the Pu-YSZ fueled core might become a problem, but is possible to be reduced by adjusting the initial plutonium enrichment.     

高温气冷堆和轻水堆超铀元素管理特性研究

乏燃料中长寿命锕系元素对环境造成长期潜在危害,本文研究球床高温气冷堆不同燃料循环中超铀元素的产生和焚烧特性。在250 MW球床模块式高温气冷堆示范电站HTR-PM铀钚循环的乏燃料中提取铀和钚作为核燃料,设计了PuO₂和MOX燃料元件,将新设计的燃料元件重新装入与HTR-PM相同结构和尺寸的堆芯,分别形成纯钚燃料循环和MOX燃料循环。采用高温气冷堆物理设计程序VSOP,研究了高温气冷堆一次通过燃料循环和不同闭式燃料循环的超铀元素焚烧特性,并与轻水堆燃料循环结果进行比较和分析。结果表明：高温气冷堆一次通过燃料循环超铀元素生成率约为轻水堆的1/2;高温气冷堆闭式燃料循环能有效嬗变超铀元素。     

HTGR reactor physics and fuel cycle studies

The high-temperature gas-cooled reactor (HTGR) appears as a good candidate for the next generation of nuclear power plants. In the “HTR-N” project of the European Union Fifth Framework Program, analyses have been performed on a number of conceptual HTGR designs, derived from reference pebble-bed and hexagonal block-type HTGR types. It is shown that several HTGR concepts are quite promising as systems for the incineration of plutonium and possibly minor actinides.These studies were mainly concerned with the investigation and intercomparison of the plutonium and actinide burning capabilities of a number of HTGR concepts and associated fuel cycles, with emphasis on the use of civil plutonium from spent LWR uranium fuel (first generation Pu) and from spent LWR MOX fuel (second generation Pu). Besides, the “HTR-N” project also included activities concerning the validation of computational tools and the qualification of models. Indeed, it is essential that validated analytical tools are available in the European nuclear community to perform conceptual design studies, industrial calculations (reload calculations and the associated core follow), safety analyses for licensing, etc., for new fuel cycles aiming at plutonium and minor actinide (MA) incineration/transmutation without multi-reprocessing of the discharged fuel.These validation and qualification activities have been centred round the two HTGR systems currently in operation, viz. the HTR-10 and the HTTR. The re-calculation of the HTTR first criticality with a Monte Carlo neutron transport code now yields acceptable correspondence with experimental data. Also calculations by 3D diffusion theory codes yield acceptable results. Special attention, however, has to be given to the modelling of neutron streaming effects. For the HTR-10 the analyses focused on first criticality, temperature coefficients and control rod worth. Also in these studies a good correspondence between calculation and experiment is observed for the 3D diffusion theory codes.     

基于先进节块法的六边形三维中子物理程序的开发与验证

六边形燃料组件在液态金属冷却快堆尤其是钠冷快堆中被广泛应用,针对这类堆型的设计与安全分析需要对堆芯中子通量与中子流进行三维全堆芯耦合计算。经过多年发展,目前已有多种解析节块法、积分节块法、节块展开法等先进节块法能在笛卡尔坐标系下较为精确求解多维中子扩散方程。本文通过径向半解析节块法耦合轴向高阶节块展开法的综合节块方法开发了反应堆三维中子物理计算软件SA HNHEX,并对VVER 440二维、三维基准题进行建模与仿真计算。计算结果与参考值符合较好,初步验证了使用该方法进行反应堆堆芯中子扩散计算的正确性。     

高温气冷堆乏燃料后处理首端技术研究进展

高温气冷堆乏燃料采用后处理路线能充分利用核资源并减少需要最终地质处置的核废物量,有利于核能的可持续发展。传统的LWR乏燃料后处理首端过程不能用于处理高温气冷堆的乏燃料。高温气冷堆乏燃料元件及包覆层颗粒的破碎是首端处理技术的难点。破碎乏燃料元件及去除石墨的方法主要有机械碾碎法、燃烧法、脉冲电流法等;破碎及去除碳化硅的方法有传统机械碾碎法,以及正在发展中的熔融法、气流喷射粉碎法等,其中,气流喷射粉碎法具有较好的发展前景。目前,尚无一种理想的技术来解决高温气冷堆乏燃料后处理中的首端过程问题,需进一步开展高温气冷堆乏燃料后处理技术的研究。     

高温和超高温气冷堆动力转换方案研究

动力转换单元是高温和超高温气冷堆的重要组成部分。本文对高温和超高温气冷堆的动力转换单元进行研究。从4个关键参数（反应堆出口温度、反应堆入口温度、压缩比和主蒸汽参数）入手，对5个循环方案进行比较分析。综合考虑各种工程因素，上位循环为简单氦气透平循环、下位循环为有再热的蒸汽轮机循环的联合循环方案是具有竞争力的，其中下位循环在高温气冷堆范围是亚临界参数循环，在超高温气冷堆范围是超临界参数循环。联合循环可实现高温和超高温气冷堆热量的高效率转化，且反应堆入口温度在反应堆压力壳材料允许的范围内，具有足够的安全性。     

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.     

Computational tracking of BN-600 operation

Computational tracking of BN-600 operation is described. The high quality of computational tracking is largely due to the nature of a fast reactor, in this case BN-600. Unlike reactors with a thermal neutron spectrum, in a fast reactor, because the prompt and delayed fission neutrons as well as the absorbed neutrons are almost in the same energy range as the fast neutrons, a computational cell can be confidently homogenized and the reactor is strongly coupled to the neutron field. These are the reasons why the behavior of the reactor can be successfully predicted by means of computational programs which are based on the diffusion approximation neglecting the anisotropy of the interaction of the neutrons and the heterogeneity of the medium.