Explicit Time Integration Scheme Using Krylov Subspace Method for Reactor Kinetics Equation

The spatial discretization form of the space-dependent reactor kinetics equation is a first-order simultaneous ordinary differential equation in time. Conventional numerical methods of the space-dependent kinetics equation, i.e., the generalized Runge-Kutta method, the implicit method (backward Euler method), and the Theta method, are based on the time difference approximation. However, the present study adopts the analytical solution of the space-dependent kinetics equation expressed by the matrix exponential and no time difference approximation is used. In this context, our present approach is classified as an explicit method in which no iteration calculation on space and energy is necessary. The Krylov subspace method is used to evaluate the matrix exponential observed in the solution of the spatially discretized space-dependent kinetics equation. The Krylov subspace method is implemented into a space-dependent kinetics solver. In order to examine the effectiveness of the Krylov subspace method, the TWIGL benchmark problem is analyzed as a verification calculation. The calculation results show the effectiveness of the present method especially in the step reactivity perturbation.     

双约束核素筛选与燃耗链压缩算法研究

在进行反应堆燃耗计算时,由于评价核数据库中各核素反应截面、寿命差异大,因此形成的燃耗矩阵规模大、刚性强。为降低燃耗矩阵规模、改善矩阵病态程度,有必要研究适用于多种堆芯设计研发需求的燃耗链压缩算法,并形成压缩燃耗链和数据库。首先建立了核素筛选标准,根据各个核素对中子吸收率和重要核素核子密度的贡献率对核素重要性进行排序筛选,研究了基于中子吸收率和重要核素产量贡献率的双约束燃耗链压缩算法,并完成相关程序模块的开发。通过对Kylin-2程序数据库压缩的计算分析,验证了该燃耗链压缩算法的可行性。采用压缩数据库可使其在保持原有计算精度的基础上大幅减少计算时间、提高计算效率;通过燃耗链压缩算法的研究与压缩数据库的实现,为从评价数据库出发制作压缩数据库提供了技术支撑。      

Development of a Method for Evaluation of Pin-wise Power Distribution in Fuel Assemblies of Fast Reactors

In the design of fast reactor core with higher burnup and higher linear power, prediction accuracy of burnup history of fuel pin should be upgraded so as to assure fuel integrity without extra design margin under increased neutron fluence and burnup. A method is studied to predict fuel pin-wise power and its burnup history in fast reactors accurately based on an analytic solution of diffusion theory equation on hexagonal geometry with boundary condition from core calculation by finite-differenced diffusion calculation code. The present method is applied to a fast reactor core model, and its accuracy in predicting fuel pin power is tested. The result is compared with the reference solution by the finite difference calculation with very fine mesh. It is found that the present method predicts the power peaking factors in fuel assemblies accurately. The fuel pin-wise nuclide depletion calculation is also done using neutron fluxes for each fuel pin. The result shows that the fuel pin-wise depletion calculation is very important in predicting the burnup history of the fuel assembly in detail.     

离散纵标屏蔽计算空间自适应方法研究

离散纵标法是目前国际上通用的核装置辐射屏蔽计算的主要方法之一。空间变量离散误差对离散纵标屏蔽计算的精度至关重要。实际屏蔽计算中存在较强的非均匀性,传统的空间离散方法不能高效地在全局达到较高精度。本文采用线性间断有限元方法进行空间离散,由基于两网格的误差估计和基于残差的误差估计驱动空间网格自适应细化;基于树状结构的六面体网格,对传统的输运扫描进行改进,在粗-细网映射中保持零阶、一阶空间矩守恒。数值结果表明：线性间断有限元方法具有较好的射线传递特性和空间收敛性;自适应算法能较好地对通量密度间断、通量密度梯度大、光学厚度大的区域进行网格细化。在达到相同计算精度时,自适应方法所需的网格数较均匀细分的方法减少约1个数量级,能有效提高屏蔽计算效率。     

回溯算法在燃耗计算中的应用

采用解析解的线性核素链方法在进行燃耗计算时首先根据分治和递归的策略将燃耗矩阵进行解耦,形成具有马尔科夫特性的线性核素链。然后通过对每一条链的解析计算得到所有相关核素的核密度、活度、衰变热等数据。然而在核素链的构建过程中需对每一个可能的核反应路径进行计算。欲保证计算的精度和效率,需寻求一种既能覆盖所有反应路径、又能根据问题描述和约束条件进行自动搜索的算法。本文通过对各种搜索算法的分析和比较并根据燃耗链构建过程的特点,最终采用回溯算法进行深度优先搜索,在搜索过程中完成燃耗链的构建和计算,从而形成问题相关的、具有高精度的自适应燃耗算法。同时结合燃耗过程和回溯算法的特点进行了解空间和时间复杂性的分析。将所开发的多群点燃耗计算程序与蒙特卡罗输运计算程序MCMG-Ⅱ进行耦合,通过对中国实验快堆首炉堆芯燃耗的计算和分析完成程序的初步验证。     

基于二十面体间断有限元离散求积组的IRI-TUB基准题验证

精确可靠的屏蔽设计是保证核装置安全性的重要组成部分,离散纵标法是应用最广泛的确定论屏蔽计算方法。对于角通量密度各向异性较强的屏蔽问题,求积组精度不足会导致离散误差较大,严重影响屏蔽计算的准确性与可靠性。本文结合间断有限元思想,构造正二十面体线性及二次间断有限元离散求积组,并优化求积组权重及方向保证权重严格非负。采用球谐函数数值积分及IRI-TUB基准题验证求积组的计算精度与适应性。数值结果表明,二十面体线性间断有限元离散求积组在1/20球面内能准确积分对应0阶和1阶球谐函数,且具有4阶收敛性;对于IRI-TUB基准题,反应率计算值与实验测量值的相对偏差小于25%。二十面体间断有限元离散求积组能适用于角通量密度各向异性较强的屏蔽问题,从而提高屏蔽计算的可靠性。     

A New Mixed Method with Finite Difference and Finite Element Method for Neutron Diffusion Calculation

A new method for obtaining three-dimensional neutron flux distribution in a reactor has been developed by taking into account the fact that the X-Y planar geometry is generally complex but the geometry along Z-axis is simple. In this method, the finite element method is applied to the X-Y plane calculation and the finite difference method to the Z-axis. For solving a three-dimensional neutron diffusion equation, these two methods are iterated successively until a consistency of the leakage coefficients is attained between the two. The present method is embodied as a computer program FEDM for FACOM M200 computer. With this program, a three-dimensional diffusion calculation was performed for comparing some numerical results with those by a conventional standard computer code ADC. The comparison has shown that they agree well with each other. Computing time required for this problem by the FEDM was shorter than that by the ADC for obtaining same accuracy on the eigenvalue. To indicate usefulness of this method, a demonstration calculation for a reactor with a complex geometry was performed, which was a difficult case to calculate with a conventional finite difference code.     

蒙特卡罗燃耗计算程序MCNTRANS的开发与验证

本文介绍了开发的蒙特卡罗燃耗计算程序MCNTRANS。MCNTRANS的中子学计算参数直接采用MCNP5程序的反应率计算值,燃耗计算方法采用图论算法跟踪燃耗链,同时,对实际燃耗过程进行详细分析以提高计算精度与程序适用性,并使用预估 校正方法以获取较大的燃耗计算步长。程序计算结果通过OECD/NEA与JAERI燃耗基准题实验结果进行验证,并与其他程序的计算结果进行比较。结果表明,MCNTRANS程序在不同燃耗深度下的计算结果和实验值与其他程序的计算值符合较好,部分锕系核素与裂变产物的计算精度更高。     

基于偏离效应核素筛选方法的水冷聚变堆源项计算

活化腐蚀产物是水冷聚变堆正常运行过程中主要的放射性源项，一般采用解析方法求解，但解析方法无法在满足精度要求的同时提高计算效率。本文提出一种基于定量化偏离效应分析的核素筛选方法，以放射性活度和剂量率2个参数定义偏离效应指标，通过分析偏离效应指标，筛选出满足接收准则的核素，以确定计算所需要的目标核素，这种分析方法既能满足精度需求，又能提高计算效率。将该核素筛选方法应用于国际热核聚变实验堆（ITER） 限制器-外包层水冷回路 （LIM-OBB）的活化腐蚀产物源项分析，并与此问题下的高精度基准解进行对比。结果表明，57Co、58Co、55Fe、51Cr等主要活化腐蚀产物核素的比活度计算结果相对于基准解的偏差均控制在1.5%以内；应用核素筛选方法后的计算效率相对于基准解的计算效率提高了279倍。      

Theoretical Study on New Bias Factor Methods to Effectively Use Critical Experiments for Improvement of Prediction Accuracy of Neutronic Characteristics

Extended bias factor methods are proposed with two new concepts, the LC method and the PE method, in order to effectively use critical experiments and to enhance the applicability of the bias factor method for the improvement of the prediction accuracy of neutronic characteristics of a target core. Both methods utilize a number of critical experimental results and produce a semifictitious experimental value with them. The LC and PE methods define the semifictitious experimental values by a linear combination of experimental values and the product of exponentiated experimental values, respectively, and the corresponding semifictitious calculation values by those of calculation values. A bias factor is defined by the ratio of the semifictitious experimental value to the semifictitious calculation value in both methods. We formulate how to determine weights for the LC method and exponents for the PE method in order to minimize the variance of the design prediction value obtained by multiplying the design calculation value by the bias factor. From a theoretical comparison of these new methods with the conventional method which utilizes a single experimental result and the generalized bias factor method which was previously proposed to utilize a number of experimental results, it is concluded that the PE method is the most useful method for improving the prediction accuracy. The main advantages of the PE method are summarized as follows. The prediction accuracy is necessarily improved compared with the design calculation value even when experimental results include large experimental errors. This is a special feature that the other methods do not have. The prediction accuracy is most effectively improved by utilizing all the experimental results. From these facts, it can be said that the PE method effectively utilizes all the experimental results and has a possibility to make a full-scale-mockup experiment unnecessary with the use of existing and future benchmark experiments.     

二维中子输运问题的离散纵标短特征线方法研究

离散纵标法是求解中子输运方程的主要数值方法之一,空间变量离散及误差控制对保证输运计算精度至关重要。传统有限差分离散方法对于特定模型会产生非物理振荡问题,粗网精度不足使得低阶差分方法的应用具有局限性。本文研究了二维常数和线性短特征线方法,短特征线空间离散基于中子输运的特征线解,根据输运方程的空间矩守恒构造网格角通量密度完成输运方程求解。选取固定源和临界问题进行测试验证并分析了网格敏感性。数值结果表明,线性短特征线离散对网格敏感性较低,较常数短特征线和低阶差分方法具有更高的计算精度及效率。     

微观燃耗方程的求解算法比较与性能分析

燃耗方程的求解是燃耗计算的核心。常见的算法包括泰勒方法、Pade方法、子空间方法、切比雪夫有理近似方法和龙格库塔法等。通过数值实验,对每种算法在精度、效率、稳定性方面进行分析比较。结果表明：子空间方法、泰勒方法在计算效率方面具有优势;计算精度及稳定性方面,泰勒方法和Pade方法均占优势。综合考虑,泰勒方法在3个方面均表现突出,可作为燃耗计算的优选算法。     

基于非均匀变分节块法的pin-by-pin计算加速算法研究

计算效率是制约pin-by-pin计算工程应用的主要因素之一。本文利用三维扩散的非均匀变分节块法的非均匀节块的描述能力,在不改变原问题栅元均匀化材料分布的前提下,将传统pin-by-pin计算中使用的均匀材料细网剖分方式替代为非均匀材料粗网剖分方式（粗网加速方法）,既能保证pin-by-pin的计算分辨率,又能显著降低红 黑迭代所需的浮点数操作数目,减小内迭代的计算代价。针对外迭代,运用广义矩阵分离加速（GPM）算法和粗网有限差分（CMFD）算法提高源迭代的收敛速度,降低计算时间。数值结果表明,提出的加速算法能在保证计算精度的前提下,有效提高pin-by-pin计算的效率。     

Comparison and Analysis of Floor Response Spectrum Interplolation Methods

In general the response spectrum values corresponding finite damping ratio is defined, the rest response spectrum need to be acquired by interplolation methods. The familiar interpolation methods are linear interpolation and exponential interpolation. Because Duhamel integration used to calculate the response spectrum is an exponential function including the damping ratio, the exponential interpolation usually be used in the interpolating calculation.     

燃耗信任制下燃耗计算对临界计算的偏差及不确定度的研究

为量化燃耗信任制中燃耗计算传递给临界计算的不确定度,本文基于参数统计法对燃耗计算的核素偏差及偏差不确定度展开分析,并以蒙特卡罗（MC）抽样方法计算的kinf不确定度为基准,比较不同抽样方法对临界计算不确定度的影响。结果表明,核素偏差与偏差不确定度是随样品燃耗变化的分段函数。对于临界计算,拉丁超立方抽样（LHS）方法与MC抽样方法的kinf不确定度计算结果吻合较好,且LHS方法可考虑参数间的相关性,计算结果更真实,可进一步提升电厂的经济性。     

General solution of Bateman equations for nuclear transmutations

The paper concerns the linear chain method of solving Bateman equations for nuclear transmutation in derivation of the general solution for linear chain with repeated transitions and thus elimination of existing numerical problems. In addition, applications of derived equations for transmutation trajectory analysis method is presented.     

基于等效几何理论的复杂几何燃料共振计算方法研究

针对各种研究堆、实验堆以及新型反应堆中广泛应用的复杂几何燃料的共振计算难题,本文基于全局 局部耦合策略开展了可处理复杂几何燃料的等效几何共振计算方法研究。针对复杂几何燃料的孤立问题,基于燃料的逃脱概率守恒,建立了复杂几何燃料模型的等效一维圆柱（或平板）燃料模型;基于燃料到外围结构材料区的碰撞概率守恒,获得了燃料外围结构材料的等效尺寸;根据复杂几何燃料的丹可夫因子守恒,建立了等效一维圆柱（或平板）燃料外围的慢化剂尺寸;针对等效一维圆柱（或平板）燃料模型,采用伪核素子群方法进行了有效自屏截面计算。将该方法应用于非棒状几何燃料的共振计算,结果表明,该方法具有很强的几何处理能力,且具有较高的计算精度和计算效率。     

线性子链法在脉冲中子活化计算中的应用

核聚变装置大多在脉冲工况下运行,不同的脉冲运行模式会对材料活化计算产生影响,脉冲的处理方法以及活化计算方法的选择直接决定了计算结果的精度。本文采用线性子链法和解析解公式计算反应链中各核素的数量随时间的变化情况,并通过回溯算法搜索所有参与计算的反应链。针对脉冲中子活化问题,将真实脉冲通过稳态（SS）方法、等效稳态（ESS）方法、连续脉冲（CP）方法进行等效处理,从而简化计算过程,并在此基础上编制了用于脉冲中子活化计算的TACT程序。最后基于天然Fe活化基准题,根据惯性约束聚变装置（IFE）和磁约束聚变装置（MFE）的典型脉冲周期对TACT程序进行测试计算,比较了各种脉冲处理方法的准确度。结果表明：对于IFE和MFE的典型脉冲运行模式,以ESS为前段的CP方法的准确度均优于其他方法;对于CP方法,只需适当保留末尾的真实脉冲数即可达到一定的精度。     

基于能谱重建技术的全身计数器γ能谱分析

为提高全身计数器γ能谱分析精度，开展了基于能谱重建技术的γ能谱分析方法研究。首先建立方法的原理框架；然后进行应用实验，使用一台立式NaI型全身计数器测量含放射性的BOMAB人体模型，并通过建模和蒙特卡罗模拟计算测量矩阵；最后使用boosted-Gold算法求解出射能谱，并将结果与Genie 2000软件进行比较。结果显示，boosted-Gold算法在参数p取1～10时能准确重建出理论的核素出射能谱，实现对所有核素的准确识别，且每种核素的活度计算误差均小于10%，这一结果显著优于Genie 2000软件。     

Interference Effect of Strong Scattering Resonances on Elastic Removal Cross Sections

The interference effect from the strong scattering resonance on the elastic removal cross sections was investigated for the core composition of fast reactors. To find the relation of the group elastic removal cross sections of background nuclides to the scattering property of the mixture, they were numerically calculated in the energy ranges of typical resonances. It was shown that the interference effect could be taken into account in the conventional group constant set by using two different methods.

In the first method, the shielding foctors of the background nuclides were characterized by the parameters ξ and σ₀ for the resonance nuclide. The interpolation scheme was similar to that adopted in the conventional set. In the second method, the shielding factors of the imaginary background nuclide were linearly fitted to those of the resonance nuclide. The composition dependence of macroscopic cross sections could be easily obtained with use of the linear relation of which coefficients were determined, beforehand, for the typical core composition. The accuracy of the second method was examined by comparing with the exact values. The present method could predict the macroscopic elastic removal cross sections within the errors of several percents.