微观燃耗方程求解方法研究与数值验证

研究分析了求解燃耗方程的多种计算方法,包括泰勒级数展开(Taylor)方法、Pade近似(Pade)方法、尺度平方(Scale)方法、特征值(Eig)方法、切比雪夫有理近似(Cram)方法、拉格朗日插值(Lagrange)方法、牛顿插值(Newton)方法、范德蒙矩阵方法和子空间(Krylov)方法,比较分析了各算法在计算效率和计算精度的优劣,最终确定了Cram方法为求解燃耗方程的优选算法。采用Cram方法开发完成了燃耗方程的求解程序,并进行了基准题的验证。结果表明,开发完成的燃耗方程求解程序具有较高的计算精度。     

高阶预估-校正燃耗方法在压水堆组件计算中的应用

压水堆燃料组件输运燃耗耦合计算通常采用的是传统的预估-校正(PC)燃耗方法。然而,该方法本身的假设导致其存在一定的计算误差。为进一步提高燃耗计算的精度,本文针对传统的预估-校正燃耗方法的缺陷研究了改进的预估-校正燃耗方法,改进了对核反应率进行修正的高阶预估-校正燃耗方法,并在Bamboo-Lattice程序中进行了程序实现,对该方法进行了验证分析。结果表明:改进的预估-校正燃耗方法和高阶预估-校正燃耗方法在保证计算效率的前提下提高了燃耗计算的精度。     

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。     

COSINE软件包组件计算程序LATC的燃耗计算模块开发与验证

燃耗计算是反应堆组件参数计算程序的核心功能之一,其计算精度直接影响堆芯物理计算精度。本文系统研究了组件参数计算程序中燃耗计算方法,建立了燃耗计算理论模型,给出了能有效解决燃耗方程刚性的数值方法,根据此方法编制了LATC程序的燃耗计算模块并进行了数值验证。计算结果表明,该燃耗计算模块精度较高,在大燃耗步、深燃耗下仍可得到合理可信的结果。     

反应堆组件参数计算程序中燃耗方程数值解法研究

本文介绍了组件参数计算程序中燃耗计算理论模型,给出了求解燃耗方程的两种数值方法,编制了相应的计算程序,并将其计算结果与解析解的计算结果进行了对比分析,验证了两种数值方法的有效性。对两种数值方法的计算效率进行了比较,结果表明：两种数值方法均能取得较高的计算精度,但在计算速度及对初始时间步长取值的限制方面,Rosenbrock方法明显优于龙格库塔方法。     

消息传递并行燃耗程序MCBMPI的栅元验证

程序采用模块化思想,其中输运部分采用MCNP5程序的消息传递并行版本MCNP5MPI,燃耗计算采用截断泰勒展开的矩阵指数法、TTA线性子链解析法和高斯-赛德尔迭代法三者相结合的燃耗求解方法,并行策略为对多燃耗区采用区域分解的MPI消息传递并行,完成了并行化蒙特卡罗燃耗程序MCBMPI的研制。整个程序系统仅由MCNP5MPI和燃耗程序组成,其中燃耗程序包含了对多燃耗区的区域分解并行功能、核素转换与衰变计算功能以及与MCNP5MPI的数据交换功能。并以压水堆栅元燃耗基准题对程序进行验证,验证结果表明:该程序可用于多燃耗区的并行燃耗计算,伴随计算机硬件性能的改善可显著提高计算效率。     

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。     

基于高阶CRAM的燃耗程序开发与验证

本文基于高阶切比雪夫有理近似方法（CRAM）研制了点燃耗程序ICRAM，并内耦合于蒙特卡罗输运程序OpenMC，形成了一套燃耗计算分析程序OPICE。与传统部分分式分解（PFD）形式的CRAM相比，高阶不完全局部分解（IPF）形式的CRAM具有数值稳定性好、计算精度高和步长包容性更好等特点，满足高保真燃耗计算发展的需求。为提高耦合计算精度，OPICE采用了预估-校正和子步法两种耦合策略，支持纯衰变、定通量和定功率3种计算模式。通过OECD/NEA压水堆栅元燃耗基准题和快堆燃耗基准题的验证，程序计算结果与实验值及各参考值吻合良好，初步验证了OPICE的正确性与有效性。     

反应堆核-热-燃耗多物理耦合框架研究与应用

近年来随着高性能计算技术的不断发展,依托先进的超级计算机和数学物理计算方法,对核反应堆开展多物理、多尺度计算成为前沿研究热点。根据反应堆堆芯多物理耦合分析需求,研究了多物理耦合算法,构建了基于中子输运、燃耗、热工子通道的堆芯多物理耦合系统,完成耦合程序开发,实现中子物理、燃耗、热工子通道的多物理耦合计算。利用压水堆组件模型与快堆模型开展输运-燃耗耦合计算测试和核-热耦合计算测试,初步验证了耦合系统功能。     

基于蒙特卡罗方法的燃耗计算误差研究

基于蒙特卡罗方法进行燃耗计算时,随着燃耗加深,燃耗的计算误差逐渐增大。本文针对蒙特卡罗方法的燃耗计算误差进行研究,并采取修正措施改善燃耗计算的精度。结果表明：采用无偏差最小方差(UMV)修正可改善统计误差的传递效应,采用密度修正可保证蒙特卡罗输运计算的准确性,在此基础上局部优化燃耗截面库,进一步改善了燃耗计算的精度,为其工程应用奠定了基础。     

Evaluation and enhancement of COBRA-TF efficiency for LWR calculations

Detailed representations of the reactor core generate computational meshes with a high number of cells where the fluid dynamics equations must be solved. An exhaustive analysis of the CPU times needed by the thermal-hydraulic subchannel code COBRA-TF for different stages in the solution process has revealed that the solution of the linear system of pressure equations is the most time consuming process. To improve code efficiency two optimized matrix solvers, Super LU library and Krylov non-stationary iterative methods have been implemented in the code and their performance has been tested using a suite of five test cases. The results of performed comparative analyses have demonstrated that for large cases, the implementation of the Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) Krylov method combined with the incomplete LU factorization with dual truncation strategy (ILUT) pre-conditioner reduced the time used by the code for the solution of the pressure matrix by a factor of 20. Both new solvers converge smoothly regardless of the nature of simulated cases and the mesh structures and improve the stability and accuracy of results compared to the classic Gauss–Seidel iterative method. The obtained results indicate that the direct inversion method is the best option for small cases.     

Resonance Self-Shielding Corrections for Activation Cross Section Measurements

The Pade approximations of the Doppler broadening function ψ(θ, x) have been used for the calculations of resonance self-shielding factors used in activation measurements. It is shown that this method of the calculations is effective from the point of view of fastness and accuracy.     

隐式重启的Arnoldi方法及其在高阶谐波求解中的应用

Krylov子空间方法的出现是近年来大型线性方程组和特征值问题求解领域的重大进展,介绍其中一类适用于求解反应堆k-本征值问题的隐式重启的Arnoldi方法(IRAM),以及该方法在高阶谐波求解中的应用。研究结果表明,IRAM方法求解高阶谐波具有和源修正法同样的精度,但计算速度更快,尤其是当所求的谐波阶次较高时,IRAM方法可获得10倍以上的速度优势。同时,IRAM方法还具备较好的处理重特征值问题的能力。     

Reduction of MOC discretization errors through a minimization of source ratio variances

A new technique to reduce discretization errors for ray tracing in the method of characteristics (MOC) is proposed focusing on depletion calculations of single and multi-assembly geometries. In order to efficiently carry out depletion calculations, a calculation scheme using the superhomogenization (SPH) method can be used. However, the discretization errors are caused by changes of neutron sources and total cross sections according to a depletion. This fact means that improvement of accuracy cannot be expected by the calculation scheme with the SPH method when changes of the above parameters are significant. In order to mitigate this problem, a new approach is developed. In the new approach, the discretization errors are reduced by minimizing a variance of a certain parameter which is composed of a ratio of neutron source to total cross section. The verification results suggest that accuracy is degraded by the SPH method as expected especially in a geometry where neutron sources and total cross sections are drastically changing through a depletion. On the other hand, the new approach gives more accurate results compared to the conventional MOC in all calculation cases. Consequently, improvement of calculation efficiency by the new approach is confirmed.     

适用于光厚、强散射介质的SN方程快速求解策略

为实现反应堆大厂房屏蔽问题的快速计算,需要建立一种能够尽可能减少数值负注量率、保证迭代格式的线性特性、同时能够在较大的网格内取得良好精度、计算量较小的离散纵标方法（SN）空间离散格式。本研究基于单群SN固定源输运方程的空间解析解,采用解析基函数展开方法实现SN空间离散;为了提高计算效率,采用权重系数方法,避免单个网格内大量的指数运算;研究高阶源项的计算方法,提高数值计算精度;最后基于Krylov子空间方法实现自散射源项的快速迭代计算。数值结果表明该方法可在材料区域较为均匀的光厚介质中取得较大的优势,可用于反应堆大厂房屏蔽问题的快速计算。      

堆用蒙卡程序燃耗计算功能开发

堆用蒙卡程序(RMC)是由清华大学工程物理系REAL实验室自主开发的用于反应堆物理分析的中子输运蒙卡程序,本文主要介绍其燃耗计算功能的开发与验证。RMC的燃耗计算功能具有的特点:内部耦合ORIGEN,相比于外耦合方式,更加灵活和高效;使用基于能谱的单群截面统计方法,可在保证精度的前提下,显著提高计算效率;采取预估修正和中点近似等多种燃耗步策略,减小大燃耗步长时的计算误差。通过计算压水堆栅元、沸水堆组件、快堆等一系列基准题和算例,验证了RMC燃耗计算的正确性和速度优势。     

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.     

Acid Digestion of Radioactive Combustible Wastes

An iteration method using the Pade approximation is described to accelerate the inner iteration of finite difference equations of two-dimensional diffusion equation In the case of void problems where the system includes regions of very low density, the convergence rate of the usual Iteration method becomes extremely slow, and it becomes often impossible to obtain a converged solution. It is found that the present method using the Pade approximation can give the converged solution for such void problems.     

A Krylov–Schur solution of the eigenvalue problem for the neutron diffusion equation discretized with the Raviart–Thomas method

Mixed-dual formulations of the finite element method were successfully applied to the neutron diffusion equation, such as the Raviart–Thomas method in Cartesian geometry and the Raviart–Thomas–Schneider in hexagonal geometry. Both methods obtain system matrices which are suitable for solving the eigenvalue problem with the preconditioned power method. This method is very fast and optimized, but only for the calculation of the fundamental mode. However, the determination of non-fundamental modes is important for modal analysis, instabilities, and fluctuations of nuclear reactors. So, effective and fast methods are required for solving eigenvalue problems. The most effective methods are those based on Krylov subspaces projection combined with restart, such as Krylov–Schur. In this work, a Krylov–Schur method has been applied to the neutron diffusion equation, discretized with the Raviart–Thomas and Raviart–Thomas–Schneider methods.     

基于分段高斯积分的在线多温度核截面生成方法研究

反应堆运行过程中温度不断变化,在模拟中常采用在线多普勒展宽方法生成各种温度下的中子核截面。已有的在线截面生成方法中,SIGMA1方法精度较高,但由于其使用了误差函数及泰勒级数展开方法,截面的生成效率偏低。本文基于FDS团队自主研发的超级蒙特卡罗核模拟软件系统SuperMC,针对不同能段截面的特点,发展了基于分段高斯积分的在线多温度核截面生成方法,在多普勒展宽共振峰较密集的区域使用高斯-厄米特积分方法,在低能区域使用高斯-勒让德积分方法,在保证核截面精度的同时提高了截面生成效率。通过典型核素截面的对比以及临界安全基准例题与多普勒反应性系数基准例题的测试,本文方法与SIGMA1方法相比平均计算效率提高5倍以上,且展宽温度越高,效率提升越明显。证明了该方法能够快速并准确地生成各种温度下的中子核截面,可用于反应堆多物理耦合计算。