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。     

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。     

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。     

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。     

基于求积组局部细化技术的SN屏蔽计算方法

辐射屏蔽设计是保证核装置安全性的重要组成部分,离散纵标法是屏蔽计算的主要方法之一。在具有狭长孔道的屏蔽问题中,由于中子角通量密度呈强各向异性分布,特别在孔道内其分布存在极大峰值,传统求积组难以实现计算精度与效率之间的平衡。为此,本文基于勒让德-切比雪夫求积组的离散特点,研究局部范围内多层极角细化技术,提高求积组积分角通量密度的精度。在极角细化的基础上,进一步研究偏倚求积组以提高计算效率,并开展相关收敛分析。对国际权威基准题Kobayashi的测试分析表明,极角细化技术可有效提高带有孔道屏蔽问题的计算精度。     

角度自适应离散纵标输运计算方法

精确的屏蔽计算方法是核装置辐射屏蔽设计的重要基础,离散纵标法(S_N)是主要的屏蔽计算方法之一。本文基于价值理论的目标导向与角度自适应相结合的方法,有效地减弱了角度的离散误差。求解输运共轭方程获得目标函数的重要性分布,采用局部角度离散误差与目标函数的重要性加权,产生后验误差估计,为角度自适应过程提供判断依据。角通量密度的映射采用多项式权重法和球谐函数拟合法。数值结果表明,对于具有直孔道或曲折孔道的屏蔽问题,在相同精度下离散角度数减少了1～2个数量级,极大地减少了计算量。角度自适应方法以较少的离散方向获得了准确的计算结果,有效地减弱了角度离散误差对屏蔽计算精度的影响。     

角度自适应离散纵标输运计算方法

精确的屏蔽计算方法是核装置辐射屏蔽设计的重要基础,离散纵标法(SN)是主要的屏蔽计算方法之一。本文基于价值理论的目标导向与角度自适应相结合的方法,有效地减弱了角度的离散误差。求解输运共轭方程获得目标函数的重要性分布,采用局部角度离散误差与目标函数的重要性加权,产生后验误差估计,为角度自适应过程提供判断依据。角通量密度的映射采用多项式权重法和球谐函数拟合法。数值结果表明,对于具有直孔道或曲折孔道的屏蔽问题,在相同精度下离散角度数减少了1～2个数量级,极大地减少了计算量。角度自适应方法以较少的离散方向获得了准确的计算结果,有效地减弱了角度离散误差对屏蔽计算精度的影响。     

基于多次碰撞源的屏蔽计算方法研究

离散纵标（SN）方法在求解过程中将空间变量和角度变量进行离散,空间变量和角度变量的离散误差控制对保证计算精度至关重要。本文基于射线追踪研究了多次碰撞源方法,通过计算在选定区域内粒子发生多次碰撞的通量密度,将孤立源等效为计算模型内的分布源进行离散纵标输运计算。选取自设屏蔽问题及Kobayashi基准题进行测试验证并对结果进行分析。数值结果表明,自设屏蔽问题中多次碰撞源方法较首次碰撞源方法能有效缓解二次射线效应问题;Kobayashi基准题计算结果与基准值相对误差的均方根小于3%。多次碰撞源方法有效地减弱了离散误差,提高了屏蔽计算的准确性与可靠性。     

基于多次碰撞源的屏蔽计算方法研究

离散纵标(S_N)方法在求解过程中将空间变量和角度变量进行离散,空间变量和角度变量的离散误差控制对保证计算精度至关重要。本文基于射线追踪研究了多次碰撞源方法,通过计算在选定区域内粒子发生多次碰撞的通量密度,将孤立源等效为计算模型内的分布源进行离散纵标输运计算。选取自设屏蔽问题及Kobayashi基准题进行测试验证并对结果进行分析。数值结果表明,自设屏蔽问题中多次碰撞源方法较首次碰撞源方法能有效缓解二次射线效应问题;Kobayashi基准题计算结果与基准值相对误差的均方根小于3%。多次碰撞源方法有效地减弱了离散误差,提高了屏蔽计算的准确性与可靠性。     

非结构网格中子输运方程的球谐函数解法研究

从新的二阶自共扼角通量密度(SAAF：Self-Adjoint Angular Flux)中子输运方程出发．利用球谐函数对角度变量进行展开,导出了一组关于空间变量的偏微分方程组,中子通量密度的各个分量相互耦合,应用一定的迭代策略进行迭代求解。针对每一个方程,应用有限元方法对非结构网格进行离散求解。据此编写了二维球谐函数方法输运计算程序,对一系列基准题进行校算的数值结果表明,该方法具有较高的计算精度,克服了射线效应,并能用于非结构网格。     

特征线几何预处理方法比较

网格划分、特征线间距、角度求积组、极角数目和方位角大小等几何预处理过程对特征线法的计算精度和计算效率有较大影响。基于步特征线法开发输运程序,通过数值计算验证所开发程序的正确性并分析两种特征线扫描方法(首尾相间循环扫描法、首尾相接循环扫描法)以及网格划分、特征线间距、角度求积组、极角数目、方位角大小对计算精度的影响。结果表明,开发的程序准确可靠;首尾相间循环扫描方法的收敛速度比首尾相接循环扫描方法慢。     

Analytical reconstruction scheme for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates transport model in slab geometry

Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two steps for the analytical reconstruction of the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S_N) transport model in slab geometry. The first step of the algorithm is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the grid set up on the spatial domain. The second step is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S_N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction techniques, as described in this paper.     

球谐函数有限元程序NECP-FISH的开发及其在聚变堆包层中子学分析中的应用

球谐函数有限元方法采用非结构网格求解中子输运方程,具备处理复杂几何的能力;同时又可避免离散纵标方法所造成的射线效应。本文从一阶中子输运方程出发,通过方程的弱形式推导了球谐函数多尺度有限元方法,并基于此方法开发了中子学分析程序NECP-FISH。通过在前后处理平台SALOME中开发接口程序,实现了程序的建模可视化和计算结果可视化。应用此程序计算了氦冷陶瓷包层,数值结果表明NECP-FISH对中子通量密度、氚增殖比和中子释热的计算结果与蒙特卡罗程序NECP-MCX吻合良好。氚增殖比相对偏差为0.56%,所有区域的中子释热偏差均在6%以内。     

Sub-cell balanced nodal expansion methods using S4 eigenfunctions for multi-group SN transport problems in slab geometry

A highly accurate S₄ eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S_N order angular quadrature using two sub-cell balance equations and the S₄ eigenfunctions of within-group transport equation. The four eigenfunctions from S₄ approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes.     

Characteristics of Discrete Sn Calculation for Angular Distribution and Scalar Flux of Neutrons Penetrating through Media

The significant discrepancies often observed between the discrete Sn calculations and the measurements of the angular flux spectrum of neutrons at an angle of 0° have been studied for the benefit of analyses of time-of-flight measurements. Examination of the uncollided angular flux and scalar flux distribution yielded information on the relation between the accuracies obtainable in the calculations and the order of quadrature set used therein. Predictions on the angular flux in graphite resulting from the use of S ₁₆, S ₃₂ and S ₄₈ quadratures, and on the scalar flux in water from the S ₁₆ quadrature were compared with the results of measurements and of PALLAS transport calculations. It was found as a result that the. S ₄₈ quadrature is most suitable for analyzing the 0° angular flux spectrum of the time-of-flight measurements, and that the S ₁₆ quadrature is sufficient for scalar neutron flux calculations for reactor shields. The spurious fluctuations observed in the ANISN angular distributions are not due to insufficiency in the number of iterations in computation, but to the coarseness of the spatial intervals used.     

A finite element method for neutron transport—III. Two-dimensional one-group test problems

The even-parity transport equation for an isotropic scattering medium is applied using a maximum principle to determine the angular flux in a square lattice cell with a cylindrical fuel element, a square isotropic source in a corner of an absorbing shield and a dog-leg duct through an absorbing shield. The finite element solutions obtained are compared with an exact solution for the cell, and benchmark results for the square source and duct problem. The accuracies achieved for the fluxes in the cell problem are everywhere better than 0.75% and high accuracy is achieved for the other test problems. The linear elements, used for the spatial dependence of the angular flux in conjunction with a spherical harmonic expansion for the angular dependence, provide a flexible means of treating awkward geometries. At present the equations are assembled and solved using the UNCLE code, which uses direct Gaussian elimination. This process limits the speed of the finite element method to about 1/3 of the Fletcher finite difference spherical harmonics method for the square source problem. This latter method is, however, limited to systems with geometries defined by co-ordinate surfaces, whereas the finite element method can be used for any region that can be triangulated.