R-Z几何中子输运方程的球谐函数方法

从二阶自共轭角注量率(SAAF: Self-Adjoint Angular Flux)中子输运方程出发,在二维圆柱坐标系下利用球谐函数对角度变量进行展开,推导出了一组关于空间变量的偏微分方程组,然后采用有限元方法进行了空间离散,编写了二维圆柱坐标系下的球谐函数输运计算程序.对一系列例题进行校验的数值结果表明,该方法具有较高的计算精度,克服了射线效应.     

深度学习方法求解中子输运方程的微分变阶理论

中子输运方程是核反应堆物理分析计算的基本方程，针对深度学习技术求解输运方程因定积分项带来的困难，本文提出了微分变阶理论：将输运方程定积分项变换为对应的原函数，其他部分的角通量密度项表示为原函数高阶微分形式，从而将具有微积分形式的输运方程转换为纯粹的高阶微分方程；给出了变换后的原函数定解约束条件，以及对应的边界条件形式；构造了由原函数方程、边界条件、原函数定解、特征值约束共同形成的加权损失函数，利用深度学习使得神经网络逼近原函数；通过将原函数求导进行微分降阶，最终得到原输运方程角通量密度的数值解。针对多个平板、球几何例题进行了数值验证，获得了具有连续性特点的计算结果，证明了本文理论及相关方法的正确性，从而为中子输运方程的数值求解方法探索新的技术途径。     

运动增殖系统内中子引发持续裂变链的概率

针对具有一定速度的流动介质构成的增殖系统,依据概率守恒关系,在相对速度相空间建立中子引发裂变链概率的微分-积分方程,推导考虑流体宏观运动影响的表达式。在一维球对称坐标系下,采用离散纵标(SN)方法计算考虑和不考虑流体情形中子引发裂变链的概率,并分析其随时间演化过程的差异。结果表明,堆体材料沿径向方向向外运动时,近似考虑流体运动中子引发持续裂变链的概率计算结果高于不考虑流体运动的计算结果,在流体最大速度为30cm/μs(接近1keV的中子速度)时,二者的差别约为6%。对运动介质宏观运动影响的考虑,提高了实际物理建模的合理性,对于堆体的不同体元具有膨胀和压缩等复杂运动形态或体元的运动速度较高的情形,近似考虑流体运动影响是非常必要的。     

ADS次临界反应堆的中子共轭方程

与临界反应堆相比,ADS次临界反应堆的外源中子和裂变中子的空间分布具有严重的不均匀性,对应的中子价值也不同。本工作对次临界反应堆的稳态输运方程作分群扩散近似,得到了多群方程,进一步推导出按堆芯功率归一化的中子共轭方程表达式和与功率相关的中子价值函数表达式,给出了次临界反应堆中子价值的物理意义。由稳态中子共轭方程组出发,给出了两种带外加中子源的次临界反应堆增殖因数的表达式。     

用于复杂环境下中子时空动力学计算的简化球谐函数方法

将简化球谐函数(SPN)方法用于离散输运时空动力学方程的角度变量,应用有限元方法离散其空间变量,用全隐式向后差分离散时间变量,用时间积分法求解缓发中子先驱核浓度方程,建立了复杂环境下输运时空动力学计算的理论模型.根据该模型编制了非结构网格多维输运时空动力学计算程序,数值计算结果表明,该方法可以应用于复杂环境下中子输运时空动力学计算.     

浅超瞬发临界系统中子引发持续裂变链的概率

根据中子在核系统中发生不同反应的概率,推导了中子引发持续裂变链概率W( r ,E, Ω ,t)满足的方程;在定态、浅超瞬发临界前提下,采用二阶近似和微扰方法,得到了引发中子源分布下中子引发概率的表达式。由表达式和Godiva-Ⅱ、Caliban、CFBR-Ⅱ脉冲堆的参数得到中子引发脉冲的平均概率分别为0.00032、0.00054和0.00027,采用Godiva-Ⅱ、Caliban自发裂变源引发脉冲实验数据对理论结果进行了比较和分析讨论。     

定态中子输运方程本征值计算方法研究

散射源项各向异性展开阶数较大或者离散纵标方法的角度离散方向较多时,中子输运方程本征值的计算迭代容易失败。为了克服该问题,本文通过数学上的推导,构造了中子输运方程α本征值迭代求解的一种新方法,数值算例表明该方法提高了收敛速度,不收敛的问题也得到明显改善。对keff本征值的计算进行改进,改进后的方法不依赖迭代初值,数值算例表明改进方法的计算结果较好。     

界面流方法二维六角形组件计算

讨论了用界面流方法计算二维六角形组件中子通量分布。从积分输运方程出发,导出了一种简便的数学模型,在子区内采用平源通量近似,并假设中子发射和散射为各向同性。在子区表面上,中子通量的空间分布为常数,中子角通量分布通过伴随勒让特多项式展开表示,采用DP_1近似。推导出界面流方程组,给出了泄漏、穿透几率矩阵及其矩阵元素的表达式及计算方法。根据提出的数学模型,编制了TPHEX程序,对二维六角形组件进行了计算,本程序可用于水堆六角形燃料组件计算。     

中子动力学方程新解法

研究了中子动力学方程的新解法，导出了一个新的中子增殖表达式，此表达式为单项指数与，与老的两项指式相比，应用范围广，计算精度高，可用于定量分析。     

NECP-X中基于改进泄漏项分割技术的二维/一维耦合输运方法

二维/一维耦合输运方法较好地平衡了效率与精度，因此被广泛应用于一步法全堆芯输运计算。二维/一维耦合输运方法中，由于泄漏项在方程右端，导致二维特征线法(MOC)计算时方程右端总源项在迭代过程中可能成为负值，造成迭代发散。本文针对二维/一维耦合输运计算中的负源项问题，提出了一种改进的泄漏项分割方法。新的泄漏项分割方法可在不造成计算精度损失和仅增加有限内存的条件下，显著提高二维/一维耦合输运方法的稳定性。通过强泄漏算例、C5G7基准题、VERA-3A基准题等进行测试，表明该方法对提高二维/一维耦合输运方法稳定性具有显著的效果。     

球坐标系下中子输运方程泄漏项的简便推导

An ingenious method has been discussed to provide a brief way for the derivation of the streaming term expression in the spherical geometry coordinate system. Instead of finding the differential relationship between the dihedral angle and the neutron transport distance, finding the geometry relationship between the dihedral angle and other plane angles is much easier. And then the differential relationship (easy to be derived) between the other plane angles and the neutron transport distance can be used to derive the expression of the streaming term in the spherical geometry coordinate system indirectly but easily. This method makes the derivation process easy and intuitive, with clear physical picture.     

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。     

Spherical harmonics method for neutron transport equation based on unstructured-meshes

Based on a new second-order neutron transport equation, self-adjoint angular flux (SAAF) equation, the spherical harmonics (PN) method for neutron transport equation on unstructured-meshes is derived. The spherical harmonics function is used to expand the angular flux. A set of differential equations about the spatial variable, which are coupled with each other, can be obtained. They are solved iteratively by using the finite element method on unstructured-meshes. A two-dimension transport calculation program is coded according to the model. The numerical results of some benchmark problems demonstrate that this method can give high precision results and avoid the ray effect very well.     

Lattice Boltzmann method for simulation of time-dependent neutral particle transport

In this paper,a novel model is proposed to investigate the neutron transport in scattering and absorbing medium.This solution to the linear Boltzmann equation is expanded from the idea of lattice Boltzmann method (LBM) with the collision and streaming process.The theoretical derivation of lattice Boltzmann model for transient neutron transport problem is proposed for the first time.The fully implicit backward difference scheme is used to ensure the numerical stability,and relaxation time and equilibrium particle distribution function are obtained.To validate the new lattice Boltzmann model,the LBM formulation is tested for a homogenous media with different sources,and both transient and steady-state LBM results get a good agreement with the benchmark solutions.     

Lattice Boltzmann method for simulation of time-dependent neutral particle transport

In this paper,a novel model is proposed to investigate the neutron transport in scattering and absorbing medium.This solution to the linear Boltzmann equation is expanded from the idea of lattice Boltzmann method (LBM) with the collision and streaming process.The theoretical derivation of lattice Boltzmann model for transient neutron transport problem is proposed for the first time.The fully implicit backward difference scheme is used to ensure the numerical stability,and relaxation time and equilibrium particle distribution function are obtained.To validate the new lattice Boltzmann model,the LBM formulation is tested for a homogenous media with different sources,and both transient and steady-state LBM results get a good agreement with the benchmark solutions.     

Application of forward and adjoint Monte Carlo coupling technique to detector system designs

Forward and adjoint Monte Carlo coupling technique has been developed for analyzing neutron streaming in a system with large geometry. Particles (neutron and adjoint particle) are scored by surface type estimators such as the next event surface crossing estimators and the boundary crossing estimators. The detector response is calculated by folding the calculated neutron and adjoint angular fluxes. The reliability and efficiency for this method were studied by solving a sample problem of neutron streaming through narrow sodium pipe embedded in an iron shield. This method turned out to give a figure of merit several times better than the conventional method. The applicability of the method to detector system design has been demonstrated by calculating the signal to noise ratio for the fuel failure detector with delayed neutron detection method, which is located behind the reactor shield of concrete. This method gives an advantage in clarifying the spatial channels for neutron streaming.     

New Efficient Albedo Monte Carlo Method for Neutron Streaming Analyses

An efficient albedo Monte Carlo method newly developed has been studied by analyzing two types of experiments on neutron streaming. The method is characterized by employing the energy-angle dependent doubly differential albedos for slab, which can be calculated in a short computer time with a one-dimensional transport theory, such as the Sn method and more efficient invariant imbedding method. This paper describes the features of the present albedo Monte Carlo method, including fundamental formulas. In the analyses of the neutron streaming experiments, the calculated results agreed with the measured data within a factor of 2 for a benchmark experiment at the YAYOI reactor and within a factor of 3 for an SNR sodium duct mock-up experiment.

It is concluded that the present albedo Monte Carlo method is practical and applicable to the reactor shielding analysis concerning radiation streaming.     

Identification and properties of the fundamental expansion functions for neutron transport in an infinite homogeneous medium

Starting from the basic expression for the neutron flux due to a point source in an infinite homogeneous scattering and absorbing medium, the first few fundamental expansion functions corresponding to successive collisions are identified, and their analytic properties are presented, in spherical and plane geometry. Various representations of the functions are obtained in the form of power series, an expansion in a series of exponential integrals, and other integrals. The adequacy of traditional asymptotic forms is considered.     

A least-squares finite-element Sn method for solving first-order neutron transport equation

A discrete ordinates finite-element method for solving the two-dimensional first-order neutron transport equation is derived using the least-squares variation. It avoids the singularity in void regions of the method derived from the second-order equation which contains the inversion of the cross-section. Different from using the standard Galerkin variation to the first-order equation, the least-squares variation results in a symmetric matrix, which can be solved easily and effectively. To eliminate the discontinuity of the angular flux on the vacuum boundary in the spherical harmonics method, the angle variable is discretized by the discrete ordinates method. A two-dimensional transport simulation code is developed and applied to some benchmark problems with unstructured geometry. The numerical results verified the validity of this method.