波纹管对气体离心机流场影响的数值研究

波纹管是超临界气体离心机的核心部件,可改变转子流场的空间结构.为了研究波纹管对气体离心机流场的影响,在单向关联水力学模型和Iguassu离心机模型基础上,在交错网格上离散二维N-S方程组,并使用同伦算法和牛顿迭代法求解,对包含内、外波纹管的流场分别进行数值模拟.结果表明,外波纹管对环流几乎没有影响,但在不改变贫取料压强...     

一种地面放射性污染分布重建算法的研究

提出了一种基于低空测量数据的地面放射性污染分布重建算法,该算法可以应用在"脏弹"爆炸后放射性污染分布重建计算中。该算法通过求解探测器响应系数方程组进而重建出地面污染分布,研究显示该算法在探测高度小于50 m时能比较好地重建地面放射性污染的分布。     

一种地面放射性污染分布重建算法的研究北大核心CSCD

提出了一种基于低空测量数据的地面放射性污染分布重建算法,该算法可以应用在"脏弹"爆炸后放射性污染分布重建计算中。该算法通过求解探测器响应系数方程组进而重建出地面污染分布,研究显示该算法在探测高度小于50 m时能比较好地重建地面放射性污染的分布。     

基于Chan算法和Taylor级数混合算法的到达时差定位

结合Chan算法和泰勒级数展开法的优点,提出了一种基于Chan算法初值选取与泰勒级数展开法精确迭代的时差定位方法.该算法充分发挥了Chan算法初值估计性好和泰勒级数展开法收敛速度快的优点.仿真结果表明,在参数设置合理的前提下,相比Chan算法和泰勒级数展开法,该混合算法性能稳定,时差测量精度为10μs时,均方根误差较Clan算法定位结果减少了64m.     

核素深度分布就地测量中病态线性方程组的迭代解法

在就地γ谱仪地面放射性核素深度分布测量研究中遇到了病态线性方程组的求解问题,方程组系数矩阵条件数达3×10~8.此方程组的求解特殊性在于:一是病态性十分严重,二是保证方程组解的非负性才符合实际.尝试多种解法不奏效的情况下,借助于行列均衡化处理技术、最大似然法非线性方程组建立和相应的EM迭代法,求解获得了满意结果.     

气体离心机贫料挡板结构参数优化的数值研究

采用有限差分方法离散线性化的Navier-Stokes方程组,并用追赶法求解线性代数方程组,得到了离心机内部流场分布。采用改进的径向平均法求解丰度方程,得到单机分离功率的数值结果。以分离功率为目标函数,选用序列二次规划算法,结合iSight软件的优化功能对离心机贫料挡板的结构参数进行优化计算。计算结果表明：针对特定离心机模型,贫料挡板结构参数优化后可以改善内部环流,提高分离功率3.93%;离心机内部流场对挡板结构参数的变化响应敏感,其机理复杂,有待深入研究。     

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。     

点堆中子动力学方程的指数基函数法求解

给出了一个求解点堆中子动力学方程组的指数基甬数法.该方法通过将点堆中子动力学方程组变成矩阵形式,利用指数函数为基甬数的特点将其显式化,并根据初始条件求得各项系数,进而获得方程组的解.对阶跃、线性和正弦等不同反应性输入进行了计算.结果表明,指数基函数法过程简捷明了、易于编程,是一种计算速度较快、精度较高、适用性较强的求解点堆中子动力学方程的方法.     

用数值分析方法来解密度计率定方程

本文详细介绍了用数值分析求解密度计率定方程组的原理和方法,讨论了方程组的化简、迭代函数的初值选择、迭代函数及其收敛性以及计算机程序编制流程图。本方法为核密度计的现场率定提供了一种简便易行、准确可靠的新途径。     

用高阶泰勒多项式积分方法求解点堆中子动力学方程

在求解点堆中子动力学方程组中,对中子密度使用分段全隐式高阶泰勒多项式近似技术,给出一求解点堆中子动力学方程组的数值积分方法,并对该方法进行了修正优化.实例计算并与传统的三阶Hermite插值多项式法的比较表明:该方法能显著消除刚性方程组带来的数值计算不利因素,对给定的反应性输入能够取得较高精确度的数值结果,计算过程简洁,且计算速度快,通过对高阶泰勒多项式的修正,计算精度有了进一步提高,可适宜于反应堆中子动力学控制的设计分析和仿真计算.     

Investigation of Dual Polarization Reflectometry for Determination of Plasma Density and Magnetic Field in a Spherical Tokamak

The paper deals with dual polarization reflectometry as a method for determination of plasma density and poloidal magnetic field profile in low aspect ratio tokamaks. A numerical iteration algorithm is developed and solutions for integral equations for O- and X-modes are presented. The numerical calculations confirm the use of the iterative algorithm for effective reconstruction of the density and magnetic field profile.     

A mixed implicit/explicit procedure for soil-structure interaction

This paper describes an efficient method for the solution of dynamic soil-structure interaction problems. The method which combines implicit and explicit time integration procedures is ideally suited to problems in which the structure is considered linear and the soil non-linear. The equations relating to the linear structures are integrated using an unconditionally stable implicit scheme while the non-linear soil is treated explicitly. The explicit method is ideally suited to non-linear calculations as there is no need for iterative techniques. The structural equations can also be integrated explicitly, but this generally requires a time step that is much smaller than that for the soil. By using an unconditionally stable implicit algorithm for the structure, the complete analysis can be performed using the time step for the soil. The proposed procedure leads to economical solutions with the soil non-linearities handled accurately and efficiently.     

Application of Galerkin Finite Element Method to Subchannel Analysis

Most of the computer codes based upon subchannel analysis, which are important for thermal hydraulic analysis of the reactor core, use the finite difference method to solve the set of equations. In the present study, however, the Galerkin finite element method was tried, with the result that more accurate solutions and more efficient calculations were obtained than those by the finite difference method. The results of error evaluation obtained herein are useful for application of this method to actual subchannel analysis codes and to other general thermal hydraulic analysis codes. As an example, steady-state single-phase subchannel analysis was performed.     

Solution of Multi-Dimensional Neutron Transport Equation by Finite Element Method

A scheme of treatment with the finite element Galerkin method is proposed for the approximation of solutions of multidimensional steady state neutron transport equations, and it is proved that the approximate solutions yielded by the treatment converge to the solutions of the transport equations under reasonable hypotheses. These approximate solutions are used also to show the existence of weak solutions of transport equations. Finally, based on the Galerkin method, the conditions for convergence are discussed for the multi-group approximation and for the method of spherical harmonics.     

Basic Characteristics of Centrifuges, (III)

A method of numerically integrating the Navier-Stokes equations is presented for axisymmetric compressible flows. A modified Newton's method is employed to determine the steady motion of gas in a rotating cylinder without the use of a time-consuming marching process with respect to time. A suitable form of the finite difference equations gives a computationally-stable integration with reasonable representation of the spatial characteristics of the flow. The method includes a Gaussian elimination procedure which consists of the transformation of the Jacobian matrix to a triangular matrix followed by the backward substitution. By using an auxiliary constant matrix algorithm, the method gives the solution within reasonably acceptable computation time.

As an example of the method, some features of solutions are presented for the steady flow of UF₆ gas in the centrifuges which have the openings for feed and withdrawal on the end plates.     

Comparison of depletion algorithms for large systems of nuclides

In this work five algorithms for solving the system of decay and transmutation equations with constant reaction rates encountered in burnup calculations were compared. These are Chebyshev rational approximation method (CRAM), which is a new matrix exponential method, the matrix exponential power series with instant decay and a secular equilibrium approximations for short-lived nuclides, which is used in ORIGEN, and three different variants of transmutation trajectory analysis (TTA), which is also known as the linear chains method. The common feature of these methods is their ability to deal with thousands of nuclides and reactions. Consequently, there is no need to simplify the system of equations and all nuclides can be accounted for explicitly.The methods were compared in single depletion steps using decay and cross-section data taken from the default ORIGEN libraries. Very accurate reference solutions were obtained from a high precision TTA algorithm. The results from CRAM and TTA were found to be very accurate. While ORIGEN was not as accurate, it should still be sufficient for most purposes. All TTA variants are much slower than the other two, which are so fast that their running time should be negligible in most, if not all, applications. The combination of speed and accuracy makes CRAM the clear winner of the comparison.     

A “two-grid” acceleration of binary stochastic mixture deterministic transport iterations in slab geometry

Particle transport in stochastic mixtures has been an area of active research during the last decade. The primary focus has been on the development of simple, efficient models that approximate the behavior of transport solutions which have been ensemble-averaged over a large number of realizations of the mixing statistics. These approximate models are often written as coupled systems of transport equations. The stochastic nature of this problem can be naturally incorporated into Monte Carlo transport codes, but there have also been efforts to solve these coupled equations deterministically. In this paper, we develop an efficient iterative technique for the deterministic solution of the coupled transport equations of the Levermore–Pomraning mix model. The basis for its development is the observation that these equations are similar in structure to traditional multigroup transport equations with upscattering. We provide the results of a Fourier analysis of this technique, and compare these with observed convergence rates from the implemented algorithm.     

Finite element analysis of linear and nonlinear heat transfer

The finite element method is rapidly becoming a popular procedure for the evaluation of thermal stresses in complex structures. In linear analysis the method has been used extensively and has been coupled with stress analysis computer programs in order to automate thermal stress analysis. However, for the method to be effective, efficient numerical techniques need to be used. The purpose of this paper is to survey the recent developments in linear heat transfer analysis and, specifically, to present the techniques that permit the practical analysis of large and complex three-dimensional heat conduction problems. Typical practical problems are described and solution times are presented. In the analysis of systems with nonlinear thermal properties the method has had limited application. In this paper the general formulation of the incremental equations used in nonlinear heat transfer analysis are presented. An efficient numerical solution of the equations is given. Several types of nonlinearities are discussed and the solutions of some typical problems are presented.     

An implicit three-dimensional finite-element formulation for long-duration structural analysis of piping systems

This paper describes an implicit three-dimensional finite-element formulation for the structural analysis of reactor piping systems. The numerical algorithm considers hoop, flexural, axial, and torsion modes of the piping structures. It is unconditionally stable and can be used for calculation of piping response under static or long duration dynamic loads.The method uses a predictor-corrector, successive iterative scheme which satisfies the equilibrium equations. A set of stiffness equations representing the discretized equations of motion are derived to predict the displacement increments. The calculated displacement increments are then used to correct the element nodal forces. The algorithm is fairly general, and is capable of treating large displacements and elastic-plastic materials with thermal and strain-rate effects.The implicit-time integration scheme described herein has been incorporated into the three-dimensional piping code SHAPS. Two sample problems are presented to illustrate the analysis. The first problem deals with a dynamic analysis of a pipe-elbow loop. The second problem studies the piping response to seismic excitation. The results are discussed in detail.     

Resonance self-shielding calculation using subgroup method and ABC algorithm

In this study, we propose a new method to optimize subgroup parameters for resonance self-shielding calculation. Our approach integrates the merits of both the subgroup method and ABC optimization technique to effectively evaluate self-shielded resonance cross-sections. The ABC algorithm is used to obtain subgroup level in a way that guarantees reproduction of shielded effective cross sections in the subgroup formulation. The temperature dependency of the cross-section is included in both subgroup level and subgroup weight. We used the conjugate gradient method based on the normal equations (CGNR) to evaluate the subgroup weights. An iteration technique is also used to consider the resonance interference. The proposed method is verified by analyzing Rowlands benchmark problems and Mosteller benchmark problems and comparing the obtained results with corresponding Monte Carlo solutions. The multiplication factor results show small errors and also good agreement.