Higher-order approximate solutions of fractional stochastic point kinetics equations in nuclear reactor dynamics

Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.

Effective point kinetic parameters calculation in Tehran research reactor using deterministic and probabilistic methods

The exact calculation of point kinetic parameters is very important in nuclear reactor safety assessment, and most sophisticated safety codes such as RELAP5, PARCS,DYN3D, and PARET are using these parameters in their dynamic models. These parameters include effective delayed neutron fractions as well as mean generation time.These parameters are adjoint-weighted, and adjoint flux is employed as a weighting function in their evaluation.Adjoint flux calculation is an easy task for most of deterministic codes, but its evaluation is cumbersome for Monte Carlo codes. However, in recent years, some sophisticated techniques have been proposed for Monte Carlo-based point kinetic parameters calculation without any need of adjoint flux. The most straightforward scheme is known as the ‘‘prompt method'' and has been used widely in literature. The main objective of this article is dedicated to point kinetic parameters calculation in Tehran research reactor(TRR) using deterministic as well as probabilistic techniques. WIMS-D5B and CITATION codes have been used in deterministic calculation of forward and adjoint fluxes in the TRR core. On the other hand, the MCNP Monte Carlo code has been employed in the ‘‘prompt method''scheme for effective delayed neutron fraction evaluation.Deterministic results have been cross-checked with probabilistic ones and validated with SAR and experimental data. In comparison with experimental results, the relativedifferences of deterministic as well as probabilistic methods are 7.6 and 3.2%, respectively. These quantities are10.7 and 6.4%, respectively, in comparison with SAR report.

Analytical solution of modified point kinetics equations for linear reactivity variation in subcritical nuclear reactors adopting an incomplete gamma function approximation

The present work aims to achieve a fast and accurate analytical solution of the point kinetics equations applied to subcritical reactors such as ADS (Accelerator-Driven System), assuming a linear reactivity and external source variation. It was used a new set of point kinetics equations for subcritical systems based on the model proposed by Gandini & Salvatores. In this work it was employed the integrating factor method. The analytical solution for the case of interest was obtained by using only an approximation which consists of disregarding the term of the second derivative for neutron density in relation to time when compared with the other terms of the equation. And also, it is proposed an approximation for the upper incomplete gamma function found in the solution in order to make the computational processing faster. In addition, for purposes of validation and comparison a numerical solution was obtained by the finite differences method. Finally, it can be concluded that the obtained solution is accurate and has fast numerical processing time, especially when compared with the results of numerical solution by finite difference. One can also observe that the gamma approximation used achieve a high accuracy for the usual parameters. Thus we got satisfactory results when the solution is applied to practical situations, such as a reactor startup.

49-2游泳池式轻水反应堆池底点缺陷超声测量技术研究

为掌握49-2游泳池式轻水反应堆(简称49-2堆)堆水池铝质池底点缺陷的现状,以进一步为堆水池的服役性能评估提供数据支撑,确保反应堆的安全稳定运行,根据池底结构、池内介质、池壁材料等信息,研发了水浸超声测量系统,对池底点缺陷的分布情况进行了全面检查,实现了点缺陷深度的精确测量。该研究实现了首次对49-2堆池底点缺陷实际状态的远程水下无损检测,检测结论显示:与历史数据相比,池底点缺陷的分布和点坑深度测量数据基本一致,最大点坑深度为1.495 mm。研究结论为49-2堆池底材料的时限老化分析提供了重要数据支撑,研发的水下超声测量技术也可应用于同类型池式堆堆容器及乏燃料贮存池的老化管理工作以及服役寿命分析论证工作中。

核热推进系统分析程序模型与计算方法初步研究

核热推进(NTP)系统具有高比冲、大推力和工作时间长等特点,在深空探测和轨道机动等方面具有明显的优势。系统性能分析是NTP系统研发与设计的重要内容。结合对国际历史上已开发程序的分析以及现阶段的研发需求,将系统性能分析划分为稳态设计点性能分析与优化、稳态非设计点性能分析以及瞬态性能分析3个主要环节。在清华大学核能与新能源技术研究院自主开发的核动力发动机系统分析程序PANES基础上,提出了基于“流网-热网”的系统分析程序框架,并建立了反应堆中子动力学与涡轮泵动态特性等数学模型,提出了对应的计算分析方法,拓展了原程序的功能。该工作为NTP系统设计方法的进一步研究和应用提供了重要基础。

反射中子对金属快中子脉冲堆特性参数的影响研究

快中子脉冲堆对墙壁反射中子比较敏感,反射中子会改变快中子脉冲堆波形,当反射中子较多时可能会对脉冲堆的运行安全造成不利影响。本文建立了考虑墙壁反射中子效应的点堆动力学方法、蒙特卡罗中子学计算方法和ANSYS热力学计算方法三者耦合的“核-热-力”耦合方法,并对含有墙壁反射中子效应的快中子脉冲堆Godiva-Ⅰ瞬态过程进行分析。结果表明:反射中子使脉冲后沿提高,使冲坪时的反应性变低,使堆芯位移、应力有所提高。

基于两点模型的堆芯功率多目标保性能控制

现阶段能源产业需要核电站能够根据实际功率需求对输出功率进行调整,因此压水堆堆芯负荷跟踪运行是现阶段压水堆商业化运行的重要需求之一.为了避免运行过程中由于堆芯功率分布不均匀导致的氙震荡、热点等问题,对堆芯运行过程中产生的轴向功率偏差进行控制也是压水堆安全运行的关键.基于中子动力学方程、反应性反馈方程和热工水力学方程,结合堆芯功率空间耦合构建了压水堆堆芯功率两节点模型,并在这一模型的基础上增加负荷跟踪和轴向功率偏差跟踪量.根据这一模型设计了能够实现负荷跟踪控制和轴向功率分布控制并且具有抗时变性的LPV-LQR多目标控制器.在经典的多个瞬态工况下进行仿真的结果表明,LPV-LQR控制器具有良好的负荷跟踪控制和轴向功率分布控制能力,并且能够更好适应堆芯功率系统的时变性.

测压点的设置对脱硝SCR反应器阻力测定的影响

随着水泥企业氮氧化物超低排放工程(主要为SCR脱硝技术路径)的推广普及,众多水泥企业的生产管理者越来越关注建设SCR系统给原生产线带来的阻力增加,如何优化设计与系统集成技术的最佳匹配是众多环保科技工作者重点要解决的问题。文章简要介绍了在建设SCR系统的时候,科学设置测压点对于系统压差尤其是SCR反应器压差的测定准确性和生产管理准确调度都非常有意义。

蜡油加氢裂化装置生产工业粗白油的工艺优化

在中国石油云南石化有限公司210万t/a蜡油加氢裂化装置上,通过采取提高反应器床层温度,优化产品馏分,升高航空煤油(航煤)和柴油闪点等措施,生产出工业粗白油产品。结果表明:装置工艺操作参数优化后,生产的柴油达到5号粗白油标准,航煤除芳烃质量分数外,其他达到3号粗白油标准,但航煤、柴油、粗白油原料的总收率降低5.33个百分点;高温能够促进多环芳烃加氢反应的进行,有利于改善产品油的颜色;航煤中轻馏分含芳烃质量分数最高;提高分馏塔塔顶温度和航煤塔塔底温度,增加柴油塔汽提蒸汽量后,航煤和柴油的闪点分别由48,91℃升高至69,125℃;投用柴油脱水装置后,柴油含水量仅为85μg/g。

Development of a dynamics model for graphite-moderated channel-type molten salt reactor

A molten salt reactor(MSR) is one of the six advanced reactor concepts selected by the generation Ⅳ international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding and transuranics transmutation. A dynamics model for the channel-type MSR is developed in this work based on a three-dimensional thermal–hydraulic model(3DTH) and a point reactor model. The 3DTH couples a three-dimensional heat conduction model and a one-dimensional single-phase flow model that can accurately consider the heat conduction between different assemblies. The 3DTH is validated by the RELAP5 code in terms of the temperature and mass flow distribution calculation. A point reactor model considering the drift of delayed neutron precursors is adopted in the dynamics model. To verify the dynamics model, three experiments from the molten salt reactor experiment are simulated. The agreement of the experimental data and simulation results was excellent.With the aid of this model, the unprotected step reactivity addition and unprotected loss of flow of the 2 MWt experimental MSR are modeled, and the reactor power and temperature evolution are analyzed.

Characteristics of a reactor with power reactivity feedback

The point-reactor model with power reactivity feedback becomes a nonlinear system. Its dynamic characteristic shows great complexity. According to the mathematic definition of stability in differential equa- tion qualitative theory, the model of a reactor with power reactivity feedback is judged unstable. The equilibrium point is a saddle-node point. A portion of the trajectory in the neighborhood of the equilibrium point is parabolic fan curve, and the other is hyperbolic fan curve. Based on phase locus near the equilibrium point, it is pointed out that the model is still stable within physical limits. The difference between stabilities in the mathematical sense and in the physical sense is indicated.

A New Formulation to the Point Kinetics Equations Considering the Time Variation of the Neutron Currents

The system of point kinetics equations describes the time behaviour of a nuclear reactor, assuming that, during the transient, the spatial form of the flux of neutrons varies very little. This system has been largely used in the analysis of transients, where the numerical solutions of the equations are limited by the stiffness problem that results from the different time scales of the instantaneous and delayed neutrons. Its derivation can be done directly from the neutron transport equation, from the neutron diffusion equation or through a heuristics procedure. All of them lead to the same functional form of the system of differential equations for point kinetics, but with different coefficients. However, the solution of the neutron transport equation is of little practical use as it requires the change of the existent core design systems, as used to calculate the design of the cores of nuclear reactors for different operating cycles. Several approximations can be made for the said derivation. One of them consists of disregarding the time derivative for neutron density in comparison with the remaining terms of the equation resulting from the P1 approximation of the transport equation. In this paper, we consider that the time derivative for neutron current density is not negligible in the P1 equation. Thus being, we obtained a new system of equations of point kinetics that we named as modified. The innovation of the method presented in the manuscript consists in adopting arising from the P1 equations, without neglecting the derivative of the current neutrons, to derive the modified point kinetics equations instead of adopting the Fick’s law which results in the classic point kinetics equations. The results of the comparison between the point kinetics equations, modified and classical, indicate that the time derivative for the neutron current density should not be disregarded in several of transient analysis situations.

Neutron Flux Signal Acquisition from Plant Instrumentation Channel of Research Reactor for Reactivity Calculation

A design for instantaneous neutron flux signal acquisition system is being carried out for reactivity measurement of the nuclear research reactor. It is a computer-based digital data acquisition system that can perform continuous monitor and measurement of reactivity inserted into or removed from the research reactor. The acquisition system accomplishes with two major parts. The first part is an interfacing PCI based data acquisition card and the corresponding driver software intending to on-line acquisition of neutron flux signals from plant instrumentation channel. The second part incorporates the high-level Visual Basic real time program, indigenously developed for computation of reactivity by the solution of neutron point kinetic equations and other relevant functional modules like input file logging, reactivity calculation, graphics demonstration etc.

Robust nonlinear control for nuclear reactors using sliding mode observer to estimate the xenon concentration

This paper presents findings on the sliding mode controller for a nuclear reactor. One of the important operations in nuclear power plants is load following. In this paper, a sliding mode control system, which is a robust nonlinear controller, is designed to control the pressurizedwater reactor power. The reactor core is simulated based on the point kinetics equations and six delayed neutron groups. Considering neutron absorber poisons and regarding the limitations of the xenon concentration measurement, a sliding mode observer is designed to estimate its value, and finally, a sliding mode control based on the sliding mode observer is presented to control the core power of reactor. The stability analysis is given by means Lyapunov approach; thus, the control system is guaranteed to be stable within a large range. The employed method is easy to implement in practical applications, and moreover,the sliding mode control exhibits the desired dynamic properties during the entire output-tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed observerbased controller in terms of performance, robustness and stability.

A Casimir-Dark Energy Nano Reactor Design—Phase One

A phase one design of a new free energy nano reactor is presented. The design is based on a basically topological interpretation of the Casimir effect as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. In particular we view dark energy, Hawking negative energy, Unruh temperature and zero point vacuum energy as being different sides of the same multi-dimensional coin. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so-called missing dark energy density of the cosmos. We start with a general outline of the theoretical principle and basic design concepts of a proposed Casimir dark energy nano reactor. In a nutshell the theory and consequently the actual design depend crucially upon the equivalence between the dark energy density of the cosmos and the faint local Casimir effect produced by two sides boundary condition quantum waves. This Casimir effect is then colossally amplified as a one internal quantum wave representing a Hartle-Hawking state vector of the universe pushing from the inside against the boundary of the universe with nothing balancing it from the non-existent outside. This strange situation becomes completely natural and logical when we remember that the boundary of the universe is a one sided M&#246bius like manifold. In view of the present theory, this is essentially what leads to the observed accelerated expansion of the cosmos. As in any reactor, the basic principle in the present design is to produce a gradient so that the excess energy on one side flows to the other side. Thus in principle we will restructure the local topology of space using material nanoscience technology to create an artificial local high dimensionality with a Dvoretzky theorem like 96 percent volume measure concentration. Without going into the intricate nonlinear dynamics and technological detail, it is fair to say that this would lead us to pure, clean, free energy obtained directly from the topology of spacetime via an artificial singularity. Needless to say, the entire design is based completely on the theory of quantum wave dark energy proposed by the present author for the first time in 2011 in a conference held in the Bibliotheca Alexandrina, Egypt and a little later in Shanghai, Republic of China. The quintessence of the present theory is easily explained as the Φ3 intrinsic Casimir topological energy where Φ=?(√5-1)/2 is produced from the zero set Φ of the quantum particle when we extract the empty set quantum wave Φ2 from it and find Φ-Φ2=Φ3 by restructuring space via conducting but uncharged plates similar to that of the classical Casimir experiments. Our proposed preliminary design of this Casimir-spacetime artificial singularity reactor follows in a natural way from the above.

0.4 kV小型水电站发电机中性线电流过大分析及处理

部分0.4 kV小型水电站发电机中性点直接接地,会导致中性线电流过大,机组发热,效率降低等现象。文中论述了0.4 kV小型水电站发电机中性线电流过大的主要原因,中性点接地电流过大的危害和解决办法。通过对单相接地时故障电容电流的分析计算,判断改造的可行性,结合朱树桥电站工程实例,给出了中性线的电压和电流计算方法,确定了选用接地电抗器的选型参数。本处理方案既抑制了发电机中性线电流,又符合继电保护的要求,达到了保障机组安全运行的目的,为小型水电站发电机中性点接地方式设计和改造提供参考依据。

加氢反应器温度测控方案探讨

本文主要介绍几种可用于加氢反应器的温度测量元件及其结构并讨论其优缺点。结合实际项目案列,阐述加氢反应器温度测控方案,包括T型梁热电偶、多点柔性热电偶、表面热电偶在加氢反应器温度测量中的组合应用,为加氢反应器温度测量方案提供参考。

基于Py-GC联用的煤快速热解实验研究

采用居里点裂解仪—气相色谱仪(Py-GC)联用的方法研究了4种煤的快速热解特性,分析了挥发分主要气相产物及其析出规律。结果表明,大于等于50%的挥发分在热解初期(t≤2 s)释放,采用箔片装载方式的居里点裂解仪完全热解1 mg煤样需要10 s;挥发分主要气相产物中,各气体组分的生成量(mmol/gcoal)顺序为H2>CH4>CO>CO2>C2(C2H6、C2H4)>C3(C3H8、C3H6);挥发分释放量随热解温度的升高而增加,相同热解条件下,次烟煤挥发分的释放率高于贫煤和无烟煤;H2和CH4的生成量依赖于热解温度,热解温度越高,H2和CH4的生成量越多;CO和CO2的生成量不仅与热解温度相关,而且与煤中的氧含量紧密相关,氧含量越高的煤热解生成的CO和CO2越多;C2和C3气体的生成量相对于其他气体很少,体积占挥发分气相产物的5%。

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函数法。该方法通过将点堆中子动力学方程组变成矩阵形式,利用指数函数为基函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。

临界反应堆阶跃正反应性输入时中子密度响应的近似修正解

通过修正单组缓发中子先驱核衰变常量A值，使点堆中子动力学方程单组缓发中子模型在正反应性阶跃输入时的数值计算结果趋近于六组缓发中子模型数值计算结果。在此基础上，用修正后的单组模型解析方法进行计算。结果表明：采用修正后的单组解析方法计算阶跃正反应性输入的中子密度响应，计算结果与六组的接近，满足工程计算精度要求，同时计算简便，避免了刚性问题，可以实现快速计算。