Thermal unsteady regimes in one-dimensional flow of heat generating fluids

The thermal unsteady regimes in one-dimensional flow of heat generating fluids, caused by flow-rate changes, are studied when heat is transferred to surroundings of constant temperature. The heat generation is a function of time and temperature. General results are then applied to solve particular situations. Some numerical results are related and a short discussion is given.     

Power series solution method for solving point kinetics equations with lumped model temperature and feedback

Point kinetics equations are stiff differential equations, and their solution by the conventional explicit methods will give a stable consistent result only for very small time steps. Since the neutron lifetime in a LMFBR is very short, the point kinetics equations for LMFBRs become even stiffer. In this study the power series solution (PWS) method is applied for solving the point kinetics equations for a typical LMFBR. A Fortran program is developed for accident analysis of LMFBRs with the PWS method for solving the point kinetics and a lumped model for solving the heat transfer equations. A new technique is developed with fixing factor to find out the average temperature at the peak power node (PPN) without performing temperature calculations at all axial nodes in a reactor fuel pin. The temperature at PPN also decides whether the reactor is within the design safety limit (DSL) or it has entered a serious transient that may lead to an accident. The coupled heat transfer and point kinetics models for a peak power node give the average fuel, clad and coolant temperatures. For the transient over power accidents (TOPA), this is the best way for calculating the temperature, with minimum amount of computations. TOPA analyses are carried out with PWS method. It is found that the PWS methodology uses a small number of numerical operations, while the computational time and the accuracy are comparable with the available fast computational tools. This methodology can be used in nuclear reactor simulation studies and accident analysis.     

Analysis of transient heat conduction with phase changes by a boundary integral equation method

A combined method of a latent heat model and a boundary integral equation is presented for solving transient heat conduction problems with solidification and melting. Some typical problems are solved in order to confirm the validity of the proposed method. The present results show good agreement with results obtained by using finite difference, finite element and boundary element methods. It is shown that the method admits the use of rather large time steps and a relatively coarse mesh. The computational property of the function which is introduced in deriving the boundary integral equation is discussed in connection with a condition for smooth motion of the interface.     

A Monte Carlo approach to the theoretical prediction of temperature noise in LMFBR sub-assemblies

A candidate technique for detecting incipient blockages in the fuel sub-assemblies of liquid-metal-cooled fast-breeder reactors is the measurement of coolant outlet temperature fluctuations caused by turbulence. A theoretical basis for the method is required, and one model is discussed in this paper.

The model requires the paths of individual fluid particles to be traced, allowing their motions to vary randomly, subject to certain constraints of the turbulent motion. It is a Monte Carlo method, already used successfully in predicting the transport of scalar fluctuations. Its advantage is that it allows actual time-dependent temperatures to be computed, and so various methods of analysis (power spectral density, amplitude probability distribution, for example) can be examined. The effect of heat conduction is neglected at present.

Computed results show the way in which mean temperature and rms temperature-noise profiles develop in a turbulent flow in a pipe downstream of a plane at which a steady mean profile is maintained. Power spectral densities and amplitude-probability densitiesare presented, and it is shown how an amplitude-probability density plot distinguishes between a temperature-gradient input profile and a gaussian input profile.

Comparisons are given with experimental measurements made in representative heated pin rigs in sodium, with good agreement. Some of the problems associated with extrapolation to real sub-assemblies are discussed.     

Tritium Isotope Separation by CO2 Laser Irradiation at Dry Ice Temperature

A computational method based on boundary element method (BEM) has been developed to analyze transient temperature distribution in a three-dimensional solid having non-linear boundary condition (for example boiling or thermal radiation). To obtain high numerical accuracy, the heat transfer coefficient which depends on the surface temperature was approximated as a linear combination of interpolation functions with respect to time and analytical time integration of the non-linear term included in boundary integral equation was made.

To investigate feasibility of the present method, it was applied to calculations of the temperature distribution in an infinite flat plate cooled on one side. The heat transfer co-efficient of cooling surface was in proportion to n-th power of the surface temperature. Results are (1) the method has given a stable solution for non-linear boundary value problems such as conventional BEM could not solve, (2) it has given an accurate solution for large time increment except for first time step, and (3) an optimal relaxation factor decreases with strength of non-linearity of the heat transfer coefficient.

Applying the method to thermal analysis of limiter and divertor plate installed in a fusion test facility and fusion reactor respectively, availability of the method has been confirmed.     

Chemical Tracer Method for Measurement of Flow Rates in Closed Conduits

Thermal output in a nuclear power plant is verified by a calorimetric heat balance on the secondary system of the power plant. The calorimetry involves the precise measurement of the feed water flow rate which should be designed to have ±1:0% of uncertainty. However, the indication of feed water flow rate obtained by a differential pressure measurement across a venturi can be affected by instrument errors, fouling, or a poorly developed velocity profile. These factors can lead to an inaccurate mass flow rate and consequently, an inaccurate estimate of power. The purpose of this study is to develop verification methods with accuracy better than ±0:5% for high-precision flow measurement to be used for measuring feed water flow rate. Such an improvement saves electric power. For a typical Korean nuclear power plant of 1,000MW, 10MW would be potentially saved. This chemical tracer method is a testing process using a tracer, which can be applied to quantify losses in electrical output caused by incorrect measurement of feed water flow rate. This method has a good response to changes in the flow rate. An accuracy better than 0.5% is expected for feed water flow measurement, provided that the feed water system is stabilized during the test.     

电子束辐照钻石热传导过程的数值模拟

应用Matlab程序，对钻石内部和边界采用不同的差分迭代格式，计算模拟了其中的热传导过程。数值计算结果，所用方法与PDE工具箱的计算精度相当，但计算时间明显缩短。同时讨论了辐照时间、吸收剂量率、环境温度等因素对于钻石内部温度分布的影响，这对于钻石的辐照工艺具有重要意义。     

Development of versatile nuclear heating calculation system in MARBLE

A versatile nuclear heating calculation system is developed in MARBLE, a neutronics calculation platform based on the object-oriented language. The system provides a variety of heating calculation methods, from the conventional simple methods based on energy-independent Q-values to a detailed method based on NJOY/HEATR. A particular feature is in hybrid methods that consider energy dependence employed in NJOY/HEATR in the system. The hybrid methods provide tools to assess errors in the simple methods and to evaluate the heat transport property by neutrons and photons precisely. The accuracy of the hybrid methods and the errors in the simple methods are investigated in a Monju design calculation. It is confirmed that the hybrid methods realize the nuclear heating by the detailed method within an accuracy of 0.1%. The neglect of incident energy dependence of the fission Q-value in the simple methods causes clear overestimation in the Q-value but its influence on the total heating is less than 1%. In the heat transport evaluation, it is observed that the heat transported from the fuel regions mainly appears in the blanket regions and the contribution by neutrons is larger than that by photons.     

可靠性数据威布尔分析中秩评定算法改进研究

随着概率安全分析工作的深入发展,可靠性数据及其分析工作越来越显示出其重要的价值和作用.威布尔分析方法是一种常见的可靠性数据分析方法,并被广泛应用于工程实际.在总结了威布尔分析方法中应用较为广泛的几种中位秩计算公式的基础上,利用遗传算法对其一般表达式中的待定参数进行优化,进而提出了改进型的中位秩计算公式.实例证明利用改进后的中位秩计算公式,可以减小秩评定过程的误差,提高可靠度计算的精度.     

HD－8004型NaI（T1）闪烁谱仪测量自然γ能谱的精度

本文简述了自然γ能谱测量与分析精度的重要性，采用ＮａＩ（Ｔ１）闪烁谱仪进行自然γ能谱测量及分析的基本原理与方法。介绍了低水平自然γ能谱测量时为提高精度拟采取的措施；简介了ＨＤ－８００４型ＮａＩ（Ｔ１）闪烁谱仪的结构与指标；提供了为油田部分岩样进行自然γ能谱测量与分析的应用效果等。这对自然γ能谱测量工作的广泛开展及其精度的研究的深入探讨是十分有益的。     

放射性核废料自埋过程中的热量阈值

针对恒释热率热源接触熔化，提出了热量阈值的概念。分析计算了典型反应堆核废料自埋接触熔化过程中的热量阈值和达到阈值的时间以及相应的熔化深度，并与相关文献结果进行比较，指出了相关文献中的一些错误，得出了一些有意义的结论。     

放射性同位素X荧光测井技术的研究

对放射性同位素源Ｘ荧光测井技术的井液效应，井壁不平度效应和基体效应分别提出了实用的校正技术。野外锶矿Ｘ荧光测井试验表明：Ｘ荧光测井确定的锶矿层厚度和平均品位与传统的岩芯化学分析结果相比较，其相对误差〈１０％，符合锶矿储量计算要求；Ｘ荧光测井可在井场实时提供测井结果，而耗时却短得多。     

基于衰变热的堆芯重要核素选取

衰变热在反应堆设计及安全分析中至关重要,目前计算衰变热主要基于行业标准和专用程序两种方法。通过对PWR燃料组件分别采用两种方法进行计算分析,相互验证了结果。详细分析了停堆不同时刻多种核素对衰变热的贡献,筛选出主要贡献者,为堆芯源项核素的选择提供参考。结果显示约50个核素即可包络停堆后100 h~50 a内95%以上的衰变热贡献。并对标准与程序结果的差异进行了分析,提出了标准适用范围的建议。     

Measurement and Evaluation on Pulsing Characteristics and Experimental Capability of NSRR

The NSRR programme is in progress in JAERI using a pulsed reactor to investigate fuel behaviors under the reactivity-initiated accident conditions. Pulsing characteristics and experimental capability, especially heat deposition in test fuel rods given by a single pulse are key parameters to this purpose.

In pulsing performance tests, it has been ascertained that the maximum pulsing with 4.67$ (=3.41%δk) brings peak reactor power of 21,100 MW and core energy release of 117 MW·sec. The calculated time responses of reactor power, fuel temperature and cladding surface temperature as well as these maximum values at various pulse sizes agreed well with measured data. In addition, it has been also ascertained by measurement as well as analysis that there are no essential differences in pulsing characteristics between the pulsing from critical and that from subcritical.

The heat deposition in a test fuel rod given by a single pulse is much enough as predicted, and a 2.6% enriched BWR type fuel rod gains about 230cal/g-UO₂ in the maximum pulsing. In case of irradiation of clustered five test fuel rods by a single pulse, heat deposition reduces by about 20% for a surrounding rod and about 40% for a center rod in comparison with that in a single rod irradiation.     

Exact Error Estimation for Solutions of Nuclide Chain Equations

The exact solution of nuclide chain equations within arbitrary figures is obtained for a linear chain by employing the Bateman method in the multiple-precision arithmetic. The exact error estimation of major calculation methods for a nuclide chain equation is done by using this exact solution as a standard. The Bateman, finite difference, Runge-Kutta and matrix exponential methods are investigated.

The present study confirms the following. The original Bateman method has very low accuracy in some cases, because of large-scale cancellations. The revised Bateman method by Siewers reduces the occurrence of cancellations and thereby shows high accuracy. In the time difference method as the finite difference and Runge-Kutta methods, the solutions are mainly affected by the truncation errors in the early decay time, and afterward by the round-off errors. Even though the variable time mesh is employed to suppress the accumulation of round-off errors, it appears to be nonpractical. Judging from these estimations, the matrix exponential method is the best among all the methods except the Bateman method whose calculation process for a linear chain is not identical with that for a general one.     

Radiation Dosimeters for High Dose by Commercial PMOS Transistors Using Normalized Drain Current as Dosimetric Parameter

A PMOS transistor that is commercially available device can function as a practical radiation dosimeter for high dose. A new dosimetric parameter, that is shift rate of drain current, is proposed and demonstrated to reduce the possible errors of measurement. The calibration curve of dosimetric parameter vs. radiation dose shows a very linear characteristic. Some modifications were suggested to compensate the room temperature effects. The gate bias can be applied to further increase the dosimetric sensitivity and extend the dose of radiation measurement to a lower range.     

Fluid-to-fluid scaling of heat transfer in circular tubes cooled with supercritical fluids

Experimental investigations of heat transfer at prototypical conditions of supercritical water cooled reactors (SCWRs) are strongly limited due to their huge technical and financial efforts required. One of the possible solutions is the application of model fluids, which have much lower critical pressure and critical temperature. Model fluid technique has been widely applied in the thermal-hydraulic studies of nuclear engineering. In spite of growing activities of heat transfer at supercritical conditions using model fluids, there does still not exist any reliable fluid-to-fluid scaling methods, to transfer the test data in model fluids directly to the conditions of prototype fluid. This paper presents a fluid-to-fluid scaling method for heat transfer in circular tubes cooled with supercritical fluids. Based on conservation equations and boundary conditions, one set of dimensionless numbers and the requirements of a complete scaling are determined. Scaling of pressure and temperature ensures the similarity of thermo-physical properties of various fluids. A new dimensionless number, presenting the product of the so-called pseudo Boiling number, Reynolds number and Prandtl number, is applied to scale heat flux. The distortion approach is used to scale mass flux. The scaling of heat transfer coefficient is based on Nusselt number. In addition, a new approach is introduced to validate the scaling law. The validation results show good feasibility and reasonable accuracy of the proposed scaling law. Assessment of scaling factors of various parameters indicates the high feasibility of Freon-134a as model fluid for SC water. Some guidelines can be derived for the future experimental investigations on heat transfer at supercritical pressures using model fluid techniques.     

Implementation of field-aligned coordinates in a semi-Lagrangian gyrokinetic code for tokamak turbulence simulation

Field-aligned coordinates have been implemented in the gyrokinetic semi-Lagrangian code NLT,Ye et al (2016 J.Comput.Phys.316 180),to improve the computational efficiency for the numerical simulations of tokamak turbulence and transport.4D B-spline interpolation in fieldaligned coordinates is applied to solve the gyrokinetic Vlasov equation.A fast iterative algorithm is proposed for efficiently solving the quasi-neutrality equation.A pseudo transform method is used for the numerical integration of the gyro-average operator for perturbations with a high toroidal mode number.The new method is shown to result in an improved code performance for reaching a given accuracy.Some numerical tests are presented to illustrate the new methods.     

200MW 核供热堆的非线性动态模型

本文为２００ＭＷ核供热堆建立了一个用于大功率运行范围控制系统仿真的非线性动态模型。模型除了采用点中子动态方程、集中参数的慢化剂温度和燃料温度负反馈等压水堆控制系统常用的建模方法之外，为了使模型适用于大功率运行范围，还重点考虑了主回路自然循环对堆芯内冷却剂和燃料棒之间的传热系数、主换热器换热系数、主回路时间常数的影响，以及二回路流量变化引入的非线性。仿真结果表明，模型具有较高的精度，可用于控制系统仿真。     

Computational-experimental method of evaluating the measurement error in the fuel-element cladding temperature during the simulation of emergencies

The objective of this work is to develop a computational-experimental method of determining the systematic error in measurements of the temperature of cooled fuel-element cladding using a thermocouple secured along the generatrix of the cladding. A method of nondestructive diagnostics of the quality of the thermal contact of the working end of a thermocouple with fuel-element cladding and the conditions for its heat exchange with the coolant and their effect on the measurement error in the temperature of the cooled cladding is examined. The method is based on thermal probing of a thermocouple by passing a current through the thermal electrodes and recording and processing the responses in the presence and absence of the coolant. A relation is derived for the systematic error with stationary and linearly growing cladding temperature. The experimental and computational results for the systematic errors are presented.