Fast Neutron Spectra from Natural Uranium Target Bombarded with High Energy Electrons

The numerical solution of the transport equation has the errors caused by the approximations used in the computational method. In the past estimations of these errors have been performed experimentally. In the present study, formulas to estimate the errors have been derived on the basis of the perturbation theory. This method enables us to deterministically estimate the numerical errors due to the iteration, spatial discretization and Legendre polynomial expansion of scattering transfer cross sections.

Using the error estimation method developed in the present study, two examples of error analyses were carried out to confirm its validity and applicability to error estimation for a practical purpose. The errors of the calculated tritium breeding ratio for ⁷Li in a infinite slab geometry were estimated, and they agreed well with the values predicted from direct calculation. As the second example, error analysis was carried out for one-dimensional nuclear calculations on two types of commercial fusion reactor blankets. In this analysis the tritium breeding ratio and the fast neutron leakage flux from the inboard shield were investigated, and the errors from different causes were quantitatively compared.     

小型压水堆压力容器内部三维流场计算

In the reactor safety analysis process, it is important to obtain an accurate flow field inside the pressure vessel. Taking the small pressurized water reactor as the research object, the computational fluid dynamics (CFD) method was used to calculate and analyze the internal flow field of the reactor pressure vessel, and the fuel assembly flow distribution and the lower head mixing characteristics were obtained. The results show that the maximum flow distribution coefficient of the fuel assembly is 1.032, the minimum value is 0.934, and the overall flow distribution is characterized by “large in the middle and small in the edge” under the high-speed symmetrical inlet condition of the two pumps. The flow vortex of the lower head is enhanced, and the uneven distribution of the flow distribution of the fuel assembly is increased, under the high-speed asymmetric inlet condition of the pump. The minimum mixing factor of the coolant flow at the core inlet was calculated to be 0.022 due to the insufficient mixing characteristics of the lower head.     

小型压水堆压力容器内部三维流场计算

反应堆安全分析过程中,获得反应堆压力容器内部准确的流场至关重要。以小型压水堆为研究对象,运用计算流体力学（CFD）方法对反应堆压力容器内部流场进行计算分析,获得燃料组件流量分配和下封头混合特性。结果表明:两泵高速对称入口条件下,燃料组件流量分配系数最大值为1.032,最小值为0.934,且流量整体分布呈现“中间大、边缘小”的特点;一泵高速非对称入口条件下,下封头流动漩涡增强,燃料组件流量分配的不均性增大;下封头混合特性计算得到堆芯入口冷却剂流量混合因子最小值为0.022,下封头冷却剂混合能力不足。      

超临界水通道内压降特性分析

超临界水冷堆是以超临界水作为冷却剂和慢化剂的第4代核能系统之一，超临界水在拟临界区附近剧烈的物性变化会给通道内的压降特性带来影响。本文分析了超临界条件下重力压降、加速压降和摩擦压降的特点，并对具体的计算方式提供了一些建议和参考：重力压降需考虑沿程的积分效应；基于隐式PKN公式得到了显式PKN公式，用于求解等温流动摩擦系数；采用CFD数值分析工具比较了超临界条件下不同摩擦关系式的异同，发现Kirillov公式与CFD计算结果较为接近。     

Plant Operator Performance Evaluation System

A plant operator performance evaluation system to analyze plant operation records during accident training and to identify and classify operator errors has been developed for the purpose of supporting realization of a training and education system for plant operators. A knowledge engineering technique was applied to evaluation of operator behavior by both event-based and symptom-based procedures, in various situations including event transition due to multiple failures or operational errors The system classifies the identified errors as to their single and double types based on Swain's error classification and the error levels reflecting Rasmussen's cognitive level, and it also evaluates the effect of errors on plant state and then classifies error influence, using “knowledge for phenomena and operations”, as represented by frames. It has additional functions for analysis of error statistics and knowledge acquisition support of “knowledge for operations”.

The system was applied to a training analysis for a scram event in a BWR plant, and its error analysis function was confirmed to be effective by operational experts.     

Statistical error estimation of the Feynman-α method using the bootstrap method

Applicability of the bootstrap method is investigated to estimate the statistical error of the Feynman-α method, which is one of the subcritical measurement techniques on the basis of reactor noise analysis. In the Feynman-α method, the statistical error can be simply estimated from multiple measurements of reactor noise, however it requires additional measurement time to repeat the multiple times of measurements. Using a resampling technique called “bootstrap method,” standard deviation and confidence interval of measurement results obtained by the Feynman-α method can be estimated as the statistical error, using only a single measurement of reactor noise. In order to validate our proposed technique, we carried out a passive measurement of reactor noise without any external source, i.e. with only inherent neutron source by spontaneous fission and (α,n) reactions in nuclear fuels at the Kyoto University Criticality Assembly. Through the actual measurement, it is confirmed that the bootstrap method is applicable to approximately estimate the statistical error of measurement results obtained by the Feynman-α method.     

Safety of Super LWR, (I) Safety System Design

This paper describes design concept of safety system of the high-temperature supercritical pressure light water cooled reactor with downward-flow water rods (Super LWR). Since this reactor is once-through cooling system without water level and coolant circulation, the fundamental safety requirement is keeping core coolant flow rate while that of light water reactors (LWR) is keeping coolant inventory. “Coolant supply from cold-leg” and “coolant outlet at hot-leg” are needed for it. The advantage of the once-through cooling system is that reactor depressurization induces core coolant flow and cools the core. The downward-flow water rod system enhances this effect because the top dome and the water rods supply its water inventory to the core like an “in-vessel accumulator.” The safety system of the Super LWR is designed referring to those of LWR in consideration of its characteristics and safety principle. “Coolant supply” is kept by high-pressure auxiliary feedwater system and low-pressure core injection system. “Coolant outlet” is kept by safety relief valves and automatic depressurization system. The Super LWR is equipped with two independent shutdown systems: reactor scram system and standby liquid control system. The capacities and the actuation conditions determined in this study are to be used in safety analysis.     

CFD analysis for thermal mixing in a subcooled water tank under a high steam mass flux discharge condition

A Computational Fluid Dynamics (CFD) analysis for a thermal mixing test was performed for 30 s to develop the methodology for a numerical analysis of the thermal mixing between steam and subcooled water and to apply it to Advanced Power Reactor 1400 MWe (APR1400). In the CFD analysis, the steam condensation phenomenon by a direct contact was simulated by the so-called condensation region model. Thermal mixing phenomenon in the subcooled water tank was treated as an incompressible flow, a free surface flow between the air and the water, and a turbulent flow, which are implemented in the CFX4.4. The comparison of the CFD results with the test data showed a good agreement as a whole, but a small local temperature difference was found at some locations. A sensitivity analysis was performed to find the reason of the temperature difference. The commercial CFD code of CFX4.4 together with the condensation region model can simulate the thermal mixing behavior reasonably well when a sufficient number of mesh distributions and a proper numerical method are selected.     

压力容器形状偏差对安全性能的影响

压力容器制造过程中总会存在形状偏差,设计者应能明确可接受的形状偏差是多少。本文以有限元应力计算为基础,分析了整体形状偏差所造成的筒体和封头的一次应力的变化情况及其对压力容器安全性能的影响,得出了一些具有普遍意义的结果,并以ＨＴＲ－１０反应堆压力容器为例,根据设计和制造中的具体情况,分析了可接受的形状偏差限值。     

Benchmark and parametric study of a passive flow controller (fluidic device) for the development of optimal designs using a CFD code

A passive flow controller or a fluidic device (FD) is used for a safety injection system (SIS) for efficient use of nuclear reactor emergency cooling water since it can control the injection flow rate in a passive and optimal way. The performance of the FD is represented by pressure loss coefficient (K-factor) which is further affected by the configuration of the components such as a control port direction and a nozzle angle. The flow control mechanism that is varied according to the water level inside a vortex chamber determines the duration of the safety injection.This paper deals with a computational fluid dynamics (CFD) analysis for simulating the flow characteristics of the FD using the ANSYS CFX 11.0. The CFD analysis is benchmarked against existing experimental data to obtain applicability to the prediction of the FD performance in terms of K-factor. The CFD calculation is implemented with Shear Stress Transport (SST) model for a swirling flow and a strong streamline curvature in the vortex chamber of the FD, considering a numerical efficiency.Based on the benchmark results, parametric analyses are performed for an optimal design of the FD by varying the control port direction and the nozzle angle. Consequently, the FD performance is enhanced according to the angle of the control port nozzle.     

熔盐球床堆堆芯入口热工水力特性数值分析

堆芯入口流场设计是小型固态燃料熔盐堆系统项目内容之一,它对反应堆结构的稳定性、堆芯温度和流场分布有着非常重要的影响。研究了熔盐流道流通面积变化对堆芯入口温度、流场分布及压降的影响,优化熔盐流道几何结构。以小型熔盐球床堆模型为研究对象,取符合实际边界条件的输入参数,通过改变熔盐流道流通面积,使用计算流体力学(Computational Fluid Dynamics,CFD)通用程序Fluent 16.0对堆芯入口内熔盐的热工水力特性进行数值模拟。在考虑实际下反射层流道的流通面积占比最大为18.14%下,研究了熔盐流道流通面积占比在区间[0,15.00%]变化。结果表明,堆芯活性区熔盐最高局部热点温度随熔盐流道流通面积比的增大而增高;堆芯入口内的压降随下反射层熔盐流道流通面积比的减小而增大;在径向方向上流进孔道的熔盐流速随着孔道远离堆芯位置而增大。本研究可为小型固态燃料球床熔盐堆优化设计提供一定的参考价值。     

一种新的编码故障树事故分析法

介绍了一种新的编码故障树的事故分析方法，并利用其对部分已发生过的灾难性事故进行分析与综合，指出人的可靠性研究与组织管理因素是提高系统可靠性的重要保证。     

双环路压水堆非对称入口条件下物理-热工特性研究

双环路压水堆存在反应堆入口流量、温度不对称的非正常运行工况。本文建立了基于CFD方法的反应堆整体三维流场模型,并耦合中子动力学计算程序和RELAP5程序,对这种非对称入口条件下的反应堆物理-热工特性进行了数值模拟。结果表明：反应堆入口流量不对称会加剧堆芯入口流量分配的不均匀性,并进一步导致局部功率变化,对反应堆安全不利;在入口温度不对称的条件下,冷却剂在下腔室的混合非常不充分,并导致堆芯入口温度分布不均匀,引起局部功率变化较大,对反应堆安全不利。     

Experimental CFD grade data for stratified two-phase flows

Stratified two-phase flows were investigated at two test facilities with horizontal test-sections. For both, rectangular channel cross-sections were chosen to provide optimal observation possibilities for the application of optical measurement techniques. In order to show the local flow structure, high-speed video observation was applied, which delivers the high-resolution in space and time needed for CFD code validation.The first investigations were performed in the Horizontal Air/Water Channel (HAWAC), which is made of acrylic glass and allows the investigation of air/water co-current flows at atmospheric pressure and room temperature. At the channel inlet, a special device was designed for well-defined and adjustable inlet boundary conditions. For the quantitative analysis of the optical measurements performed at the HAWAC, an algorithm was developed to recognise the stratified interface in the camera frames. This allows to make statistical treatments for comparison with CFD calculation results. As an example, the unstable wave growth leading to slug flow is shown from the test-section inlet. Moreover, the hydraulic jump as the quasi-stationary discontinuous transition between super- and subcritical flow was investigated in this closed channel. The structure of the hydraulic jump over time is revealed by the calculation of the probability density of the water level. A series of experiments show that the hydraulic jump profile and its position from the inlet vary substantially with the inlet boundary conditions due to the momentum exchange between the phases.The second channel is built in the pressure chamber of the TOPFLOW test facility, which is used to perform air/water and steam/water experiments at pressures of up to 5.0 MPa and temperatures of up to 264 °C, but under pressure equilibrium with the vessel inside. In the present experiment, the test-section represents a flat model of the hot leg of the German Konvoi pressurised water reactor scaled at 1:3. The investigations focus on the flow regimes observed in the region of the elbow and of the steam generator inlet chamber, which are equipped with glass side walls. An overview of the experimental methodology and of the acquired data is given. These cover experiments without water circulation, which can be seen as test cases for CFD development, as well as counter-current flow limitation experiments, representing transient validation cases of a typical nuclear reactor safety issue.     

Molecular Approach to Sodium Vapour Condensation,Rewetting and Vaporization in LMFBR Bundle under Hypothetical Accident Conditions

In the frame of safety analysis of Liquid Metal Fast Breeder Reactors (LMFBRs) under hypothetical Unprotected Loss-of-Flow (ULOF) conditions, two phase flow of sodium is simulated in a reactor core. Traditional approaches used in safety analysis codes to simulate sodium vapour condensation and vaporization rely upon application of macroscopic semi-empirical correlations for heat transfer and vapour condensation or evaporation rates. As an alternative to this macroscopic approach, we developed a microscopic methodology based upon the application of the basic laws of the kinetic theory for the determination of the evaporation and condensation rates of vapour in a reactor bundle. This microscopic approach is based upon a Monte Carlo simulation of the molecular trajectories, collision rates between vapour molecules and of the molecules with the surfaces of the claddings of the pins of a reactor bundle. The pins surfaces are treated in the Monte Carlo simulation as diffusely reflecting surfaces. Scattering of sodium particles is simulated with the “hard sphere” collision model. The “step splitting” technique is applied, which consists in separating the collisions dynamic calculation from collisionsless paths of the molecules. Vapour particles are assumed to condense on the surfaces of the pins when, after diffuse reflection, their velocity would be less than one third of the most probable velocity corresponding to the wall temperature. Rewetting of dried out regions of the cladding surfaces is simulated with a dynamic film model which computes the velocity distribution of the liquid across the film thickness and then the mean liquid film velocity. Evaporation of sodium molecules from the film yields a source of molecules which re-enter into the Monte Carlo calculation of the molecular dynamic approach. The coupling of the micro- and macroscopic models has been applied to the numerical simulation of an out-of pile sodium boiling experiment run at the Nuclear Research Center of Karlsruhe, Germany.     

压水堆高保真换料循环计算功能开发与验证应用

在自主开发的数值反应堆物理计算程序NECP-X基础上开发了压水堆的换料循环计算功能，并针对某M310机组首循环、第2循环和第3循环的启动物理实验，以及针对前2个循环的燃耗进行了精细建模计算。计算值与实测值的比较结果表明：首循环、第2循环和第3循环启动物理实验的临界硼浓度、控制棒价值、温度系数计算结果误差均较小，符合验收准则；不同燃耗深度下的临界硼浓度、堆芯功率分布与实测值的比较结果显示，稳定燃耗点处最大硼浓度偏差为-39ppm(1ppm=10^-6)，最大的组件功率误差小于4.5%，随着燃耗的加深，堆芯功率的分布逐渐展平，误差逐渐减小。计算结果表明NECP-X程序已经具备商用压水堆启动物理实验和多燃料循环的计算能力。     

Development of a “best representativity” method for experimental data analysis and an application to the critical experiments at the Toshiba NCA facility

For nuclear critical experiments, it is essential to certify similarities of the experiment with the objective of the actual reactor conditions or actual reactor equipment. To judge the applicability of the experimental data, the concept of a “representativity factor” has recently been adopted in the critical experiment field, particularly for fast breeder reactors and future reactor studies. In this study, we extended this concept to the design of a light water reactor system. We developed a new numerical evaluation method and a calculation system. The method is based on a linear combination of the sensitivity coefficient vector of an experiment in which the representativity factor to the target system is maximized to utilize experimental data effectively. Simultaneously, using the measurement data of critical experiments, the method enables us to evaluate calculation errors caused by errors or uncertainties of physical parameters. The derivation of the new calculation method is explained first. We then qualify it with a sample calculation, presenting numerical results for three kinds of critical experiments conducted at the Toshiba Nuclear Critical Assembly facility. Finally, the results are compared with those of an extended bias factor method to clarify the performance of the new method.     

Three-dimensional analysis of flow characteristics on the reactor vessel downcomer during the late reflood phase of a postulated LBLOCA

A three-dimensional CFD analysis has been performed on the flow characteristics in the reactor vessel downcomer during the late reflood phase of a postulated large-break loss-of-coolant accident (LBLOCA), in order to validate the modified linear scaling methodology that was applied in the MIDAS test facility of Korea Atomic Energy Research Institute. The vertical and circumferential velocity similarities are numerically tested for the 1/1 and 1/5 linear scale models for the APR1400 reactor vessel downcomer. The effects of scale on flow patterns, pressure and velocity distributions, and the impinging jet behavior are analyzed with the FLUENT code. In addition, a simplified half cylinder model with a single emergency core cooling (ECC) nozzle is numerically tested to investigate the scale effect on the spreading width and break-up of ECC water film. The qualitative and quantitative results indicate that the 1/5 modified linear scale model of the reactor vessel downcomer would reasonably preserve the hydrodynamic similarity with APR1400.     

数值堆热工流体程序CVR-PACA验证及典型应用

谱元方法是一种高精度的数值计算方法,采用该方法开发了数值堆高精度热工水力并行CFD计算程序CVR-PACA。应用CVR-PACA对单棒光棒通道湍流流场、3×3光棒棒束湍流流场、Matis-H压水堆棒束通道基准题、19棒带绕丝组件通道湍流流场进行了仿真计算。通过与实验测量值对比,研究定量验证了大涡模拟(LES)模型及非稳态雷诺时均(URANS)模型对各类棒束通道流场预测的准确性。算例在建模过程中采用网格分裂技术实现了复杂几何的纯六面体网格划分,用于支撑谱元方法计算。研究较为全面地积累了高精度谱元方法模拟流场流动及换热的建模经验,获取了各类棒束通道内丰富的流动和换热细节,获得的建模经验能更加精准有力地指导相关设计的优化改进。     

严重事故下反应堆压力容器下封头耦合烧蚀传热分析

核电站严重事故发生后,反应堆压力容器（RPV）固壁在熔池作用下会发生烧蚀、减薄。开展RPV下封头耦合烧蚀传热分析对堆坑注水有效性论证和RPV剩余壁厚确认有重要的理论指导意义。本文以CPR1000反应堆压力容器为研究对象,在FLUENT 17.2平台下,基于动态网格方法和UDF二次开发,构建了综合考虑RPV固壁瞬态烧蚀与导热、RPV内壁热流密度再分布及RPV外壁过冷沸腾的全耦合计算模型,获取了9 000 s内的堆坑两相流场分布和RPV固壁烧蚀温度场,分析确定了最小剩余壁厚和发生位置。结果表明：使用动态网格捕捉壁面烧蚀的方法可行,本文全耦合计算模型在分析RPV固壁瞬态烧蚀过程方面有一定优势。