Procedure for probabilistic safety assessment of leaks and breaks of piping systems

The estimation of leak and break frequencies in piping systems is part of the probabilistic safety assessment of technical plants. In this paper, a statistical method based on the evaluation of German operational experience for piping systems with different diameters is described because an earlier estimation has been updated and extended introducing new methodical aspects and data. A major point is the inclusion of structural reliability models based on fracture mechanics calculation procedures. As an example of application the statistical estimation method for leak and break frequencies of piping systems with a nominal diameter of 50 mm (the volume control system of a German pressurized water reactor) was updated. Moreover, the evaluation of the operational experience was extended to 341 years with respect to cracks, leaks and breaks in the volume control system of German pressurized water reactors (PWR). Using the actual database, new calculations of leak and break frequencies have been performed and the results have been compared with previous values.     

基于多因素元件停运模型的电网失负荷计算

电网失负荷计算能反映电网事故的严重程度,是电网运行安全风险评估的重要内容。基于多因素对电网元件停运概率的影响,分析了电网元件停运概率的可修复失效模型、老化失效模型及天气相依的偶然失效模型三者之间的关系,采用并集的概念建立了电网元件停运概率模型,在此基础上提出了一种电网失负荷计算方法。以IEEE-RTS79系统为例,采用蒙特卡洛法对系统状态进行抽样,通过该失负荷算法计算出电网失负荷概率及失负荷量,验证了该种方法的有效性和可行性。     

合空变涌流谐波对直流系统换相失败的影响及分析方法

变压器空载合闸会产生含有大量谐波成分的励磁涌流,多重谐波综合作用会对直流系统造成影响,引发换相失败。为此,首先通过谐波换相系数分析得出直流系统换相失败原因为多重谐波中低次谐波的影响;其次通过基波电压幅值变化与过零点位移两个方面定义谐波综合影响因数,评价多重谐波对直流系统换相过程的影响程度;再以实际宜华±500kV直流输电系统仿真模型,结合1 000kV主变模型进行仿真计算,计算谐波综合影响因素。研究结果验证了仿真过程中7次换相失败的发生。     

Power station condensers their design and failure modes

The steam condenser plays an essential part in conventional and nuclear power generation. It is often neglected, by not being inspected regularly, by not maintaining tubes in a clean condition and not ensuring the cooling water is in a suitable chemical state to preserve tube cleanliness. Consequently, its efficiency suffers and if tubes begin to fail then an expensive episode of repairs and unreliability becomes apparent. This paper explains the role that the condenser plays and describes some of the damage mechanisms that affect the entire condenser. Those mechanisms will continue to cause leaks until the root causes of the failures are identified and changes made to materials, water treatment, or plant operations to eliminate them. This article describes some of the more common condenser tube failure mechanisms and provides a brief discussion of how they might be prevented.     

A sensitivity study in probabilistic fracture mechanics analysis of light water reactor carbon steel pipe

Through the efforts in leak-before-break research for light water reactor pipings based on deterministic fracture mechanics analysis, simple models which evaluate pipe fracture behavior are being established. Using these models it is also becoming possible to apply probabilistic fracture mechanics analysis. This paper describes an example of such an analysis, using these proposed models.

Since the authors' interests are in the range of uncertainty of the calculated failure probability, the effects of changes in the input parameters or the analytical conditions are also estimated by a sensitivity analysis. The results show that the calculated failure probability may be influenced significantly by changes in parameters concerning initial crack size distributions, and that effects due to a change in the leak detection model may appear after long operation of the plant.     

An assessment of failure probability in elastic-plastic conditions where stable tearing has occurred

An analysis is presented for calculating the failure probability of a structure subject to general elastic-plastic loading and where the fracture mode is ductile. The main statistical variables considered are fracture toughness, flow stress and defect size.The analysis is based on a development of the R6 methodology of defect assessment. The concept of a maximum load locus is developed from the failure assessment line. The maximum load locus is used to predict those combinations of materials properties and defect size that might combine to predict structural failure after some stable crack growth. The method of determining the maximum load locus is described and some examples presented.The maximum load locus is used to estimate the failure probability on the first loading of a structure. It is also shown that the maximum load locus can be used to estimate the failure probability of a proof loaded structure where, in general, there may be a change in the dominant failure mode between proof and fault loadings. Detailed examples are presented to illustrate the analysis.     

A procedure for estimation of pipe break probabilities due to IGSCC

A procedure has been developed for estimation of the failure probability of weld joints in nuclear piping susceptible to intergranular stress corrosion cracking. The procedure aims at a robust and rapid estimate of the failure probability for a specific weld with known stress state. Random properties of the crack initiation rate, the initial crack length, the in-service inspection efficiency, and the leak rate, are taken into account. A computer realization of the procedure has been developed for user-friendly applications by design engineers. Some examples are considered to investigate the sensitivity of the failure probability to different input quantities.     

Locating a leaking crack by safe stimulation

A few Zr-2·5 Nb alloy pressure tubes in CANDU nuclear reactors have leaked through cracks that have grown by delayed hydride cracking (DHC). In some instances, tubes contained confirmed leaks that were leaking at a rate too low for precise identification of the leaking channel. Controlled stimulation of DHC can be used to help locate these leaks by extending the crack and increasing the leak rate without approaching crack instability. In the event of a leak being detected, a plant operator can gain time for leak location by a heating and unloading manoeuvre that will arrest crack growth and increase the critical crack length. This manoeuvre increases the safety margin against tube rupture. If required, the operator can then stimulate cracking in a controlled manner to aid in leak identification. Sequences of temperature and load manoeuvres for safe crack stimulation have been found by laboratory tests on dry specimens and the efficacy of the process has been demonstrated, partly in a power reactor, and partly in a full-scale simulation of a leaking pressure tube.     

The effect of characteristic crack sizes on the leak-before-break case of pressure vessels and piping with multiple cracks

The Leak-Before-Break (LBB) case of pressure vessels and piping is achieved with the sufficient margin between detectable leak and catastrophic break. Therefore, the respective characteristic crack sizes, i.e. leak size (the crack size at which leakage amount is great enough to be detected) and the break size (the crack size at which crack propagation becomes unstable) are two important governing parameters for the LBB case. In multiple crack situations, the initial crack distribution and crack coalescence behavior are also LBB governing factors. The multiple crack condition related parameters would affect the LBB margin with the characteristic crack sizes together. The effects of multiple cracks on the LBB case, with respect to the different characteristic crack sizes are investigated in the present article by means of computer simulation. The simulation results show that, in multiple crack situation, the LBB margin is not so sensitive to characteristic crack sizes as in single crack situation.     

兆瓦级风力机结构系统可靠性分析的样本分数阶矩最大熵方法

以兆瓦级风力机塔架和叶片极限载荷的概率外推模型为基础,结合载荷动态响应峰值的独立同分布假设和三参数威布尔模型,外推获取了正常湍流和极端湍流强度条件下风力机关键部件长期服役载荷概率分布;进一步通过无量纲极值统计量定义系统失效的结构可靠性状态函数,结合样本分数阶矩和最大熵理论提出兆瓦级风力机关键部件结构可靠性分析的数值方法,对比湍流模型对兆瓦级风力机关键部件结构失效概率的影响。计算结果表明：样本分数阶矩最大熵方法能有效重构结构可靠性状态函数的概率分布;基于无量纲极值统计量的系统可靠性建模方法能有效表征风力机关键部件耦合相关失效问题,结合该文方法可获得系统失效概率的准确预测结果;湍流模型对风力机结构失效概率影响较大,难以预先判定何种模型将得到结构失效概率的保守预估结果,需结合IEC 61400-1标准中的设计载荷工况细致分析后才能确定。     

Enhancement of leak rate estimation model for corroded cracked thin tubes

During the last couple of decades, lots of researches on structural integrity assessment and leak rate estimation have been carried out to prevent unanticipated catastrophic failures of pressure retaining nuclear components. However, from the standpoint of leakage integrity, there are still some arguments for predicting the leak rate of cracked components due primarily to uncertainties attached to various parameters in flow models. The purpose of present work is to suggest a leak rate estimation method for thin tubes with artificial cracks. In this context, 23 leak rate tests are carried out for laboratory generated stress corrosion cracked tube specimens subjected to internal pressure. Engineering equations to calculate crack opening displacements are developed from detailed three-dimensional elastic-plastic finite element analyses and then a simplified practical model is proposed based on the equations as well as test data. Verification of the proposed method is done through comparing leak rates and it will enable more reliable design and/or operation of thin tubes.     

Failure probability of nuclear piping due to IGSCC

A simple model for the estimation of the pipe break probability due to IGSCC is developed and discussed. It is partly based on analytical procedures, partly on service experiences from the Swedish BWR program. Some rough estimates of the resulting break probabilities indicate that further studies are urgently needed. A sensitivity study is performed and it is found that the uncertainties about the initial crack configuration are the most important contributors to the total uncertainty. The results of inservice inspection are studied and it is found that the inspection intervals need to be shortened if a significant reduction in the failure probabilities is to be obtained.     

The effects of air leaks on solar air collector behaviour

The construction of conventinal solar air collectors and the fact that they will operate with a significant pressure difference between the heated air stream and ambient, suggests that significant quantities of air may leak into or out of them. A search of the literature reveals no consideration of the effects these air leaks may have on the validity of collector efficiency measurements, on the efficiency itself, or indeed what the meaning of efficiency is under such operating conditions. This paper discusses the meaning of collector efficiency when leaks into the collector occur, analyses the effects on efficiency measurements, and solves the collector efficiency for the simple case of a constant leakage rate along the collector. Assuming that air leaking in from ambient can replace deliberate fresh air supply to the load as in building heating, then significant measurement errors are made if air leaks in to the collector are not accounted for. Further, the collector efficiency is increased over the no leak case, so that complex construction methods to make the collector air tight are probably not warranted.     

一起罕见的GK1c型机车冷却风扇偶合器故障的分析与处理

介绍了GK1c型机车冷却风扇偶合器的概况及其常见故障现象和处理方法。针对一起罕见的泵轮轴断裂故障进行了系统分析，简单介绍了对此故障的处理方法，并提出了一些建议。     

The relationship between load factors and failure probabilities determined from a full elastic-plastic probabilistic fracture mechanics analysis

The premise of assessing defects from an estimate of the failure probability, rather than from an estimate of the minimum load to cause failure, is discussed.A procedure is presented for incorporating a full elastic-plastic failure analysis into probabilistic fracture mechanics. This is based on the failure avoidance diagram developed by Milne et al.² and the probability of fracture for any assessment point on the diagram.Numerical examples are presented where failure probabilities are compared with the load factors necessary to elevate the assessment point onto the failure avoidance curve. Both absolute and time-dependent failure probabilities are considered. In general, constant load factors do not correspond to constant failure probabilities. The relationship between the two factors depends on the distribution of materials parameters used. General applications for the consideration of a probabilistic assessment of defects are discussed.     

Effect of spatial correlation on the failure probability of pipelines under corrosion

Corrosion in pipelines has been probabilistically modeled. However, the potential effect of spatial correlation of corrosion defects, in several segments of a pipeline, on its failure probability has not received much attention.In this paper, several degrees of spatial correlation are assumed for the corrosion in determined segments of a pipeline and their effects on the global reliability are examined.The pipeline is assumed to be a series system. The failure mode is considered to be controlled by the stresses due to internal pressure and the presence of corrosion. Component reliability is calculated by First Order Second Moment approximations. First order bounds are used to define the limits for the global failure probability by assuming first, either no correlation (independent pipeline segments) and, secondly, perfect correlation between segments.Then, second order bounds are estimated to improve the calculation of the failure probability by including the correlation coefficients mentioned above.The correlation degree between failure modes at two pipeline segments increases with the degree of correlation of the corrosion initial depths located at these segments. Also, for a correlation coefficient between corrosion depths larger than 0.6, its contribution to the correlation between failure modes becomes significant and, therefore, should be accounted for.When the specific correlation degree between corrosion defects at adjacent pipeline segments is considered in the calculation of an example pipeline failure probability, this probability is narrowly bounded between 0.58 and 0.59, as compared to the usual practice where this correlation is assumed to be either 0 or 1 for which the failure probability is bounded between 0.49 and 0.79.The formulation may be used to set optimal maintenance schedules for pipelines under corrosion.     

基于混合量测状态估计的保护隐性故障检测系统

继电保护装置的隐性故障可能导致装置失效,不能有效发现电力系统故障,严重时甚至引起电网连锁故障,目前尚缺乏有效手段对其进行检测。为此提出利用SCADA及WAMS采集电网数据进行混合量测状态估计得到系统状态作为参考值,将该参考值与保护信息系统接受的继电保护装置测量数据进行比较,若差值超过预设门槛值,则可判定保护装置存在隐性故障,并在此基础上建立隐性故障检测系统。算例测试结果表明,该系统能在稳态时长期在线检测隐性故障,且在节点量测信息出现偏差时仍能有效检测隐性故障。     

Probabilistic fracture mechanics analysis of nuclear piping considering variation of seismic loading

In conventional probabilistic fracture mechanics (PFM) analyses, seismic loading is considered as a large deterministic value, although there exists the variation of the seismic load as well as response of building and components. On the other hand, such stochastic behaviours have already been taken into account in the field of seismic probabilistic safety assessment. This paper proposes a new PFM model for nuclear piping that takes into account the variation of seismic loading. The distribution in ground acceleration is modelled with the seismic hazard curve. The distribution in piping response during a seismic event is modelled with a log–normal distribution. Since the seismic load has large variation, when not adopting an upper limit to the distribution in seismic stress, the break probability calculated from the present PFM analysis becomes equal to the probability that the seismic stress exceeds the collapse stress of a sound pipe. This implies that the existence of a crack has no effect in these PFM analyses, and this result does not satisfy the purpose of PFM analysis to evaluate the failure probability per crack. Therefore, the seismic stress was limited to the collapse stress of a sound pipe in the present PFM analysis to evaluate the conditional break probability per crack.     

Equivalent life distribution and fatigue failure probability prediction

Equivalent fatigue life distributions under two-level cyclic stress are analyzed experimentally, and a model of describing equivalent life distribution is presented. Based on the equivalent life distribution model, an “equivalent damage – equivalent life distribution” method is developed to predict fatigue failure probability under variable amplitude loading. The underlying principles are fatigue damage accumulation rule and “load cycles – fatigue life” interference theorem. In the equivalent damage – equivalent life distribution method, two parameters, i.e. mean and standard deviation of the (equivalent) life distribution are used to describe cumulative fatigue damage effect. A basic feature of the equivalent damage – equivalent life distribution method is its capability of reflecting the loading history dependent change of the equivalent life distribution. Tests under multi-level stress show a good agreement between predicted fatigue failure probability and the test results.     

Analytical and experimental investigation of small-scale unintended releases of hydrogen

Knowledge of the concentration field and flammability envelope from a small-scale hydrogen leak is an issue of importance for the safe use of hydrogen. A combined experimental and modeling program is being carried out by Sandia National Laboratories to characterize and predict the behavior of small-scale hydrogen releases. In contrast to the previous work performed by Sandia on large, momentum-dominated hydrogen leaks, these studies are focusing on small leaks in the Froude number range where both buoyant and inertial forces are important or, in the limit, where buoyancy dominates leak behavior. In the slow leak regime-buoyant forces affect the trajectory and rate of air entrainment of the hydrogen jet leak and significant curvature can occur in the jet trajectory. Slow leaks may occur from leaky fittings or o-ring seals on hydrogen vehicles or other hydrogen-based systems where large amounts of pressure drop occur across the leak path. Low-pressure electrolyzers or vents on buildings or storage facilities containing hydrogen are also potential sources for slow leaks.