Investigation on the interaction effect of two parallel axial through-wall cracks existing in steam generator tube

It is commonly required that steam generator tubes wall-thinned in excess of 40% should be plugged. However, the plugging criterion is known to be too conservative for some locations and types of defects and its application is confined to a single crack. In the previous study, the conservatism of the present plugging criterion of steam generator tubes was reviewed and a crack coalescence model applicable to steam generator tubes with two collinear axial through-wall cracks was proposed. Since parallel axial cracks are more frequently detected during in-service inspections than collinear axial cracks, the studies on parallel axial cracks spaced in circumferential direction are necessary. The objective of this paper is to investigate the interaction effect between two parallel axial through-wall cracks existing in a steam generator tube. Finite element analyses were performed and a new failure model of the steam generator tube with these types of cracks is suggested. Interaction effects between two adjacent cracks were investigated to explain the deformation behavior of cracked tubes.     

Modelling the early development of secondary side stress corrosion cracks in steam generator tubes using incomplete random tessellation

A thorough understanding of the secondary side stress corrosion cracking of Inconel 600 in steam generator (SG) tubes seems to be still somewhat in the future. Especially the early phase of the development of cracks, also called the initiation phase, is beyond the present state-of-the-art explanations. An effort was, therefore, made to propose modelling and visualisation of the kinetics of secondary side stress corrosion crack initiation and growth on the grain-size scale:

An incomplete random tessellation is used to approximate the random planar grain structure.

The crack initiation is modelled by random processes, taking into account the most important factors such as proximity of the aggressive medium and the orientation of the grain boundaries relative to the stress field.

The stochastic process describing crack growth accounts for crack branching, coalescence and interference between neighbouring cracks.

Several numerical examples are provided to demonstrate the versatility of the proposed method. Reasonable qualitative agreement with metallographic results is shown.     

Stress identification in steam generator tubes from profile measurements

An identification method devoted to the determination of stresses in tubes, by means of profile measurements, available from on site non-destructive evaluations, is presented here. From the only furnished data (the radial displacement component w on the inner wall), the computation of the strain, and consequently the stresses in the elastic-plastic range, is made within the framework of the shell theory. For this purpose, we need to determine the associated curvature w″: this step is an ill-posed problem because of the lack of continuity with respect to the discrete data. This difficulty is overridden by means of an appropriate regularization procedure. The predictive ability of the method has been tested by comparison with direct simulations; we present an industrial application. This diagnosis tool has been applied successfully to PWR steam generator tubes (in the roll expansion transition zone) and vessel closure head penetrations.     

Development of probability of detection functions for evaluating integrity of axial outside diameter stress corrosion cracks in steam generator

The reliability of an eddy current testing (ECT) inspection system depends upon the inspection technique and quality of analyst. In evaluating the integrity of a steam generator (SG) tube, degradation detection and sizing accuracy are considered performance measures of the nondestructive evaluation (NDE) system. A probability of detection (POD) model serves as a functional measure of the ability of an NDE system to detect degradation. It is one of the inputs in the operational assessment, and it is used to estimate the degradation during service via ECT of the SG tube. In this study, the POD functions of the inspection technique and analyst were obtained to quantitatively analyze the ECT bobbin probe for axial outside diameter stress corrosion cracks in SG tubes. This should serve to evaluate the integrity of the SG tubes. The depth and amplitude of defects were used as parameters of the POD model. Hit (detection) and miss (no detection) binary data obtained from destructive and nondestructive inspection of cracked tubes were also used.     

Simulation of stress corrosion crack growth in steam generator tubes

Assuming a small axial surface crack inside a steam generate (S/G) tube, stress corrosion crack growth is simulated by using finite element method. Pressure difference and residual stresses induced from the roll expansion are considered as applied forces and Scott's crack growth equation based on the stress intensity factor is used. Stress intensity factor distribution along crack front, variation of crack shape and crack growth rate are obtained during the crack growth. From the results, it is noted that for the given residual stress distribution, variation curve of the crack aspect ratio during the crack growth is uniquely determined. In addition, the curve shows nearly constant crack aspect ratio during the initial crack growth stage. When adjacently growing two small cracks are coalesced to form a longer crack, the growth rate of crack depth is increasing but that of crack length is decreasing, and the crack aspect ratio is converging to the original variation curve during the subsequent crack growth.     

Determination of equivalent single crack based on coalescence criterion of collinear axial cracks

In a nuclear power plant the steam generator tubes cover a major portion of the primary pressure-retaining boundary. Thus, very conservative approaches have been taken in the light of steam generator tube integrity. According to the present criteria, tubes wall-thinned in excess of 40% should be plugged whatever the cause. However, many analytical and experimental results have shown that no safety problems exist even with thickness reductions greater than 40%. The present criterion was developed about 20 years ago when wear and pitting were dominant causes for steam generator tube degradation, and it is based on tubes with single cracks regardless of the fact that the appearance of multiple cracks is more common in general. The objective of this study is to review the conservatism of the present plugging criteria of steam generator tubes and to propose a new coalescence model for two adjacent through-wall cracks existing in steam generator tubes. Using the existing failure models and experimental results, we reviewed the conservatism of the present plugging criteria. In order to verify the usefulness of the proposed new coalescence model, we performed finite element analysis and some parametric studies. Then, we developed a coalescence evaluation diagram.     

Modeling of eddy current probe response for steam generator tubes

Sample calculations were performed with a three-dimensional (3D) finite-element model to describe the response of an eddy current (EC) probe to defects in steam generator (SG) tubing. Such calculations could be very helpful in understanding and interpreting EC probe response to complex tube/defect geometries associated with the inservice inspection (ISI) of SG tubes. The governing field equations are in terms of coupled magnetic vector and electric scalar potentials in conducting media and of total or reduced scalar potentials in nonconducting regions. To establish the validity of the model, comparisons of the theoretical and experimental responses of an absolute bobbin probe are given for two types of calibration standard defects. Simulation results are also presented on the effect of ligament size in axial cracks on bobbin probe response.     

Flow-induced vibration and fretting-wear predictions of steam generator helical tubes

This paper addresses the potential flow-induced vibrations and fretting-wear of helically coiled tubes of the once-through steam generator employed at an integral type nuclear reactor, where the tubes are subjected to liquid cross-flow externally and multi-phase flow internally. The thermal-hydraulic conditions of both tube side and shell side flow fields are predicted using a general purpose computational fluid dynamics code using the finite volume element modeling. To get the natural frequency and corresponding mode shape of the helically coiled tubes with various conditions, a finite element analysis code is used. Based on the results of both the thermal-hydraulic analysis of helically coiled tube steam generator and the modal analysis of the tubes, predictions of turbulence-induced vibration, fluidelastic instability and fretting-wear of the helically coiled tubes are performed. In the predictions, special emphasis is placed on determining the effects of the number of supports, coil diameter and helix pitch on the natural vibration mode, turbulence vibration amplitude, fluidelastic instability and fretting-wear characteristics of the tubes. The results provide the technical information and bases needed by designers and regulatory reviewers for evaluating the design.     

Prediction of crack coalescence of steam generator tubes in nuclear power plants

Prediction of failure pressures of cracked steam generator tubes of nuclear power plants is an important ingredient in scheduling inspection and repair of tubes. Prediction is usually based on nondestructive evaluation (NDE) of cracks. NDE often reveals two neighboring cracks. If the cracks interact, the tube pressure under which the ligament between the two cracks fails could be much lower than the critical burst pressure of an individual equivalent crack. The ability to accurately predict the ligament failure pressure, called “coalescence pressure,” is important. The failure criterion was established by nonlinear finite element model (FEM) analyses of coalescence of two 100% through-wall collinear cracks. The ligament failure is precipitated by local instability of the ligament under plane strain conditions. As a result of this local instability, the ligament thickness in the radial direction decreases abruptly with pressure. Good correlation of FEM analysis results with experimental data obtained at Argonne National Laboratory’s Energy Technology Division demonstrated that nonlinear FEM analyses are capable of predicting the coalescence pressure accurately for 100% through-wall cracks. This failure criterion and FEA work have been extended to axial cracks of varying ligament width, crack length, and cases where cracks are offset by axial or circumferential ligaments.     

Simulation of the fluid-structure-interaction of steam generator tubes and bluff bodies

The accuracy of computational fluid dynamics in simulating the cross-flow around a steam generator and the feasibility of a full scale coupled CFD/FEA fluid-structure-interaction (FSI) analysis is examined through successive validations.The study begins with a comparison between experiment and computation of flow within a stationary tube bank. Results from the simulation of an individual tube experiencing two-degree-of-freedom flow-induced vibration (at a Reynolds number of 3800) are then shown to compare favorably to experimental results. Finally, free vibration of a single cantilevered hydrofoil is simulated with comparison of mean square acceleration at resonant and non-resonant velocities, respectively. The magnitudes and frequencies of vibration are shown to be accurately captured.     

Plastic limit load analysis for steam generator tubes with local wall-thinning

This paper introduces the study of experimental and numerical analysis for plastic limit loads of Inconel 690 steam generators (SG) tubes with local wall-thinning defects. Meanwhile, the effect of the three dimensions of a local wall-thinning defect on the plastic limit load of SG tubes is analyzed.A test facility which can test both burst pressure and plastic limit load of SG tubes was established and SG tubes with 3 typical types of defects were tested by using the facility. A regularization method for local wall-thinning defect is proposed and the finite element method was used to analyze the plastic limit load of SG tubes with defects. Compared with the experimental results of SG tubes with real defects, the calculated values of plastic limit load for SG tubes with regularized defects are conservative.Based on finite element method, the effect of the three dimensions of local wall-thinning defects on plastic limit loads of defected Inconel 690 SG tubes has been got. The studied results show that the defect depth of a local wall-thinning defect is the main factor influencing the plastic limit load of SG tubes, on the other hand, both the longitudinal length and the circumferential length of a defect have effect on the plastic limit load of SG tubes.It is found that in some cases, when the longitudinal length and the circumferential angle of a local wall-thinning defect exceed some extent, the effect of the longitudinal length and the circumferential angle on plastic limit load can be ignored.     

Prediction of structural integrity of steam generator tubes under severe accident conditions

Available models for predicting failure of flawed and unflawed steam generator tubes under normal operating and design-basis accident conditions are reviewed. These rate-independent flow stress models are inadequate for predicting failure of steam generator tubes under severe accident conditions because the temperature of the tubes during such accidents can reach as high as 800°C where creep effects become important. Therefore, a creep rupture model for predicting failure was developed and validated by tests on unflawed and flawed specimens containing axial and circumferential flaws and loaded by constant as well as ramped temperature and pressure loadings. Finally, tests were conducted using pressure and temperature histories that are calculated to occur during postulated severe accidents. In all cases, the creep rupture model predicted the failure temperature and time more accurately than the flow stress models.     

带螺旋缠绕管的双面加热管套管直流蒸汽发生器稳态换热研究

介绍了一种新型的内管为螺旋管的管套管式双面加热直流蒸汽发生器.为编写稳态换热分析程序建立了一种固定二次侧焓值边界计算模型.该模型依据二次侧流体相的变化,将蒸汽发生器划分为三个分区:单相液区、两相区和单相汽区.程序的计算结果与文献中实验结果吻合较好,并从计算结果分析得出了该蒸汽发生器的一些结构参数对换热效果的影响规律.     

Safety and availability of steam generator tubes affected by secondary side corrosion

The outside diameter stress corrosion cracking at tube support plates became the dominating ageing mechanism in steam generator tubes made of Inconel 600. A variety of maintenance approaches were developed and implemented world-wide to enable safe and reliable plant operation with affected tubes. Despite different philosophical and physical backgrounds involved, all applied approaches satisfy relevant regulatory requirements. The main goal followed in this paper is to quantify the degree of safety which is achieved through the implementation of selected maintenance approaches. A method is proposed which measures the operational safety and availability through three efficiency parameters: probability of steam generator tube rupture; predicted accidental leak rates through the defects in the tube bundle; and number of plugged tubes. An original probabilistic model quantifies the probability of tube rupture, while procedures available in literature were used to evaluate the accidental leak rates. A numerical example is based on data from the Kr ko NPP (PWR 623 MWe). The maintenance strategies analyzed are: (a) traditional defect depth (40%) plugging criterion; (b) alternate plugging criterion (bobbin coil voltage as defined by EPRI and US NRC); (c) combination of traditional and alternate plugging criteria; and (d) no plugging at all. Advantages of the defect specific approaches (b) and (c) over the traditional one (a) are clearly shown. The efficiency of the traditional approach (a) is shown to be comparable to the no plugging at all approach (d). Finally, a sensitivity analysis aimed at ranking of the input parameters is presented. Uncertain failure models are shown to be the major contributor to the scatter of obtained results.     

Thermal resistance contributions of oxides growth on Incoloy 800 steam generator tubes

The primary and secondary circuits of nuclear power plants have different water chemistries, corrosion product sources, temperatures and flow rates. All these parameters promote the growth or deposition of oxides of different compositions and morphologies on the surfaces of the steam generator (S.G.) tubes. This paper presents a methodology to evaluate the relative contributions to the total heat transfer resistance due to the different oxide layers. The values obtained from a sample of Alloy 800 tube at room temperature are similar to those encountered in the open literature at high temperatures. Important future planning guidelines for decontamination and/or chemical cleaning of S.G. units can be obtained from these results.     

Predicting the accumulated number of plugged tubes in a steam generator using statistical methodologies

A steam generator (SG) plays a significant role not only with respect to the primary-to-secondary heat transfer but also as a fission product barrier to prevent the release of radionuclides. Tube plugging is an efficient way to avoid releasing radionuclides when SG tubes are severely degraded. However, this remedial action may cause the decrease of SG heat transfer capability, especially in transient or accident conditions. It is therefore crucial for the plant staff to understand the trend of plugged tubes for the SG operation and maintenance. Statistical methodologies are proposed in this paper to predict this trend. The accumulated numbers of SG plugged tubes versus the operation time are predicted using the Weibull and log–normal distributions, which correspond well with the plant measured data from a selected pressurized water reactor (PWR). With the help of these predictions, the accumulated number of SG plugged tubes can be reasonably extrapolated to the 40-year operation lifetime (or even longer than 40 years) of a PWR. This information can assist the plant policymakers to determine whether or when a SG must be replaced.     

Surry steam generator - examination & evaluation

This report summarizes research conducted during the fourth year of the five year Steam Generator Group Project. During this period the project conducted numerous nondestructive examination (NDE) round robin inspections of the original Surry 2A steam generator. They included data acquisition/analysis and analysis-only round robins using multifrequency bobbin coil eddy current tests. In addition, the generator was nondestructively examined by alternate or advanced techniques including ultrasonics, optical fiber, profilometry and special eddy current instrumentation. The round robin interpretation data were compared. To validate the NDE results and for tube integrity testing, a selection of tubing samples, determined to be representative of the generator, was designated for removal. Initial sample removals from the generator included three sections of tube sheet, two sections of support plate and encompassed tubes, and a number of straight and U-bend tubing sections. Metallographic examination of these sections was initiated. Details of significant results are presented in the following paper.     

Characterization and structural integrity tests of ex-service steam generator tubes at Ontario Power Generation

The Canadian Nuclear Standard CSA N285.4 requires the periodic metallurgical examination of removed ex-service steam generator tubes. This paper describes the practices used for the characterization and structural integrity tests of ex-service steam generator tubes at Ontario Power Generation (OPG). It shows that there is no degradation of mechanical properties of Monel 400 tubes after 7-18 effective full power years (EFPY) of operation and Incoloy 800 tubes after more than 10 EFPY of operation.     

Effects of fabrication process on microstructure and texture of Inconel 690 tubes for steam generator

The main goal of this research was to investigate the relationship between the grain boundary misorientation and the precipitation of intergranular M₂₃C₆ carbides during the pilgering process and the heat treatment of Inconel 690 tubes for steam generators. The M₂₃C₆ carbides behavior is obviously influenced by the grain boundary character and interfacial energy. The grain boundary misorientation of the Inconel 690 tubes was investigated by electron backscattered diffraction of carbide precipitates at these grain boundaries. Numerous M₂₃C₆ carbide precipitate at the large angle grain boundaries with high interfacial energy.