Coalescence evaluation of collinear axial through-wall cracks in steam generator tubes

To maintain the structural integrity of steam generator tubes, usually, 40% of wall thickness plugging criterion has been adopted. However, since the criterion is applicable only for the steam generator tube containing a single crack, the interaction effect of multiple cracks cannot be considered. In this paper, the coalescence pressure of tube with dual cracks is evaluated based on detailed three-dimensional elastic–plastic finite element analyses. In terms of the crack configuration, collinear axial through-wall cracks with various length, distance and ratio between individual cracks are selected. The applicability of failure pressure prediction models recently proposed by the authors was verified by comparing the finite element analyses results with corresponding experimental data for tubes with two identical cracks. Further, in order to quantify the effect of crack length ratio on failure behavior, the failure pressure prediction model was used expansively for tubes containing different-sized cracks and a coalescence evaluation diagram was developed.     

Restraining effect of support plates on the limit loads for circumferential cracks in the steam generator tube

The steam generator in a nuclear power plant is a large heat exchanger that uses heat from a reactor to generate steam to drive the turbine generator. Rupture of a steam generator tube can result in release of fission products to environment outside. Therefore, an accurate integrity assessment of the steam generator tubes with cracks is of great importance for maintaining the safety of a nuclear power plant. The steam generator tubes are supported at regular intervals by tube support plates and rotations of the tubes are restrained. Although it has been reported that the limit load for a circumferential crack is significantly affected by boundary condition of the tube, existing limit load solutions do not consider the restraining effect of tube support plate correctly. In addition, there are no limit load solutions for circumferential cracks in U-bend region with the effect of tube support plate. This paper provides detailed limit load solutions for circumferential cracks in top of tube sheet and the U-bend regions of the steam generator tube with the actual boundary conditions to simulate the restraining effect of the tube support plate. Such solutions are developed based on three-dimensional (3-D) finite element analyses. The resulting limit load solutions are given in a polynomial form, and thus can be simply used in practical integrity assessment of the steam generator tubes.     

The effect of tube rupture location on the consequences of multiple steam generator tube rupture event

A multiple steam generator tube rupture (MSGTR) event has never occurred in the commercial operation of nuclear reactors while single steam generator tube rupture (SGTR) events are reported to occur every 2 years. As there has been no occurrence of a MSGTR event, the understanding of transients and consequences of this event is very limited. In this study, a postulated MSGTR event in an advanced power reactor 1400 (APR1400) is analyzed using the thermal-hydraulic system code, MARS1.4. The APR1400 is a two-loop, 3893 MWt, PWR proposed to be built in 2010. The present study aims to understand the effects of rupture location in heat transfer tubes following a MSGTR event. The effects of five tube rupture locations are compared with each other. The comparison shows that the response of APR1400 allows the shortest time for operator action following a tube rupture in the vicinity of the hot-leg side tube sheet and allows the longest time following a tube rupture at the tube top. The MSSV lift time for rupture at the tube-top is evaluated as 24.5% larger than that for rupture at the hot-leg side tube sheet.     

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.     

Probabilistic modelling of steam generator tube pitting corrosion

Pitting corrosion is a serious form of degradation in steam generator (SG) tubing of some nuclear stations. The nature and extent of the pitting process is assessed through inspection programs, typically using various eddy current (EC) techniques, while the impact of pitting is minimized through deposit removal maintenance activities such as water lancing and chemical cleaning of SGs. This paper presents a probabilistic model of SG tube pitting corrosion that incorporates trends observed from a large EC inspection database from a nuclear generating station. The pitting occurrence process is modelled as a stochastic Poisson process and the pit size is treated as a random variable. The model is statistically calibrated with the available EC inspection data. The model is applied to estimate the probability of tube leakage, forced outage rate and the distribution of the number of tubes plugged per SG in a given operating interval. The proposed model is useful in optimizing strategies for the life-cycle management of SGs.     

Development of stabilizers for steam generator tube repair

Fluidelastic stability, turbulence-induced and vortex-induced vibration analysis of different types of stabilizers for repairing steam generator tubes are presented. The performances of the different designs are compared with that of a common basis — the virgin tube. It was found that in addition to permitting the stabilized tubes to remain in operation, the sleeve has the additional merit of being the best performer of all the designs. In addition, it is adaptable to remote installation.     

Detection of steam generator tube leaks in pressurized water reactors

This report addresses the early detection of small steam generator tube leaks in pressurized water reactors. It discusses the third, and final, year's work on an NRC-funded project examining diagnostic instrumentation in water reactors. The first two years were broad in coverage, concentrating on anticipatory measurements for detection of potential problems in both pressurized- and boiling-water reactors, with recommendations for areas of further study. One of these areas, the early detection of small steam tube leaks in pressurized water reactors (PWRs), formed the basis of study for the last year of the project.Four tasks are addressed in this study of the detection of steam tube leaks.

1. (1) Determination of which physical parameters indicate the onset of steam generator tube leaks.

2. (2) Establishing performance goals for diagnostic instruments which could be used for early detection of steam generator tube leaks.

3. (3) Defining the diagnostic instrumentation and their location which satisfy Items 1 and 2 above.

4. (4) Assessing the need for diagnostic data processing and display.

Parameters are identified, performance goals established, and sensor types and locations are specified in the report, with emphasis on the use of existing instrumentation with a minimum of retrofitting. A simple algorithm is developed which yields the leak rate as a function of known or measurable quantities. The conclusion is that leak rates of less than one-tenth gram per second should be detectable with existing instrumentation.     

Overview of steam generator tube degradation and integrity issues

The degradation of steam generator tubes in pressurized water nuclear reactors, and, in particular, the stress corrosion cracking (SCC) of Alloy 600 tubes, continues to be a serious problem. Primary water SCC is commonly observed at the roll transition zone (RTZ), at U-bends and tube denting locations, and occasionally in plugs and sleeves. Outer-diameter SCC (ODSCC) and intergranular attack (IGA) commonly occur near tube support plate (TSP) crevices, near the tube sheet in crevices, or under sludge piles, and occasionally in the free span. A particularly troubling recent trend has been the increasing occurrence of axial and circumferential cracking at the RTZ on both the primary and secondary sides. Outer-diameter stress corrosion cracking in TSP crevices, commonly consisting of segmented axial cracks with interspersed uncracked ligaments, is also becoming more common. Despite recent advances in inservice inspection (ISI) technology, a clear need still exists for quantifying and improving the reliability of ISI methods with respect to the probability of detection of the various types of flaws and their accurate sizing. These improvements are necessary to permit an accurate assessment of the consequences of leaving degraded tubes in service over the next reactor operating cycle. Degradation modes such as circumferential cracking, intergranular attack, and ODSCC at the TSP have affected a large number of tubes. New regulatory guidance is being developed that requires the development and implementation of a steam generator management program that monitors tube condition against accepted performance criteria to ensure that the tubes will perform the required safety function over the next operating cycle. In formulating new guidance for the implementation of alternate repair criteria, the U.S. Nuclear Regulatory Commission is also evaluating the contribution to overall plant risk from severe accidents. Preliminary analyses are being performed for a postulated severe-accident scenario that involves station blackout and loss of primary feedwater, in order to determine the probability of failure for degraded tubes.     

套管式直流蒸汽发生器动态特性仿真研究

套管式直流蒸汽发生器是一种采用双面传热的新型蒸汽发生器.在中心管和环管外侧与环形通道流体间热流密度相等的假设基础上,合理选择集中参数并应用可动边界的处理方法对套管式直流蒸汽发生器传热管进行了动态仿真.仿真结果与热工水力定性机理分析结果及相关的试验结果相符,从而验证了仿真方法是有效的.     

Root causes of intergranular attack in an operating nuclear steam generator tube

This paper reports the secondary side intergranular attack of an Alloy 600 tube, which was located within sludge piles in the hot-leg side of an operating nuclear steam generator. Carbide distribution along the grain boundaries and chromium depletion were analyzed using optical microscopy and transmission electron microscopy. Local crevice chemistry in contact with the defect was also assessed from the hideout return test data and oxide film analysis results using energy dispersive spectroscopy. The main causes of this defect are discussed based on the microstructure, local chemistry and operation temperature.     

Investigation on two-phase flow instability in steam generator of integrated nuclear reactor

In the pressure range of 3-18MPa,high pressure steam-water two-phase flow density wave instability in vertical upward parallel pipes with inner diameter of 12mm is studied experimentally.The oscillation curves of two-phase flow instability and the effects of several parameters on the oscillation threshold of the system are obtained.Based on the small pertubation linearization method and the stability principles of automatic control system,a mathematical model is developed to predict the characteristics of density wave instability threshold.The predictions of the model are in good agreement with the experimental results.     

Anisotropic modelling of tube bundle flow during steam generator wet layup

Tube bundle flow can be considered as a porous medium flow and a fluid continuum can be established by introducing the porosity which is a ratio of fluid volume to total volume. Darcy's flow regime applies for the tube bundle flow of low Reynolds number during steam generator wet layup circulation. A general three-dimensional formulation appears as a steady-state heat conduction equation with source term and anisotropic conductivities. Solution to such an equation with appropriate boundary conditions can be obtained by any finite element computer program which solves anisotropic heat conduction problems. Capability of anisotropic modelling has been demonstrated by a sample problem of axisymmetric tube bundle flow with orthotropic hydraulic conductivities which are derived according to the existing empirical correlations for friction factors.     

Effects of tube rupture modeling and the parameters on the analysis of multiple steam generator tube rupture event progression in APR1400

A multiple steam generator tube rupture (MSGTR) event in APR1400 has been investigated using the best estimate thermal hydraulic system code, MARS1.4. The effects of the parameters such as the number of ruptured tubes, rupture location, affected steam generator on the analysis of the MSGTR event in APR1400 are examined. In particular, tube rupture modeling methods, single tube modeling (STM) and double tube modeling (DTM), are compared. The APR1400 is found to have the capability of allowing more than 30 min to operators for the MSGTR event of five tubes. The effects of rupture location on the MSSV lift time is not significant in the case of STM, but the MSSV lift time for tube-top rupture is found to be 25.3% larger than that for rupture at the hot-leg side tube sheet in the case of DTM. The MSSV lift time for the cases that both steam generators are affected (4C5x, 4C23x) are found to be larger than that of the single steam generator cases (4A5x, 4B5x) due to a bifurcation of the primary leak flow. The discharge coefficient of Cd is found to affect the MSSV lift time only for a smaller value of 0.5. It is found that the most dominant parameter governing the MSSV lift time is the leak flow rate. Whether any modeling method is used, it gives the similar MSSV lift time if the leak flow rate is close, except in the case where both steam generators are affected. Therefore, the system performance and the MSSV lift time of the APR1400 are strongly dependent on the break flow model used in the best estimate system code.     

Corrosion aspects of Ni-Cr-Fe based and Ni-Cu based steam generator tube materials

This paper reviews corrosion related issues of Ni-Cr-Fe based (in a general sense) and Ni-Cu based steam generator tube materials for nuclear power plants those have been dealt with for last more than four decades along with some updated information on corrosion research. The materials include austenitic stainless steels (SSs), Alloy 600, Monel 400, Alloy 800 and Alloy 690. Compatibility related issues of these alloys are briefly discussed along with the alloy chemistry and microstructure. For austenitic SSs, stress corrosion cracking (SCC) behaviour in high temperature aqueous environments is discussed. For Alloy 600, intergranular cracking in high temperature water including hydrogen-induced intergranular cracking is highlighted along with the interactions of material in various environments. In case of Monel 400, intergranular corrosion and pitting corrosion at ambient temperature and SCC behaviour at elevated temperature are briefly described. For Alloy 800, the discussion covers SCC behaviour, surface characterization and microstructural aspects of pitting, whereas hydrogen-related issues are also highlighted for Alloy 690.     

Effective heat conductivity of fuel element bundles and steam generator tube bundles

Effective heat conductivity of rod and tube bundles is one of thermophysical properties necessary for calculation of thermo hydraulic characteristics of heat producing devices, heat exchange devices and steam generators. This report introduces results of mathematical modeling of effective heat conductivity of transversally anisotropic rod bundles in solid conductive medium. The considered bundles represented cylindrical rods fitted in corners of stretched and compressed in direction of heat transfer rectangular and triangular grids. The calculated results were compared to analytical solutions and previous numerical results.     

Structural integrity evaluation method for overheating rupture of FBR steam generator tube

This paper describes a structural integrity evaluation method for a SG tube of FBR in case of sodium–water reaction and creep rupture tests to obtain the strength of the tube material. In the SG of FBR, if intermediate size of water/steam leak (1–2 kg s⁻¹) would occur from a tube, it could cause overheating rupture of the multiple tubes surrounding the initially failed tube due to generated sodium–water reaction heat. In the ultra-high temperature condition, the creep strength of the material is one of the dominant factors for failure behavior. Accordingly, we tried to apply the creep failure criterion for the overheating rupture of the SG tube. The creep rupture tests have been performed at ultra-high temperature conditions ranging from 1223.2 to 1323.2 K. The test material is ‘Mod .9Cr–1Mo steel’ which is one of the candidate materials for the tubes of the future SG of FBR. The test results have shown that tube rupture depends on the creep strength of the material; hence, instantaneous rupture does not occur even if the stress exceeds the design value of ultimate tensile strength. The test data have been suitably expressed using the Larson–Miller Parameter, and a structural integrity evaluation method based on the sum of the use-fraction associated with the creep damage has been proposed. Based on this method, the structural integrity of the tube in the sodium–water reaction flame has been evaluated. The results show that it is important to detect the initial leak of the tube within a short period and to reduce the steam pressure more rapidly by SG blowdown.     

The thermal-hydraulics of a simulated PWR facility during steam generator tube rupture transients

The thermal-hydraulics of the semi-scale test facility during steam generator tube rupture transients were investigated in this paper. The test facility simulates the main features of a Westinghouse four-loop pressurized water reactor (PWR) plant.The constructed analytical model simulated both the intact and broken loops, and included the vessel (lower plenum, core, upper plenum, upper dome), the hot legs, pressurizer and the primary and secondary sides of the U-tube steam generators. The two-phase Modular Modeling System code, which was developed by the Electric Power Research Institute, and the EASY5 simulation language were used in carrying out the calculations. A control model was developed to simulate the major facility control systems and to perform the necessary control functions.Calculations were carried out during the first three hundred seconds of the event, where the automatically functioning plant protection system components were assumed to operate. The impact of reactor scram, pressurizer heater activation, main steam isolation valve closure, emergency core cooling system activation, pump trip, main feedwater termination, auxiliary feedwater injection, and atmospheric dump/safety relief valves opening/closing on the system response was calculated.The time histories of the thermal-hydraulic conditions, such as pressure and temperature, are presented for one, five and ten-tube ruptures. Comparisons with experimental data and RELAP-5 (MOD 1.5) calculations are also given.     

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.