Vibrations of probe used for the defect detection of helical heating tubes in a fast breeder reactor: Part 3. The mechanism of the vibration and the countermeasures

An eddy current testing (ECT) probe is used for the diagnosis of helical heating tubes installed in the Japanese fast breeder reactor “Monju”. Vibrations of the ECT probe occur and make the diagnosis difficult. In our previous study, several characteristics of the vibrations were elucidated through some experiments, and we took some empirical countermeasures against the vibrations. Further, we showed that the vibrations were caused by Coulomb friction through some numerical simulations. In this paper, firstly, the return process of the ECT probe out of the heating tube is considered since only the insertion process of the ECT probe was considered in our previous study. Following this, the efficacy of the proposed vibration countermeasures is evaluated by way of numerical simulation. The mechanism of the vibration and the countermeasures are discussed on the basis of the entire behavior of the probe, which was obtained by a numerical simulation. Lastly, an improvement in the countermeasure is proposed. The validity of the improvement is demonstrated through a numerical simulation both in the insertion and the return processes.     

Vibrations of probe used for the defect detection of helical heating tubes in a fast breeder reactor: Part 2. Vibration analysis and numerical simulations

A detection of a defect of a helical heating tube installed in the fast breeder reactor “Monju” in Japan is done by a feeding of an eddy current testing (ECT) probe with magnetic sensor into the tube. An undesirable vibration of the ECT probe always happens under a certain condition and makes the inspection difficult. Several characteristics of the vibration have been made clear by some experiments using a mock-up, but the essential factor of the vibration is still unclear. In this paper, a numerical simulation of the vibration is implemented on the assumption that the vibration is caused by Coulomb friction. An analytical model, which is obtained as a lumped mass model, is a large-scale non-linear vibration system and many computational costs are ordinarily required to carry out the simulations. The Transfer Influence Coefficient Method is applied so that the simulation is efficiently carried out. The results of simulation qualitatively agree well with the experimental results. It confirms the validity of the assumption that the vibration is caused by Coulomb friction.     

A case study on detection and sizing of defects in steam generator tubes using eddy current testing

Eddy current testing (ECT) method is widely used to detect various types of defects occurring in nuclear steam generator tubes. Therefore, the reliability of its detection and sizing accuracy for defects should be validated. For this purpose, two tubes with defect signals were pulled from an operating steam generator and destructively examined. The defect type was a circumferential crack for one tube and an intergranular attack (IGA) for the other tube. The plus point coil probe showed a better capability to detect and size both a circumferential crack and a volumetric IGA than pancake and bobbin coil probe. The destructive results are correlated with the ECT results obtained during the in-service inspection.     

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.     

Steam generator tube vibration tests

The buildup of magnetite in the steam generators of some pressurized water reactors had led operators to propose chemical cleaning to remove this product. In some cases, the volume of magnetite formed by the corrosion of the carbon steel has been sufficient to cause “denting” or reduction of the outer diameter of the tubes where they pass through the support plates. The US Nuclear Regulatory Commission has expressed concern that the resulting increased clearances may allow an increased level of flow-induced vibrations in chemically cleaned steam generators that could lead to high tube wear rates and unacceptable levels of tube failure.A project has been undertaken by Pacific Northwest Laboratory to address the effects of increased tube/tube-support clearances and to provide the NRC with criteria to evaluate licensees' specific proposals for chemical cleaning of steam generators. The first phase of the project consists of flow tests to establish the forcing boundary conditions, using clearances representing various conditions following chemical cleaning. The second phase consists of accelerated wear tests to determine the potential wear rates possible based on the vibrations characterized in the flow tests.     

Mechanical integrity analysis of TMI-1 OTSG unplugged tubes

Small I.D. circumferential defects have been identified in many steam generator tubes. The origin of the cracks is known to be chemical, not mechanical. A fracture mechanics evaluation has been conducted to ascertain the stability of tube cracks under steady-state and anticipated transient conditions. A spectrum of hypothetical crack sizes was interacted with tube stresses derived from the load evaluation using the methods of linear elastic fracture mechanics (LEFM). Stress intensities were calculated for part-through wall cracks in cylinders combining components due to membrane stress, bending stress, and stresses due to internal pressure acting on the parting crack faces as the loads are cycled.The LEFM computational code, “BIGIF”, developed for EPRI, was used to integrate over a range of stress intensities following the model to describe crack growth in INCO 600 at operating temperature using the equation (ΔK)^3.5.The code was modified by applying ΔK_Th, the threshold stress intensity range. Below ΔK_Th small cracks will not propagate at all. Appropriate R ratio values were employed when calculating crack propagation due to high cycle or low cycle loading.Cracks that may have escaped detection by ECT will not jeopardize tube integrity during normal cooldown unless these cracks are greater than 180° in extent. Large non-through-wall cracks that would jeopardize tube integrity are not expected to evolve because in axi-symmetric tensile stress fields, cracks propagate preferentially through the tube wall rather than around the circumference. Tube integrity can be demonstrated for mid-span tube regions and for the transition region as well.The as-repaired transition geometry is a design no less adequate than the original. The as-repaired condition represents an improvement in the state of stress due to mechanical and thermal loads as compared to the original.     

螺旋管管束流体诱发振动的实验研究

根据200MW高温气冷堆蒸汽发生器的结构参数建立了实验研究模型,并针对相邻两层旋向相同的螺旋管管束,在横向流的冲刷下,对管子的动态响应进行了实验研究。实验结果表明,螺旋管管束的流体诱发振动响应与直管相比存在一定的差别;200MW高温气冷堆蒸汽发生器的设计避免了管束的大振幅振动。     

An experimental-stochastic and theoretical analysis of the density wave instability in a helical monotube vapour generator

Some of the AGR Nuclear Power Plants in the UK contain helical forced-flow once-through steam generators. The design of these plants and their associated control policies and systems to ensure stable operation over an adequate range of operating conditions has proved a difficult task, and has required a close study of the dynamic performance of helical two-phase systems, and particularly of instability mechanisms.A combined theoretical and experimental study has been carried out to investigate the dynamics of two-phase flow in such arrangements, with special reference to density wave oscillations.An “Arcton-113” closed loop comprising a helical, electrically heated, once-through tube in a parallel channel design has been constructed and operated.The inherent noise of the flowrate signal with the hidden periodicities present in the vapour generator have been recorded and analysed using stochastic facilities and techniques in order to determine the dynamic behaviour of the system.The observed density wave oscillations are compared with the analytical predictions from a computerised distributed parameter time-varying linearised analysis of the conservation equations of the two phases. We consider the slip between the two phases, variable friction factors, as well as variable heat flux by taking into account the dynamics of the heater wall.The experimental-stochastic analysis gives insight into the phenomenon and meaningful results which are in accordance with the theoretical predictions.     

Elementary catastrophe theory modelling of duffing's equation for seismic excitation of nuclear power facilities

Elementary catastrophe theory can provide conceptual insight into some aspects of a variety of problems in dynamics. It is a qualitative tool with some quantitative results. In this paper, it is applied to forced nonlinear vibrations of seismic disturbances, which may be approximated by Duffing's equation. The behavior of such a system fits naturally into ECT modelling, where changes in parameters of the system lead to “jump” type behavior. The important conclusion is that nonlinear oscillators can exhibit elementary catastrophes, but the design engineer may be able to manipulate characteristics of the system in order to avoid the “jump” behavior of the response.     

Influence of contact conditions on vibration induced wear of metals

Unfavourable design characteristics of nuclear power plant steam generators and heat exchangers in general may result in vibration induced tube wear. A systematic investigation was performed on the contact conditions which may appear between heat exchanger tubes and tube support structure and the influence of different parameters e.g., normal contact force, on the resulting steady state wear rates. It is concluded that not only are contact forces and sliding distances important in the wear process but also the type of relative motion has a decisive influence on the resulting wear rates. For a certain “work rate”, the wear rate caused by repeated impact motions between tube and tube support structure may be an order of magnitude higher than that caused by only sliding motion. This is the result of different operating wear mechanisms which are discussed in this paper.     

Development of a hybrid ECT sensor for JSFR SG double-wall tubes

A new design has been adopted for the steam generator (SG) tubes of the Japan Sodium-cooled Fast Reactor (JSFR) using double-wall tubes. This paper estimates and assesses the effectiveness of detecting defects in SG double-wall tubes of the JSFR by using combined high-frequency eddy current testing (ECT) and low-frequency remote field eddy current sensors. We confirm that the proposed hybrid ECT sensor is highly sensitive to small defects, fatigue cracks, and other defects even when located under support plates of tubes. The parameters of the hybrid ECT sensor are designed and optimized to detect small defects using accurate numerical simulations based on the finite element method, using an in-house developed code. The sensitivity and high performance of the hybrid ECT sensor was validated with experimental measurements.     

高温气冷堆螺旋管式直流蒸汽发生器热工水力学

高温气冷堆蒸汽发生器具有一次侧氦气工质、二次侧直流、螺旋管结构、工作温度高等特点,其热工水力特性与传统压水堆自然循环蒸汽发生器存在很大区别。针对高温气冷堆蒸汽发生器的特点,对其基础热工水力及特有热工水力学问题进行了阐述,主要包括螺旋管内单相及两相流阻及换热计算、横掠螺旋管束流阻及换热计算、温度均匀性及两相流不稳定性等。同时介绍了清华大学核能与新能源技术研究院针对高温气冷堆蒸汽发生器热工设计、温度均匀性及两相流不稳定性等热工水力学问题所开发的一维稳态程序、一维瞬态程序、二维分析程序和方法,并对分析结果和结论进行了讨论。相关研究方法、程序和结论对其他相似参数螺旋管和直管式直流蒸汽发生器具有参考和借鉴意义。     

Thermal hydraulic study on a high-temperature gas–gas heat exchanger with helically coiled tube bundles

An experimental study was carried out to investigate flow-induced vibration, heat transfer and pressure drop of helically coiled tubes of an intermediate heat exchanger (IHX) for the HTTR, using a full-size partial model and air as the fluid. The test model has 54 helically coiled tubes separated into three layer bundles, surrounding the center pipe. The vibration of the tube bundles was mainly at the center pipe, and the individual vibrations of the tube bundles were not significant under the operation conditions of the IHX. The heat transfer of the tube outside, due to forced convection, was obtained as a function of Re^0.51Pr^0.3, and the friction factor, depending on the tube arrangement, was proportional to Re^−0.14.     

BWR online monitoring system based on noise analysis

A monitoring system for during operation early detection of an anomaly and/or faulty behavior of equipment and systems related to the dynamics of a boiling water reactor (BWR) has been developed. The monitoring system is based on the analysis of the “noise” or fluctuations of a signal from a sensor or measurement device. An efficient prime factor algorithm to compute the fast Fourier transform allows the continuous, real-time comparison of the normalized power spectrum density function of the signal against previously stored reference patterns in a continuously evolving matrix.The monitoring system has been successfully tested offline. Four examples of the application of the monitoring system to the detection and diagnostic of faulty equipment behavior are presented in this work: the detection of two different events of partial blockage at the jet pump inlet nozzle, miss-calibration of a recirculation mass flow sensor, and detection of a faulty data acquisition card. The events occurred at the two BWR Units of the Laguna Verde Nuclear Power Plant.The monitoring system and its possible coupling to the data and processing information system of the Laguna Verde Nuclear Power Plant are described. The signal processing methodology is presented along with the introduction of the application of the evolutionary matrix concept for determining the base signature of reactor equipment or component and the detection of off normal operation conditions.     

基于RELAP5的螺旋管蒸汽发生器热工水力程序研发与验证

由于较高的换热效率和紧凑的结构设计,螺旋管式直流蒸汽发生器（HCOTSG）在多种模块化小型堆的设计中得到了广泛应用。RELAP5作为广泛应用于反应堆热工水力特性分析的大型系统程序之一,采用的热工水力关系式仅针对直管模型开发,不适用于HCOTSG一次侧和二次侧。本文选用螺旋管及横掠管束的热工水力模型,基于RELAP5程序开发了HCOTSG模块。采用实验数据及程序对比等方式对螺旋管模块的流动和换热模型进行了单独验证,利用开发的RELAP5-HCOTSG程序针对国际革新安全反应堆（IRIS）的蒸汽发生器设计进行了整体的热工水力模拟,与原始RELAP5的计算相比,RELAP5-HCOTSG程序计算得到的热工水力参数与设计值符合良好,确认了本文开发的程序模块在HCOTSG热工水力分析中的适用性。     

Structure of air–water two-phase flow in helically coiled tubes

Air–water two-phase flow in helically coiled tubes is investigated experimentally to elucidate the effects of centrifugal acceleration on the flow regime map and the spatial and the temporal flow structure distribution. Three kinds of test tubes with 20 mm inner diameters including a straight tube are used to compare the turbulent flow structure. Superficial velocities up to 6 m/s are tested so that the centrifugal Froude number covers a range from 0 to 3. The interfacial structure is photographed from two directions by a high-speed video system with synchronized measurement of local pressure fluctuations. The results reveal that the flow transition line alters due to centrifugal force acting on the liquid phase in the tube. In particular, the bubbly flow regime is narrowed significantly. The pressure fluctuation amplitude gets large relatively to the average pressure loss as void fraction increases. The frequency spectra of the pressure fluctuation have plural peaks in the case of strong curvature, implying that the periodicity of slugging two-phase flow is collapsed by an internal secondary flow activated inside the liquid phase. Moreover, under large Froude number conditions, the substantial velocity of the gas phase that biases to the inner side of the helical coil is slower than the total superficial velocity because the liquid flow is allowed to pass through the outer side and so resembles a radial stratified flow.     

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.     

Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow

Double sensor probe and hotfilm anemometry methods were developed for measuring local flow characteristics in bubbly flow. The formulation for the interfacial area concentration measurement was obtained by improving the formulation derived by Kataoka and Ishii. The assumptions used in the derivation of the equation were verified experimentally. The interfacial area concentration measured by the double sensor probe agreed well with one by the photographic method. The filter to validate the hotfilm anemometry for measuring the liquid velocity and turbulent intensity in bubbly flow was developed based on removing the signal due to the passing bubbles. The local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter, liquid velocity, and turbulent intensity of vertical upward air–water flow in a round tube with an inner diameter of 50.8 mm were measured by using these methods. A total of 54 data sets were acquired consisting of three superficial gas flow rates, 0.015–0.076 m s⁻¹, and three superficial liquid flow rates, 0.600, 1.00, and 1.30 m s⁻¹. The measurements were performed at the three locations: L/D=2, 32, and 62. This data is expected to be used for the development of reliable constitutive relations which reflect the true transfer mechanisms in two-phase flow.     

Local heat transfer and hot-spot factors in wire-wrap tube bundle

Heat transfer coefficients and hot-spot factors have been determined from measured local temperatures and calculated local mass flux in seven adjacent tubes and associated subchannels of a 61 wire-wrap tube bundle characteristic of the blanket of a GCFR (Gas Cooled Fast Reactor). The bundle consisted of 2.11 cm OD stainless steel tubes on a triangular array with a pitch/diameter ratio of P/D = 1.05. The helical wire of 0.1067 cm in diameter was coiled on the tube with a respective initial orientation of 0–120–240°C and 30.48 cm helical pitch. The experiment used water at atmospheric pressure and temperature as coolant. The resulting dimensionless correlation for heat transfer is applicable to gases and all non-metal fluids in one phase flow when the fluid properties at subchannel bulk temperature are used. This correlation is based on local subchannel mass flux and is applicable to all wire-wrap configurations. Local subchannel mass fluxes were determined with a computer program COBRA IV and used to correlate the average Nusselt number for each subchannel in terms of local Reynolds number and fluid Prandtl number. The differences of up to 19% between that correlation and the one presented in earlier work are discussed in the text. The hot-spot factors on the convective heat transfer coefficient for tubes and subchannels are given as a function of Reynolds number based on a bundle average mass flux and a local subchannel hydraulic diameter. These factors are specific to the bundle configuration and are also dependent on the wire-wrap configuration.     

高压及超临界压力下螺旋管内单相水摩擦压降特性实验研究

在较宽的参数范围内对高压及超临界压力下单相水流经立式螺旋管的摩擦压降特性进行实验研究。研究表明,对于高压工况,在高雷诺数Re条件下的水力粗糙区,管壁粗糙度对摩擦压降的影响要远大于二次流的影响,故单相水在螺旋管内的摩擦压降基本可直接采用直管的相关公式来预测;对于超临界压力工况,在物性变化剧烈的拟临界区内,采用高压工况计算公式所得的摩擦压降预测值要明显偏低于实验值。