Fluidelastic instability (FEI) in tube arrays has been studied extensively experimentally and theoretically for the last 50 years, due to its potential to cause significant damage in short periods. Incidents similar to those observed at San Onofre Nuclear Generating Station indicate that the problem is not yet fully understood, probably due to the large number of factors affecting the phenomenon. In this study, a new approach for the analysis and interpretation of FEI data using machine learning (ML) algorithms is explored. FEI data for both single and two-phase flows have been collected from the literature and utilized for training a machine learning algorithm in order to either provide estimates of the reduced velocity (single and two-phase) or indicate if the bundle is stable or unstable under certain conditions (two-phase). The analysis included the use of logistic regression as a classification algorithm for two-phase flow problems to determine if specific conditions produce a stable or unstable response. The results of this study provide some insight into the capability and potential of logistic regression models to analyze FEI if appropriate quantities of experimental data are available.

Recently, tube-to-tube wear indications of triangular tube bundle steam generators (SGs) caused by fluidelastic instability (FEI) in the in-plane direction of U-bend region (in-plane FEI) have been reported. Several experiments were conducted to investigate the characteristics of in-plane FEI by our research groups. In a series of experiments, particular characteristics of in-plane FEI were found. For example, there are the critical velocity difference between the in-plane and the out-of-plane directions, the difference between straight tube bundle tests and U-bend tube bundle tests, etc. To explain these characteristics, unsteady fluid force acting on tubes were measured. The experimental investigation was conducted under high temperature and high-pressure steam–water flow conditions close to the SGs. Stability analyses were conducted using the measured unsteady fluid forces as inputs. First, stability analyses were done to simulate straight tube bundle tests. Analysis results agreed well with experiments and it could explain the effect on critical velocity trend by number of flexible tubes and directions of vibration. Second, U-tube stability analyses were performed by applying unsteady fluid force coefficients for each location of U-bend tube finite element method (FEM) model. From the results, mechanisms of in-plane FEI were understood.

Flow-excited acoustic resonance is a design concern in many industrial applications. If not treated, it may lead to excessive vibrational loads, which could subsequently result in premature structural failure of critical equipment. For the case of tube bundles in heat exchangers, several acoustic damping criteria were proposed in the literature to predict the occurrence of resonance excitation. However, these criteria, in some cases, are not reliable in differentiating between the resonant and nonresonant cases. A primary reason for that is the geometrical differences between reduced scale models and full-scale tube bundles, and their effect on the flow-sound interaction mechanism. Therefore, the effect of two geometrical aspects, namely, the duct height and the cylinder diameter, on the self-excited acoustic resonance for single cylinders in cross-flow is experimentally investigated in this work. Changing the duct height changes the natural frequency of the excited acoustic modes and the duct's acoustic damping and radiation losses. Changing the cylinder diameter changes the flow velocity at frequency coincidence, the pressure drop, and Reynolds number. It is found that increasing the duct height decreases the acoustic impedance, which makes the system more susceptible to resonance excitation. This, in turn, changes the magnitude of the acoustic pressure at resonance, even for cases where the dynamic head of the flow is kept constant. The acoustic attenuation due to visco-thermal losses is quantified theoretically using Kirchhoff's acoustical damping model, which takes into account the geometrical aspects of the different ducts. Results from the experiments are compared with the acoustic damping criteria from the literature for similar cases. It is revealed that the height of the duct is an important parameter that should be included in damping criteria proposed for tube bundles of heat exchangers, as it controls the acoustic damping and radiation losses of the system, which have been over-looked in the past.

A Code Case in the framework of the Nuclear Codes and Standards of Japan Society of Mechanical Engineers (JSME) has been published to incorporate seismic design evaluation methodologies for piping systems by detailed inelastic response analysis and strain-based fatigue criteria as an alternative design rule to the current rule, in order to provide a more rational seismic design evaluation by taking directly the response reduction due to plasticity energy absorption into account. The Code Case provides two strain-based criteria: one is a limit to maximum amplitude of equivalent strain amplitude derived from detailed analysis and the other is a limit to the fatigue usage factor also based on the equivalent strain amplitude. Some discussions are provided on the adequacy of additional damping in the simplified inelastic analysis and the safety margin and reliability of fatigue evaluation by the detailed inelastic response analysis provided in the Code Case.

In recent years, in a newly installed replacement steam generator, in-plane (IP) fluid elastic instability (FEI) for the heat transfer tubes has occurred. The fluid elastic instability is one of the severe vibrations in the heat transfer tube bundle and should be avoided. There have been many studies on the out-of-plane (OOP) fluid elastic instability, and the design evaluation guideline based on Connors' equation and the results of flow tests has been established. On the other hand, no evaluation guideline has been established for in-plane fluid elastic instability, and no critical coefficient has been determined in high-temperature, high-pressure steam–water two-phase conditions. Therefore, in this paper, in order to develop the guideline for evaluating in-plane fluid elastic instability, the critical coefficients were obtained using two types of test equipment for rotate triangular array in two-phase flow (SF 6 ethanol) simulating steam–water flow under high-temperature and high-pressure conditions.

Acoustic pressure pulsations can be problematic in industrial pipelines, especially when the excitation frequency matches an acoustic resonance frequency of the pipeline. The objective of this paper is to investigate the effectiveness of Helmholtz resonators (HRs) in multiple arrangements on the attenuation of acoustic pressure pulsations in piping systems. In a resonant pipeline (i.e., an acoustic standing wave scenario), maximal attenuation is achieved when the HR is inserted at the acoustic pressure antinode. The insertion loss (IL) in an off-resonant system is found to be relatively consistent, unless there is a coupling between the HR and the downstream end termination in which case there is a decrease in attenuation. Multiple, small-volume HRs in various configurations can achieve the same level of damping as that of a single HR with the same total volume. Moreover, it is shown that the use of multiple HRs placed at strategic spacing intervals along the length of a pipeline can yield significant acoustic damping, without the need for characterizing the acoustic waves in the pipeline system. An axial spacing of a quarter wavelength of the frequency of interest between multiple HRs is shown to increase the peak attenuation, which is indicative of a favorable coupling between HRs. The effect of flow velocity and its directionality with respect to the sound source is also investigated. The results presented in this paper provide practical techniques that can be used for the implementation of HR in pipeline systems.

A procedure is described for risk-based seismic performance assessment of pressurized piping systems considering ratcheting. The procedure is demonstrated on a carbon steel piping system considered for OECD-NEA benchmark exercise on quantification of seismic margins. Initially, fragility analysis of the piping system is carried out by considering variability in damping and frequency. Variation in damping is obtained from the statistical analysis of the damping values observed in earlier experiments on piping systems and components. The variation in ground motion is considered by using 20 strong motion records of the intraplate region. Floor motion of a typical reactor building of a nuclear power plant under these actual earthquake records is evaluated and applied to the piping system. The performance evaluation of the piping system in terms of ratcheting is carried out using a numerical approach, which was earlier validated with shake table ratcheting tests on piping components and systems. Three limit states representing performance levels of the piping system under seismic load are considered for fragility evaluation. For each limit state, probability of exceedance at different levels of floor motion is evaluated to generate a fragility curve. Subsequently, the fragility curves of the piping systems are convoluted with hazardous curves for a typical site to obtain the risk in terms of annual probability of occurrence of the performance limits.

Fluid-elastic instability (FEI) is the most dangerous vibration mechanism in tube arrays. As the research shows in the recent years, the mechanism of FEI turns to be clear, but threshold prediction in low mass damping parameter (MDP) tube arrays is still not accurate because of the complexity of the instability mechanism. In this work, computational fluid dynamics (CFD) simulation is first validated by comparison with the water tunnel experiments in four kinds of tube arrangements and then extended to two-phase flow to get more data in low MDP range. Using fluid force coefficients calculated by CFD simulation, unsteady modeling of the tube model is established and the critical velocities match well with experiment and CFD simulation results. The effect of tube arrangement and Reynolds number on the fluid force coefficients and the predicted critical velocity is studied according to the unsteady flow theory. The results show that instability critical velocity of the normal triangular array can be underestimated at MDP lower than 1. When the frequency ratio (streamwise direction to transverse direction) decreases to below 0.8 in the rotated triangular array, the streamwise instability occurs earlier than transverse instability. The methods and conclusions in this paper can be used in FEI analysis in both streamwise direction and transverse direction.

An experimental program was carried out by subjecting normal square finned tube arrays to gradually increasing water cross flows. In all, total six tube arrays were tested—three having pitch ratio 2.1 and remaining three of pitch ratio 2.6. Under each category, three arrays tested were: plain array, coarse finned array, and fine finned array. The objective of the research was to determine the fluid velocity at which each of the six arrays becomes fluidelastically unstable. The experiments were started with tests on plain arrays to establish them as a datum case by comparing their test results with published results on plain arrays having lower pitch ratios. This was then followed by testing of finned arrays to study the effect of fins on the instability threshold. The tubes were subjected to a gradually increasing flow rate of water from 10 m 3 /h to the point where instability was reached. The results of the present work are compared with author's earlier published results for parallel triangular arrays in water. The research outcomes help to study the effect of pitch ratio, tube array pattern, and fin density on the instability threshold. The results show that instability is delayed due to the addition of the fins. It is also concluded that normal square arrays should be preferred over parallel triangular arrays to avoid fluidelastic vibrations. The vortex shedding behavior studied for all the arrays shows that small peaks before fluidelastic instability are due to vortex shedding.

This paper explored and compared the effectiveness of the inline and the branching redesign strategies used to control water-hammer surges initiated into existing steel piping systems. The piping system is handled, at its transient sensitive regions, by replacing an inline, or adding a branching, short-section made of high- or low-density polyethylene (HDPE or LDPE) pipe-wall materials. The Ramos model was used to describe the transient flow, along with the method of characteristics implemented for numerical computations. The comparison of the numerical solution with experimental data available from the literature and alternative numerical solution evidenced that the proposed model could reproduce satisfactorily the magnitude and the phase shift of pressure head evolution. Further, the robustness of the proposed protection procedures was tested with regard to water-hammer up- and down-surge mechanisms, taken separately. Results demonstrated that both utilized techniques provided a useful tool to soften both water-hammer up- and down-surges. Additionally, the amortization of pressure-head-rise and -drop was sensitive to the short-section material and size. Moreover, the branching strategy illustrated several enhancements to the inline one in terms of period spread-out limitation, while providing acceptable pressure-head damping.

This study describes inelastic seismic design of piping systems considering the damping effect caused by elastic–plastic property of a pipe support which is called an elastic–plastic support. Though the elastic–plastic support is proposed as inelastic seismic design framework in the Japan Electric Association code for the seismic design of nuclear power plants (JEAC4601), the seismic responses of the various piping systems with the support are unclear. In this study, the damping coefficient of a piping system is focused on, and the relation between seismic response of the piping system and elastic–plastic behavior of the elastic–plastic support was investigated using nonlinear time history analysis and complex eigenvalue analysis. The analysis results showed that the maximum seismic response acceleration of the piping system decreased largely in the area surrounded by pipe elbows including the elastic–plastic support which allowed plastic deformation. The modal damping coefficient increased a maximum of about sevenfold. Furthermore, the amount of the initial stiffness of the elastic–plastic support made a difference in the increasing tendency of the modal damping coefficient. From the viewpoint of the support model in the inelastic seismic design, the reduction behavior for the seismic response of the piping system was little affected by the 10% variation of the secondary stiffness. These results demonstrated the elastic–plastic support is a useful inelastic seismic design of piping systems on the conditions where the design seismic load is exceeded extremely.

Fluidelastic instability (FEI) is the most harmful vibration mechanism for heat exchangers. Due to the inevitable manufacturing precision and assembly error, natural frequencies of tubes are not equal in the ideal condition. In order to describe the dispersion characteristic of tube bundles, a new factor named dispersion ratio is proposed in this paper. A series of tubes experiments in normal square and rotated triangular array with pitch ratio s = 1.4 and s = 1.28 were designed and conducted with high-speed camera and visual image processing system. Results show that FEI behaviors of tubes were greatly affected by tubes array geometry, pitch ratio, and dispersion ratio. Reduced critical velocity (V cr ) increased with dispersion ratio in normal square array but no obvious phenomenon was observed in rotated triangular array.

Flow-induced vibration analysis of the San Onofre Nuclear Generating Station (SONGS) replacement steam generators (RSG) is made using nonproprietary public data for these steam generators on the Nuclear Regulatory Commission public web site ( www.NRC.gov ). The analysis uses the methodology of Appendix N Section III of the ASME Boiler and Pressure Vessel Code, Subarticle N-1300 Flow-Induced Vibration of Tubes and Tube Banks. First, the tube geometry is assembled, and overall flow and performance parameters are developed at 100% design flow; then, the analysis is made to determine the flow velocity in the gap between tubes and tube natural frequencies and mode shapes. Finally, the mass damping and reduced velocity for tubes on the U bend are assembled and plotted on the ASME code Figure N-11331-4 fluid elastic stability diagram.

Flow-induced vibrations of tubes in two-phase heat exchangers are a concern for the nuclear industry. Electricité de France (EDF) has developed a numerical tool, which allows one to evaluate safety margins and thereafter to optimize the exchanger maintenance policy. The software is based on a semi-analytical model of fluid-dynamic forces and dimensionless fluid force coefficients which need to be evaluated by experiment. A test rig was operated with the aim of assessing parallel triangular tube arrangement submitted to a two-phase vertical cross-flow: a kernel of nine flexible tubes is set in the middle of a rigid bundle. These tubes vibrate as solid bodies (in translation) both in the lift and drag directions in order to represent the so-called in-plane and out-of-plane vibrations. This paper outlines the experimental results and some detailed physical analysis of some selected points of the experiment series: the response modes are identified by means of operational modal analysis (OMA) (i.e., under unmeasured flow excitation) and presented in terms of frequency, damping, and mode shapes. Among all the modes theoretically possible in the bundle, it was found that some of them have a higher response depending on the flow velocity and the void fraction. Mode shapes allow to argue if lock-in is present and to clarify the role of lift and drag forces close to the fluid-elastic instability (FEI).

The simple tube and channel theoretical model for fluidelastic instability (FEI) in tube arrays, as developed by Hassan and Weaver, has been used to study the effects of pitch ratio and mass ratio on the critical velocity of parallel triangular tube arrays. Simulations were carried out considering fluidelastic forces in the lift and drag directions independently and acting together for cases of a single flexible tube in a rigid array and a fully flexible kernel of seven tubes. No new empirical data were required using this model. The direction of FEI as well as the relative importance of fluid coupling of tubes was studied, including how these are affected by tube pitch ratio and mass ratio. The simulation predictions agree reasonably well with available experimental data. It was found that parallel triangular tube arrays are more vulnerable to streamwise FEI when the pitch ratio is small and the mass-damping parameter (MDP) is large.

Natural gas is relatively clean, and its demand is currently increasing. In most cases, gas fields are located at the bottom of the sea. Therefore, floating production, storage, and offloading (FPSO) systems are now attracting considerable attention. This paper is related to the dynamical design of a FPSO system; in particular, it focuses on the free surface elevation induced by the waves in a horizontal cylindrical and axisymmetric liquid vessel with end caps. In this study, the theory of the wave height and resonant frequency in a horizontal cylinder subjected to pitching via external excitation is developed. Then, a theory taking into account the effect of perforated plates is introduced. A special discussion is made with regard to the number and location of the perforated plates and the effect of a partial opening in a perforated plate on the damping. Finally, the experimental data of resonant wave heights up to the third mode are shown in comparison to the theoretically derived results.

A three-way water hydraulic pressure reducing valve (PRV) was developed in this paper for a test equipment in laboratory for adapting complex conditions. The designed PRV has a damping chamber with an orifice located at the spring chamber. Two types of throttles and orifice diameter were investigated through dynamic simulation and optimization, and their dimensions were determined and applied to the manufactured valve prototype. The static and dynamic performances of the valve were tested by experiments. At the preset pressure of 5.0 MPa, the outlet pressure variations for the pressure-reducing port and the relief port, are 0.73 MPa and 1.44 MPa, respectively, while the flow variation is up to 18.0 l/min. The experimental rising times and settling times of the PRV under the inlet pressure step for preset pressures of 5.0 MPa are 33.7 ms and 120.2 ms, respectively, and the overshoot is 3.76%. The test results at each preset pressure agree well with the simulation which verifies that the simulation model can be used to predict the dynamic performance of the PRV. The experimental results for the valve under flow step input conclude that it can work stably at small flow state. The research indicates that making the spring chamber a damping chamber by using an orifice is a feasible way to increase the pressure stability and the dynamic performance of the PRV. However, the damping effect of this structure is insufficient at high working pressure.

Experimental measurements of the steady forces on a central cluster of tubes in a rotated triangular array ( P / D = 1.5 ) subjected to two-phase air–water cross-flow have been conducted. The tests were done for a series of void fractions and a Reynolds number (based on the pitch velocity), Re = 7.2 × 10 4 . The forces obtained and their derivatives with respect to the static streamwise displacement of the central tube in the cluster were then used to perform a quasi-steady fluidelastic instability analysis. The predicted instability velocities were found to be in good agreement with the dynamic stability tests. Since the effect of the time delay was ignored, the analysis confirmed the predominance of the stiffness-controlled mechanism in causing streamwise fluidelastic instability. The effect of frequency detuning on the streamwise fluidelastic instability threshold was also explored. It was found that frequency detuning has, in general, a stabilizing effect. However, for a large initial variance in a population of frequencies (e.g., σ 2 = 7.84 ), a smaller sample drawn from the larger population may have lower or higher variance resulting in a large scatter in possible values of the stability constant, K , some even lower than the average (tuned) case. Frequency detuning clearly has important implications for streamwise fluidelastic instability in the steam generator U-bend region where in-plane boundary conditions, due to preload and contact friction variance, are poorly defined. The present analysis has, in particular, demonstrated the potential of the quasi-steady model in predicting streamwise fluidelastic instability threshold in tube arrays subjected to two-phase cross-flows.

The development of a theoretical model for fluidelastic instability (FEI) in tube arrays is presented. Based on the simple model of Lever and Weaver, it considers a group of seven tubes which move in both the streamwise and transverse directions. The analysis does not constrain either tube frequency or relative mode shape so that the tubes' behavior evolves from a perturbation naturally. No additional empirical input is required. A particular case is used to evaluate the model's performance and the ratio of streamwise-to-transverse natural frequency is varied. Both streamwise and transverse directions of FEI are predicted and the results agree well with experimental observations.

A semi-analytical method to examine the influences of the axial variations in the tube vibration amplitude and flow velocity on the critical flow velocity is investigated. We illustrate that neglecting the axial variation in the tube vibration amplitude can result in an overestimation of the critical flow velocity (nonconservative estimate) when the flow velocity is nonuniform. A condition under which such overestimation arises is derived by the transformation of the eigenvalue problem that is made to take into account the axial variations in the tube vibration amplitude and flow velocity. This condition is the existence of a positive correlation between the deviations of two functions: one representing the axial variation in the flow velocity and the other square of the function representing the nonuniformity of the tube vibration amplitude. The case with marked partial admission is investigated through physical consideration for this flow-induced vibration problem. We also study cases where the difference between tube eigenfrequencies in the flow and transverse directions results in a transition in the instability direction, from the transverse direction to that of flow.