High pressure experiments were done to determine the pressure effect on multiphase induced forces. To that end, a series of water/gas, oil/gas and oil/water/gas vibrations measurements were performed at 10, 25, 45 and 80 bar at different liquid and gas rates in a horizontal, 2″, double Uloop test section installed at the Equinor Porsgrunn site. At higher pressures the vibration amplitude decreased inversely proportional to the pressure. This was measured for both oil and water. Based on the vibration data, the forcing spectrum was reconstructed. In this the same decreased trend was observed, indicating that a changed damping is not the cause of the reduced vibrations. In the forcing spectra the main effect was a higher energy content at lower frequencies. No clear shift in the peak frequency was measured.

The flow induced vibration is the important phenomena when designing piping system and rigorous analysis method without excessive conservatism is highly demanded. Recently guidelines published by Energy Institute is often applied in design phase of piping system to consider the vibration risk in design; however, the safety factor for the method is not fully investigated, especially, for example, the effect of the piping layout, flexibility factor of bend, extrapolation to large bore headers, etc .... In previous paper, Authors investigated the forcing function due to turbulence flow at the bend by using LES-CFD analysis and quantified the random force fluctuation at the 90 degrees miter bend and two smooth bends and showed that random vibration analysis with these forcing functions can be used to assess the risk of piping vibration. In this paper, the authors conducted a series of random vibration analysis on the beam mode vibration of typical piping systems. The design variable, such as piping diameter, diameter to thickness ratio, number of flow direction change in each span, and support span were varied as a parameter of the design and evaluated the magnitude of stress and vibration level. The results were compared with the LOF score provided by Energy Institute Guidelines and clarified the difference in design margin of the methods. In conclusions, provides some guidance to reasonably apply the screening method in the design phase of the piping system.

Integrity of a piping system is a prerequisite for personnel safety and operational reliability in industries where pipelines are critical means of transferring products from one process point to the other, such as power plants, refinery plants, and chemical industries. An essential aspect of designing a reliable piping system is to design supports of suitable load carrying capacity. This also depends on accurate determination of expected support loads including loads due to vibration of the system. Piping design codes such as ASME B31.3 and B31.1 provide a general framework but do not address vibration and its impact from a detailed perspective. In many situations, the potential impact of vibration is overlooked during support load determination. In recent piping system construction, the effect of vibration has increased due to increase in fluid flow rates and use of high strength thin wall materials. Common factors that contribute to vibration include: turbulent flow (flow induced vibration, FIV), relief valve operation (acoustic induced vibration, AIV), rotating and reciprocating equipment (pulsation induced vibrations, PIV). The effect of vibration depends on the strength of excitation and the flexibility of the piping system. As vibration of the piping system increases, loads transfer to the pipe supports also increase. Catastrophic failure of a piping system can occur if its natural frequency lock-in with the frequency of the excitation source. For holistic system integrity, the loads induced due to vibrations need to be accounted for in the support design. In this paper, we investigate the contributions of the various vibration loads in a piping system, the effect of neglecting the various vibration loads on the system integrity, and an empirical method to readily determine the vibration loads to reduce cost and time require in support design processes.

Turbulence induced vibrations are most commonly encountered in industrial piping’s. Several guidelines are available for knowhow and its mitigation in piping designs and acceptable limits of vibration beyond which fatigue failure may occur in pipes. In present paper, it has been emphasized to predict potential turbulence induced vibrations at Design Stage rather than to have the expensive trouble-shooting solutions after the fabrication of system. The detailed review of currently available methods for assessing flow-induced vibrations in piping systems, including current limitations in existing codes and guidelines are discussed. These limitations are centered on the empirical approach currently taken in codes and guidelines. In present paper, a rational approach has been proposed in which the turbulent kinetic energy of the fluid flow is compared against the kinetic energy required to vibrate the pipe beyond its allowable level of vibration. The proposed method has been accessed using a documented case study. The parameters needed to evaluate the relative energies of vibration to turbulent kinetic energy of the fluid flow can be determined from FEA software, which make the present approach practically feasible for the mitigation at design stage.

Formerly, an entire catalogue of 90 deg. branch connections called Sweeplus ® was developed and accessed to mitigate acoustic induced vibration (AIV) in piping systems exposed to high frequency vibration. Parameters related to cyclic loading was completed on the Sweeplus ® fitting to determine the stress intensification factor (SIF) and flexibility factor (k-factor), in accordance with the latest revision of ASME B31J-2017 code and reported in this paper. A Sweeplus ® fitting was welded in a Markl test fixture and controlled through LabView software. The testing configuration and equipment were those used in Kahn test reported in WRC 329. K-factor tests were conducted for the in-plane thru both branch and header piping, and the out-of-plane thru branch. SIF tests were performed in the out-of-plane thru branch. The tests confirmed the SIF of Sweeplus ® is less than one which means the fatigue life of Sweeplus ® is significantly extended, not only under high frequency AIV excitation, but also under low frequency flow induced vibration (FIV) and thermal loading.

One of the challenges of analyzing flow-induced vibration in piping systems is determining how to analytically characterize the loading related to the source of the vibration. Simplified methods can be sufficient for evaluating an existing piping configuration through correlation with vibration measurements. However, if vibration mitigation is required a more thoughtful analysis approach should be used so that the anticipated vibration responses of the post-modification piping configuration can be more accurately determined. Two case histories are presented that illustrate analysis approaches used to evaluate the severity of flow-induced piping vibration and also develop effective vibration mitigation designs. The analysis approaches used in both cases involved the simulation of vibration loading based on limited vibration data. Using the analysis approaches that were developed, vibration restraints were able to be effectively located and designed. The effectiveness of the analytically determined vibration mitigation solutions was confirmed by post-modification testing and observation.

As the most dangerous flow-induced vibration (FIV) mechanism, fluid-elastic instability is always accompanied by the wake shedding. If both of the two FIV mechanisms are considered, fluid forces in this condition can be quite complex. In this paper, a time-domain model based on unsteady flow theory was used to investigate the fluid-elastic instability in a rotated triangular tube array. The vortex shedding forces were simplified as harmonic forces. Computational fluid dynamics (CFD) was used to get the fluid force coefficients with vortex shedding. The model was established by a finite element code with MATLAB software and simulation results agreed with the experiment results. The results showed the critical instability velocity can be influenced by vortex shedding forces, and double peaks can be found in the frequency spectrum of displacements of tubes. The time-domain displacements showed the phases had been impacted by the shedding and periodic characteristic was found in the displacements results. The model can also be adopted in fluid-elastic instability analysis in other tube arrangements and flow conditions.

This paper describes the work performed to study the shell mode vibration of a large cross-section flue gas duct. The work involved the collection of field vibration data, as well as predictive computational models associated with finite element analysis (FEA) and computational fluid dynamics (CFD). The goal of this work was to use predictive models to ascertain whether a proposed design change would reduce the vibration levels of the duct under similar operating conditions. The vibration observed in the duct was identified as a flow induced vibration (FIV) which excited the shell modes of the duct walls. This case study serves as an example of using predictive computational models (FEA and CFD), calibrated with vibration response data from field measurements, to represent the real world situation as closely as possible within specified budget and schedule constraints. Such calibrated models can be useful for forecasting the effectiveness of various proposed design changes.

The added mass coefficient is an important parameter when calculating the flow induced vibration (FIV) in heat exchangers. The calculation method of the added mass coefficient for tube bundles in triangular and square arrays had been presented in relevant standards which like GB/T 151. Presently, concentric arrays of tube bundles are applied extensively in the heat exchangers at nuclear power plants. However, the method for calculating the added mass coefficient of tube bundles in concentric arrays has not been given in these standards. In this paper, in order to calculate the added mass coefficient of a central flexible tube surrounded by rigid tubes in concentric arrays, the fluid-structure interaction models of tube bundles has been established by ANSYS CFX. The influence of the circumferential and radial distance of the tube bundles on the added mass coefficient has been studied by calculating the natural frequency. The results are expected to provide the calculation reference for added mass coefficient of the tube bundles in concentric arrays. The coupling vibration of tube bundles in concentric arrays has been studied by the other model which is made up of all the flexible tubes, and the coupling vibration of the tube bundles is simulated by the rigid wall motion of ANSYS CFX. According to simulation results, there exists a band of amplitude peaks in the coupling vibration of the tube bundles. It is shown that as the circumferential and radial distance increases, the band of amplitude peaks becomes narrow.

Flow-induced vibrations of Steam Generator tube bundles are a major concern for the operators and designers of nuclear power plants. In order to predict damages due to such vibrations, predictive calculations are performed, both by designers and by operators, which allow one to evaluate safety margins and thereafter to optimize the SG maintenance policy. In cases when semi analytical models of fluid-dynamic forces are used, together with corresponding dimensionless fluid force coefficients, closures are assessed by experiment. The database of dimensionless coefficients should then cover relevant tube bundle configurations. Within this framework, a test rig which was available at EDF was modified in order to arrange different pitch-to-diameter ratio bundles and different tube diameters. This paper discusses the fluid-induced forces measured on a set of flexible tubes placed in a triangular pitch bundle both in the lift and drag directions. Two-phase flow excitation spectra are presented as well.

In order to better understand the mechanisms of fretting wear damage of guide cards in some Pressurized Water Reactor (PWR) Nuclear Power Plant (NPP), an experimental investigation is undertaken at the Magaly facility in Le Creusot. The test rig consists of a complete Rod Cluster with eleven Guide Cards, submitted to axial flow inside a water tunnel. In order to mimic the effect of fretting wear, the four lower guide cards have enlarged gaps, so that the Control Rods are free to oscillate. The test rig is operated at ambient temperature and pressure, and Plexiglas walls can be arranged along its upper part, and a series of camera records the vibrations of the control rods above and below the guide cards. The vertical flow velocity is in the range of a few m/s. Beam-like pinned-pinned modes at about 5 Hz are observed, and oscillations of several mm of the central rods are measured, which come along with impacts at the higher flow velocities. A simple non-linear calculation reveals that the main effect of the impacts between Control Rods and Guide Cards is an increase of the natural frequency of the rods by about 10%. Furthermore, as the vibration spectra collapse remarkably well with the flow velocity, the experiments prove that turbulent forcing is responsible for the large oscillations of the control rods, no other mechanism being involved.

Flow induced vibration of a single cylinder and two cylinders assembled in the configurations tandem and side-by-side are experimentally investigated in the present study. The rigid cylinder free to vibrate is fixed in two blades, forming two different configurations, to allow transversal and longitudinal vibration, respectively. The mass ratio, m* ranged between 158 and 643 while the damping ratio, ζ, ranged between 0.0006 and 0.005. The pairs of cylinders present a space ratio of 1.26 (P/D and L/D) and one of the cylinders is fixed while the second one is free to vibrate. The aerodynamic channel used in the analysis presents test section with 0.146m height and 0.193m width, the study is executed using accelerometer and hot wire anemometry. The velocity on the test section is varied and generates reduced velocity, Vr = U/fnD, between 4 and 30. The displacement amplitudes, Y/D, are obtained using integration of the acceleration signals, and the root mean square results are adopted. Fourier spectral analysis and continuous wavelets are employed in the analysis of acceleration and velocity signals. The higher amplitudes happen in two distinct reduced velocities and were associated with the vibration modes of the cylinder free to vibrate. In the case with two cylinders side-by-side the amplitude is higher and present small variation on the reduced velocity of occurrence in comparison with single cylinder. For the case with cylinders in tandem the presence of the cylinder in the wake of the cylinder free to vibrate generated amplification of the response in high reduced velocities.

Vortex Shedding at pipe junctions can create pressure pulsations and flow-induced vibrations. The flow through one pipe may result in a shear layer at the junction with a second pipe. Instabilities such as vortex shedding in the shear layer can then excite acoustic modes in the second pipe, especially when the flow in the secondary pipe is stagnant or weak. The effect is the excitation of a pipe organ mode, which under certain conditions, may result in unacceptable noise and/or vibration levels. Within the nuclear industry this phenomenon has been most frequently observed in boiling water reactors (BWRs), resulting in vortex-induced, main steam line associated stand pipe acoustic resonances. This phenomenon has not been typically observed in pressurized water reactors (PWRs), especially in primary coolant loops due to the lengths of pipe needed to support acoustic resonances in water systems relevant to driving lower order structural piping modes. However, if certain conditions exist, PWRs do contain large sections of piping which can be susceptible to such flow-induced adverse noise and vibration effects. This paper describes the evaluation and mitigation of structural vibrations due to a vortex-induced excitation of an acoustic mode of a large side branch pipe in a high-energy, water-filled, PWR piping system. Specifically, an acoustic resonance was observed and structurally significant resultant vibration levels were measured on a safety related piping system directly connected to a PWR primary reactor coolant system (RCS) between the reactor and a steam generator. A rapidly employed evaluation program was implemented, which included significant in-situ structural vibration measurements that informed a combination of acoustic, structural, and fluid-domain numerical modeling evaluations. These evaluations were performed in concert to provide both root cause insights and candidate mitigation strategies. Candidate mitigation strategies were then evaluated prior to inplant implementation via further modeling evaluations and a model-scale testing program. This paper describes the primary vibration characteristics of interest of the affected piping system, the data analyses and modeling methods used to successfully identify the vibro-acoustic phenomena, the developed mitigation strategies, and verification of the final mitigation strategy via model-scale with final demonstration occurring in the plant prior to fuel load.

Fluidelastic instability (FEI) is well known to be a critical flow-induced vibration concern for the integrity of the tubes in nuclear steam generators. Traditionally, this has been assumed to occur in the direction transverse to the direction of flow but the tube failures at San Onofre Nuclear Generating Station (SONGS) in Los Angeles proved that this assumption is not generally valid. A simple tube-in-channel theoretical model was previously developed to predict streamwise as well as transverse FEI in a parallel triangular tube array. This predicted that this array geometry was particularly sensitive to streamwise FEI for high mass-damping parameters and small pitch ratios, the conditions in which the SONGS failures occurred. The advantage of this simple modelling approach is that no new empirical data are required for parametric studies of the effects of tube pattern and pitch ratio on FEI. The tube-in-channel model has been extended to in-line square, normal triangular and rotated square tube arrays and the stability of these geometric patterns are analyzed for the effects of varying pitch ratio and the mass-damping parameter. The results are compared with the available experimental data and conclusions are drawn regarding the relative vulnerability of these different tube array geometries to streamwise FEI.

Combustion turbines are frequently used because they provide the most power in the smallest footprint and their modular design makes them an economical choice. These machines are used across all land-based industries as well as marine applications. The exhaust system must perform its basic function of conducting exhaust gases, which can be as high as 1250° F (675° C), safely away from the adjacent equipment and workers, and mitigate the exhaust noise under a wide range of requirements and conditions. In addition, new requirements limit shell temperatures and exhaust leakage to prevent fire or explosion of fuel gas that may leak from equipment (ATEX). This paper presents a review of the analytical processes used in the development of a silencer system to achieve optimal performance metrics. These systems are typically comprised of parallel baffles for a wide range of conditions including aero-acoustical performance, system pressure and high flow rates, thermal stresses, environmental conditions (ocean, seismic and wind), flow-induced vibration, corrosion, and fatigue – design life analysis. The specific requirements of the baffle design will be discussed through a specific case study relative to typical rectilinear (parallel) baffles used in many installations, including land-based power generation plants (Figure 1), and offshore platforms (Figure 2). This paper will discuss the analytical methods used to address these challenges via a case study. A combination of static, vibration-pulsation and dynamic structural analysis with specific attention to the seismic analysis of the parallel baffles used in skirt and structural steel supported vessels, as well as acoustical design and flow modeling techniques are used to evaluate the design options.

As the transport artery for the reactor coolant, high-energy piping systems are the links that maintain the normal operation of each system and play a crucial role in ensuring the normal operation and safety of the reactor in nuclear power plants. During the long-term operation of the reactor, stress concentration may be induced at the weak links in the pipeline systems, such as the elbow and the tee pipe structures, under the loads of high temperature, high pressure, flow-induced vibration and so on, and finally resulting in crack defects. Due to the continuous fatigue load during the lifetime, the defects in the inner surface of the pipes may propagate rapidly and even penetrate through the wall thickness, leading to the leakage of coolant and seriously affecting the safe operation of the reactor. In order to ensure the normal function of the pipeline system and meet the service requirements, this paper studies the fatigue crack propagation problems in elbows and tee pipe in the reactor pipe systems to ensure the safe operation of the pipeline. According to the RCC-MR A16 code, the fatigue crack propagation calculation program is compiled for the elbow and tee pipe made of austenitic steel to study the fatigue crack growth process and the influencing factors of crack propagation.

The heat transfer tube of steam generator is an important part of the primary loop boundary, the integrity is crucial to the safe operation of the whole reactor system; the flow induced vibration is one of the main factors leading to the failure of heat transfer tube in steam generator. Both ASME and RG1.20 have made a clear requirement for the analysis and evaluation of the flow induced vibration of steam generator. The flow induced vibration of heat transfer tube in two-phase flow is the difficult and important content in the analysis. In this paper, the finite element model of heat transfer tube is established and the modal analysis is carried out. Then in order to evaluate the influence of two-phase flow in the secondary side and support boundary constraint, the analytical results are compared with the natural frequencies of the heat transfer tube measured in the two-phase flow test. On the basis of accurate simulation of the dynamic characteristics of heat transfer tube in two-phase flow, the paper calculate the turbulent excitation response and the fluidelastic instability ratio aiming at the main mechanism causing the flow induced vibration of heat transfer tube in two-phase flow. Firstly, the modified PSD of turbulent excitation is proposed on the foundation of root mean square displacement amplitude of heat transfer tube measured in two-phase flow test. The calculation result of the amplitude of heat transfer tube with different void fraction can envelope the test result by using the modified PSD as input, and the safety margin is reasonable. Then we also verify whether the analysis conclusion of fluidelastic instability is in agreement with the test. Finally, the analytical technique is applied to the analysis of flow induced vibration of steam generator to verify the design of structure. The paper studies on flow induced vibration analysis and evaluation a heat transfer tube of steam generator in two-phase flow. The analysis program of flow induced vibration on the basis of the test results. The investigation can be used for the risk prediction and evaluation of flow induced vibration of heat transfer tube in two-phase flow, solve the technical difficulties of flow induced vibration analysis in two-phase flow, and provide the technical support for the flow induced vibration analysis of steam generator.

For verifying the structural integrity of the reactor internals (RIs) in a pressurized water reactor (PWR) plant, it is important to estimate the vibration response of the core barrel (CB) due to flow turbulence. Instead of scale model test, the computational fluid dynamics (CFD) has been expected as a method to predict the turbulence forcing function for the response analysis of the CB. In this article, a hybrid approach combining empirical equations based on flow test and CFD analysis is proposed in order to predict the turbulence forcing function. The scale model test of new RIs, which were developed by Mitsubishi Heavy Industries, Ltd., was conducted, and the pressure fluctuations for the turbulence forcing function and the vibration response of the CB were measured. The pressure fluctuations were calculated by CFD analysis, and the vibration analysis using the turbulence forcing function determined from the calculated pressure fluctuations was performed. This article provides the scale model test data and the empirical equations of the turbulence forcing functions, and validation results of the proposed method to predict the turbulence forcing function using CFD.

The steam generator (SG) is a key component in the PWR nuclear power plant. U-shaped tube bundles are subjected to cross flow in inlet and bend sections. According to the design standards of steam generators, short-term flow induced vibration (FIV) damage could be avoided, but wear and corrosion of tubes still exists. Both fluid and structure parameters are needed in FIV analysis. As direct modeling of SG flow field is almost infeasible, the porous medium model has been widely used instead. Using porous medium model can only obtain the gap velocity approximately by mathematical methods with many other unclear parameters. A combination method of direct modeling and porous medium model was established in this research. The direct modeling section could give the details of fluid forces and the accurate gap velocity. Using the fluid forces, explicit dynamic analyses of tube with supports were carried out to get FIV response and contact forces. In this paper, a typical SG model was studied in designed experimental conditions, and the results were compared with published literatures. The results demonstrate that the numerical simulation along with the combination model and explicit dynamic analysis can provide new methods into the flow-induced vibration and fretting wear of multi-span U-tubes which can be applied into future design for steam generators and other heat exchangers with large size.

Fuel rods are subjected to both axial and lateral flow in the reactor core. In this study, we present a study on the flow induced vibration (FIV) and fretting wear of fuel rod with failed clamping at grids. First, according to the flow distribution around a type of pressurized water reactor (PWR) fuel rod, the power spectral density (PSD) is obtained to characterize the turbulence excitation. Next, by combining the correlation PSD test parameters, the mean square value of the vibration displacement of each rod mode is found, and then the wear depth of dimple position is calculated based on the ARCHARD wear formula. The clamping of fuel rod at various grids may fail due to inaccurate manufacturing, fuel transportation and in-core irradiation. The absence of clamping force would significantly influence the rod mode and thereby changes its FIV responses. Simulation results show that the failure of the leaf spring has negligible effect on the rod natural frequency whereas the dimple failure near the location with larger FIV amplitude has a much significant effect. The lateral flow velocities at the inlet and outlet of the core are larger. For the fully clamped fuel rod, the response amplitude of turbulent excitation at the bottom and top of the fuel rod is larger. This is even more obvious with a failed dimple at these locations. Comparatively, the effect of dimple support failure in the middle is less influential. The influence of dimple support failure over the rod wear depth depicts basically the same trend as on the maximum FIV amplitude. In addition to the FIV amplitude, wear depth is also related to rod natural frequency. By examining the multiplication of amplitude and frequency at the top and bottom grid, we found that the dimple failure has greater impact at the top grid.