Investigation of In-Flow Fluidelastic Instability of Square Tube Arrays Subjected to Air Cross Flow

In-flow instability of tube arrays is a recent major issue in heat exchanger design since the event at a nuclear power plant in California [1]. In our previous tests [2], the effect of the pitch-to-diameter ratio on fluidelastic instability in triangular arrays is reported. This is one of the present major issues in the nuclear industry. However, tube arrays in some heat exchangers are arranged as a square array configuration. Then, it is important to study the in-flow instability on the case of square arrays. The in-flow fluidelastic instability of square arrays is investigated in this report. It was easy to observe the in-flow instability of triangular arrays, but not for square arrays. The pitch-to-diameter ratio, P/D, is changed from 1.2 to 1.5. In-flow fluidelastic instability was not observed in the in-flow direction. Contrarily, the transverse instability is observed in all cases including the case of a single flexible cylinder. The test results are finally reported including the comparison with the triangular arrays.

Measurement of Flow-Induced Forces: A Single Flexible Tube in a Rigid Triangular-Pitch Bundle Subjected to Two-Phase Cross-Flow

Flow-induced vibrations of Steam Generator tube bundles are a major concern for the operators of nuclear power plants. In order to predict damages due to such vibrations, EDF has developed the numerical tool GeViBus, which allows one to asses risk and thereafter to optimize the SG maintenance policy. The software is based on a semi analytical model of fluid-dynamic forces and dimensionless fluid force coefficients which need to be assessed by experiment. The database of dimensionless coefficients is updated in order to cover all existing tube bundle configurations. Within this framework, a new test rig was presented in a previous conference with the aim of assessing parallel triangular tube arrangement submitted to a two-phase cross-flow. This paper presents the result of the first phase of the associated experiments in terms of force coefficients and two-phase flow excitation spectra for both in-plane and out-of-plane vibration.

A Study on Leakage Flow Induced Vibration From Engineering Viewpoint

Leakage-flow-induced vibration for a relatively short gap is studied analytically to provide useful information to design structures that include a leakage flow. The relationship between the analysis of a one-dimensional system and that of an annular gap is explained first. Then, the mechanism of flutter-type instability is reproduced from previous study after correcting an error. Finally, the self-excited vibration potential of an engineering system is shown from sample calculations. It is shown that an axial flow becomes dominant in the short-gap approximation, and in this case, the analysis of a one-dimensional flow can be expanded to that of an annular flow. The result that negative damping can occur in the case of a divergent passage owing to the delay induced by fluid inertia was obtained from a previous study. It was suggested analytically that the damping ratio could become negative and its absolute value could become more than 10% in a system that is frequently encountered in a plant, if the natural frequency decreases. The value could be sufficient to generate self-excited vibration.

Uncertainty Quantification of Aeroacoustic Power Sources in Corrugated Pipes

Gas transport in corrugated pipes often exhibit whistling behavior, due to periodic flow-induced pulsations generated in the pipe cavities. These aero-acoustic sources are strongly dependent on the geometrical dimensions and features of the cavities. As a result, uncertainties in the exact shape and geometry play a significant role in determining the singing behavior of corrugated pipes. While predictive modelling for idealized periodic structures is well established, this paper focusses on the sensitivity analysis and uncertainty quantification (UQ) of uncertain geometrical parameters using probabilistic models. The two most influential geometrical parameters varied within this study are the cavity width and downstream edge radius. Computational Fluid Dynamics (CFD) analysis was used to characterize the acoustic source. Stochastic collocation method was used for propagation of input parameter uncertainties. The analysis was performed with both full tensor product grid and sparse grid based on level-2 Clenshaw-Curtis points. The results show that uncertainties in the width and downstream edge radius of the cavity have an effect on the acoustic source power, peak Strouhal number and consequently the whistling onset velocity. Based on the assumed input parameters distribution functions, the confidence levels for the prediction of onset velocity were calculated. Finally, the results show the importance of performing uncertainty analysis to get more insights in the source of errors and consequently leading to a more robust design or risk-management oriented decision.

Energy Approach for Determine Frequency and Amplitude of Vibration of Piping With Closed Side Branches

This article suggests calculation method for frequency and amplitude of acoustic vibration in piping with closed side branches, caused by gaseous running flow. The calculation algorithm consists of following steps: i) local excitation system is defined; ii) different combinations of boundary conditions are formed; iii) for fixed pair of boundary conditions ratio of stored in system energy and radiated from boundaries energy is written; iv) for every frequency energy functional is maximized to find boundary conditions; v) resonance frequencies are determined from plotting a curve of maximal energy ratio vs. frequency. Energy approach was further developed to analyze amplitude of vibration. For amplitude determine balance between injected energy (which depends on the Strouhal number and is defined from experimental data for laboratory geometries), and radiated from boundaries energy is written.

Modelling of Streamwise and Transverse Fluidelastic Instability in Tube Arrays

The development of a theoretical model for fluidelastic instability in tubes arrays is presented. Based on the simple model of Lever and Weaver, it considers a group of 7 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’ behaviour 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 fluidelastic instability are predicted and the results agree well with experimental observations.

Fluid-Elastic Instabilities of Clamped-Clamped Aligned and Inclined Cylinders in Turbulent Axial Flow

Fluid-elastic instabilities arise due to the coupling of structural motion and fluid flow. In the specific case of a clamped-clamped cylinder in axial flow, it will buckle at a sufficiently high flow velocity and start to flutter at even higher flow velocities. This dynamic behavior is of importance to nuclear reactor core design, undersea pipe lines and devices for energy harvesting. In this contribution, the fluid forces and the dynamics of a flexible clamped-clamped cylinder in turbulent axial flow are computed numerically. In contrast to present analytical approaches, this numerical model does not require to tune parameters for each specific case or to obtain coefficients from experiments. To provide insight in the way viscous fluid forces affect the dynamics of a cylinder in axial flow, fluid forces are computed on rigid inclined cylinders, mimicking the damping force experienced by the same cylinder moving perpendicular to the axial flow. The computations showed the existence of two different flow regimes. Each regime gave rise to a different lift force behavior, which will also influence the damping of the coupled system. Furthermore it is shown that the inlet turbulence has a non-negligible effect on these forces and thus on the dynamics of the cylinder. Next, the dynamics of a flexible cylinder clamped at both ends in axial water flow are computed by means of a methodology developed earlier. The results are successfully compared with dynamics measured in experiments available in literature. Computationally it was found that the cylinders natural frequency decreases with increasing flow velocity, until it loses stability by buckling. The threshold for buckling is in quantitative agreement with experimental results and weakly nonlinear theory. Above this threshold, the amplitude of the steady deformation increases with increasing flow speed. Eventually, a fluttering motion is predicted, in agreement with experimental results. It is also shown that even a small misalignment (1°–2°) between the flow and the structure can have a significant impact on the coupled dynamics.

On the Effect of Water Film on Flow-Induced Pulsations in Closed Side Branches in Tandem Configuration

Previous studies demonstrate that the presence of liquid strongly influences the pressure pulsation amplitudes of flow induced pulsations. In particular, in case of annular flow (thin liquid film on the walls) the pulsations can be eliminated. The present study aims at evaluating the contribution of the liquid film to the pulsation reduction. Experiments have been performed in a tandem configuration with two side branches upward oriented. The side branches have the same diameter as the main pipe. A first set of experiments has been conducted with the injection point located far upstream the upstream side branch. To isolate the sole effect of the film, a second and a third set of experiments have been performed with the injection point located close upstream the T-junction with the injection such that a thin film only was generated. In the first configuration (far upstream), the pulsation level decreases with increasing liquid rate. The reduction in amplitude compares well with the assumption of added damping in the length between the two side branches. A similar decrease in pulsation amplitude was obtained in the second configuration. However, the amplitude reduction depends on the local liquid flow pattern at the (upstream) side branch and in particular on whether liquid bypasses the side branch or it interferes with the shear layer. This indicates that acoustical damping is the main effect and small amounts of liquid do not significantly interfere with the shear layer.

Proposed Changes to the ASME Boiler and Pressure Vessel Code Section III Appendix N for Flow-Induced Vibrations

This article outlines changes proposed for implementation in the ASME Boiler and Pressure Vessel Code Section III Appendix N pertaining to Flow-Induced Vibrations (FIV). Several portions of Appendix N were originally written multiple decades ago and are not necessarily readily prescriptive for present-day analyses. An ASME Task Group on Flow-Induced Vibrations has been formed to identify areas of improvement to Appendix N so that the Appendix may be more useable in present-day FIV analyses, and a means of establishing consensus for characterization of this complex phenomena. This paper identifies opportunities for improvement to portions of Appendix N pertaining to Turbulence, Acoustic, and associated Structural Dynamic Modeling, and Data Processing. Specific suggestions are made for the following: Characterization of acoustic damping and acoustic harmonic responses, updated considerations for aeroacoustic phenomena, structural damping quantification of nuclear components, systematic approaches to modeling (random) turbulence-induced vibrations (including RMS-to-Peak ratio), considerations for leakage flow-induced instabilities, and opportunities to employ computational methods are discussed. Opportunities for the applicability of data processing algorithms such as the proper orthogonal decomposition and circumferential wavenumber decomposition are also discussed and an updated methodology for combination of random and deterministic loads for FIV analyses is presented.