Experimental Identification of Fluid-Elastic Coupling Forces on a Square Tube Bundle Subjected to Single-Phase Cross-Flow

The importance of fluid-elastic coupling forces in tube bundle vibrations is well documented and can hardly be over-emphasized, in view of their damaging potential. Even when adequate tube supports are provided to suppress fluid-elastic instabilities, the flow-coupling forces still affect the dynamical tube responses and remain a significant issue, in particular concerning the vibro-impact motions of tubes assembled using clearance supports. Therefore, the need remains for more advanced models of fluid-elastic coupling, as well as for experimental flow-coupling coefficients to feed and validate such models. In this work, we report an extensive series of experiments performed at CEA-Saclay leading to the identification of stiffness and damping fluid-elastic coefficients, for a 3×5 square tube bundle (D = 30 mm, P/D = 1.5) subjected to single-phase transverse flow. The bundle is rigid, except for the central tube which is mounted on a flexible suspension (two parallel steel blades) allowing for translation motions of the tube in the lift direction. The system is thus single-degree of freedom, allowing fluid-elastic instability to arise through a negative damping mechanism. The flow-coupling stiffness and damping coefficients, Kf(Vr) and Cf(Vr), are experimentally identified as functions of the reduced velocity Vr. Identification is achieved on the basis of changes in tube vibration frequency and reduced damping as a function of flow velocity, assuming a constant fluid added mass. In the present experiments, coefficient identification is performed well beyond the instability boundary, by using active control, thereafter allowing exploration of a significant range of flow velocity. The modal frequency and the modal mass of the system are respectively modified by changing the tube suspension stiffness, and/or by adding a mass to the system. We can thus assert how the fluid-elastic coefficients change, for this configuration, with these two system parameters, all other parameters being kept constant. The results obtained from the configurations tested suggest that formulations for coefficient reduction may be improved, in order to better collapse the identified data.

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Fluid-Elastic Coefficients in Single Phase Cross Flow: Dimensional Analysis, Direct and Indirect Experimental Methods

Volume 4: Fluid-Structure Interaction ◽

10.1115/pvp2019-93984 ◽

2019 ◽

Author(s):

Romain Lagrange ◽

Philippe Piteau ◽

Xavier Delaune ◽

Jose Antunes

Keyword(s):

Experimental Data ◽

Flow Velocity ◽

Dimensional Analysis ◽

Single Phase ◽

Tube Bundle ◽

Elastic Coupling ◽

Coupling Coefficients ◽

Dimensionless Parameters ◽

Flow Coupling ◽

Elastic Coefficients

Abstract The importance of fluid-elastic forces in tube bundle vibrations can hardly be over-emphasized, in view of their damaging potential. In the last decades, advanced models for representing fluid-elastic coupling have therefore been developed by the community of the domain. Those models are nowadays embedded in the methodologies that are used on a regular basis by both steam generators providers and operators, in order to prevent the risk of a tube failure with adequate safety margins. From an R&D point of view however, the need still remains for more advanced models of fluid-elastic coupling, in order to fully decipher the physics underlying the observed phenomena. As a consequence, new experimental flow-coupling coefficients are also required to specifically feed and validate those more sophisticated models. Recent experiments performed at CEA-Saclay suggest that the fluid stiffness and damping coefficients depend on further dimensionless parameters beyond the reduced velocity. In this work, the problem of data reduction is first revisited, in the light of dimensional analysis. For single-phase flows, it is underlined that the flow-coupling coefficients depend at least on two dimensionless parameters, namely the Reynolds number Re and the Stokes number Sk. Therefore, reducing the experimental data in terms of the compound dimensionless quantity Vr = Re/Sk necessarily leads to impoverish results, hence the data dispersion. In a second step, experimental data are presented using the dimensionless numbers Re and Sk. We report experiments, for a 3 × 5 square tube bundle subjected to water transverse flow. The bundle is rigid, except for the central tube which is mounted on a flexible suspension allowing for translation motions in the lift direction. The evolutions of the flow-coupling coefficients with the flow velocity are determined using two different experimental procedures: (1) In the direct method, an harmonic motion of increasing frequency is imposed to the tube. (2) In the indirect method, the coefficients are obtained from the modal response of the tube (frequency, damping). The coefficient identification was performed well beyond the system instability boundary, by using active control, allowing an exploration of a significant range of flow velocity. For a given Sk, the results show that: (a) at low Re, the flow-coupling coefficients are close to zero; (b) at intermediate Re, the flow stabilizes the tube; (c) at high Re, the flow destabilizes the tube, leading to a damping-controlled instability at a critical Re. Reducing the data in terms of Re and Sk clarifies the various experimental “branches”, which are mixed when using Vr. The two identification techniques lead to reasonably compatible fluid-elastic coefficients.

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Critical Velocity of a Non-Linearly Supported Multi-Span Tube Bundle

Volume 9: 6th FSI, AE and FIV and N Symposium ◽

10.1115/pvp2006-icpvt-11-93024 ◽

2006 ◽

Author(s):

M. K. Au-Yang ◽

J. A. Burgess

Keyword(s):

Flow Velocity ◽

Critical Velocity ◽

Tube Bundle ◽

Normal Modes ◽

Cross Flow ◽

Time History ◽

Tube Bundles ◽

Cross Flow Velocity ◽

The Cross ◽

The Time Domain

The phenomenon of fluid-elastic instability and the velocity at which a heat exchanger tube bundle becomes unstable, known as the critical velocity, was discovered and empirically determined based upon single-span, linearly supported tube bundles. In this idealized configuration, the normal modes are well separated in frequency with negligible cross-modal contribution to the critical velocity. As a result, a critical velocity can be defined and determined for each mode. In an industrial heat exchanger or steam generator, not only do the tube bundles have multiple spans, they are also supported in over-sized holes. The normal modes of a multi-span tube bundle are closely spaced in frequency, and the non-linear effect of the tube-support plate interaction further promotes cross-modal contribution to the tube responses. The net effect of cross-modal participation in the tube vibration is to delay the instability threshold. Tube bundles in industrial exchangers often have critical velocities far above what were determined in the laboratory based upon single-span, linearly supported tube bundles. In this paper, the authors attempt to solve this non-linear problem in the time domain, using a time history modal superposition method. Time history forcing functions are first obtained by inverse Fourier transform of the power spectral density function used in classical turbulence-induced vibration analyses. The fluid-structure coupling force, which is dependent on the cross-flow velocity, is linearly superimposed onto the turbulence forcing function. The tube responses are then computed by direct integration in the time domain. By gradually increasing the cross-flow velocity, a threshold value is obtained at which the tube response just starts to diverge. The value of the cross-flow velocity at which the tube response starts to diverge is defined as the critical velocity of this non-linearly supported, multi-span tube bundle.

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Fluid-Elastic Vibration of Cross-Shaped Tube Bundle in Mixed Cross and Parallel Flow: Measurement of Gap Flow Velocity and Vibration Characteristics

Volume 9: 6th FSI, AE and FIV and N Symposium ◽

10.1115/pvp2006-icpvt-11-93900 ◽

2006 ◽

Author(s):

Fumio Inada ◽

Takashi Nishihara ◽

Jun Mizutani

Keyword(s):

Flow Velocity ◽

Tube Bundle ◽

Cross Flow ◽

Vibration Characteristics ◽

Parallel Flow ◽

Water Tunnel ◽

Flow Component ◽

Shaped Tube ◽

Excited Vibration ◽

Flow Components

A cross-shaped control rod guide tube bundle is proposed for the lower plenum structure in the next-generation LWR, ABWR-II. In our previous studies, we measured the local fluid excitation forces acting on a cross-shaped tube bundle as well as the self-excited vibration characteristics in pure cross flow in water tunnel tests. In the reactor conditions, the flow field around the tube bundles contains mixed cross and parallel flow components. In this study, water tunnel tests under mixed cross and parallel flow conditions were preformed to understand the influence of the balance of parallel and cross flow components on vibration response. The distributions of the flow direction and flow velocity in the gap between the adjacent tubes were measured with circular Pilot tubes in detail. It was found that the critical flow velocity of self-excited vibration was not influenced by the parallel flow component, but depended only on the cross flow component.

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Experimental identification of the fluid-elastic coupling forces on a flexible tube within a rigid square bundle subjected to single-phase cross-flow

Journal of Fluids and Structures ◽

10.1016/j.jfluidstructs.2019.02.001 ◽

2019 ◽

Vol 86 ◽

pp. 156-169 ◽

Cited By ~ 1

Author(s):

Philippe Piteau ◽

Xavier Delaune ◽

Laurent Borsoi ◽

Jose Antunes

Keyword(s):

Single Phase ◽

Cross Flow ◽

Elastic Coupling ◽

Experimental Identification ◽

Flexible Tube

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116 A Measurement of Gap Flow Velocity Regarding the Evaluation of Fluid-Elastic Vibration of Tube Bundle : A Measurement Example for Tube Bun dle in Mixed Parallel and Cross Flow

The Proceedings of the Dynamics & Design Conference ◽

10.1299/jsmedmc.2005._116-1_ ◽

2005 ◽

Vol 2005 (0) ◽

pp. _116-1_-_116-6_

Author(s):

Fumio INADA ◽

Takashi NISHIHARA ◽

Koji KAWAMURA ◽

Akira YASUO ◽

Shinichi KOSUGIYAMA ◽

...

Keyword(s):

Flow Velocity ◽

Tube Bundle ◽

Cross Flow ◽

Elastic Vibration ◽

Gap Flow

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Two-Phase Cross-Flow Excitation of a Normal Square Tube Array: Experiments and Analysis

5th International Symposium on Fluid Structure International, Aeroeslasticity, and Flow Induced Vibration and Noise ◽

10.1115/imece2002-32762 ◽

2002 ◽

Cited By ~ 1

Author(s):

Paul Feenstra ◽

David S. Weaver ◽

Tomomichi Nakamura

Keyword(s):

Heat Exchanger ◽

Vortex Shedding ◽

Single Phase ◽

Tube Bundle ◽

Cross Flow ◽

Scale Model ◽

Phase Flow ◽

Heat Exchanger Tube ◽

Two Phase ◽

Exchanger Tube

Laboratory experiments were conducted to determine the flow-induced vibration response and fluidelastic stability threshold of a model heat exchanger tube bundle subjected to a cross-flow of refrigerant 11 (R-11). The tube bundle consisted of a normal square array of 12 tubes with outer tube diameters of 7.11 mm and a pitch over diameter ratio of 1.485. The experiments were conducted in a flow loop that was capable of generating single-phase and two-phase cross-flows over a variety of mass fluxes and void fractions. The primary intent of the research was to improve our understanding of the flow-induced vibrations of heat exchanger tube arrays subjected to two-phase cross-flow. Of particular concern was the effect of array pattern geometry on fluidelastic instability. The experimental results are analysed and compared with existing data from the literature using various methods of parameter definition. Comparison of amplitude response in liquid flow with previous results shows a similar occurrence of symmetric vortex shedding that validates the scale model approach in single-phase flow. It was found that the introduction of a small amount of bubbles in the flow disrupted the vortex shedding and thereby caused a significant reduction in streamwise vibration amplitude. The fluidelastic stability thresholds for the present array agree well with results from previous studies. Furthermore, a good collapse of the stability data from various investigations is obtained when the fluid density is defined using the slip model of Feenstra et al. [1] and when an effective two-phase flow velocity is defined using the interfacial velocity model of Nakamura et al. [2].

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In-Line and Cross-Flow Coupling Vibration Response Characteristics of a Marine Viscoelastic Riser Subjected to Two-Phase Internal Flow

Shock and Vibration ◽

10.1155/2021/7866802 ◽

2021 ◽

Vol 2021 ◽

pp. 1-27

Author(s):

Xueping Chang ◽

Jinming Fan ◽

Wenwu Yang ◽

Yinghui Li

Keyword(s):

Flow Velocity ◽

Volume Fraction ◽

Sea Water ◽

Coupling Effect ◽

Cross Flow ◽

Internal Flow ◽

Water Flow Velocity ◽

Response Characteristics ◽

Flow Coupling ◽

Axial Tension

This paper studies the in-line and cross-flow coupling vibration response characteristics of a marine viscoelastic riser subjected to two-phase internal flow and affected by the combined effects of several parameters including the volume fraction of gas phase, sea water flow velocity, viscoelastic coefficient of the marine riser, axial tension amplitude, and the in-line and cross-flow coupling effect taking into account both the geometric and hydrodynamic nonlinearities. On the base of extended Hamilton’s principle for open systems, the dynamic equations of the marine viscoelastic riser subjected to the axial tension and gas-liquid-structure interaction are established. Two distributed and coupled van der Pol wake oscillators are utilized to model the fluctuating lift and drag coefficients, respectively. The finite element method is adopted to directly solve the highly coupled nonlinear fluid-structure interaction equations. Model validations are firstly performed through comparisons with the published experimental data and numerical simulation results, and the characteristic curves of the in-line and cross-flow vibration pattern, the in-line and cross-flow displacement trajectories, the in-line and cross-flow space-time response of displacement, and the in-line and cross-flow space-time response of stress versus different parameters are obtained, respectively. The results show that the volume fraction of gas phase, sea water flow velocity, viscoelastic coefficient of marine riser, axial tension amplitude, the in-line and cross-flow coupling effect, and multiphase internal flow velocity have significant influences on the dynamic response characteristics of the marine viscoelastic riser. Furthermore, the maximum displacements and stresses of the marine viscoelastic riser can be increased or decreased depending on the internal flow velocity, and the critical internal flow velocities result in the increase of mode order for different cross-flow velocities. It is also demonstrated that appropriate viscoelastic coefficients are very important to effectively suppress the maximum displacements and stresses.

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