Fluidelastic Coupling Research Articles

Numerical continuation and stability of nonlinear systems with distributed delays: Application to fluid-induced impacts of tubes in cross-flow

Fluid–elastic instability is the main source of concern during the design of heat-exchanger tube bundles. The associated research has focused on the understanding of the physical mechanisms behind this phenomenon and the establishing of models capable of predicting its onset; also some concomitant work has been done to establish post-instability behaviour and to prevent from excessive wear in possible sliding contacts. Moreover, the existing studies make use of time-integration methods alone for this purpose, through which it is difficult to get a comprehensive insight of global dynamics. Continuation methods, which give access to unstable branches and precise bifurcation information, are a precious tool to unfold the attainable dynamic regimes. In this paper, the parametric behaviour of two representative systems under cross-flow excitation is explored through pseudo arc-length continuation with mean flow velocity as a main driving parameter, wherein the nonlinear modal equations of motion are solved by harmonic balance at each step. As the quasi-unsteady model used for fluid–elastic coupling introduces convolution integrals, this approach is quite natural and we show that, despite some difficulties regarding the treatment of stiff intermittent contacts, it allows for a thorough exploration of the system’s response. For the first case -a benchmark model-, increasingly complex dynamics arise as more modes are kept in the truncated modal basis, which is due to a series of modal interactions as the impacts distribute mechanical energy from the linearly-unstable first mode to the higher ones. This can be anticipated by studying the nonlinear normal modes of the system, as they expose the allowed internal resonances. In the second case, consisting of a realistic heat-exchanger tube configuration, a similar pattern is observed.

Design of a one-dimensional underwater acoustic leaky wave antenna using an elastic metamaterial waveguide

Acoustic imaging in water traditionally relies on phased arrays of active electro-acoustic transducers to steer acoustic energy in specific directions. One potential alternative approach to steer acoustic beams is to use a single transducer attached to a dispersive antenna that radiates or receives acoustic energy from different directions as the frequency of operation changes. This is known as a leaky wave antenna (LWA). While LWAs have been proven effective in beam steering for electromagnetic and air-borne acoustic waves, the design of an analog device in water presents a unique challenge due to the low contrast in acoustic impedance between elastic solids and water, which necessitates the consideration of fluid-elastic coupling in the design of the elastic LWA. This work presents an approach to design an elastic metamaterial waveguide coupled to an external fluid domain as one means to create an acoustic LWA for underwater operation. Forward-to-backward radiation is achieved through the design of mass-in-cavity structures that produce simultaneous negative effective mass and modulus by considering fluid-elastic coupling. The design is presented through finite element analysis of individual unit cells and a water-loaded elastic LWA. A design example is presented that steers through backfire to endfire as a function of input frequency.

Experimental identification of the fluid-elastic coupling forces on a flexible tube within a rigid square 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, in a water test-loop. 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. The maximum value of the Reynolds number ranged from 105 to 2.16 105 (based on the maximum pitch velocity), according to the tested configuration. 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.

Time-domain numerical simulations of a loosely supported tube subjected to frequency-dependent fluid–elastic forces

Flow-induced vibrations of heat-exchanger tubes are extensively studied in the nuclear industry for safety reasons. Adequate designs, such as anti-vibration bars in PWR steam generators, prevent excessive vibrations provided the tubes are well supported. Nevertheless, degraded situations where the tube/support gaps would widen, must also be considered. In such a case, the tubes become loosely supported and may exhibit vibro-impacting responses due to both turbulence and fluid–elastic coupling forces induced by the cross-flow. This paper deals with the predictive analysis of such a nonlinear situation, given the necessity of taking into account both the strong impact nonlinearity due to the gap and the linearized fluid–elastic forces. In time-domain numerical simulations, computation of flow-coupling forces defined in the frequency-domain is a delicate problem. We recently developed an approach based on a hybrid time–frequency method. In the present paper a more straightforward and effective technique, based on the convolution of a flow impulse response pre-computed from the frequency-domain coefficients, is developed. Illustrative results are presented and discussed, in connection with the previous hybrid method and with experiments. All results agree in a satisfactory manner, validating both computational methods, however the convolutional technique is faster than the hybrid method by two orders of magnitude. Finally, to highlight the subtle self-regulating frequency effect on the stabilization of such system, additional demonstrative computations are presented.

不連続繊維強化プラスチックの成形過程予測のための流体弾性体連成解析手法の提案

不連続繊維強化プラスチックの成形過程予測のための流体弾性体連成解析手法の提案

Competition between Turbulence and Fluid-Elastic Forces in the Response of a Loosely Supported Tube under Cross-Flow

In some degraded situations of heat-exchangers, tubes may be loosely supported while subjected to intense cross-flow generating both turbulence and fluid-elastic forces, and so have vibro-impacting responses. This paper aims at providing a better understanding of the dynamics of such systems in which the conjunction of stops with gaps, broadband random excitation, and fluid-elastic coupling forces, either stabilizing or destabilizing, produces some rather amazing effects linked to a general capacity for the system to be auto-adjusted by the impacts. It is especially shown, (i) how a non-linear gap-system “escapes from instability” by reinforcing the sequence of impacts, (ii) the almost perfect time-history mirror symmetry between the works of turbulence and fluid-elastic forces in the energy balance; (iii) the dissipative aspect of turbulence in some cases. Moreover the paper deals with the relative weight of turbulence and fluid-elastic forces in the tube response that notably depends on the gap size. For this, turbulence is considered as a perturbation of limit cycles obtained when the fluid-elastic forces are the only acting fluid-forces. The study is based on configurations mainly 1-DOF, like the one that has been experimentally tested, but extrapolations for real tube bundle are evoked in conclusion.

Influence of the mass ratio on the fluidelastic instability of a flexible cylinder in a bundle of rigid tubes

Several linear lumped-parameter models were proposed in the past to identify the main mechanisms underlying the cross-flow instability of a single flexible cylinder in tube bundles. Basing on such models, we analyze the influence of the mass ratio when the cylinder vibrates in the transverse direction, without structural damping (corresponding to a zero Scruton number). For two selected mass ratios, we focus on this linear interaction plotting the poles of the fluid–structure system as a function of the reduced velocity (root locus). This asymptotic approach allows a better understanding of the combined influence of the transient fluidelastic coupling and the mass ratio.

Experiments and computations of a loosely supported tube in a rigid bundle subjected to single-phase flow

In this paper the problem of computing the nonlinear vibro-impact responses of loosely supported heat-exchanger tubes subjected to fluidelastic coupling forces, as well as to the turbulence excitation from transverse flows, is addressed. Emphasis is on the fluidelastic modeling within a time domain nonlinear framework, as well as on the stabilizing effect of impacts on the fluidelastic coupling forces. Theoretical computations of the linear and vibro-impacting regimes of a flow-excited flexible cantilever test tube, within a rigid 3×5 square bundle, are based on the experimentally identified fluidelastic coupling force coefficients and turbulence spectrum. Computations are then compared with the experimental vibratory responses, enabling a full validation of the modeling approach. Furthermore, interesting conclusions are drawn, concerning (a) the energy balance between sources and sinks, for a vibro-impacting tube subjected to fluidelastic forces and (b) the dependence of the vibration response frequency on impacts at the loose supports, and their effect on the nonlinear restabilization of fluidelastically unstable tubes. Details on the following aspects are reported in the paper: (1) numerical modeling of the fluidelastic coupling forces for the time domain computations; (2) experimental identification of the fluidelastic coupling coefficients; (3) computations and experiments of both linear and vibro-impacting responses under the combined action of turbulence and fluidelastic coupling and (4) energy aspects of the vibro-impacting fluidelastically coupled tube responses.

Prediction of Flow-Induced Vibrations in Tubular Heat Exchangers—Part I: Numerical Modeling

Flow-induced vibrations due to crossflow in the shell side of heat exchangers pose a problem of major interest to researchers and practicing engineers. Tube array vibrations may lead to tube failure due to fretting wear and fatigue. Such failures have resulted in numerous plant shutdowns, which are often very costly. The need for accurate prediction of vibration and wear of heat exchangers in service has placed greater emphasis on the improved modeling of the associated phenomenon of flow-induced vibrations. In this study, the elastodynamic model of the tube array is modeled using the finite element approach, wherein each tube is modeled by a set of finite tube elements. The interaction between tubes in the bundle is represented by fluidelastic coupling forces, which are defined in terms of the multidegree-of-freedom elastodynamic behavior of each tube in the bundle. Explicit expressions of the finite element coefficient matrices are derived. The model admits experimentally identified fluidelastic force coefficients to establish the final form of equations of motion. The nonlinear complex eigenvalue problem is formulated and solved to determine the onset of fluidelastic instability for a given set of operating parameters.

Numerical Simulation of Fluid-Structure Interaction Using Modified Ghost Fluid Method and Naviers Equations

In this work, we deal with the 1D compressible fluid coupled with elastic solid in an Eulerian-Lagrangian system. To facilitate the analysis, the Naviers equation for elastic solid is cast into a 2×2 system similar to the Euler equation but in Lagrangian coordinate. The modified Ghost Fluid Method is employed to treat the fluid-elastic solid coupling, where an Eulerian-Lagrangian Riemann problem is defined and a nonlinear characteristic from the fluid and a Riemann invariant from the solid are used to predict and define the ghost fluid states. Theoretical analysis shows that the present approach is accurate in the sense of approximating the solution of the Riemann problem at the interface. Numerical validation of this approach is also accomplished by extensive comparison to 1D problems (both water-solid and gas-solid) with their respective analytical solutions.

Active Vibration Control for the Measurement of Fluidelastic Effects

A new method based on active vibration control is proposed to investigate fluidelastic coupling effects beyond fluidelastic instability. This active control method allows to extend the range of flow velocity explored for single input-single output control systems. The method is applied on a flexible tube inserted in a rigid bundle in water and air-water cross-flows. This structure becomes unstable for high flow velocities, fluidelastic forces then causing the damping of the fluid-structure system to fall towards zero. The active control method allows to carry out tests beyond the fluidelastic instability. The flow velocity range explored is doubled in two-phase flow.

COINCIDENCE OF THERMOELASTIC AND THERMOVISCOUS ACOUSTIC WAVES IN FLUID-FILLED ELASTIC TUBES

Thermoelastic and thermoviscous acoustic wave propagation in fluid-filled steel tubes is studied using the exact three-dimensional (3-D) fluid-elastic coupled system equations for the vibration in the n=0 and 1 circumferential modes. Water- and air-filled tubes are examined. The water-filled steel tube shows a strong fluid–elastic coupling effect in the lower frequency range and the air-filled tube shows a strong thermal effect for all frequencies. An 88·9 mm outer diameter tube with 3·05 mm wall thickness is used for the study. Due to the fluid–elastic coupling introduced for air having a specific heat ratio of 1·4 (the solution uncouples when the ratio is 1·0), thermal effects are seen to be very important with the modal attenuation rate being at least 32% underestimated if the thermal effect is not included in the air–steel system. A coincidence phenomenon is accurately found directly from the coupled modes in the fluid–elastic coupled system. When coincidence occurs, the axial modal attenuation rate drops sharply, allowing the exact determination of the coincidence frequency by locating the local minimum of the modal spatial attenuation rate with increasing frequency. In the water–steel system, the coincidence frequency is seen to be 8% in error if methods are employed using the uncoupled theory for the separate fluid and elastic wall.

The Effect of Platen Fins on the Flow-Induced Vibrations of an In-Line Tube Array

This paper presents the results of an experimental study of the effect of streamwise “platen” fins on the fluidelastic instability of an in-line tube array. The fins are fixed parallel to the axis of the tubes in the streamwise direction and effectively prevent any transverse flow between streamwise tube rows. A geometrically identical, dynamically scaled bundle of finless tubes were used as a datum case for comparison. The results showed that, while the fins eliminate vortex shedding, they enhance the fluidelastic coupling between adjacent tubes and substantially reduce the stability threshold.

Fluid-structure coupling between a vibrating cylinder and a narrow annular flow

This paper presents an analytical investigation of the fluidelastic coupling between an axial annular flow and a flexible vibrating axisymmetrical structure. The model presented is suited to single-phase, incompressible, viscous fluids and to annular flows of variable cross-section, axially symmetrical when the structure is motionless. An experimental validation of this model is presented at the end of the paper: the results obtained with the numerical model are compared with experimental data for an oscillating cylinder free to vibrate under the effect of a variable-cross-section annular flow.

Flow‐induced vibrations of tube arrays in cross‐flow

AbstractExisting heat exchanger design criteria do not satisfy the continually increasing requirements for greater efficiency or mass flux and energy throughput. Occasionally, failures appear even after only a few hours of operation, as shown in section 3. A long series of experiments, often carried out on original scale, did lead to the derivation of a large number of empirical expressions; however, physical explanations of the complex tube‐failure interactions could not as yet be found. In contrast, experiments with a well defined simple model, whereby the tube deflections were recorded digitally and, at the same time, tube‐fluid interactions were registered on a high‐speed film, show that elementary “fluid transport mechanisms” control the stability behaviour of the heat exchanger tubes. Vibration excitation mechanisms such as “galloping”, “jet switching” and “whirling” (fluid elastic coupling) proved, with their characteristics, as typical for the vibration behaviour of single rows within the tube array, but not for the vibration phenomena of tube bundles.