Techniques for estimating the unknown functions of incomplete experimental spectral and correlation response matrices

In this paper, we propose analytical and numerical straightforward approximate methods to estimate the unknown terms of incomplete spectral or correlation matrices, when the cross-spectra or cross-correlations available from multiple measurements do not cover all pairs of transducer locations. The proposed techniques may be applied whenever the available data includes the auto-spectra at all measurement locations, as well as selected cross-spectra which implicates all measurement locations. The suggested methods can also be used for checking the consistency between the spectral or correlation functions pertaining to measurement matrices, in cases of suspicious data. After presenting the proposed spectral estimation formulations, we discuss their merits and limitations. Then we illustrate their use on a realistic simulation of a multi-supported tube subjected to turbulence excitation from cross-flow. Finally, we show the effectiveness of the proposed techniques by extracting the modal responses of the simulated flow-excited tube, using the SOBI (Second Order Blind Identification) method, from an incomplete response matrix

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

EXPERIMENTAL INVESTIGATION OF IN-FLOW FLUIDELASTIC INSTABILITY FOR SQUARE TUBE BUNDLES SUBJECTED TO SINGLE-PHASE AND TWO-PHASE TRANSVERSE FLOWS

International audienceThe in-flow fluidelastic instability of tube bundles prompted renewed interest since the recent unanticipated failure of the replacement steam generators at the San Onofre nuclear power station. A literature review on the topic discloses contrasting views, depending on the tube bundle and flow configuration addressed. The present paper reports extensive experiments, performed at CEA-Saclay, on the in-flow fluidelastic features of square bundles. A 5x3 square bundle with P/D=1.5 and D=30mm was subjected to single-phase and two-phase air-water (with homogeneous void fractions 80%, 90% and 98%) transverse flows, for four different flexibility configurations. The flexible tubes were mounted using anisotropic supports, only allowing for in-flow vibrations. This is the first time that in-flow test results are obtained for square bundles subjected to two-phase flows. As main conclusion from the experiments in both single and two-phase flows, no instability was observed for all tested configurations. These results support those obtained by previous authors for similar tested configurations and highlight the contrasting in-flow fluidelastic behavior of triangular and square bundles

An evaluation of methods for the time-domain simulation of turbulence excitations for tube bundles subjected to non-uniform flows

International audienceThe present paper addresses the problem of achieving adequate modelling of the turbulence excitations,when performing nonlinear time-domain computations for the predictive dynamical analysis of gapsupported tube bundles of nuclear power-plant components – namely steam generators. Although in mostpublications the details on time-domain implementations of turbulence excitations are seldom supplied, it is anontrivial task to provide adequate time-domain force functions which rightly account for the spectralproperties, the space correlation, as well as the local magnitude of the flow velocity field. Oversimplifiedapproaches may lead to inadequate modelling of the excitation, and hence to unreliable predictive results.We recently proposed a simple and consistent method to simulate the continuous space-correlated flowforce field (Antunes et al, 2008), using a finite set of uncorrelated discrete random forces, which arecomputed based on the theoretical formulation for the linear modal responses of the excited tube. Here weinvestigate whether such computationally efficient approach is effective, even when dealing with thenonlinear vibro-impact responses of gap-supported tubes subjected to non-uniform flows. Illustrative linearand nonlinear tube response computations using our simple excitation method are compared with thoseobtained by modelling the turbulence through a partially correlated random field, computed using the morecomputationally intensive techniques developed by Shinozuka et al (1971, 1990)

Identification of Random Excitation Fields From Vibratory Responses With Application to Multisupported Tubes Excited by Flow Turbulence

In this paper, we address the identification of the spectral and spatial features of random flow excitations for multisupported tubular components such as steam generator tubes and nuclear fuel rods. In the proposed work, source identification is performed from a set of measured vibratory responses, in the following manner: (1) The modal response spectra and modeshape amplitudes at the measurement locations are first extracted through a blind decomposition of the physical response matrix, using the second order blind identification (SOBI) method; (2) the continuous modeshapes are interpolated from the identified values at the measurement locations; (3) the system modal parameters are identified from the modal responses using a simple single degree of freedom (SDOF) fitting technique; (4) inversion from the modal response spectra is performed for the identification of the modal excitation spectra; (5) finally, an equivalent physical excitation spectrum as well as the flow velocity profiles are estimated. The proposed approach is illustrated with identification results based on realistic numerical simulations of a multisupported tube under linear support conditions

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

International audienceIn 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

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

Experiments and computations of a loosely supported tube under two-phase buffeting and fluid-elastic coupling forces

International audienceIn a recent paper we addressed the problem of predicting the nonlinear vibro-impact responses of looselysupported heat-exchanger tubes subjected to single-phase turbulence and fluid-elastic coupling forces fromtransverse flows. Here, we extend that previous work to two-phase flows, by presenting nonlinear time-domainpredictive computations, as well as validation experiments, of the vibro-impacting dynamical tube responses, when subjected to the combined action of two-phase random buffeting excitation and fluid-elastic coupling forces. Emphasis is on the fluid-elastic modeling within a time-domain nonlinear framework, as well as on the stabilizing effect of impacts on the fluid-elastic coupling forces. Computations of the vibro-impacting regimes of a flow-excited cantilever test tube, within a rigid 3x5 square bundle, are based on the experimentally identified two-phase fluidelastic coupling force coefficients and random excitation spectra, as a function of the homogeneous flow velocity, for a void fraction of 85 %. Computations are then compared with the experimental vibratory responses, enabling a satisfying preliminary validation of the modeling approach for two-phase flows

A new method for the generation of representative time-domain turbulence excitations

In this paper we address the issue of generating, from the spectral and spatial parameters of turbulent flow excitations, time-domain random excitations suitable for performing representative nonlinear numerical simulations of the dynamical responses of flow-excited tubes with multiple clearance supports. The new method proposed in this work, which is anchored in a sound physical basis, can effectively deal with non-uniform turbulent flows, which display significant changes in their spatial excitation properties. Contrary to the classic technique developed by Shinozuka and coworkers, which generates a large set of correlated physical forces, the proposed method directly generates a set of correlated modal forces. Our approach is particularly effective leading to a much smaller number of generated time-histories than would be needed using physical forces to simulate the turbulence random field. In the case of strongly non-uniform flows, our approach allows for a suitable decomposition of the flow velocity profile, so that the spectral properties of the turbulence excitation are modeled in a consistent manner. The proposed method for simulating turbulence excitations is faster than Shinozuka׳s technique by two orders of magnitude. Also, in the framework of our modal computational approach, nonlinear computations are faster, because no modal projection of physical turbulent forces is needed. After presenting the theoretical background and the details of the proposed simulation method, we illustrate it with representative linear and nonlinear computations performed on a multi-supported tube