Laurent Borsoi

Simple Relations for Estimating the Unknown Functions of Incomplete Experimental Spectral and Correlation Response Matrices

In this paper we suggest two simple 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 formulae 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 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.

Vibro-Impact Experiments and Computations of a Gap-Supported Tube Subjected to Single-Phase Fluid-Elastic Coupling Forces

In this paper we address the problem of computing the nonlinear vibro-impact responses of gap-supported heat-exchanger tubes subjected to fluid-elastic coupling forces, as well as to the turbulence excitation from transverse flows. 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. Theoretical computations of the linear and vibro-impacting regimes of a flow-excited cantilever test tube, within a rigid 3×5 square bundle, are based on the experimentally identified fluid-elastic 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 fluid-elastic forces; (b) the dependence of the vibration response frequency on impacts at the loose supports, and their effect on the nonlinear re-stabilization of fluid-elastically unstable tubes. Details on the following aspects are reported in the paper: (1) Numerical modeling of the fluid-elastic coupling forces for time-domain computations; (2) Experimental identification of the fluid-elastic coupling coefficients; (3) Computations and experiments of both linear and vibro-impacting responses under the combined action of turbulence and fluid-elastic coupling; and (4) Energy aspects of the vibro-impacting fluid-elastically coupled tube responses.Copyright

Computation of a Loosely Supported Tube Under Cross-Flow by a Hybrid Time-Frequency Method

Flow-induced vibrations of heat-exchanger tubes are particularly analyzed in the nuclear industry for safety reasons. Adequate designs, such as anti-vibration bars in PWR steam generators, prevent any 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 situation, based on a time-frequency hybrid method, given the necessity of taking into account both the strong impact nonlinearity due to the gap and the linearized fluid-elastic forces defined in the frequency domain. It comprises four parts.1) The experimental campaign carried out at CEA Saclay on this issue, with a rigid square bundle surrounding a flexible cantilever tube under water cross-flow, is briefly recalled.2) The hybrid time-frequency method is presented. The technique consists in an iterative solving, going back and forth from the frequency domain to the time domain, until convergence. Focus is made on the key points that are the algorithm convergence, and the non-causality of fluid-elastic forces stemming from the extrapolation of the frequency-limited experimental data.3) The experimental and computational results are compared for a large range of flow velocities and three values of gaps, with a satisfying overall agreement. The comparison includes also previous results obtained from a simplified method based on the concept of “instantaneous” frequency.4) Finally two a priori surprising behaviors are noted in the energy balances that have been computed: the sometimes dissipative aspect of turbulence forces, and the “mirror effect” between the work of turbulence and fluid-elastic forces.Copyright

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.

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 Shinozuka technique, 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.Copyright

Identification of the Turbulence Force Field Excitation From a Set of Vibratory Responses of a Multi-Supported Tube

In this paper we address the identification of the spectral and spatial features of random flow excitations, for multi-supported 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 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 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 spectra as well as the flow velocity profiles are estimated. The proposed approach is illustrated with identification results based on realistic numerical simulations of a multi-supported tube under linear support conditions.Copyright