Philippe Piteau

TIME-DOMAIN MODELING OF THE RANDOM VIBRATIONS OF TUBES SUBJECTED TO TURBULENCE-CONVEYING FLOWS

The vibrations of multi-supported tubes subjected to flow excitation have been the subject of active research for many years, in particular connected with the critical design of heat exchangers and fuel bundles of nuclear power facilities. Because tubes are often loosely supported, their nonlinear dynamics are conveniently addressed through time-domain numerical simulations, for the predictive analysis with respect to wear and fatigue. Turbulence is one of the main excitation mechanisms which drive tube vibrations. We recently revisited the problem of random excitation generation in the time domain, for transverse flows. A new simplified an efficient technique was developed, which properly emulates the spectral and spatial features of the turbulence force field. Results were successfully compared with those from another generation method based on the classical work by Shinozuka and co-workers. In the present paper, we extend our previous work by modeling the time-domain random excitation from flows which display a significant axial velocity component, leading to the convection of turbulence fluctuations. This problem has been addressed by many authors in the past, mainly focusing on linear analysis in the frequency domain, for flow-excited plates, pipes and tubes. Here, for the purpose of nonlinear analysis, we focus on two techniques for generating time-domain turbulence excitations which properly account for the effects of the axial transport term in convective flows. We start by extending our original random force generation method, in order to emulate axial turbulent flows. For the purpose of physical discussion and computational efficiency evaluation, we also implemented an updated version of Shinozuka’s excitation generation technique. We discuss the use of random forces applied at fixed locations, but also investigate the use of axially convected travelling forces. The practical significance of the cross-spectral convection term is evaluated for pure axial and mixed flows. Finally, because time-domain dynamical simulations of practical interest are usually two-dimensional, we discuss the correlation of the orthogonal random forces generated along the motion directions, when simulating two-dimensional turbulence fields.Copyright

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

Experiments on the Nonlinear Dynamics of Parallel Plates Subjected to Squeeze-Film Forces

Squeeze film dynamical effects are relevant in many industrial components, bearings and seals being the most conspicuous applications. But they also arise in other industrial contexts, for instance when dealing with the seismic excitation of spent fuel racks. The significant nonlinearity of the squeezefilm forces prevents the use of linearised flow models, therefore a fully nonlinear formulation must be used for adequate computational predictions. Because it can accommodate laminar and turbulence flow effects, a simplified bulk-flow model – based on gap-averaged Navier-Stokes equations and incorporating all relevant inertial and dissipative terms – was previously developed by the authors (Antunes & Piteau, 2010), assuming a constant skin-friction coefficient. In this paper we introduce an improved theoretical formulation, fully developed elsewhere (Piteau & Antunes, 2010), such that the dependence of the friction coefficient on the local flow velocity is explicitly accounted for, so that it can be applied to laminar, turbulent and mixed flows. The main part of the paper is then devoted to the presentation and discussion of the results from an extensive series of experiments performed at CEA/Saclay. The test rig consisted on a long gravity-driven instrumented plate of rectangular shape colliding with a planar surface. Theoretical results stemming from both analytical flow models are confronted with the experimental measurements, in order to assert the strengths and drawbacks of the simpler original model, as well as the improvements brought by the new but more involved flow formulation.

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

A Theoretical Series Solution for the Dynamics of Finite-Length Bearings and Squeeze-Film Dampers

In this paper we develop a non-linear dynamical solution for finite length bearings and squeeze-film dampers based on a Spectral-Galerkin method. In this approach the gap-averaged pressure is approximated, in the lubrication Reynolds equation, by a truncated double Fourier series. The Galerkin method, applied over the residuals so obtained, generate a set of simultaneous algebraic equations for the time-dependent coefficients of the double Fourier series for the pressure. In order to assert the validity of our 2D–Spectral-Galerkin solution we present some preliminary comparative numerical simulations, which display satisfactory results up to eccentricities of about 0.9 of the reduced fluid gap H/R. The so-called long and short-bearing dynamical solutions of the Reynolds equation, reformulated in Cartesian coordinates, are also presented and compared with the corresponding classic solutions found on literature.© 2003 ASME