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. (authors)