Fluid-Elastic Coefficients in Single Phase Cross Flow: Dimensional Analysis, Direct and Indirect Experimental Methods

Abstract

Abstract The importance of fluid-elastic forces in tube bundle vibrations can hardly be over-emphasized, in view of their damaging potential. In the last decades, advanced models for representing fluid-elastic coupling have therefore been developed by the community of the domain. Those models are nowadays embedded in the methodologies that are used on a regular basis by both steam generators providers and operators, in order to prevent the risk of a tube failure with adequate safety margins. From an R&D point of view however, the need still remains for more advanced models of fluid-elastic coupling, in order to fully decipher the physics underlying the observed phenomena. As a consequence, new experimental flow-coupling coefficients are also required to specifically feed and validate those more sophisticated models. Recent experiments performed at CEA-Saclay suggest that the fluid stiffness and damping coefficients depend on further dimensionless parameters beyond the reduced velocity. In this work, the problem of data reduction is first revisited, in the light of dimensional analysis. For single-phase flows, it is underlined that the flow-coupling coefficients depend at least on two dimensionless parameters, namely the Reynolds number Re and the Stokes number Sk. Therefore, reducing the experimental data in terms of the compound dimensionless quantity Vr = Re/Sk necessarily leads to impoverish results, hence the data dispersion. In a second step, experimental data are presented using the dimensionless numbers Re and Sk. We report experiments, for a 3 × 5 square tube bundle subjected to water transverse flow. The bundle is rigid, except for the central tube which is mounted on a flexible suspension allowing for translation motions in the lift direction. The evolutions of the flow-coupling coefficients with the flow velocity are determined using two different experimental procedures: (1) In the direct method, an harmonic motion of increasing frequency is imposed to the tube. (2) In the indirect method, the coefficients are obtained from the modal response of the tube (frequency, damping). The coefficient identification was performed well beyond the system instability boundary, by using active control, allowing an exploration of a significant range of flow velocity. For a given Sk, the results show that: (a) at low Re, the flow-coupling coefficients are close to zero; (b) at intermediate Re, the flow stabilizes the tube; (c) at high Re, the flow destabilizes the tube, leading to a damping-controlled instability at a critical Re. Reducing the data in terms of Re and Sk clarifies the various experimental “branches”, which are mixed when using Vr. The two identification techniques lead to reasonably compatible fluid-elastic coefficients.