Xavier Delaune

A new analytical approach for modeling the added mass and hydrodynamic interaction of two cylinders subjected to large motions in a potential stagnant fluid

Abstract A potential theory is presented for the problem of two moving circular cylinders, with possibly different radii, large motions, immersed in an perfect stagnant fluid. We show that the fluid force is the superposition of an added mass term, related to the time variations of the potential, and a quadratic term related to its spatial variations. We provide new simple and exact analytical expressions for the fluid added mass coefficients, in which the effect of the confinement is made explicit. The self-added mass (resp. cross-added mass) is shown to decrease (resp. increase) with the separation distance and increase (resp. decreases) with the radius ratio. We then consider the case in which one cylinder translates along the line joining the centers with a constant speed. We show that the two cylinders are repelled from each other, with a force that diverges to infinity at impact. We extend our approach to the case in which one cylinder is imposed a sinusoidal vibration. We show that the force on the stationary cylinder and the vibration displacement have opposite (resp. identical) axial (resp. transverse) directions. For large vibration amplitudes, this force is strongly altered by the nonlinear effects induced by the spatial variations of the potential. The force on the vibrating cylinder is in phase with the imposed displacement and is mainly driven by the added mass term. The results of this paper are of particular interest for engineers who need to understand the essential features associated with the vibration of a solid body in a still fluid.

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

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