Gap Effect on the Random and Fluid-Elastic Forces Acting in the Vibration of a Loosely Supported Tube Under Cross-Flow

In degraded situations of heat-exchangers, tubes may become loosely supported while subjected to intense crossflow which generates both turbulent and fluid-elastic forces. The vibro-impacting regimes that result have been studied by the authors during these last few years, based on analytical experiments and numerical simulations. Taking advantage of this material, the paper aims at showing some dynamic effects that have been observed and drawing lessons concerning the vibration of tubes under cross-flow when they are linearly unstable. If the fluid-elastic damping drops until the total damping becomes negative when the flow reduced velocity increases, a non-linear gap-system escapes from instability by reinforcing the sequence of impacts and its apparent frequency. On the other hand, the turbulent excitation is characterized by broadband PSDs that decrease with frequency. Thus the vibro-impacting response of the tubes results from a competition between the turbulent and fluid-elastic forces, according to a process that depends on the gap size. The fluid-elastic coupling forces may be either stabilizing (positive damping) or destabilizing (negative one), and, in a more amazing way, the random forces may be dissipative. The paper illustrates the previous points from the tested experimental configuration which was mainly 1-DOF. Dimensionless results are given for this configuration. Extensions to more realistic tubes are discussed from numerical simulations of a straight beam with three loosely supports. The starting point of simulations is though experiments where the fluid-elastic forces would act, but not the turbulent ones, which would produce limit cycles in the phase space. Turbulence is then considered as perturbation of limit cycles, and as shown below by notably introducing a dimensionless “gap-turbulence” parameter, smaller the gap sizes are, larger the relative weight of turbulence is. The Rice frequency and the mean impact force are indicators of this relative weight and the competition between the fluid-forces. From this general understanding, and using preliminary results with the beam model, a few guidelines are finally evoked for determining allowable gaps sizes in degraded situations. But a lot of work has to be done with more sophisticated models to concretize these ideas.