Fluidelastic instability of tube arrays in nonuniform flow: Effect of multimode coupling

Fluidelastic analysis of a tube array usually considers a transverse vibration mode and a streamwise vibration mode for each tube. The underlying effect of multimode coupling is often neglected. For an array of multi-span tubes with closely spaced modes exposed to nonuniform flow, the effect of multimode coupling on fluidelastic instability may be non-negligible but the effect remains unclear. To fill this gap, this paper analyzes the effect of multimode coupling on the fluidelastic instability of tube arrays in a nonuniform flow. The main purpose is to quantify the multimode coupling effect on the instability threshold and figure out conditions under which the multimode coupling effect becomes significant. Equations of motion for the fluidelastic vibrations of an array of multi-span tubes in general nonuniform flow are presented. A mode-by-mode tracing method is introduced to iteratively search for the critical mode (i.e., the mode that initiates the instability) and determine the critical flow velocity. Two case studies involving the fluidelastic analyses of different tube arrays demonstrate the effects of multimode coupling. It is concluded that the multimode coupling may affect the critical flow velocity and the vibration mode and hence the wear pattern due to fluidelastic vibrations. For the considered two case studies, the reductions of critical flow velocities due to multimode coupling can become as high as 40%. The overall effect depends on the mode that initiates the instability and the modal velocity integrals and frequency ratios of the coupling modes. For an array of flexible tubes, the multimode coupling effect on the critical flow velocity is insignificant if the tubes' natural frequencies are perfectly tuned. However, the multimode coupling effect contributes to affect the critical flow velocity if there is a detuning between natural frequencies of respective tubes, and/or between the streamwise and transverse frequencies of every single tube. These conclusions highlight the necessity to consider the multimode coupling effect in fluidelastic analysis of tube arrays with closely spaced modes. (c) 2022 The Author(s). Published by Elsevier Ltd.