The influence of mode dominance and traveling waves on flexible cylinder flow-induced vibration

Abstract

Flexible cylinder flow-induced vibration exhibits complex variations in space and time. Sheared current profiles lead to variable excitation along the length. To characterize these spatial-temporal variations, a proper orthogonal decomposition (POD) is conducted and two parameters are defined based on the POD analysis results. The number of dimensions of the flexible cylinder flow-induced vibration is reduced from infinite degrees of freedom to a few dominant proper orthogonal modes in the cross-flow and in-line directions sufficient to characterize the response properly. A mode dominance factor is proposed, which characterizes whether the response is single-mode dominated or reveals the participation of multiple modes contributing to the total response. To further tell the difference between traveling waves and standing waves, a traveling wave index is proposed. The statistics of the mode dominance factor and the traveling wave index are presented for a set of flexible cylinder VIV experiments. It was found that cross-flow VIV response is more traveling wave-dominated in sheared flow than in the uniform flow. The sensitivity of the statistics with the number of sensors, the region of the pipe where the analysis was conducted, and the length of the time-averaged moving windows are also discussed. The estimate of the mode dominance factor can be affected by the number of sensors due to aliasing. As the window length increased, the mode dominance factor decreased, because more time was available for the response to change within the longer window length. Moreover, extending the region of analysis from the power-in region near the high flow speed end to the whole pipe in linearly sheared flows, low frequency and high-frequency excitation, acting concurrently, are routinely found to exist.