Vortex modes in the wake of an oscillating long flexible cylinder combining POD and fuzzy clustering

Abstract

A method combining proper orthogonal decomposition (POD) and Fuzzy Clustering (FC) is used as a pattern recognition technique, in order to identify vortex modes in digital particle image velocimetry (DPIV) data, obtained in the wake of a long flexible circular cylinder undergoing vortex-induced vibrations. The POD allows a low-dimensional description of the wake, so the the fuzzy c-means algorithm can be used for clustering in a reduced order problem. The output is a set of well-defined flow clusters representing the vortex patterns found in the wake. This methodology provides an alternative, easier to automate when dealing with large amounts of data, to instantaneous or phase averaged representations of vortex wakes. Phase averaging becomes difficult and tedious when applied as in this case, to wakes of bluff bodies undergoing non-periodic motions. The DPIV data were obtained at two elevations along the length of a long flexible circular cylinder model, which had an aspect ratio (length over diameter) of about 94. The experiments were carried out in a water channel with flow speeds up to 0.75 m/s, giving Reynolds numbers, based on the external diameter of the cylinder, in the range from 1,200 to 12,000. The set-up allowed changes in the fundamental natural frequencies, which resulted in reduced velocities based on that frequency (velocity divided by frequency and external diameter), up to 15. The mass ratio of the model (mass divided by mass of displaced fluid) was around 1.8.