Observation of lock-in for viscoelastic fluid–structure interactions

Abstract

Under the right conditions, viscoelastic fluids can exhibit elastic flow instabilities in the absence of inertia. If the fluid is in contact with a flexible or flexibly-mounted structure, these elastic flow instabilities lead to time-dependent forces on the structure, which can cause the structure to oscillate. This constitutes a new class of Viscoelastic Fluid–Structure Interactions (VFSI). Up until now, the VFSI reported in the literature demonstrated a one-way coupling between the fluid and the structure where little feedback from the structure to the flow was observed. Here, we report for the very first time, the presence of a lock-in behavior in VFSI. We have designed and conducted a set of experiments in which the frequency of the elastic flow instabilities and the natural frequency of the flexible structure become equal as the flow velocity is increased, and therefore lock-in is observed. We present amplitude and frequency responses of two sets of flexibly-mounted cylinders over a range of Weissenberg numbers and reduced velocities to show the lock-in range. The time-varying flow fields inside and outside the lock-in range were studied through streak-line imaging and particle image velocimetry. The viscoelastic lock-in range was observed for a Weissenberg number range of 5≤Wi≤15 for one of the cylinders tested and for a range of 20≤Wi≤30 for the other. For both cylinders, the lock-in started at a reduced velocity of Vr≈1.5. In Cylinder 1, the lock-in ended at Vr≈4, while for Cylinder 2 the end of the lock-in was not observed, because the data points did not cover a wide enough range. Similar to the lock-in observed in the typical VIV response in a Newtonian fluid, the frequency of the elastic flow instability was found to increase with increasing flow velocity before plateauing at the natural frequency of the cylinder in the lock-in range. Unlike the VIV response of a Newtonian fluid, where the lock-in range corresponds to the maximum observed amplitude of oscillations, in VFSI the amplitude of oscillations reached a plateau while in lock-in, but increased with Weissenberg number and reduced velocity before and after the lock-in range.