Viscoelastic flow-induced oscillations of a cantilevered beam in the crossflow of a wormlike micelle solution

Abstract

Abstract We investigate the interactions between a cantilevered flexible beam and cross-flow of a viscoelastic fluid. Unlike Newtonian fluids, viscoelastic fluids exhibit elastic flow instabilities even in the absence of inertia. These elastic flow instabilities drive the oscillations of flexible structures placed in their flow path. In this work, the fluid–structure interactions between the flow of viscoelastic wormlike micelle solution and a flexible cantilevered beam is studied as a function of the Weissenberg number and the beam’s tip angle. At low Weissenberg numbers, the flow remained stable and the beam deflected in the direction of flow. As the Weissenberg number was increased, a separated vortex appeared upstream of the cantilever near its tip. At a critical Weissenberg number of W i = 11 , the flow became unstable. For beams with small tip angles of 0° and 25°, no oscillations were observed. However, for beams with larger tip angles of 45° and 65°, oscillatory motions coupled to the flow instability were observed, where the amplitude of the beam oscillations increased with increasing tip angle. Particle image velocimetry measurements showed that the elastic flow instability was characterized by the periodic formation of strong fluid jet that originated upstream of the beam in a region of strong extensional flow where it likely resulted from the local breakdown of the wormlike micelle solution. This jet was accompanied by a pair of counter-rotating vortices on its sides as it entrained fluid around the tip of the beam. The frequency of oscillations of the beams with large tip angles increased monotonically with Weissenberg number, while their amplitudes of oscillations initially increased with Weissenberg number before decaying to zero for W i > 20 , despite the fact that the flow remained unstable. Our results showed that oscillations were only possible when the tip of the cantilevered beam made a positive angle with respect to the primary incoming flow direction.