Experimental investigation of purely elastic instabilities in periodic flows

Abstract

Purely elastic instabilities in the flows of polyisobutylene-based Boger fluids in the periodic channel (PC) and past a (linear) periodic array of closely spaced cylinders (PAC) in a channel have been experimentally examined. The test geometries have the same wavelength and amplitude associated with the periodic variation in the cross-sectional area. Pressure measurements show temporal fluctuations that appear when the Weissenberg number exceeds approximately 0.7 and 1.1 for the PC and PAC geometries, respectively. Flow visualization using digital particle imaging velocimetry (DPIV) shows that below the critical Weissenberg number, flows are two-dimensional and steady consisting of slow vortex motion in the wake region for the flow past the PAC flow and in the near wall region for the PC flow. Inception of flow instability results in the breakdown of the symmetric vortices in the flow past the PAC flow and in time-dependent vortex motion in the PC flow. The onset of flow instability is also accompanied by enhanced flow resistance. The power spectral composition of the pressure fluctuations is uniform along the flow direction for both geometries. This implies that in time-dependent simulations a unit cell with periodic boundary conditions can faithfully represent these geometries. The onset Weissenberg number values, when scaled with the maximum curvature of the streamlines, are very close to each other indicating that the instability arises from the coupling between streamline curvature and elastic normal stresses.