Viscoelastic fluid flow past a confined cylinder: Three-dimensional effects and stability

Abstract

The flow of viscoelastic fluids past a confined cylinder in a rectangular duct was investigated experimentally and numerically in order to assess the three-dimensional effects associated with cylinder aspect ratio (AR) and the fluid rheology. The blockage ratio was 50%, the cylinder aspect ratios were ARŒ16, 8 and 2, and the flow conditions tested varied from creeping flow conditions up to the onset of time-dependent flow. Three viscoelastic fluids were tested, namely a shear-thinning and two Boger fluids, and the results were compared against the numerical and experimental data for Newtonian fluids. For the shear-thinning fluid, and in the range of Deborah numbers (De) studied (0.025oDeo0.99), elastic instabilities appear upstream of the cylinder above a critical Deborah number, that depends on the aspect ratio. In contrast, for the Boger fluids the flow remained symmetric both upstream and downstream of the cylinder in the range of Deborah numbers studied (Deo1.3). For all non-Newtonian fluids studied, the streamwise velocity profiles show that the length required to achieve the fully developed velocity downstream of the cylinder increases with De and AR.