Creeping Flow of Viscoelastic Fluid Over an Elliptic Cylinder

Abstract

Viscoelastic fluids, combining both viscous and elastic properties, are widely used in industrial processes involving polymer solutions. Although extensive research exists on flow around circular cylinders, the behaviour of viscoelastic fluid past elliptical cylinders has not been thoroughly investigated. This study numerically examines the steady, two-dimensional creeping flow of an Oldroyd-B viscoelastic fluid over an unconfined elliptic cylinder at a fixed low Reynolds number (Re=0.01). The influence of the solvent viscosity ratio (β=0.1 and 0.9) and Deborah number (De= 0.025 and 1.5) on flow characteristics is analysed using OpenFOAM with the RheoTool Solver. Results reveal that increasing the Deborah number leads to a pronounced peak in the pressure coefficient at the front stagnation point, indicating significant elastic contributions. The velocity profiles display a central velocity reduction due to flow separation, with negligible differences across the studied values. An increase in Deborah number leads to a significant rise in normal stress difference at the flow centreline, especially for low β values, indicating strong elastic effects.