Influence of solvent viscosity ratio on the creeping flow of viscoelastic fluid over a channel confined circular cylinder

Abstract

In this study, the role of solvent viscosity ratio (β) on the creeping flow characteristics of Oldroyd-B fluid over a channel-confined circular cylinder has been explored numerically. The flow governing equations have been solved by RheoTool, an open-source toolbox based on OpenFOAM, employing the finite volume method for extensive ranges of Deborah number (De=0.025–1.5) and solvent viscosity ratio (β=0.1–0.9) at a fixed wall blockage (B = 0.5). The present investigation has undergone extensive validation, with available literature under specific limited conditions, before obtaining detailed results for the relevant flow phenomena, such as stream function, pressure and stress contour profiles, pressure coefficient (Cp), wall shear stress (τw), normal stress (τxx), first normal stress difference (N1), and drag coefficient (CD). The flow profiles have exhibited a distinctive behavior characterized by a loss of symmetry in the presence of pronounced viscoelastic effects. The results for low De notably align closely with those for Newtonian fluids, and the drag coefficient (CD) remains relatively constant regardless of β, as the viscoelastic influence is somewhat subdued. These observations indicate that at high De and low β, viscoelasticity causes asymmetry in creeping flow around a circular cylinder. With an increase in De, the maximum velocity in gap between cylinder and channel walls increases; however, the cylinder experiences significantly less drag force. Within this parameter range, the prevailing force governing the flow is the pressure drag force.