Dynamics and friction losses of the flow of yield-stress fluids through 90° pipe bends

Abstract

We characterise the dynamics and the pressure losses of yield-stress fluid flow through 90° pipe bends using Computational Fluid Dynamics. We show that the bend can influence the flow far upstream and downstream depending on the Bingham number – the ratio of the yield-stress to viscous stresses – even under conditions where fluid inertia can be considered negligible. Moreover, non-Newtonian viscous effects counteract centrifugal forces and suppress secondary motion. We also show that the Darcy–Weisbach equation with a generalised version of the Reynolds number can accurately predict pressure losses. This applies to a wide range of bend curvatures and rheological parameters, and elastoviscoplastic fluids with Saramito-type rheology and elastic moduli as small as 500 Pa. Our model holds for multiple adjacent bends, with minimal impact from interactions between bends. Deviations from this model occur when inertial effects in the flow become significant and are smaller for yield stress fluids than Newtonian fluids.