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

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