Computational Analysis of Rheological Secondary Flow in a Pipe-Manifold Containing In-Plane Double Bends

Abstract

Non-Newtonian fluid flow in pipe bends is inevitable in industrial applications. Previous researchers have extensively explored Newtonian flow through curved ducts. However, the non-Newtonian counterpart gets little attention. We study the turbulent flow of shear-dependent fluids obeying the Power-Law model in a pipe manifold containing an in-plane double bend. Ostwald–de Waele's power law is used to model the fluid's rheology. We utilize computational fluid dynamics (CFD) to solve Reynolds-averaged Navier–Stokes (RANS) equations with the k-ε turbulence model. We validate our numerical results with previous experimental results. The in-plane double bend perturbs the flow in the pipe manifold to develop a Prandtl's secondary flow of the first kind. A fully developed flow at the bend upstream is disturbed due to the bend's curvature and regains its fully developed characteristics upon a certain downstream length after the exit of the bend. We study the rheological characteristics of the secondary flow within the bend and the evolution of fluid flow at the bend downstream. We demonstrate that the centrifugal force-dominated secondary flow increases with a decrease of the non-Newtonian power-law index. We capture the camel's-back-shaped velocity profiles within the bend due to accelerating-decelerating flow. The study reveals that the average flow velocity increases along the bend with a corresponding pressure head loss. We quantify this velocity rise by a newly introduced non-dimensional number, viz. enhancement ratio. The double bend's enhancement ratio decreases with an increase in n.