Characteristics of laminar viscous shear-thinning fluid flows in eccentric annular channels

Abstract

Laminar fully developed flows of time-independent viscous shear-thinning fluids in straight eccentric annuli are considered. The fluid rheology is modeled by the power-law constitutive equation, which is representative of many industrial process liquids. The annulus models flow channels in process heat exchangers, extruders, and drilling wells, among others. The flow cross-section geometry is mapped into a unit circle by means of a coordinate transformation, and the governing momentum equation is solved by finite-difference techniques using second-order accurate discretization. Numerical solutions for a wide variation of annuli radius ratio (0.2 ≤ r ∗ ≤ 0.8) , inner core eccentricity (0 ≤ ε ∗ ≤ 0.8) , and shear index (1 ≥n ≥ 0.2) , are presented. Both fluid rheology and annuli eccentricity are seen to have a strong influence on the flow behavior. The eccentricity causes the flow to stagnate in the narrow gap with higher peak velocities in wide gap, and large azimuthal variations in the velocity field. The fluid pseudoplasticity gives rise to even greater flow maldistribution around the annulus, with non-uniform velocity fields, wall shear-stress distribution, and friction factor characteristics.