Laminar Flow of a Herschel-Bulkley Fluid Over an Axisymmetric Sudden Expansion

Abstract

The steady flow of non-Newtonian Herschel-Bulkley fluids over a one-to-two axisymmetric sudden expansion was studied numerically. Finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations were obtained within the laminar flow regime for a range of Reynolds numbers, yield numbers, and power-law index values. The Reynolds number, based on the upstream pipe diameter and bulk velocity, was varied between 50 and 200, while the yield number was varied between 0 and 2. The power-law index values mapped the 0.6–1.2 range, allowing for the investigation of both shear-thinning and shear-thickening effects. Two distinct flow regimes are identified. One is associated with a combination of low yield numbers, high Reynolds numbers, and high power-law indexes, and exhibits a recirculating flow region at the step corner which is similar to that seen in Newtonian flows. The other flow regime, however, is characterized by a dead-zone behind the step corner, and is obtained for a combination of high yield numbers, low Reynolds numbers, and low power-law indexes. The yield number appears to be the dominant parameter affecting the shape and extent of the corner flow region as well as flow redevelopment further downstream. In general, the influence of the power-law index on the flow structure is stronger when the yield number is small. A flow character that is an exception to this general trend is the recirculating corner vortex intensity which decreases substantially with decreasing power-law index values for all investigated yield numbers.