Steady Flow of Purely Viscous Shear-Thinning Fluids in a 1:3 Planar Gradual Expansion

Abstract

Laminar flow of non-Newtonian fluid (shear-thinning) through a 1:3 planar gradual expansion is numerically investigated, for various Power-Law index (0.6, 0.8 and 1.0) and expansion angles (15, 30, 45, 60 and 90°) at different generalized Reynolds number (1 ≤ Reg ≤ 400). The study of these parameters effect on the flow pattern allowed the determination of the two critical generalized Reynolds numbers (Regcr1 and Regcr2), which correspond to the transition from the symmetric to the asymmetric flow and the appearance of the third recirculation zone respectively. The results showed that decreasing the Power-Law index or the expansion angle stabilizes the flow by increasing significantly the two critical generalized Reynolds numbers. In order to predict the two critical generalized Reynolds numbers, two correlations have been proposed.

Keywords

• Gradual expansion; Bifurcation; Shear-thinning fluid; Critical Reynolds Number; Recirculation