Steady Herschel–Bulkley fluid flow in three-dimensional expansions

Abstract

In this paper we study steady flow of Herschel–Bulkley fluids in a canonical three-dimensional expansion. The fluid behavior was modeled using a regularized continuous constitutive relation, and the flow was obtained numerically using a mixed-Galerkin finite element formulation with a Newton–Raphson iteration procedure coupled to an iterative solver. Results for the topology of the yielded and unyielded regions, and recirculation zones as a function of the Reynolds and Bingham numbers and the power-law exponent, are presented and discussed for a 2:1 and a 4:1 expansion ratio. The results reveal the strong interplay between the Bingham and Reynolds numbers and their influence on the formation and break up of stagnant zones in the corner of the expansion and on the size and location of core regions.