Steady Herschel-Bulkley fluid flow in three-dimensional expansions

In this paper we study steady flow of Herschel-Bulkley fluids in a canonica l three-dimensional expansion. The fluid behavior was modeled using a regul arized continuous constitutive relation, and the flow was obtained numerica lly using a mixed-Galerkin finite element formulation with a Newton-Raphson iteration procedure coupled to an iterative solver. Results for the topolo gy of the yielded and unyielded regions, and recirculation zones as a funct ion of the Reynolds and Bingham numbers and the power-law exponent, are pre sented and discussed for a 2:1 and a 4:1 expansion ratio. The results revea l the strong interplay between the Bingham and Reynolds numbers and their i nfluence on the formation and break up of stagnant zones in the corner of t he expansion and on the size and location of core regions. (C) 2001 Elsevie r Science B.V. All rights reserved.