3-D flow of Herschel-Bulkley fluids

Abstract

The flow of Herschel-Bulkley fluids through a sudden 3-D square with expansion height ratio of 2:1 is studied numerically by solving the mass and momentum conservation equations along with a continuous constitutive relation. Solutions are obtained for a Reynolds number equal to 1, and a wide range of dimensionless pressure gradient and rheological parameters on both unsteady and steady laminar flows with constant fluid properties. The solution was obtained using a classical Galerkin finite element formulation with a segregated solution procedure. Results are shown for the evolution in time of yielded/unyielded regions and the influence of the different parameters on the shape and extent of these regions and the volume flow rate at steady flow.