Low Reynolds-Number Pipe Flow in the Vicinity of Three-Dimensional Obstacles

Abstract

Numerical solutions of the three-dimensional Navier-Stokes equations are presented for boundary conditions corresponding to the laminar flow of Newtonian and non-Newtonian fluids in a round pipe with truncated sector-shaped obstacles. The influences of Reynolds number and sector angle on the velocity distributions, local shear stress and pressure drop are quantified and shown to be large. The results are complementary to those previously reported by Vlachos and Whitelaw (1)§ for axisymmetric obstacles, where related two-dimensional effects were quantified. They provide new information on three-dimensional, recirculating flow in ducts and form a basis for future calculations of corresponding turbulent flows.