Structure of a viscoplastic fluid flow in a pipe with a given obstruction shape

Abstract

In this paper, we present a study of the axisymmetric steady-state laminar flow of a viscoplastic fluid in a pipe with variable cross section. Mathematical formulation of the problem is written in terms of stream function and vorticity variables in a cylindrical coordinate system. Rheological behavior of the medium is described by the Shvedov-Bingham model. Coordinate transformation is carried out to implement a numerical algorithm. The problem is solved numerically using the finite-difference method and the false transient method. This paper demonstrates the effect of Reynolds number, Bingham number, and geometric parameters of a flow domain on the flow structure.