Numerical simulation of a power-law fluid flow in a channel with double constriction

Flow fields of non-Newtonian fluids in cylindrical channels with obstacles are of great interest for researchers studying the mechanics of fluids. In engineering techniques, such channels represent component parts of heat exchangers and hydraulic systems of various types. In this work, the numerical simulation of a steady non-Newtonian fluid flow in an axisymmetric pipe with two overlaps, whose geometry is described by a cosine function, is carried out. Mathematical formulation of the problem is written in terms of vortex and stream function variables. The Ostwald - de Waele model is used to describe rheological properties of the medium. The solution to a system of differential equations is obtained numerically using the false transient method. To determine the pressure field, the Poisson equation for pressure is solved. Three media are considered in the paper: Newtonian, pseudoplastic, and dilatant fluids. The influence of the Reynolds number, power-law index in the rheological model, and geometric parameters of the channel on the flow characteristics is shown as streamline distributions and functional curves.