Numerical Solution of Incompressible Flow of Power-Law Fluid through a Pipe with Abrupt Contraction.

Abstract

A numerical solution for an axisymmetric non-Newtonian flow of an incompressible inelastic power-law fluid using a primitive variable formulation is presented. The present method is based on the method of lines using the rational Runge-Kutta time integration scheme combined with the central finite difference method for the spatial discretization. The Poisson equation is solved by means of the SOR method using the concept of the SMAC method. As a test problem, numerical results for a circular pipe flow with uniform inlet velocity are shown and compared with the analytic fully developed velocity profile to test the validity of the present method. Next, numerical results for the flow through a pipe with abrupt contraction are shown. The difference between Newtonian (n=1) and non-Newtonian fluids (n=0.75 and 1.25) for the Reynolds number (Re) from 0.01 to 100 is discussed concerning the flow pattern. It is evident that the size of the secondary vortex increases with increasing volumes of n. The entry length and the excess pressure drop in the contraction increase with decreasing values of n. It is confirmed that the present method is suitable for the numerical solution of a power-law fluid.