Simulation of Incompressible Non-Newtonian Flows Through Channels with Sudden Expansion Using the Power-Law Model

Abstract

The goal of this work is to analyze incompressible Newtonian and non-Newtonian flows through channels with sudden expansion. The governing equations are solved using the finite-differences explicit Runge-Kutta time-stepping scheme in nondimensionalized form in which continuity and momentum are solved simultaneously along the grid points. The power-law model is applied to predict pseudoplastic (shear-thinning) and dilatant (shear-thickening) behavior in such expansions. The critical Reynolds number, in which the solution becomes asymmetric, is analyzed. Numerical results for a 3 : 1 expansion show good agreement with other numerical tests found in the literature for Reynolds numbers ranging from 40 to 140 for Newtonian flow. For the non-Newtonian case, a comparison with an analytical solution is presented.