Numerical Simulation of Viscoelastic Fluid Flow in a Channel

Abstract

This paper describes a method and results of the numerical simulation of viscoelastic fluid flow in a two-dimensional channel. The governing equations are solved by a finite volume method, and a segregated solution procedure based on the SIMPLE algorithm is used. The rheological behaviour of the viscoelastic fluid is described by the upper-convected Maxwell model (UCM). After calculating the cell-centre stresses from the constitutive equations, the cell-face stresses must be calculated. However, linear interpolation can lead to decoupling between velocity and stress, resulting in an oscillating (checkerboard) velocity field, even for the correct stress values. To overcome this problem, a method for the calculation of the cell-face stresses based on the Rhie and Chow interpolation is developed. The developed method is tested on the flow in a two-dimensional channel. Although the discussion is limited to the channel flow, observations and conclusions presented in the paper should also be relevant for viscoelastic fluid flows in general.