Entrance Flow Patterns in the Extrusion Flow of Polymer Solutions : Finite Difference Simulation Using the Denn Model

Abstract

The entrance flow patterns for viscoelastic fluids are simulated using the finite difference scheme. The Denn model is used as the constitutive equation. The prediction of the dimensionless size of circulating secondary flow (X) for a Newtonian fluid agrees with the experimental observations of Boger et al. and the prediction of Kim-E et al. For a power law fluid, shear thinning decreases X while shear thickening increases it. For a viscoelastic fluid we could predict the same large circulating flows as in our experimental observations for polymer solutions. Then, X for N_Re<0.1 (N_Re: Reynolds number) is the same as for the creeping flow (N_Re→0). Thus, X for the viscoelastic fluid is dependent on the Weissenberg number (N_we) for N_Re<0.1 and on N_we and N_Re for N_Re≥0.1. This result agrees with our experimental observations for polymer solutions.