On the effect of contraction ratio in viscoelastic flow through abrupt contractions

A numerical study of the creeping flow of a PTT fluid through planar sudden contractions was carried out to quantify the effect of contraction ratio upon the flow characteristics (streamlines and size and intensity of recirculation vortices). The relevant governing equations were solved with a finite volume method embodying a new high-resolution scheme (Alves et al. [Int. J. Numer. Meth. Fluids 41 (2003) 47]) for the discretisation of convection terms, which is here explained and shown to yield improved accuracy and robustness. The results of the simulations, in terms of streamline patterns, give further evidence for a lip-vortex enhancement mechanism and are in remarkable agreement with flow visualization photographs from the literature. In addition, the results show that the variation of flow features in the vicinity of the re-entrant corner, such as lip vortex size and streamlines, are dominated by downstream quantities and scale with the common definition for the Deborah number in this flow, while flow characteristics in the salient corner region scale with that Deborah number divided by the contraction ratio