Time-Weissenberg Number Superposition in 4:1 Planar Contraction Flow of a Viscoelastic Fluid

Abstract

Vortex enhancement mechanism in 4:1 planar contraction flow of a viscoelastic fluid has been investigated, where the Oldroyd-B model was considered as a constitutive equation. Finite element method was used based on the fractional step method for time marching and DEVSS/DG as a stabilizing scheme. The prediction of vortex dynamics agreed well with the experimental results. At first, a lip vortex was generated at the reentrant corner at low Weissenberg number (We). As We increases, the size of the salient corner vortex becomes reduced, while the lip vortex becomes more pronounced and finally takes over the corner vortex. The trajectory of a lip vortex at high We was found to follow the steady state positions of the lip vortex at lower We, which means that the fluid has a memory and there exists a simple relationship between We and time. Accordingly, a simple universal behavior was found to dominate the vortex enhancement mechanism in the 4:1 planar contraction flow of the Oldroyd-B fluid.