2D CONTRACTION/EXPANSION FLOWS.
Contraction/expansion flows are probably the most popular test case
for viscoelastic fluid flow simulations. Appearing in this test case is a
vortex at the salient corner of the geometry, and a geometrical
singularity at the re-entrant corner, shown in the diagram below,
where half of the pipe is shown, the dashed line being a line of
symmetry:
The geometrical singularity at the re-entrant corner is a
source of steep gradients in the flow, and is a particularly
interesting area of study as it can result in a loss of convergence
for some numerical algorithms. Development and growth of the corner
vortex is a phenomenon of interest. Predicting the conditions under
which these vortices appear is important in areas such as polymer
processing, where the recirculation zones can be detrimental to
equipment.
The graphs below show the results from a program written in
Fortran for modelling fluid flow through a contraction. The results looked at here
are for a 4:1 contraction flow on a rather coarse 32*16 grid, with
detail of the salient corner vortex shown.
The first graph is for a Newtonian fluid:
The next two graphs show the stream functions for a UCM
fluid. It isn't entirely obvious in these graphs, but
as the elasticity of the fluid increases, the salient corner vortex
increases in size and strength.
These results are presented using the package
Gsharp.
