Symmetric Geometry, but Asymmetric Flow Result

I am currently trying to model fluid flow through a pipe with a bulb in the middle, as shown below. The bulb is entirely symmetric about the center axis. However, when I run flow simulations, the resulting flow pattern is asymmetric, and I also get negative pressure warnings.I am using level 6 for the initial mesh.The inlet is a time-dependent volumetric flow rate, and the outlet condition is zero environmental pressure (or rather, 1E-12 Pascals...SW doesn't allow a zero pressure value.)

http://i46.tinypic.com/99p24h.jpg

An animation of the flow trajectories resulting from the calculation is attached below. Here is a perspective view of one of the asymmetric flow patterns.

http://i45.tinypic.com/mhw0p.jpg

Any ideas why the flow trajectories are not symmetric after the initial pulse of fluid? Also, how can the negative pressure warning (which persists through the end of the calculation) be prevented/what is causing it? Thanks.

SolidworksFlow Simulation