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Axi-symmetric will work fine, assuming you remember to scale the flow and follow the rules for axi-symmetric mesh/flow.

Asymmetry (or lack of) means you balanced a load of forces and had a perfect set up. In the experiments a slight nick in the entry port, off axis chamfer, spot of grease/fingerprint or fractionally higher flow could result in differences in the resulting bubble stream. In CFD the geometry should be good, but the mesh may be fractionally different, then there's multigrid etc. All tiny effects that can give a noticable effect. 

Consider a balance scale, if perfectly balanced and add a 0.001g mass to one side. Tiny change, but we now have a huge difference in the result.