hi HSL, the problem setup looks reasonable, a couple of questions about the setup:
1. what are lid 2 and 4 for?
2. what are you using the first real wall condition for? i don't see any conditions applied on it.
3. i noticed that the cylinders are concentric. did you mean to have the model that way? in your description i expected them to be offset.
side note, i'd recommend building the lids yourself. that way if you move the geometry the lids will update. (the lid tool lids are not parametric)
regarding mesh, the developers recommend 3-5 cells across a channel. you might need more you might need less, the only way to know for sure is to check your results against a known value and mesh convergence check. so I would start with a low value for the mesh and then move up to see if the results are changing. that is a better method than just throwing a lot of cells at it from the beginning.
thinking out loud. I'd have to do some testing but I wonder if this could be done in 2d? essentially one slice of elements. I don't know enough about the application to say whether that is valid, but I think Flow simulation would allow you to set it up as a 2d problem.