I am trying to simulate a 2D concentric annular flow, running for axisymmetric, using periodic boundary conditions but I am having convergence problems. I tried to run without axisymetric but the results that I got were different than the calculated analytical solution. My question is, what is the best way to simulate this system? Using periodic boundary conditions, 2D (and this would be), axisymmetric, 3D?

I've ran a few periodic annular simulations without a problem. What kind of mesh are you using? Are you using a turbulence model? What fluid are you simulating and what are your periodic conditions? If you turn off the axisymmetry then you're simulating channel flow (rectangular), and that's why you are getting different results.

In order to generate the mesh I've first meshed all the edges and then I generated the mesh face using Quad Elements and Map Type. I am running for laminar flow and I am using water for that. I am using mass flow rate as an input for the periodic boundary conditions. Thank you very much Gustavo.

Remember that your axis of symmetry must be the X axis.

Just the same comment as Evan. I don't see why there should be a problem modelling it in 2D-axisymmetric, just make sure your mesh is all above the X-axis (which is the axis of symmetry, or r=0 from a cylindrical point of view). If you're having convergence problems you might want to change the relaxation factors, but I'm pretty sure the defaults should be ok. Also, if you just want to know the fully developed velocity profile, like I did, I was using at least 3 elements in the y direction. Hope this helps.