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It seems that currently implemented test for axisymmetric Navier-Stokes flow only works if one prescribes the analytical solution is initial solution and does some further tricks related to pressure.

My feeling is that the current implementation, where only the areas and volumes of scvs and scvs are scaled according to the radius is not yet complete.

According to Ferziger/Peric

However, if the pressure is integrated over the CV surface as in Eq. (8.40), it is not sufficient to integrate only over
north, south, west and east cell face, as was the case in plane 2D problems - one has to consider the radial component of 
pressure forces onto the front and back surfaces

for whatever that means in the context of our staggered scheme.

Here are some further sources: http://www.mate.tue.nl/mate/pdfs/8388.pdf, https://demichie.github.io/NS_cylindrical/