Dear Ryan,

I too have solved this problem with both K-e model and K-w model, the thing you should take into mind is when using k-w model you go for the inflation layer concept and for standard wall function approach or the k-e model you go for first cell height, I would suggest you to please calculate your 1 st cell height thoroughly and then use  it for your problem, with first cell height successfully set you don want a cell growth (preferably for k-e model not for K-w) which can reduce your overall mesh count,

secondly, realizable K-e is for swirling flows where Swirl no, < 0.5  for your simple pipe flow case you should use standard K-e only,

thirdly, how your calculating the mass flow rate, it should be calculated for the bulk mean temperature and then must be implemented,

fourth, when making mesh you should see that the biasing you use for the inlet will be reserved by default for the outlet and what you got is the transition of the inflation layer from pipe wall to the pipe axis, so you should reserve the direction of the biasing manually such that mesh density lie on the wall side or the first cell height lie on the wall side.

last is your axis symmetry condition are you taking the axis of the pipe as symmetry keeping the height of the 2 D surface as a radius of the pipe or the diameter, if you are using the diameter then you are wrong, you can visit CORNELL University lecture on CFD they have silver this problem excellently

Thanks & Regards.