convergence issue flow around circular cylinder
 

I'm modeling flow about a circular cylinder in the critical to super critical region of flow. and i'm trying to do a mesh dependency study.
so i've been reading around about convergence and i know there's no set definition. some say monitor until residuals drop below certain value (0.001 or 0.000001 etc.) or go flat, that depends on the problem. others say residuals mean nothing and say put all stock into monitoring physical attributes of the flow ie lift/drag. so i've done both and i have a question about that now. and i'm monitoring my residuals which go flat but at a high level (ie high error between iteration calculation <- am i right?) so if my error is so high i've reduced my mesh to reduce it but i'm up to a 0.5 million cells currently

the picutres above (all but last) mesh has 44k cells, but i've gone up t0 0.5 million cells and had pretty much the same response. the time step is @ 0.001s which is <1% of the expected shedding frequency (i believe) . the inner iterations are at 5/timestep.

here are my C_d values
cell count Re=5e5 Re=1.5e6 Re=3e6
49,000 0.953736 0.8779298 0.75971
130,000 0.894744 0.7971384 0.666037
500,000 0.819921 0.7164173 0.695576

should i be worrying about CFL number here? should i just keep reducing my mesh size? i feel like i should be able to run a simulation as simple as this on a laptop, but if i keep growing this mesh then i fear i may not be able to. is there something simple that i'm missing?

i've since figured that i needed more inner iterations per time step. currently using flexible up to 50/timestep and getting much better convergence. this solved my high residual issue