Flow over a fixed cylinder
 

Attachment 34423

I want to model transient cross-wise two-dimensional flow over a fixed cylinder.

Should I consider a turbulence model for the fluid for Re up to 20000?

Based on attached figure from "Blevins, Flow Induced Vibration, 1990"
vortex street transforms from laminar to fully turbulent for 150<Re<300000.
But boundary layer stay laminar in this range of Re.

If so which turbulence model should I use?

Meanwhile I'v tried no turbulence modelling and the results seem good regarding Strouhal number.

I would try the SST model in that range first, and if that seems to be giving you too much dissipation int he boundary layer then move to the gamma-theta turbulence transition model.