Initial results of an ongoing Navier-Stokes Computational Fluid Dynamics study of horizontal axis tidal current turbine hydrodynamics are presented. Part of the underlying motivation is assessing the effects of the Reynolds number on turbine performance and loads in steady flow conditions and unsteady regimes. The study aims at a) providing initial verification and validation of Navier-Stokes CFD for steady and unsteady tidal turbine flows over a wide range of Reynolds numbers, and b) estimating the dependence of turbine performance and loads on this parameter, so as to enable more reliable exploitation of low-Reynolds number tank measurements for field installation analysis and design. The investigation starts from a tidal current turbine towing tank experiment conducted at the Kelvin Hydrodynamic Laboratory of Strathclyde University, compares available measured data and CFD results regarding the blade steady flow and unsteady flow due to the harmonic planar motion of the turbine, and extends the CFD analysis to the high Reynolds numbers of typical utility-scale field installations. It is found that at high (field-like) Reynolds numbers, the blade power, force and moment coefficients are about 20 percent higher than at (low) tank-like Reynolds numbers, and also that the agreement of measured and predicted loads at fairly low Reynolds numbers improves by modelling laminar-to-turbulent transition, highlighting the importance of this phenomenon in tank experiments.