How does one choose the number of blades and the diameter required for a turboprop propeller?
The prop diameter is chosen to provide suitable ground clearance for the desired installation. Then the reduction gearbox ratio is chosen to keep the prop tips subsonic. Then the number of prop blades is chosen to absorb full engine power. Compromises then get made to take advantage of off-the-shelf props in the market and standard gear ratios offered by the engine manufacturer.