It is usually a completely different group of people doing compressor aerodynamic design versus overall thermodynamic cycle design. The compressor aero group, using a variety of computer simulation codes (ranging from simple spreadsheets all the way up to 3 dimensional unsteady CFD) are going to generate a "compressor map". The compressor map gives the pressure ratio, mass flow through the compressor, and efficiency for given rotor speeds (and perhaps other variables). This allows the thermodynamic cycle guys to treat the entire compressor with just a few simple numbers. All of the details like the number of blades, the number of vanes, the stagger angles of the blades, etc, etc get boiled down to a simple map. That way the thermodynamics guy does not have to know or even care about how many blades there are. He doesn't even care how many stages are in the compressor. He just knows that at 10,000 rpm the compressor is giving him 10 lbm/s, 15:1 pressure ratio and is 90% efficient (or whatever), and at 12,000 rpm it's giving 13 lbm/s at 18:1 ratio, etc. etc. The thermodynamic cycle then takes that compressor map, along with similar input from the turbine aerodynamics guys, the combustor aerodynamics guys, the inlet and exhaust aerodynamics guys, and combines it into an overall picture of the engine performance. There will be iteration between those groups. For example, the cycle guy may determine that he has more than enough thrust but he needs more efficiency. So the compressor aero guy then changes number of blades or something, now maybe it is 9.5 lbm/s at 14.5:1 ratio but 93% efficient at 10,000 rpm.