A numerical calculations algorithm has been developed in the present work for a thermodynamics and aerodynamic design of an axial flow compressor. The design calculations were based on thermodynamics, gas dynamic, fluid mechanics, aerodynamic and empirical
relations. A two- dimensional compressible flow is assumed with constant axial and rotor blade velocities. A free –vortex swirl distributions was used in the design. These calculations include; power of the compressor, thermodynamic properties of the working fluid, stage efficiency, number of rotor and stator blades, tip and hub diameters, blade dimensions (chord, length and space) for
both rotor and stator, velocity triangles before and after the rotor, Mach number, solidity, degree of reaction, flow and blade angles (blade twist) and lift and drag coefficients along the blade and lift. A repeated stage calculation is made to calculate the above parameters along compressor stages. The twist of the blades can be calculated along the blade length at any required number of sections selected by the designers to obtain smooth blade twist profile. The developed algorithm was tested on a compressor cascade series type NACA 65(12)10 with circular camber angle of (30). The results show that; the lift coefficient decreases as mean flow angle increases, the drag coefficient increases along blade length at a mean flow angle of (15), the relative Mach number increases
along blade length as mean flow angle increases, the ratio of total drag coefficient to lift coefficient increases when the mean flow angle increases, the drag coefficient decreases along blade length as the solidity increases, the cascade efficiency increases as the mean flow angle increase to (45).