The flow at the entrance and exit of an axial-flow compressor rotor is in radial equilibrium. The…

The flow at the entrance and exit of an axial-flow compressor rotor is in radial equilibrium. The distributions of the tangential components of absolute velocity with radius are cθ1 5 ar 2 b=r; before the rotor cθ2 5 ar 1 b=r; after the rotor where a and b are constants. What is the variation of work done with radius? Deduce expressions for the axial velocity distributions before and after the rotor, assuming incompressible flow theory and that the radial gradient of stagnation pressure is zero. At the mean radius, r 5 0.3 m, the stage loading coefficient, ψ 5 ΔW=U2 t , is 0.3, the reaction ratio is 0.5, and the mean axial velocity is 150 m/s. The rotor speed is 7640 rev/min. Determine the rotor flow inlet and outlet angles at a radius of 0.24 m given that the hubtip ratio is 0.5. Assume that at the mean radius the axial velocity remained unchanged (cx1 5 cx2 at r 5 0.3 m). (Note: ΔW is the specific work and Ut the blade tip speed.)

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