A single-stage axial-flow gas turbine stage with a hub/tip ratio of 0.85 is to be designed to give a free-vortex flow after the rotor row and is required to develop 2.6 MW from a gas flow of 30 kg/s. The gas admitted is at a stagnation temperature and pressure of 1100 K and 430 kPa (abs) and the relevant gas properties are Cp = 1:15 kJ=kg and γ = 1:333. At the mean radius the blade speed is to be 250 m/s, the flow coefficient φ = 0:5, the absolute flow angle α2 = 67° , and the reaction is 0.5. The static pressure at exit is 1.02 kPa.
Sketch an appropriate velocity diagram for the stage and determine
a. the blade loading coefficient, ψ 5 ΔW=U2
b. the flow area and the hub and tip radii
c. the absolute tangential velocity components, cθ2 and cθ3, following the expansion through the nozzle
d. the reaction at the hub and tip.