Question 6.DE.16: In a reaction stage of a steam turbine, the blade angles for......
In a reaction stage of a steam turbine, the blade angles for the stators and rotors of each stage are: α_1 = 25°, β_1 = 60°, α_2 = 71.1°, β_2 = 32°. If the blade velocity is 300 m/s, and the steam flow rate is 5 kg/s, find the power developed, degree of reaction, and the axial thrust.
Figure 6.34 shows the velocity triangles.
The velocity triangles can easily be constructed as the blade velocity and blade angles are given. From velocity triangles, work output per kg is given
by:
W_t = U(C_{w1} + C_{w2})
= (300) × (450 cos 25° + 247 cos 71.1°)
= 14, 6, 354 J
Power output:
\dot{m}W_t = \frac{(5) × (1, 46, 354)} {1000} = 732 kW
Degree of reaction is given by:
L = \frac{V^2_2 – V^2_1} {2 × W_t} = \frac{443^2 – 220^2} {(2) × (14, 6, 354)} = 0.5051, or 50.51%
Axial thrust:
F = \dot{m} (C_{a1} – C_{a2}) = (5) × (190.5 – 234) = -217.5 N
The thrust is negative because its direction is the opposite to the fluid flow.
