The velocity diagram for 50% reaction turbine is shown in Figure 5.15.
Since,
Also, β1 ≠ β2, the blades are unsymmetrical and ΔVa = 0. There is no axial thrust in 50% reaction turbine. However, there will be considerable tangential thrust produced due to the pressure difference across the blades in each rotor disc since there is pressure drop of steam across the moving blades.
The diagram work per kg of steam,
Figure 5.15 Velocity Diagram for 50% Reaction Turbine
Diagram efficiency of blades
Putting u/V1 = ρ as the velocity ratio
There is an optimum value of ρ at which ηD becomes maximum. Differentiating ηD with respect to ρ and equating to zero. We get,
Example 5.2: A reaction turbine has degree of reaction 50% (i.e., Parson’s reaction turbine) and running at 600 rpm develops 10 MW using 10 kg/kWh of steam flow rate. The exit angle of the blades is 18° and the velocity of steam relative to the blade at exit is 1.5 times the mean peripheral speed. At a particular stage in the expansion, the pressure is 1.2 bar and the steam quality is 90%.
Calculate for the Stage
- Blade height assuming the ratio of Dm/hb as 12.
- Diagram power.
Solution:
Velocity triangle is shown in Figure 5.16.
Figure 5.16 Velocity Triangle
In a Parson’s reaction turbine,
Volume of steam at 1.2 bar from steam table
Example 5.3: In a four-stage turbine steam is supplied at 240 N/cm2 and 344°C. The exhaust pressure is 0.686 N/cm2 and the overall turbine efficiency is 0.72. Assuming that work is shared equally between stages and the condition line is a straight line. Find
- stage pressure.
- efficiency of each stage.
- reheat factor.
Solution:
h–s diagram for four-stage turbine is shown in Figure 5.17.
Figure 5.17 h–s Diagram
From Mollier diagram,
Since work shared is equally divided between each stage,
From Mollier diagram,
(iii) Reheat factor = Cumulative heat drop/Isentropic heat drop
Example 5.4: The enthalpy drop in the nozzle of an impulse turbine is 45 kJ/kg. The nozzle is inclined at 14° to the wheel tangent. The average diameter of the wheel is 0.3 m. Wheel runs at 10,000 rpm. Determine the blade inlet angle for sockless entry. If the blade exit angle is equal to the blade inlet angle, determine the work done per kg and also the axial thrust for flow of 1 kg/s.
Solution:
Velocity triangle is shown in Figure 5.18.
Figure 5.18 Velocity Triangle
From Eqs (5.3) and (5.4),
(Thus, the direction of Vω2 will be reverse due to –ve sing)
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