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Turbomachinery: Impulse and Reaction Turbines

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1. An impulse air turbine rotor with a blade speed (U) of 300 m/s is measured to have a relative rotor inlet velocity (W_1) of 750 m/s at an angle of 69 degrees and an outlet relative velocity (W_2) of 660 m/s. Th temperature and pressure in the rotor are 375 K, 0.83 bar. Calculate the rotor efficiency, rotational speed and power output if it has a mean blade diameter of 220 mm, a blade length of 16,, and if it has 360 degrees of full length nozzles.

At the inlet to a reaction air turbine nozzle, the total pressure and total temperature are 7,39 bar, 1240 K.
a) If the nozzle has an efficiency of 87% and if the nozzle exit/rotor inlet pressure is 4,1 bar, calculate the nozzle exit velocity (C_1).
b) If the nozzle exit angle is 65 degrees and if the rotor speed is 390 m/s, calculate the relative rotor inlet velocity (W_1).
c) If the rotor has an efficiency of 84% and an exit pressure of 1,9 bar, calculate the rotor exit relative velocity (W_2).
d) Sketch the complete velocity diagrams with approximate blade shapes.

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Solution Preview

See the attached file.
Notations and assumptions:
[ ]* = total features (like p*, T*)
cp = specific heat at constant pressure (for air at low temperatures we will take
cp = 1 kJ/kg.K and for high temperature
cp ...

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Turbomachinery: Impulse & Reaction Turbines

Question 4: An impulse air turbine has a total (on static) inlet pressure and temperature of 11,25 bar, 600 degrees K and exhausts to the atmosphere at 0.91 bar. The nozzle efficiency is 87% and its exit angle is 71 degrees. The rotor efficiency is 65%. If the blade speed if 190 m/s at the mean radius of 12cm, calculate the power output for full admission to the 2cm long rotor blades.

Question 5: It has been decided to use the following velocity diagrams for a STEAM reaction turbine stage which is expected to have a nozzle and rotor efficiency of 80% when the stage inlet total ((not static) pressure and temperature are 17 bar, 400 degrees C. Using the small segment of the enthalpy-entropy chart for steam that is suppled, plot the hs diagram for the nozzle and rotor and hence determine the outlet pressures of each.

Question 6: It has been decided to use the following velocities for a reaction turbine stage which is expected to have a nozzle efficiency of 90% and a rotor efficiency of 85% when the stage inlet total (not static) pressure and temperature are 5 bar, 1050 K. Calculate the as yet known velocities and then determine the specific work output and the outlet pressure from the rotor.

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