Page 217 - Fluid Mechanics and Thermodynamics of Turbomachinery

198 Fluid Mechanics, Thermodynamics of Turbomachinery
7. The rotor blades of an axial-flow turbine stage are 100 mm long and are designed to
receive gas at an incidence of 3 deg from a nozzle row. A free-vortex whirl distribution is
to be maintained between nozzle exit and rotor entry. At rotor exit the absolute velocity is
150 m/s in the axial direction at all radii. The deviation is 5 deg for the rotor blades and zero
for the nozzle blades at all radii. At the hub, radius 200 mm, the conditions are as follows:
Nozzle outlet angle 70 deg
Rotor blade speed 180 m/s
Gas speed at nozzle exit 450 m/s
Assuming that the axial velocity of the gas is constant across the stage, determine
(i) the nozzle outlet angle at the tip;
(ii) the rotor blade inlet angles at hub and tip;
(iii) the rotor blade outlet angles at hub and tip;
(iv) the degree of reaction at root and tip.
Why is it essential to have a positive reaction in a turbine stage?
8. The rotor and stator of an isolated stage in an axial-flow turbomachine are to be repre-
sented by two actuator discs located at axial positions x D 0 and x D υ respectively. The
hub and tip diameters are constant and the hub tip radius ratio r h /r t is 0.5. The rotor disc
considered on its own has an axial velocity of 100 m/s far upstream and 150 m/s downstream
at a constant radius r D 0.75r t . The stator disc in isolation has an axial velocity of 150 m/s
far upstream and 100 m/s far downstream at radius r D 0.75r t . Calculate and plot the axial
velocity variation between 0.5 6 x/r t 6 0.6 at the given radius for each actuator disc in
isolation and for the combined discs when
.i/υ D 0.1r t ,.ii/υ D 0.25r t ,.iii/υ D r t .