Page 138 - Fluid Mechanics and Thermodynamics of Turbomachinery

Axial-flow Turbines: Two-dimensional Theory 119
(3) To determine the conditions at nozzle exit, we have
1 2 2
T 2 D T 02 c /C p D 1200 652.86 /.2 ð 1160/ D 1016.3K
2 2
From eqn. (2.40), the nozzle efficiency is

1
h 01 h 2 T 2 /T 01
N D D
1//
h 01 h 2s 1 .p 2 /p 01 /
.
1//

∴ p 2 D 1 1 T 2 /T 01 D 1 .1 1016.3/1200//0.96 D 0.84052
p 01 N
4.0303
∴ p 2 D 4 ð 0.840052 D 1.986 bar
The mass flow is found from the continuity equation:

p 2
P m D 2 A 2 c x2 D A 2 c x2
RT 2
5
1.986 ð 10
∴ Pm D ð 0.2375 ð 242.45 D 39.1 kg/s
287.8 ð 1016.3
(4) For a tapered blade, eqn. (4.30b) gives
" #
2 412.3 2 0.51 2
c 2 2
D ð 1 D 30463.5m /s
m 3 2 0.75
where U t D 1099.6 ð 0.375 D 412.3 m/s.
3
The density of the blade material is taken to be 8000 kg/m and so the root stress is
8
2
c D 8000 ð 30463.5 D 2.437 ð 10 N/m D 243.7 MPa
(5) The approximate average mean blade temperature is
2
T b D 1016.3 C 0.85 ð .242.45/ cos 46.975/ /.2 ð 1160/
D 1016.3 C 46.26 D 1062.6K

(6) The data in Figure 4.17 suggests that for this moderate root stress, cobalt or
nickel alloys would not withstand a lifespan of 1000 hr to rupture and the use of
molybdenum would be necessary. However, it would be necessary to take account
of bending and vibratory stresses and the decision about the choice of a suitable
blade material would be decided on the outcome of these calculations.
Inspection of the data for Inconel 713 cast alloy, Figure 4.18, suggests that it
might be a better choice of blade material as the temperature stress point of the
above calculation is to the left of the line marked creep strain of 0.2% in 1000 hr.
Again, account must be taken of the additional stresses due to bending and vibration.
Design is a process of trial and error; changes in the values of some of the
parameters can lead to a more viable solution. In the above case (with bending and
vibrational stresses included) it might be necessary to reduce one or more of the
values chosen, e.g.