Page 422 - Advanced thermodynamics for engineers

412 CHAPTER 17 GAS TURBINES

Solution
The values of (n 1)/n for the polytropic compression and expansion are
for compression
n 1 1 k 1 1
¼ ¼ ¼ 0:3175
n h NC k a 0:9 3:5
for expansion

n 1 k 1 0:9
¼ h NT ¼ ¼ 0:225:
n k g 4
Under static conditions T 01 ¼ T 0a and p 01 ¼ p a so that, using the nomenclature of Fig. 17.23,

ðn 1Þ=n
T 02 p 02
¼ and yields
T 01 p 01
T 02 ¼ 288 1:65 0:3175 ¼ 337:7K
T 02 T 01 ¼ 337:7 288 ¼ 49:7K
p 03 19:0
¼ ¼ 11:51
p 02 1:65
ðn 1Þ=n
p 03 0:3175
T 03 ¼ T 02 ¼ 337:7 11:51 ¼ 734 K
p 02
T 03 T 02 ¼ 734 337:7 ¼ 396:3K:

The cold nozzle pressure ratio is
p 02
¼ r f ¼ 1:65
p a
and the critical pressure ratio for this nozzle is

p 02 1 1
¼ ¼ ¼ 1:965:
p c h 1 k 1 ii k=ðk 1Þ h 1 h 0:4 ii 3:5
h
1 1
h k þ 1 0:95 2:4
j
Thus the cold nozzle is not choked, so that p 8 ¼ p a and the bypass thrust F b is given simply by
F b ¼ _ m b V 8
The nozzle temperature drop, from Eqn (17.70),is
!
1
k 1=k
T 02 T 8 ¼ h T 02 1
j
P 02 =P a
!
1
1=3:5
¼ 0:95 337:7 1 ¼ 42:8K:
1:65