Page 409 - Advanced thermodynamics for engineers

17.2 SIMPLE GAS TURBINE CYCLE ANALYSIS 399

It will be assumed that reheat occurs to give T 5 ¼ T 3 and also that h C ¼ h T ¼ 1.0. These as-
sumptions simplify the problem.
Then energy added

(17.40)
q 203 ¼ c p T 3 T 20

q 45 ¼ c p T 5 T 4 (17.41)
The heat exchanger effectiveness is given by Eqn (17.21):

T 3 T 2
ε ¼
T 5 T 2
giving Eqn (17.28)

T 20 ¼ T 2 ð1 εÞþ εT 6
Let the pressure ratio of the plant be defined by
ðk 1Þ=k
s r ¼ p 2 p 1 (17.42)
and assume there are no pressure losses.
Then

ðk 1Þ=k

p 2
T 2 ¼ T 1 ¼ T 1 s r (17.43)
p 1
and
ðk 1Þ=k
p 6 T 5
T 6 ¼ T 5 ¼ (17.44)
p 5 s R

εT 5 εg
T 20 ¼ T 1 s r ð1 εÞþ ¼ T 1 s r ð1 εÞþ (17.45)
s R s R
This results in
q 2 3 εg
0
¼ g s r ð1 εÞ (17.46)
c p T 1 s R
Similarly

q 45 ¼ c p ðT 5 T 4 Þ
Now
k 1 k 1

T 4 p 4 k p 4 p 1 k s R
T 4 ¼ T 3 ¼ T 3 ¼ T 3 ¼ T 3 (17.47)
T 3 p 3 p 1 p 3 s r

gs R
q 45 ¼ c p T 1 g (17.48)
s r