Page 406 - Advanced thermodynamics for engineers

396 CHAPTER 17 GAS TURBINES

maintain. Aircraft gas turbines use multistage axial compressors whereas automotive turbines can
often achieve the required pressure ratio using a single stage centrifugal compressor.
It is interesting to examine what happens to efficiency and work ratio when ε ¼ 1. The efficiency of
the engine is

w net w T w C
h ¼ ¼ (17.34)
q 34 q 34
Substituting for w net from Eqn (17.13), but also including h C and h T in the terms gives

1
c p T 1 gh T 1 s r h 1 C fs r 1g
h ¼ (17.35)

1 1
c p T 1 g 1 þ ðs r 1Þ ð1 εÞþ εg 1 h 1
h C T s r
When ε ¼ 1 Eqn (17.35) reduces to
1 1

gh T 1 fs r 1g
s r h C
h ¼
1
gh T 1
s r
(17.36)
1
s r 1
h C
¼ 1 ¼ r w
1
gh T 1
s r
where r w ¼ work ratio. Hence, when a turbine is fitted with a perfect heat exchanger the work ratio
and efficiency are equal.

17.2.3 REHEATING AND INTERCOOLING
It was shown above that a heat exchanger can raise the efficiency of a gas turbine by increasing the
temperature of energy addition and decreasing the temperature of energy rejection. A similar effect can
be achieved by introducing reheat and intercooling.
A cycle with reheat is shown in Fig. 17.15(a) and (b): the turbine is divided into two sections and
the working fluid is withdrawn after the first turbine and reheated (up to approximately the peak
temperature). The effect of reheating is to raise the mean temperature of energy addition but with the
addition of extra energy and a reduced expansion ratio. The gas turbine cycle (Fig. 17.15(b)) with
reheat can be considered to be two Joule cycles combined together. The cycles are 1234 1 and 4 4564’.
0
0
The pressure ratio for the main cycle is the full compressor pressure ratio and the efficiency of this
cycle is given by Eqn (17.8) as
1
h ¼ 1
k 1
k
r p