Page 399 - Advanced thermodynamics for engineers

17.2 SIMPLE GAS TURBINE CYCLE ANALYSIS 389

In Fig. 17.7, it is possible to evaluate the mean temperature of energy transfer. If the gas were an
ideal one then its enthalpy would be

Z T Z S
h ¼ c p dT ¼ Tds; along an isobar: (17.17)
0 0
This would result in mean temperatures of energy addition and rejection of

R 3
2 Tds
T B ¼ ; (17.18)
s 3 s 2
and
R 4
1 Tds
T A ¼ : (17.19)
s 4 s 1
This means that, in Fig. 17.7, the areas 23562 and EF56E (which represent the energy addition) are
equal, as are the areas for energy rejection – 14561 and HG56H. Similarly, the areas representing work
(12341 and EFGHE) are equal. The efficiency of the Joule cycle is given by

Q A T A ðs 5 s 6 Þ T A
h Joule ¼ 1 ¼ 1 ¼ 1 : (17.20)
Q B T B ðs 5 s 6 Þ T B
This is the same efficiency as a Carnot cycle operating between the temperatures of T A and T B .
The reason the Joule cycle does not achieve the efficiency of the Carnot cycle operating between T a and
T b is because the temperature of isobaric heat reception and rejection varies as the heat transfer occurs,
and a certain amount of potential for work is lost in the irreversible heat transfer processes between the
hot and cold reservoirs and the working fluid. The only time that T A can equal T a and T B can equal T b
is for the trivial case when the whole temperature rise occurs in the compressor – and no work is
produced, as discussed above. The poor use of available energy has been discussed in Chapter 4.
Thus, the way to improve the efficiency of operation of the cycle is to increase the mean
temperature of energy addition and reduce the mean temperature of energy rejection. There are a
number of ways of achieving this and these will be discussed below.

17.2.2 GAS TURBINE WITH HEAT EXCHANGER
One method of improving the efficiency of gas turbines is to fit a heat exchanger between the exhaust
gas and that entering the combustion chamber. A schematic of such an engine is shown in Fig. 17.8.
The effect of the heat exchanger is apparent from Fig. 17.9 which shows the cycle with heat exchange.
The heat exchange is depicted by the shaded area and, in this case the heat exchanger is 100%
effective. The heat exchanger effectiveness is defined as (Fig. 17.9)
T 3 T 2
ε ¼ (17.21)
T 5 T 2
i.e. it is the actual rise in temperature achieved compared to the maximum rise that could be achieved.
In this case T 3 ¼ T 5 and T 2 ¼ T 6 .