Page 124 - Entrophy Analysis in Thermal Engineering Systems

Irreversible engines—Open cycles 117

The total enthalpy at states 5 and 6 is determined using Eq. (8.38) with
j¼5,6. The temperature of the exhaust gases at state 6 can be obtained using
Eq. (8.50).
The entropy generation due to the heat transfer process in the heat
exchanger is obtained by

Φ h ¼ S 3 S 2 Þ + S 6 S 5 Þ (8.51)
ð
ð
where S 5 and S 6 are determined using Eq. (8.39) with j¼5,6.
Like the simple gas turbine cycle, the flue gases are discharged to the
atmosphere. Thus, one would need to account for the entropy production
due to the cooling process of the flue gases from temperature T 6 down to the
ambient temperature. Hence,

ð
Φ L ¼ Q L + S 7 S 6 Þ (8.52)
T 0
where S 7 is evaluated at the ambient temperature and pressure.
The SEG of the cycle is computed using Eq. (8.53).

(8.53)
SEG ¼ Φ c + Φ h + Φ t + Φ com + Φ L + Φ fc
Note that all Φ terms in Eq. (8.53) have the units of J/(mol fuel K).

8.5.2 Numerical example
The influence of heat exchanger effectiveness on the maximum thermal effi-
ciency of the gas turbine cycle is presented in Table 8.2 for TIT¼1273K.
The figures in Table 8.2 are obtained using the same parameters given in the
caption of Fig. 8.3. The minimum SEG values are also provided in
Table 8.2. The results confirm the inverse relation between the thermal
efficiency and SEG. An inclusion of a recuperator with an effectiveness of
0.55 may only yield one percentage point increase in the cycle efficiency.
A regenerative gas turbine cycle may not be practically advantageous over
a simple cycle at low values of the effectiveness.
The advantage of employing a heat exchanger with E 0.75 is evident in
Table 8.2. The net increase in the maximum cycle efficiency compared to
the simple cycle is 4.5 percentage points at E¼0.75, which raises to 7.8 per-
centage points at E¼0.85. In the limit of ideal heat exchanger where E!1,
the maximum thermal efficiency of the cycle approaches 0.636. It must be
noted that the maximum efficiency limit of 0.636 is obtained for