Page 150 - Advanced thermodynamics for engineers

136 CHAPTER 6 FINITE TIME (OR ENDOREVERSIBLE) THERMODYNAMICS

The analytical formulae for the nondimensional power output and efficiency, as functions of the
total pressure ratio, component effectiveness for the heat exchangers (HTHE {ε HE }, hot- {ε H } and
cold-side {ε L } heat exchangers), compressor and turbine efficiencies and the thermal capacity rates of
the working fluid and the heat reservoirs, the pressure recovery coefficient, the heat reservoir inlet
temperature ratio, are derived and analysed in Ma and Turan (2009). IFGT cycles are most efficient
under low compression ratio ranges (2.0–5.0) and are ideal for micro gas turbine technology with their
low power output. The optimal total pressure ratio, p C , under maximum power output is always higher
than that under maximum cycle thermal efficiency. When either of the heat transfer effectiveness of the
hot or the cold-side heat exchanger, the pressure recovery coefficient, isentropic efficiencies of the gas
turbine and the compressor and the heat reservoir inlet temperature ratio increases, the dimensionless
power output, cycle efficiency and their corresponding optimal total pressure ratios increase. It must be
noted that the optimal total pressure ratio, p C , under the maximum cycle thermal efficiency decreases
with the increase of heat transfer effectiveness of the HTHE. The model derived can be further used to
optimise the operational parameters and forecast performance of practical IFGT configurations and
choices.
Figure 6.12 gives the particular relationship between h IFGT and P IFGT with h C ¼ 0.85, h T ¼ 0.85,
D ¼ 0.93, T Hin /T Lin ¼ 4.0 and ε H ¼ ε L ¼ 0.90, under several specific values of ε HE with a varying total
compression ratio of the compressor, p C . Figure 6.12, which shows the variation of P IFGT with h IFGT ,
indicates that the relationship is a completely closed curve; this is much different from the parabolic
curves of the Carnot cycle and the regenerated endoreversible closed Brayton cycle. It is apparent that
the operating conditions for maximum power are not the same as those for maximum efficiency. Also
Fig. 6.12 shows how important a high value of heat exchanger effectiveness, ε HE , is if a high value of
overall thermal efficiency or high power output are to be obtained.

0.6

0.5

0.4

P IFGT 0.3 = 1.0. 0.9, 0.8, 0.7
ε ΗΕ
0.2

0.1

00
0 0.1 0.2 0.3 0.4 0.5 0.6
η
IFGT
FIGURE 6.12
Variation of nondimensional power with thermal efficiency.