Theoretical and Actual Cycle Analysis
The thermodynamic analysis presented here is an outline of the air-standard Brayton cycle and its various modifications. These modifications are evaluated to examine the effects they have on the basic cycle. One ofthe most important is the augmentation of power in a gas turbine， this is treated in a special section in this chapter.
The Brayton Cycle
The Brayton cycle in its ideal form consists of two isobaric processes and two isentropic processes. The two isobaric processes consist of the combus-tor system of the gas turbine and the gas side of the HRSG. The two isentropic processes represent the compression (Compressor) and the expan-sion (Turbine Expander) processes in the gas turbine. Figure 2-1 shows the ldeal Brayton Cycle.
A simplified application of the first law of thermodynamics to the air-standard Brayton cycle in Figure 2-1 (assuming no changes in kinetic and Total output work
potential energy) has the following relationships: Work of compressor
Wc二的内α(h2 -h1) (2-1)
Work of turbine
Wt二(的内α +的内 )(h3 -h4) 58 (2-2)
Wcyc二Wt -Wc (2-3)
Heat added to system
Q2，3二的二(的内 )(h3)-内的αh2 (2-4)
内xLH. fuel内α +的
Thus， the overall cycle efficiency is
ηcyc二Wcyc/Q2，3 (2-5)
lncreasing the pressure ratio and the turbine firing temperature increases the Brayton cycle efficiency. This relationship of overall cycle efficiency is based on certain simplification assumptions such as: (1)内的α >内的， (2) the gas is caloricaly and thermallyperfect， which means that the specific heat at constant pressure (cp) and the specific heat at constant volume (cv) are constant thus the specific heat ratio古 remains constantthroughout thecycle， (3) the pressure ratio (Jp) in both the compressor andthe turbine are thesame， and (4) all components operate at 100% efficiency. With these assumptions the effect on the ideal cycle efficiency as a function of pressure ratio for the ideal Brayton cycle operating between the ambient temperature and the firing temperature is given by the following relation-ship:
I八
二(1 -Jp 1 -1古) (2-6)
ηideal古
where Pr二Pressure Ratio; and古 is the ratio of the specific heats. The above equation tends to go to very high numbers as the pressure ratio is increased.
Assuming that the pressure ratio is the same in both the compressor and the turbine the following relationships hold using the pressure ratio in the compressor:
ηideal二1 -T1 (2-7)
T2
and using the pressure ratio in the turbine
ηideal二1 -T4 (2-8)
T3
ln the case of the actual cycle the effect of the turbine compressor (ηc)， and expander (ηt) efficiencies must also be taken into account， to obtain the overall cycle efficiency between the firing temperature T and the ambient temperature Tamb of the turbine. This relationship is given in the following equation:
I八
TambJp 古
-1
古
() I八
ηtT -
ηc 1
二 I ()八 (1 -()) (2-9)
ηcycle-1 古1
古
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