Modern Engineering Thermodynamics

496 CHAPTER 13: Vapor and Gas Power Cycles
4s
p = c
1
4s 1
T
3
p = c
2s
p
s = c
3
s = c
2s
s
(a) T–s diagram
V
(b) p–V diagram
Compression
cylinder
Fuel
4
1
Isobaric
combustion
chamber
Power cylinder
Net
work
Fuel
Compressor 4 1
Turbine
Isobaric
combustion
chamber
Net
work
3
2
Air
Exhaust
(c) Brayton cycle reciprocating equipment
2
3
Air
Exhaust
(d) Brayton cycle turbo equipment
FIGURE 13.44
The open loop Brayton cycle.
BRAYTON CYCLE GAS TURBINE ENGINE
The original Brayton cycle was conceived as a closed loop external combustion hot air engine like those of Stirling and
Ericsson. However, it was found to run more reliably when it was converted into an open loop internal combustion engine,
as shown in Figure 13.44. Much later, it was discovered to be an adequate model for gas turbine engines.
The thermal efficiency of the Brayton cycle is given by
ðη T Þ Brayton = ð _W out Þ net
W
= _ pm − j _W c j
_Q H
_Q H
For the cold ASC, both the compressor and the prime mover (either reciprocating piston-cylinder or turbine) are
considered to be isentropic, and we can write
and
Since the combustion chamber is isobaric,
Then,
ðη T Þ Brayton
cold ASC
_W pm = _mðh 1 − h 2s Þ = _mc p ðT 1 − T 2s Þ
j _W c j = _mðh 4s − h 3 Þ = _mc p ðT 4s − T 3 Þ
_Q H = _mðh 1 − h 4s Þ = _mc p ðT 1 − T 4s Þ
ð
= T 1 − T 2s Þ− ðT 4s − T 3 Þ ð
= T 1 − T 4s Þ− ðT 2s − T 3 Þ
= 1 − T 2s − T 3
(13.22)
T 1 − T 4s T 1 − T 4s T 1 − T 4s
Now, from the ideal gas isentropic formula used earlier, Eq. (7.38), we see from Figure 13.44b that
T 1 /T 2s = ðp 1 /p 2s Þ k−1
so that T 2s /T 3 = T 1 /T 4s , and Eq. (13.22) becomes
ðη T Þ Brayton
cold ASC
ð Þ/k = ðp 4s /p 3
Þ ðk−1Þ/k
= T 4s /T 3
= 1 − ð T2s/T 3 − 1 ÞT 3
= 1 − T 3 /T 4s
ðT 1 /T 4s − 1ÞT 4s