Modern Engineering Thermodynamics

14.14 Reversed Brayton Cycle Refrigeration 569
14.14 REVERSED BRAYTON CYCLE REFRIGERATION
In 1844, the American physician John Gorrie (1803–1855) designed and built an air cooling apparatus in Florida
to provide air conditioning for his yellow fever patients. His machine had a piston-cylinder apparatus that
compressed air that was cooled back to ambient temperature by circulating water. The cooled compressed air
was then expanded in a second piston-cylinder apparatus that caused the air to drop to a sufficiently low temperature
to produce ice and satisfy other cooling needs. The expanded air was then drawn back into the compressor
and the cycle began again. The two piston-cylinder devices were connected together so that the
expansion work was used to offset the compression work. This was clearly a reversed, closed loop Brayton cycle,
as shown by comparing Figures 13.44 and 14.27.
The COP of an actual reversed Brayton cycle is given by
and
COP reversed
= j _Q H j
=
j _W
Brayton cycle in j net
HP
COP reversed
= j _Q L j
=
j _W
Brayton cycle in j net
R=AC
ðT 2s − T 1
ðT 2s − T 1
T 2 − T 3
(14.22)
Þ/ ðη s Þ c
− ðT 3 − T 4s Þðη s Þ c
T 1 − T 4
(14.23)
Þ/ ðη s Þ c
− ðT 3 − T 4s Þðη s Þ c
where T 2 = T 1 + ðT 2s − T 1 Þ/ ðη s Þ c and T 4 = T 3 − ðT 3 − T 4 Þðη s Þ e : Since the processes 1 to 2s and 3 to 4s are isentropic
and the processes 2s to 3 and 4s to 1 are isobaric,
T 2s = T 1 ðp 2s /p 1
Þ ðk−1
Þ/k = T 1 PR ðk−1
Þ/k
Cooling water
Q H
Q H
3
Expander
Hot air
2
Compressor
3
Hot air
2
W E
W C
Turbine
Compressor
W net
4
Cold air
1
4
Cold air
1
Q L
(a) John Gorrie’s 1844 equipment schematic
Q L
(b) A modern reversed Brayton cycle equipment
schematic
T
W E
Q H 2s
p = c
3
W C
1
p = c
4s Q L
FIGURE 14.27
The reversed Brayton cycle cooling system using air as a working fluid.
s
(c) Reversed Brayton ASC T–s diagram