Modern Engineering Thermodynamics

14.14 Reversed Brayton Cycle Refrigeration 571
b. In a more realistic analysis, we still assume ideal gas behavior, but now we introduce isentropic compressor and
expander efficiencies of (η s ) c = (η s ) e = 0.650, and use Eq. (14.23), where the coldest temperature in the cycle
is now only
and
Then, Eq. (14.23) gives
T 4 = T 3 − ðT 3 − T 4s Þðη s Þ e
= 540: − ð540: − 443Þð0:650Þ = 477 R = 17:0°F
T 2s = T 1 T 3 /T 4s =
ð530: RÞð540: RÞ
443 R
= 646 R
T
COP reversed
=
1 − T 4
ðT 2s − T 1 Þ/ðη
Brayton cycle
s Þ c
− ðT 3 − T 4s Þðη s Þ e
R=AC
530: − 477
=
½ð646 − 530: Þ/0:650Š− ð540: − 443Þð0:650Þ
= 0:220
The results of part b of this example are much more realistic than those of part a due to the large thermodynamic
irreversibilities (friction, heat loss, etc.) present in early mechanical equipment.
Exercises
28. If Gorrie had found a way to increase the isentropic efficiency of his compressor in Example 14.10 from 65.0% to 75.0%
(but the isentropic efficiency of the expander did not change), determine the new coefficient of performance of the
actual (not ASC) system assuming all the other variables remain unchanged. Answer: COP actual = 0.244.
29. A sudden heat wave causes the compressor inlet temperature in Example 14.10 to increase from 70.0°F to 95.0°F.
Determine the new actual (not ASC) coefficient of performance of the unit. Assume all the other variables remain
unchanged. Answer: COP actual = 0.384.
30. Gorrie found a way to increase the pressure ratio of his compressor in Example 14.10 from 2.00 to 3.00. Determine
the new actual (not ASC) coefficient of performance of the unit. Assume all the other variables remain unchanged.
Answer: COP actual = 0.214.
Like modern Brayton power cycles, modern reversed Brayton refrigeration cycles can be constructed with regeneration
capability (Figure 14.28). Unlike power cycles, however, regeneration in refrigeration cycles does not
improve the cycle’s thermal efficiency; instead, it reduces the COP. However, regeneration does have the advantage
of decreasing the minimum cooling temperature T 4s . Therefore, the purpose of regeneration in refrigeration
cycles is simply to be able to reach lower cooling temperatures.
The use of a modern reversed Brayton refrigeration cycle is illustrated in the following example.
Internal heat
transfer from A to B
Q L
B
Regenerator
A
Cold air
Q H
Hot air
Turbine
Compressor
W c
FIGURE 14.28
A modern reversed Brayton cycle with a regenerator.