Modern Engineering Thermodynamics

14.9 Cascade and Multistage Vapor-Compression Systems 555
HOW DO YOU LIQUEFY A GAS LIKE OXYGEN?
Though French engineer Charles Tellier (1828–1913) first suggested the concept of cascade refrigeration in 1867, the Swiss
scientist Raoul Pictet (1846–1929) first developed a dual-cascade refrigeration system and used it to produce liquid oxygen
in 1877. He used SO 2 in the high-temperature cycle and CO 2 in the low-temperature cycle. He was able to produce only a
liquid oxygen mist, but it was the beginning of cryogenic refrigeration. Hydrogen gas was first liquefied in 1898 and
helium gas was finally liquefied in 1908.
system using the same refrigerant in each cycle. However, adifferentrefrigerantisoftenusedineachcycleto
optimize overall system performance. When different refrigerants are used in the cascaded cycles, separate (or
combined) T–s diagrams must be used in the analysis. Some industrial systems require three or four cascaded
cycles to reach the desired low temperature.
The cascaded cycles are interconnected through insulated closed loop heat exchangers that function as evaporators
in the higher temperature cycle (A) and as condensers in the lower temperature cycle (B). An energy balance on an
interconnecting heat exchanger provides a relation between the mass flow rates of refrigerant in the two cycles as
Where h 2b is determined from
_m A
_m B
= h 2B − h 3B
h 1A − h 4hA
(14.9)
And the coefficient of performance for the entire cascaded system is
COP cascade =
For a dual-cascade system, Eq. (14.11) becomes
COP dual
=
cascade
_Q L
_W c−A + _W c−B
=
h 2B = ðh 2sB − h 1B Þ/ðη s Þ c−B + h 1B (14.10)
_Q L
_W c−A + _W c−B + … =
_Q L
∑ _W compressors
(14.11)
_m B ðh 1B − h 4hB Þ
_m A ðh 2sA − h 1A Þ/ðη s Þ c−A + _m B ðh 2sB − h 1B Þ/ðη s Þ c−B
(14.12)
The following example illustrates that cascading can be used to decrease the individual compressor pressure
ratios and increase the coefficient of performance of a system. However, understand that this increase in system
COP also requires an increased capital investment and increased maintenance costs.
EXAMPLE 14.6
A food-processing refrigeration unit is required to produce 40.0 tons of refrigeration at an evaporator temperature of −50.0°C
and a condenser temperature of 25.0°C. Since this temperature difference is quite large, it was decided to design a dual-cascade
unit using. R-22 in both of the cascaded loops. The intermediate heat exchanger connecting the two loops is to operate
at −20.0°C, and the isentropic efficiencies of both compressors is 80.0%. The following design specifications were then
established for the refrigeration loops shown in Figure 14.17:
Loop A
Loop B
Station 1A Station 2sA Station 3A Station 4hA
Compressor A inlet Compressor A outlet Condenser A outlet Expansion valve A outlet
x 1A = 1:00 p 2sA = 1500: kPa x 3A = 0:00 h 4hA = h 3A
T 1A = −20:0°C s 2sA = s 1A T 3A = 25:0°C
Station 1B Station 2sB Station 3B Station 4hB
Compressor B inlet Compressor B outlet Condenser B outlet Expansion valve B outlet
x 1B = 1:00 p 2sB = 300: kPa x 3B = 0:00 h 4hB = h 3B
T 1B = −50:0°C s 2sA = s 1B T 3B = −25:0°C
(Continued )