Refrigerant cycles - KHLim i-NET

ICE-E
INFORMATION
PACK
Refrigerant cycles
Fundamental
considerations
about the
thermodynamics
of inverse cycles
can help in
economic and
technological
choices for
refrigeration
systems
In the e-learning section of the
ICE-E web site, the reader can
achieve basic knowledge about
the refrigeration cycles. The
choice of the most suitable
cycle, in terms of energy
consumption reduction must be
supported by several
considerations dealing both
with thermodynamic and
technological aspects. In the
present Info Pack, fundamental
considerations about
thermodynamics are
presented, aiming at
highlighting the consequences
on cycle energetic efficiency.
Regarding technological aspects, the reader
may refer to “Refrigerants”, “Operation and
choice of compressors”, “Heat exchangers”,
“Expansion device” Info Packs.
Back to basics
The purpose of a refrigeration system is to
transfer thermal energy from a lowtemperature
source to a high-temperature
sink. From an energetic point of view, the goal
should be hit utilizing the least amount of
work, i.e. to maximize the Coefficient of
Performance (COP) for a given cooling
capacity and for fixed source and sink
temperatures. More “thermodynamically”
oriented reader could, alternatively, restate the
goal in terms of entropy: the purpose of a
refrigerating system is to transfer entropy from
a low-temperature source to a hightemperature
sink while generating the least
amount of entropy, or stated in another way
the goal is to generate the least amount of
entropy for a given cooling capacity for fixed
source and sink temperatures.
It is well known that the ideal cycle for
achieving this goal (when both the source and
the sink are isothermal) is the Carnot
Figure 1 - Carnot cycle and ideal vapor compression
refrigeration cycle

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All the design
strategies of a
vapour
compression
refrigeration
system, are
intended for
reducing the
irreversibilities
linked to
throttling,
compression and
heat transfer.
refrigeration cycle, whose work is depicted by
the area a-b-c-d in figure 1 and whose
cooling capacity is given by the area 1-4-f-g
for figure 1 (taken from Cavallini et al, 2010) .
It is also well known that increasing T L and/or
decreasing T 0 increases the cycle efficiency.
The Carnot refrigeration cycle, however,
cannot be realized via practical hardware.
Therefore, the widely used reference cycle in
practice is based on the so-called ideal vapor
compression refrigeration cycle. The cycle
shown in figure 1 contains two irreversibilities:
(1) isenthalpic expansion ( exp) and
(2) superheating of the compressor discharge
vapor ( sup) to realize a constant-pressure
heat rejection process in the condenser.
In practice, real vapor compression
refrigeration cycles include other
irreversibilities, principally among them are:
(3) non-isentropic adiabatic compression,
(4) non-isobaric heat rejection and
(5) non-isobaric heat addition.
Though not shown in the figure, two other
common modifications to the cycles are
superheating of the refrigerant at the
evaporator outlet and subcooling of the
refrigerant at the condenser outlet. Finally,
external to the cycle itself, there are large
irreversibilities associated with the heat
transfers to and from the source and sink due
to the finite temperature differences between
the refrigerant and the external heat transfer
media.
All the design strategies of a refrigeration
system (included two-stage
compression/throttling, as depicted in figures
2, 3) are intended for reducing the above
mentioned (1) and (2) irreversibilities.
Accordingly, a detailed analysis of the ideal
vapor compression refrigeration cycle, as
depicted in figure 1, gives cue on how to
reduce energy consumption for any kind of
vapour compression refrigeration cycle.
ù
Evaluating cycle performance
The most common method for evaluating the
overall thermodynamic performance of these
cycles is based on a First Law of
Thermodynamics approach, namely,
comparing the Coefficient of Performance
Figure 2. Two stage compression with
intercooler, single throttling vapour
compression cycle (and related T,s
diagram, below).
Figure 3. Two stage compression with
OFT, double throttling vapour compression
cycle (and related T,s diagram, below).

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Is a COP of 5
better than a
COP of 10 The
short answer is:
it depends.
(COP) and the Volumetric Cooling Capacity
(VCC). For a given cooling capacity, VCC
gives an indication about the compressor size
to achieve the specified cooling capacity.
The COP is the ratio of the energy
(refrigeration effect) extracted from the low
temperature source (if h is the specific
enthalpy of the refrigerant, q L=h 1 – h 4 is the
energy extracted or the so called refrigeration
effect, referring to figure 1) and the input work
(w comp=h 2-h 1). The volumetric cooling capacity
VCC is the energy extracted from the low
temperature source per unit of refrigerant
volume processed by the compressor.
One limitation to this approach is that the COP
is a function of the operating conditions (the
high-side and low-side temperatures). For
example, is a COP of 5 better than a COP of
10 The short answer is: it depends.
To overcome the mentioned limitation one
should compare the COP and the Carnot’s
cycle COP C (and this can be considered a
Second law of Thermodynamics approach):
= COP/COP C
Another way to consider and quantify the
irreversibilities is to choose an external
reference temperature T 0 (e.g., as the
temperature of the ambient) which can be
used to calculate the exergy losses. For the
example of figure 1, the external reference
temperature has to be chosen as the
temperature of the external cooling medium
(e.g., air) for the condenser. Once this is done,
the specific exergy losses can be calculated
for the four basic processes for the vapor
compression refrigeration cycle. They are
represented by the hatched areas in figure 1
(ideal reference cycle.
It is worth noting that for the ideal vapor
compression refrigeration cycle in figure 1 the
condenser exergy loss reduces to the
superheating loss ( sup), defined by the area e-
b-2, while compression and evaporation are
no-loss processes.
The magnitudes of the exergy losses for nonisobaric,
non-ideal heat transfer processes
and non-isoentropic compression (i.e.
irreversibilities (3), (4), (5), mentioned above)
described above are determined by
component and system designs, and by the
refrigerant. For example, the refrigerant
circuitry in the heat exchangers, the type of
compressor used and its design, and the
system configuration all will influence several
of the exergy losses.
Performance potential: ammonia
as an example
In the following, we consider a largely used
(old) refrigerant in refrigeration applications:
ammonia. We consider an evaporation
temperature T L = -40ºC, while the
condensation is T 0 = 40º. With reference to the
set temperatures, the Carnot cycle COP C is
2.91.
We consider no condenser subcooling or
compressor superheat, and a compressor
isentropic efficiency of 1. When the single
stage compression – single throttling is
considered, = 0.703.
Keeping fixed T L and T 0, we want now to
consider the possibility of installing a twostage
compressor, again ideally with
isoentropic behavior (figure 2). Furthermore,
an ideal intercooler is installed: i.e. it is
possible to lower the temperature of the
ammonia, after the low stage compressor
discharge (point 5, in figure 2) down to the
sink temperature (40 °C), that is a limit
situation achievable theoretically only in an
heat exchanger with infinite heat transfer area
and in perfect counter-current configuration.
The intermediate pressure (i.e. the
intercooling pressure) is set equal to the
square root of the product of condenser an
evaporator saturation pressures.
Single throttling is considered (no condensate
subcooling, no vapour superheating).
In this case superheating losses (see hatched
area indicating sup in figure 1) are reduced,
while throttling losses are the same (see
hatched area indicating exp).
According to previous considerations, we
expect an increase in (or in system COP,
since Carnot cycle COP C, is fixed at 2.91).
It is possible to calculate = 0.730. That is an
increase of less than 4 %, in comparison to
the single stage compression arrangement.
Let’s now evaluate the possibility to implement
the system configuration in figure 3, again with
fixed T L and T 0 and with no condensate
subcooling, no vapour superheating.

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Always compare
Carnot cycle
performance and
the performance
of the system
you are going to
evaluate.
You will have
quickly and
easily the first,
objective, clear,
indubitable
number for
starting your
following
technological
and economic
evaluation.
In this case, point 5 temperature can be lower
than ambient temperature, since it is not any
more linked to the external heat sink
temperature, as in the case of the intercooler
in figure 2. This should bring about a reduction
of ( sup). Furthermore, using two-stage
throttling, reduces the relevant hatched area in
figure 1 ( exp).
Accordingly, increases of about 40 % ( =
0.985). Being lower the refrigerant enthalpy at
the evaporator inlet (h 4, in figure 3), also VCC
increases.
Cascade systems
Another possibility for increasing refrigeration
system efficiency when operating with high
temperature lift (between evaporation and
condensation temperatures), is the cascade
system, as in figure 4. The condensation of
the LT cycle occurs by means of the
evaporation of the HT cycle refrigerant.
As outlined in the “Refrigerants” Info Pack,
each refrigerant operates more efficiently in a
particular temperature range. A suitable
refrigerant selection for both the “higher”
temperature cycle (HT) and the “lower”
temperature cycle (LT) allow to have higher
overall Cop, in comparison event to a 2twostage”
compression cycle operated by a single
refrigerant. Typical refrigerants choice is
carbon dioxide for the LT cycle and ammonia
for the HT cycle, but other combinations can
be found (for example R134a or R404A for
HT, instead of ammonia).
Concluding remarks
Which is the “practical” outcome of the
proposed thermodynamic consideration
(Note: as mentioned before, in this info pack
we are not considering technological aspects
like, for example, limitations in compressor
discharge temperature because of
compatibility with lubricants etc. Please
consider the relevant info packs in ICE-E web
site).
From an “economical” point of view, installing
a two-stage compressor is by far more heavy,
from an investment point of view, than using
two throttling valves or installing an
accumulator (open flash tank).
Given this economical consideration, the
thermodynamic results clearly indicate that
using the system schematic in figure 2 will
offer poor chances of recovering the higher
investment funds in short time (indeed, it is a
relatively rare system schematic, with
ammonia).
The further limited investment costs because
of one more throttling valve and one tank,
looks more promising in terms of shortening
the pay-back period.
As a concluding remark: the rather simplified
thermodynamic approach here proposed can
be considered a starting point if you are
looking for a new refrigeration system.:
If you are not a specialist in thermodynamics,
please remember of Carnot and ask to your
advisor to compare (it is rather simple, for
him), the coefficient of performance of the
system he is proposing to you (even
considering ideal processes of the refrigerant)
with the efficiency of the Carnot’s cycle.
You will have the first, objective, clear,
indubitable number for starting your following
technological and economic evaluation.
Figure 4. Cascade refrigeration system
References
Cavallini A., Zilio C., Brown J.S. (2010).
Sustainability with prospective refrigerants. In:
Proc. of Sustainable Refrigeration and Heat
Pump Technology Conference. Stockholm,
June, 13-16, ISBN: 978-2-913149-81-6
For more information, please contact: Claudio Zilio Claudio.zilio@unipd.it