Exergy Losses In Refrigerating Systems

INTERNATIONAL JOURNAL OF ENERGY RESEARCH
Int. J. Energy Res. 2003; 27:1067–1078 (DOI: 10.1002/er.936)

Exergy losses in refrigerating systems. A study for
performance comparisons in compressor and condenser

A. Stegou-Sagian,y and N. Paignigiannis
Department of Mechanical Engineering, Thermal Section, National Technical University of Athens,
9 Iroon Polytechniou Str., Zografou 15780, Athens, Greece

SUMMARY
A study is carried out to describe irreversibilities in one stage refrigerating process for vapour
compression cycle with refrigerant mixtures R-404A, R-410A, R-410B and R-507 as working fluids. They
are calculated as exergy losses by an algorithm developed on the basis of thermodynamics. The pro-
posed relationships have been derived from exergy balances on the system components. Emphasis is
placed on parameters influencing the losses and the related results are presented through Grassmann
diagrams (diagrams of exergy fluxes). Furthermore, detailed information on the variation of cycle’s
exergy efficiency with evaporating and condensing temperatures is given. Copyright # 2003 John Wiley &
Sons, Ltd.

KEY WORDS: exergy; refrigerating systems; ozone friendly mixtures

1. INTRODUCTION

All forms of energy consist of two components: exergy and anergy (Baehr, 1989), i.e.:
Energy ¼ Exergy þ Anergy ð1Þ

The term of exergy was introduced so that the limited ability of energy transformation is
demonstrated.
Taking the ability of energy transformation as a criterion of selection, energy forms are
divided in the following groups:
* energy that can be converted without any limitations, like mechanical or electrical energy;
* energy that can be limitedly converted, like heat or internal energy;
* energy that cannot be converted, like environmental internal energy.

All known thermodynamic theorems can be expressed so as to include the term of exergy. As
a result, the First Thermodynamic law has the following formulation: In all processes, the sum
of exergy and anergy remains constant. Additionally, for the Second Thermodynamic law the

n
Correspondence to: Dr. Athina Sagia, Department of Mechanical Engineering, Thermal Section, National Technical
University of Athens, 9 Iroon Polytechniou Str., Zografou 15780, Athens, Greece.
y
E-mail: asagia@central.ntua.gr

Received 5 November 2002
Copyright # 2003 John Wiley & Sons, Ltd. Accepted 5 March 2003

1068 A. STEGOU-SAGIA AND N. PAIGNIGIANNIS

main expressions are:
* In all irreversible processes, exergy is converted into anergy.
* In reversible processes, exergy remains constant.
* It is imposible to convert anergy into exergy.
Exergy losses are inevitable because all natural processes are irreversible. Technically and
economically speaking, exergy is valuable, and as a consequence, whenever we try to solve a
problem through the scope of exergy analysis, we try to find a specific exergy loss, which
minimizes operational costs.
In this article, the optimization of one stage refrigerating systems through exergy analysis was
of paramount importance. The assumption is, that the refrigeration cycle works between the
temperature of a refrigerated space To and the ambient Tu : The kind of refrigerant used and the
operating conditions are the key factors for our study.
The development of environmentally benign refrigerants remains a fundamental issue
nowadays (Cavallini, 1995; ASHRAE, 1997; Blackmore and Reddish, 1996; Ozone Secretariat,
2000); it may be enhanced with useful comparisons on the distribution of exergy losses and on
the efficiency values of vapour compression refrigerating cycles working with ozone friendly
mixtures such as R-404A, R-410A, R-410B and R-507. All these four (4) refrigerant mixtures
are characterized by a zero Ozone Depletion Potential (ODP) coefficient, thus they do not
contribute to the depletion of the ozone layer. Their per cent weight compositions can be seen in
Table I.

2. EXERGY ANALYSIS ASPECTS

Exergy (E) of an amount of heat (Q) may be defined as (Smith and Van Ness, 1975; Baehr,
1989):

Tu
E ¼ 1À Q ð2Þ
TQ
where E; Q in (J) and Tu is the ambient temperature and TQ the temperature at which Q is
absorbed (heat sink) or rejected by theÁenvironment (heat source) in (K).
À
Below ambient temperature TQ 5Tu ; the heat amount (Q) will have a negative sign, as it is
removed from the space or substance which is cooled (for example a cold storage). Thus, EðQÞ is
always a positive quantity.

Table I. The per cent weight composition of the refrigerant mixtures used in this study.
Name of refrigerant mixture Percentage of ingredients (%)
R-22 R-32 R-115 R-125 R-134a R-143a
R-404A 44 4 52
R-410A 50 50
R-410B 45 55
R-507 50 50
R-502 48.8 51.2

Copyright # 2003 John Wiley Sons, Ltd. Int. J. Energy Res. 2003; 27:1067–1078

EXERGY LOSSES IN REFRIGERATING SYSTEMS-A STUDY 1069

The exergy of the enthalpy of a process fluid (e.g. a refrigerant) is calculated by (Baehr, 1989;
Moran and Shapiro, 1993):
ex ¼ ðhx À hu Þ À Tu ðsx À su Þ ð3Þ
where e is the specific exergy in (J/kg), while x and u stand for current and ambient conditions,
respectively.
Hence, exergy loss for a steady-state process including mass flows (mj ), heat (Qj ) and work
(Wj ) passing through the system boundaries is determined by:
X X X
DEloss ¼ Ein À Eout ¼ EðQj Þ þ Wj þ mj ej ð4Þ
By refrigeration, we aim to reduce the temperature of a cold storage space (To ) below the
environmental temperature (Tu ). Because of the temperature difference ðTu À To Þ; an incoming
heat flux enters the cold storage space. In order to keep To constant, the incoming heat flux must
be constantly replaced by an outgoing heat flux. This outgoing heat flux stands for the cooling
load. The depiction of a refrigerating engine is given at Figure 1.

Q ¼ Q þ P ð5Þ
o

where Qo stands for the cooling load, Q for the rejected heat and P for the power given
at the compressor motor. Figure 2 shows the exergy flux for an irreversible refrigeration
system.
The drawbacks of irreversibilities are the following:
* increase in power demand;
* increase in the anergy flux rejected, which results in an increase of the cost of the
refrigeration system, as larger heat exchangers are required.

The exergy flux is calculated by (Baehr, 1989; Moran and Shapiro,1993):

Tu
E Qo ¼ À 1 Qo
ð6Þ
To

Figure 1. Refrigerating system. 1 ¼ Q; 2 ¼ Qo ; Q ¼ Qo þ P :



Figure 2. Diagram for an irreversible refrigeration system (1 ¼ E Qo stands for the exergy of cooling load,

while 2 ¼ B Qo denotes the anergy, 3 ¼ Eu ¼ Exergy lossesÞ:

and the anergy
Tu
B Qo ¼ Qo ð7Þ
To
As we can see in Figure 2, power P can be calculated by

P ¼ E Qo þ E u ð8Þ

The term Eu refers to exergy losses.
The efficiency or exergy efficiency factor (z) is a clear indication of the refrigerating cycle’s
performance. The exergy efficiency factor is defined as follows:

E Qo
z¼ ð9Þ
E Qo þ Eu

Figure 3 presents the key points of the one stage vapour compression refrigerating cycles. For
simplicity reasons, we will assume that there is neither subcooling nor superheating of the
suctioned vapour. The pair of points: 2–3 (discharge line pressure drop), 4–7 (liquid line pressure
drop), 6–1 (suction line pressure drop) have almost similar entropy values.
This viewpoint has been reached after extended parametric study.
Using the theory encountered in (Baehr, 1989; Moran and Shapiro, 1993; Holman, 1997), the
exergy losses occurring in all four (4) phases of the one stage refrigeration process are calculated
as follows:
* Compression losses:

Eu12 ¼ m Tu ðs2 À s1 Þ ð10Þ

Exergy losses due to the compressor motor (air-cooled compressor) may be included for a better
accuracy. These losses are calculated as follows:
1 À nmotor
Eumotor ¼ Pcompression ð11Þ
nmotor



Figure 3. Pressure–enthalpy diagram for one stage vapour compression refrigerating cycle where
12: compression (suction of no superheated vapour) 34: Desuperheating, condensation, 4: no subcooling,
75: throttling, 56: evaporation. Pressure drops: 23 discharge line, 34 condenser, 47 liquid line, 56
evaporation, 61 suction line.

So the total compression losses are:

Eucompression ¼ Eu12 þ Emotor ð12Þ

* Condensation and desuperheating losses:

Eucd ¼ Qcondensation þ Qdesuperheating À m Tu ðs3 À s4 Þ ð13Þ

* Throttling losses:

Euthrottling ¼ m Tu ðs5 À s7 Þ ð14Þ

* Evaporation losses:

Euevaporation ¼ m Tu ðs6 À s5 Þ À E Qo À Qo ð15Þ

The total exergy losses are given by

Eu ¼ Eucompression þ Euevaporation þ Eucd þ Euthrottling ð16Þ

3. EFFICIENCY AND GRASSMANN DIAGRAMS AS A FUNCTION OF
OPERATING CONDITIONS

A simulation program has been developed for the prediction of a refrigerating system eﬃciency
related to the condenser’s and evaporator’s temperature.
The necessary thermodynamic properties such as equilibrium data, enthalpy and entropy
values are calculated by Perry and Green, (1984), Reid et al. (1988), ICI Chemicals and
Polymers (1995), NIST REFPROP (1996) and equations proposed by Stegou-Sagia (1997),
Stegou-Sagia and Damanakis (1999) and Stegou-Sagia and Damanakis (2000). Comparisons



have been made with results calculated by Coolpack Software (2001) and the differences
observed were minimal. We also have to note that all the calculated enthalpy and entropy values
took into consideration the International Institute of Refrigeration standards, according to
which enthalpy and entropy values of 200 and 1 J/kgK, respectively occur at the state of
saturated water of 0 8C.
Exergy efficiency diagrams are chosen to be drawn bearing in mind the following
assumptions:
* environmental temperature (Tu ) is equal to 20 8C;
* isentropic compression efficiency (nis ) is equal to 0.75.
* compressor motor efficiency (nmotor ) is equal to 1.
* pressure drop in evaporator is equal to 10 K.
* pressure drop in condenser is equal to 10 K.
* pressure drop in suction line, discharge line and liquid line is equal to 0.2 bar.
* the temperature of the cold space is 2 8C higher than that of the evaporation
n
temperature (To ).

The diagrams of exergy efficiency for the alternative refrigerant mixtures under consideration
are plotted in comparison with the corresponding conventional ones. More specifically, the plots
of exergy efficiency related to the evaporator’s temperature have been made for a constant
condensation temperature of 30 oC, while the evaporation temperature varies within the range
of À5 to –40 8C. Also, the diagrams related to the condensation temperature have been drawn
for a constant evaporation temperature of À20 8C and the condensation temperature varies
within the range of 25–60 8C.
In order to create the exergy efficiency diagrams, we used the following methodology: By
substituting Equations (6) and (8) into Equation (9), we have:

À Á À Á
Tu =To À 1 Qo Tu =To À 1 Qo

E Qo
z¼ ¼ ð17Þ
E Qo þ E P P

since the cooling load is always an incoming heat flux to the evaporator.
However, all refrigerating systems are characterized by a specific coefficient of performance
(COP), which is equal to the ratio of the cooling load to the power given at the compressor
motor. Therefore, we get

Tu
z¼ À 1 COP ð18Þ
To

For every selected pair of evaporation and condensation temperatures and given all the above-
mentioned assumptions (all of them were used as input to the software), we were able to
calculate the exergy efficiency factor through Equation (18) for the selected refrigerant mixtures
and plot it for all the selected temperature ranges.
Particular attention is paid to the fact that the working fluids are non-azeotropic refrigerant
mixtures and show different behaviour from pure substances; the pressure–temperature curve
for saturated liquid is different from that for vapour. This is taken into account in all relevant
calculations. The system design path, due to different evaporator’s and condenser’s inlet/outlet



temperature includes:
* selection of evaporator’s outlet against the desired cold space temperature;
* condenser inlet and outlet temperatures should be sufficient to reject heat;
* liquid enthalpy at expansion device and related property data (NIST, 1996; ASHRAE,
1997) can be used to get evaporator’s inlet temperature. At all other points in the system,
the fluid behaves as normal.
For the Grassmann plots, we have used the same basic assumptions as in exergy efficiency
diagrams. Furthermore:
* the evaporation temperature which has been chosen equals À20 8C.
* the compressor motor efficiency equals 0.85.
* the cooling load equals 100 kW.
In order to calculate the exergy efficiency factors and create the Grassmann plots, we
calculated the ratio of all exergy losses involved (as expressed in Equations (10)–(15)) to the

incoming to the compressor motor exergy flux (E Qo þ Eu ).

4. RESULTS

4.1. Exergy efficiency diagrams
Based on the above-mentioned assumptions and in order to compare the exergy efficiency factors
for the refrigerant mixtures in question, we have drawn the exergy efficiency diagrams presented in
Figures 4 and 5. Figure 4 correlates the exergy efficiency factor with the condensation temperature
for constant evaporation temperature, whereas Figure 5 plots the exergy efficiency factor and the
evaporation temperature for constant condensation temperature.
As far as the exergy efficiency diagram for constant evaporation temperature is concerned, we
observe that for an increasing condensation temperature, the exergy efficiency factor is
constantly decreasing. This is absolutely explainable since, the evaporation temperature (To n)
being constant, so is the temperature of the cold space (To ), according to the assumption already
made. Taking into account the fact that the ambient temperature has also been considered to be
constant, we can easily conclude that the Tu =To ratio remains constant.
Thus, according to Equation (18), the exergy efficiency factor is only proportionate to the
COP. But according to theory, for a constant evaporation temperature, an increase of the
condensation temperature ultimately results in a decrease of the COP value, since a bigger
power of compression is needed. Consequently, and always in accordance with Equation (18),
the COP decreasing, the exergy efficiency factor is also proportionately decreased.
Based on Figure 4, we see that the conventional refrigerants generally present smaller exergy
losses (for example, R-22 has the best exergy behaviour of all with an exergy efficiency of
51.11% at a condensation temperature of 25 8C). This advantage is, however, counterbalanced
by their detrimental environmental effect (according to Montreal Protocol 2000, R-22 is
characterized by an ODP of 0.055 compared to the zero ODP factors of R-404A, R-410A,
R-410B and R-507).
Regarding Figure 5, the exergy efficiency plots have a non-symmetrical bell-shaped form,
attaining their maximum value at an evaporation temperature of either –25 or –20 8C, whereas



Comparison of exergy efficiency factors
(Evaporation temperature = -20°C)
0.55

0.50

0.45

0.40
Exergy efficiency

0.35

0.30

0.25

0.20

0.15
25 30 35 40 45 50 55 60
Condensation temperature (°C)
R-22 R-502 R-410A

R-410B R-507 R-404A
Figure 4. Comparison of the energy efficiency factors for the refrigerant mixtures in question (R-404A,
R-410A, R-410B and R-507) and their corresponding conventional ones (R-22 and R-502) for a constant
evaporation temperature of À20 8C.

the minimum value for all refrigerants is observed at an evaporation temperature of –5 8C.
In this case, the Tu =To ratio does not remain constant and consequently, the exergy efficiency
factor is dependent on both this ratio and the COP factor. Both these factors have a different
behaviour for a constant condensation temperature and a continuously increasing evaporation
temperature (as an absolute value): the Tu =To ratio keeps increasing, whereas the COP value
keeps decreasing. Thus, we cannot predict the exact form of the plots in advance. R-22
maintains the best exergy behaviour and has an exergy efficiency factor slightly exceeding 45%
at an evaporation temperature of À25 8C.

4.2. Grassmann diagrams
The calculations supporting the drawing of the Grassmann diagrams for the four (4)
environmentally friendly refrigerant mixtures in question were performed with the help of
Coolpack software. The above-mentioned Grassmann diagrams are depicted in Figures 6–9.
From the drawn Grassmann diagrams, we can conclude that the biggest occurring
exergy losses are those of compression, ranging from 34.3% (for R-410A) to 36% (for
R-404A). Compression exergy losses are followed by condensation exergy losses, which vary



Comparison of exergy efficiency factors
(Condensation temperature = 30°C)
0. 46

0. 45

0. 44
Exergy efficiency

0. 43

0. 42

0. 41

0. 40
-40 -35 -30 -25 -20 -15 -10 -5

Evaporation temperature (°C)
R-22 R- 502 R-410A

R-410B R- 507 R-404A
Figure 5. Comparison of the exergy eﬃciency factors for the refrigerant mixtures in question (R-404A,
R-410A, R-410B and R-507) and their corresponding conventional ones (R-22 and R-502) for a constant
condensation temperature of 30 8C.

Figure 6. Grassmann diagram depicting the exergy losses with the use of R-404A.



Figure 7. Grassmann diagram depicting the exergy losses with the use of R-410A.

Figure 8. Grassmann diagram depicting the exergy losses with the use of R-410B.

Figure 9. Grassmann diagram depicting the exergy losses with the use of R-507.

from 12.3% (for R-404A) to 15.4% (for R-410A and R-410B). The third biggest exergy
losses are those of evaporation, followed by throttling losses, both having values of less
than 10%.
The biggest exergy eﬃciency occurs with R-410A (39%). Additionally, we note that mixtures
with very similar compositions (like R-410A and R-410B) demonstrate similar exergy
behaviour.



Exergy losses occurring in all four (4) phases of the one stage refrigerating process can be
reduced by modifying and/or improving the refrigerating system’s equipment. For example, the
high-compression exergy losses could be diminished by using a more expensive compressor with
a higher isentropic compression efficiency. However, analysing all the methods that could
potentially be employed in order to tackle exergy losses is not the topic of this current study.

5. CONCLUSIONS

This study focused on the exergy behaviour of four (4) environmentally friendly refrigerant
mixtures. All the theory presented is in accordance with all the currently available literature on
the topic of exergy. All the calculations involved were performed with the use of specialized
computer software and comparisons were made between NIST and Coolpack software in order
to double-check all the results presented.
Although the exergy behaviour of these four (4) refrigerant mixtures is generally inferior to
that of their environmentally hazardous predecessors, their use is constantly gaining
momentum, as they can guarantee the highly craved sustainable environmental development.

NOMENCLATURE

B =anergy amount
COP =coefficient of Performance

E =exergy amount

Eu =exergy losses
e =specific exergy
h =enthalpy

m =refrigerant mass flow rate
nis =isentropic compression efficiency
nmotor =compressor motor efficiency
P
=power
Qo =cooling load

Q =rejected heat
s =entropy
To =temperature of cold space
n
To =evaporation temperature
Tu =ambient Temperature
z =exergy efficiency factor

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Cavallini A. 1995. Working fluids for Mechanical Refrigeration. Proceedings of the 19th International Congress of
Refrigeration, vol. IVa. International Institute of Refrigeration: Hague, Netherlands; 25–42.



Coolpack Software. Denmark Technical University, Department of Mechanical Engineering, 2001.
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Moran M, Shapiro H. 1993. Fundamentals of Engineering Thermodynamics (2nd edn). New York: Wiley.
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International Journal of Energy Conversion and Management 41:1345–1359.


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