Exergy analysis of a two-stage refrigeration cycle using two natural substitutes of HCFC22

Exergy analysis of a two-stage refrigeration cycleusing two natural substitutes of HCFC22

Ahmed Ouadha*, Mohammed En-nacer,Lahouari Adjlout and Omar Imine

Department of Marine Engineering, Faculty of Mechanic,University of Science and Technology at Oran,P.O. Box 1505 Oran El-M'naouar, 31000 Oran, AlgeriaE-mail: [email protected]: [email protected]: [email protected] E-mail: [email protected]*Corresponding author

Abstract: The aim of the present paper is to carry out a detailed exergyanalysis of a two-stage vapour compression cycle by calculating itscomponents exergetic losses. The exergy equations have been developedusing refrigerant thermodynamic properties computed by means of a simplemodel of local equations of states. The results of the exergy analysis of atwo-stage refrigeration system operating between a constant evaporatingtemperature of ÿ30�C and condensation temperatures of 30, 40, 50 and60�C with two natural substitutes of HCFC22, namely, propane (R290) andammonia (R717) as working fluids, are presented. It is found that the mostsignificant losses occur in the compressors, expansion valves and condenser.Furthermore, it is shown that the optimum inter-stage pressure for a two-stagerefrigeration system is very close to the saturation pressure correspondingto the arithmetical mean of the refrigerant condensation and evaporationtemperatures.

Keywords: ammonia; equations of state; exergy analysis; inter-stagepressure; natural refrigerants; propane; two-stage refrigerating cycle.

Reference to this paper should be made as follows: Ouadha, A., En-nacer,M.,Adjlout, L. and Imine, O. (2005) `Exergy analysis of a two-stage refrigerationcycle using two natural substitutes of HCFC22', Int. J. Exergy, Vol. 2,No. 1, pp.14±30.

Biographical notes: Ahmed Ouadha is Senior Lecturer at the Department ofMarine Engineering, in Oran, Algeria. He graduated from the University ofScience and Technology, in Oran, Algeria in 1995 with a BEng degree andin 1999 with a Master degree. Currently, he is Vice Head of the Departmentof Marine Engineering.

Mohammed En-nacer is currently working at Pratt & Whitney Canada, inLongueil, Quebec. He graduated from the University of Science andTechnology in Oran, Algeria in 1986 with a BEng degree and from theOdessa Institute of Marine Engineering, in Odessa, Ukraine in 1991 with aPhD degree.

Lahouari Adjlout is a Professor at the Department of Marine Engineering,in Oran, Algeria. In 1990 he graduated from Liverpool University UK, witha PhD degree. He has refereed many journal and conference papers.

Int. J. Exergy, Vol. 2, No. 1, 200514

Copyright # 2005 Inderscience Enterprises Ltd.

Omar Imine is a Professor at the Department of Marine Engineering, inOran, Algeria. He graduated from Fluid Mechanics Institute, in Marseille,France in 1988 with a PhD degree. He has authored, co-authored and refereedmany conference papers. At present, he is the Dean of the MechanicalFaculty at the University of Science and Technology, in Oran, Algeria.

1 Introduction

Traditionally, the performance analysis of refrigeration systems is carried out usingan energetic method based on the first thermodynamic law (energy balance), in otherwords by means the coefficient of performance (COP) defined as the ratio of theevaporator load to the power consumed by the compressor. Unfortunately thismethod showed its limits while failing to identify the real energetic losses in arefrigeration system, for instance it does not recognise any energetic losses during thethrottling process. On the other hand the exergetic method, based on both first andsecond laws of thermodynamics, makes it possible to evaluate the magnitude of theenergy losses in each component of the refrigeration system, and to assess the qualityof the use of this energy from a thermodynamic point of view. The exergy allows aclearer presentation and a better comprehension of thermodynamic processes byquantifying the effect of each irreversibility occurring in the system. Therefore theexergy efficiency, based on the second law, and taking into account all the lossesappearing in the refrigeration system, represents an interesting alternative formeasuring the effectiveness of refrigeration systems.

The exergy of a system is defined as the maximum shaft work that could be doneby the component of the system and a specified reference environment assumed to beinfinite, in equilibrium, and ultimately to enclose all other systems. Typically, theenvironment is specified by stating its temperature, pressure and chemical composition.Exergy is not simply a thermodynamic property, but rather is a co-property of asystem and the reference environment (Dincer and Cengel, 2001). Exergy analysisovercomes the limitations of the first and second laws of thermodynamics, and is apowerful tool for analysing both the quantity and the quality of energy utilisation.

Several studies have been carried out recently about exergy analysis ofengineering systems (Kanoglu, 2002; Moran and Sciubba, 1994; Oh et al., 1996;Yumrutas et al., 2002). Relatively few efforts on the performance optimisation oftwo-stage refrigeration systems have been made (Ratts and Brown, 2000; Zubairet al., 1996). Zubair et al. (1996) studied a two-stage refrigeration cycle by meansboth first and second law analysis. They obtained an inter-stage pressurecorresponding to the maximum of the COP. Ratts and Brown (2000) have usedthe entropy generation minimisation to determine the optimal inter-stagetemperature using only superheating and throttle losses.

The reduction of the evaporating temperature when using a single-stagerefrigeration system, in the case of cold production at low temperatures, results inthe rise of the compression ratio. The latter leads to the deterioration of energy andvolumetric performances of the compressor which means the increase in theinvestments (costs) of the refrigeration system. In order to alleviate these misdeeds, itis necessary to use multi-stage refrigeration systems.

Exergy analysis of a two-stage refrigeration cycle 15

The inter-stage pressure has a key influence on the economy of the two-stagerefrigeration systems. Several methods of selecting the inter-stage pressure exist in theliterature. The inter-stage pressure can be selected from the condition of the minimalwork consumed by the compressors (Koshkin et al., 1985). This method gives aninter-stage pressure equal to the square root of the product of the condensation andevaporation pressures. Because of the phase change in the refrigeration systems, therefrigerant cannot be governed by the perfect gas laws. Furthermore, the temperaturesat aspiration of the two stages are different. Thus the determination of the inter-stagepressure by this method is not accurate. Prasad (1981) and Zubair et al. (1996) haveused the maximisation of the COP to evaluate the optimal inter-stage pressure oftwo-stage vapour compression cycles. Ratts and Brown (2000) have used the entropygeneration minimisation to determine the optimal inter-stage temperature.

Many synthetic products, developed as substitute fluids to CFCs and HCFCs, arewidely used in the refrigeration industry. These new products are not completelyfriendly to the environment, because their contribution to the global warming potentialis not negligible. Therefore, an increasing number of scientists believe that analternative solution may be provided by using natural fluids, namely, hydrocarbons(Hammad and Alsaad, 1999; Purkayastha and Bansal, 1998) and ammonia (Stera,1994). Devotta et al. (2001) present a number of suitable refrigerants as alternativesto HCFC22 for air conditioners. Among these fluids, propane has properties veryclose to those of HCFC22. The main properties of the refrigerants, ammonia,propane and HCFC22, used in the present work, are listed in Table 1.

Table 1 Ammonia, propane and HCFC22 properties for tc� 40�C and te� ÿ30�C

HCFC22 Propane Ammonia

ODP [R11� 1] 0.05 0 0

GWP [co2� 1] 1700 0 0

tcr (K) 369.28 369.85 405.50

pcr (MPa) 4.986 4.2475 11.353

qv (kJ/m3) 1676.29 1594.44 1411.98

qe (kJ/kg) 226.48 412.57 1360.27

COP 1.96 1.86 2.04

In order to carry out the exergetic analysis, it is necessary to dispose of the accuratethermodynamic properties of the refrigerant. A model, including a set of localequations of state enabling a reliable calculation of thermodynamic properties ofrefrigerants, is developed. This set of equations consists of a vapour pressureequation, an equation for the gas phase pÿ vÿ T properties, an equation giving thesaturated liquid densities and an equation for the specific heat capacity in the idealgas domain. This model describes the behaviour of the refrigerants in different phasesin a frigorific system.

The objective of this paper is to present an exergy analysis of a two-stage vapourcompression cycle allowing the evaluation of the exergetic losses occurring in eachcomponent and then the exergetic efficiency of the refrigeration system. For this

A. Ouadha, M. En-nacer, L. Adjlout and O. Imine16

purpose, the thermodynamic properties calculations, at the main cycle points, arecarried out by means of a simple and effective model of local equations of states.Finally the inter-stage pressure leading to the optimum performance of two-stagerefrigeration cycle is discussed.

2 Thermodynamic properties

Disposing of given reliable data on the thermodynamic properties of the substitutionrefrigerants is essential, not only in order to determine the best possible choice amongthe candidates for the substitution of the traditional refrigerants, but also in order toconceive and to manufacture material without danger to the environment.

In the refrigeration systems, the refrigerant can be found in different states whichgo from the liquid under cooling to the gas state, passing by the change of phaseliquid-vapour. Generally the critical temperature is not reached. The model of thethermodynamic properties adopted is based on four basic equations: an equation ofstate for the gas state, a correlation for the saturated vapour pressure, a correlationfor the saturated liquid density and an equation of the specific heat capacity atconstant pressure in the ideal gas state.

2.1 Gas state equation

A truncated virial equation of the form (Ouadha, 1999; Ouadha et al., 2001):

Z � p:v

r:T� 1�

X3i�1

X5j�0

bij �j !i �1�

is recommended. Z is the coefficient of compressibility, � � Tcr=T is the inverse of thereduced temperature, ! � �=�cr is the reduced density and r is the gas constant. Thecoefficients bij are calculated using available data.

2.2 Vapour saturated pressure

For the vapour saturated pressure, a simple equation describing the saturation curvefrom the triple point to the critical point, with a good precision is used, which is aform proposed by McLinden (1990):

ln pr� � � a1��1ÿ �� � � a2� � a3�

1:89 � a4�3; �2�

where pcr � p=pcr is the reduced pressure and � � 1ÿ t=Tcr.

2.3 Saturated liquid density

The data of saturated liquid density were fitted to the commonly used form:

���cr � 1� d1�

0:355 � d2�2=3 � d3� � d4�

4=3 �3�where �cr critical density and � � 1ÿ T=Tcr. The term with the exponent 0.355 givesthe correct behaviour near the critical point (McLinden, 1990).

Exergy analysis of a two-stage refrigeration cycle 17

2.4 Specific heat capacity at constant pressure in the ideal gas state

The specific heat capacity at constant pressure is usually represented by a polynomialin temperature:

c0p

,R �

X3i�0

ciTir; �4�

where R � 8:3145 kJ/kgK and Tr � T=Tcr is the reduced temperature.

2.5 Calorific properties calculation

Using the four basic Equations (1) to (4) and the differential equations ofthermodynamics, it is possible to calculate the other essential thermodynamicfunctions necessary to the exegetic analysis, namely, the enthalpy and the entropywhose analytical expressions are given by the following equations:

h T; v� � � h0 ��TT0

c0v T� �dT��vv0

T@p

@T

� �v

ÿp� �

dv� p T; v� �v �5�

s T; v� � � s0 ��TT0

c0v T� � dTT��vv0

T@p

@T

� �v

ÿR

v

� �dv� R ln

v

v0�6�

with c0v � c0p ÿ R: specific heat capacity at constant volume in the ideal gas state.The constants of integration are selected according to an arbitrary state of

reference, in fact: h0(0�C)� 2000.00 kJ/kg and s 0(0�C)� 1.00 kJ/kg.K.The enthalpy and the entropy of the saturated liquid are derived starting from the

equation of Clausius-Clapeyron:

h0 T� � � h00 T; v00� � ÿ T v00 T; ps� � ÿ v0 T� �� � dpsdT

�7�

s 0 T� � � s 00 T; v00� � ÿ v00 T; ps� � ÿ v0 T� �� � dpsdT

; �8�

where, h0, s 0, v0 refer to enthalpy, entropy and specific volume, respectively, of thesaturated liquid state and, h00, s 00, v00 denote enthalpy, entropy and specific volume,respectively, of the saturated vapour state.

3 System description and exergy analysis

The exergy is another name for available energy that measures the ability of theenergy source to produce useful work. Exergy is a measure of the maximum usefulwork that can be done by a system interacting with an environment which is atconstant pressure p0 and temperature t0.

Thermodynamic analysis means generally the use of the first and second laws ofthermodynamics. The first law requires that the energy balance to be satisfied. Therequirements of the second law can be represented by the assessment of the exergy. In

A. Ouadha, M. En-nacer, L. Adjlout and O. Imine18

this case all flows crossing the limit of a system (Figure 1) are added. The system caninclude a whole machine or only parts of it, such as evaporator, compressor, etc. Inthe general case, the flows are the mechanical or electric power _Wi, the exergy of thefluids flows _miei at the entry and _mkek at the exit or the exergy of heat � _EQ�i.

Figure 1 Flows of exergy through the limits of an open system

The scheme of a two-stage refrigerating machine and its corresponding cycle areshown in Figure 2. The cycle is mainly composed by a low-pressure compressor(LPC), a flash intercooler (flash), a high-pressure compressor (HPC), a condenser,two expansion valves and an evaporator. The refrigerant, at the superheated vapourstate, enters the LP compressor where it is compressed to the flash intercooler. Theseparated vapour due to throttling (7±8) and de-superheating of the compressedvapour (5±6) yields the increased mass of vapour entering the HP compressor. Aftera second compression (3±4) the high pressure superheated vapour enters in thecondenser, where it is de-superheated, condensed and under cooled (4±7) beforebeing throttled to the flash inter-cooler (7±8). After the flash inter-cooler, the liquidpasses through the second expansion valve, where it expands to the evaporatorpressure (9±10). Finally, the refrigerant enters the evaporator, where it absorbs heatfrom the refrigerated medium (10±11). Before entering again in the LP compressor,the refrigerant is superheated by absorbing more heat in the suction line (11±1).

Figure 2 Two-stage refrigeration scheme and cycle

Exergy analysis of a two-stage refrigeration cycle 19

Knowing the thermodynamic properties in the characteristic points of the cycle, theexergetic losses, in each component of the system, can be calculated using thefollowing exergetic losses expressions:

�epipe � _mLPC h1 ÿ h11 ÿ T0 s1 ÿ s11� �� � �9�

�eLPC � _mLPCT0 s2 ÿ s1� � �10�

�eflash � _mLPC h2 ÿ h9 ÿ T0 s2 ÿ s9� �� � ÿ _mHPC h3 ÿ h8 ÿ T0 s3 ÿ s8� �� � �11�

�eHPC � _mHPCT0 s4 ÿ s3� � �12�

�econd � _mHPC h4 ÿ h7 ÿ T0 s4 ÿ s7� �� � �13�

�eexp 1 � _mHPCT0 s8 ÿ s7� � �14�

�eexp 2 � _mLPCT0 s10 ÿ s9� � �15�

�e�0 � _mLPC h11 ÿ h10� � 1ÿ T0

T�0

���� ���� �16�

�e0 � _mLPC h11 ÿ h10 ÿ T0 s11 ÿ s10� �� � �17�

�eevap � �e0j j ÿ �e�0�� �� �18�

where _mLPC, _mHPC are mass flow rate for LP compressor and HP compressor,respectively. T�0 and T0 are the cold room and ambient air temperatures, respectively.

The total exergetic loss is the sum of the exergetic losses in each components ofthe system. It can be evaluated by:

�et � �epipe ��eLPC ��eflash ��eHPC ��econd ��eexp 1 ��eexp 2 ��eevap �19�The exergetic efficiency is defined as the ratio of the desired exergy to the exergy used:

�ex ��e�0�� ��

_W� 1ÿ�et

_W�20�

where �e�0�� �� is the exergy of the cold room (desired exergy) and _W the power

consumed by the compressors (exergy used) calculated by:

_W � _mLPC h2 ÿ h1� � � _mHPC h4 ÿ h3� � �21�

4 Results and discussion

This section is devoted to the presentation of the results obtained by means acomputer programme written to calculate the performance of propane and ammoniarefrigeration cycles. The effect of the important system parameters on thecomponents exergetic losses in the cycle and the exergy efficiency is evaluated. Thecalculations were conducted for a system with 100 kW refrigeration capacity,compressor isentropic efficiency, �is � 80%, evaporation temperature, Te � ÿ30�Cand different condensation temperatures without pressure drops in the system.

A. Ouadha, M. En-nacer, L. Adjlout and O. Imine20

The performances of propane and ammonia are shown in Figure 3 by meansCOP and exergetic efficiency versus the condensation temperature. The COP of bothrefrigerants has the same pace; it decreases with the increase of the condensationtemperature (Figure 3(a)) and the ammonia has the highest values of COP. The sameconclusion can be made when analysing the exergetic efficiency (Figure 3(b)), i.e. theammonia exergetic efficiency is the highest but decreases more slowly than thepropane efficiency when increasing the condensation temperature. From the above, itis clear that out of the two refrigerants, ammonia has the best performance.

Figure 3 Performance comparison of ammonia and propane: (a) coefficient of performance;(b) exergetic efficiency

(a)

(b)

Exergy analysis of a two-stage refrigeration cycle 21

For the rest of the discussion, the exergetic efficiencies and losses are plotted as afunction of the reduced inter-stage saturation temperature � given by the followingexpression:

� � Ti ÿ Te

Tc ÿ Te�22�

where Ti, Te and Tc are intermediate, evaporation and condensation temperatures,respectively.

This representation form is chosen in order to simplify the illustration of theconsiderable influence of the intermediate pressure (temperature) on the exergeticlosses of each component and the efficiency of the machine, as will be shown below.

The exergetic losses of the two-stage refrigeration system components versusreduced inter stage saturated temperature are shown in Figure 4. For bothrefrigerants, the higher losses occur in the expansion valves, the compressors andthe condenser, while they are low and quasi-constant in the suction line and theevaporator. In the case of the propane (a), the flash intercooler, the LP compressorand the expansion valve 2, exergetic losses increase with increasing �, but the losses ofthe flash intercooler are insignificant with respect to those of the LP compressor andthe expansion valve 2. On the other hand the losses of the HP compressor andexpansion valve 1 decrease with decreasing �. For the ammonia (b), we observe that,except for the losses of the condenser being higher and decreasing with � while thoseof the propane case are quasi-constant, the evolution of the other losses versus �conserve the same trend but with different values.

In order better to show the enhancement of the two-stage compression cycleperformance with respect to single-stage cycle, the following normalised forms ofexergetic efficiency and total losses are introduced:

�exN � �exÿts�exÿss

; �23�

and

�eexN � �etotÿts�etotÿss

: �24�

The single-stage compression cycle exergetic losses and efficiencies are listed inTable 2. The calculations were performed for a system with 100 kW refrigerationcapacity and an isentropic efficiency of the compressor equal to 80%.

The evolution of the normalised exergetic efficiencies according to inter-stagereduced temperature � variation with different refrigerant condensation temperaturesis presented in Figure 5. The normalised exergetic efficiencies have the samebehaviour, i.e. they have minimum values for � � 0 and � very close to 1 (0.90 to 0.94for ammonia and 0.94 to 0.97 for propane) and they reach maximum values at � inthe neighbourhood of � � 0:5.

Figure 6 shows the influence of the reduced inter-stage temperature � on thenormalised total exergetic losses. As expected, it is noted that the normalised totalexergetic losses have the same form for various temperatures of condensation, i.e. theyhave maximum values for � � 0 or � very close to 1 (0.90 to 0.94 for ammonia and 0.94to 0.97 for propane) and minimal values close to � � 0:5. Furthermore, the increase incondensation temperature lowers the minimum of the normalised total exergetic losses.

A. Ouadha, M. En-nacer, L. Adjlout and O. Imine22

Figure 4 Components exergetic losses in two-stage refrigerating system: (a) ammonia; (b) propane

(a)

(b)

Table 2 Exergetic efficiency and losses for a single-stage cycle

Refrigerant te (�C) tc (

�C) �exss (%) �etss (kW)

Ammonia ÿ30.0 30 47.13 21.25

40 46.85 26.04

50 46.02 31.67

60 44.76 38.29

Propane ÿ30.0 30 44.55 23.57

40 42.64 30.89

50 39.62 41.15

60 35.54 56.28

Exergy analysis of a two-stage refrigeration cycle 23

Figure 5 Influence of conjugate inter-stage temperature and condensation temperature onthe exergetic efficiency: (a) ammonia; (b) propane

(a)

(b)

A. Ouadha, M. En-nacer, L. Adjlout and O. Imine24

Figure 6 Influence of conjugate reduced inter-stage temperature and condensationtemperature on the total exergetic losses: (a) ammonia; (b) propane

(a)

(b)

Exergy analysis of a two-stage refrigeration cycle 25

5 Optimum inter-stage pressure

In the light of the discussion of Figures 5 and 6, we can conclude that the mostefficient cycles are those operating with a saturation intermediate temperature veryclose to an arithmetic mean of condensation and evaporation temperatures. Thisconclusion is also reached when conducting the same study using the coefficient ofperformance (COP) instead of exergetic efficiency. Indeed, Table 3 shows a perfectconcordance between the optimum intermediate temperatures obtained using eitherthe maximum COP or the maximum exergetic efficiency for both refrigerants.

Table 3 Optimal inter stage temperature comparison of ammonia and propane

Refrigerant tcond (�C) ti opt. (COP max) (�C) tI opt. (�ex max) (�C)

Ammonia 30 ÿ4.222504 ÿ4.22250440 0.4721069 0.4721375

50 5.175781 5.17546

60 10.090060 10.089840

Propane 30 ÿ0.7738647 ÿ0.773742740 4.948669 4.948761

50 10.896270 10.896270

60 17.278230 17.278230

In order to determine more accurately the optimal inter-stage pressure (temperature),a simple analytical method, comprising three steps, is proposed:

Step 1: the normalised exergetic efficiency is fitted according to a polynomial form:

�exN �X5i�0

ai �i �25�

Step 2: the derivation of the normalised exergetic efficiency is carried out:

d�exNd��X

i � ai � �iÿ1 �26�

Step 3: the maximum normalised exergetic efficiency is obtained by equalisingEquation (26) to zero and solving:

d�exNd�� 0: �27�

The inter-stage reduced temperatures corresponding to the maximum exergeticefficiency and COP with different condensation temperatures, obtained by themethod proposed above, are listed in Table 4.

A. Ouadha, M. En-nacer, L. Adjlout and O. Imine26

Table 4 Reduced inter-stage temperature corresponding to the maximum exergetic efficiency

Refrigerant tc (�C) ���exnmax� ��COPmax� Difference (%)

Ammonia 30 0.445 0.424 4.72

40 0.440 0.431 2.05

50 0.435 0.433 0.46

60 0.430 0.437 1.63

Propane 30 0.487 0.469 3.70

40 0.499 0.468 6.21

50 0.511 0.494 3.33

60 0.524 0.515 1.72

The evolution of the optimal inter-stage temperature with the condensationtemperature, for propane and ammonia, is represented in Figure 7. For bothrefrigerants, the optimal inter-stage temperature increases with an increase incondensation temperature. The propane has an optimal inter-stage temperaturehigher than that of the ammonia.

Figure 7 Comparison of inter stage optimal temperature for ammonia and propane

We notice that the results obtained by this method confirm the conclusion madefrom the exergetic efficiency plots and Table 3, i.e. the most efficient cycles areoperating with an inter-stage reduced temperature � very close to 0.5. A very goodagreement between the two approaches is noted. The latter confirm that the optimal

Exergy analysis of a two-stage refrigeration cycle 27

inter-stage pressure of the two-stage cycle corresponds to an inter-stage saturationtemperature equal to the arithmetic mean of the condensation and evaporationtemperatures. This conclusion is the same as that made by Zubair et al. (1996).

6 Conclusions

The exergy analysis of a two-stage compression cycle is carried out in the presentstudy to evaluate the magnitude of exergetic losses in each component of therefrigeration system. The calculations were performed by means of a computerprogramme based on exergetic losses expressions and a simple set of local equationsof state allowing reliable computation of the refrigerants thermodynamic properties.The results show that the refrigeration system working with ammonia is moreefficient. The greatest part of the exergetic losses takes place in the condenser, thecompressors and the expansion valves.

The economically successful passage from a single-stage refrigerating machine toa two-stage machine, in the case of a high-pressure ratio, is largely dependent uponthe selection of the inter-stage pressure. In the present study we propose thedetermination of the inter-stage pressure with a simple an effective method based onthe selection of the inter-stage pressure corresponding to maximum exergeticefficiency, i.e. a minimum of exergetic losses. The optimal inter-stage pressure foundis the saturated vapour pressure corresponding to a temperature equal to thearithmetic mean of the condensation and evaporation temperatures.

The approach based on the exergetic efficiency is more effective for refrigerationsystem analyses because it takes into account all losses occurring in the system. Thisallows us to identify the less efficient components and attempt to improve them.Furthermore the exergetic efficiency value ranging between 0 and 1 is moreconvenient than the coefficient of performance generally greater than 1.

References

Devotta, S., Waghmare, A.V., Sawant, N.N. and Domkundwar, B.M. (2001) `Alternatives toHCFC-22 for air conditioners', Appl. Thermal Eng., Vol. 21, pp.703±715.

Dincer, I. and Cengel, Y.A. (2001) `Energy, entropy and exergy concepts and their roles inthermal engineering', Entropy, Vol. 3, pp.116±149.

Hammad, M.A. and Alsaad, M.A. (1999) `The use of hydrocarbons mixtures as refrigerants indomestic refrigerator', Appl. Thermal Eng., Vol. 19, pp.1181±1189.

Kanoglu, M. (2002) `Exergy analysis of multistage cascade refrigeration cycle used for naturalgas liquefaction', Int. J. Energy Res., Vol. 26, pp.763±774.

Koshkin N.N. et al. (1985) Machines Frigorifiques, Leningrad, Mashinostoenye.

McLinden, M.O. (1990) `Thermodynamic properties of CFC alternatives: a survey of theavailable data', Int. J. Refrig., Vol. 13, pp.149±162.

Moran, M.J. and Sciubba, E. (1994) `Exergy analysis: principles and practice', ASME Journalof Engineering for Gas Turbines and Power, Vol. 116, pp.285±290.

Oh, S., Pang, H., Kim, S. and Kwak, H. (1996) `Exergy analysis for a gas turbine cogenerationsystem', ASME Journal of Engineering for Gas Turbines and Power, Vol. 118, pp.782±791.

A. Ouadha, M. En-nacer, L. Adjlout and O. Imine28

Ouadha, A. (1999) `Evaluation thermodynamique des fluids frigorigeÁ nes de remplacement',Master Thesis, University of Sciences and Technology, in Oran, Algeria, pp.14±28.

Ouadha, A., Adjlout, L. and En-nacer, M. (2001) `Thermodynamic tables of CFCsalternatives', in First International Chemical Engineering Conference, September 17±19,Amman, Jordan.

Prasad, M. (1981) `Optimum inter stage pressure for 2-stage refrigeration system', ASHRAEJournal, Vol. 23, pp.58±60.

Purkayastha, B. and Bansal, P.K. (1998) `Experimental study on HC290 and a commercialliquefied petroleum gas (LPG) mix as suitable replacements for HCFC22', Int. J. Refrig.,Vol. 21, pp.3±17.

Ratts, E.B. and Brown J.S. (2000) `A generalized analysis for cascading single fluid vapourcompression refrigeration cycles using an entropy generation minimization method', Int.J. Refrig., Vol. 23, pp.353±365.

Stera, A.C. (1994) `Utilisation de l'ammoniac en marine', Rev. GeÂn. Froid, pp.30±31.

Yumrutas, R., Kunduz, M. and Kanoglu, M. (2002) `Exergy analysis of vapor compressionrefrigeration systems', Exergy, Vol. 2, pp.266±272.

Zubair, S.M., Yaqub, M. and Khan, S.H. (1996) `Second-law-based thermodynamic analysisof two-stage and mechanical-subcooling refrigeration cycles', Int. J. Refrig., Vol. 19,No. 8, pp.506±516.

Nomenclature

Cp Specific heat at constant pressure (kJ/kgK)

GWP Global warming potential

h Specific enthalpy (kJ/kg)

_m Mass-flow rate (kg/s)

ODP Ozone depletion potential

P Pressure (MPa)

Qe Refrigerating effect (kJ/kg)

Qv Volumetric refrigerating effect (kJ/m3)

r Gas constant (kJ/kgK)

s Specific entropy (kJ/kgK)

T Absolute temperature (K)

v Specific volume (m3/kg)

_W Compressor capacity (kW)

Z Coefficient of compressibility

Greek symbols

�e Exergy losses (kW)

� Efficiency

� Reduced inter-stage temperature

� Density (kg/m3)

! Reduced density

Exergy analysis of a two-stage refrigeration cycle 29

Subscripts

0 Environment

c Condensation

cr Critical state

e Evaporation

ex Exergetic

i Inter-stage

n Normalised

r Reduced

ss Single-stage

tot Total

ts Two-stage

Exponents

0 Ideal gas state0 Saturated liquid state00 Saturated vapour state

A. Ouadha, M. En-nacer, L. Adjlout and O. Imine30