Revista Mexicana de ngeniería uímica - SciELOflowing along the shell and water flowing inside the tubes (as secondary fluid). In contrast, in the shell and tube evaporator the

Revista Mexicana de Ingeniería Química

CONTENIDO

Volumen 8, número 3, 2009 / Volume 8, number 3, 2009

213 Derivation and application of the Stefan-Maxwell equations

(Desarrollo y aplicación de las ecuaciones de Stefan-Maxwell)

Stephen Whitaker

Biotecnología / Biotechnology

245 Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo

intemperizados en suelos y sedimentos

(Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil

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S.A. Medina-Moreno, S. Huerta-Ochoa, C.A. Lucho-Constantino, L. Aguilera-Vázquez, A. Jiménez-

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259 Crecimiento, sobrevivencia y adaptación de Bifidobacterium infantis a condiciones ácidas

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L. Mayorga-Reyes, P. Bustamante-Camilo, A. Gutiérrez-Nava, E. Barranco-Florido y A. Azaola-

Espinosa

265 Statistical approach to optimization of ethanol fermentation by Saccharomyces cerevisiae in the

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(Optimización estadística de la fermentación etanólica de Saccharomyces cerevisiae en presencia de

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271 Localización de una planta industrial: Revisión crítica y adecuación de los criterios empleados en

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J.R. Medina, R.L. Romero y G.A. Pérez

Vol. 13, No. 3 (2014) 957-968

EXERGETIC ANALYSIS OF A REFRIGERATION SYSTEM

ANALISIS EXERGETICO DE UN SISTEMA DE REFRIGERACIONJ. M. Belman-Flores∗, A. Gallegos-Munoz, J. M. Riesco-Avila, A. Zaleta-Aguilar, J. M. Mendoza-MirandaDepartment of Mechanical Engineering, Engineering Division, Campus Irapuato-Salamanca, University of

Guanajuato, Salamanca, Gto., Mexico.Received March 4, 2014; Accepted October 4, 2014

AbstractThis paper presents the exergy analysis of an experimental refrigeration system that operates with the refrigerant R134a.The research is based on analyzing the influence of six operational and controllable parameters of the experimental setupsuch as the compressor frequency of operation, the degree of static superheat, and the temperature of the secondary fluids (atthe inlet of the evaporator and the condenser) on the exergy destruction. Thus, the results show that most exergy destructionis located in the condenser, followed by the compressor, the expansion valve and the evaporator. Furthermore, the highestexergetic efficiency is obtained by a decrease in the temperature of the secondary fluid inside the evaporator, and by anoperation of the compressor at low speed. The efficiency of the compressor is also included in the analysis, which is aparameter that determines the exergy destruction of the largest component. Finally, a function of the exergetic efficiency isestablished in order to find those magnitudes of operational parameters that contribute to improving this efficiency.

Keywords: irreversibilities, vapor compression, exergy, R134a, controllable parameters, combined efficiency.

ResumenEn este trabajo se presenta el analisis exergetico de un sistema experimental de refrigeracion que trabaja con el refrigeranteR134a. El trabajo desarrollado analiza la influencia de seis parametros operacionales y controlables de la instalacionexperimental como: la frecuencia de operacion del compresor, el grado de sobrecalentamiento estatico y la temperatura delos fluidos secundarios (a la entrada del evaporador y condensador), sobre la destruccion de exergıa. Ası pues, los resultadosmuestran que la mayor destruccion de exergıa es localizada en el condensador seguida por el compresor, la valvula deexpansion y el evaporador. Por otro lado, la eficiencia exergetica mas alta es obtenida mediante un decremento de latemperatura del fluido secundario en el evaporador, ademas de un manejo bajo de la velocidad del compresor. Tambien enel analisis se involucra la eficiencia combinada del compresor, la cual resulta en un parametro que determina el componentecon mayor destruccion de exergıa. Asimismo, se establece una funcion de la eficiencia exergetica para la busqueda deaquellas magnitudes de los parametros operacionales que contribuyan a mejorar dicha eficiencia.

Palabras clave: irreversibilidades, compresion de vapor, exergıa, R134a, parametros controlables, eficiencia combinada.

∗Autor para la correspondencia. E-mail: [email protected]

Publicado por la Academia Mexicana de Investigacion y Docencia en Ingenierıa Quımica A.C. 957

Belman-Flores et al./ Revista Mexicana de Ingenierıa Quımica Vol. 13, No. 3 (2014) 957-968

1 Introduction

Refrigeration systems are extremely important indaily life, especially in terms of preserving food,health, and comfort. Nowadays, a large number ofrefrigeration systems are based on vapor compressionsystems, which currently represent 10% of the totalenergy demand (Dubey et al., 2010). The escalatingcost in energy and its inefficient use, the indirectcontribution in greenhouse gases emitted in theatmosphere, among other parameters, were the issuesthat trigger the improvement of the performanceof vapor compression systems. Performance andoptimization of such systems can be carried out usingeither energy or exergy analyses. Due to the fact thatexergy analysis is a thermodynamic technique basedon the second law of thermodynamics, it providesan alternative when comparing processes and systemsrationally and meaningfully (Dincer and Kanoglu,2010). An exergy analysis is usually aimed todetermine the maximum performance of the systemand to identify sites of exergy destruction. In theliterature review of this area, there are numerousworks dealing with exergy analysis of compressionrefrigeration and air conditioning systems. Yumrutaset al., (2002) developed a computational modelbased on exergy analysis for studying the effects ofevaporating and condensing temperatures on pressurelosses, exergy losses, second law efficiency, andthe coefficient of performance, COP, of a vaporcompression system that works with ammonia. Theirresults showed that the second law efficiency andCOP increase, and exergy losses decreased when thetemperature difference between the evaporator andrefrigerated space was decreased. Su and Chen (2006)presented a theoretical study of exergetic efficiencyoptimization of a Carnot refrigeration system withmultiple irreversibilities, namely finite-rate heattransfer, the internal dissipation of the working fluid,and the heat leak between the heat reservoirs. Asa result of this research, they derived the maximumexergetic efficiency, and observed that it occurs whenthe temperature ratio between cold side and hot sideprocesses is slightly lower than that of the temperatureratio of the two reservoirs. Chen and Su (2005)reported an optimization of the exergetic efficiencyfor a theoretical irreversible Brayton refrigerationcycle. The efficiency optimization was implementedby considering the isentropic temperature ratio, andthe allocation factor of the thermal conductance asparameters. The maximum exergetic efficiency occurswhen the isentropic temperature ratio is slightly

greater than the temperature of the two reservoirs.They concluded that the method of exergetic efficiencyoptimization is an important and effective criterionfor the evaluation of a refrigeration cycle. Arora andKaushik (2008) presented a theoretical performanceanalysis of the R502 and its substitutes (R404A andR507) based on energy and exergy concepts. Theparameters computed were COP, exergy destruction,exergetic efficiency, and efficiency defects in thesystem. Ahamed et al., (2011) reviewed theexergy analysis of a vapor compression systemand summarized the main parameters that affectexergy, namely evaporating temperature, condensingtemperature, sub-cooling, and compressor pressure.Kizilkan et al., (2010) presented an exergy analysisfor an experimental variable-speed system workingwith R404A in order to determine irreversibility ratesand exergy efficiencies of each system component aswell as the overall system. Their results showed thatthe major irreversibility occurred in the compressorfollowed by the condenser, the evaporator, and theexpansion valve for different compressor frequencies.However, they do not explore any other parameterbesides the drive frequency, such as volumetricflow and inlet temperatures for secondary fluids inboth, the evaporator and the condenser. Apreaet al., (2003) performed an exergy analysis ofa vapor compression refrigeration plant while therefrigeration capacity was controlled by varying thecompressor speed. They evaluated the completeplant and its individual components to pinpoint thegreatest contribution to the decrease of the exergyperformance. They proposed and tested threeworking fluids R407C, R507, and R417A. The authorsconcluded that the best performance was related toR407C, and the contribution of the compressor tothe overall irreversibility was the most relevant. Inthis context, Kalaiselvam and Saravan (2009) appliedexergy analyses to different scroll compressors usingR22, R417A, and R407C to determinate the totalexergy losses. The eco-friendly refrigerant R417Acan be used as an alternative rather than R407Cin order to preserve the exergy loss. Padilla etal., (2010) followed an exergy approach in order toevaluate the thermodynamic performance of R413Ain an unmodified R12 domestic refrigerating system.They carried out twelve experimental tests in acontrolled environment during the selected coolingprocess from evaporator outlet temperature, rangingbetween 288[K] to 263[K] by varying the evaporatorand condenser air-flows to simulate different workingconditions. Their results showed that the overall

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energy and exergy performance of the system workingwith R413A is consistently better than that of R12.Lugo-Leyte et al., (2013) developed a thermodynamicand exergetic analysis applied to vapor compressionrefrigeration cycle with refrigerant R134a. Theyobtained the irreversibilities of each equipment,the exergetic operation cost in function of theenvironmental temperature and the temperature of therefrigerated spaced.

The main purpose of this paper is to evaluatethe exergy destruction and exergetic efficiency of thecomplete refrigeration plant using an experimentallyvalidated coupled model. The analysis takes intoaccount the variation of key parameters easilyobtained and controlled, such as the compressor drivefrequency, superheating degree, secondary volumetricflow rates, and secondary fluid inlet temperatures.All of those variables enable a better understandingof the influence from the parameters present ina refrigeration system as opposed to analyzingonly the effect of compressor drive frequency asin the literature. Finally, a maximization ofexergetic efficiency is implemented to determine thebest combination of controllable parameters, whichimproves the exergy performance of the refrigerationplant.

2 Description of the experimentalplant

The vapor compression refrigerator used fordeveloping the exergy analysis is shown in Fig. 1.The experimental plant basically consists of a vaporcompression circuit and two secondary fluid circuits:the condensing water loop and a heat load simulationsystem. This experimental plant can work with therefrigerant R134a. The main components of thevapor compression refrigerator are: an open typereciprocating compressor, a shell and tube condenser,an expansion valve, and a shell and tube evaporator.In the shell and tube condenser, there is refrigerantflowing along the shell and water flowing inside thetubes (as secondary fluid). In contrast, in the shelland tube evaporator the refrigerant flows inside thetubes, and brine water-propilenglycol (50/50% byvolume) flows in the shell. The load simulationsystem consists of a tank with an electrical resistanceand a variable speed pump to control the thermalload of the evaporator. The condensing system isused to set the water conditions at the condenserusing a commercial chiller that has a variable speed

1

Fig. 1. Vapor compression plant.

Expansion valve Compressor

Condenser

Evaporator

aec asc

ase aee

water

brine

1

23

4

65

7

a)

b)

Fig. 2. a) Schematic diagram of a single-stage refrigeration system and b) P-h diagram of the

single-stage refrigeration system.


pump. With these two systems it is possible tocontrol the secondary fluid conditions at the evaporatorand condenser. The experimental setup is fullyinstrumented with sensors to measure key variablessuch as: pressure, temperature, volumetric and massflow rate, compressor drive frequency and energyconsumption. The signals generated by all sensors, aswell as those provided by the measuring devices, aregathered by a National Instruments data acquisitionsystem.

Fig. 2 shows both the schematic and the P-h diagram of the refrigeration system. The vaporcompression process begins when the refrigerant iscompressed until it reaches the condensing pressure(process 7-1). Before the compressed refrigerantenters the condenser inlet, heat transfer to theenvironment is carried out through the discharge lineand the oil separator areas causing a desuperheatingof refrigerant vapor (process 1-2). The refrigerantvapor is then condensed by removing the heat throughthe secondary fluid into the condenser until therefrigerant reaches a subcooled condition. Afterthe condenser, the liquid refrigerant has an extrasubcooling, S C, measured in states 3 and 4. Theliquid refrigerant enters the expansion valve whereit expands to the evaporating pressure (process 4-5). At the evaporator, refrigerant cools the brinewater-propilenglycol (process 5-6). Finally, afterthe evaporator, the refrigerant is superheated, S S ,measured in states 6 and 7.

3 Exergy analysis

In thermodynamics, the exergy of a system is definedas the maximum work possible during a process that

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1


Expansion valve Compressor

Condenser

Evaporator

aec asc

ase aee

water

brine

1

23

4

65

7

a)

b)

Fig. 2. a) Schematic diagram of a single-stage refrigeration system and b) P-h diagram of the

single-stage refrigeration system.

Fig. 2. a) Schematic diagram of a single-stage refrigeration system and b) P-h diagram of the single-stagerefrigeration system.

brings this system into equilibrium with theenvironment conditions (Kotas, 1995). When thesystem and its environment reach equilibrium, theexergy of the system will be zero. The methodof the exergetic analysis is based on the secondlaw of thermodynamics and enables the designersto identify location, the cause and the magnitudeof losses in the thermal systems. In the exergybalance, the destroyed exergy represents the real lossin the quality of energy that cannot be identified bymeans of the energy balance, since a conservationof energy is always considered (Tsatsaronis, 1993).The exergy analysis has been used by many authorsto perform the evaluation of the efficiency ofrefrigeration systems (Srinivasan et al., 2003; Taoet al., 2010; Fabrega et al., 2010). Thus, the exergyanalysis is a thermodynamic tool that can be usedto evaluate the performance of refrigeration systemby determining the magnitude and location of theprocess irreversibility (losses of energy quality),making it possible to study the changes of operationalparameters of the process.

By applying the first and second laws ofthermodynamics, the general expression of exergybalance in any system is (Moran and Shapiro, 2007):∑(

1−T0

T

)Q− W +

∑in

mψ−∑out

mψ− Ed = 0 (1)

The first term of Eq. (1) takes into account allheat transfer interactions of the system with itssurroundings through the boundary at temperature T .The second term is the exergy interaction by work.

The third and fourth terms are the exergy due to thefluid flow crossing the system boundaries. Finally, thefifth term measures the irreversibilities in the systemanalyzed.

The potential work or exergy of a fluid flowneglected the change in kinetic and potential energyis expressed as:

ψ = h− h0 − (T0)(s− s0) (2)

In Eq. (2) enthalpy and entropy are measured withrespect to a dead state at 101.3[kPa] and 298.15[K].The general exergetic efficiency is defined as:

ηII = 1−Exergy DestroyedExergy Supplied

(3)

The exergy destruction rate in each system componentis calculated using eqs. (4-8).

Compressor. The exergy balance applied to thecompressor, taking into account the exergy transferredto the surroundings by heat transfer, and according toFig. 2 is:

Ed,comp = Wcomp−

(1−

T0

Tw,comp

)Qcomp+mre f (ψ7−ψ1)

(4)where temperature Tw,comp is the boundarytemperature located at the wall of the compressionchamber of the compressor, which is defined asan average obtained through thermal images of thecompressor (see Fig. 3). The value is 350.65 [K] (77.5[ºC]).

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2

Fig. 3. Infrared thermal image of the test facility compressor.

23.0°C

101.4°C

40

60

80

100

Fig. 4. Infrared thermal image of the discharge line.

2

Fig. 3. Infrared thermal image of the test facility compressor.

23.0°C

101.4°C

40

60

80

100


Fig. 3. Infrared thermal image of the test facilitycompressor.


Discharge line. Considering that the boundariesof the discharge line are the walls of the pipe, andtherefore its temperature is the wall temperature, Tw,dl,the exergy balance for this component is defined as:

Ed,dl = mre f (ψ1 −ψ2)−(1−

T0

Tw,dl

)Qdl (5)

The discharge line is added into the exergy analysisin order to predict more accurately the total exergydestruction of the experimental test facility, taking intoaccount the heat loss by the discharge line and theoil separator. Fig. 4 presents a thermal image of thedischarge line and oil separator of the experimentalvapor compression; the wall temperature is obtainedfrom the discharge line model shown in Fig. 4, whichonly illustrates the average of wall temperature.

Condenser. Assuming negligible heat transferto the surroundings, the exergy destruction rate atcondenser is defined as:

Ed,cond = mre f (ψ2 −ψ3) + maec(ψaec −ψasc) (6)

Expansion valve. In this device, the heat transferto the surroundings was neglected because thedimensions of this component are relatively small.

Ed,ev = mre f (ψ4 −ψ5) (7)

Evaporator. Heat transfer is between the refrigerantand the water-propilenglycol brine stream since theevaporator is isolated from its surroundings. Theexergy destruction is expressed as:

Ed,evap = mre f (ψ5 −ψ6)− maee(ψb,in −ψb,out) (8)

The exergy change for brine water-propilenglycol

(assuming no pressure drop) is:

ψb,in −ψb,out = Cp,b

[(Taee −Tase)− (T0) ln

(Tase

Taee

)](9)

The overall exergy destruction for the vaporcompression system is defined as the individualcontribution of each system component:

Ed,total = Ed,comp+Ed,dl+Ed,cond+Ed,ev+Ed,evap (10)

Therefore, the second law efficiency for therefrigeration system is:

ηII,cycle = 1−Ed,total

Wcomp + maecψaec + maeeψaee(11)

Eqs. (1-11), for the exergetic analysis ofthe refrigeration system are incorporated to theexperimental validated model by using the softwareEES®. This model is based on mathematicalexpressions which come from fundamental physicsand empirical correlations established on the basis ofan experimental test. The validation of the modelwas performed using R134a for a wide range ofoperating conditions of the test bench. For moredetails and information on this model (Belman et al.,2010). Table 1 presents the range for each controllableparameter in the experimental plant. Also, thetable shows information about operating parameters:the evaporating and condensing temperatures, therefrigerant temperature at the compressor outlet,the compressor power and cooling capacity. Theoperational parameters depend on the controllableparameters.

In order to find controllable parameters thatachieve a maximum exergetic efficiency of the cycle,

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and according to the topological structure proposedin the physical model by Belman et al., (2010), itis possible to include an expression involving theexergetic efficiency of the cycle in correlation to thecontrollable parameters. Thus Eq. [12] represents thevariable which is going to be maximized, and it is alsoprogrammed in the EES. The method used to solve theoptimization is the Conjugate Directions method, inwhich the maximum number of times in equations aresolved, which may be specified, along with the relativetolerance. The basic notion behind this method isto use a one-dimensional series of searches to locatethe optimum which is a function, in this case, of theparameters: f ,Caec,Caee,Taec,Taee,S S , (Belegunduand Chandrupatla, 2011).

max(ηII,cycle) = g( f ,Caec,Caee,Taec,Taee,S S ) (12)

Eq. (12) assumes that the exergetic efficiency can beevaluated as a function of the controllable parameterspresented in table 1.

4 Results and discussionIn order to analyze the effect of controllableparameters on the exergy destruction in differentcomponent, five parameters are keep constantand one is varying within its operational range.Thermodynamics properties of all the streams of theprocess necessary for the calculation of the destroyed

exergy in the cycle, were obtained using the softwareEES. Fig. 5 shows the behavior of the exergydestruction rate when varying the compressor drivefrequency between 35 to 50 [Hz], this behavioris based on fixed controllable parameters. Thecompressor and the condenser are the two componentswith major exergy destruction rate followed by theexpansion valve and evaporator, respectively. Whenexamining in detail Fig. 5, the rate of exergydestruction at the compressor is 0-12% higher thanobtained at the condenser when varying the drivefrequency from 35 to 41 [Hz]. However, when thecompressor drive frequency is greater than 41 [Hz]the condenser exergy destruction rate becomes greaterthan the compressor by 0-13%. The decrease ofexergy destruction after 41 [Hz] is due to a smallerentropy change in the compressor process. Theexergy destruction at the expansion valve is about 0-8% higher than the evaporator. Similar tendenciesto those are reported by Aprea et al., (2003). Thecompressor exergy destruction rate has this behaviordue to mechanical and electrical losses because themotor and the transmission are connected to thecompressor, which defines the combined efficiency.Therefore, the exergy destruction in the compressoris caused by the refrigerant vapor that is warm at theinlet of the cylinder, the imperfection of the paddingbetween the piston and the cylinder, and the losses inthe suction and discharge valves.

Table 1. Practical parameter ranges in refrigeration plant.

Controllable parameters

Volumetric flow of water (condenser) [m3 h−1] 0.6-1.2Volumetric flow of water-propylene glycol (evaporator) [m3 h−1] 1.5-3.0Static super heating degree [K] 5-9Evaporator input temperature (brine) [K] 280.15-290.15Condenser input temperature (water) [K] 288.15-303.15Frequency [Hz] 35-50

Operating parameters

Evaporating temperature [K] 265-282Condensing temperature [K] 313-333Outlet compressor temperature [K] 330-370Compressor power [kW] 1.4-3Cooling capacity [kW] 5-9

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3

36 38 40 42 44 46 48 500.2

0.3

0.4

0.5

0.6

0.7

Frecuency [Hz]

Exe

rgy

dest

ruct

ion

[kW

]

Compressor CondenserCondenser Expansion valveExpansion valve EvaporadorEvaporador

Caec=1.2 [m3h-1]

Caee=3 [m3h-1]Taec=303.15 [K]

Taee=280.67 [K]SS=5 [K]

Fig. 5. Exergy destruction rate vs compressor drive frequency.

36 38 40 42 44 46 48 500.04

0.042

0.044

0.046

0.048

0.05

0.052

0.054

Frecuency [Hz]

Mas

s flo

w ra

te [

kg/s

]

Fig. 6. Mass flow rate varying the compressor drive frequency.

3

36 38 40 42 44 46 48 500.2

0.3

0.4

0.5

0.6

0.7

Frecuency [Hz]

Exe

rgy

dest

ruct

ion

[kW

]

Compressor CondenserCondenser Expansion valveExpansion valve EvaporadorEvaporador

Caec=1.2 [m3h-1]

Caee=3 [m3h-1]Taec=303.15 [K]

Taee=280.67 [K]SS=5 [K]

Fig. 5. Exergy destruction rate vs compressor drive frequency.

36 38 40 42 44 46 48 500.04

0.042

0.044

0.046

0.048

0.05

0.052

0.054

Frecuency [Hz]

Mas

s flo

w ra

te [

kg/s

]

Fig. 6. Mass flow rate varying the compressor drive frequency.

Fig. 5. Exergy destruction rate vs. compressor drivefrequency.

Fig. 6. Mass flow rate varying the compressor drivefrequency.

4

1.6 1.8 2 2.2 2.4 2.6 2.8 30.2

0.3

0.4

0.5

0.6

0.7

Evaporator volumetric flow [m3h-1]

Exe

rgy

dest

ruct

ion

[kW

]

Compressor CondenserCondenser Expansion valveExpansion valve EvaporatorEvaporator

Caec=1.2 [m3h-1]

f=50 [Hz]

Taec=303.15 [K]

Taee=280.67 [K]

SS=5 [K]

Fig. 7. Exergy destruction rate vs volumetric flow rate at the evaporator.

0.6 0.7 0.8 0.9 1 1.1 1.20.2

0.3

0.4

0.5

0.6

0.7

Condenser volumetric flow [m3h-1]

Exe

rgy

dest

ruct

ion

[kW

]


Caee=3 [m3h-1]

f=50 [Hz]

Taec=303.15 [K]Taee=280.67 [K]SS=5 [K]

Fig. 8. Exergy destruction rate vs volumetric flow rate at the condenser.

4

1.6 1.8 2 2.2 2.4 2.6 2.8 30.2

0.3

0.4

0.5

0.6

0.7

Evaporator volumetric flow [m3h-1]

Exe

rgy

dest

ruct

ion

[kW

]


Caec=1.2 [m3h-1]

f=50 [Hz]

Taec=303.15 [K]

Taee=280.67 [K]

SS=5 [K]

Fig. 7. Exergy destruction rate vs volumetric flow rate at the evaporator.

0.6 0.7 0.8 0.9 1 1.1 1.20.2

0.3

0.4

0.5

0.6

0.7

Condenser volumetric flow [m3h-1]

Exe

rgy

dest

ruct

ion

[kW

]


Caee=3 [m3h-1]

f=50 [Hz]

Taec=303.15 [K]Taee=280.67 [K]SS=5 [K]

Fig. 8. Exergy destruction rate vs volumetric flow rate at the condenser.

Fig. 7. Exergy destruction rate vs. volumetric flow rate atthe evaporator.

Fig. 8. Exergy destruction rate vs. volumetric flow rate atthe condenser.

Thus, the real power input to the compressordepends on the state of the transmission and electricalmotor driven by the compressor. So, a change infrequency, compression ratio and superheating degree,increase the exergy destruction rate. Fig. 6 shows theeffect of frequency on the refrigerant mass flow rate,obviously the refrigerant mass flow rate increases witha higher frequency. Note that the frequency is withinoperational limits of the compressor.

The exergy destruction rate is showed in Fig. 7when the brine volumetric flow varies between 1.5-3.0 [m3h−1]. It can be observed that the condenser

presents the highest exergy destruction rate followedby the compressor, the expansion valve, and theevaporator. At the condenser, the exergy destructionrate is 0.043 [kW] while the exergy destruction rateat the compressor, the expansion valve, and theevaporator are 0.029 [kW], 0.012 [kW] and 0.003[kW] respectively. This caused by the brine flowrate at evaporator. Increasing volumetric flow rate atthe evaporator mainly increase parameters such as therefrigerant mass flow rate as well as evaporating andcondensing pressures/temperatures. In this case, thelower increase observed at the evaporator (see Fig.

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7) occur because the streams are close to a minimalrelation of a temperature difference between therefrigerant and the brine streams, so, the volumetricflow rate has a limiting effect on exergy destructionrate.

Within the parameters that influence therefrigeration system, one of the most important isthe condensing agent. Depending on the volumetricflow rate and water temperature (secondary fluid),the global system results can have a better or worseperformance. Fig. 8 depicts the influence ofvolumetric flow of water on the exergy destruction ratein the system components. The increase in condensingagent (water) is reflected in a significant variationin both condensing and evaporating conditions, aswell as a decrease in vapor quality at the evaporatorinlet. This variation does not affect significantly therefrigerant mass flow rate. In the condenser, theexergy destruction rate diminishes about 0.082 [kW]due to the decrease in the condensing conditions,which are close to the reference state conditions.Furthermore, the condenser has a larger temperaturedifference between its streams that comes to contributeto diminish exergy destruction rate. In the compressor,the exergy destroyed practically remains constant,diminishes about 0.010 [kW] because the exergydifference between inlet and outlet is approximatelythe same for all range of conditions. The changein exergy destruction rate at the expansion valvedecreases about 0.087 [kW]. At the evaporator, theexergy destruction rate increases because a decrease inevaporating conditions occurs, which causes that thetemperature difference between refrigerant side andbrine side moves away from the minimal temperaturedifference, this variation is about 0.038 [kW]. So,the highest exergy destruction is at the condenser,and similar result is demonstrated by Aminyavariet al., (2014). With the performance shown in theabove figures, it can be concluded that the volumetricflow of the secondary fluids affect slightly the exergydestruction of the components except the condenser.

Fig. 9 presents exergy destruction rate whenthe static superheating degree, SS, controlled byexpansion valve varies between 5-9 [K]. This rangewas selected because superheating degree above 9[K] diminishes the volumetric efficiency and below 5[K] potentially affects the compressor by introducingliquid refrigerant. The variation of this parametertriggers the decrease in both the refrigerant massflow rate and evaporating conditions at the evaporator,which implies an increase in exergy destruction rateat the evaporator. A maximum change of exergydestruction rate at evaporator is about 0.049 [kW]. At

the rest of system components the exergy destructionrate diminishes due to the decrease in the refrigerantmass flow rate. The maximum exergy destructionrate is 0.054 [kW] at the condenser, 0.071 [kW] atthe compressor, and 0.023 [kW] at the expansionvalve. It is observed in the figure that the exergyvariations are minimal with a higher superheatingdegree operationally. A greater magnitude of thisparameter can be achieved by adjusting the valvespindle. However in this particular installation, agreater fluctuation in the mass flow measurement ofthe refrigerant is perceived, therefore an appropriatevalue for this is 9 [K].

Fig. 10 shows the trend of the exergydestruction rate as a function of propylene glycolbrine temperature at inlet of evaporator. Thisvariation mainly increases the refrigerant mass flowrate, evaporating and condensing conditions due toits dependency on the temperature of secondary inletfluid at evaporator which affects both evaporatorand condenser. Therefore, by increasing thesecondary inlet fluid temperature at the evaporatorthe exergy destruction rate at the condenser is of0.242 [kW], 0.146 [kW] at the compressor, 0.057[kW] at the expansion valve, and 0.158 [kW] atevaporator. Contrasting with the results obtained withthe variation of volumetric flow rate, the variation ofinlet temperature at evaporator increases drasticallythe temperature difference between refrigerant andsecondary fluid, not only at evaporator but also inthe condenser. In general, the temperature differencebetween the brine and refrigerant in the evaporatorincreases. The larger heat transfer temperaturedifference will lead to a larger exergy loss in theevaporator. Fig. 11 shows exergy destructionrate as a function of secondary fluid temperaturecondenser inlet. The increase of inlet temperatureof the secondary fluid impacts the condensing andevaporating pressures/temperatures. A decrease inexergy destruction rate for both condenser andevaporator is observed due to the narrow temperaturedifference between the refrigerant and secondaryfluid. The decrease in exergy destruction rate atthe evaporator and the condenser are 0.075 [kW]and 0.127 [kW], respectively. For compressor andexpansion valve the exergy destruction rate increasesdue to the increase in compression ratio. The increasein exergy destruction rate is 0.032 [kW] for thecompressor and 0.134 [kW] for the expansion valve.From the parameter variation, it can be seen thatthe condenser has the greatest exergy destruction ratefollowed by the compressor, the expansion valve andthe evaporator.

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5

5 6 7 8 90.2

0.3

0.4

0.5

0.6

0.7

Superheating degree [K]

Exe

rgy

dest

ruct

ion

[kW

]


f =50 [Hz]

Caec=1.2 [m3h-1]

Taee=280.67 [K]

Caee=3 [m3h-1]Taec=303.15 [K]

Fig. 9. Effect of superheating degree in the exergy destruction rate of refrigeration system components.

282 284 286 288 2900.2

0.3

0.4

0.5

0.6

0.7

Evaporator input temperature [K]

Exe

rgy

dest

ruct

ion

[kW

]


f =50 [Hz]Caec=1.2 [m3h-1]

SS=5 [K]

Caee=3 [m3h-1]Taec=303.15 [K]

Fig. 10. Exergy destruction rate vs propylene glycol brine inlet temperature at evaporator.

5

5 6 7 8 90.2

0.3

0.4

0.5

0.6

0.7

Superheating degree [K]

Exe

rgy

dest

ruct

ion

[kW

]


f =50 [Hz]

Caec=1.2 [m3h-1]

Taee=280.67 [K]

Caee=3 [m3h-1]Taec=303.15 [K]

Fig. 9. Effect of superheating degree in the exergy destruction rate of refrigeration system components.

282 284 286 288 2900.2

0.3

0.4

0.5

0.6

0.7

Evaporator input temperature [K]

Exe

rgy

dest

ruct

ion

[kW

]


f =50 [Hz]Caec=1.2 [m3h-1]

SS=5 [K]

Caee=3 [m3h-1]Taec=303.15 [K]

Fig. 10. Exergy destruction rate vs propylene glycol brine inlet temperature at evaporator.

Fig. 9. Effect of superheating degree in the exergydestruction rate of refrigeration system components.

Fig. 10. Exergy destruction rate vs propylene glycol brineinlet temperature at evaporator.

6

288 290 292 294 296 298 300 3020.2

0.3

0.4

0.5

0.6

0.7

Condenser input temperature [K]

Exe

rgy

dest

ruct

ion

[kW

]


f =50 [Hz]Caec=1.2 [m3h-1]

SS=5 [K]

Caee=3 [m3h-1]Taee=280.67 [K]

Fig. 11. Exergy destruction rate vs secondary fluid inlet temperature at condenser.

36 38 40 42 44 46 48 500.2

0.4

0.6

0.8

1

1.2

1.4

Frecuency [Hz]

Exe

rgy

dest

ruct

ion

[kW

]

Compressor, h=60%

CondenserCondenserExpansion valveExpansion valveEvaporadorEvaporador

Caec=1.2 [m3h-1]Caee=3 [m3h-1]Taec=303.15 [K]Taee=280.67 [K]SS=5 [K]

Compressor, h=50%Compressor, h=50%Compressor, h=40%Compressor, h=40%

Fig. 12. Comparison of the exergy destruction rate at the system when the combined efficiency varies.

6

288 290 292 294 296 298 300 3020.2

0.3

0.4

0.5

0.6

0.7

Condenser input temperature [K]

Exe

rgy

dest

ruct

ion

[kW

]


f =50 [Hz]Caec=1.2 [m3h-1]

SS=5 [K]

Caee=3 [m3h-1]Taee=280.67 [K]

Fig. 11. Exergy destruction rate vs secondary fluid inlet temperature at condenser.

36 38 40 42 44 46 48 500.2

0.4

0.6

0.8

1

1.2

1.4

Frecuency [Hz]

Exe

rgy

dest

ruct

ion

[kW

]

Compressor, h=60%

CondenserCondenserExpansion valveExpansion valveEvaporadorEvaporador

Caec=1.2 [m3h-1]Caee=3 [m3h-1]Taec=303.15 [K]Taee=280.67 [K]SS=5 [K]

Compressor, h=50%Compressor, h=50%Compressor, h=40%Compressor, h=40%

Fig. 12. Comparison of the exergy destruction rate at the system when the combined efficiency varies.

Fig. 11. Exergy destruction rate vs secondary fluid inlettemperature at condenser.

Fig. 12. Comparison of the exergy destruction rate at thesystem when the combined efficiency varies.

Based on the last performance (figs. 10 and 11), weconclude that the temperatures of the secondary fluidshave a higher impact on the exergy destruction of thevarious components, and thus, this represents controlparameters of great importance in the search for betterexergetic performance.

To go further about the effect of the compressoron the exergy destruction in the system, it isnecessary to involve its combined efficiency. Thecombined efficiency includes the electromechanicaland transmission inefficiencies as well as theinefficiencies that occur inside the compressor as a

result of friction. So, when the combined efficiencydecreases, the irreversibility at compressor increasesas it is shown in Fig. 12. So, the highestexergy destruction rate is located at the compressorwhen combined efficiency decreases from 60% to40%. Therefore, the exergy destruction rate at thecompressor depends on other parameters such as thetransmission system and the heating in the compressor.For instance, the increase in exergy destruction rateat the evaporator increases more than 90% when thecombined efficiency decreases to 40%.

Finally, Fig. 13 shows the exergetic efficiency

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versus the compressor drive frequency in orderto determine the influence of varying controllableparameters. The changes in secondary volumetric flowrates do not have a significant influence in exergeticefficiency of the cycle. When the static superheatingdegree increases, the exergetic efficiency decreasesabout 10% with high compressor drive frequency.When increasing the inlet temperature at evaporatorto 290.15 [K], the exergetic efficiency decreases about40% compared with the minimum evaporator inputtemperature 280.15 [K]. The change in evaporatorinput temperature is the most represented variation inthe exergetic efficiency of vapor compression system.The increase in inlet temperature of condensing agentproved a slight rise in exergetic efficiency, because ata high inlet temperature of secondary flow rate the

exergy difference at the condenser diminishes, and theexergetic efficiency increases.

When intending to propose new controllableparameters the major objective is the reduction of theexergy destruction. Table 2 shows the controllableparameters which an achieved higher efficiency. Theoptimum values shown in the table were obtainedusing the Eq. [12]. These parameters are onlyindicative of operating conditions in which therefrigeration system runs with the best exergeticefficiency, but as it is known, it is always necessary tosatisfy a certain thermal load (cooling capacity), alsothe condenser inlet temperature depends largely onprevailing environmental conditions. Therefore thesevalues represent only a reference state.

Table 2. Optimum controllable parameters for the experimental refrigerationplant.

Volumetric flow of water (condenser) [m3 h−1] 0.9071Volumetric flow of water-propylene glycol (evaporator) [m3 h−1] 1.5Static superheating degree [K] 9Evaporator input temperature (brine) [K] 280.15Condenser input temperature (water) [K] 303.15Frequency [Hz] 35

7

36 38 40 42 44 46 48 500.3

0.4

0.5

0.6

0.7

Frecuency [Hz]

Exe

rget

ic e

ffici

ency

Taee =280.15 [K]Taee =290.15 [K]Taee =290.15 [K]

Taec =288.15 [K]Taec =288.15 [K]Taec =303.15 [K]Taec =303.15 [K]

SS=9 [K]SS=9 [K]

Caee =1.5 [m3h-1]Caee =1.5 [m3h-1]Caec =0.6 [m3h-1]Caec =0.6 [m3h-1]

Fig. 13. Exergetic efficiency of refrigeration system varying the controllable parameters. Fig. 13. Exergetic efficiency of refrigeration system varying the controllable parameters.

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Conclusions

In this paper an exergetic analysis of an experimentalrefrigeration system using the refrigerant R134a wasperformed to identify and quantify the exergeticlosses. This analysis shows the behavior of exergydestruction rate under the influence of controllableparameters that are easily accessible in such facilities:compressor drive frequency, volumetric flow rate andthe temperature of the secondary fluids (water andbrine), and the static superheating degree. Also,the analysis includes the influence of the combinedefficiency of the compressor on the global system.

Through the exergetic analysis it was observedthat the major exergy destruction rate is located atcondenser followed by the compressor, the expansionvalve, and the evaporator. The temperature of thesecondary fluids, and to a lesser extent, the volumetricflow rate are the parameters which most significantlyinfluence the exergy destruction. The contribution ofthe compressor to the overall irreversibility is the mostrelevant, its frequency driven and combined efficiencywere the parameters considered in this analysis.The variation in combined efficiency depends onconditions of the transmission system, the heat transferrate in the compressor, among others. By applyingthe simple Conjugate Directions method, the optimumcontrollable parameters that represent the maximumexergetic efficiency of the cycle were found. It isrelevant to say that changes of controllable parametersrequire also a specific study such as the use of anoptimization method (for instance, thermoeconomicmethodology). Finally, it is concluded that the exergyanalysis is essential for the refrigeration system.

NomenclatureC volumetric flow rate [m3h−1]Cp specific heat [kJkg−1K−1]f frequency [Hz]h specific enthalpy [kJkg−1]m mass flow rate [kgs−1]Q heat transfer rate [kW]s specific entropy [kJkg−1K−1]S S superheating degree [K]T temperature [K]T0 dead state temperature [K]W power [kW]ηII exergetic efficiencyEd exergy destruction rate [kW]ψ specific flow exergy [kJkg−1]

Subscriptsaec inlet secondary fluid (condenser)asc outlet secondary fluid (condenser)aee inlet secondary fluid (evaporator)ase outlet secondary fluid (evaporator)b brinecomp compressorcond condenserdl discharge lineevap evaporatorev expansion valvein inletout outletre f refrigerant1,2,3, . . . thermodynamic state

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Revista Mexicana de ngeniería uímica - SciELOflowing along the shell and water flowing inside the tubes (as secondary fluid). In contrast, in the shell and tube evaporator the