Influence of two internal irreversibilities on the new thermo-ecological criterion for three-heat-source refrigerators

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Influence of two internal irreversibilities on the new thermo-ecological criterion for three-heatsource refrigerators Brigitte Astrid Medjo Nouadje a,b,c,*, Paiguy Armand Ngouateu Wouagfack b,c, Re´ne´ Tchinda b,c a

LATEE, Department of Physics, University of Yaounde I, PO Box 812, Yaounde, Cameroon L2MSP, Department of Physics, University of Dschang, PO Box 67, Dschang, Cameroon c LISIE, University Institute of Technology Fotso Victor, University of Dschang, PO Box 134, Bandjoun, Cameroon b

article info

abstract

Article history:

Irreversibility is a phenomenon that affects much the performance of absorption refrig-

Received 14 May 2013

eration systems. Internal irreversibility is produced by the dissipation of the working fluid.

Received in revised form

This paper studies and analyzes the effect of two internal irreversibilities parameters (the

30 August 2013

internal irreversibility parameter for generatoreabsorber assembly and the internal irre-

Accepted 21 September 2013

versibility parameter for condensereevaporator assembly) on the optimal ecological per-

Available online 2 October 2013

formances of an irreversible three-heat-source absorption refrigerator based on the ECOP criterion. The results obtained show that the internal irreversibility parameter for

Keywords:

condensereevaporator assembly affects more the ecological performance of the system

Absorption refrigeration system

than the internal irreversibility parameter for generatoreabsorber assembly. This is of

Internal irreversibility

importance to the optimal design and performance improvement of absorption refrigera-

Optimization

tion cycles.

Ecological coefficient of

ª 2013 Elsevier Ltd and IIR. All rights reserved.

performance

Influence de deux irre´versibilite´s internes sur les nouveaux crite`res thermo-e´cologiques des re´frige´rateurs a` triple source de chaleur Mots cle´s : System syste`me frigorifique a` absorption ; Irre´versibilite´ interne ; Optimisation ; Coefficient de performance e´cologique

* Corresponding author. LATEE, Department of Physics, University of Yaounde I, PO Box 812, Yaounde, Cameroon. Tel.: þ237 98 04 86 90. E-mail address: [email protected] (B.A. Medjo Nouadje). 0140-7007/$ e see front matter ª 2013 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2013.09.040

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Nomenclature

K  Q R S T U

total heat-transfer area (m2) coefficient of performance ecological coefficient of performance internal irreversibility parameter internal irreversibility parameter for generatoreabsorber assembly internal irreversibility parameter for evaporatorecondenser assembly thermal conductance (kW K1) rate of heat transfer (kW) specific cooling load (kW m2) specific entropy generation rate (kW K1 m2) temperature (K) overall heat-transfer coefficient (kW K1 m2)

Symbol  s

entropy generation rate (kW K1)

A COP ECOP I I1 I2

1.

Introduction

Real absorption refrigeration machines suffer from irreversibility problems during their process since the rate of heat exchange between the system and the environment is not infinitesimally large (Qin et al., 2013). Irreversibilities are caused by finite-rate heat transfers, heat leakages between the system and external reservoirs and internal dissipations of the working substance (Chen, 1999; Qin et al., 2013; Yan and Lin, 2002). They are classified into two main types: internal irreversibilities and external irreversibilities (Sallah ElDin, 1999; Wijeysundera, 1997). The internal irreversibility occurs within the boundaries of the system during the process (Sallah El-Din, 1999) while the external irreversibility occurs outside the system boundaries during the process (Kan et al., 2010; Sallah El-Din, 1999). The former has more impact on the performance of the system than the latter (Bhardwaj et al., 2005). The effects of the internal and external irreversibilities on the performance of the heat engines and absorption refrigeration systems have been studied respectively by Ust et al. (2005a,b; 2006a,b,c) and Yan and Lin (2002), Chen L. et al. (1999, 2002), Qin et al. (2010), Zheng et al. (2003a), Kodal et al. (2003), Bautista and Mendez (2005), Tao et al. (2009), Ust (2010) and Ngouateu Wouagfack and Tchinda (2011a) based on the coefficient of performance, the cooling load, the thermo-economic criterion, the thermoecological criterion and the ecological coefficient of performance. The above referenced works do not distinguish the internal irreversibility for evaporatorecondenser assembly from the internal irreversibility for generatoreabsorber assembly. Bhardwaj et al. (2003, 2005), Chen J. et al. (2002) and Sahin et al. (2001) have analyzed the performance of absorption refrigeration systems considering these two internal irreversibilities parameters. Bhardwaj et al. (2005) have established that the internal irreversibility for evaporatorecondenser assembly has much effect than the internal irreversibility for generatoreabsorber assembly on maximum

x εr

119

heat leakage coefficient (kW K1 m2) coefficient of performance for reversible three heat-source refrigerator

Subscripts 1 working fluid in generator 2 working fluid in evaporator 3 working fluid in absorber and condenser A absorber C condenser E evaporator env environment conditions G generator L heat leakage max maximum O absorber and condenser m at maximum ECOP

coefficient of performance. The same result has been obtained in the case of heat pump by Xiling et al. (2011). These performance works are based on the first law of thermodynamic and therefore they do not take into account the environment aspect. The thermo-ecological criterion and the ecological coefficient of performance are the performance criterions which take into account environmental aspect. Recently, Ust et al. (2005b) and Ngouateu Wouagfack and Tchinda (2011b) compared these two ecological criterions and established that a system working at the maximum ECOP function produces less entropy generation rate and more coefficient of performance for refrigerators or efficiency for heat engines than it produces when working at the maximum ecological function (E). The present paper aims to study and discuss the effect of internal irreversibility for

Fig. 1 e Schematic diagram of an absorption refrigerator (Ngouateu Wouagfack and Tchinda, 2011a).

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2. Thermodynamics analysis of an irreversible three-heat-source refrigerator system

Fig. 2 e Irreversible cycle model of an absorption refrigerator (Ngouateu Wouagfack and Tchinda, 2011a).

generatoreabsorber assembly and the internal irreversibility for evaporatorecondenser assembly on the performance of irreversible three-heat-source absorption refrigeration working at the maximum ECOP function.

It is well known that an absorption refrigeration system has four main components: a generator, an absorber, a condenser and an evaporator (Bhardwaj et al., 2003, 2005; Chen et al., 2004, 2006; Chen and Schouten, 1998; Qin et al., 2013; Zheng et al., 2004; Ngouateu Wouagfack and Tchinda, 2011a, 2011b, 2013). The diagram of an absorption refrigeration system is represented in Fig. 1. In this model Q_ G is the rate of heat absorbed from the heat source at temperature TG to generator, Q_ C is the heat rejection rate from the condenser to the heat sink at temperature TC, Q_ A is the heat rejection rate from the absorber to the heat sink at temperature TA and Q_ E is the heat input rate from the cooling space at temperature TE to the evaporator. The work input required by the solution pump is negligible compared to the energy input to the generator and therefore, is often neglected in the analysis (Chen J. et al., 2002; Chen et al., 2004, 2006; Chen and Schouten, 1998; Ngouateu

Fig. 3 e Variations of ECOP objective function with respect: a) to temperature (T1) of the working fluid in generator, b) to temperature (T2) of the working fluid in evaporator and c) to temperature (T3) of the working fluid in absorber and condenser for I2 [ 1 and various I1.

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Wouagfack and Tchinda, 2011a). According to first law of thermodynamics, we have: Q_ G þ Q_ E  Q_ C  Q_ A ¼ 0

(1)

When the absorber temperature is equal to the condenser temperature, absorption refrigeration systems operate between three temperature levels. The performance of an absorption refrigeration system is closely dependent on the irreversible factors (Chen, 1999). Then, when analyzing the performance of this system, many considerations should be made (Chen, 1997, 1999; Chen J. et al., 2002; Ngouateu Wouagfack and Tchinda, 2011a): the cycle of the working fluid consists of three irreversible isothermal processes and three irreversible adiabatic processes. The temperatures of the working fluid in the three isothermal processes are different from those of the external heat reservoirs such that the heat is transferred under a finite temperature difference, as shown in Fig. 2. In this figure, Q_ O ¼ Q_ C þ Q_ A , T1 and T2 are respectively the temperatures of the working fluid in the generator and evaporator. T3 is the temperature of the working fluid in the condenser and absorber assuming that the working fluid temperature is the same in these two components (Chen J. et al., 2002; Ngouateu Wouagfack and Tchinda, 2011a, 2013). Q_ L is the heat leakage from the heat sink to the cooled space. The heat exchanges between the working fluid and heat reservoirs obey a linear heat transfer law, such that the equation of heat transfer can be written as (Chen et al., 2005; Chen J. et al., 2002; Chen and Schouten, 1998; Ngouateu Wouagfack and Tchinda, 2011a, 2013; Wu et al., 1997): Q_ G ¼ UG AG ðTG  T1 Þ

(2)

The absorption refrigeration system does not exchange heat with the other external reservoirs except for the three heat reservoirs at temperature TG, TE and TO, so the total area of heat transfer between the cycle system and the external heat reservoirs is given by the relationships (Ngouateu Wouagfack and Tchinda, 2011a): A ¼ AG þ AE þ AO

Q_ L ¼ KL ðTO  TE Þ

(3)

(4)

with AO ¼ AA þ AC. In Equations (2)e(4), AG, AE, AA and AC are the heattransfer areas of the generator, evaporator, absorber and condenser respectively, while UG and UE are the overall

COP ¼

(6)

where KL is the heat leakage coefficient. An absorption refrigeration system can be treated as a combined cycle of a heat engine for generatoreabsorber assembly and a refrigerator for evaporatorecondenser assembly (Bhardwaj et al., 2003, 2005). Thus, two internal irreversibilities parameters can be introduced to study the effect of internal dissipations of working fluid on the system: the internal irreversibility for generatoreabsorber assembly and the internal irreversibility for evaporatorecondenser assembly as given by Bhardwaj et al. (2003, 2005). According to the second law of thermodynamics, two irreversibilities factors could be introduced, I1 for generatoreabsorber assembly and I2 for evaporatorecondenser assembly: I1 ¼

Q_ A T3 Q_ G

ðI1  1Þ

(7)

ðI2  1Þ

(8)

T1 Q_ C T

I2 ¼ Q_ 3 T2

and Q_ O ¼ UO AO ðT3  TO Þ

(5)

The rate of heat leakage Q_ L from the heat sink at temperature To to the cold reservoir at temperature TE is given as (Ngouateu Wouagfack and Tchinda, 2011a):

E

Q_ E ¼ UE AE ðTE  T2 Þ

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When the cycle of the working fluid in the generatoreabsorber assembly and in the evaporatorecondenser assembly is reversible, I1 ¼ I2 ¼ 1. When the cycle of the working fluid in the generatoreabsorber assembly and in the evaporatorecondenser assembly is irreversible, I1 > 1 and I2 > 1. Using Equations (1), (2) and (8), we obtain the coefficient of performance, the specific cooling load and the specific entropy generation rate of a three-heat-source absorption refrigerator as given by Equations (9), (10) and (12), respectively:


  Q_ E  Q_ L T2 ðT1  I1 T3 Þ 1 I2 T3 T1 ðI2 T3  T2 Þ I1 T3 ðI2 T3  T2 Þ 1  xðTO  TE Þ þ þ þ ¼ T1 ðI2 T3  T2 Þ UE ðTE  T2 Þ UO T2 ðT3  TO Þ UG ðTG  T1 ÞT2 ðT1  I1 T3 Þ UO ðT3  TO ÞT2 ðT1  I1 T3 Þ Q_ G (9)

R¼

1  1 I2 T3 T1 ðI2 T3  T2 Þ I1 T3 ðI2 T3  T2 Þ Q_ E  Q_ L þ þ þ ¼  xðTO  TE Þ UE ðTE  T2 Þ UO T2 ðT3  TO Þ UG ðTG  T1 ÞT2 ðT1  I1 T3 Þ UO ðT3  TO ÞT2 ðT1  I1 T3 Þ A

heat-transfer coefficients of the generator and evaporator respectively, and it is assumed that the condenser and absorber have the same overall heat transfer coefficient UO (Chen and Schouten, 1998; Ngouateu Wouagfack and Tchinda, 2011a).

S¼

s_ ¼ A

Q_ O Q_ L TO

_

_

_

 QTGG  Q ETEQ L A

(10)

(11)

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 S¼

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1 1  TE TO

 1    T1 ðI2 T3  T2 Þ 1 I2 T3 T1 ðI2 T3  T2 Þ I1 T3 ðI2 T3  T2 Þ 1 þ þ þ xðTO  TE Þ þ εr T2 ðT1  I1 T3 Þ UE ðTE  T2 Þ UO T2 ðT3  TO Þ UG ðTG  T1 ÞT2 ðT1  I1 T3 Þ UO ðT3  TO ÞT2 ðT1  I1 T3 Þ (12)

where x ¼ KL/A is the heat leakage coefficient and εr ¼ (TG  TO/TG)(TE/TO  TE) is the coefficient of performance for a reversible three-heat-source refrigerator. According to the definition of the general thermo-ecological criterion function (Ust, 2009; Ust and Sahin, 2007; Ngouateu Wouagfack and Tchinda, 2011a), the new thermo-ecological objective function called ecological coefficient of performance (ECOP) of a three-heat-source absorption refrigerator system with two internal irreversibility parameters is written as: ECOP ¼

ECOP ¼

Q_ E  Q_ L Tenv s_

Tenv



1

1 TE

 T1O

(13)



1

where Tenv is the temperature in the environment conditions. When I1 ¼ I2 ¼ I, we obtain the results of Ngouateu Wouagfack and Tchinda (2011a).

3. Coefficient of performance, specific cooling rate and specific entropy generation rate at maximum new thermo-ecological The Equation (14) can be maximized (or optimized) with respect to T1, T2 and T3. The optimization is carried out analytically.

1 n io1 h T3 ðI2 T3 T2 Þ I2 T3 1 1 ðI2 T3 T2 Þ 1  xðTO  TE Þ UE ðTE T2 Þ þ UO T2 ðT3 TO Þ þ UG ðTGTT þ UO ðTI31T 1 ÞT2 ðT1 I1 T3 Þ O ÞT2 ðT1 I1 T3 Þ

2Þ εr TT12 ðIðT21TI3 T 1 T3 Þ

(14)

Fig. 4 e Variations of ECOP objective function with respect: a) to temperature (T1) of the working fluid in generator, b) to temperature (T2) of the working fluid in evaporator and c) to temperature (T3) of the working fluid in absorber and condenser for I1 [ 1 and various I2.

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Fig. 5 e Variations of ECOP objective function with respect to the specific cooling load: (a) for I2 [ 1 and various I1 values, and (b) for I1 [ 1 and different values of I2.

Fig. 6 e Variation of ECOP objective function with respect to the specific generation rate: (a) for I2 [ 1 and various I1 values, and (b) for I1 [ 1 and different values of I2.

vECOP ¼0 vT3 Then, starting from Equation (14) and applying the following extremal conditions: vECOP ¼0 vT1

(15)

vECOP ¼0 vT2

T1m ¼

(16)

0

I1 TG



B b1 @1  n UE xD1 þU2E xD2

2TO





UO xþUE xD5 UO UE

TO TE TE

h



þ U2E x D3 þD4

TO TE TE



1

1

1

C i1=2 oA þ I1

TO TE TE

4UE xD4

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(17)

we obtain the following optimal relation: qffiffiffiffiffiffiffiffiffiffiffiffiffiffi  qffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi I2 I21 UG TG T1 I1 I22 UE TE T1 I1 I2 UO 1  TO T1 1 1 ¼ 2 1 ¼ 3 (18) Combining Equations (18) and (17) yields the optimal temperature of the working fluid in the generator (T1m), evaporator (T2m) and condenser and absorber (T3m) at the maximum ECOP: where

(19)

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T2m ¼

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0 B b2 @1  n UE xD1 þU2E xD2

T3m

I2 TE

 2TO





UO xþUE xD5 UO UE

TO TE TE

h



þ U2E x D3 þD4

TO TE TE



1

1

TO TE TE

1

(20)

C i1=2 oA þ I2

4UE xD4

n  h  1 i1=2 o  E E UE xD1 þ U2E xD2 TOTT þ U2E x D3 þ D4 TOTT  4UE xD4 E E ¼  1  E 2 UO x þ UE xD5  UO UE TOTT E

D1 ¼ b1 TE b1 b2 TO 2b1 I2 TO 1; D2 ¼ 12b1 TE þ2b1 b2 TO þ4b1 I2 TO  D3 ¼ b21 T2E þ2b21 b2 TO TE þb21 b22 T2O ; D4 ¼ 4UO b1 TO TE I2 T2O qffiffiffiffiffiffiffi qffiffiffiffiffiffiffi D5 ¼ b2 þb1 b2 þb1 I2 ; b1 ¼ I1UUGO ; b2 ¼ I2UUEO (22)

Fig. 7 e Variation of ECOP objective function with respect to the coefficient of performance: (a) for I2 [ 1 and various I1 values, and (b) for I1 [ 1and different values of I2.

(21)

Substituting Equations 19e21 into Equations (9), (10), (12) and (14) gives the maximum ecological coefficient of performance (ECOPmax), the corresponding coefficient of performance (COP), specific cooling load (Rm) and specific entropy generation rate (Sm).

Fig. 8 e Variation of the optimal ecological coefficient of performance with respect to: (a) the internal irreversibility of generatoreabsorber assembly for various I2 values and (b) the internal irreversibility of evaporatorecondenser assembly for various I1 values.

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Fig. 9 e Variation of the optimal coefficient of performance with respect to: (a) the internal irreversibility of generatoreabsorber assembly for various I2 values and (b) the internal irreversibility of evaporatorecondenser assembly for various I1 values.

4.

Results and discussion

Numerical calculations are carried out by employing the relevant values TG ¼ 403 K, TO ¼ 303 K, Tenv ¼ 290 K, TE ¼ 273 K, UG ¼ 1163 W m2 K1, UE ¼ 2326 W m2 K1, UO ¼ 4650 W m2 K1 taken from Ngouateu Wouagfack and Tchinda (2011a) and Zheng et al. (2003b). MATLAB software is used for numerical calculations and to plot the curves. The variations of the ecological coefficient of performance function for the three-heat-source absorption with respect to the working fluid temperatures, specific cooling load and specific entropy generation rate for various internal irreversibility parameters values (I1 and I2) are shown in Figs. 3e6. From these figures, one can observe that as the internal irreversibility parameters increase, the maximum ECOP objective function which is reached for a relatively low value of the specific entropy generation rate decreases. This decrease is more accentuated with the internal irreversibility parameter

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Fig. 10 e Variation of the optimal specific cooling load with respect to: (a) the internal irreversibility of evaporatorecondenser assembly for various I2 values and (b) the internal irreversibility of generatoreabsorber assembly for various I1 values.

for evaporatorecondenser assembly (I2) out of the endoreversible state. Fig. 5 reveals the optimal operating region of an irreversible absorption refrigeration system (Ngouateu Wouagfack and Tchinda, 2011a). At the same values, the internal irreversibility for the evaporatoregenerator assembly has more effect on the optimal region than the internal irreversibility for the generatoreabsorber assembly. The variation of ECOP objective function with respect to the coefficient of performance for various values of I1 and I2 are represented in Fig. 7a and b. From these figures, it can be seen that when I1 or I2 increase the ECOP and COP value decrease. This decreasing is more pronounced with I2. Fig. 8a and b show the effects of I1 and I2 on the ECOPmax respectively. It can be observed that ECOPmax decreases with the increasing of I1 and I2. This decreasing is significant with I2. In Fig. 9a and b are respectively presented the effects of I1 on the optimal coefficient of performance (COPm) for different values of I2, and the effects of I2 on the optimal coefficient of performance (COPm) for different values of I1. We can observe that when both internal irreversibility parameters increase

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respectively. As expected, it can be seen that the specific entropy production rate increases when both of the internal irreversibility parameters increase.

5.

Conclusion

The ecological performance optimization for a three-heatsource irreversible absorption refrigeration system with the losses of heat-resistance, heat leakage, internal irreversibility for generatoreabsorber assembly and the internal irreversibility for condensereevaporator assembly by considering the ecological coefficient of performance (ECOP) as objective function has been investigated in this paper. The maximum ecological coefficient of performance and the corresponding coefficient of performance, cooling load and entropy production rate has been determined. The effects of internal irreversibility parameter for generatoreabsorber assembly and the internal irreversibility parameter for condensereevaporator assembly on the general and optimal ECOP have been investigated and discussed. The results show that internal irreversibility of condensereevaporator assembly has much impact on the system than the internal irreversibility for generatoreabsorber assembly. Considering these results, this study gives a contribution to the ecological design of absorption refrigeration systems by paying more attention to condensereevaporator assembly.

Acknowledgments The present research work was carried out in LISIE and LATEE. All the senior researchers of these laboratories are gratefully acknowledged for their helpful comments. We also thank the administrators of these laboratories for the opportunity.

references

Fig. 11 e Variation of the optimal specific entropy generation rate with respect to: (a) the internal irreversibility of evaporatorecondenser assembly for various I2 values and (b) the internal irreversibility of generatoreabsorber assembly for various I1 values.

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