optimization of a solar driven adsorption refrigeration system.pdf

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Optimization of a solar driven adsorption refrigeration system

K.C.A. Alam *, B.B. Saha, A. Akisawa, T. Kashiwagi

Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho,

Koganei-shi, Tokyo 184 8588, Japan

Received 15 December 1999; accepted 29 August 2000

Abstract

This paper deals with the thermodynamic optimization of a solar driven adsorption refrigeration system.

An externally irreversible but internally endoreversible model has been employed to analyse the optimum

conditions for which the maximum refrigeration eect can be achieved. It is seen that a chiller attains its

highest capacity if the thermal conductances of the heat exchangers are distributed properly. It is also seen

that half of the total thermal conductances are allocated between the condenser and adsorber heat ex-

changers that release heat to the external ambient. The coecient of performance (COP) for the optimum

conditions is also presented. It is observed that the COP opt increases in parallel with the dimensionless

collector stagnation temperature, sst, as well as with the increase of the required refrigeration space tem-perature, sL, while the COPopt decreases as the ratio of collector size to the cumulative size of all four heat

exchangers, B, increases. 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction

From the early age of power generation, scientists and engineers have been concerned over the

design of a power plant. An optimal design of a plant can reduce the overall cost and can provideits best performance. Therefore, various methodologies have been developed for the purpose of

developing the plant design ever since the steam engine was invented. The thermodynamic op-timization technique is one of the most widely used methodologies. This method is known asentropy generation minimization in engineering thermodynamics. A brief discussion of its de-velopment is presented by Bejan [1].

During the last two decades, many optimization studies for heat engines based on endore-versible and irreversible models have been performed by considering nite time and nite size

Energy Conversion and Management 42 (2001) 741753

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* Corresponding author. Tel./fax: +81-42-388-7076.

E-mail address: [email protected] (K.C.A. Alam).

0196-8904/01/$ - see front matter

2000 Elsevier Science Ltd. All rights reserved.P I I : S0196- 8904( 00) 00100- X


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constraints. External irreversibilities due to heat resistance between the heat reservoirs and aninternally reversible heat engine have been discussed by Curzon and Ahlborn [2], in which two

heat sources, namely hot end and cold end heat exchangers, have been taken into account. Bejan[3] investigated the optimal condition for a heat transfer irreversible (internally endoreversible)

power plant considering three heat sources: the hot end, the cold end and the heat leaking sides.He showed that the eciency of a power plant could be maximized if the total investment is

divided optimally between the external thermal conductance and internal thermal resistance.Later, Bejan [4] proved that the power output of a power plant could be maximized by properlybalancing the size of the heat transfer equipment.

In the eld of refrigeration, Bejan [5] and Bejan et al. [6] applied the optimization technique andmodelled the refrigeration load based on the power input and heat rejection to the ambient. In

Nomenclature

a constant in Eq. (7)b constant in Eq. (7)A heat transfer areaAc collector areaB dimensionless collector size parameter, Eq. (20)COPopt coecient of performance for optimum conditionGT irradiance on collector surfaceI irreversibility factor, Eq. (11)QA adsorber heat transferQCON condenser heat transferQEVA evaporator heat transfer

QH heat inputR residual vectorTA temperature of heat transfer uid in adsorberTCON temperature of heat transfer uid in condenserTH temperature of collectorTHC temperature of heat transfer uid in desorberTL temperature of cold spaceTLC temperature of heat transfer uid in evaporatorTst collector stagnation temperatureT0 ambient temperature

U overall heat transfer coecient based on Av conductance ratio for condenserx conductance ratio for evaporator

y conductance ratio for collectorz conductance ratio for adsorbergC collector eciencys dimensionless temperature

742 K.C.A. Alam et al. / Energy Conversion and Management 42 (2001) 741753


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these studies, the authors demonstrated that the maximum refrigeration eect could be accom-

plished by allocating the heat exchange equipment optimally. Sun et al. [7] and Ni et al. [8] in-vestigated the optimal performance of an endoreversible heat pump to analyse a reasonable

heating load and coecient of performance (COP) bound for designing a real heat pump. Re-cently, El-Din [9] employed the idea of optimization for a totally irreversible refrigeration systemby considering only two external heat transfer irreversibilities.

In recent years, heat driven refrigeration systems have drawn considerable attention due to

their lower environmental impact and large energy saving potential. Another interesting feature ofthis system is that the chiller/heat pump can be operated by thermal heat, such as waste heat fromindustries or by solar heat. From this context, Sokolov and Hersagal [10] optimized the system

performance of a solar driven, year-round ejector refrigeration system. Vargas et al. [11] inves-tigated the optimal condition for a refrigerator driven by a solar collector considering the three

heat transfer irreversibilites. Later, Chen and Schouten [12] discussed the optimum performanceof an irreversible absorption refrigeration cycle in which three external heat transfer irreversi-

bilities have been considered. Recently, Chen [13] extended the idea of Chen and Schouten [12] fora two stage irreversible absorption refrigeration cycle.

In any adsorption refrigeration system, there are four heat transfer reservoirs, namely the

desorber, adsorber, condenser and evaporator. All of those components operate at dierenttemperature levels, although the condenser and adsorber release heat to the environment. Becauseof the dierent operating temperatures, at least four external heat transfer irreversibilities are

present in an adsorption refrigeration system, but all the authors considered only up to three heattransfer irreversibilities to optimize the refrigeration/heat pump system. In the present paper, thefour irrversibilities due to the heat transfer resistances have been taken into account. The main

objective of this study is to nd the optimum distribution among the heat exchanger surfaces of a

solar driven adsorption chiller for which the system attains its maximum capacity and to deter-mine the COP for the optimal conditions.

2. Theoretical model

The main components of a solar driven adsorption refrigeration system are a solar collector, a

desorber, an adsorber, a condenser and an evaporator, as shown in Fig. 1. In an adsorption cycle,the working uid is operated in a cycle and exchanges heat with the four heat exchangers, namely

the desorber, adsorber, condenser and evaporator. During the cycle, the desorber receives the heat

load, QH, from the heat source (solar collector) at temperature, TH, while the evaporator seizes theheat load, QEVA, from the refrigeration space at temperature, TL. The condenser and adsorberrelease heat transfers, QCON and QA, respectively, to the external ambient at temperature, T0. In

this analysis, it is assumed that there is no heat loss between the solar collector and the desorberand no work exchange occurs between the refrigerator and its environment. According to the rstlaw of thermodynamics,

QH QEVA QCON QA 1

In this present investigation, it is also assumed that there is an external heat transfer irre-versibility at each heat exchanger caused by the nite heat conductance between the working uid

K.C.A. Alam et al. / Energy Conversion and Management 42 (2001) 741753 743


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and the four heat exchangers as shown in Fig. 2. It is always considered that the heat transfers of

an irreversible cycle are aected by thermal resistances which follow the linear law. Therefore,heat transfer equations for the four heat exchangers can be written as,

QH UA H TH THC 2

QA UA A TA T0 3

QCON UA CON TCON T0 4

QEVA UA EVA TL TLC 5

The heat input QH can also be estimated by the following expression

QH ACGTgC 6

where AC represents the collector area, GT is the irradiance at the collector surface and gC stands

for the collector eciency. The eciency of a collector can be calculated as [9],

gC a b TH T0 7

where a and b are two constants that can be calculated, as discussed by Sokolov and Hershagal[10]. Eq. (7) can be rewritten by introducing the collector stagnation temperature Tst as follows:

gC bTst TH 8

where TstTst TH, for which gC 0 is given by,

Tst T0 aab 9

The equation for heat input QH can be rewritten by combining Eqs. (6) and (8) as follows:

QH ACGTbTst TH 10

Fig. 1. Schematic of a solar driven adsorption refrigeration system.



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A series of irreversibilities, for example heat transfer, throttling, mixing and internal dissipationof the working uid, which are responsible for entropy generation are always present in a real heat

driven refrigerator [12]. According to the second law of thermodynamics, one may write,

QCONaTCON QAaTAQHaTHC QEVAaTLC

IP 1 11

where I is an irreversibility factor. When I b 1, the refrigerator operates totally irreversibly, whenI 1, the refrigerator is known as internally endoreversible. In this analysis, it is assumed that therefrigerator is externally irreversible, but internally endoreversible, i.e. I 1. The proportionalityfactors UA in Eqs. (2)(5) are known as the thermal conductances for the respective heat ex-changers, which are dened as the product of the overall heat transfer coecient U and the heattransfer area A of the respective heat exchangers. The total thermal conductance of the four heat

exchangers is assumed xed,

UA UA H UA A UA CON UA EVA 12

In terms of non-dimensional forms, the heat transfer rate Eqs. (2)(5) and Eqs. (1) and (11) can be

written as follows:

QH B sst sH 13

Fig. 2. The heat transfer irreversible model of a solar driven adsorption refrigeration system.



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QH y sH sHC 14

QA z sA 1 15

QCON 1 x y z sCON 1 16

QEVA x sL sLC 17

QH QEVA QCON QA 18

QHsHC

QEVAsLC

QCONsCON

QAsA

19

where the following group of non-dimensional transformations is imposed:

sH THT0

Y sLC TLCT0

Y sL TLT0

sCON TCON

T0Y sA

TA

T0Y sHC

THC

T0

QH QH

UAT0Y QEVA

QEVA

UAT0Y QCON

QCON

UAT0Y QA

QA

UAT0Y B

bACGT

UAX

20

Here, B is the parameter which describes the size of the collector relative to the cumulative sizeof the four heat exchangers, and x, y and z are conductance allocation ratios, dened as

x UA EVAUA

Y y UA HUA

Y z UAAUA

21

According to the constraint property of thermal conductance UA in Eq. (12), the thermal con-ductance distribution ratio for the condenser can be written as,

m UA CON

UA 1 x yz 22

3. Optimization techniques

The main objective of the present analysis is to nd the optimum allocation among the heat

exchanger inventory of a heat driven adsorption refrigerator for which the maximum refrigeratorload (QEVA) can be achieved. It can be shown from Eqs. (13)(19) that QEVA is a function ofB, sst,sH, sA, sCON, sL, x, y and z. In this analysis, the temperature dierence of the heat transfer uid in

the condenser and adsorber is assumed very small (%0.02). This assumption is reasonable becausethe heat transfer uid in both the condenser and adsorber exchange heat with the heat sink atequal temperature. To maximize the refrigeration load, QEVA, one needs to solve the non-linear set

of Eqs. (13)(19). The NewtonRaphson method with appropriate initial guesses was employedfor solving the above set of non-linear equations. Newtons method has been adopted to maximize



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QEVA by optimizing sH, x, y and z and varying some selected parameters to generate the results

shown in Figs. 37. The convergence criteria for both the maximization technique and solving the

Fig. 3. The eect of dimensionless stagnation temperature sst on (a) optimal dimensionless collector temperature, (b)

optimal distribution of the thermal conductance among the four heat exchangers: collector, adsorber, condenser and

evaporator.



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Fig. 4. The eect of dimensionless collector size B on (a) optimal dimensionless collector temperature, (b) optimal

distribution of the thermal conductance among the four heat exchangers: collector, adsorber, condenser and evapo-

rator.



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Fig. 5. The eect of dimensionless refrigeration space temperature, sL on (a) optimal dimensionless collector tem-

perature, (b) optimal distribution of the thermal conductance among the four heat exchangers: collector, adsorber,

condenser and evaporator.



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non-linear set of equations is taken as jRj26 107, where jRj2 stands for the Euclidian norm of the

residual vector. A subroutine subprogram of Dennis and Schnabel [14] is used in this computa-

tional technique to conrm that the function attains its maximum point. The results obtained bythis numerical method are presented and discussed in the following section.

Fig. 6. COP for optimum condition against sst for dierent B.

Fig. 7. COP for optimum condition against sst for dierent sL.



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4. Results and discussion

It is reported that the adsorption refrigeration system can be operated by mid to lower driving

heat source temperatures, TH, (60 $ 200), for producing refrigeration load temperatures, TL,between 15C and 15C [15]. In terms of non-dimensional form, these ranges can be estimated,respectively, as 1.11.5 for the driving heat temperature and 0.80.95 for the refrigeration spacetemperature. Therefore, the dimensionless collector stagnation temperature, sst, has been varied

from 1.1 to 1.5, and the dimensionless refrigeration space temperature, sL, has been set from 0.8to 1.

Fig. 3a shows the optimal value of dimensionless collector temperature sH against the di-

mensionless collector stagnation temperature sst, while Fig. 3b displays the eect of the stagnationtemperature sst on the optimum balance of thermal conductance of the four heat exchangers.

From Fig. 3a, it is observed that the optimum collector temperature sHYopt increases with theincrease of stagnation temperature sst. It is worth mentioning that sHYopt is always greater than s

1a2

st

,

as shown by Bejan et al. [6] and Vargas et al. [11]. From Fig. 3b, it may be seen that an increase instagnation temperature sst leads to an increase in optimum evaporator thermal conductance and adecrease in optimum collector thermal conductance, but the optimal thermal conductance de-

mand for the adsorber and condenser remain the same as sst increases. It is also noted from thesame gure that the adsorber and condenser take half of the total thermal conductance, which isalso in accord with the results of Bejan et al. [6] and Vargas et al. [11], as both condenser and

adsorber release heat to the ambient.The eects of dimensionless collector size Bon the optimal dimensionless collector temperature

sHYopt and on the optimal demand of thermal conductance among the four heat exchangers are

presented in Fig. 4a and b, respectively. One may see from Fig. 4a that the parameter B has a

negligible eect on sHYopt ifBis greater than 0.2. From Figs. 3a and 4a, it may be concluded that thecollector stagnation temperature has more eect on the optimal collector temperature than that onthe relative size of collector. It can be seen from Fig. 4b that UAEVAYopt decreases as well asUAHYopt increases marginally as Bincreases. The interesting conclusion is that the heat exchangerstaking heat from the outside and releasing heat to the external ambient, share thermal conductancedemands equally. The adsorber and condenser also share their demands almost equally.

The results plotted in Fig. 5a and b illustrate the sHYopt and optimal allotment of thermal

conductance among the collector, adsorber, condenser and evaporator heat exchangers againstthe dimensionless refrigeration load temperature sL. It is observed from Fig. 5a that sL has analmost negligible eect on sHYopt. That means the optimal collector temperature is not strongly

dependent on the required refrigeration space temperature. An increase (a decrease) in the optimalthermal conductance of the evaporator (collector) has been seen in Fig. 5b with the increase of

refrigeration space temperature, while the total demands for evaporator and collector are alwaysalmost 50% of the total thermal conductance. The same distribution for the optimal thermal

conductance of the adsorber and condenser has been seen as it is observed for other cases.The eects ofsst, Band sL on the coecient of performance COPopt QEVAYmaxaQHYopt for the

optimum condition of this system have been presented in Figs. 6 and 7. One may see from Fig. 6

that an increase in sst leads to an increase in COPopt. These results reect actual conditions be-cause, in general, an increase in driving heat source temperature leads to an increase in COP[16,17]. It is also observed that the primary eect of increasing the relative size of the collector



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B causes a decrease in COPopt. From Fig. 7, it can be seen that the COPopt and sL increases si-

multaneously. The reason is that an increase in sL represents the increase of required refrigerationspace temperature. The higher the refrigeration space temperature is, the lower is the required

heat input, which leads COPopt to increase.

5. Conclusions

A thermodynamic optimization of a solar driven adsorption refrigerator has been presented in

this study. An internally endoreversible model has been analysed numerically to nd the optimalconditions of a solar driven adsorption chiller. The following conclusions can be drawn from thisanalysis.

1. The optimum sHYopt depends strongly on the collector stagnation temperature, but B and sLhave negligible eects on sHYopt.

2. UAEVAYopt gains with the expense of UAHYopt as sst, sL increase as well as B decreases.3. The combined share of the adsorber/condenser conductances is xed almost in all cases, and

they share their demand equally.4. The optimal thermal conductance of the heat exchangers that take heat from the heat source is

almost equal to the thermal conductance of the heat exchangers that release heat to the externalambient.

5. The COPopt increases as sst and sL rise, but decreases as B increases.

Finally, it may be concluded that the maximum refrigeration eect can be achieved from anadsorption refrigeration system by distributing the thermal conductance among the adsorber,

condenser, evaporator and collector heat exchangers optimally.

References

[1] Bejan A. Entropy generation minimization. New York: CRC Press; 1996.

[2] Curzon FL, Ahlborn B. Eciency of a Carnot engine at maximum power output. Am J Phys 1975;43:22.

[3] Bejan A. Theory of heat transfer-irreversible power plants. Int J Heat Mass Transfer 1988;31:1211.

[4] Bejan A. Theory of heat transfer-irreversible power plants. II. The optimal allocation of heat exchange equipment.

Int J Heat Mass Transfer 1995;38:433.

[5] Bejan A. Theory of heat transfer-irreversible refrigeration plants. Int J Heat Mass Transfer 1989;32:1631.[6] Bejan A, Vargas JVC, Sokolov M. Optimal allocation of heat exchanger inventory in heat driven refrigerators. Int

J Heat Mass Transfer 1995;38:2997.

[7] Sun F, Chen W, Chen L, Wu C. Optimal performance of an endoreversible Carnot heat pump. Energy Convers

Mgmt 1997;38:1439.

[8] Ni N, Chen L, Wu C, Sun F. Performance analysis for endoreversible Brayton heat pump cycle. Energy Convers

Mgmt 1999;40:393.

[9] El-Din MMS. Optimization of totally irreversible refrigerators and heat pumps. Energy Convers Mgmt

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[10] Sokolov M, Hershgal D. Optimal coupling and feasibility of a solar powered year-round ejector air conditioner.

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[11] Vargas JVC, Sokolov M, Bejan A. Thermodynamic optimization of solar-driven refrigerators. J Solar Energy

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[12] Chen J, Schouten A. Optimum performance characteristics of an irreversible absorption refrigeration cycle. Energy

Convers Mgmt 1998;39:999.

[13] Chen J. Performance characteristics of a two-stage irreversible combined refrigeration system at maximum

coecient of performance. Energy Convers Mgmt 1999;39:1939.

[14] Dennis JE, Schnabel RB. Numerical methods for unconstrained optimization and nonlinear equations. Englewood

Clis, NJ: Prentice-Hall; 1983.

[15] Saha BB. Performance analysis of advanced adsorption cycle. PhD Thesis, Tokyo University of Agriculture and

Technology, Japan, 1997.

[16] Boelman EC, Saha BB, Kashiwagi T. Experimental investigation of a silica gelwater adsorption refrigeration cycle

the inuence of operating conditions on cooling output and COP. ASHRAE Trans Res 1995;101:358.

[17] Saha BB, Boelman EC, Kashiwagi T. Computer simulation of a silica gelwater adsorption refrigeration cycle the

inuence of operating conditions on cooling output and COP. ASHRAE Trans Res 1995;101:348.


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