Thermodynamic Modelingof Absorption Chiller andComparison withExperiments

K. C. NG, H. T. CHUA, and QIAN HAN

Department of Mechanical & Production Engineering, National University of Singapore, Singapore

T. KASHIWAGI, A. AKISAWA, and T. TSURUSAWA

Department of Mechanical Systems Engineering, Tokyo University of Agriculture & Technology,

Tokyo, Japan

A simple and accurate thermodynamic model is presented for a four-heat-reservoir, absorptionchiller. The performance of chillers, as described by 1/COP, is expressed in terms of the dominantexternal and internal losses that stem from the nite-rate heat transfer and internal entropy

generation in the absorber, condenser, generator, and evaporator. It is found that the relativecontributions from these losses of absorption chillers govern their behavior over a wide range of

cooling capacities. The successful formulation of the thermodynamic model, as presented in this

article, implies that all previous endoreversible approaches are inadequate because they cannotportray the real behavior of absorption chillers accurately. At best, these models give only the upper

bounds of experimental realities and thus they can be viewed only as subsets of the generic

thermodynamic approach described here. To this end, we present evidence from an experimentalfacility to show that true absorption chiller behavior is governed by the presence of three key

competing losses, namely, the nite-rate heat transfer losses, the internal dissipative losses, and

heat leaks.

Recently, Grazzini [1] and Gordon and Ng [25]pioneered a generic thermodynamic model for chillersthat includes the effect of internal dissipative (entropyproduction) losses. They deemed both external and in-ternal losses to be signi cant and indispensable in the

K. C. Ng gratefully acknowledges the generous hospitality of the Depart-

ment of Mechanical Systems Engineering at Tokyo University ofAgriculture

& Technology (TUAT) during part of the research, and the Japan Society for

the Promotion of Science (organized by Kyoto University) for the funding

of his visit to Japan in December 1995.

Address correspondence to Dr. K. C. Ng, Department of Mechanical &

Production Engineering, National University of Singapore, 10 Kent Ridge

Crescent, Singapore 119260. E-mail: mpengkc@nus.edu.sg

modeling of chiller performance. By the rubric chillers,they refer to refrigeration units and heat pumps with allkinds of powering sources, such as electricity, naturalgas, and steam.

Chiller performance, in general, can be adequatelyrepresented by the characteristic plots of 1/COP ver-sus the reciprocal of the cooling capacity. Distinctive

qualitative description of chiller performance is shownby the linear and nonlinear parts of such characteris-tic plots, as shown in Figure 1 for both endoreversibleand real chillers. Endoreversible chillers are machines

that consider only nite-rate heat transfer losses or

simply external losses. In reality, the behavior of real

42 heat transfer engineering vol.20 no.2 1999

Figure 1 Qualitative characteristicplot of 1/(COP) versus 1/(cooling capacity) for endoreversible and thermodynamic models.

chillers is governed by external and internal dissipativelosses as well as heat leaks from all processes in themachine. The main advantages of developing a generalthermodynamic model are that (1) it can be useful asa diagnostic tool for engineers working at sites, (2) itprovides ameans of predictingchiller performance overa practical range of coolant conditions, and (3) mostimportant, it gives a basic framework for understand-ing the behavior of all forms of cooling devices. Thus,the thrust of thermodynamic modeling lies in the factthat,while introducingas littlespeci c detail as possibleabout the chillers, it captures the major irreversibilitiesthat govern theworking principles of chillers at assortedheat source and coolant conditions. However, this doesnot imply that the importance of distributed modelingfor detailed component design of chillers can be su-perseded. Thermodynamic modeling offers engineersand scientists a simple but accurate means of evaluat-ing chiller performance.

Referring to Figure 1, it is observed qualitatively thatthere are dominant irreversibilities(entropy production)within any chiller that militate against slow chiller op-eration (and hence low heat transfer rates), as well asagainst fast operation or high cooling rates. At theseextremes, the performance index or simply the coef- cient of performance (COP) of a chiller is generallypoor, and most chiller manufacturers appear to designtheir chillers such that a near-optimal COP is achievedat around the nominal capacity. COP is de ned hereas the ratio of the useful effect from the chiller to theenergy (either mechanical or thermal) input. Based on

these observations, one concludes that there exists a re-gion between the slow and fast operations where theCOP is maximum.

In recent years, Gordon and Ng [25] and Chua et al.[69] have demonstrated with experimental evidencethat most chillers have been con gured to operate neartheir optimal COPs at their designed cooling capacities.For conditions lower than the designed or rated capac-ity, some chillers can operate far into the linear sectionof the characteristic plot of Figure 1. This is particu-larly true for absorption chillers, but with one proviso:performance data from commercially available absorp-tion machines cover not only the linear regime of thecharacteristic curve, they can also span marginally intononlinear regions on both sides of the local optimum.

Many previous attempts to model chillers have beenmade from the viewpoint of nite-timethermodynamics[1123], called simply endoreversible models. Hitherto,more than a dozen such articles on endoreversible mod-eling, or variants of such modeling with heat leaks, havebeen cited. However, predictions from these modelswere far from satisfactory when compared with the be-havior of real chillers, particularly for the low-cooling-capacity regions. This is because the endoreversiblemodels consider nite-rate heat transfer as the sole irre-versibility. Consequently, they predict that the COP de-creases monotonically as the cooling rate increases. An-other common but unnecessary constraint used in someendoreversible modeling of absorption chillers is theseparate requirement of non-negative entropy changefor the condenserevaporator (condensergenerator)

heat transfer engineering vol.20 no.2 1999 43

and the absorbergenerator (absorberevaporator) pairs[11, 20, 23]. This is obviously an untenable constraintfor real absorption chillers because the cyclic working uid (refrigerant) interacts with all four heat reservoirs.In recent articles of the authors [8, 9], they have demon-strated that such constraints could be violated. Thiswas con rmed by experimental observations from realcommercial chillers, where a negative entropy changewas recorded for the above-mentioned pairs of heat ex-changer but a net positive entropy change wasmeasuredfor the whole chiller, thus satisfying the second Lawof Thermodynamics. A similar argument based on re-versible absorption chillers has also been highlightedby Abrahamsson and Jernqvist [24].

Recognizing that theabsorber and thecondenser tem-peratures in real chillers are different [8, 9], we presenta four-heat-reservoir, thermodynamic model that treatsnot only the external losses due to nite-rate heat trans-fer but includes the presence of internal dissipativelosses and heat leaks of absorption chillers. The ther-modynamic model employs only the basic laws of ther-modynamics, and it makes no unnecessary constraint asreported in some endoreversible models. We emphasizethat our model presented here differs from the previousones in that it considers the case withsubstantial internalheat leaks between the internal chambers of an absorp-tion chiller, such generator to condenser and absorberto evaporator; such heat leaks are commonly found insmall-scale experimental facilities. To strengthen theusefulness of the model, we furnish some experimen-tal data from an experimental, single-stage absorptionchiller to demonstrate the formulation of characteristicplots and to show how the key competing losses, men-tioned earlier, govern the true behavior of absorptionchillers.

Figure 2 shows a schematic of a single-stage absorp-tion chiller that employs thermal energy as the drivingforce, rather than electrical power to run a compres-sor, as in vapor-compression chillers. The heating ef-fect (latent or sensible) at the generator drives part ofthe volatile (e.g., water vapor) component of the work-ing solution pair (e.g., LiBrwater solution) into vaporphase, with the reverse process being carried out in theabsorber. The condenser and the evaporator serve thesame functions as in conventional machines. The pres-ence of a generator and an absorber in these thermallydriven machines gives rise to two distinct extrema forthe theoretical construct of 1/COP versus the recipro-cal of the cooling capacity. One extrema pertains tomaximum COP at a nominal cooling capacity, whilethe other indicates the maximum cooling capacity butat a lower COP. It is noted that beyond the maximumcooling capacity, the upper end of the characteristiccurve exhibits a trend similar to the lower linear regime

Figure 2 Schematic of single-stage absorption chiller. The dottedarrows show the direction of regenerative heat transfer, while the

augmented dotted arrows show the directions of internal heat leaks

between contiguous hot and cold compartments.

in Figure 1 the COP of the chiller increases with in-creasing cooling capacity. Although such a qualitativetrend appears to match the behavior of real chillers, itrepresents an irrational or low COP regime for chillersto operate in. Thus, this is a region disfavored by chillermanufacturers. As predicted by the thermodynamicmodel, there exists a more realistic, energy-ef cient re-gion in the theoretical construct, where the COPs aremore comparable with those reported in the catalogs ofcommercial chillers, as cited in [3, 4].

THERMODYNAMIC MODEL

Absorption chillers are designed to interact with atleast four or more heat reservoirs and not the three heatreservoirs that can be found in the literature. In thissection, we employ the basic laws of thermodynamicsto arrive at a generic system performance parameter thatcan capture the behavior of an absorption chiller. Vir-tually no system constraint is applied to the absorptionplant other than a few basic de nitions. We consider achiller of this type operating cyclically and at steadystate transients are ignored.

The model developed here is an extension of ourprevious work [3, 8] because it includes the effect ofinterchamber or simply internal heat leaks that occurbetween the generatorcondenser and the evaporatorabsorber pairs. Such an approach for the bypass heatleak is similar to a heat leak model for a refrigerationplant that was pioneered by Bejan [12]. On the otherhand, signi cant external heat leaks to or from the am-bient are accounted for at the generator and evaporatoronly. They are lumped into the heat transfer terms. In

44 heat transfer engineering vol.20 no.2 1999

reality, heat leaks occur continuously along the surfacesof the piping and heat exchange vessels. Since the pip-ings and exchangers are usually well insulated, theseeffects are generally small compared to the heat trans-fer quantities of the heat exchangers.

Internal energy is a state function, so the internalenergy change over a cycle sums to zero. The energybalance for an absorption chiller of the type shown inFigure 2 can be expressed as

Qrej Qe Qle Qg + Qlg = 0 (1)

All quantities here are cycle-average rates and are takenas positive values, where their directions of energy oware depicted in Figure 2.

It is noted that internal heat leaks do not appear inthe enthalpy balance of Eq. (1), but their effects areaccounted for in the entropy balance. For these internalheat leaks,

Qla e = Ka e(Ta Te)

and

Qlg c = Kg c(Tg Tc)

Theamount of internal leak depends on the design of thevessel and the provision of suf cient thermal insulationat the walls separating the chambers. Should the wallsbe poorly designed, a signi cant amount of internal heatleaks can occur, whichmust be accounted for during theentropy balance.

Prior to applying the entropy (also a state function)balance, we introduce a dimensionless variable, N , toindicate the ratio of heat rejection via the absorber tothe total rejection (or heat absorbed by generator andevaporator). The entropy balance for the working uidsin the four heat reservoirs is given by

(1 N )Qrej Qlg cTc

+N Qrej + Q

la e

Ta

(Qe + Q

la e + Q

le)

Te

(Qg Qlg c Qlg)Tg

= D Sint 0 (2)

where D Sint represents the entropy generation due toheat and mass transfer in the generator and absorber,pressure drop, and throttling in the chiller. D Sint is anon-negative quantity as dictated by the Second Law ofThermodynamics.

Noting that COP is de ned as the ratio of the Qe toQg , from these two equations one can express the keysystem variable, 1/COP, as

1

COP=[1/ (SRT)e] + ( D Sint / Qe) + ( S 2i= 1 L1, i / Qe) + ( S 2j= 1 L2, j / Qe)

1/ (SRT)g(3)

where S 2i= 1 L1,i and S 2j= 1 L2, j refer to the intercham-ber heat leaks and the heat leaks from exchangers to theenvironment, respectively. For clarity, these terms arewritten as follows:

L1,a e = Qla e ( 1Te

1

Ta )L1,g c = Q

lg c ( 1Tc

1

Tg )and

L2,e = Qle

1

(SRT)e

L2,g = Qlg

1

(SRT)g

where

1

(SRT)e=

1

Te

1

Tc N ( 1Ta

1

Tc)and

1

(SRT)g=

1

Tc

1

Tg+ N ( 1Ta

1

Tc )The terms (SRT)e and (SRT)g are the system refer-ence temperatures. It should be pointed out these SRTsare not directly measurable temperatures but rather arecomputed from other process average temperatures ofthe heat exchangers and the variable N .

As can be deduced from Eq. (3), the contributionsto 1/COP of the chiller can therefore be viewed asstemming from (1) the nite-rate heat transfer lossesof heat exchangers, (2) the internal dissipative (entropygeneration) losses within the absorption chiller dueto pressure and chemical potential drops, and (3) theinternal (interchamber) and external (to the environ-ment) heat leaks. For a well-con gured chiller, the con-tributions from the rst two terms are of similar mag-nitude, while the contribution from external heat leaksis usually small, typically less than 5%. If internal heatleaks are signi cant between the generatorcondenser

heat transfer engineering vol.20 no.2 1999 45

or the absorberevaporator pair, then the terms involv-ing the thermal conductances (Kg c, Ka e) need to beaccounted for in Eq. (3). If one were to assume asimple three-heat-source model, then the terms associa-ted with the temperature difference between the ab-sorber and the condenser would be omitted from themodel.

The above derivation involves terms associated onlywith the temperatures of the working uids (e.g., LiBrsolution orwater).For amorepracticaluse of themodel,one would like to include the coolant temperaturesassociated with the heat reservoirs, namely, the genera-tor, condenser, absorber, and evaporator. The followingequations relate the working refrigerant temperatures tothe coolant temperatures:

Qg = (mCE )g(Tg,i Tg) (4a)

Qc = (1 N )Q rej = (mCE )c(Tc Tc, i ) (4b)

Qa = N Q rej = (mCE )a(Ta Ta, i ) (4c)

Qe = (mCE )e(Te, i Te) (4d)

We have assumed a water- red mode of heat trans-fer in this case, but if the generator is steam- red, thethermal conductance term is replaced by the productof overall heat transfer coef cient and the area, i.e.,(UA). In commercial absorption chillers, the absorberand condenser are usually cooled by a single stream ofcoolant owing in series. The condenser inlet tempera-ture is then constrained by

Tc, i = Ta, i +N Q rej

(mC )a(5)

To assist one to understand themodel better, it is pos-sible to make some simplifying analysis relating to thekey variables such as D Sint ! 0. With this assumption,one observes how unrealistic the endoreversible mod-eling for absorption chillers can be when compared tothe behavior of real chillers. Nevertheless, the endore-versible approach can serve as a benchmark comparisonfor the ef ciency of generic plants. It allows engineersto appreciate the existence of both the external and inter-nal losses within the thermodynamic cycle of a chiller.For example, in a endoreversible model with internalheat leaks, i.e., D Sint and Q

lg or e ! 0, the characteristic

expression simpli es to

( 1COP)endo =(SRT)g

(SRT)e+ (SRT)g

S 2i= 1 L1, iQe

(6)

This is equivalent in concept to the model derived byBejan [18], which included external nite-rate heattransfer losses and internalheat leaks as themain sourcesof losses in a chiller. Although this expression can pro-vide a qualitative minimum for 1/COP in the charac-teristic plot, it still falls short of describing fully thebehavior of a real chiller.

In the limit where Qe ! 0, the reversible COP ofthe model approaches that of the three-heat-reservoirCarnot COP, which is

1

COP=

Tg, i

Te, i

(Ta, i Te, i )(Tg, i Ta,i )

(7)

Note that only the coolant temperatures are used here,and cooling capacity has been reduced to zero.

Chiller Optimization

The theoretical optimization of the thermodynamicmodel involves the extremization of Eq. (3) with re-spect to the system constraints of Eqs. (4) and (5). Itssolution is based on the inlet coolant temperatures tothe heat exchangers of an absorption chiller. Owing tothe complexity of these equations, only numerical solu-tions for the stable behavior of chillers can be obtained.An examination of the behavior of such a chiller revealsthat, within the expected energy-ef cient regime of thecharacteristic plot (as described in Figure 1), there ex-ists an optimum for the 1/COP at the set of coolantconditions. One obtains the local optima by partial dif-ferentiating the 1/COP variable with respect to (1) theratio of heat rejection between the absorber and the totalrejected heat (i.e., the value N ) and (2) the reciprocal ofthe cooling capacity, 1/Qe, that is,

(1/ COP)

N= 0 (8a)

and

(1/ COP)

(1/ Qe)= 0 (8b)

In the optimizationexercise, the internal dissipative lossterm, D Sint , and the values of the thermal conductancesin the exchangers are held constant and these values aredetermined at the measured coolant conditions. This isa fair exercise because it is independent of network con- gurations aswell as refrigerant properties. Ourmotiva-tion is in essence close to that of Carnot speci cally,we aspire to construct an existence map for absorp-tion chillers that is allowable or permitted by the laws

46 heat transfer engineering vol.20 no.2 1999

Table 1 Measured results of absorption chiller [25]

Te, i (C) Tg , i (C) Tc, i (C) 1/COP Qe (kW) Qa (kW) N

8.4 61.0 31.0 7.40 0.151 0.532 0.347

9.4 65.2 31.0 2.59 0.780 1.32 0.416

10.8 70.3 31.0 2.00 1.59 2.37 0.462

12.4 75.5 30.9 1.77 2.49 3.45 0.478

13.8 79.8 31.0 1.67 3.27 4.45 0.494

15.2 85.0 30.9 1.59 4.11 5.52 0.507

16.4 90.1 31.0 1.56 4.89 6.39 0.506

17.7 95.1 31.0 1.53 5.70 7.42 0.514

of thermodynamics but with the following objectives:(1) to locate the extrema of the existence map at a givenset of chiller conditions, and (2) to evaluate the poten-tial design amelioration based on the proximity of thedesigned point to the thermodynamic optimum. Thisapproach is also consistent with the main thrust of theFTT analysis.

COMPARISON OF THEORY AND EXPERIMENT

We now present a comparison between theory andexperiments. The data set comes from an absorptionchiller of a commercial company in Japan [25], work-ing in close association with the Tokyo University ofAgriculture & Technology. It is a water- red, single-stage machine. For conciseness, Table 1 gives the mea-sured results, while Table 2 gives the estimated resultsof the plant at various coolant and heat source tem-peratures. The experimental facility is well equippedand calibrated.Suf cientlydetailedmeasurements weretaken so that a quantitative analysis based on the ther-modynamic model could be conducted. For ease ofcomparison, the temperature of the cooling water tothe absorbercondenser and outlet temperature of thechilled water are preset to 31C and 8C, respectively.It is noted that the internal dissipative losses ( D Sint)and the thermal conductance terms are computed basedon the internal temperatures of the heat exchangers.From the given set of coolant temperatures and the

Table 2 Estimated results of absorption chiller (Ka e = 0.000884 kW/K, Kg c = 0.00337 kW/K)

(mCE)e (mCE)g (mCE)a (mCE)c D SintTe, i (

C) Tg , i (C) Tc, i (C) (kW/K) (kW/K) (kW/K) (kW/K) (kW/K) Qle (kW) Tg (C) Tc (C) Ta (C) Te (C)

8.4 61.0 31.0 0.420 0.686 0.748 0.614 0.000146 0.265 59.4 33.0 31.7 8.0

9.4 65.2 31.0 0.639 0.849 0.751 0.616 0.000188 0.373 62.8 34.8 32.7 8.2

10.8 70.3 31.0 0.623 0.971 0.751 0.616 0.000292 0.373 67.1 36.9 34.1 8.2

12.4 75.5 30.9 0.643 1.01 0.753 0.618 0.000424 0.309 71.2 39.2 35.5 8.5

13.8 79.8 31.0 0.645 1.09 0.755 0.619 0.000516 0.305 74.8 41.1 36.8 8.7

15.2 85.0 30.9 0.663 1.05 0.754 0.618 0.000660 0.231 78.8 43.1 38.2 9.0

16.4 90.1 31.0 0.677 1.05 0.755 0.619 0.000834 0.138 82.9 45.1 39.4 9.2

17.7 95.1 31.0 0.678 1.01 0.756 0.620 0.000996 0.019 86.5 47.0 40.8 9.3

calculated values of internal dissipative losses, a the-oretical construct of each data point is then evaluated.The locus of all measured data points, projected ontothe 1/COP 1/Qe plane, is indicated by a full line inFigure 3.

The linear regime of Figure 3 shows that the per-formance of the single-stage absorption chiller is dom-inated by the effects of internal dissipative losses inthe cycle as well as internal heat leaks. For the sameexperimental conditions (as in Tables 1 and 2), Table 3shows the distribution of 1/COP contributions in per-centages from the effects of nite-rate heat transfer, in-ternal entropy production, and heat leaks for each ofthe data points examined. The data set is obtained forthe case without the use of surfactant. At a low heatsource temperature of 61C, the internal losses (dis-sipative plus interchamber heat leaks) were found tobe of the order of 60%, while the external heat ex-changer contribution is about 14.6% and external heatleaks contribute the remaining 25.6%. Despite the lowamount of refrigerant ow (hence low cooling capac-ity), the large amount of internal losses contributioncan be attributed to the presence of interchamber heatleaks of 14.2%. However, the relative contribution formexternal losses improves as generator inlet water tem-perature increases. For example, at an inlet tempera-ture of 90C, the heat transfer losses in the exchangerbecomes dominant at about 65%. Intercomponentheat leaks at higher inlet water temperatures areinsigni cant.

heat transfer engineering vol.20 no.2 1999 47

Figure 3 Measured performance of single-stage absorption chiller with and without the effect of surfactant.

Table 4 offers a comparison between: (1) 1/COPandN values at the assorted experimental conditions (con-sistent with Tables 1 and 2) for the actual chiller; and(2) minimum realizable 1/COPfor each of the part-loadconditions and the associated nominal N and Qa val-ues at the corresponding optima. The fact that the realexperimental chiller incurred higher heat rejectionsat the absorber, as well as higher heat leaks in theinterchambers of the exchangers, is revealed here bythe large differences between the optimal and the actualvalues, particularlyat low part loads. At the rated condi-tion of 90C, however, the designer of the experimentalchiller has opted for higher Qe but at the expense of aslightly lower chiller COP as compared with the pre-dicted COP. This seems to be the design trend of chiller

Table 3 Distribution of 1/COP contributions in the single-stage absorption chiller(without surfactant)

Heat leaks, Heat leaks,

Heat leaks absorber generator

Generator External Internal to ambient evaporator condenser 1/COPinlet temp. heat transfer dissipative (external) (internal) (internal) (value at

(C) effect (%) effect (%) (%) (%) (%) 100%)

61 14.6 45.6 25.6 6.7 7.5 7.39

65 41.1 31.1 19.6 3.6 4.5 2.59

70 52.8 29.3 12.4 2.3 3.2 1.99

75 59.1 29.4 7.3 1.6 2.6 1.77

80 62.7 27.7 5.8 1.35 2.2 1.66

85 64.9 28.4 3.6 1.1 1.99 1.59

90 65.77 29.5 1.85 0.9 1.85 1.55

95 67.3 29.8 0.22 0.84 1.7 1.52

manufacturers, who have demonstrated that chiller tech-nology has evolved empirically toward a region near tothe thermodynamic optimal [9]. It is also interestingto note that the actual N is quite close to the optimalvalue of 0.448, which has been shown to remain quiteconstant over a large region of part-load.

Effect of Surfactant

Theeffect of adding suitable surfactant, namely ethyl-hexanol, is demonstrated here using the same character-istic plot. For this particular experimental unit, a smallvolume (less than 1%) of the mentioned surfactant isintroduced into the absorber. The role of surfactant re-duces the surface tension of LiBrwater solution at the

48 heat transfer engineering vol.20 no.2 1999

Table 4 Comparison of optimal and actual conditions at various hot water inlet temperaturesto generator (without surfactant)a

Generator Predicted

inlet water Predicted (1 N )/Qa Predicted Measuredtemperature Qe (kW) /(kW) 1/COP Measured (1 N )/Qa Measured(C) (optimal) (optimal) (optimal) Qe (kW) /(kW) 1/COP

61 0.999 0.4496/2.152 2.649 0.151 0.653/0.532 7.39965 1.378 0.4483/2.231 2.602 0.779 0.584/1.319 2.59070 1.779 0.4483/3.113 1.961 1.589 0.538/2.372 1.99775 2.204 0.4483/3.499 1.737 2.489 0.521/3.450 1.77380 2.558 0.4483/3.806 1.578 3.269 0.506/4.454 1.66585 2.968 0.4484/4.133 1.447 4.109 0.493/5.515 1.59390 3.397 0.4484/4.509 1.365 4.889 0.494/6.391 1.55795 3.792 0.4488/4.780 1.281 5.699 0.486/7.415 1.529

a The temperatures of the water to the condenser and from the evaporator are held constant at

31C and 8C, respectively.

absorber and generator. Under the same in uence ofheat transfer rates, the processes of mass absorptionand desorption at the mentioned exchangers were en-hanced by as much as 1525%, as shown by the lowerset of lines in Figure 3. The heat and mass transferenhancement are commonly known as the Marangoniconvection effect [26]. Such improvements in the exper-imental data are also marked by a change of the gradient(internal losses) as well as a reduction of the intercept(heat transfer losses) values.

CONCLUSIONS

The simple thermodynamic model described herecaptures accurately the key dominant losses that gov-ern the performance of a four-heat-reservoir, single-stage LiBrwater absorption chiller. Introducing as littlespeci c details about the chiller but incorporating thekey losses, namely, (1) nite-rate heat transfer losses,(2) internal dissipative losses, and (3) heat leaks, thethermodynamic model provides better insight for un-derstanding chiller behavior over a wide span of oper-ating conditions. The model presented in this article isgeneric to all absorption chillers, while endoreversiblemodeling of absorption chillerswould appear as subsetsto this generalizedmodel.We also point out that some ofthe constraints needed in endoreversible modeling areunnecessary and untenable. Through the measured dataof a real chiller, the model has shown quantitatively thatthe presence of external and internal dissipative losses(entropy generation) are the key to portraying the cor-rect trend of commercial absorption chillers. The effectof heat leaks is generally small except at low coolingloads.

Besides the general performance of absorption chill-ers, a comparison of chiller behavior to optimal per-

formance was also studied. At a prescribed set of waterinlet temperatures, the relative position of the measuredpoint to the predicted thermodynamic optimal gives anindirect indication as to which type of chiller lossesare dominating or, alternatively, what design improve-ments one needs to incorporate. Via the experimentalresults of a single-stage absorption chiller, the authorshave demonstrated convincingly the usefulness of thethermodynamic modeling, in particular, its worthinessas a postdesign evaluation tool.

NOMENCLATURE

C speci c heat of coolant, kJ/kg.KCOP coef cient of performance ( = Qe/ Qg)E effectiveness of heat exchangerK internal heat leak conductance, kW/KL heat leaks term, kW/Km mass ow rate, kg/sQ heat transfer rate, kWT temperature, KUA heat exchanger thermal conductance, kW/KD Sint total internal entropy generation, kW/KN ratio of heat rejection by absorber to the total

heat rejection of chiller

Subscripts

1 index denoting effects from interchamber heatleaks

2 index denoting heat leaks to and from environ-ment

a absorbera e absorber to evaporatora, i absorber coolant inletc condenserc, i condenser coolant inlet

heat transfer engineering vol.20 no.2 1999 49

e evaporatore, i evaporator coolant inletg generatorgc generator to condenserg, i generator heat source inleti coolant inletrej Rejection of heat

Superscript

l Heat leaks (external or internal)

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K. C. Ng obtained a B.Sc. (Hons. Mech. Eng.)in 1975 and a Ph.D. in 1980 from the Univer-

sity of Strathclyde in Glasgow (U.K.). Prior to

joining the National University of Singapore, he

worked as a project engineer at Babcock Power

Ltd, U.K. His research interests are (1) model-

ing and testing of chillers, (2) design of solar

hot water systems for industrial applications, and

(3) two-phase ows in boilers. He has published

over 40 international journal articles. Profession-

ally, he is a corporate member of the Institutions of Engineers of Singapore

and of the IMechE (U.K.). He is a registered Professional Engineer (P.Eng.)

in Singapore.

Takao Kashiwagi obtained his B.Eng., M.Eng.,and Ph.D. in 1970, 1972, and 1975, respectively,

from the Tokyo Institute of Technology (TIT),

Japan. In 1972, he joined the Faculty of Engi-

neering of the Tokyo University of Agriculture

& Technology (TUAT), initially as an Associate

Professor, and he was promoted to Professor in

1987. He spent his sabbatical at the NBS Center

forFireResearch, U.S.Department ofCommerce,

in 1980 to 1981. His major interests are energy

systems, refrigeration and air conditioning, and applied thermal engineering.

Professor Kashiwagi has won many awards in the eld of refrigeration, such

50 heat transfer engineering vol.20 no.2 1999

as those from the Japanese Association of Refrigeration of 1985, 1986, 1990,

and 1995. He also won an award at the International Absorption Heat Pump

Conference 96, Montreal, Canada.

He is active in both professional and government organizations. He is an

appointed member to (1) the Board of Trustees of the Japanese Society of

Mechanical Engineers, (2) the Environmental Engineering Division of the

Japanese Academic Council of Research, (3) Vice-Chairman of the Institute

of Refrigeration (Commission B1), and (4) a Japanese representative mem-

ber of the International Energy Agency (IEA). He is also an active and a

valuable member of the Advisory Committee for Energy of MITI, Japan, as

well as the Science and Technology Agency and Inter-Government Panel on

Climate Change.

Atsushi Akisawa received his B.Eng., M.Eng.,

and Ph.D. from the University of Tokyo, Japan,

In 1985, 1987, and 1995, respectively. Prior to

his academic appointment at the Tokyo Univer-

sity of Agriculture & Technology, he worked as

a researcher at the Mitsubishi Research Institute

Inc., Japan, from 1987 to 1992. He is now an

Associate Professor in the Faculty of Engineer-

ing. His research interests are (1) modal analysis

of urban energy systems, (2) cascaded use of en-

ergy for energy conservation, and (3) application

of absorption and adsorption chillers.

heat transfer engineering vol.20 no.2 1999 51