A New Approach to the Exergy Analysis of Absorption Refrigeration Machines_SD

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Energy 33 (2008) 890–907

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A new approach to the exergy analysisof absorption refrigeration machines

Tatiana Morosuka,�, George Tsatsaronisb

aInstitute of Marine Propulsion Plants Operation, Maritime Academy of Szczecin, Waly Chrobrego 1-2, 70500 Szczecin, PolandbInstitute for Energy Engineering, Technische Universitat Berlin, Marchstr. 18, 10587 Berlin, Germany

Received 24 April 2007

Abstract

Splitting the exergy destruction into endogenous/exogenous and unavoidable/avoidable parts represents a new development in the

exergy analysis of energy conversion systems. This splitting improves the accuracy of exergy analysis, improves our understanding of the

thermodynamic inefficiencies and facilitates the improvement of a system.

An absorption refrigeration machine is used here as an application example. This refrigeration machine represents

the most complex type of a refrigeration machine, in which the sum of physical and chemical exergy is used for each material

stream.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Exergy analysis; Exergy destruction; Avoidable exergy destruction; Endogenous exergy destruction; Absorption refrigeration machine

1. Introduction

An exergy analysis identifies the location, magnitude andsources of thermodynamic inefficiencies in an energyconversion system. This information is used for comparingvarious systems. An exergy analysis is the first step for theexergoeconomic analysis of energy conversion and energy-intensive chemical systems.

In a conventional exergetic evaluation of the kthcomponent of a system, the following variables areused [1–3]:

�
exergy destruction rate that depends on the mass flowrate through the component and the specific entropygeneration within it
_ED;k ¼ T0_Sgen;k ¼ T0 _mksgen;k (1)

e front matter r 2007 Elsevier Ltd. All rights reserved.

ergy.2007.09.012

ing author. Tel.: +49 30 314 24765; fax: +49 30 314 21683.

esses: [email protected] (T. Morosuk),

.tu-berlin.de (G. Tsatsaronis).

/www.iet.tu-berlin.de/efeu (G. Tsatsaronis).

exergetic efficiency
�
�k ¼_EP;k

_EF ;k

¼ 1�_ED;k

_EF ;k

(2)

�
exergy destruction ratios
yk ¼_ED;k

_EF ;tot

, (3)

and

y�k ¼_ED;k

_ED;tot

. (4)

The exergy balance for the kth component is

_EF ;k ¼ _EP;k þ _ED;k, (5)

and for the overall system

_EF ;tot ¼ _EP;tot þX

k

_ED;k þ _EL;tot. (6)

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Nomenclature

_E exergy rate (W)e specific exergy (J/kg)f circulation ratio of the mixture with concentra-

tion xR (kg/kg)h specific enthalpy (J/kg)_m mass flow rate (kg/s)

p pressure (Pa)_Q heat rate (W)

q specific heat (J/kg)S entropy (J/K)s specific entropy (J/kgK)p pressure (Pa)T temperature (K)_W power (W)

w specific work (J/kg)x concentration (kg/kg)y exergy destruction ratio (dimensionless)

Greek symbols

D difference� exergetic efficiencyZ isentropic efficiency

Superscripts

AV avoidableCH chemicalEN endogenousEX exogenousM mechanicalPH physicalT thermalUN unavoidable

Subscripts

A weak solutioncold low temperature

D destructionD concentration of the working fluid in the basic

processgen generationF fuelhybrid hybrid cyclehot high temperatureideal ideal cyclej jth flowk kth componentL lossesP productR strong solutiontot overall system0 thermodynamic environment

Abbreviations

A absorberARM absorption refrigeration machineG generatorCD condenserCM compressorEV evaporatorEX expanderH hybrid condition or cycleHU hybrid condition or cycle with unavoidable

exergy destructionI ideal condition or cycleT theoretical condition or cycleT turbineTVM throttling valve for the mixtureTVR throttling valve for the refrigerantP pumpR real condition or cycleRU real condition or cycle with unavoidable exergy

destruction

T. Morosuk, G. Tsatsaronis / Energy 33 (2008) 890–907 891

The purpose of this paper is to demonstratethat additional information, crucial for the improve-ment of a system can be obtained when the exergydestruction within each component is split into meaningfulparts.

Splitting the exergy destruction into endogenous/exogen-

ous [4–6] and unavoidable/avoidable parts [5,7,8] representsa new direction in exergy analysis, which can be calledadvanced exergy analysis. These splittings improve theaccuracy of exergy analysis and our understanding of thethermodynamic inefficiencies, and facilitate an exergoeco-nomic optimization.

2. Definitions and illustration

2.1. Endogenous and exogenous parts of the exergy

destruction

The total exergy destruction within the kth componentis split into endogenous and exogenous parts _ED;k ¼

_EEN

D;k þ_E

EX

D;k. Here _EEN

D;k is the endogenous part of exergy

destruction, associated only with the irreversibilitiesoccurring within the kth component when all othercomponents operate in an ideal way and the componentbeing considered operates with its current efficiency. _E

EX

D;k is

ARTICLE IN PRESST. Morosuk, G. Tsatsaronis / Energy 33 (2008) 890–907892

the exogenous part of exergy destruction within the kthcomponent and is caused in the kth component by theirreversibilities that occur in the remaining components.These splittings enable engineers working in systemoptimization to estimate the exergy destruction in acomponent caused by the component itself on one handand by the remaining components on the other hand. Thisinformation can be used to decide whether engineersshould focus on the component being considered or onthe remaining system components, in order to effectivelyimprove the overall performance.

2.2. Unavoidable and avoidable parts of the exergy

destruction

Only a part of the exergy destruction rate within acomponent can be avoided. The exergy destruction ratethat cannot be reduced due to technological limitationssuch as availability and cost of materials and manufactur-

ing methods is the unavoidable ( _EUN

D;k) part of the exergy

destruction. The remaining part represents the avoidable

( _EAV

D;k) part of the exergy destruction. Thus, splitting the

exergy destruction into unavoidable and avoidable parts in

the kth component _ED;k ¼ _EUN

D;k þ_E

AV

D;k provides a realistic

measure of the potential for improving the thermodynamicefficiency of a component.

Fig. 1. Theoretical energy conversion system.

2.3. Combination of the two splittings

Using an appropriate method [5] we can calculate theunavoidable endogenous exergy destruction within the kthcomponent when all the remaining components operatewithout irreversibilities. This calculation allows us then toobtain the unavoidable endogenous exergy destruction andsubsequently the avoidable endogenous, the unavoidableexogenous and the avoidable exogenous parts of exergydestruction within the kth component.

The endogenous avoidable part of the exergy destructioncan be reduced through improving the efficiency of the kthcomponent. The exogenous avoidable part of the exergydestruction can be reduced by a structural improvement ofthe overall system or by improving the efficiency of theremaining components and of course by improving theefficiency in the kth component.

The endogenous unavoidable part of the exergy destruc-tion cannot be reduced because of technical limitations forthe kth component. The exogenous unavoidable part of theexergy destruction cannot be reduced because of technicallimitations in the other components of the overall systemfor the given structure.

This information is extremely useful for the iterativeexergoeconomic optimization of energy conversion systems[3,7,8]. The designer is guided (a) to focus only on theendogenous avoidable and exogenous avoidable exergydestructions and to compare their costs with avoidable

investment costs, and (b) to consider the appropriatemeasures (referring to the component being considered, tothe efficiency of the other components, or to the structureof the overall system) that have the potential for reducingthe exergy destruction.

2.4. Illustration with the aid of a theoretical system

To demonstrate the concepts introduced in the previoussection, we first use a theoretical energy conversion systemconsisting of three components A, B and C in series(Fig. 1).The following assumptions were made: The fuel of

component A ( _EF ;A) is the fuel of the overall system( _EF ;tot). The product of component A ( _EP;A) is the fuel forcomponent B ( _EF ;B), and the product of component B

( _EP;B) is the fuel for component C ( _EF ;C). The product ofcomponent C ( _EP;C) is the product of the overall system( _EP;tot). The value of the product of the overall systemremains constant for the analysis _EP;tot ¼ const. Theexergetic efficiencies eA, eB and eC can be varied indepen-dently from each other.

2.4.1. Endogenous and exogenous parts of the exergy

destruction

The exergy destruction in component C can be

determined from Eqs. (2) and (5) as _ED;C ¼ _EP;C1�C� 1

� �¼

_EP;tot1�C� 1

� �. There is only endogenous exergy destruction

in component C ( _ED;C ¼ _EEN

D;C) because the value of_ED;C is

a function of the exergetic efficiency of this component

only ( _EEX

D;C ¼ 0).

The exergy destruction in component B can be deter-

mined similarly by _ED;B ¼_EP;tot�C

1�B� 1

� �. The exergy

destruction in component B depends on the exergeticefficiencies of both components B and C. Thus, there areendogenous and exogenous parts of the exergy destruction

for component B. The value _EEN

D;B can be determined if

component B operates with its current efficiency(eB(=const)o1), while component C is ideal (eC=1)

_EEN

D;B ¼_EP;tot

1�B� 1

� �. Then the exogenous exergy destru-

ction within component B becomes _EEX

D;B ¼_EP;tot

1�B� 1

� �1�C� 1

� �:

The equation for the exergy destruction within compo-nent A can be determined similarly by _ED;A ¼_EP;tot�C �B

1�A� 1

� �. The endogenous part of exergy destruction

in component A can be determined when eA(=const)o1

ARTICLE IN PRESST. Morosuk, G. Tsatsaronis / Energy 33 (2008) 890–907 893

but eB=1 and eC=1: _EEN

D;A ¼_EP;tot

1�A� 1

� �. The exogen-

ous part of the exergy destruction in component A then

becomes _EEX

D;A ¼_EP;tot�C �B

1�A� 1

� �1

�B�C� 1

� �:

2.4.2. Unavoidable and avoidable parts of the exergy

destruction

The unavoidable part of the exergy destruction in the kthcomponent can be determined by calculating the exergydestruction for the overall system under the assumptionthat each component operates with its unavoidablethermodynamic inefficiencies. For the system shown in

Fig. 1 the value _EUN

D;tot can be calculated as

_EUN

D;tot ¼_E

UN

D;A þ_E

UN

D;B þ_E

UN

D;C ¼ EP;tot

1

�UNC �UN

B

1

�UNA

� 1

� ��

þ1

�UNC

1

�UNB

� 1

� �þ

1

�UNC

� 1

� ��.

The avoidable part of exergy destruction for the overallsystem is

_EAV

D;tot ¼_ED;tot � _E

UN

D;tot ¼_ED;A � _E

UN

D;A

� �þ _ED;B � _E

UN

D;B

� �þ _ED;C � _E

UN

D;C

� �.

2.4.3. Combining the two options for splitting the exergy

destruction

The endogenous unavoidable part of the exergy destruction

( _EEN ;UN

D;K ) is the exergy destruction occurring within the kth

component when this component operates at its maximalattainable efficiency (�UN

k ) while all other components operatein an ideal way. For the theoretical system in Fig. 1 we write:

_EEN ;UN

D;C ¼ _EP;tot

1

�UNC

� 1

� �,

_EEN ;UN

D;B ¼ _EP;tot

1

�UNB

� 1

� �,

and

_EEN ;UN

D;A ¼ _EP;tot1

�UNA

� 1

� �.

The remaining parts of the exergy destruction in the kthcomponent are determined by the following simple equations:

_EEN ;AV

D;k ¼ _EEN

D;k �_E

EN ;UN

D;k ; _EEX ;UN

D;k ¼ _EUN

D;k �_E

EN ;UN

D;k ,

and

_EEX ;AV

D;k ¼ _EEX

D;k �_E

EX ;UN

D;k .

It is apparent that the sum of all four parts equals the totalexergy destruction within the component:

_EEN ;UN

D;k þ _EEX ;UN

D;k þ _EEN ;AV

D;k þ _EEX ;AV

D;k ¼ _ED;k.

3. Theoretical absorption refrigeration machine

A simple schematic of an absorption refrigerationmachine (ARM) is shown in Fig. 2a. For the thermo-dynamic cycle of an ARM, two heat sources and one sinkat different temperature levels are necessary [9,10]:

�
High-temperature heat source _Qhot (at Thot) as externalenergy (exergy) for the generator. This heat source isassociated with the fuel for the overall ARM, i.e._EF ;G ¼ _EF ;tot. For the ideal ARM: _Qhot ¼
_QG andThot=T11=T12.
� Middle-temperature heat sink _Q0 (T0)as cooling medium
for the condenser and absorber. For the ideal ARM:_Q0 ¼

_QA þ_QCD and T0=T13=T14=T15=T16.

�
Low-temperature heat source _Qcold (Tcold) as productfrom the evaporator. This heat source is associated withthe product of the overall ARM, i.e. _EP;E ¼ _EP;tot ¼
const for the analysis. For the ideal ARM: _Qcold ¼_QEV

and Tcold=T17=T18.

For simplifying the thermodynamic and the exergeticanalysis of an ARM, the overall process can be presentedas two separate (direct and inverse) Carnot cycles [10,11](Figs. 2b and c). In the present paper the same approach isused for evaluating the exogenous and endogenous exergydestruction in each component of an ARM. The conditionsfor the analysis of the ideal process include: _Qcold ¼ const

and _W direct ¼ _W inverse; Thot ¼ const and TG ¼ const;T0 ¼ const and TA ¼ const, TCD ¼ const; Tcold ¼ const

and TEV ¼ const.The ideal operation of a component is needed to estimate

the endogenous exergy destruction in the remaining systemcomponents.If we now introduce to the ideal process an irreversibility

only in the kth component, then the exergy destruction inthis component represents the endogenous exergy destruc-

tion _ED;k ¼ _EEN

D;k. The condition _Qcold ¼ const corresponds

to _Einverse

P;tot ¼ const; the condition _W direct ¼ _W inverse corre-

sponds to _Edirect

P;tot ¼ const if irreversibilities are introduced

only in the direct cycle.

3.1. Inverse cycle analysis

The inverse cycle includes four components: compressor(CM), condenser (CD), expander (EX) and evaporator(EV).The exergy destruction rates in the components of the

inverse cycle (Figs. 2b and 3a) are calculated by

_ED;CM ¼ _W CM � _E5 � _E8

� , (7)

_ED;CD ¼ _E5 � _E6

� � _E16 � _E15

� , (8)

_ED;EX ¼ _E6 � _E7

� � _W EX , (9)

ARTICLE IN PRESS

Fig. 2. Simple, one-effect absorption refrigeration machine (ARM): (a) schematic; (b) schematic-equivalent; (c) cycle of ARM on a T–s -diagram as two

separate Carnot cycles.

Fig. 3. Analysis of an ideal cycle, a real cycle and the required hybrid cycles: (a) inverse; (b) direct.

T. Morosuk, G. Tsatsaronis / Energy 33 (2008) 890–907894

_ED;EV ¼ _E7 � _E8

� � _E18 � _E17

� . (10)

In the following we introduce the terms used for thecycles involved in splitting the exergy destruction withinthe kth component into the endogenous and exogenousparts.

The ideal cycle consists only of reversible processes. Thesymbol I denotes the ideal cycle.

The hybrid cycle consists of one irreversible process whileall others are reversible processes. The symbol H is used fordescribing the points of the hybrid cycle.

The real cycle (symbol R) consists only of irreversibleprocesses.

The ideal inverse cycle consists of the states 5I–6I–7I–8I.The mass flow rate of the working fluid of the ideal inverse

cycle is determined by _m5I�6I�7I�8I ¼_Qcold

h8I�h7I:

In the following, we successively introduce irreversibil-ities in each component while keeping the operation of theremaining components ideal. In this way the hybrid cyclesare created:Introducing a temperature difference in the evaporator

equal to the temperature difference in the real processDTEV ¼ Tcold � TEV , the hybrid cycle becomes 5I–6I–

7Ha–8R and the corresponding mass flow rate is_m5I�6I�7Ha�8R ¼

_Qcoldh8R�h7Ha

:


The endogenous part of the exergy destruction in theevaporator is calculated by

_EEN

D;EV ¼ _m5I�6I�7Ha�8Rðe7Ha � e8RÞ � _m17�18hybrid

e 18ideal� e 17

ideal

� �

¼ _m5I�6I�7Ha�8Rðe7Ha � e8RÞ � _EQcold. ð11Þ

The ideal expander operates between states 6I and 7I,whereas the expansion process with irreversibilities is6I–7Hb (a hybrid cycle with irreversibilities only in theexpander is 5I–6I–7Hb–8I). For the real ARM, theexpansion process with irreversibilities is equivalent tothe throttling process. An analytical expression for theirreversibilities in expansion process is w EX

hybrid¼ w EX

ideal� ZEX .

The endogenous part of the exergy destruction in the realexpansion process is

_EEN

D;EX ¼ _m5I�6I�7Hb�8I s7Hb� s6I

� �T0 (12)

where _m5I�6I�7Hb�8I ¼_Qcold

h8I � h7Hb

.

The ideal heat removing process in the condenser is5I–6I. After introducing a temperature difference equal tothe temperature difference in the real process(DTCD ¼ TCD � Tenv), the hybrid cycle with irreversibilitiesonly in the condenser becomes 5Ha–6R–7I–8I, where_m5Ha�6R�7I�8I ¼ _m5I�6I�7I�8I : The endogenous part ofthe exergy destruction in the condensation process is

_EEN

D;CD ¼ _m5Ha�6R�7I�8I e5Ha � e6R

� � _m15�16

hybride 16

ideal� e 15

ideal

� �,

(13)

with

_m5Ha�6R�7I�8I h5Ha � h6R

� ¼ _m15�16

hybridh 16

ideal� h 15

ideal

� �.

The ideal compressor operates between states 8I and 5I

and the hybrid compression process between the tempera-tures of the ideal cycle (T0 and Tcold) is 8I–5Hb. The hybridcycle with irreversibilities only in the compression processis 5Hb–6I–7I–8I. Thus, the specific work of the compres-

sion process is w CMhybrid

¼

w CMidealZCM

: The endogenous part of the

exergy destruction in the compression process is

_EEN

D;CM ¼ _m5Hb�6I�7I�8I ðs5Hb� s8I ÞT0

¼ _m5Hb�6I�7I�8I w CMhybrid� ðe5Hb

� e8I Þ

� �ð14Þ

where

_m5Hb�6I�7I�8I ¼ _m5I�6I�7I�8I .

The cycle 5R�6R�7R–8R corresponds to the inversecycle with irreversibilities in all processes, i.e. to the realcycle. The value of the mass flow rate of the working fluidof the real cycle is _m5R�6R�7R�8R ¼

_Qcoldh8R�h7R

:

At this point we can conclude that introducingirreversibilities in one component of the inverse cycleinfluences, in general, the other components by increasingtheir entropy generation rate _Sgen;k through an increase inthe mass flow rate of the main working fluid and, as aconsequence in some cases, of the secondary workingfluids. The mass flow rate of the main working fluidchanges only if the difference (h8–h7) changes through achange of the irreversibilities within the sub-system. Thegraphical representation of the difference (h8–h7) is the area(d–8–7–c) on a T–s diagram (Fig. 3a). This area isassociated with the value of the specific cold heat rate.Finally,

_W inversereal¼ _m5R�6R�7R�8R

wCMideal

ZCM

� w EXideal� ZEX

� �. (15)

The unavoidable part of the exergy destruction in the kth

component of the inverse thermodynamic cycle ( _EUN

D;CM ,

_EUN

D;CD,_E

UN

D;EX ,_E

UN

D;EV ) can be determined by calculating a

cycle similar to the 5R�6R�7R–8R where all irreversi-bilities correspond to their unavoidable values associatedwith DTUN

CD , DTUNEV , ZUN

CM and ZUNEX .

The endogenous unavoidable part of the exergy destruc-

tion can be calculated for each component ( _EEN ;UN

D;CM ,

_EEN ;UN

D;CD , _EEN ;UN

D;EX , _EEN ;UN

D;EV ) according to Eqs. (11)–(14) using

the values DTUNCD ;DTUN

EV ; ZUNCM and ZUN

EX together with the

corresponding values of the mass flow rates of the mainworking fluid and the secondary working fluids.

3.2. Direct cycle analysis

The direct cycle consists of the following four compo-nents: generator (G), turbine (T), absorber (A) and pump(P). The exergy destruction rates in these components(Figs. 2b and c and 3b) are calculated by

_ED;P ¼ _W P � ð _E1 � _E4Þ, (16)

_ED;A ¼ ð _E3 � _E4Þ � ð _E14 � _E13Þ, (17)

_ED;T ¼ ð _E2 � _E3Þ � _W T , (18)

_ED;G ¼ ð _E11 � _E12Þ � ð _E2 � _E1Þ. (19)

The exergy destruction rate in each component will beanalyzed using Eq. (1) and Fig. 3b.The ideal direct cycle consists of the states 1I–2I–3I–4I.

The mass flow rate of the working fluid of the direct cycle isdetermined by

_m1I�2I�3I�4I ¼_W direct

w Tideal� w P

ideal

� � .

Let us introduce successively irreversibilities in eachcomponent of the direct cycle.

ARTICLE IN PRESST. Morosuk, G. Tsatsaronis / Energy 33 (2008) 890–907896

Introducing a temperature difference in the generator

equal to the temperature difference in the real cycle, DTG ¼

Thot � TG; the hybrid cycle becomes 1Ha–2R–3I�4I and the mass flow rate for this cycle is

_m1Ha�2R�3I�4I ¼_W direct

w Thybrid� w P

hybrid

¼_W direct

ðh2R � h3I Þ � ðh4I � h1HaÞ.

The endogenous part of exergy destruction in thegenerator is calculated by

_EEN

D;G ¼ _m11�12hybrid

e 11ideal� e 12

ideal

� �� _m1Ha�2R�3I�4I e2R � e1Ha

� ,

(20)

with

_m1Ha�2R�3I�4I h2R � h1Ha

� ¼ _m11�12

hybridh 11

ideal� h 12

ideal

� �.

The higher the irreversibilities in the generator, the largerthe mass flow rate _m11�12 when the thermodynamicproperties of points 11 and 12 remain unchanged.

The ideal heat removing process in the absorber is 3I–4I.After introducing a temperature difference equal to thetemperature difference in the real cycle, DTA ¼ TA � T0

the hybrid cycle with irreversibilities only in the absorber

becomes 1I–2I–3Ha–4R. The endogenous part of theexergy destruction of the absorption process is

_EEN

D;A ¼ _m1I�2I�3Ha�4Rðe3Ha � e4RÞ � _m14�13hybrid

e 14ideal� e 13

ideal

� �,

(21)

with

_m1I�2I�3Ha�4Rðh3H1� h4R

Þ ¼ _m14�13hybrid

h 14ideal� h 13

ideal

� �.

As before, the higher the irreversibilities in the absorber,the larger the mass flow rate _m13�14 when the thermo-dynamic properties of points 13 and 14 remain unchanged.

The ideal turbine operates between states 2I and 3I,whereas the expansion process with irreversibilities is2I–3Hb (a hybrid cycle with irreversibilities only in theexpander is 1I–2I–3Hb–4I). The specific work obtainedfrom the turbine can be determined by w T

hybrid¼ w T

ideal� ZT .

The endogenous part of exergy destruction in the realturbine is

_EEN

D;T ¼ _m1I�2I�3Hb�4I ðs3Hb� s2I ÞT0 (22)

where _m1I�2I�3Hb�4I ¼_W direct

w Tideal� ZT � w P

ideal

� � .

The ideal pump operates between states 4I–1I. Thehybrid process for the pump (4I–1Hb) is between thetemperatures of the ideal cycle (Thot and T0). The hybridcycle with irreversibilities only in the pump is1Hb–2I–3I–4I. The corresponding specific work for the

pump is

w Phybrid

¼

w Pideal

ZP

and the endogenous part of exergy destruction of the pumpbecomes

_EEN

D;P ¼ _m1Hb�2I�3I�4I ðs1Hb� s4I ÞT0, (23)

where

_m1Hb�2I�3I�4I ¼_W direct

w Tideal�

w PidealZP

� � .

The cycle 1R�2R�3R�4R corresponds to the real directcycle. The value of the mass flow rate of the working fluidof the direct cycle taking into account all irreversibilities is

_m1R�2R�3R�4R ¼_W direct

w Tideal� ZT �

w PidealZP

� � .

The mass flow rate of the working fluid of the directcycle changes every time irreversibilities are introduced ineach component because the area (1�2�3�4) associatedwith the value of the specific work for the direct cycle(wdirect ¼ wT�wP) never remains constant.The unavoidable part of the exergy destruction in each

component of the direct thermodynamic cycle ( _EUN

D;G,_E

UN

D;A,

_EUN

D;T ,_E

UN

D;P) can be determined by calculating a cycle similar

to 1R�2R�3R�4R where all irreversibilities correspond totheir unavoidable values, associated with DTUN

G , DTUNA ,

ZUNT and ZUN

P .The endogenous unavoidable part of the exergy destruc-

tion can be calculated for each component ( _EEN ;UN

D;G ,

_EEN ;UN

D;A , _EEN ;UN

D;T , _EEN ;UN

D;P ) according to Eqs. (20)–(23) using

the values DTUNG , DTUN

A , ZUNT and ZUN

P together will thecorresponding values of the mass flow rates of the mainworking fluid and the secondary working fluids.

4. Real absorption refrigeration machine

4.1. General aspects

The widely used algorithm for creating the real thermo-dynamic cycle of an ARM is the following [9]:

TEV ¼ T18 � DTEV ; TEV ! pEV ;

pA ¼ pEV 1� DpA

� ;

TCD ¼ T15 þ DTCD; TCD ! pCD;

pG ¼ pCD 1þ DpG

� ;

T2 ¼ T11 � DTG;

T4 ¼ T13 þ DTA;

xA ¼ CðT2; pGÞ;

xR ¼ CðT4; pAÞ;

xD ¼ CðT5; pCDÞ;

T1� ¼ CðX R; pGÞ:

9>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>;

(24)


The temperature T5 represents the middle temperatureof the vaporization process in the generator as T5 ¼

(T2+T1*)/2. For the mixtures ‘‘refrigerant–absorbent’’ suchas LiBr–H2O, it is always xD ¼ 1. For mixtures such asH2O–NH3, we have xDo1.

For the analysis of an ARM we will use the regularpractice of splitting the overall system of ARM into twosub-systems [10,11]:

�
Basic process (condenser, throttling valve and evapora-tor). The basic process is described by three processes ofthe inverse thermodynamic cycle (condensation, expan-sion and evaporation). The cycle of a basic process is5–6–7–8. The working fluid of the basic process is amixture with concentration xD, the mass flow rate ofwhich can be determined by
_m basicprocess

¼_Qcold

qcold

¼_Qcold

ðh8 � h7Þ, (25)

where _m5 ¼ _m6 ¼ _m7 ¼ _m8 ¼ _m basicprocess

:

�
Thermo-chemical compressor (generator, absorber, throt-tling valve and pump). The working fluid of the thermo-chemical compressor is a mixture with concentrations xR
for the strong solution and xA for the weak solution. Thethermo-chemical compressor is described by all processes ofthe direct thermodynamic cycle and the compressionprocess from the inverse thermodynamic cycle. The cycleof a thermo-chemical compressor is 30–4–1–1*–2–3. Themass flow rate of the mixture with the concentration xR is

_m4 ¼ _m1 ¼ f � _m basicprocess

. (26)

The mass flow rate of the mixture with the concentrationxA is

_m2 ¼ _m3 ¼ ðf � 1Þ � _m basicprocess

, (27)

where the circulation ratio of the mixture with theconcentration xR should be calculated as

f ¼xD � xA

xR � xA

. (28)

The mass flow rates of the heating and cooling media(secondary working fluids) of ARM should be determinedfrom the energy conservation equations for the corre-sponding component:

�
Generator
_QG ¼ _m basicprocess½ðh5 � h2Þ þ f ðh2 � h1Þ� ¼ _m11�12ðh11 � h12Þ.

(29)

�
Absorber
_QA ¼ _m basicprocess½ðh8 � h3Þ þ f ðh3 � h4Þ� ¼ _m13�14ðh14 � h13Þ.

(30)

Condenser
�
_QCD ¼ _m basicprocessðh5 � h6Þ ¼ _m15�16ðh16 � h15Þ. (31)

�
Evaporator
_QEV ¼ _m basicprocessðh8 � h7Þ ¼ _m17�18ðh17 � h18Þ. (32)

The compression process in the pump can be assumed asan ideal one (s4=s1) because the value _W P is very small(usually _W P=(0.01y0.015) _QG and introducing the realvalue as

_WPZP

cannot give any significant influence tothe analysis. Thus, the pump will be excluded from theanalysis [9–11].

4.2. Exergy analysis

Let us analyze all processes in an ARM from theexergetic point of view. Corresponding to Eq. (3a) theexergy balances for components of ARM are:

_ED;G ¼ ð _E11 � _E12Þ � ð _E2 þ _E5 � _E1Þ, (33)

_ED;A ¼ ð _E3 þ _E8 � _E4Þ � ð _E14 � _E13Þ, (34)

_ED;CD ¼ ð _E5 � _E6Þ � ð _E16 � _E15Þ, (35)

_ED;TVR ¼ ð _EM

6 �_E

M

7 Þ � ð_E

T

7 �_E

T

6 Þ, (36)

_ED;EV ¼ ð _E7 � _E8Þ � ð _E18 � _E17Þ. (37)

Two throttling valves exist in the ARM: the throttlingvalve for the mixture with the concentration xA (TVM)working at a temperature above T0 and the throttling valvefor the mixture with the concentration xD (TVR) workingat temperature below T0.According to the definition of the product and the fuel

[1,3] we analyze differently the TVM and the TVR. Thepurpose of the throttling valve TVM is only to decrease thepressure of the mixture with the concentration xA from pG

down to pA. Thus, TVM represents a dissipative compo-nent. The purpose of the throttling valve for the mixturewith the concentration xD (TVR) is to achieve a low

temperature ð _EP;TVR ¼ _ET

7 �_E

T

6 Þ at the expense of me-

chanical exergy ð _EF ;TVR ¼ _EM

6 �_E

M

7 Þ [6].

For the exergetic analysis of an ARM, we split the totalexergy associated with a material flow into its physical andchemical parts for flows _E1 through _E8

_Ej ¼ _EPH

j þ_E

CH

j (38a)

or

_Ej ¼ _mkePHj þ _mkeCH

j . (38b)

The specific physical exergy of the jth flow is

ePHj ¼ hj � hj;0 � T0ðsj � sj;0Þ. (39)

ARTICLE IN PRESS

Fig. 4. The reference points 0 for calculating the exergy values for

mixtures with various concentrations (xA, xR, xD, etc.).


For flows _E6 and _E7 splitting the physical exergy intothermal and mechanical parts is necessary [12]

ePHj ¼ ½ðhj � hj;MÞ � T0ðsj � sj;M Þ�p¼const|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

eT

þ ½ðhj;M � hj;0Þ � T0ðsj;M � sj;0Þ�T0¼const|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}eM

ð40Þ

with the point M defined at the pressure p and thetemperature T0.

The specific chemical exergy of the jth flow for themixture ‘‘refrigerant–absorbent’’ can be calculated as [1]

eCHj ¼ xj � e

CHrefrigerant þ ð1� xjÞ � e

CHabsorbent þ wrev

Xj, (41)

with

wrevXj¼ ½hj;0 � xjhrefrigerant;0 � ð1� xjÞhabsorbent;0�

� T0½sj;0 � xjsrefrigerant;0 � ð1� xjÞsabsorbent;0�, ð42Þ

where wrevXj

is the specific work associated with the mixing ofpure refrigerant (xD ¼ 1) and pure absorbent (xD ¼ 0).

Let us illustrate the location of the points mentionedabove on a h–x diagram (Fig. 4). The points 0 for the pureabsorbent and the pure refrigerant are fixed. The positionof point 0 for calculating the physical exergy will depend onthe concentration of the mixture (x). Many points arelocated on the isotherm of T0 (for example, T0 ¼

293.15 1C) at pressure p0 (for example, p0 ¼ 0.1MPa)—Fig. 4.

Thus, for the exergetic analysis of ARM three values ofthe specific chemical exergy should be determined forconcentrations xA, xR and xD as well as three points 0 forcalculating the physical exergy at the respective concentra-tions of the mixture.

4.3. Exergy analysis of the real cycle

All calculations reported here were conducted with theaid of the EES software [13].

For the analysis of an ARM, the following operationalconditions were used here: The temperatures T11, T13, T15,T17 and T18 are known and cannot be changed but thevalues of T12, T14 and T16 are variable (Fig. 2a). Theworking fluid is a mixture NH3–H2O, the cold heat rate is_Qcold ¼ 100 kW; Thot ¼ T11 ¼ 413.2 K; T0 ¼ T13 ¼ T15

¼ 293.2 K; Tcold ¼ T18 ¼ 263.2 K; T17 ¼ 268.2K. Notethat all heat transfer processes can be assumed as isobaric.

Fig. 5 represents the real thermodynamic cycle of anARM with all irreversibilities included: DTCD; DTEV; DTG

and DpG; DTA and DpA. For the real ARM we assumedDTCD ¼ 5K; DTEV ¼ 5 K; DTG ¼ 10K and DpG ¼

0.02MPa; DTA ¼ 3K and DpA ¼ 0.015MPa as shown inTable 1.

For the exergetic analysis of an ARM the values

eCHabsorbent ¼ eCH

H2O ¼ 45 kJ/kmol and eCHrefrigerant ¼ eCH

NH3¼

336 684 kJ/kmol were used [1,14]. For the real system we

present the detailed exergetic analysis (Tables 1, 2 and 10)but for further calculations only the final results are given.For the cycles discussed below (Figs. 6–8), the values of

T11 and the corresponding mass flow rate _m11�12 as well asT13 and _m13�14; T15 and _m15�16; T17, T18 and _m17�18 remainconstant. These values are given for the real cycle in Table1 and are not repeated in Tables 3–9.

4.4. Exergy analysis of the theoretical cycle

The thermodynamic analysis discussed above hasshown that creating a theoretical cycle of an ARM isnecessary for splitting the exergy destruction withineach component into the endogenous and exogenousparts. Note that for the theoretical cycle both thrott-ling valves TVM and TVR should be replaced byexpanders according to Figs. 2b and c and 3, i.e. s2=s3and s6=s7 [5,6].For creating the theoretical cycle, the following assump-

tions are usually made [9]: DTCD ¼ 0; DTEV ¼ 0; DpG ¼ 0;DpA ¼ 0; T2 ¼ T11 and T4 ¼ T13. These conditions corre-spond to the maximal value of f (Eq. (28)) whichsimultaneously is the necessary and the sufficient conditionfor defining the theoretical thermodynamic cycle of anARM for the energy analysis.


The creation of a theoretical cycle of an ARM for theexergetic analysis needs some additional discussion: Theconditions T2 ¼ T11 (DTG ¼ 0) and DpG ¼ 0 describethe theoretical heat and mass transfer in the generator.

Table 1

Thermodynamic data for the real ARM

Stream Material flow _m (kg/s) T (K) p (MPa) x (kg/kg) h (kJ/kg) s

1R NH3–H2O 0.6727 296.2 1.204 0.4374 �131.5 0

1*R NH3–H2O 0.6727 355.7 1.204 0.4374

2R NH3–H2O 0.4308 403.1 1.204 0.2227 414.7 1

3R NH3–H2O 0.4308 353.7 0.201 0.2227 414.7 1

4R NH3–H2O 0.6727 296.1 0.201 0.4374 �132.7 0

5R NH3–H2O 0.1969 379.4 1.003 0.9074 1603.0 5

6R NH3–H2O 0.1969 301.0 1.003 0.9074 63.55 0

7R NH3–H2O 0.1969 260.5 0.236 0.9074 63.55 0

8R NH3–H2O 0.1969 263.1 0.236 0.9074 571.3 2

11R Air 14.23 413.2 0.15 414.6 7

12R Air 14.23 373.2 0.15 374.0 6

13R Water 4.477 293.2 0.1 83.93 0

14R Water 4.477 313.2 0.1 167.6 0

15R Water 3.625 293.2 0.1 83.93 0

16R Water 3.625 313.2 0.1 167.6 0

17R Air 19.88 268.2 0.1 414.6 7

18R Air 19.88 263.2 0.1 307.6 6

Fig. 5. The real cycle of an absorption refrigeration machine (30—

saturated liquid; 300—saturated vapor; 1*—beginning of the boiling

process for a mixture with the concentration xR in the generator).

Similarly, the conditions T4 ¼ T13 (DTA ¼ 0) and DpA ¼ 0correspond to the theoretical heat and mass transferprocesses in the absorber. The conditions DTCD ¼ 0 andDTEV ¼ 0 correspond only to xD ¼ 1 and cannot beassumed for the exergetic analysis of an ARM if xDo1.A more general case is the one in which xD is kept constant,thus DTCD ¼ const and DTEV ¼ const (where the valuesDTCD and DTEV correspond to the real cycle), i.e.pEV ¼ const and pCD ¼ const for the analysis. The condi-tions T6 ¼ T15 and T8 ¼ T17 are assumed for the theore-tical condenser and evaporator, respectively.Fig. 6 shows the theoretical cycle of the ARM, the

calculation data of which are given in Tables 3 and 10.

5. Splitting the exergy destruction

5.1. Unavoidable and avoidable parts

For splitting the total exergy destruction within eachcomponent of the ARM (according to Section 2.2) into theunavoidable and avoidable parts we need to create a cyclewith only unavoidable irreversibilities (Fig. 7). To calculatethe values of unavoidable irreversibilities, the followingassumptions were made: T8 ¼ T17–DT8 with DT8 ¼ 0.2 K;T6 ¼ T15+DT6 with DT6 ¼ 0.2K; DTG ¼ 0.2K andDpG ¼ 0.005MPa; DTA ¼ 0.2K and DpA ¼ 0.005MPa.Note that for the exergetic analysis of the ARM with

unavoidable exergy destruction both throttling valves areincluded in the structure of ARM.The thermodynamic data for this cycle are given in Table

4, and the avoidable and unavoidable parts of the exergydestruction are given in Table 10.

5.2. Endogenous and exogenous parts

The theoretical basis for calculating the endogenousexergy destruction and the endogenous unavoidable exergy

(kJ/kgK) eCH (kJ/kg) ePH (kJ/kg) eM (kJ/kg) eT (kJ/kg) e (kJ/kg)

.2012 8599 6.023 8605

.652 4337 73.91 4411

.706 4337 57.91 4395

.2012 8599 4.843 8604

.218 17 959 353.1 18 312

.444 17 954 212.9 212.4 0.5 18 167

.496 17 959 197.6 102.2 95.4 18 157

.429 17 959 138.7 18 098

.077 53.76 53.76

.974 43.47 43.47

.296 0 0

.572 2.73 2.73

.296 0 0

.572 2.73 2.73

.077 1.138 1.138

.778 1.658 1.658

ARTICLE IN PRESS

Table 2

Thermodynamic properties used for the exergetic calculations of the mixture NH3-H2O for the points of the real cycle

For a point T (K) p (MPa) x (kg/kg) h (kJ/kg) s (kJ/kg �K)

Reference points 4, 1 293.2 0.1 0.4374 77.75 0.9356

2, 3 293.2 0.1 0.2227 �63.18 0.2737

5, 6, 7, 8 293.2 0.1 0.9074 1167 4.933

11,12,17,18 293.2 0.1 293.4 6.847

13,14,15,16 293.2 0.1 83.93 0.2962

Point M 6 293.2 1.003 0.9074 26.11 0.3181

Point M 7 293.2 0.2362 0.9074 1075 4.271

Fig. 6. The theoretical cycle of an absorption refrigeration machine. Fig. 7. Cycle of an absorption refrigeration machine having only the

unavoidable irreversibilities.


destruction is the same. Therefore, two different values ofefficiency are used in the calculation:

�
the real efficiency of a component is used to calculate theendogenous part; � the efficiency corresponding to the unavoidable exergy
destruction is used for calculating the endogenousunavoidable part of the exergy destruction.

In the following we briefly discuss the application ofthese concepts to the components of an ARM. The values

of the endogenous and exogenous exergy destruction aswell as the splitting of exergy destruction into four partsare given in Table 10.

5.2.1. Generator

Initially we assume that only the generator of the ARMoperates with irreversibilities while all other componentsare theoretical (Fig. 8a). The operating conditions of thegenerator are given by DTG and DpG, with DTG ¼ 5K andDpG ¼ 0.02MPa for calculating the value of _E

EN

D;G andDTG ¼ 0.2K and DpG ¼ 0.005MPa for calculating the

ARTICLE IN PRESS

Fig. 8. Hybrid cycles of an absorption refrigeration machine for calculating the endogenous exergy destruction in the (a) generator; (b) absorber;

(c) condenser; and (d) evaporator.


value of _EEN ;UN

D;G . The thermodynamic data for calculatingthe endogenous and endogenous unavoidable exergydestruction in the generator are given in Table 5.

5.2.2. Absorber

The endogenous exergy destruction within the absorberis calculated at DTA ¼ 5K and DpA ¼ 0.015MPa when allother components are theoretical. The value of endogenousunavoidable exergy destruction corresponds toDTA ¼ 0.2K and DpA ¼ 0.005MPa (Fig. 8b and Table 6).

The throttling valve TVM is a dissipative component. Ifwe assume that this component serves exclusively the

absorber then we should consider the two componentstogether and calculate the exergy destruction in a hybridprocess in which only the absorber and the TVM areirreversible. The endogenous exergy destruction for thesystem (absorber+TVM) amounts to 30.4 kW whereas theendogenous exergy destruction of the absorber alone is29.92 kW. It is apparent that the effect of TVM is relativelysmall.

5.2.3. Condenser

Now we assume that only the condenser in the ARMoperates with irreversibilities while all other components

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Table 3

Thermodynamic data for the theoretical ARM

Stream Material flow _m (kg/s) T (K) p (MPa) x (kg/kg) e (kJ/kg)

1T NH3–H2O 0.2914 293.2 1.003 0.4847 9553

2T NH3–H2O 0.1628 413.1 1.003 0.1507 3009

3T NH3–H2O 0.1628 370.0 0.2362 0.1507 2996

4T NH3–H2O 0.2914 293.1 0.2362 0.4847 9552

5T ¼ 5R NH3–H2O 0.1286 379.4 1.003 0.9074 18 312

6T NH3–H2O 0.1286 293.1 1.003 0.9074 18 172

7T NH3–H2O 0.1286 260.4 0.2362 0.9074 18 163

8T NH3–H2O 0.1286 268.1 0.2362 0.9074 18 075

12T Air 14.23 352.7 0.15 39.49

14T Water 4.477 305.2 0.1 1.0

16T Water 3.625 306.5 0.1 1.237

Table 4

Thermodynamic data for the ARM having only unavoidable irreversibilities


1RU NH3–H2O 0.3119 293.4 1.054 0.4742 9342

2RU NH3–H2O 0.1808 413.0 1.054 0.16 3192

3RU NH3–H2O 0.1808 367.9 0.2244 0.16 3180

4RU NH3–H2O 0.3119 293.4 0.2244 0.4742 9341

5RU NH3-H2O 0.1311 379.4 1.003 0.9074 18 312

6RU NH3–H2O 0.1311 293.4 1.003 0.9074 18 172

7RU NH3–H2O 0.1311 260.4 0.2362 0.9074 18 161

8RU NH3–H2O 0.1311 268.0 0.2362 0.9074 18 076

12RU Air 14.23 389.3 0.15 47.23

14RU Water 4.477 305.9 0.1 1.128

16RU Water 3.625 306.8 0.1 1.284

Table 5

Thermodynamic data for the hybrid ARM with irreversibilities only in the generator

Material flow Stream Endogenous Stream Endogenous unavoidable

_m (kg/s) T (K) p (MPa) x (kg/kg) e (kJ/kg) _m (kg/s) T (K) p (MPa) x (kg/kg) e (kJ/kg)

NH3–H2O 1H 0.3360 293.2 1.204 0.4847 9553 1HU 0.2960 293.2 1.054 0.4847 9553

NH3–H2O 2R 0.2074 403.1 1.204 0.2227 4411 2RU 0.1674 412.9 1.054 0.16 3192

NH3–H2O 3H 0.2074 356.7 0.2362 0.2227 4394 3HU 0.1674 368.6 0.2362 0.16 3178

NH3–H2O 4T 0.3360 293.1 0.2362 0.4847 9552 4T 0.2960 293.1 0.2362 0.4847 9552

NH3–H2O 5R 0.1286 379.4 1.003 0.9074 18312 5R 0.1286 379.4 1.003 0.9074 18 312

NH3–H2O 6T 0.1286 293.1 1.003 0.9074 18172 6T 0.1286 293.1 1.003 0.9074 18 172

NH3–H2O 7T 0.1286 260.4 0.2362 0.9074 18163 7T 0.1286 260.4 0.2362 0.9074 18 163

NH3–H2O 8T 0.1286 268.1 0.2362 0.9074 18075 8T 0.1286 268.1 0.2362 0.9074 18 075

Air 12H 14.23 389.5 0.15 47.28 12HU 14.23 390.1 0.15 47.45

Water 14H 4.477 305.7 0.1 1.096 14HU 4.477 305.3 0.1 1.017

Water 16H 3.625 306.5 0.1 1.237 16HU 3.625 306.5 0.1 1.237


are theoretical. The real condition for the condenser is theplacement of point 6 on the line of saturated liquid(Figs. 6 and 8c). Thus, this assumption should be used alsofor calculating the value of _E

EN

D;CD. The value of theendogenous unavoidable exergy in the condenser corre-sponds to T6=T15+DT6 with DT6=0.2K (Fig. 8c andTable 7).

5.2.4. Evaporator

Now the evaporator in the ARM operates under realconditions while all other components are theoretical(Fig. 8d). The real condition for the evaporator forcalculating the value of _E

EN

D;EV is T8 ¼ T18; the value ofthe endogenous unavoidable exergy destruction can becalculated if T8 ¼ T17+DT8 with DT8 ¼ 0.2K (Table 8).

ARTICLE IN PRESS

Table 6

Thermodynamic data for the hybrid ARM with irreversibilities only in the absorber



NH3-H2O 1H 0.3394 296.2 1.003 0.4374 8605 1HU 0.3008 293.4 1.003 0.4742 9342

NH3–H2O 2T 0.2108 413.1 1.003 0.1507 3009 2T 0.1722 413.1 1.003 0.1507 3009

NH3–H2O 3H 0.2108 365.9 0.2008 0.1507 2994 3HU 0.1722 368.7 0.2244 0.1507 2995

NH3–H2O 4R 0.3394 296.1 0.2008 0.4374 8604 4RU 0.3008 293.3 0.2244 0.4742 9341

NH3–H2O 5R 0.1286 379.4 1.003 0.9074 18 312 5R 0.1286 379.4 1.003 0.9074 18 312

NH3–H2O 6T 0.1286 293.1 1.003 0.9074 18 172 6T 0.1286 293.1 1.003 0.9074 18 172

NH3–H2O 7T 0.1286 260.4 0.2362 0.9074 18 163 7T 0.1286 260.4 0.2362 0.9074 18 163

NH3–H2O 8T 0.1286 268.1 0.2362 0.9074 18 075 8T 0.1286 268.1 0.2362 0.9074 18 075

Air 12H 14.23 388.5 0.15 47.05 12HU 14.23 389.9 0.15 47.39

Water 14H 4.477 306.4 0.1 1.222 14HU 4.477 305.4 0.1 1.049

Water 16H 3.625 306.5 0.1 1.237 16HU 3.625 306.5 0.1 1.237

Table 7

Thermodynamic data for the hybrid ARM with irreversibilities only in the condenser



NH3–H2O 1T 0.3035 293.2 1.003 0.4847 9553 1T 0.2917 293.2 1.003 0.4847 9553

NH3–H2O 2T 0.1695 413.1 1.003 0.1507 3009 2T 0.1629 413.1 1.003 0.1507 3009

NH3–H2O 3T 0.1695 370.0 0.2362 0.1507 2996 3T 0.1629 370.0 0.2362 0.1507 2996

NH3-H2O 4T 0.3035 293.1 0.2362 0.4847 9552 4T 0.2917 293.1 0.2362 0.4847 9552

NH3–H2O 5R 0.134 379.4 1.003 0.9074 18 312 5R 0.1288 379.4 1.003 0.9074 18 312

NH3-H2O 6R 0.134 301.0 1.003 0.9074 18 167 6RU 0.1288 293.4 1.003 0.9074 18 172

NH3–H2O 7H 0.134 260.5 0.2362 0.9074 18 155 7HU 0.1288 260.4 0.2362 0.9074 18 163

NH3–H2O 8T 0.134 268.1 0.2362 0.9074 18 075 8T 0.1288 268.1 0.2362 0.9074 18 075

Air 12H 14.23 389.3 0.15 47.25 12HU 14.23 390.2 0.15 47.48

Water 14H 4.477 305.7 0.1 1.085 14HU 4.477 305.2 0.1 1.003

Water 16H 3.625 306.7 0.1 1.279 16HU 3.625 306.5 0.1 1.238

Table 8

Thermodynamic data for the hybrid ARM with irreversibilities only in the evaporator



NH3–H2O 1T 0.4088 293.2 1.003 0.4847 9553 1T 0.2933 293.2 1.003 0.4847 9553

NH3–H2O 2T 0.2283 413.1 1.003 0.1507 3009 2T 0.1638 413.1 1.003 0.1507 3009

NH3–H2O 3T 0.2283 370.0 0.2362 0.1507 2996 3T 0.1638 370.0 0.2362 0.1507 2996

NH3–H2O 4T 0.4088 293.1 0.2362 0.4847 9552 4T 0.2933 293.1 0.2362 0.4847 9552

NH3–H2O 5R 0.1805 379.4 1.003 0.9074 18 312 5R 0.1295 379.4 1.003 0.9074 18 312

NH3–H2O 6T 0.1805 293.1 1.003 0.9074 18 172 6T 0.1295 293.1 1.003 0.9074 18 172

NH3–H2O 7T 0.1805 260.4 0.2362 0.9074 18 163 7T 0.1295 260.4 0.2362 0.9074 18 163

NH3–H2O 8R 0.1805 263.1 0.2362 0.9074 18 098 8RU 0.1295 268.0 0.2362 0.9074 18 076

Air 12H 14.23 381 0.15 45.24 12HU 14.23 390.1 0.15 47.45

Water 14H 4.477 307.8 0.1 1.49 14HU 4.477 305.2 0.1 1.008

Water 16H 3.625 311.9 0.1 2.409 16HU 3.625 306.6 0.1 1.253


5.2.5. Throttling valve (TVR)

The presence of a throttling valve in the schematic of anARM means real conditions for the expansion process.Thus, the endogenous exergy destruction and the endo-genous unavoidable exergy destruction in the throttling

valve TVR are equal. A cycle with the TVR can beobtained if in the theoretical ARM (Fig. 6) point 6corresponds to point 7, as in Fig. 5 for the real ARM(Table 9).Note that the throttling valve is the only component in a

refrigeration machine that cannot be improved through

ARTICLE IN PRESS

Table 9

Thermodynamic data for the hybrid ARM with irreversibilities only in the throttling valve TVR


1T NH3–H2O 0.2947 293.2 1.003 0.4847 9553

2T NH3–H2O 0.1646 413.1 1.003 0.1507 3009

3T NH3–H2O 0.1646 370.0 0.2362 0.1507 2996

4T NH3–H2O 0.2947 293.1 0.2362 0.4847 9552

5R NH3–H2O 0.1301 379.4 1.003 0.9074 18312

6T NH3–H2O 0.1301 293.1 1.003 0.9074 18 172a

7H NH3–H2O 0.1301 260.4 0.2362 0.9074 18 161a

8T NH3–H2O 0.1301 268.1 0.2362 0.9074 18075

12H Air 14.23 390.0 0.15 47.42

14H Water 4.477 305.4 0.1 1.023

16H Water 3.625 306.7 0.1 1.265

aWhere eT6 ¼ 0.1 kJ/kg and eM

6 ¼ 212.5 kJ/kg; eT7 ¼ 99.9 kJ/kg and eM

7 ¼ 102.2 kJ/kg.


changes in the same component. Decreasing the exergydestruction in the throttling valve can be achieved onlythrough decreasing the exogenous part of the exergydestruction, i.e. through improving the other componentsand their structure in the overall system.

6. Results and discussion

All results from the exergy analysis are summarized inTable 10. A conventional exergy analysis (without splittingthe exergy destruction) would suggest that first thecomponents with the highest values of y�k (Eq. (4)) shouldbe improved. Thus, the components should be improved inthe following order: absorber (40.4%), generator (39.2%),condenser (16.4%) and evaporator (1.2%).

When we consider the information provided through thesplittings of the exergy destruction (Table 10), the

following additional conclusions are obtained: _EUN

D;tot ¼

70.96 kW (or 65.8% of the total exergy destruction) within

the real ARM is unavoidable, while _EEN ;UN

D;tot ¼ 54.61 kW

(or 50.1%) depends on the components themselves. Thus,the total exergy destruction in the real ARM after allpossible improvements cannot be lower than 54.61 kW.

Now we will describe the iteration steps for improvingthe ARM according to the information related toendogenous avoidable and exogenous avoidable exergydestruction within each component (last two columns inTable 10).

The component that should be improved first is the

generator: The value EEN ;AVD;G is the highest among all

components, and _EEN ;AV

D;G 4 _EEX ;AV

D;G . This means that

improving the generator itself is more important fordecreasing the value of _ED;G than improving othercomponents. In addition, an improvement in the generatorwill reduce the exergy destruction also in other compo-nents, in which the exogenous avoidable exergy destructionis larger than the endogenous avoidable.

The absorber is the component that should be improvedin the second place based on the value of EEN ;AV

D;A (4.48 kW).

It should be mentioned, however, that this value is by afactor of 2.9 lower than the value of EEX ;AV

D;A . This meansthat the total exergy destruction in the absorber canbe reduced mainly through improvements in othercomponents.

The potential for improving just the condenser isrelatively small and this component can be improvedmainly through reducing the exergy destruction in other

components because of _EEN ;AV

D;CD 5 _EEX ;AV

D;CD :

We obtain interesting information from the advancedexergetic analysis of the evaporator. Splitting the exergydestruction into endogenous and exogenous parts for the

evaporator shows that _EEN

D;EV4 _ED;EV , thus _EEX

D;EVo0. The

same occurs when calculating the value of endogenous

unavoidable exergy destruction: _EEN ;UN

D;EV 4 _EUN

D;EV with

_EEX ;UN

D;EV o0 and _EEX ;AV

D;EV o0. A detailed analysis of this

effect can be made with the aid of Fig. 9 where theprocesses of condensation, throttling (or expansion) andevaporation on a T-s diagram (created for the mixture withconcentration xD) are given.

The line 5R–6R–7R–8R represents the cycle of the basicprocess with real irreversibilities according to Fig. 5. Forthis case the value of the mass flow rate is determined as

_m basicprocess

¼_Qcold

h8R�h7R¼ 0.1969 kg/s (Table 1).

For calculating the value of the endogenous exergydestruction in the evaporator, the operating conditions forthe condenser and the TVR change (according to theinformation provided in Section 4.4, Fig. 8d and Table 8).Now the evaporation process begins at point 7T instead ofpoint 7R. This leads to a decrease of the value of thetemperature at the inlet of the evaporator (T7ToT7R andh7Toh7R) and to a decrease of the value of

_m basicprocess

¼_Qcold

h8R�h7T¼ 0.1805 kg/s. The value of the endogen-

ous exergy destruction in the evaporator is larger than theexergy destruction in the real process because the increasein specific entropy generation outweighs the effect of thedecrease of the mass flow rate.

ARTIC

LEIN

PRES

S

Table 10

Summary of the results from advanced exergy analysis of the ARMa

Component Real ARM Theoretical ARM _EEN;UN

D;k

(kW)

_EUN

D;k

(kW)

_EAV

D;k

(kW)

_EEN

D;k

(kW)

_EEX

D;k

(kW)

Splitting ð _ED;kÞreal (kW)

_EF ;k

(kW)

_EP;k

(kW)

_ED;k

(kW)

ek

(%)

yk

(%)

yka

(%)_E

UN

D;k (kW) _EAV

D;k (kW)

_EEN;UN

D;k

(kW)

_EEX ;UN

D;k

(kW)

_EEN;AV

D;k

(kW)

_EEX ;AV

D;k

(kW)

Thermo–chemical

compressor

G 146.4 104.1 42.29 71.1 28.9 39.2 15.87 28.94 13.35 38.85 3.44 28.69 0.25 10.16 3.19

(68.4%) (31.6%) (91.9%) (8.1%) (67.8%) (0.6%) (23.9%) (7.7%)

A 55.76 12.22 43.53 21.9 29.7 40.4 24.31 26.08 17.45 29.92 13.61 25.44 0.64 4.48 12.97

(59.9%) (40.1%) (68.7%) (31.3%) (58.4%) (1.5%) (10.3%) (29.8%)

Pb 0.81 0.81 0

Basic process CD 27.61 9.896 17.71 35.8 12.1 16.4 13.54 13.72 3.99 14.09 3.62 13.55 0.17 0.54 3.45

(77.5%) (22.5%) (79.6%) (20.4%) (76.5%) (0.9%) (3.1%) (19.5%)

TVR 21.74 18.72 3.02 8.6 2.1 2.8 – 1.392 1.628 1.365 1.655 1.365 0.027 0 1.628

(46.1%) (53.9%) (45.2%) (54.8%) (45.2%) (0.9%) (53.9%)

EV 11.59 10.36 1.23 89.4 0.8 1.2 0.88 0.816 0.414 1.371 –0.141 0.9 –0.084 0.471 –0.057

(66.7%) (33.6%) (111%) (–11%) (73.2%) (–6.8%) (38.3%) (–4.7%)

Overall

system

147.2 10.36 107.78 7.07 73.6 100 54.6 70.95 36.83 85.6 22.18 69.945 1.0 15.651 21.181

(50.1%) (65.8%) (34.2%) (79.4%) (20.6%) (64.9%) (0.9%) (14.5%) (19.7%)

For the ARM, the exergy loss is _EL;tot ¼ _E14 þ _E16 ¼ 22.12 kW.aTVM is a dissipative component. The exergy destruction within the TVM, which is not split, is not shown in this table.bThe pump was assumed to be ideal.

T.

Mo

rosu

k,

G.

Tsa

tsaro

nis

/E

nerg

y3

3(

20

08

)8

90

–9

07

905

ARTICLE IN PRESS

Fig. 9. T–s diagram for the NH3-H2O mixture with the concentration xD

used to explain the advanced exergetic analysis of the evaporator.


A similar analysis can be conducted when calculating thevalue of the endogenous unavoidable exergy destruction inthe evaporator (process 7T–8RU in Fig. 9 and Table 8),where T8RU4T8R and h8RU4h8R, thus _m basic

process¼

_Qcoldh8RU�h7T

¼ 0.1295 kg/s.

Let us now assume that the designer would like toimprove the evaporator so that the schematic of the ARM(Fig. 2a) and the concentration xD ¼ 0.9047 kg/kg remainconstant. Note that the values T17, T18 and _m17�18 cannotbe changed because they represent the product of theoverall ARM. For the real ARM T8 ¼ T18 and there isonly one way for decreasing the value of entropygeneration in the evaporator. It is changing the thermo-dynamic parameters at point 7R, that means changing thelocation of point 7R on a T–s diagram, for example, aspoint (7R) in Fig. 9. The location of point 7R depends onthe location of point 6R. Therefore, the location of point6R should also be changed, for example, point (6R) inFig. 9, through increasing the temperature and pressure atpoint (6R). Increasing the pressure pCD leads to an increasein the value of pG and, therefore, in the values of exergydestruction in all components of the ARM through anincrease in the values of the specific entropy generation ineach component and of the mass flow rate of the workingfluid because (h8R–h7R)4(h8R–h(7R)).

The above discussion shows that decreasing the exergydestruction within the evaporator leads to an increase inthe other components. This is denoted by the negative sign

in the values of _EEX ;UN

D;EV and _EEX ;AV

D;EV :

Improving the condensation and evaporation processesis possible only by structural changes in the overall ARM,i.e. through introducing a rectification (or rectification–dephlegmation) process after the generator. This processgives the possibility to vary the value of concentration xD

(i.e. varying the temperature glide at pCD and pEV), which

leads to lower exergy destructions in the condenser andevaporator.The results obtained through an advanced exergy

analysis for the ARM cannot be compared directly withthe results by other authors. There are many publicationswhere only a conventional exergy analysis for the ARM isused. For example, one of the first publications whereexergy analysis was applied to an ARM is Ref. [15] and hasbeen repeated many times, since then (e.g., [16]). Even thesensitivity exergy-based analysis for an ARM given inRef. [17] does not provide detailed information about theinterconnections among components within an ARM andmisses some options for improving an ARM.Some of the results presented here have been found

qualitatively in other studies [9,18] of an ARM (not usingthe exergy concept). However, none of these studies couldfind all the results reported here (obtained directly throughan advanced exergy analysis) and assign numbers to theconclusions.

7. Conclusions

The advanced exergetic evaluation of an ARM suppliesuseful additional information that is not provided by anexergy analysis without splitting the exergy destructionwithin the components of an ARM.The avoidable exergy destruction identifies the potential

for improving each system component. The values of theavoidable endogenous and avoidable exogenous exergydestruction establish the relative importance of improvingsingle components and the structure of the overall system.The advanced exergetic evaluation can be extended to

consider components in pairs or larger groups in an effortto completely understand the thermodynamic interactionsamong the system components. However, all theseconsiderations become more powerful when they are usedfor the exergoeconomic evaluation of the same system. Insuch a calculation, not only the exergy destruction, but alsothe investment cost for each system components is splitinto avoidable/unavoidable and endogenous/exogenousparts [19]. An advanced exergoeconomic evaluation shouldbe conducted only when the investment costs for thedifferent cases can be assessed with acceptable accuracy,whereas an advanced exergetic evaluation, as reportedhere, is always helpful.

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A New Approach to the Exergy Analysis of Absorption Refrigeration Machines_SD

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