A SOLAR ADSORPTION REFRIGERATION SYSTEM OPERATING AT NEAR ATMOSPHERIC PRESSURE

7/27/2019 A SOLAR ADSORPTION REFRIGERATION SYSTEM OPERATING AT NEAR ATMOSPHERIC PRESSURE

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MONASH UNIVERSITYTHESIS ACCEPTED IN SATISFACTION OF THEREQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYON .-,.. 7 F e b r u a r y 2 0 0 3

V Sec. Research G radu ate School CommitteeUnder the copyright Act 1968, this thesis must be used only under thenormal conditions of scholarly fair dealing for the purposes ofresearch, criticism or review. In particular no results or conclusionsshould b e extra cted f rom it, nor should it be copied or closelypara phrase d in whole or in part without the written consent of theau thor . P rope r wr i t t en acknowledgem ent shou ld b e m ade fo r anyassistance obtained f rom this thesis .


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AddendumQuestion: The examiner understands that the candidate constructed a re frigerat ion system test rig, bu twonder why the refrigeration characteristics such as the refrigeration capacity and the COP of thesystem are not prese nted in the thesis.Answer: One of the major objectives of this thesis is to study the fea sibility of solving the prob lem ofair leaking into the adsorption refrigeration system which works at vacuum pressure. In order to seethe progress of the adsorption and the cooling effect (eg, dew, frost) objectively, the evaporator ismade w ith glass, and it is not insulated. This ar range ment, on the other hand, ma kes it difficult toprecisely measure the refrigerat ion capacity. Therefore , the experimental refrigerat ion capacity andthe Coefficient of Performa nce (COP) of the system a re not prese nted.Question: Some key points of heat t ransfer analyses on the collector/desorption bed need to beclarified, for instance:o The desorption process is a problem of forced convection with variab le fluid prope rties;why did the candidate model the problem as a conduction problem (Eq. 4.1)?Justification is nee ded in this rega rd.

o Compa ring Eqs. (4.1) and (4.16)s why is the ter md2T/dz2

omitted? Physically, both the concentration and the tem pera ture vary along the z-axis.Answer: Yes, the desorption process is also a problem of forced convection with variable fluidpropert ies. But the main concern here is the fixed bed b eing heated by the bou ndary , the pipe. For afluid flowing at steady rate through the voids in a column, to simplify the calculation, it could beapproximately taken as a conduction problem, and one of the expressions of the effective (apparent)be d conductivity is given b y Flix and Neill (McAda ms, Heat T ransmission, 1954).Yes. Eq. (4.1) is the ge nera l one . In our application, the ma in concern he re is the fixed be d, especiallythe adsorbent particles, being heated by the boundary. Since the heat (solar radiation) falling on thepipe is the same along the axis, to simplify the calcu lation, it is assumed that ther e is no tempera turegradient in the adsorb ent pa rticle column along the z-axis. So that term

82T/dz2is omitted in Eq. (4.16).Question: The da ta prese nted in Figs 4.4 and 4.5 need to be explained b eca u se it is strange why a ll thetempe ra ture s at differe nt r adial positions fall in a single linear line.

Answer: I feel a little b it strange too. I think there are severa l rea sons for the r esu lts.> The diameter of the pipe is small.> The effective therma l conductivity of the packed b ed is high (with the gas flowingthrough the b ed, the temperature distribut ion is even ra dial ly).> The accur acy of therma l couples is limited (0.3C).Question: The definition of the temperature difference given by Eq. (5.37) lacks physical sense. Theuse of log mean temperature will avoid the problem encountered by the candidate for calculatingoutlet tempe ratur es.Answer: Yes, the log mean temperature difference is definitely a good one. The reason to use thetemper atur e differe nce defined by Eq.(5.37 ) is that it is simple and e asy for the following calculation.


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A SOLAR ADSORPTION REFRIGERATIONSYSTEM OPERATING AT NEAR A TM OSPHER ICPRESSURE

Ying Y ou, Dip., MEngSci.

A thesis submitted in fulfilment of the requirements for the degr ee ofDoctor of Philosophy

GIPPSLAND SCHOOL OF ENGINEERINGMONASH UNIVERSITY

JUNE 2001


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11

Contents

Abstract viStatement viiiAcknowledgments ixNomenclature x

1 Literature Review and Tasks of the Thesis 11.1 Backgrou nd 11.2 Sola r Refrigera t ion 11.3 Re sea rch Hy pothesis 21.4 Ob jectives and Scopes 31.5 Re la t ed Li te ra tu re r ev i ew 4

1.5.1 Principle of Solar Adsorp tion Re frigera tion 41.5.2 The Popula r Adsorbe nt - Refrigerant Pai r s 5

2 Working Substance: The Selection and the Adsorption Equilibrium 102 .1 The Pre l iminary Se lection for Adsorb ent , Refrigera nt , and the

Pre ssure -adjust ing Agent for our Pur pose 102.1.1 The Refrigerant Me thanol 112.1.2 The Pre ssure -adjust ing Agent Some Inert Ga s 112 .1 .3 The Adsorbent Molecu l a r S ieves and Act iva t ed Ca rb on 12

2 .2 Sorce Theore t ica l Background 132 .2 .1 The Physical and Chemical Prope rt ies of Pu re Me thanol 132.2 .2 Isotherm Adsorption Equa tion: D-A Equa tion 142 .2.3 Isotherm Adsorption Equ ation: In? 1/TEquation 162 .2.4 He at of Adsorption Clau sius-Clape ry on Equ ation 172.2 .5 The Desorption and the Adsorption Tlire shold Te mpe ra tur es 18

2 .3 Te st of the adsorption prope rty (P-r- .v) 212 .3 .1 The Test Rig for P-T-x Relat ionship Te st 212 .3 .2 Expe r imenta l P rocedu re s 212 .3 .3 Expe r iment Da ta P rocess: 5A Molecu l a r S ieve - Methanol 222 .3 .4 Expe r iment Da ta P rocess: Activa t ed Ca r bon 20 7E4 - Methanol 23


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1113 The Experimental Study of the Adsorption Refrigeration System Working

at near Atmospheric Pressure 2 63 .1 Refrigera tion Ob serva tion (withou t Pre ssure -adjusting Ga s) 2 6

3 .1.1 The Refrigera tion Ob serva tion Rig 2 63.1.2 5A Molecular Sieve Methanol 2 73 .1.3 13X Molecular Sieve Methanol 283.1.4 Activated Carbon 20 7E4 M etha nol 28

3 .2 Refrigera tion Ob serva tion (with Pre ssure -adjusting Ga s) The Development of the Workab le Refrigera tion Test Rig 293 .2.1 The Obse rvation in the Old Test Rig 293.2.2 The New experiment Rig 29

3.3 The Experimental Procedu res 313 .3.1 The Refrigera tion Observa tion Experiment Procedure s and Results 313.3 .2 The Refrigeration Experiment Procedure s (for Rea dings' Taking) 34

4 Heat Transfer Analysis on the Collector/Desorption Bedin the Heating Processes 3 54.1 Phy sical and Ma thematical Models 3 54.2 Some composite qua ntities of the Collector/Desorption Bed 3 7

4.2.1 V olum etric Hea t Capacity {pc) 3 74.2 .2 The Effective Therma l Conductivity of Packed Bed with Still Fluid (bo.o) 374.2 .3 The Effective Therma l Conductivity of Packed Bed with fluid flow (k biM) 39

4.3 Solution Approa ches Finite-Differe nce Formu lations for Cy lindrical Region 404.4 Hea t Tra nsfer Analy sis on the Collector/Desorption Bed

in Hea ting and He ating/Desorption Proce sses 434.4.1 The Governing Equa tions and Conditions 434.4.2 The Nu mer ical Solution 44

4.5 The Theore tical Solution Compared to the Experimental Data 46

5 The First Law Analysis of the Solar Adsorption Refrigeration Cycle 485.1 Conserva tion of Energy Principles 485.2 Energy Analysis on Processes and the Cycle 49

5.2.1 Hea ting Proce ss 12 495.2 .2 Hea ting Process 23 (Desorption Per iod) 545.2.3 Cooling Process 34 625.2.4 Refrigera tion Period 41 (Adsorption/Refrigera tion Process) 62

i


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IV5.2 .5 COP of the Ideal Refrigera t ion Cycle 65

6 Adsorption M a s s Transfer Analysis .716.1 Adsorpt ion Ma ss Transfe r Ana lysis 71

6.1.1 The Ma croscopic Conservation Equa tions in the Adsor ption Bed 716.1.2 The Isotherm al Expression q =f(c) 7 46.1.3 The External Ma ss Tra nsfer Coefficient kt- 156.1.4 The Part icle-phase Transfe r Coeff icient kp 7 66.1.5 The Equ ations of the Overal l Transfer Coefficient koi- a nd kop

for the Cy lindrical Pellet 806.2 Applica tion 81

6.2 .1 The Maximum V e locity of the Stream 816.2.2 The Ra te of the Adsorption 82

6.3 The Theore t ica l Resu l t s Compared to the Expe r imenta l Da ta 856.4 The Super f icia l V elocity and the Rate of Cooling 87

7 Availability (Exe rgy ) Ana l y s is of the Solar Adsorption R efrigeration system 897 .1 Exe r gy 89

7 .1.1 Exergy of a Closed System Restricted De ad Sta te 897 .1.2 Flow Exergy Restricted Dead State 907 .1 .3 Exe rgy of a Closed System Unrest ricted Dea d Sta te ( the Total Exer gy) 917 .1.4 Flow Exergv Unrest ricted Dead State ( the Tota l Exe rgy ) 927.1.5 The Exergy of Mixture s 937 .1.6 The Exergy Tra nsfer Accompanying Hea t 957 .1 .7 The Exe rgy Transfe r Accompanying Work 957 .1.8 The Qu ali ty of Solar I rra diance 967.1.9 The I rreve rsibi l ity / ( the Exergy Loss) 96

7 .2 Exe r gy Ana lysis of the Adsorption Refrigera tion Sy stem 997 .2.1 He ating Proce ss 12 997 .2.2 Hea ting Process 2 3 (Desorption Period) 1027.2 .3 Cooling Process 34 1057.2.4 Refrigera t ion Period 41 (Adsorption Pro ce ss) 1057.2 .5 The Relat ive Exergy Loss and Exergetic Efficiency

for the Processes and the Cvcle 107

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8 The Simulation of the Per formance of the Adsorption Re frigera tion Cy clePowe re d by Solar Radiat ion 1168.1 The Solar Radia tion 1168.2 Collector Performance 1188.3 The Simulation of the Performance of the Adsorption Refrigera tion Cy cle

Powered by Solar Radiation 1228.3.1 The Tem pera ture of the Collector and the Useful Hea t Collected 1228.3.2 The Simulation of CO P 12 78.3.3 The Simula tion of the Exer getic Efficiency 128

8.4 The Sum ma ry of Useful Formulae 131

9 Some Sugge stion and Guidelines for the Design of the Prototy pe 1339.1 The Collector/Adsorption Bed 1339.2 The Condenser 1349.3 The Evapora tor/Cooling Chamb er 1359.4 The System 136

Conclusions 138Re comme ndations for Fu rthe r Wo rk 141

References 142

Publications 150


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VI

Abst r ac tTc solve the leaking problem faced by solar adsorption refrigeration systems currently working atvacuum pressure, this thesis carried out a comprehensive study on the hypothesis of adjusting thesystem's working pressure to around atmospheric by using a selected adsorbent and introducing apre ssure adjusting ga s in the system.

The first chapter presents the hypothesis of the research. Then the objectives and scopes of thisstuds- a re identified. The related pre viou s studies a re also comprehensively reviewed.

Chapter two firstly describes the selection of the adsorbent, the refrigerant, and the pressure-adjusting gas. Then, the pressure - temperature - concentration relationships for Molecular Sieve5A Methanol, and Activated Carb on 207 E M ethanol are tested, re spectively. The keythermod\Tiamic properties (e.g., the heat of adsorption) are also determined here in mathematicalexpressions.

The experimental study of the system is the task of chapter 3. Activated carbon/methanol isfinally selected as the adsorbent/refrigerant pair, and helium as the pressure-adjusting agent. Thenthe setting up of the indoor simu lation refrigera tion r ig developed for working ar our "heatmospheric pressure, and the experimental procedures are described. The results of theexperiments are presented in the following chapters with the theoretical results.

Chapter 4 describes the heat transfer analysis on the collector pipe in the heating and theheating/desorption processes. A semi-empirical equation of the temperature variation with time inthe collector pipe is obtained.

Chapter 5 contains the energy analysis on the cycle. The energy balance equation is firstlyextended to the situa tion with hea t depletion. The re lationship of Coefficient of Performa nce (COP)of the cycle and the operation temperatures is derived and shown on figures. The COP of thesystem without the pressure-adjusting gas is also shown in the figures for the convenience ofcomparison.

Adsorption analysis is conducted in chapter 6 since the inert gas in the system increases theadsorption resistance for the refrigerant. Based on the analysis on the adsorption mechanisms, somederivates (eg. the rate of adsorption and cooling) were derived and expressed in equations andfigure s. The e xperimental da ta are also shown in the figure s.


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vnIn a complete and advanced analysis, the quality of energy should also be analyzed. In chapter

8, firstly the exergy for mixtures and the irreversibilHy are developed. Then a detailed exergyana lysis on the processes and the whole cycle is car ried out.

The foregoing work is based on the constant heating flux. A simulation of the performance ofthe system powered by solar radiation which changes with time is conducted in chapter 8. Thissimulation can be refereed in the prototype design. An index of the useful formulae is alsopresented in this chapter.

In the last chapter of thesis (chapter 9), some suggestions ar e prese nted for the prototype design.

This study shows the hypothesis proposed here can be realized and the models presented heredescribe the performance of the system well. This study may be of benefit to the effects to removethe leaking problem faced b y the systems cu rre ntly working at vacuum pressu re .


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Vl l l

StatementThis thesis, except with the committee's approval contains no material which has b ee n a ccepted forthe awa rd of any other degree or diploma in any university or otlier institution and to the b est of thecandidate's knowledge, the thesis contains no material previously published or written by anotherper son, except where due reference is made in the text of the thesis.

Ying You


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1? ix

i

I

AcknowledgmentsWork described in this thesis was car r ied out at the School of Engineer ing at Gippsland, MonashUnive rs i ty .

Most of All. the author wishes to thank his supervisor , Professor Jim Jarvis, Head of the school,for his kind concern and support to the author .

Specia l thanks a r e owed to Dr Er ic Hu ( the au thor 's pr incipa l supe rvisor , now a t DeakinUnive rs i ty) for his inva luab le advice , guidance , and encouragement ove r the ent i r e pe r iod ofresearch. Dr Hu led the solar uti l isation research group at Gippsland School of Engineer ing wherethe r ese a r ch was ini ti a t ed.

Thinks a r e a lso due to a l l members who have he lped with the project , especia l ly Dr Mir -Akba rHessami (the Department of Mechanical Engineer ing, CL/ion), A/Professor Ibrahim Yousef. a ndA/Professor David Wood (the University of Newcastle) for their comments, and Mr Ian Bowden,Mr Ken Phelps and Mr Glenn Azlin for their wonderful work without that the experimentalprojects could not have be en pu rsue d.

The au thor is indebted the Commonweal th Depar tment of Educa^on, Tra ining, and YouthAffairs (DETYA) for providing the fund for the solar re fr igera tion pr oject, and Monash Universityfor providing the Monash Graduate Scholarship (MGS) which made this study possible.

Finally, the author wishes to thank all members of his family, especially his hardworkingparents, his wife and his son for their understanding and support .


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t1

NomenclatureX

aAbBc

CcpCy

CsCOPaD

AA-A/DpDp\iAAeEE,exE xEx'f

FFoGh

HiI

Solid par ticle surface areaor activityor whe re context indicatesA r e aor where context indicatesS tr e am exe rgy pa r ame t e rwher e context indicatesSpecific heator concentration for liquidor par tial pressure for gasor where context indicateswher e context indicatesConstant pressur e specifichea tConstant volume specifiche a tSpecific heat for entropyCoefficient of PerformanceDiamete rDiamete ror Parameter in D-Aequa t ionsor diffusivityEffective intrapeiietdiffusivityKnudsen diffusivityMolecular diffusivityPore diffusivityPore molecular diffusivitySurface diffusivityAxial dispersion coefficientwhere context indicatesEnergyEquation of timeSpecific exergyExergyExergy functionFugaci tyor dilution factor forir radianceor where context indicatesF r e e ene rgyor radiacion shape factorFou r i e r numbe rGibbs functionSpecific enthalpyor heat transfer coefficientEnthalpyor length of the hot su rfaceRelative exergy lossIr reversibil i tyDiffuse irradiance

IdirIrIoJHhikKkBk fkPkof

kopKEIL

mMn

NNup.PPePrPEqqo0Q*o vQ'rR

Direct i r r adianceRef lect i r r adianceExt r a t e r r es t r i a l i r r adiancey-factor for hea t t r ansfe ry- factor for ma ss t r ansfe rThermal conductivityHe nr y ' s cons tan tor extinction coefficientBol tzmann's constantExte rna l mass t r ansfe rcoefficientPa r t icle -phase mass t r ansfe rcoefficientOverall transfer coefficient tothe su r f ace a r ea of theparticleOverall t ransfer coefficient tothe volume of the par ticleKinetic energyLengthLengthor dis tance be tween twosu r f ace sM a s sor intege r (1, 2 , or 3 )Molecule weightPa r amete r of the D-Aequa t ionor number of pe l l e ts pe rvolumeor day of y e a ro r g lazed nu mb e rM o le n u mb e r so r g lazed nu mbe rNuss e l t numbe rP r e s s u r ePec l e t numbe rP r andt l numbe rPotential energythe amount adsorbed inequi l ib r iumMaximum amount o fadso r b a t e in the adso r b en tHeat f lowNon-convective heat t ransferp e r a r e aHea t gene r a t ion pe r uni tvolumeHea t gene r a t ion in a sy s temRadiusor corre lation coefficientRadius

If


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X I

RaReResSScttos(isTuuu sVVWU/" 0

X

XO

z,

or gas constantRay l e igh numb e rContact thermal resistanceReynolds numberSpecific entropyentropyScmidt numbe rTimeApparent solar t imeLocal standard timeTemperatureSpecific internal energyInternal energyor heat transfer coefficientSuperficial velocitySpecific volum eVolumeor velocityWorkor volume of the adsorba teadso r b ed in a unit mass ofadso r b en tMaximum volume ofadso r b a t e in a unit mass ofadso r b en tThe ma ss of the adsorbateadso r b ed in a unit mass ofadso r b en tor the mole fractionmaximum mass oi adsorba tein a unit mass of adsorbentElevationor axial coordinate/distance

Greek lettersaPyA5

neo POs6'A

Thermal diffusivityor absorptivityAffinity coefficientor volume coefficientActivity coefficientChangeSolar declinationAdsorption potentialor emissivityor voidageor Lennard-Jones forceconstantor exergetic efficiencyEfficiencyExcess t empera tu r eor incident angleTilt angle of the collectorplaneZenith angleAngle of refractionLatitude

Vpa

T

( j > P


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XII

'HeiinLleaklo cmixMethnfne toPprpro0rrecrefrevs

HeliumInlet stateInlet stateLiquidor lossLeakageLocal stateQu antity for mixtur e(s)MethanolNon-flow processNet quantityCentre line of the collectort u b eAdsorption pellet/particleor collector pipePressure-adjusting gasprojectedQu antity related to heatRefrigerantor radiative heat transferReceiverReference stateReversibleSaturated stateor solidor surface of the bedor solar

to tuVVWe0

Collector tu b eor top of the pipeTotal amountUsefulQu antity per unit volumeVapou rQu antity related to workIncident angleRestricted dead state

Superscriptschtmto t0

-

*

Chemical propertyThermomechanical propertyTotal amountUnrestricted dead stateDot over symbol denotestime rateBar over symb ol denotesavera ge quantityor pa rtial mole propertyWa ve-line over symboldenotes mole qu antityQuantity in equilibrium withthe re lated qua ntity


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1Li te r a tu r e Review a nd Ta sks of the Thesis

1.1 B A C K G R O U N D

Energy and the envi ronment a r e two of the most impor tant issues in the cu r r ent wor ld. Nowadaysmost electr icity is generated by consuming fossil fuels such as coal, oil and natural gas. Not only dofossil fuels have a l imited life but their combustion emissions have ser ious negative impacts on ourenvironment such as adding to the greenhouse effect and causing acid rain. As a potential clean andsus ta inab le ene rgy source , sola r ene rgy is ge t t ing more a nd more a t t ent ion.

In many places a round the wor ld, especia l ly in the thi rd wor ld count r i es and some ru r a l andisolated areas in the t ropical zone, refr igeration tecliniques are much needed to preserve foodstuffsand medical supplies and for ai r conditioning. However , the lack of infrastructure, especially the lackof a r e l i ab le e ne rgy supply , a nd the l ack of tr a ined se rvice pe rsonnel pr e vent the use of convent iona lrefr igeration methods. On the other hand, solar radiation is ubiquitous, and solar radiation is verystrong in the t ropical zone where there is much need for refr igeration air conditioning. Solar energy-is of ten the only r eadi ly ava i l ab le ene rgy source the r e , and sola r -powered r e f r ige r a t ion technologyhas the potential to store per ishable food and vaccines and for ai r conditioning for these par ts of theworld. Even in the urban areas, the use of solar energy can help to reduce the emission of thecombustion products exhausted from the conventional power plants.

1 .2 SOLAR REFRIGERATION

Refrigeration is defined as the process of extracting heat f rom a lower temperature heat source,substance, or cooling medium, and transfer r ing it to a higher temperature heat sink. A refr igerationsystem is a combination of components and equipment connected in a sequential order to produce therefr igeration effect. The refr igeration systems commonly used for general purposes can be classifiedas vapor compress ion sys tems and sorpt ion sys tems. The former a r e dr iven by mechanica l(e lect r ica l ) ene rgy and the l a t te r a r e dr iven by the rmal ene rgy .

Normal ly the r e a r e two ways of r e f r ige r a t ion powered by sola r ene rgy . One is to conver t sola rradiation to electr icity by means of photovoltaic cells (ASHRAE, 1996; Kreith and West, 1997) torun an ordina ry va por compress ion r e f r ige r a tor . Thou gh the smal l s ize (50 li tr e ) PV r e f r ige r a tors a r eava ilab le, i t is nece ssary to redu ce the cost other wise i t is difficult to afford by the u ser in deve loping


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2countr ies if there is no financial assistance from the government or other sources. Another problemre lated to PV refr igera tor is that i t em ploys a conventional compre ssion refr igerator u sing HC FC s asthe refr igerants. The HCFCs stil l have some ozone depletion potential (ODP) and high globalwarming potential (GWP). which has resulted in the global phase-out schedule (Wang. 1993). As thealternative refr igerants are explored, new refr igeration forms are also actively exploited.

The second method uses solar thermal radiation to drive the sorption (absorption or adsorption)r e f r ige r a t ion sys tems. Sorpt ion r e f r ige r a t ion devices a r e hea t -ope r a ted cycles . They use much less ,even no, e l ect r ica l ene rgy as compared with the vapour compress ion cycles . Fur the rmore , they canu ss envi ronmenta lly be nign working f lu ids such a s ammonia , methanol or wate r a s r e f r ige r a nt thusr edu cing the use of HCF Cs. Among them the ab sorpt ion r e f r ige r a t ion sys tems such as wa te r - l i thiumbromide absorpt ion, ammonia-wate r absorpt ion and ammonia-wate r -hydrogen cycles (ASHRAE,1994) have been thoroughly studied and widely used; however , i t is the adsorption and solid sorptioncycles tha t have a dis t inct advantage in us ing was te hea t in r e l a t ive ly low tempera tu r es l ike tha tcollected by flat-plate solar collectors. Unlike the steam driven absorption chiller and the direct-fi redsystems, there is no need to consume fossil fuels . Furthermore, the supply of sunshine and the needfor refr igeration both reach maximum levels in the same seasons. Therefore, the solar adsorption andsolid sorption refr igera tion seem to b e the promising refr igera tion technique.

1 .3 RESEARCH HYPOTHESIS

Although the r e have been many s tudies on sola r r e f r ige r a t ion sys tems and some advanced sys temshave been deve loped, unfor tuna te ly , no sola r r e f r ige r a t ion sys tems or chi l l e r s have widespreadpractical application. One of the shortcomings is that all the solar refr igeration systems cur rentlystudied work either at high positive pressure ranges, such as ammonia refr igeration systems, or athigh vacuum r anges l ike wate r and nie thanol r e f r ige r a t ion sys tems. For example , the wate r sys temusua l ly works in the 1.24-92.5 mmHg pressu r e r ange ; and the methanol sys tem normal ly works a t10-400 mmHg pre ssu r e r ange . In r e fr ige r a t ion sys tems working a t the high pos it ive pr e ssu r e r a nges ,the refr igerant can escape to the environment, which not only results in the decrease of therefr igeration performance but may also endanger the health of local people, especially for highlytoxic substances such as ammonia. For refr igeration systems working at the high vacuum ranges, themaintenance of the high vacuum degree in the whole system is cr i t ical for such systems'performance. This makes it difficult to deliver the refr igeration units to, and maintain them in, theab ove me ntioned r emote a r e as whe re such units a r e in much demand. That is one of the main r e asonswhy to date such green refr igeration units/air conditioners have not yet been popular isedcomme rcia l ly . So fa r the r e has b een no s tudy address ing this problem. To solve the l ea kage prob lemfaced by the sola r adsorpt ion sys tem cur r ent working in the vacuum pressu r e , a r esea rch hypothes is


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3has been put forward by the author that the working pressure of the system could be adjusted toatmospheric by using some proper adsorbent and introducing some pressure-adjusting gas in thesystem. This thesis conducts a compr ehe nsive study on this hy pothesis.

1.4 OBJEC TIV ES AND SCOP ESThe general ob jectives and scopes of this resea rch a re to: justify the re sear ch hypothesis b y expe riment; u nderstand the working mechanisms of such systems and eva luate the performance to revea l and

eva luate the factors affecting the performa nce of the system; explore the possib ility of implementing the idea to the vacu u m adsorption refrigera tion system s

powered by solar radiation.The research includes the following specific objectives. They are to:

provide the guidelines and expe rience for the selection of the suitab le adsorbent / refrigerant pairand the pressu re-adjusting gas;

develop the re frigera tion expe rimental rig which can work at ab out atmospheric pressu re ; understand the heat transfer char acte ristics of the collector/genera tor in the hea ting and

heating/desorption process; eva lua te the coefficient of per forma nce (COP ) of the re frigera tion system ; revea l the adsorption cha ra cter istics for the collector/adsorption b ed for the adsor ption/

refrigeration process; eva luate the e xergy (availab ility ) a naly sis for the components/process and the cycle of the

refrigeration system; eva luate the performance of the re frigera tion cycle powered by solar ra diation by simulation; and provide sugge stions/guidelines for the design of such a prototype .

The project consists of the following scope s. The selection of the adsorb ent, re frigera nt and the pre ssur e-adjusting ga s, and the investigation of

the relationship of pressure-temperature-concentration (P-T-x) for the adsorbent/refrigerant pairsby test.

The development of the re frigera tion experimental rig working at ab out a tmospheric pre ssur e,and conducting experimental tests.

The heat transfer ana lysis for the collector/gener ator for the heating and he ating/desorptionprocess.

The first law of thermody namics (energy ) analysis of the re frigeration system.


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4 The a dsorption ma ss t ransfe r a naly sis for the collector / adsorption be d for the adsorption /

refr igeration process. The exer gy (availab il ity) ana lysis for the components/process and the cycle of the re fr igera tion

sys tem. The simu lation of the perform ance of the refr igeration cycle powered b y solar ra dia tion. Su ggestions and guidelines for the design of such a prototype .

1.5 R E L A T E D L I T E R A T U R E R E V I E W

1.5.1 Pr inciple of Sola r Adsor pt ion Ref r ige r a t ionAlmost a l l sol id mate r i a ls have the capaci ty to adsorb /absorb wate r vapor and gases by phys ica land/or chemica l forces . The sol id mate r i a ls used on adsorb /ab sorb pu rpose a r e ca l l ed the adsor b en ts .The mois tu r e or gases adsorbed/absorbed can be dr iven out f rom the adsorbent by hea t ing, and thecooled 'dry ' adsorbents can adsorb /absorb mois tu r e or gases aga in. The popula r adsorbents a r esome solid sa lts, sil ica-gal, zeolite , and a ctivated car b on.

It is convenient to describe the adsorption refrigeration cycles in a P-T-x ( P r e s s u r e - T e mp e r a t u r e :Concentration) diagram as shown in Figure 1.1. The ideal cycle consists of two isoster (constant-volume) processes (1-2 and 3-4) and two isobar (constant-pressure) processes (2-3 and 4-1).

The cycle star ts f rom state 1 (in the morning) as the sun r ises. The te mpe ra tu re of thecollector/generator increases thus the pressure increases until state 2 is reached. After thetempera tu r e of the col lector /gene r a tor r e aches the desorpt ion thr eshold t empera tu r e (s ta t e 2) , theheating/generation process star ts . In this process, the temperature of the collector r ises, while thepressu r e r emains a t the condense r pr essu r e . Dur ing the isoba r ic process , the adsorba te is dr iven offuntil the minimum concentration of the refr igerant (corresponding to the maximum temperature) .During this process, the generated vapour is condensed in the condenser and is collected in ther ece ive r / evapora tor .

When the collector/adsorption bed is cooled by the ambient in the evening, the pressure in thecollector/adsorption bed decreases until the evaporating pressure (state 4). Then the adsorbent star tsto adsorb the vapour vaporised at the evaporator thus the refr igerating effect is produced. Thisprocess ends when the concentration of adsorbate in the adsorbent reaches the maximum (state 1).The cy cle is then r epea ted.


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LnPPc

Te T, T c T3 T4 T3 -1/7

Figure 1.1 The P-T-x diagram of the ideal basic adsorption cycle

1.5.2 The Popular Adsorbent-Refrigerant Pairs

Solid Salts and the Refrigerants

Michael Faraday in 1824 first discovered the sorption refrigeration principle (Hahre, 1988) and heused AgCl-NH^ as the working pair and got the cooling effect. But AgCl has several shortcomingsand was ab andoned.

Nielsen and Worse-Schimdt (1977) built an indoor test rig and investigated the heat and masstransfer in the adsorption and dcsorption processes for Calcium-Ammonia. After detailedinvestigations on NH3CaCl; and NH 3Sr CI;, Nielsen (1981) concluded that solid C a d : andSrCI; could be used for solar refrigeration. Worse-Schimdt (1979) designed a demonstration plantfor a net amount of cooling of approximately 800 0 kJ per da y . The testing showed that the pr ocessCOP was 0.34 and the total solar COP was 0.096. Iloeje (1985) tested a Calcium-Ammonia solarrefrigera tor over the a nnual climate va riations at Nsukka, Nigeria. He a lso investigated the effect ofcharging pressure on COP with three different pressures and carried out the parameter analysis onthe performance of the NH3CaCl; solar refrigeration. Based on his experimental work, he and hiscoworkers (1995) developed a simple ma thema tical model and computer program to the system andcar ried out the pa ra me tric stu dy on the system with the view to optimising the design.

A better but more expensive working pair is SrCb-NHj. Dornier, a Germany Company,manufactured a solar refrigerator which uses the compound material 1MPEX(80% SrCb+2 0% Graphite) as the adsorbe nt and NH3 as the adsorba te (Bansal et a L 1997). The he at


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wa s supplied b y an evacu ated sola r hea t p ipe . The IMPEX has a h igh coeff ic ient for he at and ma sstransfer and a good adsorption property. The refr igeration capacity is 1.5 kWh per day. Bansal et al.(1997) carr ied out the theoretical and experimental analyses to this refr igerator using themeteorological data fo r Delhi . The maximum theore t ica l COP was 0 .143, but the tes t ing COP wasonly 0 . 0 8 1 . They thought that the wea ker sola r r ad ia t ion due to the pollut ion and dust wa s the r ea sonfor the low testing COP and suggested a redesign of the system according to the local meteorologicalcondition. Erhard and Hahne (1997) also carr ied out the theoretical and experimental study on theSrCli-NHs system and made a s imula te p rogram.

Silica-Gal and the Refrigerants

In 1930s" G. E. Hulse invented silica-galsulfur oxidised adsorption refr igeration system. Plankand Kuprianoff (1960) investigated the possibility of using silica-galpropanone in solarrefr igeration systems. Eggers-Lura (1978) designed an adsorption refr igeration system. Sakoda andSuzuki! (1984) investigated the silica-galwater adsorption system for solar cooling. Sakoda andSuzuki (1986) built a small silica-galwater cooling unit and proposed a simple model which caninterpret the experimental results well. Their sensitivity study showed that the heat transfer areabetween the adsorbent packed bed and its container had a considerable effect on the COP and theysuggested that the heat t r ansfe r a r e a should b e approximate ly 0 .4 m :/kg adsorbent to obtain the sola 'rthermal COP of 0.4. Kluppel and Gurgel (1988) reported a solar cooled drinking fountain usingsil ica gel - wa te r pai r with an aver age CO P of 0 .0 7 . Cho and Kim (1992) developed a te s t se t and asimulation code to study the effects of component heat transfer rate on the cooling capacity of asilica-galwater adsorption cooling machine. Watable and Yanadori (1994) studied the coolingcharac te r is t ic of s i l ica galethanol . Tanaka e t a l . (1983) ca r r ied out an exper imenta l s tudy on acompact silica-galwater refr igeration system which was thought to have a better performance thanthe t r adi t ional ones . There a lso have been severa l cycles p roposed to r educe heat inherent in ba tch-cycle operation and hence improve cycle efficiency. Saha et al. (1995) investigated analytically theper fomiance of a th ree-s tage s i l ica-galwater adsorpt ion chi l le r to use the nea r -ambientt empe r a t u r e was t e h ea t b e tween 55 and 4:''' and exper imenta l ly , by Saha and Kashiwagi (1997) .Boelman et al. (1997) studied the influence of thermal capacitance and heat exchanger UA-valued onthe cooling capacity, power density, and COP of a silica gel-water chiller . Alam et al. (2000)investigated the effect of heat exchanger design on the system perfomiance of silica gel adsorptionref r igera t ion systems.


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Zeolite {and Zeolite Molecular Sieves) and Refrigerants

The possibility of using the zeolite-water pair was studied as early as 1974 (Techemev, 1974).Techernev (1974. 1978, 1982, 1984) studied solar cooling with zeolite, and he built and tested asmall cooling cab inet with the volu me of 100 dm3. Meu nier and M ischler (1979) and Gu illeminot eta l. (1980) also reported the application of zeolite. Guilleminot and Meunier (1981) tested a smallexperimental unit. Monnier and Dupont (1982) carried out the numerical optimization and fieldtesting for a zeoiite-water close cycle solar refrigeration. Grenier et al. (1988) built a largeexperimental solar adsorption cold store with the a re a of the collectors 0.8m2 and the volum e of thecooling space 12 m3. In Gu illeminot's a nd Gre nier 's case s, the net solar COP wa s ab ou t 0 .1, theefficiency of the collectors was approximately 0.33 and the cycle COP was also 0.33. Hinotani andKanatani (1983) made a small experimental apparatus to obtain fundamental data for the design ofthe Ze olite-Water solar refrigeration system. The per formance of the system wa s simu lated with anevacuated glass tube collector with heat pipe. The COP of the system was from 0.02 to 0.05. Afteraging test on several metals, it was suggested copper should be used for further industrialdevelopment. These results showed that the Zeolite-Water could be used either in the small or thelarge refrigeration systems.

Shelton et al. (1989) conducted a ramp wave analysis of a solid - vapour heat pump usingzeoliteammonia pair. The heat transfer fluid is circulated to reduce the heat required from theexternal source by hea t recover}'.

Hajji et al. (1991) carried out a dynamic analysis for a solar adsorption refrigerator using zeolite13X-\vater and Chabazite-methanol as working pairs. Zhu et al. (1992) investigated experimentallythe 13X zeolite - water chiller. Chang and Roux (1995) carrie d out a thermodyna mic ana lysis for asolar zeolite refrigeration system.

The Zeopower Company produced a Zeolite-Water solar refrigerator a long time ago (Tchernev,1979). It was re ported that the system could produce 9.8 kg ice pe r day per n r of collector a re a for atotal solar input of 20 MJ/m : under the typical climatic condition of Boston. Later, the ZeopowerCompany developed a nother solar Zeolite-Water solar r efrigerator for the domestic and recre ationalmarkets (Tchernev. 1984) which could produce about 0.9 kWli for each square meter of collectorwith a solar input of 6 kWh and the e fficiency is 15% according to the report.

In order to improve the efficiency of adsorption refrigeration, Tan and Wang (1998) researchedthe double effect cascade adsorption systems using silica-water/zeolite-water and zeolite-water/zeolite-water respectively.


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8

Activated Carbon and Refrigerants

Pons and Guilleminot (1986) designed an activated carbon-methanol solar adsorption ice maker ar idbui l t a p rototype in Orsay. The sola r col lec tor was 6 m : in a r ea and conta ined 130 kg of A.C., thecondenser was a i r -cooled and the evapora to r had a net p roduct ion of 30-35 kg ice per sunny day.Tlie net sola r COP was 0 .12. Pons and Grenie r (1987) p resented the exper imenta l data f rom thisprototype. The measured net sola r COP was 0 .12 when the incident sola r energy Q, was 22 MJ/m 2and 0.1 when Q, was 19 MJ/m 2 . Based on the P-T-x data dete rmined b y Sr idhar (1987) , Exel l (1987)designed and fabr ica ted a charcoal-methanol ice maker . The sola r col lec tor was 0 .97 m 2 a ndcontained 18 kg char coal. 2.5 kg ice at -1 to -3C could be produ ced for a good day . Pa ssos a ndEscobedo (1989) presented an analytical model for the solar adsorption cooling cycle using theact ivated carb on-methanol pai r . Medini e t a l . (1991) se t u p a non-valve a c t ive ca rb on-me thanol sola rice ma ker with the 0 .8 m 2 collection surface with a view to build an industrial machine. This machineproduced 4 kg of ice per day in summer. With a collection efficiency of 0 .41, it is possible to obtaina gross solar COP of 0.15. However, because of insufficient insulation of the ice bank, the net COPobta ined was half that value . Tan e t a l . (1992) s tudied an ac t ive ca rbon-methanol sola r ice makerwith the collector area 1.1 m 2 and the r ef r igera to r volume 103 l i t r es . The maximum net COP of thema chine w as 0 .15 and the exper imenta l value was ab out 0 .11. Boub akr i e t a l . (1992) r epor ted thei rexper imenta l s tudy of th ree charcoal-methanol ice makers with the col lec to-condese (assembly ofsola r col lec tor and condenser in a unique component) opera ted in Agadir , M orocco. They ob ta ined anominal production of 4 kg of ice per squ ar e mete r col lec tor for 60 % of the per iod of the expe r ime nt .The net sola r COP was be tween 0 .08 and 0.12. Huang e t a l . (1992) bui l t a p rototype of sola rpowered ice maker (no valve cycle and air natural cooling). The results showed that the thisref r igera to r could produce 4 .5 kg ice per day in winte r and 2-3 kg ice per day in summer . The netsola r COP was 0 .1-0.12 and 0.08 r espect ively . Cr i toph (1994) bui l t and tes ted an ac t ive ca rbon-ammonia solar refr igerator for vaccine cooling. The collector was 1.4 m 2 and contains 17 kg ofcar b on. I t is possible 10 produce u p to 4 kg of ice per day in a d iurnal cy cle . Bentaye b e t a l . (1995)introduced a model which took account of the real operation for an activated carbon-methanol solarrefr igerator. Their numerical simulation showed that the behaviour of the refr igerator is differentfrom one climate to the other . Critoph (1996) presented the results of heat transfer tests on a carbon-am monia exper ime nta l genera tor together with future p lans fo r a one ton per day sola r ice ma ker . Hu(1996) presented some further applications of the program developed and validated before in theinvestigation of the non-valve carbon-methanoi solar refr igerator. Follin et al. (1996) studied theinfluence of microporous characteristics of activated carbon on the performance of an adsorptioncycle for refr igeration. Chen et al. (1997) studied the activated carbon - ethanol refr igeration systemand showed that e thanol could be a subst i tu te fo r methanol . Wang e t a l . (1997) invest igated the


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9feas ibi l ity of u s ing ac t ive ca rb on f ibre (ACF) as the adsorb ent in adsorption r ef r igera t ion a nd foundthat ACF-methanol has good potent ia l as an adsorpt ion r ef r igera t ion pai r . L i and Sumathy (1999)bui l t a sola r ice maker us ing ac t ivated carbon and methanol with an exposed a r ea of 0 .92 m 2 a naabout 4-5 kg ice could be p roduced with the COP of about 0 .1-0.12. Wang e t a l . (1999) developedan ac t ivated cs rbon-methanol adsorpt ion r ef r igera to r us ing spi r a l p la te heat exchangers asabsorbe rs , and more than 2 .6 kg ice per day per kg ac t ivated carbon with a COP of 0 .13 can beobta ined. Li e t a i . (2000) designed an adsorpt ion bed for ac t ivated carbon - methanol r ef r igera t ionsys t em.

Douss and Meunie r (1989) p roposed a cascading adsorpt ion cycle in which an ac t ive ca rbon-methanol cycle is topped b y a ze ol ite-wate r cycle . This a r r a ngement ma kes i t possib le to obta in , forexa mple , b oth s tea m and ice with r edu ced heat input f rom the exte rna l sou rce .

Grenie r and Pons (1983) pointed that the COP of ac t ivated carbon-methanol sys tem was higherthan those of zeoi i te s ieveswater sys tems a t about 120C. Meunie r e t a l . (1986) comparedsynthetic zeolitewater , synthetic zeolitemethanol, and charcoal-methanol combinations andfound that the ac t ivated-charcoal-methanol gave a be t te r COP genera l ly , but that the zeol i tewatersystem was be t te r when the d iffe r ence be tween the n ightt ime ambient tempera ture and theevapora t ing tempera ture was par t icula r ly h igh. Afte r compar ing AC35-methanol with zeol i te 13X-wate r , Meunie r suggested that the zeol i te combinat ion would be super io r only when the tempera turel i f t (adsorpt ionevapora t ing tempera ture) exceeded 45C. But the compar ison was based on theheat input. Taking account of the collector efficiency which decreases with increasing temperature,the charcoal-methanol combinat ion might be super io r a t even higher tempe ra ture l if ts .

Owing to the differences in the raw material used, the activated condition (activated temperature,etc.), process employed and the degree of activated (activated time, etc.), the properties of theact ivated carbon such as porosi ty , pore s ize , and sur face a r ea fo r adsorpt ion vaiy f rom oneapplication to another. The adsorption properties for individual particular activated charcoal andmethanol combinat ion a r e norma lly tes ted in labora to r ies .

Sridhar (1987), Eltom and Sayigh (1994), Passos et al. (1986), Grenier and Pons (1983), and Huand Exell (1993) tested the adsorption capacities for different charcoals. Based on his COPcalcula t ion of ideal cycles , Hu (1993) pointed out that the charcoal 2 0 7E4 f rom UK wa s sui tab le forice making for t ropical a r eas (h igh peak col lec tor tempera ture) . Hu (1998) a lso s tudied the thermaldecomposition of methanol in solar powered adsorption refr igeration systems.


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10

- M

Working Substance: The Selection and the AdsorptionEquilibrium

Before considering .he solar adsorption refrigeration system, the adsorbent/refrigerant working pairmust be selected and its adsorption property evaluated. The adsorbent we are searching for shouldhave selective adsorption property in addition to the other general adsorption properties required. Inthis cha pter, the possible working pa irs and the pressure-adjusting agent were selected from gene ra lconsiderations, and the adsorption properties for the working pairs were tested. The adsorptionequilibrium was described by Dubinin and Astakhov (D-A) equation, and the test data (pressure P,t empera ture T, and concentration x) were expressed in the inP \IT chart. Some of thethermodynamics of adsorption (the heat of adsorption and the desorption and the adsorptionthreshold temperatures) for the following analyses were also conducted in this chapter. The heat ofadsorption was determined by employing the Clausius-Claperyon equation, while the desorption andthe adsorption tlireshold temper atu re s we re determined by three approaches. It is shown that the D-AEquation and Simplified Pressure Equation approach is simple and accurate.

2 .1 THE PRELIMINARY SELECTION FOR ADSORBENT, REFRIGERANT ANDPRESSURE-ADJUSTING AGENT FOR OUR PURPOSE

The selection of the working substance for our purposes, i.e., to make the system work at aboutatmosphe ric pre ssure , should b e b ased on the two sets of properties required: The gener al adsorptive prope rties, i.e., in solar application temper atu re ra nge, it nee ds to work

well. The adsorb ent should have selective adsorption proper ty, i.e., it should not adsorb tl- "essur e-adjusting agent.

The adsorbent used in industry usually has a micro-porous structure. An ideal adsorbent forrefrigeration should meet the following requirements: The specific surface area should be large andthere should be the micropores; The adsorption capacity should be large; The adsorption forceshould be small and the regeneration temperature should be low; The heat of adsorption should besmall; There is no reaction with the adsorbate; The velocity of adsorption should be quick so it iseasy to achieve the adsorption equilibrium; The specific heat should be small and conduction heattransfer high so to quicken the adsorption/desorption processes; High hardness or resistance to


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11abrasion; The flow resistance for gases should be small; Being able to be regenerated and reusedmany times; Ea sy to a vailab le; Cheap; etc.

An ideal refrigerant for adsorption refrigeration should meet the following requirements. Highenthalpy of evaporation at the required evaporator temperature; Low freezing temperature;Relatively high critical temperatures; Positive evaporating pressure; Relatively low- condensingpressure; Good heat transfer characteristics; Low water solubility; Inertness and stability;Missliamnisbility; Nonexplosive whek saiNf-d with air; Nontoxicity; Nomrritability; Noncorrosive;Rela tive low cost; Be e asy Jo detect in case of lea ks.

It is almost impossible to find an adsorbent and a refrigerant to satisfy all the above-mentionedre qu irem ents. The most used a dsorb ent in refrigeration is silica gel, zeolite, and activated ca rb on andthe m ost use d refrigerants a re ammonia, water, a nd methanol.

2 .1 .1 The Ref r ige r an tMethanol

We would like ou r new r efrigera tor to have the potential of making ice, so methanol is chosen as therefrigera nt. The advantages of u sing methanol as the refrigerant a re : It can eva pora te at a tempe ra tur e be low 0C (its Melting Point is -93.9C); Its molecule is small (4 A) and it can be ea sily adsorb ed in micropores with the diam ete r ltoS

than 20 A; Its normal boiling point (65C) is higher than room tem per atu re , which mea ns the me thanol

refrigeration system always works at pressures lower than atmospheric. It is the leakageprob lem of this kind of systems tha t this rese ar ch is aimed to solve.

Its enthalpy of vaporisation is significant (ab out 1100 kJ/kg). so a good COP of its cy cle maybe expected.

Non-irritability. Non-corrosive.

2.1.2 The Pressur e-adjust ing Agent Some Iner t Gases

IIt is known that the satura tion temper atu re of vapour in a gas mixture depends only on the va pou r'spartial pressure and would not be affected by the presence of the other gases. Therefore, some gasmay be filled in the system to raise the pressure of the system to atmospheric pre ssure . In order toachieve this goal some points shou ld be met.


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12Firstly the gas should not re act with the rest of the system (the machine ma ter ial, the a dsorbe nt,

and the adsorbate). Thus some inert gas may be a good choice. Secondly, in order to act as thepressure-adjusting agency, the gas should not be condensed in the working temperature range noradsorbe d b y the adsorb ent. Inert gases such as Helium a nd Argon meet these r equ irem ents.

2.1.3 T he Adsorb ent Molecula r Sieves and Activated Ca rb on

The adsorbent for our proposes should have a selective adsorption property. That is to say, theadsorbe nt should adsorb the refrigerant only a nd should not adsorb the pre ssure -adjusting ga s.

The molecular sieves have an excellent property for selective adsorption. Zeolite MolecularSieves (MSs) are highly porous dehydrated crystalline zeolite. The pores are precisely uniform indiameter and of molecular dimensions. Therefore, they adsorb selectively only those molecules whichare small enough to enter the pore system. That is why they are called molecular sieves. Besides,their adsorptive performance is strongly affected by the polarity, the polarizability, the bondcharacter, and the molecular weight of the adsorbed substance. The 'Sieving" action, and the highaffinity for a certain adsorb ate give them their unique properties as molecular adsor b ent. There fore,zeolite molecu lar sieves a re the. first materials selected natura lly as the adsorb ent for ou r pu rpose.

Since the critical molecular diameter of methanol is 0.44 nm, the pore diameter of the adsorbentselected should be greater than that value, so the adsorbent can adsorb the vapour molecules of therefrigerant, the me thanol. 5A MS (pore diameter 0.5 nm) and J3XMS (pore diameter 1.0 nm) meetthis re quireme nt.

)i is also tru e that the diameters of the inert gases a re smaller than the pore diam eter of the chosenadsorbent (the critical molecular diameter of argon is 0.38 nm and helium is 0.2 nm), but theirpolar ities and molecular weights determine that they can be displaced by me thanol. He re Helium, aweaker affinity inert gas, is chosen as the pressure-adjusting agency. Argon will also be tried in theexpe riment to see the e ffect of the de nsity (molecular weight) of the ga s on the cy cling.

Car b on ha s be en known throughout history as an adsorbe nt, and it has be en we ll documented thatActivated Carbon (carbonaceous material like coal, lignite, wood, nut shell, petroleum andsometimes synthetic high polymers thermal decomposed and then activated with steam or carbondioxide a t elevated tempera ture 70 0-1000 C) and methanol pair ha s an excellent refrigera tionperformance. The advantage s of using activated carb on as the adsorbe nt ar e: Activated Carb on has a significant capa city of adsorption.


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13 Activated Car b on + Me thanol can work a t a s high a s 150C without decomposition. He nce

Activated Carbon + Methanol seems to be a suitable pair for a solar refrigeration systemworking at the tempera ture range tha t the flat-plate collectors can re ach.

o Activated Carb on can b e made to suit pa rticula r a pplications by var y ing the activation time andtempera ture , etc. Activated Carb on can b e manu factu red ea sily b y local industry .

Activated Carb on is chea p.

All the above-mentioned advantages show that the Activated Carbon + Methanol seems to be agood pair for solar re frigera tion with the flat-plate collectors.

Carbon Molecular Sieve (CMS) is an interesting form as of activated carbon since it not onlyretains the advantages of the activated carbon, e.g.. high adsorption capacity and easy desorption,bu t a lso has a unifomi and narrow micropore size distribu tion. Both of the chara cter istics seem to beimportant for our purpose. As for the zeolite molecular sieve, it is the difference of the affinities ofthe ga s and the vapour to the a dsorb ent, ra ther than the 'sieving a ction' of the adsorbent, decides thepriority of the adsorption. Foitunately , inert gase s a re hardly adsorbed by common adsorb ents in thenormal temperature range. Therefore, some inert gas can be used in the system as the carrier gas,and activated carb on, rather than carb on molecu lar sieve, as the a dsorbe nt.

2 .2 SOME THEORETICAL BACKGROUND

2.2.1 The Physical and Chemical Pr ope rt i es of Pu re Me thanol

I

The vapour pressure P (Pa) of methanol in a limited tempera ture range ca n be described by Antoineequation (Boublik et al, 1973; see also Cheng and Kung, 1994)

log? = 10.20587 - 1582.271/( r- 33.424)288.0 K < T < 3 56.8 K, error < 0.0 6%

(2.1)

with an error less than 0.06%. For a wider range of temperature, Dauber and Danner (1984)suggested

ln P = 109.93 - 7 47 1.3 /7 - 13.988 In T+ 0.015281 T175.6 K < T< 512.6 K, error < 1%

(2.2)

For satu ra ted density of methanol liquid ps (kg/m3), Dau be r and Da nner (1984) suggestedIn ps = 3 .6541 + 1.62055 [1 + (1 - 77 512.63)17:7 :] (2.3)

175.6 K


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3 14Based on the tab le given b y Liley (1982 ), Exeli et al. (1987 ) computed the prope rties of methanol

as a function of tempe ra ture from the re gression formulas:

Saturation vapour pr essu re in b ar :lnP, = 12.6973 -4024.3ZT-87582 .885/T2 (2.4)

250K


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S .

15s = AF =/PPs VdP = -RJ\n(P/P s) (2.7)

where AF is the free energy change, R is the gas constant, T is the a bsolute temper ature of theadsorbent/adsorbate, Ps is the satura ted vapour pre ssur e of the a dsorb ate a t temperature T, and P isthe equ ilibrium gas-phase pa rtial pre ssur e of the adsorba te;

Substituting for finto Eq. (2.6). the Dubinin-Radushkevich (D-R) equ ation is written a sW = Woexp(-D(rin(P/P)f) (2.8)

where D-kR^/fi2 and Wo and D are determined by experimental measurement.

Eq. (2.8) is valid for temperature sufficiently below the critical temperature Tc (T239C.

Since it was found exper imentally that for some su b stance s u iere were deviations from the ab oveexpression, Dubinin and Astakhov (1970) introduced an improved and more general form of the D-R Iequation, which is called the D-A equation, to fit the experimental data better. The D-A equationcontains a third variab le n and the form is

W = Woexp{-D[nn(P/P)]n} (2.9a)or x = xoexp{-D[T\n(Ps'P)}"} (2.9b)where n is usually between 1 and 3, and equals 2 in the D-R equation, and x is the massconcentration.

Taking logarithms we obtain the linear form\nW = lnW 0-D[Tln(P/P)] n (2.10)

The paramete rs W o and D can be determined experimentally by plotting \nW\s [T\n(P/P)]" for avariety of value s of n from measurements ofW, T and P.

The introduction of the new parameter n helps to improve the fit but it does not necessarily havea ny direct physical mea ning (Critoph, 1988). Pons and Gre nier (1986) also pointed ou t that the D-Aequation is not thermodynamically correct near saturation because the predicted heat of adsorptiondoes not tend to the heat of vaporisation of the adsorbate. The D-A equation is known to deviatefrom experimental data for very small and very large values of W. They suggested a linear potentialexpr ession which does not have this defect b u t it is not nece ssary for the work in this stu dy .


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162.2.3. Isotherm Adsorption Equation: inP \IT Equation

The saturation pressure P s of the refrigerant can be approximately expressed as a function oftemperature as following (Smith, 1996)

(2.11)where A and B are constants.

For methanol, according to Eq.(2.4), A and 5 can b e determined b y following e xpressions:(a) at a state with tempera ture T

andA = 12.6973 + 87582.885/7*5 = 4 0 2 4 . 3 7 + 1 7 5 1 6 5 . 7 7 / r

(2 .12a)(2 .13a)

and (b) in a proce ss the ave rage A and BA = 12.6973 + 87582.885/(7, Tu)

and = 402 4.37 + 87582 .885(/T, + 1/TU)(2 .12b)(2 .13b)

where 7/ and Tu are the lower and the upper temperatures in the range the saturation methanolexperiencing in the process.

Similar ly, the pressure -tempe ratu re rela tionship of an adsorbate can also be simply e xpressed a s\nP=b*(-J/T) + a (2.14)

To determine a and b (the intercept and the slope for a constant mass concentration line on thelnP vs -1/Tdiagram, respectively), rewrite D-A equation \nW = \nlV0-D{T\n{PsP))" a s

InP = c*(-7 /7 )+lnP, (2 .15)where c = (ln(W0/W)/D) " = (\n(X(/xyD) and x is the mass of the adsorba te adsorbed.

Substitute Eq. (2.11) into Eq. (2.15), we have Eq. (2.14) (InP = b*{-l'T)^ a), and(2.16)


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17With a series of a a nd b, a set of lines for a particular adsorbate/adsorbent pair can be drawn in

the lnP 1/T t diagram. The parame ters Wo, D, n, and thus b are determined by adsorption test .In order to make the diagram more rea dable, the pressure P rather than lnP is denoted in the v-axiala nd T in the x-axial along with -1/T in practice. Fig. 1.1. shows such a diagram and an idealadsorption r efrigera tion cycle in the diagra m schema tically .2 .2 .4 He a t of Adsorpt ion Clausius-Claper yon Equa t ion

Under the a ssumption that the specific volume of the gas is much gr ea ter than that of the liquid, thespecific volume of the liquid is negligible, and if the pre ssur e is low enough so the ga s can b e trea tedas the ideal gas, the equilibrium vapour-liquid phase transformation for a pure fluid can be expressedb y Clausius-Claperyon equ ation (Smith, et al. 1996)

dlnP/dT = hjg/RT3 (2 .17)where hjs is the latent enthalpy of the liquid to vapour pha se transforma tion.

The Clausius-Claperyon equation is also applicable to gas adsorption equilibrium. The analogousequation :?or adsorption is (Smith, 1996)

(d\nP/oT)x - had /RT (2.18)

wher e the sub script x signifies that the derivative is taken a t constant concentration a dsorb ed and hadis the isosteric (constant volume) heat of adsorption and is a function of the concentration .v, thema ss of refrigera nt a dsorb ed pe r u nit mass of adsorb ent.

Rewrite the Eq (2.17) and (2 .18), we geth, = 6 l n P R (2.19)

Js d(-\/T)andf P\nP \ R ( 2 . 20 )

which mean that h/ s and had can be obtained from the slopes of the equilibrium lines for the purerefrigerant and for a constant concentration x on the lnP vs - / T diagram.1 A therma lly isolated system can b e put into a state of negative tempe ra ture . If tempe ratu re were defined asthe negative reciprocal of the conventional temperature, ie, New temperature 0= - 1 / Old tempera ture T.temperature would vary smoothly from minus infinity (what we now called a bsolute zero) through ze ro, andon to plus infinity (Atkins, 1994).


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18

Comparing Eq. (2.20) with Eq. (2.14), it is easy to seef K*=bxR ( 2 . 2 1 )~h

That is to say that the heat of adsorption had is just the multiplication of the slope b of a constantconcentra tion line on lnP vs (-J/T) diagram and the ga s constant R.

2.2.5 The D esorption and the Adsorption Threshold Temperatures

In Fig. 1.1, T2 and T4 are tlie threshold temperatures at which the desorption and adsorption startsrespectively, Pc is the condenser pre ssure and Pe is the e vaporator pressure , respectively.

It is difficult to measure the threshold temperatures experimentally. Nevertheless, it can bedetermined b y three theoretical approaches.

By Clausius-Claperyon Equation

Integration of E q . (2.17) from state e to c, and Eq. (2.18) from state 1 to 2

(2.22)a nd

P c tAhJxl"Tzir " ~^rdT ( 2 . 2 3 )e 'Since the values of haj and h J S onl\- change a little in the integration temper ature range s, they ma}'

be supposed to be constants, or thought as the average value s over the temperature range. Therefore

l n / J - l n P = ( - -}h,JR ( 2 . 2 4 )and

\nPc-\\\Pe=\ - |(/7 A IR (2.25)

,T 1 Equa t ing the two integrals gives

4 1 1 hfg i li ( Te Tc(~-) (2-26) vnu K

Similarly


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>Sf"

191 1 h fg 1 1+ ( (2.27)

By D-A Equation and Pressure Equation

We have shown that the D-A equation can be rewritten as Eq. (2.15) and the saturation pressure P sof the refr igerant can b e e valuated by Eq (2 .4). The genera l form for Eq (2.4) can b e e xpressed a s

lnP, = A 0+At/T+A2'f (2 .28)whe r e t o , Aj. a nd A2 are constants.

Combining Eq. (2.15) a nd Eq. (2.28) y ields(Ao- \nP)T? -(c-Ai)T + A2 = 0 (2.29)

Thusc = (Ao + - L + - 4 - - In P)T (2 . 3 0 )

and

2(A (> - In P)

and the larger value should b e taken respectively for T.

The desorption threshold tempe ra ture T2 is given by

-4A2(A 0 - l n P )

(P x -A x)Mcx -A])2-4A,(A0-\nPc)= v j^ 1' V v w ^ ^J cj_\ P )

The adsorption threshold tempera ture T4:

4 2K-InP. )where cv = (A + 4 - + -^ - - In Pc )T,.

^ The larger value should be taken respectively for T2 and 7V


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2 0For example, if 7*1=293.15 K (20 C), 7>=383 .!5 K (110 C), 7^=268.15 K (-5C)? and 7 > 3 0 8 .15

K (35 C)? in case of methanol, lnP=-3.5287, ln? e=-1.2848, >40=12.6973 , ^ ,=-4024.37 7", A2=-87582 .885, it is calcu lated that r := 3 3 7 . 3 9 K and 7 "4=332.32 K.

By D-A Equation and the Simplified Pressure EquationEq. (2.14) (lnP = b*(-lT)+ a) can be rewritten a s

T = b/(a - In?)That means - In/",)

and T2 = Hxwhere P e and P c is the eva porator a nd the condenser pre ssure , respectively, and a\ =A(T\).

(2.34)(2.35)(2.36)

Therefore

Similarly, we have

where a^A (T^).

T - ax-\nPe

l, =4 a.-lnP.

(2.37)

(2.38)

For example, if 7>=293.15 K (20C), r 3 =383 .15 K (110C), 7> 2 68.15 K (-5C), and 7 >3 0 8.15K (35C), in case of methanol, lnP=-3.5287, lnP c=-1.2848, a ,= 13.7165, and


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ft

2 12 .3 TES T O F ADSORPTION PRO PERTY {P-T-x)

2.3.1 The Te st Rig for P-T-x Relationship Test

As mentioned above, the P-T-x (pressure, temperature, and concentration) diagram for the workingpair (adsorbent/adsorbate) is a powerful and convenient: tool for analysing a particular adsorptionrefrigeration cycle. The test rig used to investigate the P-T-x relationship for the adsorbent/adsorbatepairs a t Monash University is shown in Fig. 2 .1.

METHANOL

zxm, I'UUSSUBTv 7i i VESSUL J /I 2_ /1

Figu re 2.1 The test rig for the P-T-x relationship

2 . 3 .2 Expe r imenta l P rocedu res

This test measures the changes in pressure P for given changes of T for fixed concentrations x. Theprocedures a re1) Put the desorbed adsorbent sample in the pressure-monitored vessel (the short cylindrical vessel).2) Char ge the a dsorb ate (methanol) into the gra dua ted glass tube (the long methanol flask).3) Hea t and V acuu m the adsorbe nt sample to remove gases from the adsorbent.4) V acui 'M the adsorba te tu be to remove gases from the adsorbate space.5) Let the adsorbe nt adsorb a certain amou nt (volume ) of adsorb ate.6) Hea t the pressure -monitored vessel from the initial (amb ient) tempe ratu re to 50C (the ma ximum

tempera ture of the pressure sensor) by step of 5C. The time step is set by 15 minutes (this time


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' 4

2 2step is enough for the adsorption equilibrium to set u p from one state to the ne xt state ). When themaximum tem pera ture is rea ched, let the pressure vessel cool down to the a mb ient tempe ra tur e.

7) Repeat step 6 tliree time s to obtain a verage value s for one concentration.8) Repe at step 5 to 7 for other concentra tions.

2 3 .3 Exper iment D ata Process: 5A Molecular Sieve Met! inol

The first working pair wa s 5A molecular sieve and methanol. The test data a re listed in ta b le l.

ft

T a b l e l i

T ( K )2 8 8 . 1 52 9 3 . 1 52 9 8 . 1 53 0 3 . 1 53 0 8 . 1 53 1 3 . 1 53 1 8 . 1 53 2 3 . 1 5

D - T - x D a t a o f 5 A M o le c ul a r S i e v e M e t h a n o l A d s o r p t i onW ( l / k g )P s ( k P a )9 . 7 9 0 4 61 2 . 8 7 5 0 81 6 . 7 6 6 9 52 1 . 6 3 4 0 52 7 . 6 6 9 9 23 5 . 0 9 6 0 14 4 . 1 6 3 95 5 . 1 5 7 6 5

0 .0 48 0 6 6 0 .0 65 34 4 0 .0 72 7 9 0 . 0 8 1 2 6 0 .0 8 6 7 9 2 0 . 0 8 9 4 4 3 0 . 0 9 1 9 5 2P ( k P a )

0 . 0 2 5 4 5 50 . 0 3 7 0 5 20 . 0 5 3 2 2 50 . 0 7 5 5 10 . 1 0 5 8 6 10 . 1 4 6 7 4 80 . 2 0 1 2 6 10 . 2 7 3 2 2 3

0 . 1 1 0 2 9 90 . 1 5 6 5 8 20 . 2 1 9 5 60 . 3 0 4 2 8 80 . 4 1 7 0 5 80 . 5 6 5 6 2 40 . 7 5 9 4 61 . 0 1 0 0 4 1

0 . 2 0 9 8 3 40 . 2 9 4 6 3 30 . 4 0 8 7 7 90 . 5 6 0 7 4 90 . 7 6 0 9 7 71 . 0 2 2 1 9 31 3 5 9 7 8 81 . 7 9 2 2 2

0 . 4 4 0 7 2 10 . 6 1 1 0 4 30 . 8 3 7 4 6 61 . 1 3 5 2 9 71 . 5 2 3 1 4 82 . 0 2 3 4 4 62 . 6 6 2 9 8 73 . 4 7 3 5 4 2

0 . 6 8 7 8 6 60 . 9 4 6 4 8 51 . 2 8 7 7 2 11 . 7 3 3 3 3 52 . ? Q 9 5 8 23 . 0 4 7 8 6 73 . 9 8 5 4 5 25 . 1 6 6 2 0 6

1 . 6 0 8 0 0 82 . 1 8 0 7 6 22 . 9 2 5 7 5 13 . 8 8 5 2 5 45 . 1 0 9 5 4 76 . 6 5 7 9 2 58 . 5 9 9 ; S 21 1 . 0 1 5 7 4

4 . 0 3 8 1 6 85 . 3 9 1 1 8 27 . 1 2 3 9 5 39 . 3 2 2 4 21 2 . 0 8 7 1 61 5 . 5 3 4 9 5 -1 9 . 8 0 0 4 72 5 . 0 3 7 8 8

By varying the value of n , a linear relationship oflnWand (21n(P/P))" with the best correlationcoefficient r was ob tained. For the 5A molecular sieve and methanol. when /;=2.3 4, r=0 .997 . The D -A Re prese ntation is shown be llow.

300

y =-0.0018x -9.2809

(r in(Ps/P) )A2.34*E-5

Figu re 2.2 The D-A Representation for 5A molecular sieve a nd methanol


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23From the D-A Representation, it v/as found that and JFf=9.3817x10"" m/(kg adsorbent) and

>=0.0018172*10\ ThereforeIn? = [5+20 32 .11l6(~1nW-92Z09) }aiA](-V7)+A

or 1/2.3+1In? = [5+20 3 2 .1116(-lav-2 .5748)"-H(-l 'T)+^

where x=pW and p= Af-so= 817.378 kg/m3(Eq. 2.5).

(2 .40a)

(2 .40b)

if

r

The P-T-x (pressure, temperature, and concentration) relationship is shown in the In? ITchart a s Figure 2 .3.

a 0.1

0 . 0 1

- M e t

i yy

/ i

/ y

x=

id l

1 i 0.074

OlL/ I

//I

0./ I/

/

///

/ V

//

y -

//

07/

1 0.0/4V~7

-Y-U hJ__J/

A

/

6 0.01 ///

5 0.0/ J

4 0.03 .' / \J/I /I /

/ / /T w/ ! /

//h \AHV\f,f

/

/ ! /! 1V/1 /

A/ >r 1 /i//

1

!Vfi*t

\I 10 -7 Ns/m (4.5)

For example, if we take the temper ature range Ti -T? as 293 .15-337 K (Chapter 2 ), the avera gethermal conductivity ks,,.2= kHe = 0.1573 W/m/C.

After the temperature reaches the desorption threshold temperature, methanol is desorbed. Theheat conductivity of the gas m ixtu re can be approximated b y

in which1 +M JL

v "j

(4.6)

(4.7)

where .v,, //,, and M, a re the mole fraction, the viscosity, and the mole weight of the /th species (Bird,et al, 1960). The mole fra ction of the /th species ca n b e determined as follows.


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3 9

In this process, the part ia l pressure of the methanol vapour is the saturat ion pressurecorresponding to the condenser tempe ra ture . If the condenser tempera ture is 35 C, Pji/ef/l,35c=0.2767b ar (Eq (2 .4)). The pa rtial pre ssur e of Helium is determined a s follows.

In the process of charging methanol, the evaporating temperature was maintained above 0C(chapter 3). Taking it as 2C, the partial pressure of methanol is the saturated pressure at thistemperature (0.0457 bar). In the process of charging Helium, if the environment tempe ratu re is 20C and the total pressure of the system is one atmosphere, ie, 1.01325 ba r , the pa r t i a l pressu re ofhelium is 0.96755 bar. At the condenser temperature of 35C in the condensing pro cess, the par tialpressu re of helium is Pnejsc = PHCZOC X (30 8.15) / (293 .15) = 1.017056 ba r. The total pressur e in thecondensing process is 1.29376 b a r .

There fore, the mole fraction of the two species Xsutk^ / W / P = 0 . 2 1 4 , and xHe - 0 .786.

For methanol, kgMetk=0.0157 W/m/C (Cheng and Kung, 1994). For helium, in the temperaturerange 337-383.15 K (Chapter 2) the average thermal conductivity kHe = 0.173 W/m/C from Eq.(4.5). So for the ga s mixture ks = kmix = 0 .0886 W /m/C from Eq. (4.6).

i T

Therefore, according to Eq. (4.3), the effective thermal conductivity of the place in the packedbed be fore and after the desorption threshold tempe ratur e is kbe M.2~ 0.38 W/m/C (in proce ss 1-2)and kbc,0,2.3 0 .28 W/m/C (in process 2 -3), re spectively.

Alternatively, kbeiOf ks can b e correlated b y plotting it against kj ks for va rious void fractions bySchumann and V oss (McAda ms, 1954) where ks is the therma l conductivity of tlie solid pa rticle . Theresults from the two approaches are coincident.

4.2.3 The Effective The rm a l Condu ctivity of Packe d Be d with Fluid Flow, /rbc,uWhen a fluid flows at steady rate through the voids in the column, the equation for the effective(apparent) bed conductivity of the adsorption bed, which consists of the adsorbent porous pellethaving the apparent conductivity kpe and interpellet voidage teemed with gases of conductivity ks,was given by Felix and Neill (McAdam s, 1954). In SI system, it can b e expre ssed a s

y. 0.3048 N o i ; 3.65 + 0 . 0 1 0 6 - ^ -ev (4.8)


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4 0for cylindrical packing flowed heated and cooled a ir u pwar d throu gh voids, where D t is the insidediameter of tu b e, D p is the diame ter of pa rticle, u/xs the supe rficial velocity' b ase d on the total cr osssection without particles respectively, v is the kinematic viscosity of fluid, and s is the adsorptionbe d porosity'.

The kinematic viscosity of fluid

After the tempe ra ture along the centre line of the bed re aches the desorption threshold temper atu re ,there is me thanol desorbe d. The kinema tic viscosity of the mixtu re is Vm;x =//mix /pmvs. where //mi* andp m iK a re the viscosity' and the density of the m ixtu re , re spectively.

The viscosity of the gas mixtur e can b e approximately b y (Bird, et al, 1960)(4.9)

The viscosity / / of methanol vapou r a t 25C is 96.1xlO"7 Ns/m 2 (Cheng and Kung, 1994), and theaverage value of// of Helium in the temperature range 33 7-3 83.15 K (chapter 2 ) can be taken a s//2-3,He=225.433xl0" 7Ns/nr (Eq. 4.5). So the viscosity of the mix tu r e //m ix =156 .739x l0 '7 Ns/m 2 .

The density of the mixtur e which can b e expressed a s p=pae +Aie and /?, = P-J(R\T). Taking thevalues for PUe and PHe , we have Aie.35c = 0 .2 7 67 xl0 5/ (8134/32) / (308.15) = 0.3456 kg/m 3 , andpHe.35c =1 .0 17 0 6x l0 5/ (8134/4) / (308.15) =0.1588 kg/m 3 . In the heating bed, taking the averagetemperature as the reference temperature , we have A =A,35cx308.15/r 2 . 3 . I f the ave rage t empera tu reis taken as 3 60.0 8 K, p^ k = 0.29577 kg/m3, and p^ = 0 .1359 kg/m 3 , and p = 0.43 165 kg/m3 .

There fore, the kinematic viscosity of the m ixtu re v2.3 =vm;x =ju mK /p mi s =36 3 . 1 05 x l 0 ' 7 n r / s .

Taking D, = 48.5*10"3

m, Dp = 4*10'3

m, e = 0.42, kpe = 0.716 W/m/K, ks,.3 = 0.0886 W/m/K,v,.3 = 363 .105*10" 7 nr /s into Eq. (4.8), we have k^-is =3.2 1 W/m/K for , =0.3 m/s.

4 .3 SOLUTION APPROACHESCYLINDRICAL REGION

FINITE-DIFFERENCE FORMULATIONS FOR

Analytic Approach V s. Nume rical Approa ch

There are two approaches in solving the heat-conduction equations. One is analytic and the other oneis numerical (Gebhart, 1993). The analytic technique (Carslaw and Jaeger, 1959) is based on


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41generating solutions in mathematical form. The relevant differential equations, subject to idealisedb oundar y and initial conditions, often r esu lts in a definite solu tion; However , a n impor tant limitationof the analytical technique is that solutions commonly result only for very simple or idealisedgeometric regions and initial a nd boundarv' conditions. On the other ha nd, num e rica l me thods providea very suitable and convenient alternative. In this thesis, nume rical methods a re adopted.

1 - s i

The Finite-Difference Repr ese ntation V s. the Finite-Eleme nt R ep re senta tion

There are two commonly-used numerical methods for heat transfer analysis: one is the finite-differe nce re pre sentation, the other is the finite-element re pre sentation. The finite-differ ence method(Croft and Lilley, 1977) converts the partial differential equations, the PDE, and the boundingconditions, BC , into the finite-differ e nce equ ations solved at individu al gr id points. T he finite-element method also represents the region of calculation by finite subdivisions. However, there ismuch flexibility in the choice of the grid in finite-element ana lysis. There fore, irre gu lar regions andcomplicated b oundar y conditions may b e analysed a lmost as simply a s very re gu lar ones. The finiteelement itself comprises a group of closed associated nodal points, and interrelates all of theconstitue nt nodal points. In our ca se, the geometry is simple enough to u se the finite-differe ncerepresentation.

Finite-Differe nce Form u lations for Cy lindrical Region

For an internal no de at constant and uniform conductivity premise, the finite-difference equation inimplicit form at time level p corre sponding to Eq. (4.1) is

(4.10)

Figure 4.1 The representation of two-dimensional temperature fields in cylindrical region.


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42

At node 0 (the centre line of the cylindrical be d).

A-\

f .

0

Figu re 4.2 The r epre sentation of two-dimensional tem pera ture fields in cylindrical region

and the finite-differe nce equ ation is- 1 0.0.it , Tp+ ] TpO.O.A- J 0 .0^ J

The surface (the boundary) and the region immediatel)- inside it of the cylindrical geometry areshown in Fig. (4 .3 )

Figu re 4.3 Nu mer ical formulation at curved b ounding sur faces of a cylindrical re gion

There are five conductive paths affecting the surface region of TSiStS. They a re from 7^.;^, , 7^ ./^,Ts.s+i,s, Tw.h a nd Ts,StS+1. In addition, surface flux Qa{sss) and convection loading at the surface areincluded, as O^^RAfiAz and h(Te-Ts,s,s)RA0Az. The distributed source flux Qv,(s,s,s) a r i s e s i n t h evolume element RA


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43

kRA(j)Azi

2 AzpcRA(f>AzAr

4.4 HEAT TRANSFER ANALYSIS ON THE COLLECTOR/DESORPTION BED INHEATING AND HEATING/DESORPTION PROCESSES

As mentioned ab ove, the he ating process ca n b e divided into two steps. In tlie first step (from state 1to 2), there is no adsorbate desorbed theoretically, so the heat effect is zero and the density of thepellet is approximateK' constant. In the second step (from state 2 to 3 ), tlie a dsorb ate is desorb ed, sothe heat effect, the change s of tlie density a nd the a ppar ent tlier mal condu ctivity of the pellet, and theeffect of convention mu st be take n into a ccou nt.

4.4.1 The Governing E quations and Conditions

From state 1 to 2, the he at conduction e qua tion can be simplified as, d 2 T \cT, ad, dT^T dr~ r r a- cr (4.13)

The initial condition is

and the bou ndary condition is

drdT .

(4.14)

(4.15a)

(4.15b)where m cs, cCi,? and Tcs is the ma ss, the specific heat and the temper atu re of the collector/genera tor.

From state 2 to 3 , the he at conduction equ ation is

ct dr1 r dr pc r dr dr pc

and the boundary conditions ar e in the same form as in step 1.

(4.16)


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The so-called hea t sink*

= - (1 - e)ppnRDx0 (A - In P e):T[(A - In Pc )T - B}"'' e xp{-D[(A - In Pe )T - B)"}

44

(4.17)

It is difficult to get the a na htic solutions for all of these e qua tions.

4.4.2 T he Nu me rical Solutions

Usingfinite-differencemethods, we can get the numerical solutions for the energy equ ations for thetwo hea ting steps. Ther e ar e two finite-diffe re nce schemes: the explicit scheme and the implicitscheme. Although the former offers computational convenience, it suffers from limitations on theselection of the increment of time and resu lts in a very lar ge numb ers of time inter vals. To re du ce theamount of computation time, the fa tter is employed in the analy sis car ried ou t here .

To simplify the e xpre ssions of the finite-differe nce e qu ations, introducing the finite-differ enceform of the Fou rie r nu mb er which is defined as

Fo = aA t /(Ar) : (4.18)

In step 1, the finite-differenceequations in implicit form are4Fo)T0p+] - 4FoT^ = To"

j^FoTtf = T>(4.19)(4.20)

where2FoTf\x + (1 + 2Fo)TspA = Tf

m r TP*] _T Pmc'g('c/g 'c'g Jc/

pcAr

_ 1 c / g= J

(4.21)

(4.22)

where A is the a re a of the contact, A-2nR b], and Rc is the contact therma l re sistance per a re a . So Eq.(4.21) can b e e xpressed as

2Fo + 2F o Ar_ (4.23)

From Eq (4.22 ), we also have


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45AAtclgCclg-"e cc/ Rc c> s clgCclgRe

Eqs. (4.19), (4.20). (4.23), and (4.24) can be used tosolve temperature distribution in thishea ting step.

%

Wlien the t empera ture of a place in the bed reaches the desorption threshold tempe ra ture , step 2starts at this place . Since there is refrigerant desorbed, the properties at the point will change withthe time, and when the fan runs, a further change of the properties at the point will take place.Tlierefore. the changing pr oper ties should be used in the evaluation for this step. To simplify thecalculation, the thermal conductivity k in the following finite-difference equations and Fourie rnumber Fo is taken as two constant values according to the temperature of the centre line of theheating bed (one is for the points where the t empera ture is equal to orgreate r than, but thetempera ture of the centre line is less than, the desorption threshold tempe ra ture , and the other is afterthe temperature of the centre line reaching thedesorption threshold temperature). The finite-difference equ ations in this step are

4Fo)Tfl -

\FoTp~l =TP+2 / J x>1 ' k

(4.25)

(4.26)

IF o Ar

andAAt

+ m^gcclgRcAAtRc

whereQl ^-^-o)ppnRDx0{A-\nPc)% p{{A'\nPc)r i'' -B]"

exp{-D[(A~lnP c)T / -B]"}^ ~TP= 0 , 1 , , ^ - 1 ,^ ( 4 . 2 9 )

At

To save the energy used inthe heating process 1-2so as to improve the Coefficient of thePerformance (COP) of the system, the fan is switched on only when the t empera ture of the centreline of the bed reaches the desorption threshold temperature T2. T2 can be determined theoretically(chapter 2 ).

For example, in our case the adsorption bed, /=0.53 m and /? 6=2.425xl0 ' : m. IfTe= 2C, Tc=35C, T, = 20C, T3 =110C, and the activated carb on/methanol we tested is used as the working


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i-'

4 6pair, the value s for the numer ical a nalysis can b e ob tained. Sub stituting kbc.0.1-3 ~ 0.38 W/m/C (fanoff in step 1-2). k'be.o.2-3 * 0 .28 W/m/C for the points, if there is any , where the tempe ra tur e is equ alto or greater than, but the temperature of the centre line is less than, the desorption thresholdtemperature, and kbetl = 3 .2 1 W/m/K (fan is on after the tempe ra ture of the centre line re aching thedesorption threshold tempe ra ture ), /r= 45 2 +l 147.5x kJ/m3/C, m csCc. g = 0.95x460 = 437 J/K, e =0.42, pp = 0.78xl0 3kg/m 3 , Q a0 = 82L4,/ = 821x2 tf4/> n=\34, D=14.962xlO-5, x0 =0 .298 kg / (kgadsorbent), P c =iV w/, 35c =0.2767 ba r , a nd Re = 5 x 1 0 / {kc.g+kbed) into the ab ove e qua tions andsolving them, the re sults are shown in Figu re 4.4.

T c/g40 0380360

w 34032 0300280

0 60 120 180 240 30 0 360 420/ (miii)

Figure 4.4 The temperature distribution of the heating processes in the bed (L=0.53 m and H*=0.3m/s). r c s is the temperature of the collector/generator, T s, r R b 2 , and To is the temperature of thesurface, the half radius, and the centre line of the bed, respectively.

T

= 0 .2294/R 2 =

+1

t

293 . 17 ^

, , , ,

From the figure, it can b e seen that the tempe ra ture distribu tion in the b ed is ra ther e ven, and nomatter how complicated and different in the two heating steps, the temperature of the bed is linearlyproportional to the time and the linear relationship is the same in the whole heating process (step 1and step 2) with the constant heating flux on the collector. This relationship is useflil in determiningthe heating time for the two heating steps.

4.5 THE THEORETICAL SOLUTIONS CONPARED TO THE EXPERIMENTAL DATA

To justify the theoretical re sults, it is necessary to compar e them with the corre sponding tested data.The theoretical a nd the tested te mper atu res with space and time in the heating processes ar e shown inFig. 4.5.


61/167

47It can be seen from Fig. 4.5 that the temperature distribution in the bed is really even, and the

temperature of the be d is indeed linearK' proportional to the time and the linea rly relationship is thesame in the whole hea ting proce ss (step 1 and step 2 ) with the constant hea ting flu>: on the collector.However, the tempe ra ture of the bed is a little lower than that anticipated theore tically. The rea son isthat it was assumed the bed is well insulated (adiabatic) so there is no heat exchange between thebe d/heating ma t and the environment in the theore tical ana lysis, while a ctually there is heat lost fromthe b ed/heating ma t to the environment. Since the he at loss from the b ed/heating ma t ma y differ fromone case to another, the no-hea t-loss model is used prefer ab ly.

40 03 803 603 403 2 03 0 0 (2 80

CIT

) 60 120 180 240 300 360 420/ (niin)

* R/2

ToTheoretical

Figure 4.5 The expe rimental tempe ratu re distribu tion of the heating processes in the be d (1=0.53 mand 2^=0.3 m/s). Tc,s is the tempera ture of the collector/generator, T^n, and To is the temperature o

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A SOLAR ADSORPTION REFRIGERATION SYSTEM OPERATING AT NEAR ATMOSPHERIC PRESSURE

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