Dynamic Behaviour of a Vapor Compression Refrigerator- A Theoreti

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Purdue University

Purdue e-Pubs

International Refrigeration and Air ConditioningConference

School of Mechanical Engineering

1988

Dynamic Behaviour of a Vapor CompressionRefrigerator: A eoretical and Experimental

AnalysisC. MeloFederal University of Santa Catarina

R. T. de Silva FerreiraFederal University of Santa Catarina

R. H. PereiraEmbraco

C. O. R. Negrao

Embraco

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Melo, C.; Ferreira, R. T. de Silva; Pereira, R. H.; and Negrao, C. O. R., "Dynamic Behaviour of a Vapor Compression Refrigerator: Aeoretical and Experimental Analysis" (1988).International Reigeration and Air Conditioning Conference. Paper 52.hp://docs.lib.purdue.edu/iracc/52
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DYNAMIC BEHAVIOUR OF A VAPOR COMPRESSION REFRIGERATOR:

Abstrac t

A THEORETICAL AND EXPERIMENTAL ANALYSISClaudio MeloRogerio Tadeu da S ilva Fe rre ira

Universidade Federal de Santa Catarina (UFSC)

Departamento de Engenharia MecanicaCaixa Posta l 47688049 - Flo rianopolis - SC BRAZIL

Roberto Horn Pere ira cezar Otaviano Ribeiro NegraoEmpresa B ras ile ira de compressores S/A (EMBRACO S/A)Rua Rui Barbosa, 1020caixa Postal D-27 89.200 - Jo inv il le - SC BRAZIL

This work presents th e mathematical model employed to simulatethe dynamic behaviour of a domestic re f r ig e ra to r . The componentmodels inc lude a hermetic rec ip roca ting compressor, a condenser, anevaporator, an accumulator and a cap il la ry tube.

All the components were modeled, and basic equations for themwere derived from the physica l laws ofmass and energy conservation .The simultaneous so lu tion of a l l the d if fe ren t ia l and a lgebra ic equations allows the t ran s ien t ana lys is of the re f r ig e ra t io n system.

The experimental setup employed to va lida te the computer

pred ic t ions i s a lso presented . Results o f the s imula tion werecompared with experimental re su l ts (see f igure below), and the va lid i ty of the model was confirmed.13

012 a

"'. 11"'

n 1(.)"'"'0"'"' ew"'. 7

-- ED

,l ')t l

Tir -1 f 5TARTUP 1

Refrigeran t p ressures a f te r s ta r t-up

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COMPORTEMENT DYNAMIQUE D'UN REFRIGERATEUR A COMPRESSION DE VAPEUR.ANALYSE THEORIQUE ET EXPERIMENTALE.RESUME : Cette communication presente un modele mathematique poursimuler le comportement dynamique d 'un re fr ige ra teu r manager. Lesmodeles des composants comprennent un compresseur hermetique a p is-ton, un condenseur 1 un evaporateur, un accumulateur e t un tube ca-p i l la i re .

Taus les composants ont e te modelises e t des equations fondamen-ta le s se rapportant a eux decoulent des lo is physiques de la conser-vation de la masse e t de l 'ene rg ie . La reso lu tion simultanee de l 'e n -semble des equations d iffe ren t ie l le s e t algebriques permet l 'ana lyse en regime t ran s i to i re dU systeme fr igorif ique .Le montage experimental employe pour va lider les p r e v i s ~ o n s del 'o rd ina teu r es t egalement presente. Les resu lta ts de la simulationan t ete compares aux resu lta ts experimentaux e t la va lid i te du modelea ete confirmee.

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DYNAMIC BEHAVJOUR OF AVAPOR C O ~ R E S S I O N REFRIGERATOR: ATHEORETICAL AND EXPERU1ENTALANALYSISCLAUDIO MELO (*)

ROGERIO TADEU DA SLLVA FERREIRA (*)ROBERTO HORN PEREIRA (**)CEZAR OTAVlANO RIBEIRO NEGRAO (**)( ') Department. o Mechanical EngineeringFederal Un1vers1ty of San ta CatarinaP.O . Box 47688049- Florian6polis - SC - 8ralil

(**) Empresa ~ r a s t l e ~ r a de Compressores S/A (EMBRACO)Appl1cat10n E11g1neeringP. 0 . Box u-i.l3920J - Joinvillc> - SC - B raz il NOMENCLATURE

A area m2C t h e ~ a l capacity, kJ1(D capillary tube d iamete r, m friction factorh specific en tha lpy , kJ/kg L capillary tube length, mM mass, kgm mass flow rate of refrigennt, kg/ sp pressure, PaQ heat transfer rate, kWR thennal resistance,K/kWRe Reynolds numberS quality of the refrigerant nt the capillary tube lnletT temperature , ct time, sV velocity, m/sdensity, kg/m 3Subscriptsa accumulatorb suctionc condenserd d ischarge e evapora to r f freezerg cabinet liquid refrigerantm supply airo outsidep refrigerant leav ing compressorr refrigerants superheated t refrigerant leav ing condenserv vapor refrigerantw wally refrigerant leaving capillary tube

l . INTRODUCTlONAcommon procedure inmost of the compressor and/o r refrigeratormanufacturing

companies is to perform "xperimen tal tests in order to ascertain the refrigera

torJ?erformance as a func tion of tim e. These tests are perfonned according to rder

enceil[ and normally requi.re a long period of time. One way to speed up such procedureis to employ computational tcochniques to numerically s imula te the refrigerator

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and

F ig . l - Superheated vapor model

Fig. 2 - Hea t flow diagram for the superheated flow modelApplying the continuity equa tion to the contro l volume gives

d(Mc)/dt =mp - mtApply ing the energy equa tion to the node points of Figure 2, yields

d(Mc hc 5 )/dt = p ~ - mt hcs - ~ s r w

(1)

(2}

(3)

In equa tion (2) the refrigerant internal energywas replacc:d by the: refrigeranten thalpy . In doing so, the pressure variationwith time was disregarded . TI1isassumptio n, however, has only a minor effect on the simulat ion results 161.Combining equations (1) and (2), gives:

d(h )/dt = [nL (h - h ) - Q ]!Mcs p p cs csrw c ( 4)Numerica l integrationof equa tions (J.) and (4) gives the mass of refrigerant inth e condenser, Me , and th e bulk enth8lpy of refrigerant vapor, hcs' respect ively.The density of the refrigerant vapor is found knowing the mass of vapor andthe condenser volume. The temperature and the pressure in the condenser is calculatedfrom property relations. The standard Dittus-Boelter equa tion is used to calculatedthe heat tnnsfer coeffi.cient on the inside of the tubes. TI1e heat transfer from theoutside of the tubes to the air is obta ined from re ference 191 .

2.2. Capillary tubeThe main task of the capillary tube expansion device is to main tain th e minimum

pressure ln thecondenser at which all the refrigernnt can condensate.'lhe capillary tube , although physically simple , is behaviourly complex. Someitems ofcomplex mathematical analysis are ; the friction factor for the two-ph


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asswnptions: i) the capilhry tube is a straight, horizontal, constant innercliamete r tube, i i) flow in the capillary is one-d im ensiona l, homogeneous, andadiab8tic , i i i) the refrigerant is fr(0.75 - 0.68 ln Re + 0.024(lnRe) 2 J}/ 11Erth' s


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1\pply ing the ene rgy equation to t:he node points of Fi.gu re 4, givesd(Twf)/dt { ~ w f - ~ f [ } / C w f

d(Tf)/dt {Qwff + Qfg- ~ l f } / C f d(Tm)/dt ( ~ f + ~ g - ClnlWeV - O m w e ~ -

d(Tg)/dt (Qwgg - Qfg - Q1ngl/Cgd(Twg)/d t - {Oawg - ~ g g l / C w g

Numerical int:egrat ionof equations (9 -13 ) gives the bulk temperature of t:hepoints indicated in Figure 3.3. ffiMPARISON BETWEEN LABORATORY VERSUS

COMPUTER PREDICTED RESULTS

(9 )

(10)

( ll)

(12)

(13)

In order to validate themodel, an experimental test was performed following therecomendations of reference Ill . Since one of the assumptions of capilJary tubemodel is to consider flow as adiabatic, i t was necessary , before the beginning ofthe test, to insulate the refrigerator capillary tube. After that, the refrigeratorwas placed in an environmen ta l tes t chamber, in which the ai.r temperature ismaintained in a constant value of (109.4 9f).The temperature and pressure in several locations of the refrigerator, asindicated in Figure 5, aremeasure d respectively by copper constantan th ennocouplesand stra in gage pressure transducers. Both the thermocouples and the pressuretransducers areconnec ted to a data acquisition system which registers a ll variables

within a time interval of two minutes. The pressures, arc also continuously registered

by a two-channel recorder.

ACCUMULATOR oeSUCTION LINE

10CABINET 09

Fig. 5 - Refrigeration sys tem under analysisThe results ot' such test , when compared Hith the compu ta tional results are

indicated in Figures 6 and 7 . Figure 6 shows the pressure behaviourHith time. The

results are shown only for the six f irs t minutes since the pressurevariation, aftsrthis time, is negligible. As one can see, Figure 6 indi.cates a good agre ementbetween laboratory versus model data. Figure 7 shows the freezer and cabinettemperatures vel sus time. As indicated, the steady state value of these vanablesis reached after ten !lours of operation. The agreement between the experlmental andcomputational results is also shown to be good.

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15"'o-;;:

0 12Q_ w0:: 9 .. -NUMERICAL::Jen & EX PERlMENTAL(SUCTION)nw .EXPERlMENTAL(DISCHARGE)::a. 6

3..... .................. ......,,..... ,

2 3 4 5 6TIME AFTER START-UP(min)

Fig. 6 - Refrigerant pressure versus time-_&.> 45,-----------------,-NUMER ICAL w EXPERIMENTAL(CAB INET)g; 40 EXPERIMENTAL(FREEZER1-~ 35wa.~ 30w1- 25

201510 -

...

50 2 3 4 5 6 7 8 9 10TIME AFTER START-UP (hou rs )

Fig. 7 - Freezer and cabinet temperature versus t imeTI


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good evenwith the s im plify ing assumptions used in th e model.In the nex t stage of thiswork, most of the assumptio ns will be , progressively,removed and a comparison "'ill be made between the CPU time required and the improvements on the simulation results.

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]7]

]8]]9]

5 . REFERENCESStandard IS0-24, Performance ofHousehold RefrigeratingAppliances -Refrigerators and Freezers, 1986. Beckey, T.J . , Modeling and Verification of a Vapor Compression Hea t Pump,Preprints of the 1986 International Institute of Refr igerationMeetin g, PurdueUniversity, West Lafayette , Ind iana, pp.l03-lll, August S-8, 1986.Chi, J. and Didion, D., ASnnula tion of the Transient Performance of a HeatPump, International Journal of Refrigeration, Vol. 5, n9 3, pp. 176-184, 1982.Yasuda, H., Tauber, S. and Machielsen, C.H.M., SimulationModel of a VaporCompression Refrigeration System, ASHRAE Trans

ac tions , Vol. 89 , part ZA, n9 2787,pp. 408-425, 1983.Dhar, M., Transient Analysis of Refrigeration System , Ph .D. Thesis, PurdueUniversity, 1978.Raje ndran, N. and Pate, M.B., AComputer Model of the Start-up Transients in aVapor Compression Refrigeration System. Preprints of the J986 InternationalInstitute of RefrigerationMeeting, Purdue, pp. 129-140, August S-8, 1986.Murphy, W.E. and Goldschmid t, V.W., Cyclic Characteri ,s tics of a TypicalResident ialAir Condit ioner-Modeling of Start-up Transients, ASHRAE Transac tions,Vo1.91, Part ZA, pp. 427-444, 1985.Me Arthur , J.W ., TransientHeat Pump Behaviour: ATheoretical Investigation,International Journa l of Refrigerat ion, Vol. 7, n 2, pp. 128-132, 1984.B riggs, D.E and Young, E.H ., Convection Heat T ransfe r and P ressure Drop of AirFlowing Across Triangular PitchBanks of Finned Tubes, sth NationalHeat Transfer Confe rence, Houston, Texas, 1962.

]10] Schultz, V.W., State of the Art: The Capillary Tube for, and in, VaporCompression Systems, ASHAAE Transactions Vol. 91, Part lB , pp. 92-105, 1985.i11] Erth, R.A. , Two-Phase Flow in Refrigeration Capillary Tubes: Analysis andPrediction, Ph.D . Thesis, Purdue University, 1.970.

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Dynamic Behaviour of a Vapor Compression Refrigerator- A Theoreti

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