Performance simulation of a two-evaporator refrigerator—freezer charged with pure and mixed refrigerants

Performance simulation of a two-evaporator refrigerator-freezer charged with pure and mixed refrigerants D. S. Jung and R. Radermacher Department of Mechanical Engineering, University of Maryland, College Park, M D 20742, USA Received 5 J a n u a r y 1990; revised 17 July 1990

A computer simulation of two-evaporator refrigerators charged with pure and mixed refrigerants operating on a Lorentz and Meutzner's cycle has been performed to determine possible substitutes for RI2 with an improved energy efficiency. The results for pure fluids indicate that the coefficients of performance (COPs) and volumetric capacities obtained with two-evaporator units are enhanced up to 6 and 15.5%, respectively, compared to those with single evaporator units. This is due to some of the evaporation occurring at higher temperatures in the two-evaporator units. For mixtures, a significant increase in COP of up to 18% is observed by matching the large overall drop in temperature of the air streams, 23°C, with that of refrigerant mixtures in the evaporator. The evaporator area ratio is a very important parameter and depends largely on the load distribution between the two compartments. The effect of the low temperature heat exchanger has been studied by varying its size. As the size increases, the COP also increases with a decreased pressure ratio across the compressor. An optimized two-evaporator refrigerator freezer unit charged with alternative, ozone-safe refrigerant mixtures may increase the energy efficiency considerably, helping to alleviate the environmental impact of refrigeration.

(Keywords: computer simulation; two-evaporator refrigerators; energy efficiency)

Simulation de la performance d'un r6frig6rateur-cong61ateur fi deux 6vaporateurs, charg6 avec du frigorig6ne pur ou en m61ange On a simulk par ordinateur des rbfrigbrateurs ?1 deux bvaporateurs, chargbs avec des frigorigbnes purs ou en mblange, fonctionnant selon un cycle de Lorentz et Meutzner, dans le but de dbterminer des substituts possibles du R12 avec une £fficacitb bnergbtique accrue. Les rbsultats avec les fluides purs montrent que les coefficients de perJbrmance et les puissances volumbtriques, obtenus avec des unitbs a deux bvaporateurs, augmentent de 6 et 15,5 % respectivement, par rapport h des unitbs gt bvaporateur unique, parce qu'une partie de l~vaporation se produit h une tempbrature plus blevbe dans les unitbs h deux bvaporateurs. Pour les mblanges, on observe une augmentation importante du COPjusqu'h 18 % due h une adbquation entre la chute globale et importante de tempbrature de l'air en circulation, 23 ° C, et celle du m~lange de frigorigbnes dans l'bvaporateur. Le taux de la surface bvaporante est un paramOtre trbs important et dbpend considbrablement de la distribution des charges entre les deux compartiments. On a bgalement btudib l'effet de l'bchangeur de chaleur ~ basse tempbrature par variation de sa dimension. Si la dimension augmente, le COP augmente bgalement avec un taux de compression rbduit au compresseur. Un rbfrigbrateur-congblateur h deux bvaporateurs que l'on a optimisb et chargb avec un mblange de substituts sans effet sur l'ozone, peut augmenter considbrablement l'effi'cacitb bnergbtique, ce qui contribue h diminuer l'impact de la production de Jroid sur l'environnement.

(Mots cl6s: simulation par ordinateur; r&rig6rateurs/~ deux 6vaporateurs; efficacit6 6nerg6tique)

The agreement of the Montreal ProtocoP to regulate the production and trade of ozone-depleting substances has greatly influenced the air-conditioning and refrigeration industries. At present, extensive research is being undertaken at many institutions to replace the fully halogenated chlorofluorocarbons (CFCs), R I I , R12, R I 3 B I , R113, R114 and R! 15 covered by the Montreal Protocol. One of the major uses of CFCs is in domestic refrigerator-freezers (here referred to as 'refrigerators') which predominantly utilize R12 as the working fluid. The work reported here is an extension of previous studies z dealing with conventional refrigerators with a single evaporator. In the previous work, only drop-in replacements for R 12 were considered as the replacement 014~7007/91/050254~ 10 ~C 1991 Bunerworth Heinemann Ltd and fIR

254

Int. J. Refrig. 1991 Vo114 September

would be even more costly if it were accompanied by any major system modifications. The results indicated that there are a number of mixtures which can be used as drop-in replacements. These fluids, however, are not expected to yield a significant increase in the coefficient of performance (COP) due to a small drop in temperature of the air stream in the evaporator side. In other words, one of the favourable characteristics of mixtures, a gliding temperature effect, cannot be fully utilized in conventional refrigerators with drop-in replacements due to an inherent restriction in the air stream tempera-

tures. It is expected that the greenhouse effect will be a more serious issue than ozone layer depletion in the next few

Simulation of a two-evaporator refrigerator: D. S. Jung and R. Radermacher Nomenclature

A Cp DSH DT H LMTD m P Q

REo U S T TS V VC VAo W X

Heat transfer area (m 2) Specific heat (kJ kg-~ °C-L) Degree of superheat (°C) Specified log mean temperature difference Specific enthalpy (kJ kg-~) Log mean temperature difference Mass flow-rate (kg s-~) Pressure (kPa) Rate of energy (W) Array containing residuals Overall heat transfer coefficient (W m 2K-I) Specific entropy (kJ kg-l°C 1) Temperature (K or °C) Heat transfer fluid temperature (K or °C) Specific volume (m 3 kg-1) Volumetric capacity (kg m 3) Array containing unknowns Power (W) Overall composition

Greek

~c

Isentropic compressor efficiency

decades 3. One of the most effective means of helping to solve the greenhouse problem is to increase the energy efficiency of energy conversion devices, including refrigerators. Considering that virtually every household in the developed world is equipped with a refrigerator, an increase in the efficiency of domestic refrigerators would mean considerable energy savings. Consequently, any study involving the replacement of RI2 with ozone-safe fluids should also focus on increasing the energy efficiency. The current design of the conventional one-evaporator refrigerator, however, has its own shortcomings. American standards for domestic refrigerators typically require the maintenance of 5 and - 15°C in the food compartment and freezer section, respectively. In other words, two distinct evaporator temperature levels exist. From the thermodynamic requirement that the smaller the temperature lift (the temperature difference between the condenser and evaporator), the higher the COP, the COP for cooling the food compartment is higher than that for the freezer due to the smaller temperature lift. The current configuration supplies cooling at the freezer condition of - 15°C, even if the food compartment requires cooling at 5°C. An air damper is used to maintain the food compartment temperature at 5°C. This damper splits the mass flow of air into two streams according to need. The cooling load in the food compartment is typically 40-60% of the total cooling load. Thus, for this 40-60% of the cooling load, the refrigeration cycle operates very inefficiently, without taking advantage of the smaller temperature lift necessary in this compartment. One possible solution to the above problem is to provide two independent refrigeration cycles for the freezer and food compartments. This design, with two separate refrigeration circuits, would considerably increase the initial cost of the refrigerator. Another possible means of increasing the energy efficiency is to utilize refrigerant mixtures as working fluids in refrigerators.

Chx

Heat exchanger correction factor Percentage increase in COP

Subscripts air Air stream amb Ambient c, cond Condenser e, evap Evaporator he, hte High temperature evaporator hthx High temperature heat exchanger le, lte Low temperature evaporator lthx Low temperature heat exchanger 1 Liquid max Maximum o Overall 12S Compared to R12 in a single-evaporator unit 12T Compared to RI2 in a two-evaporator unit ref Refrigerant sub Subcooled suph Superheated tp Two-phase v Vapour vc At the same volumetric capacity of R12

During the evaporation of non-azeotropic refrigerant mixtures (NARMs) at constant pressure, the saturation temperature changes due to the volatility difference of the pure components, which is termed a gliding temperature effect. By choosing a mixture with a large gliding temperature difference (GTD), two temperature level evaporation may be obtained in a single refrigeration cycle, resulting in an increase in COP with only a moderate increase in the initial cost. Figures 1 and 2 illustrate a schematic and a temperature-entropy diagram, respectively, for a two-evaporator refrigerator charged with mixtures originally proposed by Lorenz and Meutzner 4. Both the refrigerant and air stream temperatures are illustrated with heat flows for reference. Compared to the conventional unit, the only difference is the addition of a high temperature evaporator (HTE) and a low temperature heat exchanger (LTHX). At state 7, the two-phase refrigerant enters the low temperature evaporator (LTE). Evaporation occurs due to heat exchange with the freezer air stream, with the exit condition still in the two-phase region (state 10). Through the LTHX, further evaporation is achieved (from state 10 to state 11) while the liquid is being subcooled further internally (from state 9 to 12). Further heat is supplied by the food compartment air stream in the HTE to complete the evaporation and usually superheated vapour leaves the evaporator (state 1). During evaporation through the LTE, LTHX and HTE, the refrigerant temperature rises for mixtures (gliding temperature effect), while it remains constant for pure components without consideration of the pressure drop. On examining the temperature-entropy diagram (Figure 2), it can be seen that it is possible to match the overall GTD of the refrigerant to the overall temperature drop of the two air streams in both compartments (roughly AT= TS~ - T S 7 = 20-300C). This solves the previous problem in one evaporator unit of having a smaller temperature drop in the air stream (AT= 5 7°C) and Rev. Int. Froid 1991 Vo114 Septembre

255

Simulation of a two-evaporator refrigerator. D. S. Jung and R. Radermacher ( Sat. liquid ) ( Sat, vapor ) 51 14 w

I

6X

C

:

TS6

enser

[3

J~AAAAAA/%---L---~--TS3 • r"''"r

i

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High-Temperature Heat Exchanger

Com wessor High-Temperature Evaporator

-TS, -

"1" ( SatS.

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Low.Temperature

Heat Exchanger ~TSI0 I

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Evaporator Figure 1

Schematic diagram of a two-evaporator refrigerator Figure 1 Schema d'un r~'frig~rateur Zt deux ~vaporateurs

Refdgeram Air

E

5

T~

6

2 ~

9

Entropy(KJ/ KgK) Figure 2 Temperature~ntropy diagram for a two-evaporator refrigerator Figure 2 Diagramme temperature entropie pour un r~['rig~rateur

deux kvaporateurs

not allowing the maximum potential of the mixtures to be exploited. When the temperatures are well matched, the mixtures with the larger G T D yield a higher COP due to a larger reduction in the compressor work. Thus, the key point in Lorenz and Meutzner's 4 cycle is that the favourable characteristics of mixtures, i.e. the G T D in evaporation, can be fully utilized with a larger temperature drop available in the air streams. Lorenz and Meutzner 4 experimentally observed a power saving of 20% compared to that of R I 2 when an

256

Int. J. Refrig. 1991 Vo114 September

R 2 2 - R I 1 mixture at 0.5 mass fraction of R22 was used in a two-evaporator refrigerator. They also experienced a favourable control in the cycle due to the good matching of evaporation temperatures against the air temperatures in both compartments. Based on their experimental findings, certain criteria were established to help choose the best mixtures to yield a considerable gain in COP. The mixtures should have an actual G T D of roughly 20 to 25°C in the evaporator to give a good match with the air stream temperatures. Owing to pressure drop, however, the theoretical G T D in the evaporator would be near to 30°C. This means that the boiling point difference between two pure components at the evaporator pressure is close to 60°C. Another desirable characteristic is that the pure components should have high volumetric capacities. Stoecker 5 used an R I ~ R 1 1 4 mixture in a pilot refrigerator unit and failed to obtain any increase in COP, which is in sharp contrast to the results of Lorenz and Meutzner 4. An Oak Ridge National Laboratory report 6 revealed that when an R22-R114 mixture was substituted for R12 in an actual two-evaporator refrigerator unit, no significant change in performance was observed at all compositions. In recent discussion, Kruse ? presented experimental results obtained with an R 2 2 - R 142b mixture in a two-evaporator unit. Increases in the COP of 10 and 1.5% in the pull-down and steady-state tests, respectively, were observed. This strongly indicates that although the use of N A R M s is a thermodynamically sound idea, the success strongly depends on the operating conditions, applications and theoretical COPs of the chosen refrigerant pairs. As discussed by Lorenz and Meutzner 4 and Jung and Radermacher 2, a detailed thermodynamic analysis may be needed to select the proper mixtures before an expensive experimental investigation is carried out. This indicates the necessity for a proper model of two-evaporator refrigerators operating on Lorenz and Meutzner's 4 cycle. Two reports on the simulation of two-evaporator refrigerators are available. Stoecker and Walukas s obtained results with R I 2 - R ! 14 mixtures. In the simulation, two thirds of the refrigeration load was arbitrarily assumed to be performed at the LTE, with the remainder performed at the HTE. The results showed a power saving of 12% at 0.5 mass fraction of R114. The selection of R12 R114, however, is not the best possible choice according to the criteria set by Lorenz and Meutzne# because the G T D is too small with an R I 2 - R 1 1 4 mixture. Kruse 9 reported the results of the simulation of a twoevaporator refrigerator with R22 R l I 4 and R I 3 B 1 R114 mixtures. A similar approach to that of Stoecker and Walukas s was taken in the simulation. The model employed the Redlich K w o n ~ S o a v e (RKS) equation of state to compute the properties needed. The same load distribution as for Stoecker and Walukas 8 was assumed in the analysis. For R22 R114 mixtures, the theoretically calculated improvement in COP was 18 20% at 0.4 mass fraction of R22. For the R I 3 B I - R 1 1 4 mixtures, a 20% increase in COP was obtained at 0.7 mass fraction of RI3BI. The above results indicate that various features of Lorenz and Meutzner's cycle4 were not fully examined and hence a comprehensive model of two-evaporator

Simulation of a two-evaporator refrigerator. D. S. Jung and R. Radermacher

refrigerators is necessary to study the effects of load distribution, L T H X size and fluid combination. The Montreal Protocol necessitates the development of new ozone-safe refrigerants such as R123, R124, R125, R134, R134a, Rl41b, R142b and R143a. It would therefore be of interest to investigate the fluid mixtures containing these new refrigerants. The objectives of this work were to describe the simulation method, to examine various fluids of interest and to suggest any system modifications necessary. Simulation

In our previous work 2, a detailed description of singleevaporator refrigerators was given and hence only the differences are discussed here. The only changes in the single- and two-evaporator models are an additional evaporator and the L T H X (Figure 1). The total evaporator area remains the same as that in a single evaporator model to make a fair comparison. The area, however, is distributed in both compartments according to the heat transfer requirement. Initially, the size of the L T H X is designed to be 7% of the total available evaporator area with the same U as UE throughout the analysis. Later, the effect of changing the size of the L T H X while the total evaporator area is held constant is investigated. Except for the H T E and LTHX, all the other components remained unchanged. Further details are given in Jung and Radermacher 2. To compare the performance of various fluids on a fair basis, it is reasonable to require that the net refrigeration effect, Qe~p = Qh~ + Qh,¢, is constant regardless of the working fluids. This is accomplished by specifying the air stream temperatures entering and leaving the evaporators, TSm and TS7 in the LTE and TS. and TSI. in the HTE, with fixed mass flow-rates, m~,~and rht,~, generated by fans in the food compartment and freezer. As the compressor power, W~, varies with the working fluids, so does the coefficient of performance. (Note that fan power is not considered in the COP.) As W~ differs with various fluids, the heat discharged through the condenser, Q~o,d, which is the sum of Qevap and We, also depends on the fluids. The air stream temperature entering the condenser, TS6, is assumed to be at ambient. Because the volume flow-rate of the air stream on the condenser side, me, is fixed by another fan, the temperature of the air stream on the condenser side including TS3, TS4 and TS5 in Figure 1 must change to satisfy the energy balance. A proper formulation of heat transfer in the evaporator and condenser is necessary to simulate the overall system performance. The evaporators and condenser are specified by the product of an overall heat transfer coefficient and an area (UA). The overall heat transfer coefficient, U, was taken from actual measurements 6. The overall heat transfer coefficients for the condenser and the L T H X were assumed to be equal to UE. With given UA values, the heat transfer in the H T E and condenser is treated as:

LMTDht~ = (1 -f~uph~) LMTDtph¢ +.f~.ph,LMTD~uph~

(1)

LMTD,: =~ub¢LMTD,;ub,:+ (1 --f~bc--fsupc)LMTDtp~ + +.~.p~ LMTD~,p,:

(2)

Q~wp =

Ue(AjteLMTDtt~ + A ht~LMTDht~) %,

(3)

Q,:o,a= U~ At LMTD~ %,

(4)

wheref~uohc is the fraction of H T E heat in the superheated vapour portion of HTE, f~ub~,,fsup~are the fractions of the total condenser heat in the subcooled and superheated portions of the condenser, LMTDtphe, LMTDsuphe are the log mean temperature differences in the two-phase and superheated portions of the HTE, LMTDs,b,:, LMTDtp,:, LMTD,,p,: are the log mean temperature differences in the subcooled, two-phase and superheated portion of the condenser and %, is the heat exchanger correction factor to account for the effect of having cross or parallel flow heat exchange instead of pure counter-current heat exchange in the heat exchangers. Pressure drops in the condenser and evaporator are prorated according to the amount of heat transfer in subcooled, two-phase and superheated regions as (P2 and P3 are assumed initially): Pl = P2 P4 = P3 - A Pcfsupc

P5 = P3 - AP~ (1 P6 = / ° 9 =

P7 =

PI2 =

-

fsubc)

P3 - A P e

PI + APe

Ps = PI + APhe fsuphe Plo = PII =

P T - APle

(5)

where APh0 and API~ are total pressure drops across the H T E and LTE calculated as APhc = APe (Qhte/Qev,p) and APse = APe-APhe. The total pressure drops in the evaporator and condenser, APe and APe, were imposed and no pressure drop is assumed in the low and high temperature heat exchangers. The unknowns resulting from the simulation of the two-evaporator refrigerator were calculated by the Newton-Raphson (NR) method as described previously 2. The successive substitution (SS) method, which was shown to be as good as the NR method for a single evaporator model, was employed at first. The addition of another evaporator and LTHX, however, made the simulation more complicated and the successive substitution method failed. A proper model should calculate the refrigerant mass flow-rate, mrcr, rather than specifying it to reflect that mr~r varies as a working fluid is changed in the actual experiments. One of the main reasons for the failure with the SS method is the calculation of mr~r. Were mrer specified, the simulation would be much simpler and the SS method would yield results. This, however, would not yield meaningful results for proper comparison. This problem was easily handled with the NR method as it treats the simulation in a global manner with rnrer as an explicit variable. The N R method requires initial guesses for all unknown variables so that the minimum number of properties, as dictated by the Gibbs phase rule without a chemical reaction, is known to fix the state. Table 1 lists the known and unknown variables at each state point. The total number of independent variables in the simulation is 10, as listed in Table 2. As the states at each point

Rev. Int. Froid 1991 Vo114 Septembre

257

Simulation of a two-evaporator refrigerator: D. S. Jung and R. Radermacher Table 1 Known and unknown variables at each state point Tableau 1 Variables connues et inconnues 2t chaque point d'~tat

State point K n o w n (fixed) 1

T&

2

T2 : Tamb

3 4 5 6 7 8 9 10 11 12

TS6 = T~m~ T~= T & + 0 . 1 TS7 TSm TS,,

K n o w n (assumed) P~. T~ = Ts + DSH, V, P:, V2 P> $3 = S> ~ P4, X, Ps, X, P~, V6

P> H; = H~ P~, X,, P~,T~.V~ Hm : H7 Jr- Ql,,./m~r. Pm H,~ = H, -Qhtj;nrcr. P,, Ti2, P,:, V,._

Unknown H~ H> H3. H4, Hs, H~

$2 T . T& 14, TS4 T~. T &

T~. XQ7 H~. T~. T & H. Tto T. H~:

are known (either fixed or assumed), all unknowns such as enthalpy can be evaluated by the Carhahan StarlingDeSantis equation of state t°. With the N R method, typical run times on a 80386/20 M H z PC with a 80387/20 M H z maths-coprocessor were 35 and 105 s for pure and mixed refrigerants, respectively. Results and discussion

The steady-state performance simulation of the two-evaporator refrigerator cycle (TERCLE) was carried out with 14 pure refrigerants and 17 mixtures. The specified conditions for T E R C L E are as follows: superheat, 5°C; pressure drop in evaporator, 10 kPa; pressure drop in condenser, 15 kPa; compressor efficiency, 0.55; heat exchanger correction factor, 0.8; specified total cooling load, 185 W; volume flow-rate in condenser, 100 CFM; ambient temperature, 32°C; UA in evaporator and condenser, 20 and 10 W °C- ~, respectively; and total evaporator and condenser area: Ato,e= 0.2857, Atotc= 0.1428 m 2. For mixtures, the overall composition (mass fraction of the first component, always the more volatile component) varied from 0.0 to 1.0 in an interval of 0. I. In conventional single-evaporator refrigerators, all the cooling load is performed in the freezer, whereas in twoevaporator units the cooling load is distributed between the two compartments according to requirements. The first issue arising from this consideration is how to distribute the total cooling load to both evaporators. Stoecker and Walukas ~ and Kruse 9 assumed that one third of the total cooling load was performed in the H T E (Qh~c) while the remainder was in the LTE (Q~c). The A S H R A E Equipment H a n d b o o k on domestic refrigerators l~, however, indicates that roughly one half of the total cooling is required in the HTE. Private discussions with the engineers from major refrigerator manufacturing companies revealed that the fraction of Qhte varies from 0.4 to 0.6 depending on the refrigerator model. As no definite value of the fraction of Qhte seems to be known (actually it is a variable), two arbitrary cases are considered in this study: Case 1, Qkc = 67%, Qhte= 33%; and Case 2, Q,e = 50%, Qh~e= 50%. For both cases the temperatures of the air stream entering and leaving the evaporators are fixed to be T & =5, TSI~ = 0 , T&o = - 12 and T & = - 18°C, which is necessary to maintain the required temperature levels in both compartments. To consider the changes in the cooling load in both compartments for both cases, however, the volume flow-rates

258

Int. J. Refrig. 1991 Vo114 September

of the air stream in both compartments were changed accordingly. Overall, two-evaporator refrigerators are assumed to perform the same refrigeration duty (185 W) as that of a single-evaporator unit with the same evaporator and condenser area. To satisfy the energy balance between the food and freezer compartments, the total evaporator area has to be divided according to the need in both evaporators. This was also carried out by T E R C L E . The calculated area ratio, AR, is a percentage of the high temperature evaporator area to the total area. The importance of this parameter will be discussed later. The present results would be much more meaningful if they were compared to a certain baseline. For this purpose, COP~2~ = 1.345 and VC12~= 769 (kJ m -3) of a single-evaporator refrigerator charged with R I2 with all other parameters unchanged were used as baseline data 2. Figures 3 and 4 illustrate the C O P , dplzx, which is a percentage increase in COP compared to that of R12 with two evaporators, volumetric capacity and pressure ratio of 14 pure fluids for Case 1. Only a few fluids such as R22, R32, R142b and R152a have a comparable or slightly higher COP than R12, which is similar to the results obtained with a single-evaporator model. As the volumetric capacity of all pure fluids are different from that of RI 2, no single fluid seems to be a direct substitute for RI2. By having a portion of the evaporation at a higher temperature in the food compartment, the COP and VC of pure fluids are increased by up to 6 and 15.5%, respectively. This is caused directly by the elevation of the evaporator pressure, resulting in a smaller pressure ratio and a decreased vapour-specific volume entering the compressor. For Cases 1 and 2, COP of R l 2 with a twoevaporator model, the C O P r a is 3.5 and 6% larger than COP~2s while the VC of R I 2 with a two-evaporator model is 8 and 15.5% higher than that with a singleevaporator model. This is in good agreement with the thermodynamics that the smaller the temperature lift, the larger the COP. From the above observation, it can be said that the COP would increase in proportion to the fraction of Qh~. This implies that if more effective insulation is considered to reduce the heat leakage, the freezer section should be given priority. Tables 3 and 4 summarize the results obtained with 17 mixtures for both cases. The best performance was achieved with R22-R123 mixtures for both load distributions. The maximum increase in COP compared to that of R 12 with a single evaporator, qb.... was 13.53 and 18.36% with R22 R123 mixtures. This increase was achieved by two major contributions: evaporation at a higher temperature in the food compartment and well matched temperatures in the heat exchangers (mixture effect). The fraction of the increase due to the mixture effect alone is 0.75-0.8. Thus, the actual increase in COP due to the favourable thermodynamics of the mixture compared to that of R12 with a single evaporator is 10.86 (13.53 x 0.8) and 13.77 (18.36 x 0.75)% for Cases 1 and 2, respectively. Unless major changes in the compressor are considered, the volumetric capacity of the mixture should be very close to that of R I2 with a single evaporator. The COPs obtained at the compositions in which the VC of a mixture is the same as the VC of RI2, COPvc, are always less than the maximum COP, as illustrated in Tables 3

Simulation of a two-evaporator refrigerator: D. S. Jung and R. Radermacher Table 7~ Variablesand residualequationsfor the Newton Raphsonmethod Tableau 2 Variables et bquations restantes pour la mdthode Newton Raphson

Variables

Residuals

Description

VA( l )=in,o~

RE(l)= - Qh,~+ U¢Ah,~LM TDh,¢ eh~ RE(2) = - Q.~ood+ U~A~LMTD¢eh, RE(3) = - mr¢f(H,, - H~0)+ (UA L M TD) .... RE(4) = - (//6 - H,~)+ (H2 - H,) RE(5) = - H,, - H~o)+ (H~- H~.) RE(6) = - (H3 - n6) xf~ob~+ (H5 - n6) RE(7) = - (H3 -//6.) ×J~.r~+ (H3 -/44) RE(8) = -Q.o.d+m~Cp.ir x ( T S 3 - TS~,) RE(9) = - (H,- H~,) xf.uph~+ (H,- H~) RE(10) = - Q~,.+ U~A~,~LMTD~,. ct,~

Heat transfer rate equation in HTE using Eq. (1) Heat transfer rate equation in the condenser, Eq. (4) Heat transfer rate equation in LTHX Energy balance in HTHX Energy balance in LTHX Definition off, u~. Eq. (2) Definition o f ] ~ , Eq. (2) Air stream energy balance in the condenser Definition ofJ~o~h¢,Eq. (1) Heat transfer rate equation in LTE

VA(2)= ,°2 VA(3)= P3 VA(4)= T9 VA(5)= TS3 VA(6)= TS~ VA(7)= TS~ VA(8)= TS~ VA(9)= T~ VA(IO)= A~,¢

Note that Lhereis no relationship between the variables and residual equations On note qu 71 n'existe aueune relation entre les variables et les kquations restantes 1.5

25OO

TERCLE MODEL

TERCLE MODEL 2O0O

~1500

~10~ •

5011.

1.(3 3

6O 5O

0

40

-3

~-6 9

00

-12

0

0o0o . RI3B1

Rll

15 RI1 R 1 2 R I 3 B 1 R 2 2 R32 R l I 4 R I 2 3

R124

R134 RI41B R143A R134A R142B R152A

Figure 3 COP and percentage increase in COP for various pure refrigerants obtained with the two-evaporator refrigerator model Figure 3 C O P et augmentation en pourcentage du C O P pour plusieurs

RI2

.

.

R32

R22

Rl14

. . . . . R123 R134 RI41B R143A R124 R134A R142B RI52A

Figure 4 Volumetriccapacity (VC) and pressure ratio (PR) for various pure refrigerants obtained with the two-evaporator refrigerator model Figure 4 Puissance volum~trique ( V C ) et taux de compression ( P R )

ffigorig~nes purs, obtenus avec le module de r~frigkrateur ~ deux kvaporaleurs

pour plusieurs frigorig~nes purs, obtenus avee le module du r~frig~rateur h deux ~;vaporateurs

a n d 4. The m a x i m u m percentage increases in C O P v c , dpv~, are 11.52 a n d 16.95%, again observed with R 2 2 - R I 2 3 mixtures. O n l y two mixtures ( R 2 2 - R 1 2 3 a n d R32 R142b) seem to be the right substitutes for R12, with the same compressor yielding m o r e t h a n I0 a n d 16% increases in the C O P for Cases I a n d 2, respectively. It w o u l d be interesting to use the T E R C L E model to e x a m i n e the validity of the criteria set by Lorenz a n d M e u t z n e r 4 for the selection of a mixture to be used in t w o - e v a p o r a t o r refrigerators. The difference in the pure c o m p o n e n t s ' boiling p o i n t temperatures should be larger than 60°C. Usually, the e v a p o r a t o r side pressure would be close to atmospheric pressure. Hence, the n o r m a l boiling points (NBPs) of pure fluids are used to approximately calculate the difference. F i g u r e 5 shows the difference in N B P s o f various pure refrigerants. The shaded squares in F i g u r e 5 c o r r e s p o n d to the mixtures which have been s h o w n to yield more t h a n a 10% increase in C O P as listed in T a b l e 4 for Case 2. The difference in N B P s for the shaded mixtures actually varies from 27 to 74.4°C a n d n o correlation

between the C O P a n d the difference in N B P s is apparent. The best p e r f o r m a n c e was observed with R 2 2 - R 123 mixtures with a difference in N B P of 68.1°C. Even t h o u g h R23 seems to be a good candidate, yielding a wide range of the differences in NBPs with m a n y other pure fluids, its critical t e m p e r a t u r e is close to a m b i e n t t e m p e r a t u r e a n d hence only a low c o n c e n t r a t i o n of R23 m a y be practically used in a v a p o u r cycle. As the R 2 2 - R I 2 3 mixture shows the best performance, more specific discussions will be m a d e with this mixture. It was observed 2 that the m a x i m u m C O P occurs when the G T D in the e v a p o r a t o r best matches the temperature d r o p of the air stream a n d c o n d e n s e r superheat is m i n i m u m . F i g u r e 6 illustrates the COP, overall gliding temperature difference in both e v a p o r a t o r s (T8 - TT) a n d the fraction of c o n d e n s e r superheat as a function of c o m p o s i t i o n for R 2 2 - R I 2 3 for b o t h cases. It is interesting to observe that the m a x i m u m C O P indeed occurs when the G T D is close to 23°C, the overall t e m p e r a t u r e drop of the air stream in the evaporator, with a m i n i m u m

Rev. Int. Froid 1991 V o 1 1 4 Septembre

259

Simulation of a two-evaporator refrigerator." D. S. Jung and R. Radermacher Table 3 Simulation results for various mixtures for Case 1. Qk, = 67%, Qht~= 33% Tableau 3 Rksultats de simulation pour plusieurs mklanges pour le eas 1. Q~,,, = 67%, Q~,,. = 33% Mixture

COP,,,,,

R22 R 152a R22 R142b R22 R124 R22 R123 R32 R152a R32 R142b R32-- R 124 R125 R152a R125 R142b R125 R124 R 134a R 123 R 143a R 142b R143a R124 R143a R123 R 152a R 123

1.426 1.474 1.443 1.527 1.464 1.512 1.482 1.415 1.455 1.402 1.465 1.460 1.412 1.428 1.494

qbo,.,

6.00 9.60 7.29 13.53 8.85 12.41 10.18 5.20 8.18 4.24 8.92 8.55 4.98 6.17 11.07

VC . . . . .

~(~,~

CO P,~

1007 822 934 1039 1290 1349 1459 902 652 742 507 700 800 1156 487

0.6 0.5 0.5 0.8 0.4 0.5 0.4 0.3 0.3 0.3 0.7 0.3 0.3 0.8 0.6

1.41 1.48 1.43 1.50 1.41 1.49 1.44 1.41 1.45 1.4 1.42 1.46 1.41 1.4 1.40

dp~, 4.61 9.51 6.47 11.52 4.83 10.78 7.43 4.83 7.80 4.10 5.57 8.32 4.83 4.08 4.24

X,~ 0.10 0.45 0.30 0.65 0.03 0.17 0.10 0.10 0.40 0.33 0.95 0.35 0.25 0.65 1.00

Percentage increase in COP, ~, is based on the COP of RI2 obtained with a conventional single-evaporator refrigerator (COP,2s = 1.345, VC,:s = 769 kJ m % X0,,, in Tables 1 and 2 is the overall composition at which the maximum COP occurs while X~ is the overall composition at which the volumetric capacity of the mixture is the same as that of RI2 with a single evaporator L'augmentation en pourcentage du COP, dp, est fondke sur le C O P du R12 obtenu avec un rkJHg~rateur classique h ~vaporateur unique (COP;.,, = 1,345, VC;:~ = 769 k J m ~). X,,,,, dans les tableaux 1 et 2 est la composition globale ?t laquelle on obtient le C O P maximal, alors que X~, est la composition globale ?t laquelle la puissance volumktrique du mklange est la m~me que celle du R I 2 avee un seul kvaporateur

Table 4 Simulation results for various mixtures for Case 2. Q~,~= 50%, Qh,~= 50% Tableau 4 Rbsultats de simulation pour plusieurs mblanges pour le cas 2. Qt,,. = 50%, Qh,,, = 50% Mixture

COPma~

R22 R 152a R22-R142b R22- R124 R22 R123 R23 R124 R23 R152a R32 RI52a R32 R142b R32 R124 R 125 R 152a R125 R142b R 125 R 124 R134a R123 Rl43a R142b R143a R124 R143a R123 R152a R123

1.466 1.525 1.49 1.592 1.446 1.514 1.516 1.585 1.551 1.454 1.502 1.447 1.536 1.51 1.461 1.483 1.561

~b~,

VC ....

X ....

COP~

~Pv~

X~

9.00 13.40 10.78 18.36 7.50 12.60 12.71 17.84 15.31 8.10 11.67 7.58 14.20 12.27 8.62 10.26 16.05

1075 894 1010 945 845 1321 1555 1333 1574 965 708 806 480 762 997 1264 549

0.6 0.5 0.5 0.7 0.1 0.2 0.5 0.4 0.4 0.3 0.3 0.3 0.6 0.3 0.4 0.8 0.6

1.437 1.520 1.465 1.573

6.84 13.00 8.92 16.95

0.00 0.35 0.25 0.60

1.437 1.560 1.490 1.437 1.502 1.444 1.469 1.510 1.452 1.455 1.483

6.84 15.98 10.78 6.84 11.67 7.36 9.21 12.27 7.95 8.17 10.26

0.00 0.15 0.09 0.00 0.35 0.25 0.90 0.30 0.20 0.55 0.92

" The critical temperature of R23 is close to ambient temperature. Hence only mixtures at low concentrations of R23 are allowed to be substituted ,, La temp~;rature critique du R23 est voisine de la temperature ambiante. Aussi, seuls les m~;langes ~.['aibles concentrations de R23 peuvent constituer des substituts

condenser superheat, thus confirming the previous finding. Figure 7 illustrates the fraction of high temperature evaporator area, AR, for an R 2 2 - R I 2 3 mixture under two compartment loading conditions. It is seen that the AR is a strong function of composition. This is an important factor, especially in designing evaporators. An area fraction which is good for R I2 may not necessarily be valid for other fluids. Design engineers and experimentalists should be aware of this in advance in order not to make an unfair comparison of the results obtained with various fluids using the same evaporators. It is interesting to note that the maximum increase in COP occurs near the compositions at which the area fraction, AR, is close to the fraction o f Qhtc. For instance, for Case i the fraction of Qhte is 0.33 and the maximum COP occurs at 0.7-0.8 mass fraction R22 where the

260

Int. J. Refrig. 1991 Vol 14 September

fraction of the high temperature evaporator area is 0.3. A similar trend has been observed for Case 2 and with other fluid mixtures. The AR is a strong function of working fluid, overall composition and the fraction of Qhte. The most critical parameter in determining AR is the fraction of Qhtc. A computer model may be needed to calculate the amount of heat leaks to both compartments, fan power and defrost heater power. Based on this calculation, the amount o f cooling needed in both compartments can be better estimated. This, of course, would depend on the configuration (top mounted or side by side) and insulation material of a particular refrigerator. There was a concern that the LTHX may not be needed ~z. To resolve this issue, a further study of the effect of the LTHX size was conducted. The U A of the LTHX was fixed at 7% of the total U A of both evapora-

Simulation of a two-evaporator refrigerator: D. S. Jung and R. Radermacher 1.6 I

47.51 *C )

~¢~---o

R22/R123

-~

1.4 ~ ~ 1.2-

0' 1.0Increasing

NBP ( * C )

QLTE= 67%

"~ 0.8"

+

COP

QHTE = 33%

+

COND. S U P E R H E A T

~0.60.4-

\

641.7 43.1 40.4 36.9 16.8 3.3 "1241-13.2

[ ] 66.8 49.1 146.4 43.0 22,9 i 9,3

6.0

48.4 28.3 14,8 11.5 5.4 RI52a -24.6

73.6 55.9 ~ ,

49.8 29.7 16.1 12.8 6.8

30"

i.26,0

171.0 50.9

oC3

37 ?.,( ..... 14.9 I1,1 R22

t)5.9 78.3 75.6 72.1 52.0 ~

20"

1.4 ~134~

77.3 59.7 56.9 53.5 33.4 19.9 16.6 10.5 5.1

94.8 77.1

Ozone depleting substances

RI34 -19.2

72,2 54.5 ~ /

e~

~ o

.40.9

35.2 29.2 23.8 22.4 18.6 7.5

01,,80

105

87.6 84.8 81.4 61.3 47.8 44,5 38.4 33.O

755

3,5

1.2

1.6

2,............ ,313"1251.3:.5.; Y 31.6 27.9 16.8 10.4

.2

105 85.1 71.6 68.3 62.2 56.8 55.5 51.7 40.6 34.3 33.11

,3 . . . . .

,0,

3 .....

20,

.48.4

129 111 108

.5 . . . . .

10'

34.0 28.0 22.6 21.2 17.,I 6.3 ]143; -47.2

....

109

0.2 40'

56.2 52.4 ....

6.0

1.4 "~

311 .37.7 4__ -81.:

34.9 33.7 t0.~ I 24.5 II ~1.7 R23

/-

1.2" ~:Y 1.0"

+

COP

"~ 0.8

Figure 5 Difference in normal boiling points for various combinations

O

COND. SUPERHEAT

QLTE = 50% QHTE = 50%

0.6

(updated from the table by Bare ~2) Figure 5 D ~ r e n c e dam les points d'bbullition normale pour plusieurs combinaisons de m~langes (m&e ~ jour avec le tableau de Bare 12

04-

tors (20 W °C -~) for all cases investigated. With this assumption, the temperature glide of mixtures across the L T H X was up to 4°C observed with R22-R12Y Figure 8 shows the COP and pressure ratio across the compressor as a function of L T H X size for the 50% R22-50% R123 mixture• As the size of the L T H X increases, the COP also increases while the pressure ratio across the compressor decreases. In this analysis, the size of the L T H X was increased until the temperature of the liquid at the end of the LTHX, T~2,equalled the temperature of the two-phase mixture entering the LTHX, Ti0 (pinch point). This corresponds to the maximum heat exchange between the two streams occurring, with the L T H X size roughly 20% of the total evaporator UA. Beyond 20%, however, the performance was not affected, as shown by the broken lines in Figure 8. Figure 9 shows the refrigerant and air stream temperatures in both evaporators with different L T H X sizes• With an increase in the size of the LTHX, the refrigerant temperatures were adjusted to better match the air stream temperatures, resulting in a reduction of compressor work. The quality of the two-phase mixture entering the LTE decreases, while the refrigerant temperature entering LTE, TT, is almost constant, as dictated by the air stream temperature, TST. For a given mixture at X=Xo, a temperature and composition diagram (Figure 10) shows that with a decrease in quality and a constant temperature after the expansion valve, the pressure in the evaporator has to be increased• Consequently, the pressure ratio across the compressor is reduced, as shown in Figure 8. Some remarks have to be made about the use of mixtures with extremely large vapour pressure difference such as R32-R123, R32-R141b and R22-RI41b (note that the difference in NBPs shown in Figure 5 may not necessarily be the same at the condenser pressure). One problem was encountered with these mixtures on the condenser side (pinch point problem). As the gliding temperature in the condenser was too high with these

o•20-

~_.~,_._o.--~ ~ ----~--'~

0.2

lO[..., o" ~1o -

~ 0.0

0.1

0.2

GTDE

QLTE = 5 0 ~ % QHTE = 50%

0.3

0.4

0.5

0.6

0.7

0.8

09

1.0

COMPOSITION (MASS FRACTION R22)

Figure 6 COP, gliding temperature difference in evaporator (GTDE) and condenser superheat (QC~ur) for R22 R123 mixture as a function of composition under two different conditions Figure 6 COP, diff&ence de tempbrature de glissement dans I'bvaporateur ( GTDE) et surchauffe au condenseur ( QC,.p) pour le mblange R22R123 en Jonction de sa composition pour deux conditions diffbrentes de Jbnctionnement

mixtures the refrigerant leaving the condenser (point 6 in Figure 2) is no longer subcooled but in the two-phase region. What happens next is that the refrigerant temperature at point 5 (saturated liquid) is slightly below the air temperature to satisfy the energy balance, which represents a physically impossible solution. This finding indicates that in order to use these mixtures in actual refrigerators, either the condenser size or the mass flow-rate of air in the condenser should be reduced. By doing this, the condenser pressure is raised so that subcooled refrigerant is present at the outlet. This, of course, would degrade the system performance as the compressor work might be increased with a higher pressure ratio. Thus, care should be taken in the use of mixtures with a large G T D exceeding 70°C in the difference in the NBPs shown in Figure 5. Finally, the shortcomings of the current simulation will be discussed. In the heat transfer formulation, both air stream and refrigerant temperatures are assumed to be linear (A in Figure 9). In actual heat exchangers with an assumed linear air temperature distribution, the refrigerant temperature may vary irregularly (B,C,D in Figure 9) because of the non-linear slope, dT/dH, in the Rev. Int. Froid 1991 Vol 14 Septembre

261

Simulation of a two-evaporator refrigerator: D. S. Jung and R. Radermacher 70

10 R 2 2 / R 123 QLTE = 67%, QHTE = 33% PRI2= 1173 AR12 = 13.93

60 5o

5 0 % R 2 2 / 5 0 % R 123 LTHX size: 0% of evaporator UA ----o-~

PR AR

o /

o~ 0 -10

~: 30 < ,.¢ < r~ Z < O

t~

20 -30 10 -40 10

0 7o QLTE = 50%, QHTE= 50% PRI2= 11.17 ARI2 = 221

-----O-+

LTHX size: 21% of evaporator UA

PR AR

~

J

°G" 0

so ~-10

,0 3o

-20 -30 "~.-----o___._.o____o___._. o

c

~'/;L-+~i~

~ - - - ~ " ~ " L'~

I

Temperatureglide .

.

.

.

A : Ideal B,C, D : Actual

~X D

-40 0.0

0.1

02

()3

O4

O5

0.6

0.7

()8

I)9

20

10

40

60

80

100

12o

QUALITY (%)

COMPOSITION (MASS FRACTION R22)

Figure 7

Evaporator area distribution (AR) and pressure ratio (PR) for R22-RI23 mixture under two different conditions F i g u r e 7 Distribution de l'bvaporation ( A R ) et taux de compression

(PR) pour le mblange R22-RI23 dans deux conditions d_i.ffbrentes de .lonctionnement

Figure 9

R e f r i g e r a n t a n d a i r s t r e a m t e m p e r a t u r e s in t h e f r e e z e r a n d f o o d c o m p a r t m e n t e v a p o r a t o r s w i t h d i f f e r e n t sizes o f l o w t e m p e r a t u r e heat exchanger Figure 9 Tempbratures du.[~igorigbne et du courant d'air aux ~vapora-

teurs du congblateur et du compartiment pour aliments, avec diffbrentes dimensions de I'dchangeur de chaleur ~t basse tempdrature

1.6050%R22/50%R123

1.55 r...) 1.50

~

/

Pinch Point

1.45

Pinch Point

0

7 14 21 UA OF LTHX (% OF UA OF EVAPORATOR)

28

Figure 8

COP and pressure ratio (PR) across the compressor for 50% R 2 2 5 0 % R 1 2 3 m i x t u r e a s a f u n c t i o n o f size o f a l o w t e m p e r a t u r e h e a t exchanger F i g u r e 8 C O P et taux de compression (PR) au compresseur pour un

m~lange de 50 % de R22 et de 50 % de R123 en fonction de la dimension de I'~changeur de chaleur ~t basse temperature

two-phase region. This can be handled by dividing the heat exchangers into many segments and calculating the average LMTDs, which would require a much longer execution time. The overall heat transfer coefficients of all heat exchangers are assumed to be the same. This, of course, is not true in actual systems. The overall heat transfer coefficient (U) also varies from the subcooled liquid to superheated vapour regions. To obtain more accurate results, heat transfer data in all regions of the heat

262

Int. J. Refrig. 1991 Vo114 September

1.0 COMPOSITION

Figure 10

R i s e in e v a p o r a t o r p r e s s u r e w i t h i n c r e a s e d l o w t e m p e r a t u r e h e a t e x c h a n g e r size F i g u r e 10 Elbvation de la pression dans l'~vaporateur avec augmen-

tation de la dimension de l'bchangeur de chaleur ?t basse tempbrature

exchangers may be necessary. The compressor was modelled in the simplest way by specifying the isentropic efficiency. A more elaborate compressor model would yield more realistic results. Overall, despite the above shortcomings, the present model would still yield a fair relative comparison and may serve at least as a preliminary screening tool in designing highly efficient refrigerators.

Simulation of a two-evaporator refrigerator: D. S. Jung and R. Radermacher Finally, the use of N A R M s in two-evaporator refrigerators may serve as an alternative to help solve the present environmental problem by employing ozonesafe fluids on a highly energy efficient cycle. The success depends largely on the proper selection of fluids, the accurate determination of the load distribution, evaporator area ratio and L T H X size.

Conclusions Based on the computer simulation of steady-state twoevaporator refrigerators operating on Lorenz and Meutzner's 4 cycle, the following conclusions can be drawn. 1

By adding another evaporator and a low temperature heat exchanger to a conventional single evaporator refrigerator, the simulation becomes complicated, such that the successive substitution method is not successful. For the simulation of more complicated systems, the Newton-Raphson method solving simultaneously a set of non-linear equations is suggested due to its global systematic treatment of all variables. 2 The results obtained with pure fluids indicate that having a portion of evaporation at higher temperatures helps to increase the COP and VC up to 6 and 15.5%, respectively, as compared to that of a single evaporator unit. The COP would increase with a larger fraction of the high temperature cooling load, Qht~. Owing to the mismatch of volumetric capacity, no single fluid seems to replace RI2 directly unless major modifications are made in the compressor. 3 A significant increase in COP of up to 15 18% is achieved with R22-RI23 and R32 R142b mixtures, demonstrating the capability of Lorenz and Meutzner's 4 cycle. This was achieved mainly due to the good matching of the large overall temperature drop in the air streams in the two evaporators (23°C) against the overall refrigerant side temperature glide. The maximum COP seems to exist at the concentration where the G T D in the evaporator is close to the overall temperature drop of air and the condenser superheat is at a minimum. 4 The area ratio between the high and low temperature evaporators is a strong function of the load distribution, working fluids and composition. To design highly efficient refrigerators, a proper cabinet heat leak model may be needed to determine the load distribution accurately. Based on this calculation, a suitable mixture may be selected and the current simulation model would yield the required area ratio to fulfil the cooling duty in the most efficient way. 5 The effect of the low temperature heat exchanger is examined by varying its size. With an increased size of LTHX, the COP also increases while the pressure ratio across the compressor decreases. The maximum size of L T H X is limited to roughly 20% of total evaporator UA. Beyond this, no change in performance would be expected.

Acknowledgements The support for this work by Pennwalt Corporation, the US Environmental Protection Agency and the University of Maryland, College of Engineering, is gratefully acknowledged. The authors thank M. McLinden and (3. Morrison at the US National Institute of Standards and Technology for helpful discussions regarding the thermodynamic properties of refrigerant mixtures.

References 1 2 3 4

5

6 7 8 9 10

I1 12

Montreal Protocol on Substances that Deplete the Ozone Layer, Final Act, United Nations Environment Programme, Nairobi (1987) ,lung, D. S., Radermaeher, R. Performance simulation of singleevaporator domestic refrigerators charged with pure and mixed refrigerants lnt J Re/?ig (1991) 14 223 232 Hell'man, ,l. Division of Global Change, US Environmental Protection Agency, Washington, DC, personal communication (August 1989) Lorenz, A., Meutzner, K. On application of non-azeotropic two component refrigerants in domestic refrigerators and home freezers X1V hlternational Congress o[" Re/Figeration, Moscow, 1975, llR, Paris, (1975) Stoecker, W. F. Improving the energy effectiveness of domestic refrigerators by the application of refrigerant mixtures ORNL Report. ORNL/Sub 78/55463/1 (1978) A.D. Little, Inc. An evaluation of a two-evaporator refrigerator freezer using nonazeotropic refrigerant mixtures ORNL Report, ORNL/SuI~82/47952/I (1982) Kruse, H. ASHRAE Meeting, Chicago, IL, personal communication (January 1989) Stoecker, W. F., Walukas, D. J. Conserving energy in domestic refrigerators through the use of refrigerant mixtures lnt J Refrig (1981)4201 208 Kruse, H. The advantages of non-azeotropic refrigerant mixtures for heat pump application lnt J ReJrig (1981) 4 119-125 Morrison, G., MeLinden, M. O. Application of a hard sphere equation of state to refrigerants and refrigerant mixtures NBS Technical Note 1226, National Bureau of Standards, Gaithersburg, MD (1986) ASHRAE Handbook, Equipment Volume, ASHRAE, Atlanta, GA (1988) Bare, J. Air Toxics Research Division, US Environmental Protection Agency, Washington, DC, personal communication (August 1989)

Rev. Int. Froid 1991 Vo114 Septembre

263