Calculation methods for comparing the performance of pure and mixed working fluids in heat pump applications

Calculation methods for comparing the performance of pure and mixed working fluids in heat pump applications

Calculation methods for comparing the performance of pure and mixed working fluids in heat pump applications M. H6gberg, L. Vamling and T. Berntsson D...

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Calculation methods for comparing the performance of pure and mixed working fluids in heat pump applications M. H6gberg, L. Vamling and T. Berntsson Department of Heat and Power Technology, Chalmers University of Technology, S-412 96 Gothenburg, Sweden Received 7 M a y 1992; revised 10 December 1992

Three methods for comparing cycle performance of working fluids, pure as well as non-azeotropic mixtures, are investigated for two applications and for two mixture pairs, HCFC22-CFCl14 and HCFC22HCFC142b, and their pure components. The methods differ in the way of calculating the heat exchange processes. They assume, respectively, equal minimum approach temperatures, equal mean temperature differences and equal heat transfer areas. Changes of coefficient of performance (COP) with composition are explained for all methods. It is shown that transport properties must be taken into account when making rigorous comparisons between working fluids. To predict the relations between fluids with high accuracy, one must use the method with equal heat transfer areas. By the method with equal mean temperature differences, the COP can be estimated with the same accuracy for mixtures as for pure fluids, and can be used for rough estimations of the COP level with different fluids. The method of equal minimum approach temperatures should be avoided for non-azeotropic mixtures. (Keywords:heat pump;refrigerant;non-azeotropiemixture;HCFC22; CFCll4; HCFC142b; heat transfer;COP; calculation)

M6thodes de calcul pour comparer la performance de fluides de travail puts et en m61anges dans des pompes/t chaleur On dtudie trois mdthodes de comparaison de la performance des cycles de fluides actifs, soit purs soit en mklanges non azdotropiques; on choisit les couples HCFC22-CFCl14 et HCFC22-HCFC142b et leurs composants purs pour deux applications. Les mbthodes sont diffOrentes dans la fafon de calculer les processus d'dchange de chaleur. Elles supposent, respectivement, des tempbratures d'approche minimales identiques, des diffbrences de tempdrature moyennes identiques et des surfaces de transfert de ehaleur identiques. On explique les variations du coefficient de performance (COP) avec la composition, pour toutes les mdthodes. On montre que les propridtds de transport doivent ~tre prises en compte lorsqu'on effectue des comparaisons rigoureuses entre les diffdrents fluides actifs. Aria de prdvoir les relations entre les fluides avec beaucoup de prdcision, il convient d'utiliser la mdthode des surface de transfert de chaleur identiques. Avec la mdthode des diffdrences de tempdrature moyennes et identiques, on peut estimer le COP avec la m~me prdcision pour les m~langes et pour les fluides purs, et on peut l'utiliser pour des estimations approximatives du COP avec des fluides diffbrents. Il est prdfbrable de ne pas utiliser la mdthode des temperatures d'approche minimales identiques pour les mblanges non az~otropiques.

(Mots cl6s: pompe fi chaleur; frigorig+ne; m61ange non-az6otropique; R22; Rl14; R142b; transfert de chaleur; COP; calcul)

Non-azeotropic mixtures as alternatives to pure fluids in heat p u m p and refrigeration plants have been discussed for ten years or more. There are at least three main reasons for this:

1. In applications with large temperature glides of the heat sink and the heat source, the COP can be improved relative to a pure fluid. 2. With mixtures the composition can be adjusted so that desired values of, for example, the condensation pressure, evaporation pressure, pressure ratio and/or capacity can be achieved; thus the flexibility for a given plant can be increased considerably. 3. Since the Montreal protocol, mixtures have been considered as one of the possible alternatives for the solution of the C F C problem, if one can thereby achieve 0140-7007/93/060403-11 © 1993 Butterworth-Heinemann Ltd and IIR

at least the same COPs as with today's fluids. Research on various aspects of non-azeotropic mixtures is being conducted in several research organizations internationally. So far the technology has only been commercialized by a few manufacturers of equipment but several full-scale experimental or demonstration plants have been started or are planned. DU Pont 1,2 and ICI 3 work for the moment with introduction of mixtures as replacements for HCFC22 and the azeotrope, R502 ( H C F C 2 2 - C F C 115). One of the important research areas for mixtures is the approach of system simulation and comparisons with pure fluids. When introducing one (or more) component(s) into a pure working fluid, the system simulation with a mixture becomes somewhat more complex than for a pure fluid. Actually, a comparison between a mixRev. Int. Froid 1 993 Vol 1 6 No 6

403

Performance comparison of pure and mixed fluids: M. H6gberg e t a I. ture and a pure fluid can be done in several different ways, which is one important reason for the different results of some comparisons between pure fluids and mixtures, reported in the literature. This has created confusion about the possible benefits and drawbacks of mixtures in various types of applications. A system simulation can be performed more or less rigorously, depending on the aim. For a detailed design study, a rigorous computer program may be needed, whereas for an assessment of the opportunity for mixtures in a certain type of application more simple calculations may suffice. It is therefore of great importance to know how such comparison methods influence the result and the degree of error introduced when different simplifications are used. The main aim of this paper is to improve the knowledge of these aspects. The principles of the calculations and comparisons are, in this work, only discussed for heat pump applications but can also be applied to refrigeration and air-conditioning applications.

Some methods of comparison Calculations of cycle performance may be based either on the internal evaporation and condensation temperatures or on the external conditions, i.e. the application considered. The application can be specified by the required inlet and outlet temperatures of the heat source and heat sink, or by the inlet temperatures and the flows of the heat source and heat sink. For a specified heat output from the plant, the difference between the two approaches is that, for the first approach, the flow of the heat source varies between fluids, while in the second one it is the outlet temperature of the heat source that varies. The difference between the approaches (in cycle performance comparisons) is usually small. However, differences in calculated COPs between fluids will be smaller in the latter approach than in the former, since the poorer thermodynamic characteristics of a fluid are to some extent compensated for by the increase of the heat source outlet temperature. If one compares the cycle performance of different working fluids on the basis of the internal evaporation and condensation temperatures, there are, for a nonazeotropic mixture, several ways to assign these temperatures, since the saturation temperature of a mixture changes at evaporation and condensation. McLinden and Radermacher 4 have evaluated the impact on the cycle performance of different combinations of the assigned temperatures in the evaporator and condenser. They showed that the relative COPs of pure and mixed working fluids (COPpure aui~/COPmixednuid) depend entirely on the chosen reference temperatures. These results show how important it is, in comparisons between pure and mixed fluids, to assign the relevant temperatures of the mixture. Often the goal is to choose a working fluid for a specified application of a heat pump. In this paper, we have chosen to specify applications by inlet and outlet temperatures of the heat sink and heat source, since the temperature glides are of great importance when dealing with non-azeotropic mixtures. In a comparison between fluids for a specified application, there are several ways to treat the heat exchange process in the evaporator and condenser. At least three methods can be distinguished:

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1. Method I: comparisons between fluids by means of equal minimum approach temperatures in the heat exchangers. 2. Method II: comparisons between fluids by equal mean temperature differences in the heat exchangers. 3. Method III: comparisons between fluids by means of equal heat exchanger areas. In a comparison between applications, there is a principal difference between Method I on the one hand, and Methods II and III on the other. Method I is more of a design approach, in that the area of the heat transfer equipment differs for various external conditions, while in Methods II and III, the heat exchanger area is kept constant (for Method II only approximately), and thus it is the impact of variations of the external conditions that is studied in a comparison between two applications. Besides these three methods, there are two other methods for comparing pure and mixed working fluids that should be mentioned: comparisons at equal total heat exchanger area and comparisons at equal cost of the equipment. McLinden and Radermacher 4 have made an investigation by means of the method of equal total area. They optimized the COP by adjusting the relative areas of the evaporator and condenser, while keeping the total heat exchanger area per unit capacity constant. Although they found that the optimum distribution of the total area varies significantly, the COP exhibits a broad and flat peak versus the fraction of the total area in the evaporator. Thus, results from Method III would not be influenced to a large extent by another distribution of the total area between evaporator and condenser than that used in the calculations presented below. A comparison at equal cost of the equipment requires accurate cost equations for each component in the cycle (i.e. compressor, heat exchangers, etc). These equations have to take into account the size-dependent cost, the impact that the pressure level has on the cost, and the cost of the working fluids. Calculations by such a method are necessarily very detailed and beyond the scope of the work presented here. The most rigorous and accurate way to treat the heat exchange processes is to do detailed modelling of the heat transfer and pressure drop in the evaporator and condenser: to compare fluids by means of equal heat exchanger areas, as in Method III. The two major drawbacks with Method III are that the calculations are timedemanding and that the modelling of the heat transfer and the pressure drop requires detailed specifications of the design of the heat exchangers. Furthermore, since the estimation methods for transport properties are often less developed than those for thermodynamic ones, and fewer measured data of transport properties exist (especially for new fluids and mixtures), the uncertainty in the estimated transport data used in the calculations may be rather large. In Method II the calculations are simplified and no design data are needed for the heat exchangers since the mean overall heat transfer coefficients are assumed to be equal and constant along the heat exchanger area for all fluids, and all pressure drops are neglected. In this way both the variation of the heat transfer coefficient along the heat exchanger area, and the differences between fluids are neglected. Often the mean temperature difference is estimated from the logarithmic mean temperature difference (LMTD). This approach is correct if the Cp

Performance

comparison

of pure and mixed fluids: M. Hogberg et al.

7

u

Condenser

1.

/External subcooler 0.0

0.1

0.2

0.3

0.4

0.5

0.5

0.7

0.8

I

0.9

1.0

(H - Hd/(H,.. - H,u,) Figure 1 Absolute value of the temperature difference between external and internal temperatures in evaporator and condenser versus relative enthalpy change. The straight dotted lines represent the temperature difference assumption used for logarithmic mean temperature difference (LMTD) calculations. The external temperature glides are 10 K and the working fluid is the mixture HCFC22-CFC114 (30 mol. % HCFC22) Figure 1 Valeur absolue de la dtflerence de temperature entre les temperatures externe et interne dans I’evaporateur et le condenseur, enfonction du changement de l’enthalpie relative. Les lignes droites formees de points reprtsentent la dtJ&ence de temperature supposke, utilistepour les calculs de la dtj&ence de temperature moyenne logarithmique (LMTD). Les glissements de temperature externe sont de l’ordre de 10 K et le$uide actif est le melange HCFC 22-CFC 114 (30moles-% HCFC 22): Cvaporateur; - - - ~ condenevaporateur (LMTD), ___ sew; . condenseur (LMTD)

I

--+---lw

‘71

Evaporator I

I

Figure 2 Figure 2

values of the heat transfer fluids (the heat source and heat sink fluids) and the overall coefficients of heat transfer are constant, and the temperatures of the working fluid at evaporation and condensation vary linearly with the enthalpy change. The latter is true for pure fluids but not for non-azeotropic mixtures. Figure 1 shows a typical example of the discrepancies in the temperature differences in the heat exchangers between a calculation by means of the LMTD concept and a calculation by integration of the mean temperature difference. A comparison of cycle performance done at equal LMTD values in the heat exchangers is actually a special case of Method II. The simplest way to treat the heat exchange processes is to use Method I. By means of assigned minimum approach temperatures, neither the overall heat transfer coefficient nor the mean temperature difference is needed to calculate the cycle performance. One special case of this method is comparison with minimum approach temperatures of 0 K, which is the same as comparison by means of infinite areas. Calculation

model

For simplicity, a one-stage heat pump cycle is considered in this work. The cycle is shown in Figure 2. The heat output from the cycle is set to be the same for all cases. The heat pump is assumed to work between a water heat source and a water heat sink. The working fluid is assumed to be saturated at the outlet of the condenser and the evaporator. The suction gas to the compressor is superheated by internal heat exchange with the condensate. In the calculations, the system is assumed to work without an oil cooler. This simplification is further discussed below, in the section ‘Method III: Equal areas’.

\

c I

I

Schematic principle of a one-stage heat pump cycle Schema d’un cycle de pompe a chaleur monoetagee

Whenever the temperature difference between the inlet and outlet of the heat sink is large enough to make external subcooling possible, this is taken into account. External subcooling is included in the calculations and the comparisons, because it is, for a water heat sink, a simple and cheap method of increasing the coefficient of performance and the heating capacity, and it is normally used in real plants. The isentropic efficiency, 77is,is estimated as follows: 77is

=

0.81

~-o.o~P,,,~P,,

(1)

Equation (1) is based on measurements5 of the isentropic efficiency of a twin screw compressor with an adjustable built-in volume ratio. Each pair of fluid-oils has its own set of coefficients. Due to lack of data for some of the fluids, coefficients typical for CFC12 are used for all working fluids, including the mixtures. Hence the variation due to the specific fluid-oil combination is not taken into account, but the variations of efficiency with the pressure ratio are included. Since the errors in the predicted COPS of the fluids caused by variations due to the specific fluid-oil combination have the same impact in all methods, these errors will not influence the results of the comparisons between the methods. The carry-over of the oil from the compressor has not been taken into account in the estimation of either thermodynamic or transport properties, since in a well working plant with an oil separator the amount of oil in the refrigerant circuit is only a few per cent and has only a marginal effect on the heat transfer or pressure drop calculations. The thermodynamic properties are estimated with Lee and Kesler’s equation of state6, which Strom et al.1 and Gerdsmeyer and Kruse8 have, independently of each

Rev. Int. Froid 1993 Vol 16 No 6

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Performance comparison of pure and mixed fluids: M. Hdgberg et al. Table l Characteristic properties Tableau 1 Propri&&caract&istiques Component(s) CFC12 HCFC22 CFC 114 HCFC142b

M (kg kmol -~)

Tb (K)

T0 (K)

Pc (MPa)

vc (cm 3 mol <)

120.914 86.469 170.922 100.496

245.2 232.4 276.2 263.4

385.01 369.32 418.9 410.5

4.129 4.99 3.26 4.07

212.9 167.6 293.8 228.4

kij

Reference~ 17, 21 17, 21 17 17, 22

HCFC22-CFC114 HCFC22-H CFC 142b

0.97 1.00

"In those cases where two references are given, the critical properties are taken from the second reference

other, shown to be very reliable. The data used for these calculations are given in Table 1. For the mixtures, the mixing rules of P16cker et aI. 9 are used. The interaction coefficients used are also given in Table 1. The interaction coefficient for the H C F C 2 2 / H C F C 142b mixture was estimated from the data given by Valtz et al. m, and that for HCFC22/CFC114 was chosen to be within the range of interaction coefficients reported by Str6m et al.iL All heat exchangers are calculated as being of the counter-current type, since any other configuration is less efficient when the working fluid is a non-azeotropic mixture. At each point along the evaporator and the condenser, liquid and vapour are assumed to be in equilibrium. M e t h o d I: Equal minimum approach temperatures

The minimum approach temperatures of the condenser and the evaporator are assigned at 3.0 K and 3.5 K, respectively. External subcooling until a temperature difference of 3.0 K between the subcooled condensate and heat sink is included in the calculations. The superheat of the suction gas is always assigned at 10 K. M e t h o d II." Equal mean temperature differences

In this method the superheat of the gas before the compressor is always assumed to be 10 K, and external subcooling until there is a temperature difference of 3 K between the subcooled condensate and heat sink is assumed to be done in the cycle. The calculations made by this method are based on a reference application and a reference fluid, which are used to obtain suitable values of the temperature driving forces. Because the applications used as examples in this study normally work with CFC 12, it was chosen as reference fluid. The reference conditions are the same as in example A below. In this reference case for the reference fluid, the minimum approach temperatures were assigned at 3.5 K in the evaporator and 3.0 K in the condenser. The mean temperature differences in the evaporator and condenser were estimated according to Equation (2) below, and the values obtained for the reference case were assigned as reference values in the other case and for all other fluids. In the condenser, an accurate mean temperature difference has to be determined by a weighted mean value of the mean temperature differences for the superheated part and for the condensation part. The relation between the two parts is dependent on the overall coefficient of heat transfer in each part and on how large the superheat after the compressor is. To obtain a prediction of the 406

Int. J. Refrig. 1993 Vo116 No 6

dew-point temperature in the condenser, we use the mean temperature difference for the condensation part of the heat exchanger alone, a simplification implying that the lower heat transfer coefficient in the superheated part is compensated by the larger temperature difference.

ATmean=O/(gA) = 1

II'OIT--T~ dx ]]-'

(2)

(x = Ah/Ahtot; e = external; i = internal) M e t h o d III." Equal areas

In this method, the same reference case and fluid were used as those used in Method II. For CFC12 the heat exchanger areas of the evaporator, the condenser and the internal subcooler, necessary to obtain minimum approach temperatures of 3.5 K in the evaporator and 3.0 K in the condenser, and to achieve 10 K superheat of the gas in front of the compressor, were calculated. The performance of the other fluids is calculated by means of these reference areas. External subcooling until a temperature difference of 3 K is obtained is included in the cycle calculations. The heat transfer area needed in the condenser has been calculated to be the sum of two parts, cooling of the superheated vapour and the condensing part down to saturated liquid. Hence, two important simplifications have been made. First, no oil cooler after the compressor has been assumed. The compressed superheated vapour goes to the condenser, where the area needed to cool it to saturated vapour is calculated. In reality the vapour is cooled by the oil during compression in the screw compressor and the oil is thereafter cooled by the heat sink or by the condensed working fluid in a separate oil cooler. Hence, the load on the superheated part of the condenser is decreased. The degree ofoil cooling, however, can vary between different designs and is thus difficult to take into consideration in detail. The error in the calculation of the total area needed in the condenser part (i.e. condenser and oil cooler) has been calculated to be less than 3 % for all conditions used in this paper and has therefore been neglected. Second, as the external subcooling is driven to a 3 K minimum temperature difference in all cases, the heat transfer area for this heat exchanger varies between the different fluids and working conditions. The difference has been calculated to be in the worst case at least up to 9% in total condenser area. However, since an external subcooler improves the heating capacity, the size of the compressor decreases. At least when the heat

Performance comparison of pure and mixed fluids: M. Hdgberg et al. Table 2 Specificationof the design of the heat exchangers Tableau 2 Caractdristiques de la conception d'dchangeurs de chaleur Evaporator

Tube diameter (inner) 0.015 m t.3 Outer area/inner area Sum of external heat transfer resistance (referred to heat transfer fluid side) 1925 W m 2K-~ The working fluid evaporates in the tubes Condenser

Tube diameter (over fins) 0.019 m Outer area/inner area 3.5 Minimum cross-sectional area 0.1 m2 Sum of external heat transfer resistance (referred to heat transfer fluid side) 1925 W m 2K

rules given in Reid et al. 17 are used. No additional reduction of the heat transfer coefficients due to mass transfer effects is taken into account. The impact of this simplification is discussed in the section 'Results and discussion'. Conditions for the comparisons

In order to evaluate the importance of how the heat exchange processes are treated, in comparisons between pure fluids and non-azeotropic mixtures, the performances of two different applications are calculated by means of the three methods. The applications have different external temperature glides, and are within the normal working range of C F C 12. The external temperatures are:

The tube design is assumed to be in accordance with 'Tube no. 1' used by Beatty and Katz~4

Application A:

The working fluid condenses outside the tubes

Application B:

Heat Heat Heat Heat

sink source sink source

in: in: in: in:

60 15 50 15

°C °C °C °C

out: 65 °C out: 10 °C out: 65 °C out: 0 °C

Suction gas heat exchanger

Shell diameter Tube diameter (inner) Tube diameter (outer) Number of tubes

0.4 m 0.022 m 0.026 m 42

The liquid flows in the shell and the gas in the tubes sink is in liquid form, the cost for the heat exchanger area needed should in most cases be more than compensated for by the decrease in compressor cost. Therefore a manufacturer is likely to use a high degree of subcooling and the conditions chosen for the calculations should therefore be realistic. For this reason, the area needed in the external subcooler has not been included in the condenser area. In the evaporator, the tube length that gives the optimal balance with regard to the COP between heat transfer and pressure drop is used in the calculations. The importance of this tube length optimization has been shown by H6gberg et al. 12. The heat transfer in the evaporator and in the condenser is calculated by numerical integration along the heat exchangers. For calculations of local heat transfer coefficients during the evaporation, the equation of Shah 13 is used. The equation of Beatty and Katz ~4 is used to calculate the heat transfer during condensation. The heat transfer coefficents of the superheated vapour in the condenser and of liquid and vapour in the internal subcooler are calculated according to the recommendations given by Smith 15. The transport properties are estimated according to Latini et al. ~6 and Reid et aI. ~7 In Table 2 the design of the heat exchangers is specified. The designs are in accordance with those normally used in heat p u m p plants. The pressure drop in the evaporator is calculated with the equation of Storek and Brauer 18, which Mfiller-Steinhagen and Heck ~9have shown to be reliable for refrigerants. The pressure drops in the other heat exchangers are ignored, since the differences in pressure drops between the different fluids have marginal influence on the COP relations between the fluids. The same heat transfer and pressure drop equations as for pure fluids are used for the mixtures. The physical property data used in these equations are taken at the actual temperature, pressure and composition of the liquid and vapour. F o r transport properties the mixing

The temperature glides of Case A are common in CFC12 heat p u m p applications, while the temperature glides of case B have been chosen to be favourable for mixtures. Two mixtures, H C F C 2 2 - H C F C 1 4 2 b and HCFC22-CFC114, which have suitable pressures for the considered applications, are examined over their whole composition ranges. These two mixtures have different internal temperature glides, which are at a m a x i m u m of 9.5 K and 21.2 K at total evaporation at 1 bar, for the H C F C 2 2 - H C F C 1 4 2 b and H C F C 2 2 - C F C 1 1 4 mixtures respectively. The H C F C 2 2 - H C F C 1 4 2 b mixture has been suggested as an alternative to CFC12, while the H C F C 2 2 - C F C l 1 4 mixture is included in the investigation in order to show the effects for a mixture which has large internal glides. The pure fluids which are included in the investigation are the pure components of the mixtures (HCFC22, HCFC142b and C F C l l 4 ) and CFCI2. For pure HCFC22, it should be mentioned that application A requires a condenser pressure close to 2.8 M P a and in application B, the condenser pressure H C F C 2 2 is 2.5 MPa. Results and discussion Calculation results Figures 3 and 4 show the COPs of pure HCFC22, pure

HCFC142b, and mixtures of both for compositions calculated with the different methods. The results for various compositions of the mixture H C F C 2 2 - C F C 1 1 4 are shown in Figures 5 and 6. The COPs obtained with CFC12 are given in Table 3. Since the purpose of this study is to compare calculation methods, the results for CFC12 will not be compared to those for other fluids. For comparisons between non-azeotropic mixtures and pure fluids with the aim of pointing out alternatives for CFC12, see, for example, H6gberg et al. ~2 The results from Method III are assumed to be closest to the results which would have been obtained from measurements, and are thus referred to as the 'true' ones in the following discussion. E x t e r n a l subcooling-general

External subcooling always increases the COP, but the potential to utilize this fact is less for mixtures than for

Rev. Int. Froid 1993 Vo116 No 6

407

Performance comparison of pure and mixed fluids: M. Hdgberg e t al. I

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Figure 5 COP of application A calculated with the three methods for

different compositions of the HCFC22-HCFC142b mixture Figure 3 COP de l'application A calculd avec les trois rndthodes pour

different compositions of the HCFC22-CFC 1.14.mixture Figure 5 COP de l'application A calculd avec les trois mdthodes pour

diffdrentes compositions du mdlange HCFC22 HCFC142b: mdthode L . . . • mdthode II," mdthode III

diffdrentes compositions du mdthode I," . . mkthode II,"

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Figure 6 COP of application B calculated with the three methods for

diffdrentes compositions du mdlange HCFC22-HCFC142b: mdthode L • . . • m~thode II, mdthode III

different compositions of the HCFC22 CFCll4 mixture Figure 6 COP de l'application B calculd avec les trois mdthodes pour

Figure 4

Mole fraction H C F C 2 2

diffdrentes compositions du mkthode I; . . . . mkthode II;

pure fluids and depends on the internal temperature glide. As a result, when external subcooling is included in the calculations, the location of the m a x i m u m COP moves towards a higher content of the component having the highest COP, i.e. H C F C 2 2 in this work. This phenomenon is described in detail by Str6m et al. H

mdlange HCFC22-CFCl14: mdthode I l i

Table 3 COP with CFC12 for the different methods

Tableau 3 COP, obtenu avec les diffdrentes mOth•des pour le CFC12 Method I

Method

E f f e c t o f composition. The shapes of the C O P - c o m p o -

sition curves for Method I are caused by two factors: the mean temperature differences and the locations of the temperature pinch points in the heat exchangers• In

408

Int. J• Refrig. 1993 Vo116 No 6

I II III

COP Application A

COP Application B

3.45 3.45 3.35

3.10 3.32 3.21

Performance comparison of pure and mixed fluids: M. Hdgberg et al. based on very different areas for different non-azeotropic mixtures and their different compositions. The maxima and minima can be more or less broad depending on the compositions at which the locations of the pinch shift side in the evaporator and condenser. In the applications where the shifts in the evaporator and condenser occur at the same composition, the COP peaks are sharper than in cases where the shifts occur at different compositions. For an application with equal external temperature glides in the evaporator and condenser, the shifts of locations of the pinch points in the evaporator and condenser do not occur at the same composition. This is explained by the fact that the internal temperature glide in the evaporator is smaller than that in the condenser, which is due to the flashing that occurs in the expansion valve. Thus, such an application has a broad maximum/minimum.

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Figure 7 Method I: Temperature profiles in evaporator and condenser, for a pure fluid and two mixtures. Dashed lines represent heat source and heat sink. Curves i illustrate a pure working fluid, curves ii represent mixtures whose internal temperature glides match the duty, and curves iii are valid for mixtures having larger internal temperature glides in the evaporator and the condenser than the external temperature glides of the heat source and the heat sink, respectively. The pinch points for curves i are marked by P~ and these for curves iii are marked by Piii Figure 7 Mdthode I: profils de tempbrature clans l'bvaporateur et le condenseur pour un fluide pur et deux mdlanges. Les lignes en pointill& reprdsentent la source de chaleur el ]a source de froid. Les courbes i illustrent un fluide actif pur, les courbes ii reprdsent les mdlanges dent les glissements de tempdrature interne et les glissements de tempdrature externe sent identique, et les courbes iii sent valables pour les mdlanges ayant des glissements de tempbrature interne plus importants, dans l'dvaporateur et le condenseur, que ceux de la tempbrature externe de la source de chaleur et de la source de froid, respectivement. Les pincements pour les courbes i sent marquds par P, et ceux pour les courbes iii sent marqubs par Piii

Figure 7 the locations of the pinch points for different internal temperature glides are shown. For mixtures whose internal temperature glides are between those of the fluids represented by curves i and ii, the pinch points in the heat exchangers are the same as for curves i. As can be seen, the pinch points shift side in the heat exchangers when the internal temperature glides become larger than the external ones. For example, in the evaporator, for an internal temperature glide smaller than the external one, the pinch point is situated at the inlet side for the working fluid, while for an internal glide larger than the external one, the pinch point is situated at the outlet side for the working fluid. The reductions of the mean temperature differences caused by the changes of the internal temperature glides are also clearly seen in Figure 7. As the internal temperature glides increase from 0 K (pure fluid, line i) to the same glides as those of the external heat transfer fluids (line ii), the areas increase both in the evaporator and in the condenser, since a reduction in mean temperature difference leads to an increase in area. Consequently, a comparison by means of Method I is

Method H Effect of composition. As seen in Figures 3-6, the COP variation with composition is smaller in Method II than in Method I and the COP-composition curves are smoother in form than the curves for Method I. The differences in the shapes of the curves can be explained from the temperature profiles in the heat exchangers. These temperature profiles in the heat exchangers for Method II are for two applications, which have different external temperature glides, schematically shown in Figures 8a and b, and for Method I they are shown in Figure 7. As can be seen in Figure 8a, if the mean temperature differences are kept constant for a given external temperature glide, both the condenser and the evaporator dew-point temperatures increase with increasing internal temperature glides (compare the temperatures at the right of lines, i, ii and iii). Due to this, the change of the temperature lift with increased internal temperature glides is smaller and more regular for Method II than it is for Method I. Hence, also the COP changes less and more regularly in Method II. In Figures 3 and 5 it can be seen that the COP decreases with increased internal temperature glide (e.g. from composition 0 to 0.4 or from 1.0 to 0.6), while in Figures 4 and 6 the COP increases slightly when the internal temperature glide increases. The difference in the COP curves for the two applications can be explained with the aid of Figures 8a and b. In a comparison between Figures 8a and b (note that the mean values of the external temperatures are the same in both figures), it can be seen that an application with a large external temperature glide in the evaporator (Figure 8a) has a larger potential for an increase in the evaporator dewpoint temperature than an application with a small external temperature glide (Figure 8b). This is due to the fact that the maximum possible increase in the dew-point temperature in the evaporator corresponds to the difference between the inlet temperature of the external heat transfer fluid and the dew:point temperature of a working fluid with 0 K in internal temperature glide (a pure fluid). In contrast, when the internal temperature glide is increased, the dew-point temperature in the condenser increases more in the case with a small external temperature glide in the condenser than in the case with a large glide. In application A, the potential for increase in the dew-point temperature in the evaporator is limited, and Rev. Int. Froid 1993 Vo116 No 6

409

Performance comparison of pure and mixed fluids." M. HOgberg et al. ° ° .

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Figure 8 Method II: Temperature profiles in evaporator and condenser, for a pure fluid and two mixtures. In (a) an application with large temperature glides of the heat sink and source is shown; in (b) an application with small glides is shown. Dashed lines represent heat source and heat sink. (a): Curves i illustrate a pure working fluid, curves ii represent mixtures whose internal temperature glides match the duty, and curves iii are valid for mixtures having larger internal temperature glides in evaporator and condenser than the external temperature glides of the heat source and the heat sink, respectively. (b) Curves i illustrate a pure working fluid, curves ii and curves iii are valid for mixtures having larger internal temperature glides in evaporator and condenser than the external temperature glides of the heat source and the heat sink, respectively Figure 8 M~thode II: profils de temperature dans l'~vaporateur et le condenseur, pour un fluide p u r e t deux m~langes. Dans (a) on montre une application avec des glissements de ternpdrature importants de la source de froid et de la source chaude; dans (b) , on montre une application avec de faibles glissements. Les lignes en pointill~s reprdsentent la source de chaleur et la source de froid. (a) : les courbes i illustrent un fluide actif pur, les courbes ii reprdsentent les mdlanges dont les glissements de tempdrature interne et les glissements de tempdrature externe sont identiques, et les courbes iii sont valables pour les mdlanges ayant des glissements de tempdrature interne plus importants clans l'dvaporateur et le condenseur que les glissements de tempdrature externe de la source de chaleur et de la source de froid, respectivement. (b) les eourbes i illustrent un fluide actif pur, les courbes ii et les courbes iii sont valables pour des mdlanges ayant des glissements de tempdrature interne plus importants dans l'dvaporateur et le condenseur que les glissements de tempdrature externe de la source de chaleur et de la source de froid, respectivement.

the increase of the dew-point temperature in the condenser is large relative to the increase in the evaporator. Thus, the COP decreases with increased internal temperature glides. In application B, the external temperature glides are large; thus, the increase of the dew-point temperature in the evaporator has a larger influence on the pressure ratio than the increased dew-point temperature in the condenser has and the COP increases with increasing internal temperature glides.

Effect of LMTD calculations. For Method II, the importance of doing a numerical integration of the mean temperature difference instead of a simple L M T D calculation was investigated. The results indicated that the mean temperature difference can differ by as much as 20% in either direction between L M T D calculation and calculation by means of numerical integration; this is approximately equivalent to a deviation of 20% in the area as well. In spite of the large errors in mean temperature differences, the deviation in the COPs between the two ways of doing the calculations is small, as shown in Figure 9. The disagreement is only 1-2% at the most. The low impact of the large errors in mean temperature differences for the cases considered here is caused by the 410

Int. J. Refrig. 1993 Vol 16 No 6

fact that the discrepancies are mainly in different directions in the evaporator and the condenser. (The exception is HCFC22-CFC114 in the composition range 0.4~ O.6.)

Method III Effect of composition. The shapes of the COP-composition curves are essentially the same for Methods III and II, since the temperature profiles in the heat exchangers for Method III have the same shapes as those for Method II. The discrepancies between the curves are caused by the introduction of heat transfer and pressure drop in the calculations. Effect of heat transfer and pressure drop. As can be seen in Figures 3-6, the effect of including heat transfer and pressure drop in the calculations is that the COP decreases. The two factors affect the COP to different amounts. A pressure drop always reduces the COP, while using the actual heat transfer coefficient instead of that of the reference fluid may affect the COP in any direction, depending on the transport properties of the fluid in comparison to those of the reference fluid. In Figure 10,

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Figure 9 Ratios between the COPs calculated with the LMTD concept and the COPs calculated according to Method II for applications A and B Figure 9 Rapports entre les COP calculds avecla mdthode L M T D et les C O P calculus en fonction de la m~thode I I pour les applications A et B: . . . . . . H C F C 2 2 - C F C l 1 4 B; - H C F C 2 2 - C F C l 1 4 A; . . . . H C F C 2 2 - H C F C 1 4 2 b B; - HCFC2~HCFC142b A 3.7

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As can be seen in Figures ~ 6 , the shapes of the C O P composition curves for Method II and those for Method III are roughly similar, but the shapes of the curves for Method I differ entirely from those of the other two methods. Since the deviation between the results of Methods I and III (the error of Method I varies between - 4% and + 11%) is very irregularly dependent on the composition, the former method must be used with much care. In a comparison between Methods II and III, the largest deviation is found for pure CFC114, with a 12% error. The errors of the COPs are less than 2% for HCFC22, and about 5% for HCFC142b. The errors of the mixtures are in the interval between the errors of the pure components in the mixtures, and increase monotonically from one component to the other. Thus, by means of Method II the COP can be predicted with the same accuracy for a mixed working fluid as for a pure

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Effect of mass transport resistance in heat transfer. The calculations for Method III have been done without consideration of mass transport resistance in the heat transfer. The main part (approximately 80 %) of a degradation of the heat transfer coefficient of the working fluid from the ideal value (a weighted value of the heat transfer coefficients of the two pure components) is, however, taken into account in the calculations, since the transport properties are estimated at the actual composition of the vapour and of the liquid 2°. In the applications investigated and for the mixtures considered in this work, this gives an error, in the worst case, of approximately 10% in the overall heat transfer coefficient. It can be shown that a 10% lower overall heat transfer coefficient for a mixture of 50% HCFC22 and 50% CFC114 would lower the COP in application A by approximately 3%; for the H C F C 2 2 - H C F C 1 4 2 b mixture (see H6gberg et al. 12) and for other compositions of the HCFC22-CFC114 mixture, the reductions are less.

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the separate influence by each of the two factors on COP is shown for H C F C 2 2 - H C F C 1 4 2 b in application B. The influence of heat transfer alone, which is calculated using Method III neglecting the pressure drop without changing the tube length, is shown as a dotted line. As seen, both the influence of heat transfer and of pressure drop differ between the two pure fluids and hence, also

one.

The relations between the COPs of different working fluids, pure as well as mixtures, depend on which method is used for comparing the performance of pure and mixed working fluids. The order between the fluids is changed in some cases. Note especially that the composition giving the highest COP for the mixtures is not always predicted with Methods I and II.

Comparison between the applications The differences in principle between the methods are the same in both applications, although it can be seen in a comparison between the applications (Figure 3 is compared to Figure 4, and Figure 5 to Figure 6) that the relations between the COPs of the two applications are not the same for the different methods. Thus it is important to be aware of the difference between Method I, on the one hand, and Method II, on the other. The compariRev. Int. Froid 1993 Vo116 No 6

411

Performance comparison of pure and mixed fluids: M. Hdgberg et al. I

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that the discrepancies often are in different directions in the evaporator and the condenser. 5. Predictions of the capacity should be done with Method III, since Methods I and II can deviate by as much as 15% from Method III. 6. When making rigorous comparisons between different working fluids, the method with specified area has to be used, since it is essential to take the transport properties into account.

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Figure l l Capacity of application B with the mixture HCFC22CFC114, for the three methods Figure 11 Capacitd de l'application B avec le mdlange HCFC22 CFCl l 4, pour les trois mkthodes: mkthode I; . . . . mkthode II," -mdthode III

son between the COPs of the two applications by means of Method I is a sort of design approach (the areas are very different in the applications), while the comparison with Method II is rather an investigation of the effects of a change in external temperature glides in a unit with specified heat transfer areas.

Capacity The capacity of various compositions of the mixture HCFC22-CFC114 is shown for application B in Figure 11. Application B has the largest deviations between the methods. As seen in Figure 11, calculations by Methods I and II can predict the capacity, compared to that calculated by Method III, to within 15%.

References 1

2

3 4 5

6 7 8 9

Conclusions From the above discussion, the following inferences can be drawn:

10

1. Comparisons by means of Method I should be avoided for non-azeotropic mixtures, since the error is very irregularly dependent on the composition. 2. A prediction of the COP level of a non-azeotropic mixture can be made with the same accuracy as for a pure fluid with Method II, i.e. equal mean temperature differences, and the accuracy of this method is good enough for rough estimations of the COP levels of different working fluids. 3. An estimation of the mean temperature difference by means of L M T D for a non-azeotropic mixture can give errors of as much as 20%. Thus, the areas of the heat exchangers are estimated with errors of the same size when the L M T D concept is used for a mixture. 4. The difference between the COP for a non-azeotropic mixture calculated by means of an L M T D concept and that calculated by means of an integration along the heat exchanger areas is small, in spite of the large error in the mean temperature difference. This is due to the fact

11

412

Int. J. Refrig. 1993 Vol 16 No 6

12 13 14 15 16 17 18

19

Shiflett, M. B., Yokozeki, A. and Reed, P. R. Property and performance evaluation of 'SUVA' HP refrigerants as R502 alternatives Proc 1992 Int Refr Conf - Energy Efficiency and New Refrigerants, Purdue, West Lafayette (July 1992) 15-24 Shiflett, M. B., Yokozeki, A. and Bivens, D. B. Refrigerant mixtures as HCFC22 alternatives Proc 1992 Int Refr Conf Energy Efficiency and New Refrigerants, Purdue, West Lafayette (July 1992) 35-44 ICI Chemicals & Polymers KLEA 32 and KLEA blends replacements for HCFC 22 Technical Note (July 1992) McLinden, M. O. and Radermacher, R. Methods for comparing the performance of pure and mixed refrigerants in the vapour compression cycle Int J Refrig (1987) 10 318-325 Pamlin, R. Nonazeotropic mixtures as working fluids in large heat pumps. Measurements of compressor efficiency (in Swedish) Report BFR Project 820883-3, Svenska Rotor Maskiner (1982) Lee, B. and Kesler, M. K. A generalized thermodynamic correlation based on three parameter corresponding states AIChEJ (1975) 21 510-527 Str6m, K., Greu, U. and Ljungqvist, K. Representation of vapour-liquid equilibrium data for binary refrigerant mixtures J Chem Eng Data (1989) 34 252-257 Gerdsmeyer, K. D. and Kruse, H. Comparison of equations of state for application to nonazeotropic refrigerant mixtures Proc Purdue IIR meeting Prepr Purdue (July 1988) 28-37 PI6cker, U., Knapp, H. and Prausnitz, J. M. Calculation of high pressure vapour-liquid equilibrium from a corresponding-states correlation with emphasis on asymmetric mixtures Ind Chem Proc Des Dev (1978) 17 324-332 Valtz, A., Laugier, S. and Richon, D. Bubble pressures and saturated liquid molar volumes of difluoromonochloromethane-fluorochloroethane binary mixtures: Experimental data and modelling lnt J Refrig (1986) 9 282 289 Str/Jm, K., H6gberg, M. and Berntsson, T. State and transport properties of nonazeotropic mixtures and high-temperature working fluids Final Report, Part A, IEA, Advanced heat pumps Annex X I l I (1992) H6gberg, M., Vamling, L. and Berntsson, T. Nonazeotropic mixtures as substitutes for today's CFC fluids, Additional Prec. 3rd IEA Heat Pump Conference Tokyo (1990) 7-26 Shah, M. M. Chart correlation for saturated boiling heat transfer: Equations and further study A S H R A E Trans (1982) 8 185-192 Beatty, K. O. and Katz, D. L. Condensation of vapours on outside of finned tubes Chem Eng Prog (1948) 44 55-70 Smith, R. A. Vaporisers." Selection, Design & Operation, Longman Scientific & Technical, Harlow (1986) 87-91 Latini, G., Marcotullio, F. and Pontieiello, A. Dynamic viscosity of refrigerants and refrigerant mixtures: A prediction method, Proc Purdue I1R Meeting Prepr, Purdue (July 1988) 48-55 Reid, R., Prausnitz, J. M. and Poling, B. E. The Properties o f Gases and Liquids, 4th Edn, McGraw-Hill, New York (1987) Storek, H. and Brauer, H. Reibungsdruckverlust der adiabaten Gas-Fliissigkeitsstr6mung in horizontalen und vertikalen Rohren, VDI-Forsch. 11. 599 (1980) Miiller-Steinhagen, H. and Heck, K. A simple friction pressure

Performance comparison of pure and mixed fluids. M. Hdgberg et al.

20 21

drop correlation for two-phase flow in pipes Chem Eng Process (1986) 20 297 308 Jung, D. S. Horizontal-flow boiling heat transfer using refrigerant mixtures Final report, EPRI ER-6364 Project 8006-2 (1989)

Higashi, Y., Okazaki, S., Takaishi, Y., Uematsu, M. and Watanabe, K. Measurements of vapour liquid coexistence curve for

22

the binary R12-R22 system in the critical region J Chem Eng Data (1984) 39 31-36 Yada, N., Kumagai, K. and Watanabe, K. Measurements of the PVTx properties of binary refrigerant R142b + R22 system, The Second Asian Therrnophysical Properties Conference (1989) 369-374

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