HE

HEAT EXCHANGER MEAN TEMPERATURE DIFFERENCES FOR REFRIGERANT MIXTURES

A Thesis Presented to The Academic Faculty by Laura Atkinson Schaefer

In Partial Ful llment of the Requirements for the Degree Master of Science in Mechanical Engineering

Georgia Institute of Technology December 1997

ii

HEAT EXCHANGER MEAN TEMPERATURE DIFFERENCES FOR REFRIGERANT MIXTURES

Approved: Sam V. Shelton, Chairman William Wepfer Sheldon Jeter Date Approved

iii

TABLE OF CONTENTS LIST OF TABLES LIST OF ILLUSTRATIONS NOMENCLATURE SUMMARY CHAPTER I INTRODUCTION
The Need For Replacement Refrigerants Mixture Properties . . . . . . . . . . . . Zeotropes . . . . . . . . . . . . . . . . Near-azeotropes . . . . . . . . . . . . Azeotropes . . . . . . . . . . . . . . . Heat Exchanger Analysis for Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v vi viii ix 1
1 3 3 5 8 8

II III IV

DERIVATION OF THE LOG MEAN TEMPERATURE DIFFERENCE 11 A NUMERICAL METHOD FOR CALCULATING THE MEAN TEMPERATURE 18 APPLICATION OF THE NUMERICAL TECHNIQUE 22
Software Tools . . . . . . . . . . . . . . . . . . . . . . Engineering Equation Solver . . . . . . . . . . . . Refrigerant Database . . . . . . . . . . . . . . . . Calculation of the UA . . . . . . . . . . . . . . . . . Comparison of the UAs: Development of Error Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 22 23 23 26

V

RESULTS AND DISCUSSION

Ammonia-Water Mixtures . . . . . . . . Properties . . . . . . . . . . . . . . . The Fallacy of an End-Point Pinch . . Log Error Ratio for Ammonia-Water . Other Refrigerants . . . . . . . . . . . . Properties . . . . . . . . . . . . . . .

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28
28 28 30 30 31 31

iv Standard Error for R-22 Alternatives . . . . . . . . . . . . . . 34 Drop-In Replacements vs. System Recon guration . . . . . . . . 34

VI CONCLUSIONS AND RECOMMENDATIONS APPENDIX A REFRIGERANTS AVAILABLE IN REFPROP
REFPROP, Version 5.0 . . . REFPROP, Version 6.0 21 . Pure Substances . . . . . Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51
. . . . . . . . . . . . . . . . . . . .

. . . .

55
55 55 55 56

B AMMONIA-WATER EES PROGRAM C REFRIGERANT MIXTURE EES PROGRAM BIBLIOGRAPHY

57 59 61

v

LIST OF TABLES
Table 5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 Operating Pressures and Temperature Glides for NH3/H2O . . . UA, UALMTD, and LER for NH3/H2O . . . . . . . . . . . . . . . HCFC-22 Alternatives . . . . . . . . . . . . . . . . . . . . . . . . Operating Pressures and Temperature Glides for Refrigerants 1-5 Operating Pressures and Temperature Glides for Refrigerants 6-9 UA and UALMTD for Refrigerants 1-5 . . . . . . . . . . . . . . . UA and UALMTD for Refrigerants 6-9 . . . . . . . . . . . . . . . Standard Error for Refrigerants 1-9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 29 32 33 35 36 37 38 39

vi

LIST OF ILLUSTRATIONS
Figure 1-1 1-2 1-3 1-4 1-5 1-6 2-1 2-2 2-3 3-1 3-2 5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 Page Results of International Protocols . . . . . . . . . . . . . . . . . . . . A Zeotropic Mixture of Ammonia and Water . . . . . . . . . . . . . Temperature vs. Enthalpy for Water . . . . . . . . . . . . . . . . . . Ammonia-Water Mixture, Concentration = 0.98 . . . . . . . . . . . . A Near-Azeotropic Mixture . . . . . . . . . . . . . . . . . . . . . . . A Mixture With an Azeotrope At 41.18% R-125 . . . . . . . . . . . . A Counter
ow Heat Exchanger . . . . . . . . . . . . . . . . . . . . . Parallel-
ow Temperature Variation Over Area . . . . . . . . . . . . Counter
ow Temperature Variation Over Area . . . . . . . . . . . . A Counter
ow Heat Exchanger: Temperature Examined at Four Points A Counter
ow Heat Exchanger: Temperature Examined at Eleven Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NH3/H2O: Concentration = 0.99, Pinch = 1 K . . . . . . . . . . . . Concentration and Nonlinearity for NH3/H2O . . . . . . . . . . . . . Log Error Ratio vs. Pinch Point for NH3/H2O . . . . . . . . . . . . Nonlinearity of Refrigerants 1, 6, and 8 . . . . . . . . . . . . . . . . . Standard Error for Refrigerants 1-3 . . . . . . . . . . . . . . . . . . . Standard Error for Refrigerants 4-6 . . . . . . . . . . . . . . . . . . . Standard Error for Refrigerants 7-9 . . . . . . . . . . . . . . . . . . . Carnot and Lorenz Cycle Diagrams . . . . . . . . . . . . . . . . . . . 2 4 6 6 7 9 12 14 14 21 21 42 43 44 45 46 47 48 49

vii 5-9 The Liquid-Line/Suction-Line Heat Exchanger . . . . . . . . . . . . 50 5-10 The Desorber-Absorber Heat Exchange Cycle . . . . . . . . . . . . . 50

viii

NOMENCLATURE Symbols
A cp h LER m _ P PP Q SE T U
Area over which heat is transferred (m2) kJ Speci c Heat at Constant Pressure ( kg
K ) Enthalpy ( kJ ) kg Log Error Ratio (-) Mass
ow rate ( kg ) s Pressure (bar, kPa) Pinch Point (C , K ) Heat Transfer Rate (kW ) Standard Error (%) Temperature (C , K ) Overall Heat Transfer Coecient ( mkWK ) 2


Greek Characters

Temperature Dierence (C , K )

Subscripts
c h m w
Cold Stream Hot Stream Refrigerant Mixture Stream Water Stream

ix

SUMMARY
Recent protocols have reduced, and will eventually eliminate, the production and use of chloro
uorocarbons (CFCs) and hydrochloro
uorocarbons (HCFCs). While it has been possible to nd single-component replacements for CFCs such as R-12, replacements for HCFCs are generally refrigerant mixtures. These mixtures may be azeotropic, in which case single-component behavior is exhibited, nearazeotropic or zeotropic. Azeotropic refrigerant mixtures are uncommon, so it is of interest to study the characteristics of zeotropes and near-azeotropes. The temperature of a zeotropic mixtures does not remain constant throughout a heat exchanger. Furthermore, zeotropes often exhibit a nonlinear temperature/enthalpy relationship. These factors contradict some of the assumptions that are made in deriving the Log Mean Temperature Dierence (LMTD), a calculation that is used to compute the size of a heat exchanger (UA). In order to develop a more precise mean temperature dierence, the derivation of the LMTD must be revaluated. Since the temperature is not an easily-determined function of enthalpy, e the heat transfer process must be discretized and the properties determined at each point. An ammonia-water mixture is examined rst, since it is known to display a highly nonlinear temperature glide. Synthetic mixtures that are being studied by the refrigeration industry as replacements for HCFC-22 are also analyzed. In each case, the actual UA is compared to the UA found using the LMTD, and representative error scales are developed. It is found that these errors can cause a heat exchanger to be undersized by as much as a factor of fty.

x Finally, the advantages of zeotropes are also discussed, as are cycles that can utilize those advantages. Recommendations are made that the eect of the modi ed UA calculations on these cycles should be studied, and that the bene ts of natural over synthetic refrigerants should also be investigated.

1

CHAPTER I INTRODUCTION The Need For Replacement Refrigerants
Since their development in 1931, chloro
uorocarbons (CFCs) were thought to be ideal refrigerants. They had chemical stability and relatively low toxicity, making them safe for both residential and industrial use. CFCs were also quite inexpensive, resulting both in a proliferation of refrigerators and air conditioners that utilized them, and in an unwillingness to repair systems with leaks, since they could often be periodically recharged for much less. In 1974, CFCs were tentatively identi ed as destructive to the ozone layer (Domanski, 1997). For the next decade, this relationship was investigated, and a quantitative statement that tied CFCs to the depletion of ozone was released by the World Meteorological Organization and the United Nations Environment Programme (WMO/UNEP) in 1985. The Montreal Protocol (1987), which was agreed to by nearly one hundred and fty countries, froze CFC consumption in 1989 and pledged to cut it in half by 1998. In 1992, the Copenhagen Amendments went even farther, and halted the production of CFCs in developed countries by 1996. The eects of these protocols, assuming international compliance, can be seen in Figure 1-1 (Ennis, 1994). With CFCs scheduled to be phased out, hydrochloro
uorocarbons (most notably HCFC-22) gained in popularity. While their production levels were controlled by 1992, they were not scheduled for complete elimination. HCFCs were still damaging to the ozone layer, but much less so than CFCs. Their average stratospheric

2

Figure 1-1: Results of International Protocols

3 lifespan was much shorter, and not as many of them penetrated into the upper atmosphere. For example, CFC-12 has a stratospheric lifetime of 102 years, compared to a lifetime of 13.3 years for HCFC-22. Furthermore, the ozone depletion potential (ODP) of R-22 is only 5.5% of the ODP of R-12 (Sand et al., 1997). HCFCs and HCFC mixtures were developed that could serve as drop-in replacements for most of the CFCs in use. However, the excitement over HCFCs was short-lived, as the Vienna Convention of 1995 not only accelerated the HCFC-reduction timetable, but also required that their production eectively cease by 2020, with a complete cessation by 2030. Japan and some European countries have established cut-o dates that begin much earlier. In Switzerland, for example, HCFCs are banned by 2005. Once again, replacement refrigerants need to be found, but this time there are no obvious solutions. While some single-component refrigerants present reducedperformance possibilities, the solution appears to lie with synthetic mixtures. These mixtures may be azeotropic, near-azeotropic, or zeotropic.

Mixture Properties Zeotropes
For a zeotropic mixture (also known as a non-azeotropic mixture), the concentrations of the liquid and the vapor phase are never equal (Alefeld and Radermacher, 1994). This creates a temperature glide during phase change (at which point the concentrations of the vapor and the liquid are continually changing). Zeotropic mixtures are the most common type of refrigerant blend. An example of a zeotropic mixture is ammonia and water. As can be seen in Figure 1-2, at no point do the bubble and dew point lines meet (except, of course, where there is pure ammonia or pure water). When the mixture is cooled, liquid begins to form at the dew point

4

P = 15 bar 480 460 440 420 Temperature [K] 400 380 360 340 320 300 0.00 Water 0.20 0.40 0.60 0.80 1.00 Ammonia
Bubble Point Line Dew Point Line

Compositon [Mass Fraction]

Figure 1-2: A Zeotropic Mixture of Ammonia and Water

5 temperature, but this is not completed until the bubble point temperature. This dierence between the dew and bubble temperatures is known as a temperature glide. The smaller the temperature glide, the less loss of heat transfer due to concentration dierences. Generally, zeotropic mixtures are not ideally suited to be placed in existing equipment, but can bring performance improvements when used with modi ed systems. Because of the varying liquid and vapor compositions, systems employing zeotropic refrigerant mixtures must be liquid charged. Doing otherwise could change the mixture's composition, which could result in decreased performance and increased safety risks over time. Another feature common to zeotropic mixtures is a nonlinear temperature versus enthalpy pro le. A single-component or azeotropic refrigerant will have a linear temperature pro le, as in Figure 1-3, but a zeotropic mixture's pro le can be strikingly nonlinear, as seen in Figure 1-4. This sort of temperature-enthalpy behavior results in a varying speci c heat and raises the possibility of a temperature pinch within a heat exchanger, both of which complicate traditional heat exchanger calculations.

Near-azeotropes
For a near-azeotropic mixture, the vapor and liquid concentrations at a given temperature and pressure dier only slightly. Most azeotropic refrigerant mixtures become near-azeotropic when the pressure or temperature is varied from the azeotrope point. R-410A (which is also known as AZ-20 under the AlliedSignal patent) is a near-azeotropic mixture of R-32 and R-125 ( fty- fty mass percent). For standard condenser pressures and temperatures, the bubble and dew points for this concentration vary by less than 0.1 C (see Figure 1-5). Although it appears that this variation could be reduced even further by increasing the concentration of R-125, this is ac-

6

308.0 307.0

Temperature [K]

306.0 305.0 304.0 303.0

302.0 122.5

127.0

131.5

136.0

140.5

145.0

Enthalpy [kJ/kg]

Figure 1-3: Temperature vs. Enthalpy for Water

360 350

Temperature [K]

340 330 320 310 300 0 200 400 600 800 1000 1200 1400 1600

Enthalpy [kJ/kg]

Figure 1-4: Ammonia-Water Mixture, Concentration = 0.98

7

13 12 11 T [C] 10 9 8 7 0 R-32 0.2 0.4 0.6 0.8 Composition [Mass Fraction] 1 R-125

Figure 1-5: A Near-Azeotropic Mixture

8 tually undesirable. For example, R-410A was developed to serve as a replacement for HCFC-22, and changing its composition reduces its suitability for that role while also increasing its
ammability and toxicity. Near-azeotropic mixtures usually work fairly well with existing equipment.

Azeotropes
An azeotrope is de ned as a point at which the concentration of the liquid and the vapor phase is the same for a given temperature and pressure. Some mixtures have more than one azeotrope at a xed pressure or temperature, but this is uncommon. At an azeotrope, a mixture behaves like a single-constituent system. Almost all azeotropic refrigerants have a boiling point lower than either of the constituents (which is known as a minimum temperature or maximum pressure azeotrope). An exception to this is R-507, which is a fty- fty weight percent blend of R-125 and R-143a, and is proposed as a replacement for R-502. A plot of temperature versus composition for a mixture of R-125 and R-143a can be found in Figure 1-6. While an azeotropic mixture may appear to be an obvious replacement for a pure refrigerant, there is no azeotropic mixture replacement for R-22, one of the most popular of the HCFCs, which duplicates its cooling capacity and pressures. Azeotropic refrigerant mixtures are uncommon, and it appears unlikely that new azeotropes will be found.

Heat Exchanger Analysis for Mixtures
In the analysis of heat exchangers, the Log Mean Temperature Dierence (LMTD) is a standard calculation used to compute the required size (indicated by UA). The practice of using the LMTD for heat exchanger calculations dates to the 1950s (Chen, 1988). Other mean temperature methods, such as Underwood's (1933)

9

183.86 183.84 183.82 183.8 183.78 183.76 183.74 183.72 0 R-125
           

T [K]

    

0.2

0.4 0.6 0.8 Composition [Mass Fraction]

1 R-143a

Figure 1-6: A Mixture With an Azeotrope At 41.18% R-125

10
1 1 1 one-third rule (m=3 = 1 (1=3 + 2=3)), predate the LMTD, but none of them are as 2 widely used today. The LMTD ceases to be valid, however, when a zeotropic mixture that exhibits a nonlinear temperature glide is used as the working
uid. Examining Figure 1-4, it is obvious that errors would result from using the LMTD to calculate the heat exchanger size for this mixture. While the inadequacy of the LMTD has been brie
y commented on by Lundqvist (1995), he has only examined the dierences between subcooling, condensing, and superheating, and ignored the nonlinearities in the two-phase region. In order to ascertain the magnitude of the error, a numerical analysis must be performed. It is of interest to determine an alternative calculation that is applicable to zeotropes. The rst step is to return to the de nition of the mean temperature dierence in a heat exchanger. Some assumptions that are made in the formulation of the LMTD are acceptable: for example, that the overall heat transfer coecient will remain nearly constant over the heat exchanger area. Obviously, though, it cannot be assumed that the temperature will be an easily-determined function of the heat exchanged. As a result, the integral evaluation of the variance in temperature between the two streams over a dierential amount of heat transferred must instead be transformed into a summation. Since the accuracy of this method will increase with the number of steps that are taken, the step size will be made suciently small so as to minimize numerical error. The UA that is found using the traditional LMTD can be contrasted with that found using the numerical method, and the deviations compared for various possible refrigerant replacements over a range of pinch points.

11

CHAPTER II DERIVATION OF THE LOG MEAN TEMPERATURE DIFFERENCE
Using the energy equation to express the heat transferred over a section of a heat exchanger (Figure 2-1)1:

Q = m dh + h dm _ _
If the mass
ow rate through the heat exchanger is constant, this reduces to:

(2.1)

Q = m dh _

(2.2)

For
uids that have constant speci c heats and that do not undergo a phase change, a property relation is:

dh = cp dT
and, therefore:

(2.3)

Q = m cp dT _

(2.4)

Using this equation to examine the hot and cold streams separately yields: Kaka and Payko (1988) and Incropera and DeWitt (1985) provide a more c c generalized overview of the following derivation.
1Both

12

........ .

dA ( = w dx)

..... ....

Stream 1

HH 

 HH

? Q
Figure 2-1: A Counter
ow Heat Exchanger

Stream 2

13

Q = Ch dTh ; Ch = (m cp)h _ Q = Cc dTc ; Cc = (m cp)c _

(2.5) (2.6)

where  or  appears, the top sign designates parallel-
ow (Figure 2-2), and the bottom sign designates counter
ow (Figure 2-3). A heat exchanger relationship for expressing the heat transfer between
uids over a dierential area is:

Q = U (Th Tc) dA , or Th Tc = UQ dA
Rearranging equations 2.5 and 2.6 yields:

(2.7) (2.8)

dTh = Q and dTc =  Q ; so Ch Cc
1 1 dTh dTc = d(Th Tc) = Q ( C  C ) h c Dividing the above equation by equation 2.8 results in: (2.9)

d(Th Tc) = U ( 1  1 ) dA Th Tc Ch Cc

(2.10)

The conductive and convective coecients are assumed to vary only slightly over the heat exchanger area, and the temperature-enthalpy relationship is assumed

14

T Temperature, T

h1

. mh dTh T ∆T δQ Th2
h

dTc Tc1 . mc

Tc

Tc2

dA L Surface Area, A

0

Figure 2-2: Parallel-
ow Temperature Variation Over Area
. m
h1

T

h

dTh Temperature, T T T ∆T Tc2 . mc dT c T Tc
c1

h2

h

δ Q

dA

0

Surface Area, A

L

Figure 2-3: Counter
ow Temperature Variation Over Area

15 to be linear, so the overall heat transfer coecient (U ) and the speci c heats (Cc and Ch) will be considered to be independent of the area. Equation 2.10 can then be integrated over the heat exchanger:
Z side2
side1

Th Tc d(Th

1

1  1 ) Z s2 dA Tc) = U ( C C s1 h c 1) Cc (2.11)

Parallel-
ow: Counter
ow:

1 ln[ Th2 Tc2 ] = UA ( C Th1 Tc1 h

T T 1 1 ln[ Th2 Tc1 ] = UA ( C + C ) h1 c2 h c

Returning to equations 2.5 and 2.6, expressions incorporating Cc and Ch can be found:
Z side2
side1

Q =

Z s2
s1

Ch dTh

Z s2
s1

Q = 

Z s2
s1

Cc dTc

Assuming that the speci c heat is also not a function of temperature, this results in:

Q = Ch (Th2 Th1 ) Q = Cc (Tc2 Tc1 )

(2.12) (2.13)

16 Replacing the speci c heats of equation 2.11 with those found in 2.12 and 2.13 yields Parallel-
ow:

T ln[ Th2 Tc2 ] = UA [(Th2 Th1 ) + (Tc1 Tc2 )] Q h1 Tc1
Counter
ow:

T ln[ Th2 Tc1 ] = UA [(Th2 Th1 ) + (Tc2 Tc1 )] Q h1 Tc2
Rearranging to separate Q and UA results in the familiar log mean temperature dierence:

Q = UA
T1[
T
]T2 ln 1

T2


TLogMean =
T1[
T
]T2 ln 1

T2

(2.14)

It must be remembered that this equation is only applicable under a number of limiting assumptions. The mass
ow rate must be constant throughout the heat exchanger. The conductive and the convective coecients may vary over the heat exchanger area, but only slightly. The enthalpy-temperature relationship must be linear, and the speci c heats are considered to be independent of both temperature and area. From equation 2.14 it is evident that:
TLogMean;Counterflow 
TLogMean;Parallel
flow

17 for the same inlet and outlet temperatures. In order to better magnify the error resulting from the LMTD, only counter
ow heat exchanger con gurations will be studied, since that LMTD represents the maximum temperature potential for heat transfer. For counter
ow, equation 2.14 is

Q = UA (Th1 Tc2 ) 1 (TT2h2 Tc1 ) T ln[ T 2 T 1 ]
h c h c

This equation is valid only if Cc 6= Ch; otherwise, Th1 Th2 = Tc2 Tc1 and a logarithm of zero results. Finally, since the objective of this study is to correctly size heat exchangers, equation 2.14 is rearranged to nd the overall conductance multiplied by the area (UA)

UA =
T Q

LogMean

(2.15)

18

CHAPTER III A NUMERICAL METHOD FOR CALCULATING THE MEAN TEMPERATURE
For zeoptropic refrigerants, some of the assumptions from the classical LMTD derivation must be discarded. Beginning with the rst equation of Chapter II, the mass
ow rate through the heat exchanger is still assumed to be constant, but the speci c heats for both the cold and the hot streams are now not constant. In the classical LMTD derivation, it was assumed that the
uids would not undergo a phase change and that they would have constant speci c heats (so that dh = cp dT ). In this investigation, however, the more general case is studied, allowing a two-phase region of mixtures with nonlinear temperature-enthalpy curves. As discussed in the introduction, this nonlinearity results in varying speci c heats. In fact, the speci c heat is a function of both temperature and area. Returning then instead to the second de nition in Chapter II for the heat transferred between two streams in a heat exchanger,

Q = U
Tmw dA

(3.1)

where
Tmw is the temperature dierence between the zeotropic refrigerant mixture and the water at any given point. To nd the total heat transferred, equation 3.1 is integrated over the entire area of the heat exchanger.

19
Z Q0 Q
0


Tmw = 0 U dA

Z A0

A0 = the total heat exchanger area Q0 = the total amount of heat transferred
It is still reasonable to assume that the overall heat transfer coecient will be fairly constant over the area (hereafter denoted as U0). The area is nondimensionalized so that A0 = A=A0, and the above equation becomes
Z Q0 Q
0
0
Tmw = U0A0 0 dA = U0A0

Z1

(3.2)

It should be noted that, by de nition, UA is inversely proportional to the total thermal resistance. This resistance is obviously not strictly constant over the heat exchanger area; the condensation or evaporation of the
uids and the changes in temperature will aect both the thermal conductivity and the convection coecients. However, the magnitude of these variations is assumed to be small, so as to only insigni cantly aect the overall heat transfer coecient. If this is not the case, the right hand side of equation 3.2 could become quite complicated, and would require as parameters the exact speci cations of the heat exchanger under consideration. An examination of equation 3.2 reveals its similarity to equation 2.15. However, because the temperature can be radically nonlinear, the above integral cannot be evaluated in closed form (recalling that Q is a function of enthalpy). Instead, it must be replaced by a numerical integration in which the temperature dierence between the streams is found at incremental steps of the amount of heat transferred in the heat exchanger.

20

U0A0 =

Q0 X

1 Q i=0
Tmw

(3.3)

As the number of steps approaches in nity, equation 3.3 becomes identical to equation 2.15. Calculations like those above would once have required hours of expensive computer time to solve. Given current computational power and accurate properties in computer-readable form, however, they can now be performed in minutes on a desktop PC. The number of steps, then, can be made suciently large so as to give a reasonably accurate solution without demanding a signi cant increase in solution time. As a graphical representation of this improvement, compare the obvious inaccuracy of Figure 3-1 with the increased precision of Figure 3-2. Two other numerical approaches to nding a mean temperature have been suggested by Granryd and Conklin (1990). In the rst method, the temperature pro les are linearized in small segments, from which an eective speci c heat can be calculated. The second method also focuses on the speci c heat. A polynomial approximation for cp is developed from a curve t, and then integrated where appropriate. A disadvantage to both these methods is the complexity of the calculations that must still be performed once cp is found in order to determine the heat exchanger size.

21

380 370 Exact Solution Values 360 Numerical Solution Values 350 340 330 320 310 300 0 200 400 600 800 1000 Heat Transferred

T [K]

1200

1400

Figure 3-1: A Counter
ow Heat Exchanger: Temperature Examined at Four Points

380 370 Exact Solution Values 360 Numerical Solution Values 350 340 330 320 310 300 0 200 400 600 800 1000 Heat Transferred

T [K]

1200

1400

Figure 3-2: A Counter
ow Heat Exchanger: Temperature Examined at Eleven Points

22

CHAPTER IV APPLICATION OF THE NUMERICAL TECHNIQUE Software Tools

Engineering Equation Solver
Engineering Equation Solver (EES) is a software package developed by Dr. Sanford Klein of the University of Wisconsin. EES incorporates the programming structures of C and FORTRAN with a built-in iterator, thermodynamic and transport property relations, graphical capabilities, numerical integration, and many other

useful mathematical functions. By grouping equations that are to be solved simultaneously, EES is able to function at a high rate of computational speed. EES can also be used to perform parametric studies. EES was chosen for this research due to its ability to seamlessly incorporate
uid property calls. Steam tables, air tables, JANAF data, psychrometric functions, and property tables for ammonia, methane, carbon dioxide, and other
uids are built into EES. Rather than store each possible data point, the Martin-Hou equation of state (EOS) is used. Water is one exception to this, as several equations of state are used for each phase. Ammonia-water mixture properties are calculated in EES using the correlation developed by Ibrahim and Klein (1993). To expand the number of available refrigerants, an interface has been developed by Dr. Klein that allows EES to utilize the National Institute of Standards and Technology's Thermodynamic Properties of Refrigerants and Refrigerant Mixtures Database (REFPROP).

23

Refrigerant Database
REFPROP is a FORTRAN -based program that allows a user to look up thermodynamic properties for most refrigerants currently in use or under study. In addition to pure refrigerant properties, REFPROP uses either the Carnahan-StarlingDeSantis (CSD) hard sphere equation of state or the modi ed Bennedict-Webb-Rubin (MBWR) equation of state to calculate the properties of refrigerant mixtures (up to ve components per mixture are possible). The CSD EOS requires only six adjustable parameters per
uid, making it suitable for
uids where there are limited experimental observations, or where only a narrow range of study is of interest. The MBWR EOS is better for wide ranges of data, but requires a large amount of experimental information in order to t its thirty-two interaction coecients. The parameters for a number of mixtures have already been found and entered into REFPROP, but the user is responsible for matching the calculated points to experimental data for new combinations. The EES interface calls a DOS version of REFPROP in order to increase the speed of its calculations, but a Windows version is also available in a beta version still under development. The refrigerants that are available in both the DOS and the Windows versions can be found in Appendix A.

Calculation of the UA
In order to nd the UA derived in equation 3.3, the total heat transferred and the temperature dierence between the water and mixture streams must be calculated at a number of points in the heat exchanger. The heat transferred can be found by applying the energy equation to the water
owing through the heat exchanger: _ QTot = mwater (hwater;entrance hwater;exit) _ (4.1)

24 or for the refrigerant: _ QTot = mmixture(hmix;exit hmix;entrance ) _ (4.2)

where m is the mass
ow rate and h is the enthalpy. By equating 4.1 and 4.2, a mass _
ow ratio can be stated. _ mratio = m_water = hhmix;exit hmix;entrance _ mmix water;entrance hwater;exit (4.3)

The end point states for both the water and the mixture must now be determined. A pinch point (PP) and concentration must also be chosen. For airconditioning applications, a typical condenser entrance temperature for the water side is 29 C with a 5 C rise, so these are the values that will be used. The pressure in the heat exchanger (Phi ) is then found by evaluating the mixture at its exit, where the concentration, the quality (saturated liquid), and the temperature (29 C + PP) are known. With two independent properties (pressure and temperature) given, the endpoint enthalpies of the water stream can be found. Subcooling is not considered, so the mixture is entirely in the two-phase region, and its endpoint properties can be found using the pressure, concentration, and qualities of zero and one. In order to better visualize the transfer of heat between the water and the mixture streams, the total heat transferred will be rede ned on a per refrigerant mass
ow rate basis. The heat exchanger can then be divided into an arbitrary _ _ number of sections (n) of equal Q=mmix. The heat transfer per unit mass
ow rate of the mixture is directly related to the enthalpy, so an enthalpy step shall be de ned as

h hmix;step = hmix;exit n mix;entrance

25 The initial temperature dierence between the refrigerant and the water and the amount of heat transferred are known from the endpoint speci cations, and the values at each successive point in the heat exchanger (ni = 1; 2; 3 : : :) are calculated using the following equations. From equation 4.2: _ Qcumulative = q = h cum mix;step  ni mmix _ (4.4) (4.5) (4.6)

hmix = qcum + hmix;entrance q hwater = mcum + hwater;exit _
ratio

From
uid properties:

Twater = T (hwater ; Phi)

Tmix = T (hmix; Phi ; Concentration)


Tmw = Tmix Twater

(4.7)

For each desired pinch point and refrigerant, the values of qcum and
Tmw calculated in equations 4.4-4.7 are numerically integrated by EES to nd the actual UA (equation 4.4 is an implicit equation in EES). When performing the numerical integration, EES decides how many sections the heat exchanger should be divided

26 into. This stepsize is either chosen using an automatic stepsize adjustment algorithm, or is directly speci ed by the user. For this application, one hundred steps were deemed to be sucient, as smaller heat exchanger segments increased the computational time without increasing the accuracy. A variant of the trapezoidal rule is used to examine the preceding values and to calculate the next step. In order to evaluate the integral, EES uses a second order predictor-corrector algorithm. This algorithm was designed to solve problems where the integrand is a complex function of other variables. It estimates what the value of the integrand should be at each variable step, iterates until convergence, and then moves to the next step. When each step has been evaluated, the integral is solved and the UA is known.

Comparison of the UAs: Development of Error Scales
Once the UA is known, it can be compared with the heat exchanger area that is found using the traditional log mean temperature dierence method (UALMTD). This can be calculated using a slightly altered version of equation 2.15:

T1 = Tmix;entrance Twater;exit

T2 = Tmix;exit Twater;entrance LMTD = T2 TT1 ln T2 1
_ _ UALMTD = Qtotal=mmix LMTD (4.8)

27 Two separate error scales were developed to account for both major and minor discrepancies between the UA and the UALMTD. For small dierences, a standard error (SE) is adequate:

UA SE = jUA UA LMTDj  100
In this study, however, standard errors ranged from twenty percent to over three thousand percent for some mixtures. In order to provide a meaningful scale for evaluation of errors over such large ranges, a log error ratio (LER) is de ned as

LER = log( UALMTD ) UA
By using either the SE or the LER, every possible range of refrigerant UA error can be analyzed.

28

CHAPTER V RESULTS AND DISCUSSION Ammonia-Water Mixtures Properties
As can be seen from the temperature versus enthalpy pro le of Figure 1-4, ammonia-water (NH3/H2O) mixtures generally have extremely nonlinear temperature pro les. This nonlinearity indicates a potential for large error when the LMTD is used to compute the size of a heat exchanger. Therefore, an ammonia-water mixture is an ideal case for the initial application of the methods developed in Chapters III-IV. Three separate mixture concentrations were studied: ninety- ve percent, ninetyeight percent, and ninety-nine percent ammonia. These are typical concentrations for condensers in ammonia-water absorption refrigeration cycles. Furthermore, each mixture was analyzed at ve pinch points (at the refrigerant mixture entrance) ranging from 1-10 K . For each concentration and pinch, the NH3/H2O EES program (Appendix B) was executed. Given the above conditions, the temperature of the NH3/H2O refrigerant stream was found to range widely, from approximately 30 to 100 C. While the temperature glides and the operating pressures vary with both pinch and concentration, glide increases signi cantly with concentration while pressure is a weak function of pinch, as expected. The pressures and temperature glides for all the runs are listed in Table 5-1.

29

Table 5-1: Operating Pressures and Temperature Glides for NH3/H2O

Concentration = 0.95
Pinch (K) 1 3 5 7 10 P (bar) 11.119 11.793 12.497 13.233 14.397 Tglide (K ) 65.96 65.59 65.24 64.89 64.34

Concentration = 0.98
Pinch (K) 1.74 3 5 7 10 P (bar) 11.693 12.135 12.862 13.621 14.824 Tglide (K ) 49.65 49.36 48.89 48.41 47.69

Concentration = 0.99
Pinch (K) 2.47 3 5 7 10 P (bar) 12.068 12.257 12.992 13.76 14.976 Tglide (K ) 38.82 38.68 38.15 37.61 36.79

30

The Fallacy of an End-Point Pinch
The nonlinearity of NH3/H2O can lead to results that are physically unrealistic. For example, at a concentration of 99% and a pinch point of 1 K , the LMTD is kJ found to be 9.6 K , resulting in a UA equal to 132.72 kg
K . In fact, a pinch of 1 K at the mixture inlet is impossible, as demonstrated in Figure 5-1. An identical problem occurs at the same pinch for a concentration of 98%. Furthermore, by comparing the curves for a pinch point of 5 K and concentrations of ninety- ve, ninety-eight, and ninety-nine percent ammonia (Figure 5-2) it can be observed that while the nonlinearity increases with ammonia concentration, it remains strong even at ninety- ve percent. To avoid physically impossible calculations, care was taken to select pinch points where the streams' temperatures would not cross. It should be noted, however, that for NH3/H2O, all listed pinch conditions are solely applicable to the mixture entrance, as smaller temperature dierences will consistently occur within the heat exchanger. The occurrence of an internal pinch can be predicted by comparing the value of @h=@T for the refrigerant mixture at the inlet and the outlet. If


@h @T



@h > @T inlet




outlet

then an interior pinch will occur (Venkatarathnam et al., 1996).

Log Error Ratio for Ammonia-Water
As predicted, dierences between the LMTD-calculated and the actual UA were observed at every concentration and pinch point. Since these dierences can be quite large, the log error ratio was utilized. The LER does indeed provide a meaningful scale for evaluation, as the error can easily be graphically displayed (Figure 5-3).

31 Furthermore, the values of the UA, UALMTD, and LER are compiled in Table 5-2 for every run. The UAs at the smallest pinch points may appear to be excessive, but this is because the streams at these points only narrowly avoid converging in temperature. For the water and refrigerant streams to actually converge to the same temperature, the heat exchanger area would need to be in nite, a reality re
ected in the large actual UAs.

Other Refrigerants Properties
In addition to ammonia-water mixtures, zeotropic and near-azeotropic refrigerant mixtures that are currently under consideration as replacements for HCFC-22 were also analyzed. A literature search was conducted, and the most promising and/or widely endorsed mixtures were chosen for study, and are listed in Table 5-3 (all refrigerants will henceforth be referred to by their reference number). Refrigerants 1 and 8 are currently being considered by DuPont (Bivens, 1997), and refrigerant 9 (also known as AZ-20) has been developed by Allied Signal, two of the largest refrigerant producers in the United States. Refrigerants 3 through 5 were designated by Radermacher and Jung in their comprehensive survey (1993) as the most promising three-component blends. Refrigerant 2 was endorsed by Mei et al. in a follow-up study to that survey (1995). Refrigerant 2 was also earlier advocated by the Air Conditioning and Refrigeration Institute (ARI), as were refrigerants 6 and 7 (Kondepudi, 1992). Each refrigerant was analyzed at pinch points of 2 to 7 K at the mixture inlet. Refrigerant 9 is an exception to this; due to its concave rather than convex

32

Table 5-2: UA, UALMTD, and LER for NH3/H2O

Concentration = 0.95
Pinch (K) 1 3 5 7 10 UA 1392.392 342.442 204.114 146.909 104.327 UALMTD 96.175 71.188 59.882 52.63 45.16 LER 1.161 0.682 0.533 0.446 0.364

Concentration = 0.98
Pinch (K) 1.74 3 5 7 10 UA 6206.845 571.118 274.649 182.668 122.328 UALMTD 97.132 81.83 67.895 59.038 50.002 LER 1.806 0.844 0.607 0.491 0.389

Concentration = 0.99
Pinch (K) 2.47 3 5 7 10 UA 7857.926 951.709 330.693 206.368 132.644 UALMTD 100.793 94.104 77.017 66.259 55.415 LER 1.892 1.005 0.633 0.493 0.379

33

Table 5-3: HCFC-22 Alternatives # Comp. 1 Comp. 2 Comp. 3 Mass % 1 Mass % 2 Mass % 3 1 32 125 134a 0.23 0.25 0.52 2 32 125 134a 0.3 0.1 0.6 3 32 152a 124 0.2 0.2 0.6 4 32 152a 134 0.3 0.4 0.3 5 32 152a 134a 0.4 0.5 0.1 6 32 125 134a 0.1 0.7 0.2 7 125 143a 134a 0.4 0.45 0.15 8 32 134 n/a 0.5 0.5 n/a 9 32 125 n/a 0.5 0.5 n/a Name 407c

407b 410A

34 temperature pro le, its pinch was speci ed at the mixture outlet. Throughout this range, the properties of these refrigerants varied widely, as did their operating pressures and temperature glides. The glides were much smaller than those observed for NH3/H2O, but the pressures were considerably higher. Tables 5-4 - 5-5 contain a complete list of the pressures and glides for comparison purposes. Note that the temperature glides are in the range of 5 to 10 C, and that the pressures are listed in kPa rather than bar. The linearity of temperature versus enthalpy has increased, as can be seen at a pinch of 5 K for three of refrigerants in Figure 5-4, but there is still the possibility of an interior pinch. For each refrigerant and pinch, the EES program found in Appendix C was executed.

Standard Error for R-22 Alternatives
As would be expected from the smaller temperature glides, the UA error for refrigerants 1 through 9 is less than for NH3/H2O. The magnitude of the dierences can be seen in Tables 5-6 - 5-7. Because jUA UALMTDj is relatively small, the standard error calculation will produce values that are easy to evaluate both numerically (Table 5-8) and graphically (Figures 5-5 - 5-7). When a table entry is marked not applicable, an infeasible interior pinch was generated.

Drop-In Replacements vs. System Recon guration
In the search for alternatives to R-22, a primary objective of the refrigeration industry has been the discovery of a \drop-in" replacement. A drop-in replacement is one that: 1) operates under very similar pressures to,

35 Table 5-4: Operating Pressures and Temperature Glides for Refrigerants 1-5

Refrigerant # 1
Pinch (K) 2 3 4 5 6 7 P (kPa) 1399.839 1436.386 1473.632 1511.587 1550.259 1589.655 Tglide (K ) 5.189 5.154 5.118 5.081 5.044 5.006

Refrigerant # 2
Pinch (K) 2 3 4 5 6 7 P (kPa) 1381.817 1418.121 1455.124 1492.835 1531.262 1570.413 Tglide (K ) 5.447 5.412 5.377 5.341 5.305 5.268

Refrigerant # 3
Pinch (K) 2 3 4 5 6 7 P (kPa) 1093.765 1121.81 1150.374 1179.461 1209.076 1239.226 Tglide (K ) 10.07 10.03 9.988 9.947 9.904 9.86

Refrigerant # 4
Pinch (K) 2 3 4 5 6 7 P (kPa) 1128.243 1158.306 1188.955 1220.198 1252.042 1284.492 Tglide (K ) 5.971 5.938 5.904 5.87 5.835 5.799

Refrigerant # 5
Pinch (K) 2 3 4 5 6 7 P (kPa) 1240.457 1273.366 1306.912 1341.105 1375.951 1411.458 Tglide (K ) 6.879 6.849 6.819 6.789 6.758 6.726

36

Table 5-5: Operating Pressures and Temperature Glides for Refrigerants 6-9

Refrigerant # 6
P (kPa) Tglide (K )
2 n/a n/a Pinch (K) 3 4 5 6 7 1593.875 1634.642 1676.177 1718.489 1761.588 2.813 2.787 2.759 2.732 2.704

Refrigerant # 7
P (kPa) Tglide (K )
2 n/a n/a 3 n/a n/a Pinch (K) 4 5 6 7 1499.032 1537.131 1575.948 1615.493 1.245 1.228 1.212 1.196

Refrigerant # 8
Pinch (K) 2 3 4 5 P (kPa) 1511.117 1550.362 1590.347 1631.08 Tglide (K ) 8.347 8.302 8.257 8.211 6 7 1672.57 1714.824 8.164 8.116

Refrigerant # 9
Pinch (K) 2 3 4 5 P (kPa) 2197.791 2252.694 2308.622 2365.586 Tglide (K ) 0.116 0.116 0.116 0.115 6 2423.6 0.115 7 2482.678 0.114

37 Table 5-6: UA and UALMTD for Refrigerants 1-5

Refrigerant # 1
Pinch (K) 2 3 4 5 6 7 UA 7254.367 4935.324 3727.552 2986.106 2484.39 2122.149 UALMTD 7157.052 4891.5665 3703.247 2970.873 2474.0563 2114.772

Refrigerant # 2
Pinch (K) 2 3 4 5 6 7 UA 6840.15 4772.05 3655.525 2955.366 2474.807 2124.406 UALMTD 6840.782 4774.1654 3657.343 2956.769 2475.9275 2125.29

Refrigerant # 3
Pinch (K) 2 3 4 5 6 7 UA 3466.033 2816.027 2389.221 2080.984 1845.409 1658.438 UALMTD 3692.544 2971.2297 2503.058 2168.255 1914.4263 1714.205

Refrigerant # 4
Pinch (K) 2 3 4 5 6 7 UA 5032.711 3855.596 3131.735 2636.972 2275.836 1999.993 UALMTD 5437.96 4092.7362 3287.357 2746.599 2356.9411 2062.201

Refrigerant # 5
Pinch (K) 2 3 4 5 6 7 UA 5676.224 4212.46 3350.749 2779.464 2371.927 2066.072 UALMTD 5933.173 4355.0611 3441.034 2841.484 2416.9026 2100.036

38

Table 5-7: UA and UALMTD for Refrigerants 6-9

Refrigerant # 6
UA
2 n/a n/a Pinch (K) 3 4 5 6 7 9792.723 5349.748 3735.791 2870.195 2324.879 9152.4246 5153.854 3640.876 2814.8496 2289.129

UALMTD

Refrigerant # 7
UA
2 n/a n/a 3 n/a n/a Pinch (K) 4 5 6 7 11946.56 5327.101 3671.643 2822.269 11423.38 5217.044 3619.7126 2792.065

UALMTD

Refrigerant # 8
Pinch (K) 2 3 4 5 6 7 UA 5465.339 4024.631 3193.355 2646.892 2258.31 1967.168 UALMTD 4841.3632 3680.786 2975.881 2497.552 2149.9769 1885.358

Refrigerant # 9
Pinch (K) 2 3 4 5 6 7 UA 3213.858 2483.476 2027.328 1711.092 1477.374 1296.872 UALMTD 3210.3017 2481.3435 2025.898 1710.07 1476.6088 1296.289

39

Table 5-8: Standard Error for Refrigerants 1-9 Number 1 2 3 4 5 6 7 8 9 2 1.341 0.009 6.535 8.052 4.527 n/a n/a 11.417 0.111 3 0.887 0.044 5.511 6.151 3.385 6.539 n/a 8.544 0.086 Pinch (K) 4 5 0.652 0.510 0.050 0.047 4.765 4.194 4.969 4.157 2.694 2.231 3.662 2.541 4.379 2.066 6.810 5.642 0.071 0.060 6 0.416 0.045 3.740 3.564 1.896 1.928 1.414 4.797 0.052 7 0.348 0.042 3.363 3.110 1.644 1.538 1.070 4.159 0.045

40 2) has chemical properties compatible with the equipment used with, and 3) provides a refrigeration capacity at the level of the refrigerant that it replaces. While R-134a has proven to be a successful drop-in replacement for CFC-12, no completely satisfactory drop-in replacement has been found for R-22. However, both R-407c and R-410a work fairly well for selected applications, and are likely to become the preferred replacements for existing systems. Zeotropes and near-azeotropes should not just be thought of as straight replacements, though. For a pure refrigerant, there is usually a trade-o between improving the eciency and the volumetric capacity. Zeotropic mixtures can mitigate this somewhat (Didion and Bivens, 1990). A zeotropic mixture in the two-phase region constantly changes its composition as temperature changes, making it possible to control composition during operation. The greatest potential, though, is a result of a zeotrope's gliding temperature. When properly utilized, this can actually result in eciencies that are higher than those demonstrated by R-22. The diagram for a Lorenz cycle demonstrates that entropy generation can be reduced (below that of a Carnot cycle) if temperature pro les are properly matched (Figure 5-8). The Lorenz cycle consists of two constantentropy adiabatic expansion or compression processes and two constant-heat capacity heat transfer processes (Cavallini, 1996). Unfortunately, the nonlinearity of the temperature versus the enthalpy creates diculties in accurately matching the pro les for a Lorenz cycle. Three ways to correct this are through chemical, mechanical, and thermal controls. The chemical approach uses an additional component to linearize the temperature pro le. The mechanical approach cuts o the phase-change process so that the majority of the heat exchanger has a minimum temperature dierence. The thermal approach adds additional heat processes so that the heat exchange avoids pinch points. Each of

41 these approaches also has the advantage of separating the interdependency of the composition and temperature glides (Didion and Bivens, 1990). The characteristics of zeotropes and near-azeotropes can also be exploited in other ways. For example, the addition of a liquid-line/suction-line heat exchanger (Figure 5-9) results in impressive eciency improvements. The idea of a desorberabsorber heat exchange cycle (Figure 5-10) is fairly old, but it can take unique advantage of zeotropic properties. Whatever cycle is chosen, the results of this study can be used to more accurately determine the size of the heat exchangers.

42

345 340 335 330 NH3/H2O

T [K]

325 320 315 310 305 300 0 193 386 579 771 964 Water 1157 1350

Q/m [kJ/kg]

Figure 5-1: NH3/H2O: Concentration = 0.99, Pinch = 1 K

43

380 370

Ammonia Concentration = 0.95, Pinch = 5 [K]
NH3 /H2 O

360 350

T [K]

340 330 320 310 300 0 207 414 621 829 1036 1243 1450 Water

Q/m [kJ/kg]
360 350 340

Ammonia Concentration = 0.98, Pinch = 5 [K]
NH3 /H2 O

T [K]

330 320 310 300 0 193 386 579 771 964 1157 1350 Water

Q/m [kJ/kg]
345 340 335 330

Ammonia Concentration = 0.99, Pinch = 5 [K]
NH3/H 2O

T [K]

325 320 315 310 305 300 0 217 433 650 867 1083 1300 Water

Q/m [kJ/kg]

Figure 5-2: Concentration and Nonlinearity for NH3/H2O

44
Ammonia Concentration = 0.95
2.0

1.6

Log Error Ratio

1.2

0.8

0.4

0.0 0 5 10 15 20

Pinch [K]

Ammonia Concentration = 0.98
2.0

1.6

Log Error Ratio

1.2

0.8

0.4

0.0 0 5 10 15 20

Pinch [K]

Ammonia Concentration = 0.99
2.0

1.6

Log Error Ratio

1.2

0.8

0.4

0.0 0 5 10 15 20

Pinch [K]

Figure 5-3: Log Error Ratio vs. Pinch Point for NH3/H2O

45

313.0

Refrigerant # 1, Pinch = 5 [K]
Refrigerant

310.3

T [K]

307.5 Water 304.8

302.0

0

4000

8000

12000

16000

. . Q/m [kJ/kg]
310.0

Refrigerant # 6, Pinch = 5 [K]

Refrigerant

308.0

T [K]

306.0

Water

304.0

302.0

0

3500

. . Q/m [kJ/kg]

7000

10500

14000

316.0 314.0 312.0

Refrigerant # 8, Pinch = [5]
Refrigerant

T [K]

310.0 308.0 306.0 304.0 302.0 Water

0

4500

. . Q/m [kJ/kg]

9000

13500

18000

Figure 5-4: Nonlinearity of Refrigerants 1, 6, and 8

46

Refrigerant 1
1.4 1.2 1 % Error 0.8 0.6 0.4 0.2 0 2 3 4 5 Pinch (K) 6 7

Refrigerant 2
0.05 0.04 % Error 0.03 0.02 0.01 0 2 3 4 5 Pinch (K) 6 7

Refrigerant 3
6.3 5.8 % Error 5.3 4.8 4.3 3.8 3.3 2 3 4 5 Pinch (K) 6 7

Figure 5-5: Standard Error for Refrigerants 1-3

47

Refrigerant 4
8.1 7.1 % Error 6.1 5.1 4.1 3.1 2 3 4 5 Pinch (K) 6 7

Refrigerant 5
4.6 4.1 % Error 3.6 3.1 2.6 2.1 1.6 2 3 4 5 Pinch (K) 6 7

Refrigerant 6
7 6.2 5.4 % Error 4.6 3.8 3 2.2 1.4 3 4 5 Pinch (K) 6 7

Figure 5-6: Standard Error for Refrigerants 4-6

48

Refrigerant 7
4.5 4 3.5 % Error 3 2.5 2 1.5 1 4 5 Pinch (K) 6 7

Refrigerant 8
12 11 10 % Error 9 8 7 6 5 4 2 3 4 5 Pinch (K) 6 7

Refrigerant 9
0.12 0.11 0.1 % Error 0.09 0.08 0.07 0.06 0.05 0.04 2 3 4 5 Pinch (K) 6 7

Figure 5-7: Standard Error for Refrigerants 7-9

49

Carnot

Temperature

v

v

v

refrigerant

Entropy

Lorenz v
refrig eran t

v

Temperature

s oppo

ing fl

uid

v
v
s oppo ing fl uid refrig

eran

t

v
Entropy

Figure 5-8: Carnot and Lorenz Cycle Diagrams

v

v

v

v

refrigerant

v

opposing fluid

opposing fluid

v

v v

50







Evaporator






Expansion Device

Condenser





Liquid Line/Suction Line Heat Exchanger Compressor

Figure 5-9: The Liquid-Line/Suction-Line Heat Exchanger





Evaporator Expansion Device

Condenser








Compressor

Pump

Figure 5-10: The Desorber-Absorber Heat Exchange Cycle

51

CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS
While the Log Mean Temperature Dierence is often used to compute the size (UA) of a heat exchanger, this calculation becomes invalid for mixtures when the working
uid exhibits a nonlinear temperature glide. An analysis of the derivation of the LMTD reveals assumptions that must be discarded. Most notably, it can no longer be assumed that the temperature will be an easily-determined function of the heat exchanged. In the case of ammonia-water, which was selected for study due to its strong nonlinearity, calculations utilizing the LMTD resulted in dramatic errors. For small pinch points, these errors may lead to heat exchangers that are undersized by as much as a factor of fty. The LMTD is simply not valid, and a numerically calculated mean temperature should be used instead. For a given pinch point, the error generally increases with the ammonia concentration. At large pinch points, however, the magnitude of the dierences in the error decreases between concentrations. For the refrigerant mixtures proposed as replacements for HCFC-22, the error is less, but clearly still exists. The magnitude of the error does not appear to directly correlate with the size of the temperature glide, as can be observed from comparing refrigerants 1 and 2 at a pinch of 2 K . Both their operating pressures and their glides are nearly the same, but refrigerant 1 has a standard error of 1.34% while refrigerant 2 has a SE of 0.01%. In general, the UA error decreases as the size of the pinch increases for both

52 NH3/H2O and the replacement refrigerants. However, this is not the case for refrigerant 2; its error increases until a pinch of 4 K , and at that point begins to decrease. For all other refrigerants, though, the change in the error also decreases with increasing pinch, which is both mathematically and conceptually logical. Modi ed cycles to exploit the unique characteristics of mixtures should be analyzed using the correct mean temperature dierence. The potential eciency improvement could then be properly evaluated for these refrigerant mixtures. Since the majority of refrigerants being considered in applications currently satis ed by R-22 are zeotropes, both the desorber-absorber heat exchange (DAHX) cycle and the liquid-line/suction-line heat exchanger (LLSL-HX) should be considered for new systems and for retro ts. A DAHX cycle incorporates both thermal and mechanical controls to optimize the utility of a temperature glide. Thermal control is achieved through heat exchange between the evaporator and the condenser, while mechanical control is gained through the variable speed liquid pump. This desorber-absorber heat exchange can provide the same temperature lift as a conventional cycle, but over a smaller pressure lift (Didion and Bivens, 1990). So by de nition, the working
uid of a DAHX cycle must be a mixture whose constituents have very dierent boiling points; this means that a large temperature range can be covered at constant pressure through composition shifting (Radermacher, 1987). The DAHX cycle also uses a liquid-line heat exchanger with the evaporating zeotrope. An expansion device is used instead of a turbine in the compression cycle, but adding a liquid-line heat exchanger recovers the lost work. The LLSL-HX cycle subcools the high-pressure refrigerant by reducing the superheating of the vapor entering the compressor. An LLSL-HX can either improve or worsen a system's performance, depending on what working
uid is used. For R-407c, for example, employing a LLSL-HX with a counter
ow evaporator and con-

53 denser for cooling raises the eciency to 5-6% above that of R-22, even when the same alterations are made to the R-22 cycle (Bivens et al., 1995). The impact of LLSL-HX on the volumetric capacity can be even greater (Domanski, Didion and Doyle, 1994). In addition to considering new ways to utilize synthetic refrigerants, the advantages of switching to natural refrigerants should also be considered. While CFCs and HCFCs are currently designated as harmful to the environment, they were considered to be safe, and even ideal, for many years. It is unknown which synthetic refrigerants that are now thought of as benign will prove dangerous in the future. Some studies suggest, in fact, that HFC-134a may be decomposed in the troposphere by sunlight and form acid and poisonous substances (Lorentzen, 1995). On the other hand, natural refrigerants such as ammonia-water, propane, and carbon dioxide have long existed in the biosphere. Furthermore, while refrigerants such as R-410a and R-407c have zero ozone depletion potential (ODP), they do have non-trivial global warming potential (GWP). NH3/H2O, propane, and CO2 also have zero ODP, and while it is obvious that CO2 has a high GWP, the GWP of both propane and NH3/H2O is negligible. Throughout the past, the greatest concern with the use of ammonia has been safety. While it is true that ammonia can burn with air and is poisonous, current refrigeration standards and ammonia's other natural properties may oset these dif culties. Ammonia gas is much lighter than air, and can easily be vented away. If it is trapped, its strong smell serves as a warning that there is a leak. In fact, ammonia can be detected at concentrations as low as ve parts per million in air, before there is any signi cant danger. In terms of
ammability, the lower ignition limit of ammonia is three to seven times that of natural gas and most hydrocarbons. The pressure of ammonia was also once considered a limiting factor, but compared to

54 the much higher pressures of the synthetic refrigerants in this study, that should no longer be counted as a concern. Even disregarding these natural safety features, the need to create systems that are tight and stay tight lessens the danger of ammonia as a refrigerant (Lorentzen, 1995). Ammonia as a refrigerant has been applied to both industrial and residential heating and cooling units. It has been used in water chillers and heat pumps for residential buildings; direct-expansion systems for supermarket refrigeration; large heat pump plants for district heating; and central cooling of gas turbine cogeneration plants (Cavallini, 1996). Ammonia is also becoming more acceptable to the public. While more popular in Europe, especially Scandinavia and Germany, ammonia has the long-term potential to increase its U.S. market share as \green" issues gain in importance. Other natural refrigerants are also becoming more prominent: When a natural refrigerant-powered home refrigerator (marketed under the name \GreenFreeze") was recently introduced in Germany, the manufacturer sold out within weeks. So, in summary, while systems can be developed that will increase the feasibility of synthetic refrigerants as R-22 replacements, the opportunity to change existing systems should perhaps be redirected toward an eort to reduce the use of all synthetics in favor of natural replacements.

55

APPENDIX A REFRIGERANTS AVAILABLE IN REFPROP REFPROP, Version 5.0
R-11 R-114 R-125 R-143 RC270 R-245ca propane propylene R-12 R-115 R-134 R-143a RC318 R-600a butane ether R-13 R-13b1 R-123 R-123a R-134a R-141b R-152a R-218 R-227ea R-236ea R-236fa RE134 isopentane n-pentane carbon dioxide R-113 R-124 R-142b R-116 R-245cb RE245 ammonia

REFPROP, Version 6.0 21 Pure Substances
R-11 R-123 R-142b R-23 R-41 propylene R-113 R-115 R-124 R-125 R-143a R-152a R-236fa R-245ca propane butane carbon dioxide R-116 R-13 R-22 R-245fa isobutane R-12 R-134a R-227ea R-32 ammonia

56

Mixtures
R-401a R-401b R-404a R-407a R-408a R-409a R-500 R-501 R-22/isobutane/R-142b R-401c R-402a R-407b R-407c R-409b R-410a R-507a R-32/R-125 ammonia/butane R-402b R-407d R-410b

57

APPENDIX B AMMONIA-WATER EES PROGRAM
fComments are surrounded by quotes or brackets.g
FUNCTION tk(T) tk:=T+273.15 END

"converts from C to K"

Conc=0.95 Pinch=10

"Concentration of the Ammonia-Water Mixture" "Pinch Point"

fCalculating what the mdot ratio is from the end point data.g fm ratio = m w / m mg
m_ratio=(h_end_mix-h_start_mix)/(h_end_h20-h_start_h20)

CALL NH3H2O(138,TK(29)+Pinch,Conc,0:T_hi,P_hi,x_hi,h_hi,s_hi, u_hi,v_hi,Qu_hi) CALL NH3H2O(238,P_hi,Conc,0:T_1m,P_1m,x_1m,h_start_mix,s_1m, u_1m,v_1m,Qu_1m) CALL NH3H2O(238,P_hi,Conc,1:T_Nm,P_Nm,x_Nm,h_end_mix,s_Nm, u_Nm,v_Nm,Qu_Nm) h_start_h20=enthalpy(WATER,T=TK(29),P=P_hi)

58
h_end_h20=enthalpy(WATER,T=TK(34),P=P_hi) T1w=temperature(WATER,h=h_start_h20,P=P_hi) T2w=temperature(WATER,h=h_end_h20,P=P_hi)

fEntered Valuesg
EndPtQ=h_end_mix-h_start_mix h_m=Qtot+h_start_mix h_w=(Qtot/m_ratio)+h_start_h20 T_w=temperature(WATER,h=h_w,P=P_hi) CALL NH3H2O(234,P_hi,Conc,h_m:T_m,Pm,xm,hom,sm,um,vm,Qum) DELTAT_mw=T_m-T_w Delta_T_1=T_1m-T1w Delta_T_2=T_Nm-T2w

"The total heat transferred in the heat exchanger"

"Calculation of the LMTD and U0A0 using" "the traditional method"

LMTD=(Delta_T_2-Delta_T_1)/(ln(Delta_T_2/Delta_T_1)) U0A0_LMTD=(h_end_mix-h_start_mix)/LMTD

fIntegration to nd the actual U0A0g
U0A0_act=integral(1/DELTAT_mw,Qtot,0,EndPtQ)

fCalculation of the error using two error scalesg
LER=-log10(U0A0_LMTD/U0A0_act) SE=(abs(U0A0_act-U0A0_LMTD)/U0A0_act)*100

59

APPENDIX C REFRIGERANT MIXTURE EES PROGRAM
fComments are surrounded by quotes or brackets.g
FUNCTION tk(T) tk:=T+273.15 END $INCLUDE /eesw/userlib/REFPROP.TXT

"converts from C to K"

fCalculating what the mdot ratio is from the end point data.g fm ratio = m w / m mg
m_ratio=(h_end_mix-h_start_mix)/(h_end_h20-h_start_h20)

fThe components and compositions listed below vary for eachg frefrigerant mixture.g
CALL REFPROP(3,R32,R125,R134a,TQX,TK(29)+Pinch,0,0.3811,0.1796: T_hi,P_hi,v_hi,h_hi,s_hi) CALL REFPROP(3,R32,R125,R134a,PQX,P_hi,0,0.3811,0.1796:T_1m, P_1m,v_1m,h_start_mix,s_1m) CALL REFPROP(3,R32,R125,R134a,PQX,P_hi,1,0.3811,0.1796:T_Nm, P_Nm,v_Nm,h_end_mix,s_Nm) h_start_h20=enthalpy(WATER,T=TK(29),P=P_hi) h_end_h20=enthalpy(WATER,T=TK(34),P=P_hi)

60
T1w=temperature(WATER,h=h_start_h20,P=P_hi) T2w=temperature(WATER,h=h_end_h20,P=P_hi)

fEntered Valuesg
EndPtQ=h_end_mix-h_start_mix h_m=Qtot+h_start_mix h_w=(Qtot/m_ratio)+h_start_h20 T_w=temperature(WATER,h=h_w,P=P_hi) CALL REFPROP(3,R32,R125,R134a,PHX,P_hi,h_m,0.3811,0.1796:T_m, Pm,vm,hom,sm) DELTAT_mw=T_m-T_w Delta_T_1=T_1m-T1w Delta_T_2=T_Nm-T2w

"The total heat transferred in the heat exchanger"

"Calculation of the LMTD and U0A0 using" "the traditional method"

LMTD=(Delta_T_2-Delta_T_1)/(ln(Delta_T_2/Delta_T_1)) U0A0_LMTD=(h_end_mix-h_start_mix)/LMTD

fIntegration to nd the actual U0A0g
U0A0_act=integral(1/DELTAT_mw,Qtot,0,EndPtQ)

fCalculation of the error using two error scalesg
LER=-log10(U0A0_LMTD/U0A0_act) SE=(abs(U0A0_act-U0A0_LMTD)/U0A0_act)*100

61

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