Subsections

• Ammonia-Water Mixtures
• Properties
• The Fallacy of an End-Point Pinch
• Log Error Ratio for Ammonia-Water
• Other Refrigerants
• Properties
• Standard Error for R-22 Alternatives
• Drop-In Replacements vs. System Reconfiguration

Results and Discussion

 

Ammonia-Water Mixtures

Properties

As can be seen from the temperature versus enthalpy profile of Figure 1.4, ammonia-water (NH₃/H₂O) mixtures generally have extremely nonlinear temperature profiles. 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 3-4.

Three separate mixture concentrations were studied: ninety-five percent, ninety-eight percent, and ninety-nine percent ammonia. These are typical concentrations for condensers in ammonia-water absorption refrigeration cycles. Furthermore, each mixture was analyzed at five 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 significantly 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.
 
 

 

1 3 5 7 10

P (bar) 11.119 11.793 12.497 13.233 14.397

T_glide (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

T_glide (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

T_glide (K) 38.82 38.68 38.15 37.61 36.79

 

The Fallacy of an End-Point Pinch

    

Figure 5.1: NH₃/H₂O: Concentration = 0.99, Pinch = 1 K

  
 
    

Figure 5.2: Concentration and Nonlinearity for NH₃/H₂O

  

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 found to be 9.6 K, resulting in a UA equal to 132.72 [kJ/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-five, 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-five 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 differences 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

æ
ç
è ¶h ¶T
ö
÷
ø

inlet 
> æ
ç
è ¶h ¶T
ö
÷
ø

outlet 

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

Log Error Ratio for Ammonia-Water

    

Figure 5.3: Log Error Ratio vs. Pinch Point for NH₃/H₂O

  

As predicted, differences between the LMTD-calculated and the actual UA were observed at every concentration and pinch point. Since these differences 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). Furthermore, the values of the UA, UA_LMTD, and LER are compiled in Table 5.2 for every run.
 
 

 

1 3 5 7 10

UA 1392.392 342.442 204.114 146.909 104.327

UA_LMTD 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

UA_LMTD 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

UA_LMTD 100.793 94.104 77.017 66.259 55.415

LER 1.892 1.005 0.633 0.493 0.379

 

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 infinite, a reality reflected in the large actual UAs.

Other Refrigerants

Properties

   

# Comp. 1 Comp. 2 Comp. 3 Mass % 1 Mass % 2 Mass % 3 Name

1 32 125 134a 0.23 0.25 0.52 407c

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 407b

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 410A

 

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 & 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 temperature profile, its pinch was specified 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.
 
 

 

2 3 4 5 6 7

P (kPa) 1399.839 1436.386 1473.632 1511.587 1550.259 1589.655

T_glide (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

T_glide (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

T_glide (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

T_glide (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

T_glide (K) 6.879 6.849 6.819 6.789 6.758 6.726

 
 
   

2 3 4 5 6 7

P (kPa) n/a 1593.875 1634.642 1676.177 1718.489 1761.588

T_glide (K) n/a 2.813 2.787 2.759 2.732 2.704 Refrigerant # 7 Pinch (K)

2 3 4 5 6 7

P (kPa) n/a n/a 1499.032 1537.131 1575.948 1615.493

T_glide (K) n/a n/a 1.245 1.228 1.212 1.196 Refrigerant # 8 Pinch (K)

2 3 4 5 6 7

P (kPa) 1511.117 1550.362 1590.347 1631.08 1672.57 1714.824

T_glide (K) 8.347 8.302 8.257 8.211 8.164 8.116 Refrigerant # 9 Pinch (K)

2 3 4 5 6 7

P (kPa) 2197.791 2252.694 2308.622 2365.586 2423.6 2482.678

T_glide (K) 0.116 0.116 0.116 0.115 0.115 0.114

 
 
    

Figure 5.4: Nonlinearity of Refrigerants 1, 6, and 8

  

Standard Error for R-22 Alternatives

   

2 3 4 5 6 7

UA 7254.367 4935.324 3727.552 2986.106 2484.39 2122.149

UA_LMTD 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

UA_LMTD 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

UA_LMTD 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

UA_LMTD 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

UA_LMTD 5933.173 4355.0611 3441.034 2841.484 2416.9026 2100.036

 
 
   

2 3 4 5 6 7

UA n/a 9792.723 5349.748 3735.791 2870.195 2324.879

UA_LMTD n/a 9152.4246 5153.854 3640.876 2814.8496 2289.129 Refrigerant # 7 Pinch (K)

2 3 4 5 6 7

UA n/a n/a 11946.56 5327.101 3671.643 2822.269

UA_LMTD n/a n/a 11423.38 5217.044 3619.7126 2792.065 Refrigerant # 8 Pinch (K)

2 3 4 5 6 7

UA 5465.339 4024.631 3193.355 2646.892 2258.31 1967.168

UA_LMTD 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

UA_LMTD 3210.3017 2481.3435 2025.898 1710.07 1476.6088 1296.289

 

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 differences can be seen in Tables 5.6 - 5.7.
 
 

 

Number 2 3 4 5 6 7

1 1.341 0.887 0.652 0.510 0.416 0.348

2 0.009 0.044 0.050 0.047 0.045 0.042

3 6.535 5.511 4.765 4.194 3.740 3.363

4 8.052 6.151 4.969 4.157 3.564 3.110

5 4.527 3.385 2.694 2.231 1.896 1.644

6 n/a 6.539 3.662 2.541 1.928 1.538

7 n/a n/a 4.379 2.066 1.414 1.070

8 11.417 8.544 6.810 5.642 4.797 4.159

9 0.111 0.086 0.071 0.060 0.052 0.045

 
 
    

Figure 5.5: Standard Error for Refrigerants 1-3

  
 
    

Figure 5.6: Standard Error for Refrigerants 4-6

  
 
    

Figure 5.7: Standard Error for Refrigerants 7-9

  

Because |UA - UA_LMTD| 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 Reconfiguration

  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,
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-off between improving the efficiency and the volumetric capacity. Zeotropic mixtures can mitigate this somewhat (Didion & 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.
 
 

  

Figure 5.8: Carnot and Lorenz Cycle Diagrams

  

The greatest potential, though, is a result of a zeotrope's gliding temperature. When properly utilized, this can actually result in efficiencies 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 profiles are properly matched (Figure 5.8). The Lorenz cycle consists of two constant-entropy 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 difficulties in accurately matching the profiles 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 profile. The mechanical approach cuts off the phase-change process so that the majority of the heat exchanger has a minimum temperature difference. The thermal approach adds additional heat processes so that the heat exchange avoids pinch points. Each of these approaches also has the advantage of separating the interdependency of the composition and temperature glides (Didion & Bivens, 1990).
 
 

  

Figure 5.9: The Liquid-Line/Suction-Line Heat Exchanger

  
 
    

Figure 5.10: The Desorber-Absorber Heat Exchange Cycle

  

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 efficiency improvements. The idea of a desorber-absorber 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.

12/3/1997