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Analysis of zeotropic mixtures used in low-temperature solar Rankine cycles for power generation
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Solar Energy 83 (2009) 605–613 www.elsevier.com/locate/solener
Analysis of zeotropic mixtures used in low-temperature solar Rankine cycles for power generation X.D. Wang, L. Zhao * Department of Thermal Energy and Refrigeration Engineering, School of Mechanical Engineering, Tianjin University, No. 92 Weijin Road, Tianjin 300072, PR China Received 25 October 2007; received in revised form 29 September 2008; accepted 12 October 2008 Available online 14 November 2008 Communicated by: Associate Editor Robert Pitz-Paal
Abstract This paper presents the analysis of low-temperature solar Rankine cycles for power generation using zeotropic mixtures. Three typical mass fractions 0.9/0.1 (Ma) 0.65/0.35 (Mb), 0.45/0.55 (Mc) of R245fa/R152a are chosen. In the proposed temperature range from 25 °C to 85 °C, the three zeotropic mixtures are investigated as the working fluids of the low-temperature solar Rankine cycle. Because there is an obvious temperature glide during phase change for zeotropic mixtures, an internal heat exchanger (IHE) is introduced to the Rankine cycle. Investigation shows that different from the pure fluids, among the proposed zeotropic mixtures, the isentropic working fluid Mb possesses the lowest Rankine cycle efficiency. For zeotropic mixtures a significant increase of thermal efficiencies can be gained when superheating is combined with IHE. It is also indicated that utilizing zeotropic mixtures can extend the range of choosing working fluids for low-temperature solar Rankine cycles. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Zeotropic mixtures; Working fluids; Low-temperature solar Rankine cycle
1. Introduction Because of the potential in reducing consumption of fossil fuels and relaxing environmental problems, the applications of renewable energies (solar energy, wind energy, biomass and geothermal energy) to electricity generation become more and more important, and have received increasing attentions. During the last two decades, all over the world a number of researchers have worked on developing new solar thermodynamic cycles or improving existing ones. Various high-temperature systems such as single axis and two axis tracking technologies have been suggested and developed (Mills, 2004). But owing to the complex technologies and high costs, the high-temperature
*
Corresponding author. E-mail address: [email protected] (L. Zhao).
0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.10.006
solar thermal systems are generally less competitive now, especially in developing countries. At the same time, low-temperature technologies have also been developed and the efficiencies are improving. Thermodynamic cycles (especially the organic Rankine cycles) for combined power and heat system have a great potential to become competitive with fossil fuels (especially natural gas) based power systems (Goswami et al., 2004). For example, Goswami and Feng Xu proposed a new combined power/refrigeration cycle utilizing ammonia and water, of which the overall thermal efficiency reaches 23.54% (Xu and Goswami, 1999; Xu et al., 2000). Manolakosa et al. designed and built a low-temperature solar organic Rankine cycle system for reverse osmosis desalination in Greece. The working fluid is R134a that works between 35 °C and 75.8 °C, and the maximum overall system efficiency is about 4% (Manolakosa et al., 2005, 2007). Nguyen et al. developed a small-scale solar Rankine system
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designed to operate at low-temperatures for electricity generation with 4.3% efficiency (Nguyen et al., 2001). When a low-temperature solar powered organic Rankine cycle is considered, a certain challenge is the choice of the organic working fluid and the particular design of the cycle. There are several general criteria that the working fluid of low-temperature Rankine cycle system should ideally satisfy. Stability, non-fouling, non-corrosiveness, non-toxicity and non-flammability are some preferable physical and chemical characteristics (Madhawa Hettiarachchi et al., 2007). Also, for low-power turbine applications, the fluid should have a high molecular weight to minimize the rotational speed or the number of turbine stages and to allow for reasonable mass flow rates and turbine nozzle areas (Stine et al., 1985). However, in a cycle design, not all the desired general requirements can be satisfied. At the same time, the choice of working fluid can greatly affect the power plant cost. Hence, economical efficiency of the working fluid should also be considered. In recent publications, the choices of working fluids suit for the low-temperature Rankine cycles have been researched, such as Saleh et al. (2007), Madhawa Hettiarachchi et al. (2007), Tamm et al. (2004), Xu et al. (2000) and Zhang et al. (2006). In Greece, utilizing R134a, Manolakosa et al. (2007) established a low-temperature solar organic Rankine cycle system for reverse osmosis desalination. However, most of the researches and applications mentioned above are focused on the pure component working fluids for organic Rankine cycles. As to the mixed component working fluids that could be used in the low-temperature solar powered Rankine cycles, few researches and applications were reported. Saleh et al. (2007) researched 31 pure component working fluids for organic Rankine cycles between 30 and 100 °C which were typical for geothermal power plants, and a recuperator which was called internal heat exchanger (IHE) was introduced to Rankine cycle. Bahaa Saleh proved that for pure component working fluid, the increase of the thermal efficiency of the cycle was significant in the case with internal heat exchanger, while the other conditions did not change. Here, in this paper we concentrate on the performance of zeotropic mixtures utilized in the low-temperature solar Rankine cycles for power generation. Also, we will introduce the internal heat exchange to the low-temperature solar Rankine cycles. Based on that, we will analyze and compare the thermal efficiencies of the cycles at the same temperature range and under different components conditions. 2. Description of the system and the different types of Rankine cycle The low-temperature solar Rankine cycle system for electricity generation mainly consists of the following components (Fig. 1):
(1) (2) (3) (4) (5) (6) (7)
Solar collectors Expander Generator Internal heat exchanger (IHE) Condenser Storage tank Working fluid pump
The system operation is described briefly below. The working fluid is pumped to a high pressure by the feed pump (7). The high pressure liquid is firstly heated in the IHE (4), and then it is heated in the pipes of the solar collectors (1) where phase change happens. Thus, we can take the solar collector as an evaporator. The liquid temperature at the collector inlet is determined by the exhausted vapor temperature at the expander outlet and the efficiency of the IHE, while vapor at the collector outlet is various at different boiling pressures. Owing to the change of the boiling pressure, the vapor exhausted from the turbine in the Rankine cycle at the condensing pressure may be in the wet saturated, dry saturated or superheated states. In order to avoid the harmful wet stroke in the expander, superheating of the vapor at the inlet of the expander is necessary. The degree of superheating can be adjusted according to different working fluids and different working conditions. The superheated vapor is driven to the expander (2) where the generated shaft work drives the generator (3). The vapor (low pressure, saturated or superheated) at the expander outlet is directed to the IHE (4). The vapor cools down in the heat exchanger by transferring the heat to the compressed liquid. Then the working fluid is completely cooled down in the condenser (5) and the condensate is collected and stored in the storage tank (6), from where the liquid is pumped into the collectors. (Figs. 2–4) illustrate the thermodynamic processes described above. The theoretical cycle consists of the following processes:1 ? 2: Isentropic compression (working fluid pump)2 ? 2a: Isobaric internal heat exchange (IHE)2a ? 5: Isobaric heat supply (solar collectors)5 ? 6: Expansion (expander)6 ? 6a: Isobaric internal heat exchange (IHE)6a ? 1: Isobaric heat rejection (condenser). At the same time, (Figs. 2–4) also show three different types of Rankine cycles. According to the different slopes of the saturation curve in the T–S diagram, working fluids are divided to drying (Fig. 2), wetting (Fig. 3) and isentropic (Fig. 4) working fluids (Stine et al., 1985). A drying fluid has a positive slope; a wetting fluid has a negative slope, while an isentropic fluid has infinitely large slopes. It is found that in the temperature range that a low-temperature solar Rankine cycle system works (usually below 100 °C), few pure organic working fluids are isentropic. Most of them are drying or wetting. For example, the wetting working fluids include R125, R152a, R134a, R143a, ammonia and so on; while the drying working fluids include R236fa, R245fa, R601, R600, n-hexane and so on. It can be seen in Fig. 3 that if there was no or only a little overheating at the inlet of the expander, the state point 6 of
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Monitoring hole
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Generator
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Expander
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Internal heat exchanger Condenser
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Monitoring hole
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Cooling water
Working fluid pump Storage tank
Symbol
t p
Description Temperature transducer Pressure transducer
Fig. 1. Schematic of the low-temperature solar Rankine cycle system.
Fig. 2. Schematic of the Rankine cycle for pure drying working fluids.
Fig. 3. Schematic of Rankine cycle for pure wetting working fluids.
the expander outlet might drop into the two-phase region, even in the real expansion process when the entropy is increasing all the time. So, under the same working conditions, drying and isentropic fluids show better thermal efficiencies than wetting fluids, because they will not condense after the fluids go through the expander and the overheating of the vapor at the expander inlet seems to be dispensable.
Stine et al. (1985) pointed out that, for pure working fluids, drying fluids can produce cycle efficiencies almost as great as isentropic fluids if recuperator is used in the cycle. And Saleh et al. (2007) proved that. Now the question is how the thermodynamic performance is, when the mixture is used in the low-temperature solar Rankine cycle.
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Fig. 4. Schematic of Rankine cycle for pure isentropic working fluids.
Fig. 5. Schematic of the Rankine cycle for mixed drying working fluids.
3. Working fluids proposed and its theoretical thermal performance In this section, we propose three zeotropic mixtures based on different mass fractions of R245fa and R152a. They are compared in the low-temperature Rankine cycles under the same working conditions. Beyond that, a theoretical thermodynamic analysis under idealized conditions is given. 3.1. Working fluids proposed The phase change process of zeotropic mixtures is quite different with that of pure working fluids, which has obvious temperature glide during phase change. This characteristic implies that when there is an IHE more heat can be reclaimed inside the system. First, the transferred heat does not need to be supplied from outside, thus some solar collector areas can be saved. At the same time, with an IHE, the average evaporating temperature of the zeotropic will increase while the average condensing temperature will decrease. So, the economical efficiency and thermal efficiency of the low-temperature Rankine cycle will increase. Another advantage of the mixture is that, when a drying fluid and a wetting fluid are mixed, under a certain mass fraction, we can gain the isentropic working fluid. This could greatly extend the range of available working fluids for low-temperature Rankine cycles. (Figs. 5–7) illustrate the theoretical cycle processes of the zeotropic mixtures which are corresponding to (Figs. 2–4). Apparently, with different mass fractions of the components, the mixtures might be drying, wetting or isentropic. At the same time, because of the characteristic of zeotropic mixtures that there is an obvious temperature glide during
Fig. 6. Schematic of Rankine cycle for mixed wetting working fluids.
phase change, the state point 6a of IHE outlet might be in the two-phase region, which is quite is useful because the duty of the condenser is reduced. In order to investigate the thermal performance of the zeotropic mixtures used in the low-temperature Rankine cycles, we take the typical drying fluid R245fa (Fig. 2) and the typical wetting fluid R152a (Fig. 3) as the original components. Both of them have a zero ODP (Ozone Depression Potential) and quite low GWP (Global Warming Potential), so the mixtures can also be environmental friendly and relatively safe. Three typical mass fractions of R245fa/R152a are chosen, which are 0.9/0.1 (Ma),
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3.2. Thermodynamic analysis of the proposed zeotropic mixtures Throughout this investigation, the ideal Rankine cycles using Ma, Mb and Mc as the working fluids are under the same operating conditions and the irreversibilities associated with the heat transfer and compression processes are neglected. At the same time, the expansion efficiency gE in the expander is set as 80%. The theoretical schematic T–S diagrams of the cycles are the same as the graphics shown in Figs. 5–7.
Fig. 7. Schematic of Rankine cycle for mixed isentropic working fluids.
0.65/0.35 (Mb), 0.45/0.55 (Mc). Under these mass fraction conditions, the zeotropic mixtures are respectively drying (Ma), isentropic (Mb) and wetting (Mc). Some properties of the original components are listed in Table 1, and (Fig. 8) shows the T–S diagram of the three zeotropic mixtures. The dashed lines in Fig. 8 are the isobaric lines of 1 MPa. It is clear that with the mass fraction of R245fa increasing, the pressure level of the zeotropic mixture decreases. Table 1 List of the original components Original components
Molecular weight (g/ mol)
TCRIT (°C)
PCRIT (MPa)
Std 34 safety group
ODP
GWP (100 yr)
R152a R245fa
66.05 134.05
113.3 154.1
4.52 4.43
A2 B1
0 0
120 950
All properties come from Calm and Hourahan (2001).
Fig. 8. T–S diagram for the three zeotropic mixtures.
3.2.1. The given operating condition In order to analyze the performance of the working fluids in the ideal cycle, a given operating condition is necessary. In (Figs. 5–7), we set the lowest temperature of the cycle t1 = 25 °C, and the highest temperature t5 = 85 °C. In this temperature range, considering the wetting working fluid Mc might lead to liquid formation in the expander, superheating of the vapor is still considered here. The temperature difference of point 5 and point 4 is set as 5 °C. 3.2.2. Basic equations Basic equations of the cycle : t1 ¼ 25 C p1 ¼ p6 ¼ p60 ¼ p7 ¼ p6a s1 ¼ s2 p2 ¼ p3 ¼ p4 ¼ p5 ¼ p2a t5 ¼ 85 C t4 ¼ t5 5 C ¼ 80 C s5 ¼ s60 gE ¼ ðh5 h6 Þ=ðh5 h60 Þ ¼ 0:8 Solar collector heat inputðwithout IHEÞ : QE ¼ h5 h2 Solar collector heat inputðwith IHEÞ : QE ¼ h5 h2a Expansion work output : W S ¼ h 5 h6 Heat transfer in IHE : QI ¼ h6 h6a ¼ h2a h2 Condenser heat rejectionðwithout IHEÞ : QC ¼ h6 h1 Condenser heat rejectionðwith IHEÞ : QC ¼ h6a h1 Pump work input : W P ¼ h2 h1 Net power output : WN ¼WS WP The Rankine cycle efficiency defined : WN WS WP gR ¼ ¼ QE QE
ð1Þ ð2Þ ð3Þ ð4Þ ð5Þ ð6Þ ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ ð12Þ ð13Þ ð14Þ ð15Þ ð16Þ ð17Þ
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In the study, all the calculations and evaluations of the ideal Rankine cycles are based on unit mass working fluids. To make the analyses simple and clear, some assumptions are made: (1) Flow directions of working fluids in IHE are countercurrent, and leakage of heat in IHE and condenser is ignored; (2) It is considered that the temperature gliding of working fluid distributes linearly along heat exchanger and solar collector; (3) The internal resistances in heat exchanger and solar collector are negligible and the condensation and evaporation pressures of working fluids keep constant respectively; (4) The circulated compositions of the zeotropic mixtures do not change in every process of the cycle.
3.2.3. Cycle thermodynamics and thermal efficiencies of proposed zeotropic mixtures Based on the above basic equations, the results of evaluations are shown in Table 2. All the parameters used in the calculation come from NIST REFPROP 7.0 (Lemmon et al., 2002), which has a sufficient accuracy. In (Table 2), Rankine cycle thermal performances of the proposed zeotropic mixtures between 25 and 85 °C with and without IHE are compared. Some explanations need to be illuminated here. When there is no IHE in the system, it is considered that the exhausted vapor of the expander go directly to the condenser. No heat is reclaimed in the cycle, and the state points 2a and 6a will not appear. On the contrary, when the IHE is added to the system, heat energy h6 h6a will be reclaimed. In that case, in order to make the evaluation simple and clear, the authors consider that inside the IHE, there are equations QI = h6 h6a =
Table 2 Comparison of proposed zeotropic mixtures in Rankine cycle without(IHE) and with internal heat exchanger (+IHE). Components (R245fa/R152a, mass)
R245fa (1/0)
Ma (0.9/0.1)
Mb (0.65/0.35)
Mc (0.45/0.55)
Corresponding schematic diagram
Fig. 2
Fig. 5
Fig. 7
Fig. 6
Evaporation bubble-point temperature t3 (°C) Evaporation dew-point temperature t4 (°C) Evaporation temperature glide t4 t3 (°C) Evaporation pressure p3 (MPa) Condensation bubble-point temperature t1 (°C) Condensation dew-point temperature t7 (°C) Condensation temperature glide t7 t1 (°C) Condensation pressure p1 (MPa) h1 (kJ/kg) t2 (°C) h2 (kJ/kg) h3 (kJ/kg) h4 (kJ/kg) t5 = t4 + 5 (°C) h5 (kJ/kg) t6 (°C) h6 (kJ/kg) h7 (kJ/kg) s4 (kJ/K kg) s7 (kJ/K kg) v5 (m3/kg) v6 (m3/kg) Volume ratio v6/v5 t2a (°C) h2a (kJ/kg) t6a (°C) h6a = h6 + h2 h2a (kJ/kg) Dryness 6a (mol/mol) Expansion work output W1 = h5 h6 (kJ/kg) Pump work input W2 = h2 h1 (kJ/kg) Net power output W = W1 W2 (kJ/kg) Solar collector heat input h5 h2 (kJ/kg)(IEH) Solar collector heat input h5 h2a (kJ/kg)(+IEH) Rankine cycle efficiency gR = W/(h5 h2)(IEH Rankine cycle efficiency gR = W/(h5 h2a)(+IEH) Carnot efficiency gC = 1 T1/T5 Thermodynamics perfection gR/gC (IEH) Thermodynamics perfection gR/gC (+IEH)
80 80 0 0.7888 25 25 0 0.1494 233.2 25.20 233.7 312.8 466.1 85 471.9 48.3 446.62 424.1 1.793 1.756 0.02358 0.1280 5.428 41.36 256.0 25.20 424.3 overheated 25.28 0.5 24.78 238.2 215.9 10.403% 11.478% 16.760% 62.070% 68.482%
72.87 80 7.13 0.9214 25 34.58 9.58 0.2474 234.2 25.16 234.6 305.2 473.7 85 479.7 52.50 458.02 440.1 1.819 1.796 0.02195 0.08465 3.857 52.50 274.1 34.15 418.52 0.8941 21.68 0.4 21.28 245.1 205.6 8.682% 10.350% 16.760% 51.802% 61.755%
70.65 80 9.35 1.296 25 37.31 12.31 0.3955 236.8 25.35 237.5 310.0 493.9 85 500.6 48.09 477.48 465.9 1.882 1.882 0.01837 0.06259 3.407 48.09 272.7 36.12 442.28 0.9013 23.12 0.7 22.42 263.1 227.9 8.521% 9.838% 16.760% 50.841% 58.697%
73.31 80 6.69 1.625 25 34.37 9.37 0.4738 238.9 25.46 239.9 321.8 509.9 85 517.3 40.80 490.98 483.8 1.927 1.946 0.01612 0.05769 3.579 40.80 264.8 33.44 466.08 0.9325 26.32 1 25.32 277.4 252.5 9.128% 10.028% 16.760% 54.463% 59.831%
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h2a h2 and t6 = t2a. Obviously, it is impossible to achieve the equations in the IHE during the real operation, because those call for endless heat transfer time and areas. But it can be acceptable for the theoretically analyses. Just like what mentioned above, it can be easily found in Table 2 that with the increasing mass fraction increasing of R245fa, the pressure level of the zeotropic mixture decreases. Ma possesses the lowest pressure level during evaporating and condensing in the propose temperature range. That implies when the pressures of Rankine cycle are constant, Ma can reach the highest temperatures. However, Mb that is isentropic, possesses the largest temperature glides among the three mixtures, which are 9.35 °C at evaporation and 12.31 °C at condensation. Besides, under the same working condition, t6a of Mb is the highest, which is 36.12 °C. Comparing with the other two mixtures, Mb shows greater potential for heat transfer during phase change. For example, if the system is two-stage, the heat energy between point 6a and 1 could still be utilized by the lower stage. The Rankine cycle efficiencies of the zeotropic mixtures in Table 2, which are also shown in Fig. 9, show quite peculiar trend. It has been known that for pure working fluids a significant increase can be achieved if the Rankine cycle system is combined with an IHE. As zeotropic mixtures, Ma Mb and Mc show the same trend when an IHE is introduced. Comparing with the Rankine cycle system without IHE, when an IHE is used, Rankine cycle efficiencies of Ma, Mb and Mc increase 19.212%, 15.456% and 9.860% respectively. At the same time, further calculation indicates that Rankine cycle efficiency of pure R245fa increases 10.334% (from 10.403% to 11.478%) under the same working conditions (shown in Fig. 9). This result indicates that for zeotropic mixtures introducing an IHE to the system can also significantly increase the thermal efficiencies, and the effect can be more evident than that of pure fluids.
Rankine cycle efficiency %
12 without IHE with IHE
11
10
9
8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
R152a mass fraction Fig. 9. Rankine cycle efficiencies with and without IHE for R245fa, Ma, Mb and Mc.
611
Meanwhile, we can learn from Table 2 and (Fig. 9) that the isentropic zeotropic mixtures Mb possesses a lower Rankine cycle efficiency than drying mixture Ma and wetting mixture Mc. This is quite different from the pure working fluid. Bahaa Saleh, pointed out that, for pure working fluids, the general trend was that with increasing critical temperature, the thermal efficiency increased (Saleh et al., 2007). But the conclusion seems not suitable for zeotropic mixtures. For it is obviously the critical temperature of Mb is higher than Mc. As a consequence, judging by Rankin cycle efficiency, the isentropic zeotropic mixtures might not be the best choice for Rankine cycle systems. In order to make the effect of introducing an IHE to Rankine cycle more evident, thermodynamics perfections of the cycle are also mentioned in Table 2. Obviously, introducing an IHE to the system can greatly increase the thermal performances of the Rankine cycle, especially for drying zeotropic mixtures. For the design of the Rankine cycle low-temperature systems, other two important factors are the volume flow rate at the inlet of the expander and the outlet/inlet volume flow ratio. These factors directly decide the design and expense of the expander which costs almost 30% of the whole system (Stine et al., 1985). So substances with a high thermal efficiency, a low value of volume flow rate and a low value of outlet/inlet volume flow ratio are appreciated. (Table 2) shows the specific volume value v5 at the expander inlet and the volume ratio v6/v5 of the three zeotropic mixtures. When the overall expansion work output Wall is set, it is obviously at the expander inlet the volume flow rate V_ 5 ¼ v5 W all =W 1 :. Further calculations show that V_ 5 of Ma, Mb and Mc follow the same trend of v5 in Table 2. We learn that Mc possesses the lowest value of V_ 5 while Mb possesses the lowest value of v6/v5. Table 2 and Fig. 9 also show the thermal performances of pure R245fa under the prescribed conditions. Obviously, it appears the highest Rankine cycle efficiency is provided with pure R245fa, and the result is independent of the use of an internal heat exchanger. But as what we can see from Table 2, the specific volume value v5 and the volume ratio v6/v5 of pure R245fa are much higher than that of the proposed mixtures. This implies larger dimension and more expensive expander for pure R245fa. Meanwhile, we can also find from Table 2 that, for the mixtures, the exhausted vapor from IHE possesses a relatively high-temperature and dryness. Because of the mixture’s temperature glide during condensing, in the set temperature range, if a heat recovery unit is introduced between the IHE and the condenser, most of the latent heat during condensing process can be reclaimed, and the overall thermal efficiency of the system can be greatly enhanced. On the other hand, without temperature glide, pure R245fa can not utilize its latent heat during condensing process in the same temperature range, and the overall thermal efficiency of the system is limited. From (Figs. 2 to 7), it can be concluded that, when the condensation bubble-point temperature t1 is constant, the cooling water temperature
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at the condenser outlet of zeotropic mixture is definitely higher than that of pure R245fa. This is quite important to those solar Rankine systems which aim at offering power and heat at the same time. It is interesting to consider the Rankine cycle efficiency gR, the volume flow rate V_ 5 and the volume ratio v6/v5 together. For the four researched working fluids, under the prescribed conditions, none of them can possess the highest gR, the lowest V_ 5 and v6/v5 at the same time, whether with or without the IHE. Another interesting and important phenomenon is that from Fig. 9, it is clear that there might be two different mass fractions for the same Rankine cycle efficiency. These also mean more technical and economical evaluations need to make according to the real working conditions, when choosing a zeotropic mixtures for a low-temperature Rankine cycle. 3.2.4. Effect of the overheating in the Rankine cycle In Section 3.2.3, an overheating of 5 °C is proposed in the set working conditions, because Mc is a wetting zeotropic mixture. Here, the effect of the overheating in the Rankine cycle will be scanned. Firstly, the most important effect of eliminating the overheating in the cycle is that most wetting mixtures can’t be used, even in the real operation, or else we will have to face the challenge of wet expansion in the expander. For revealing the effect of overheating, the working conditions proposed in Section 3.2.3 are inherited, but the only difference is that there is no overheating at solar collector outlet. Fig. 10 illustrates the Rankine cycle efficiencies of Ma, Mb, Mc and R245fa without overheating, and shows the compare of with and without overheating. Detailed calculations show that, when there is no overheating, the Rankine cycle efficiencies for R245fa, Ma, Mb and Mc are 10.387%, 8.699%, 8.401% and 9.111% without IHE, while 11.215%, 10.014%, 9.373% and 9.651% with IHE. As shown in Fig. 10, without IHE, the efficiencies for R245fa, Ma and Mc are almost the same whether they 12.0 superheating without IHE superheating with IHE saturation without IHE saturation with IHE
Rankine cycle efficiency %
11.5 11.0 10.5 10.0 9.5 9.0 8.5 8.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
R152a mass fraction Fig. 10. Rankine cycle efficiencies compare with and without overheating.
are overheated or not, and the efficiencies difference for Mb is also small, just 1.428%. Significant increases of the efficiencies come from the introducing of IHE. For example, Ma’s efficiency without overheating but with IHE is 10.014%, even higher than Mb’s efficiency with overheating and IHE which is 9.838%. As a whole, for all the working fluids employed, it is believed that the increase of efficiencies by superheating without IHE is generally small; a more significant increase can be achieved if superheating is combined with IHE. It is necessary to point out that although superheating at the solar collector outlet can increase Rankine cycle efficiencies of the system, it may also lead to uneconomic solar collector areas. The overall heat transfer coefficient of the vapor in the solar collector tube is much lower than that of the liquid. As a result, when the vaporizer surface dries out, more heat transfer area will be required for the desired heat transfer rate. A primary experiment carried out by the authors shows that for pure R245fa used in a plat solar collector, when the vaporizer surface dries out, almost one third of the collector areas are consumed to gain a 5 °C overheating at the collector outlet. It is believed the situations for zeotropic mixtures would be quite similar. This strongly indicates that the economic factors should be considered when the overheating is set. Meanwhile, it was found during the primary experimental that the overheating at the collector outlet or the integral phase change in the solar collector is controlled by the mass flow rate of working fluid and the insolation on the collector surface. A small mass flow rate of working fluids can assure its integral phase change, but at the same time, the overall net work output would be limited. Searching for the optimal mass flow rate for the low-temperature solar Rankine cycle system would be a useful and interesting work. 4. Conclusions and suggestions In the present paper, the authors propose three typical mass fractions of R245fa/R152a, which are 0.9/0.1 (Ma), 0.65/0.35 (Mb), 0.45/0.55 (Mc). In the typical temperature range of low-temperature solar Rankine cycle system operating, they are drying, isentropic and wetting respectively. And the thermal performance investigations of them are carried out in low-temperature Rankine cycles. Because of the characteristic of zeotropic mixtures that there is an obvious temperature glide during phase change, based on the simple low-temperature Rankine cycle system, an internal heat exchanger (IHE) is introduced. Some findings concerning the proposed zeotropic mixtures are interesting. Different from the pure fluids, for the proposed zeotropic mixtures, the isentropic working fluid Mb possesses the lowest Rankine cycle efficiency all the time, comparing with the drying and wetting fluids. Calculation indicates that, under the set working conditions, introducing an IHE to the system can greatly increase the thermal performances of the Rankine cycle,
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especially for drying and isentropic zeotropic mixtures. After transferring the heat to the compressed liquid, the exhaust working fluids still possess relatively high-temperature and dryness. A heat recovery unit is proposed between the IHE and the condenser to reclaim the latent heat during condensing process. This implies the possibility of gaining a higher overall thermal efficiency by utilizing zeotropic mixtures in the solar Rankine cycle system. Under the same pressure conditions, thermal performances of no overheating and an overheating of 5 °C are compared. It indicates that for pure working fluid and zeotropic mixtures the increase of efficiencies by superheating without IHE is generally small while a more significant increase can be achieved if superheating is combined with IHE. At the same time, it is necessary to balance the efficiency factors and the economic factors, when the superheating of working fluid is set. When a working fluid is used in the low-temperature solar Rankine cycle system, one might require a high thermal efficiency gR, a low flow rate V_ 5 and a low value of v6/ v5. But on the whole, for pure fluids, drying fluids usually possess high gR and high values of v6/v5, on the contrary, wetting pure fluids possess low gR and low values of v6/ v5. High value of v6/v5 usually implies high expense of expander or turbine. Hence, the choice ranges of pure fluids for low-temperature solar Rankine cycle systems are usually limited. Meanwhile, it is interesting to find that, utilizing the proposed zeotropic mixtures, there might be two different mass fractions for the same Rankine cycle efficiency. Therefore the choice of mixing pure drying and wetting fluids brings us a wider range when we chose working fluids for lowtemperature solar Rankine cycle. Although the Rankine cycle efficiency using pure R245fa is higher than any of the zeotropic mixtures proposed in this paper, it requires a larger expander dimension. As a result, the cost of the system using pure R245fa might be much higher than the mixtures. Further research in zeotropic mixtures is justified because of the potential that it might reduce the capital cost and improve the overall thermal efficiency of Rankine cycle system. Meanwhile, although none of the three proposed mixtures by the authors can possess the highest gR, the lowest V_ 5 and v6/v5 at the same time, it is believed that when the overall power output demand is set, under the boundary
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conditions of technology and economy, the optimal mass fraction of components can be gained. And we believe that the optimization could be interesting too. Acknowledgments The authors wish to thank the Ministry of Science and Technology of China for its financial assistance within the ‘‘863” Program, Contract No. 2006AA05Z420. References Calm, J.M., Hourahan, G.C., 2001. Refrigerant data summary. Engineered Systems 18 (11), 74–88. Goswami, D.Y., Vijayaraghavan, S., Lu, S., Tamm, G., 2004. New and emerging developments in solar energy. Solar Energy 76, 33–43. Lemmon, E.W., McLinden, M.O., Huber, M.L., 2002. NIST reference fluid thermodynamic and transport properties-REFPROP. NIST standard reference database 23 (Version 7.0). Madhawa Hettiarachchi, H.D. et al., 2007. Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat sources. Energy 32, 1698–1706. Manolakosa, D., Papadakisa, G., Mohameda, Essam Sh., Kyritsisa, S., Bouzianasb, K., 2005. Design of an autonomous low-temperature solar Rankine cycle system for reverse osmosis desalination. Desalination 183, 73–80. Manolakosa, D., Papadakisa, G., Kyritsisa, S., Bouzianasb, K., 2007. Experimental evaluation of an autonomous low-temperature solar Rankine cycle system for reverse osmosis desalination. Desalination 203, 366–374. Mills, D., 2004. Advances in solar thermal electricity technology. Solar Energy 76, 19–31. Nguyen, V.M., Doherty, P.S., Riffat, S.B., 2001. Development of a prototype low-temperature Rankine cycle electricity generation system. Applied Thermal Engineering 21, 169–181. Saleh, Bahaa, Koglbauer, Gerald, Wendland, Martin, Fischer, Johann, 2007. Working fluids for low-temperature organic Rankine cycles. Energy 32, 1210–1221. Stine, William B., Harrigan, Raymond W., 1985. Solar Energy Fundamentals and Design. John Wiley and Sons, Inc., pp. 287–315. Tamm, G., Goswami, D.Y., Lu, S., Hasan, A.A., 2004. Theoretical and experimental investigation of an ammonia–water power and refrigeration thermodynamic cycle. Solar Energy 76, 217–228. Xu, F., Goswami, D.Y., 1999. Thermodynamic properties of ammonia– water mixtures for power-cycle applications. Energy 24, 525–536. Xu, Feng, Yogi Goswami, D., Bhagwat, Sunil S., 2000. A combined power/cooling cycle. Energy 25, 233–246. Zhang, X.R., Yamaguchi, H., Uneno, D., Fujima, K., Enomoto, M., Sawada, N., 2006. Analysis of a novel solar energy-powered Rankine cycle for combined power and heat generation using supercritical carbon dioxide. Renewable Energy 31, 1839–1854.
Solar Energy 83 (2009) 605–613 www.elsevier.com/locate/solener
Analysis of zeotropic mixtures used in low-temperature solar Rankine cycles for power generation X.D. Wang, L. Zhao * Department of Thermal Energy and Refrigeration Engineering, School of Mechanical Engineering, Tianjin University, No. 92 Weijin Road, Tianjin 300072, PR China Received 25 October 2007; received in revised form 29 September 2008; accepted 12 October 2008 Available online 14 November 2008 Communicated by: Associate Editor Robert Pitz-Paal
Abstract This paper presents the analysis of low-temperature solar Rankine cycles for power generation using zeotropic mixtures. Three typical mass fractions 0.9/0.1 (Ma) 0.65/0.35 (Mb), 0.45/0.55 (Mc) of R245fa/R152a are chosen. In the proposed temperature range from 25 °C to 85 °C, the three zeotropic mixtures are investigated as the working fluids of the low-temperature solar Rankine cycle. Because there is an obvious temperature glide during phase change for zeotropic mixtures, an internal heat exchanger (IHE) is introduced to the Rankine cycle. Investigation shows that different from the pure fluids, among the proposed zeotropic mixtures, the isentropic working fluid Mb possesses the lowest Rankine cycle efficiency. For zeotropic mixtures a significant increase of thermal efficiencies can be gained when superheating is combined with IHE. It is also indicated that utilizing zeotropic mixtures can extend the range of choosing working fluids for low-temperature solar Rankine cycles. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Zeotropic mixtures; Working fluids; Low-temperature solar Rankine cycle
1. Introduction Because of the potential in reducing consumption of fossil fuels and relaxing environmental problems, the applications of renewable energies (solar energy, wind energy, biomass and geothermal energy) to electricity generation become more and more important, and have received increasing attentions. During the last two decades, all over the world a number of researchers have worked on developing new solar thermodynamic cycles or improving existing ones. Various high-temperature systems such as single axis and two axis tracking technologies have been suggested and developed (Mills, 2004). But owing to the complex technologies and high costs, the high-temperature
*
Corresponding author. E-mail address: [email protected] (L. Zhao).
0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.10.006
solar thermal systems are generally less competitive now, especially in developing countries. At the same time, low-temperature technologies have also been developed and the efficiencies are improving. Thermodynamic cycles (especially the organic Rankine cycles) for combined power and heat system have a great potential to become competitive with fossil fuels (especially natural gas) based power systems (Goswami et al., 2004). For example, Goswami and Feng Xu proposed a new combined power/refrigeration cycle utilizing ammonia and water, of which the overall thermal efficiency reaches 23.54% (Xu and Goswami, 1999; Xu et al., 2000). Manolakosa et al. designed and built a low-temperature solar organic Rankine cycle system for reverse osmosis desalination in Greece. The working fluid is R134a that works between 35 °C and 75.8 °C, and the maximum overall system efficiency is about 4% (Manolakosa et al., 2005, 2007). Nguyen et al. developed a small-scale solar Rankine system
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designed to operate at low-temperatures for electricity generation with 4.3% efficiency (Nguyen et al., 2001). When a low-temperature solar powered organic Rankine cycle is considered, a certain challenge is the choice of the organic working fluid and the particular design of the cycle. There are several general criteria that the working fluid of low-temperature Rankine cycle system should ideally satisfy. Stability, non-fouling, non-corrosiveness, non-toxicity and non-flammability are some preferable physical and chemical characteristics (Madhawa Hettiarachchi et al., 2007). Also, for low-power turbine applications, the fluid should have a high molecular weight to minimize the rotational speed or the number of turbine stages and to allow for reasonable mass flow rates and turbine nozzle areas (Stine et al., 1985). However, in a cycle design, not all the desired general requirements can be satisfied. At the same time, the choice of working fluid can greatly affect the power plant cost. Hence, economical efficiency of the working fluid should also be considered. In recent publications, the choices of working fluids suit for the low-temperature Rankine cycles have been researched, such as Saleh et al. (2007), Madhawa Hettiarachchi et al. (2007), Tamm et al. (2004), Xu et al. (2000) and Zhang et al. (2006). In Greece, utilizing R134a, Manolakosa et al. (2007) established a low-temperature solar organic Rankine cycle system for reverse osmosis desalination. However, most of the researches and applications mentioned above are focused on the pure component working fluids for organic Rankine cycles. As to the mixed component working fluids that could be used in the low-temperature solar powered Rankine cycles, few researches and applications were reported. Saleh et al. (2007) researched 31 pure component working fluids for organic Rankine cycles between 30 and 100 °C which were typical for geothermal power plants, and a recuperator which was called internal heat exchanger (IHE) was introduced to Rankine cycle. Bahaa Saleh proved that for pure component working fluid, the increase of the thermal efficiency of the cycle was significant in the case with internal heat exchanger, while the other conditions did not change. Here, in this paper we concentrate on the performance of zeotropic mixtures utilized in the low-temperature solar Rankine cycles for power generation. Also, we will introduce the internal heat exchange to the low-temperature solar Rankine cycles. Based on that, we will analyze and compare the thermal efficiencies of the cycles at the same temperature range and under different components conditions. 2. Description of the system and the different types of Rankine cycle The low-temperature solar Rankine cycle system for electricity generation mainly consists of the following components (Fig. 1):
(1) (2) (3) (4) (5) (6) (7)
Solar collectors Expander Generator Internal heat exchanger (IHE) Condenser Storage tank Working fluid pump
The system operation is described briefly below. The working fluid is pumped to a high pressure by the feed pump (7). The high pressure liquid is firstly heated in the IHE (4), and then it is heated in the pipes of the solar collectors (1) where phase change happens. Thus, we can take the solar collector as an evaporator. The liquid temperature at the collector inlet is determined by the exhausted vapor temperature at the expander outlet and the efficiency of the IHE, while vapor at the collector outlet is various at different boiling pressures. Owing to the change of the boiling pressure, the vapor exhausted from the turbine in the Rankine cycle at the condensing pressure may be in the wet saturated, dry saturated or superheated states. In order to avoid the harmful wet stroke in the expander, superheating of the vapor at the inlet of the expander is necessary. The degree of superheating can be adjusted according to different working fluids and different working conditions. The superheated vapor is driven to the expander (2) where the generated shaft work drives the generator (3). The vapor (low pressure, saturated or superheated) at the expander outlet is directed to the IHE (4). The vapor cools down in the heat exchanger by transferring the heat to the compressed liquid. Then the working fluid is completely cooled down in the condenser (5) and the condensate is collected and stored in the storage tank (6), from where the liquid is pumped into the collectors. (Figs. 2–4) illustrate the thermodynamic processes described above. The theoretical cycle consists of the following processes:1 ? 2: Isentropic compression (working fluid pump)2 ? 2a: Isobaric internal heat exchange (IHE)2a ? 5: Isobaric heat supply (solar collectors)5 ? 6: Expansion (expander)6 ? 6a: Isobaric internal heat exchange (IHE)6a ? 1: Isobaric heat rejection (condenser). At the same time, (Figs. 2–4) also show three different types of Rankine cycles. According to the different slopes of the saturation curve in the T–S diagram, working fluids are divided to drying (Fig. 2), wetting (Fig. 3) and isentropic (Fig. 4) working fluids (Stine et al., 1985). A drying fluid has a positive slope; a wetting fluid has a negative slope, while an isentropic fluid has infinitely large slopes. It is found that in the temperature range that a low-temperature solar Rankine cycle system works (usually below 100 °C), few pure organic working fluids are isentropic. Most of them are drying or wetting. For example, the wetting working fluids include R125, R152a, R134a, R143a, ammonia and so on; while the drying working fluids include R236fa, R245fa, R601, R600, n-hexane and so on. It can be seen in Fig. 3 that if there was no or only a little overheating at the inlet of the expander, the state point 6 of
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p
607
tio
n
t
rr
ad
ia
2
3
So
la
Monitoring hole
G
le
ct
or
s
1
Generator
p
So
la
rc
ol
Expander
t
p
t
4
t
Internal heat exchanger Condenser
p
5
p
Monitoring hole
t
6 7
t
p
Cooling water
Working fluid pump Storage tank
Symbol
t p
Description Temperature transducer Pressure transducer
Fig. 1. Schematic of the low-temperature solar Rankine cycle system.
Fig. 2. Schematic of the Rankine cycle for pure drying working fluids.
Fig. 3. Schematic of Rankine cycle for pure wetting working fluids.
the expander outlet might drop into the two-phase region, even in the real expansion process when the entropy is increasing all the time. So, under the same working conditions, drying and isentropic fluids show better thermal efficiencies than wetting fluids, because they will not condense after the fluids go through the expander and the overheating of the vapor at the expander inlet seems to be dispensable.
Stine et al. (1985) pointed out that, for pure working fluids, drying fluids can produce cycle efficiencies almost as great as isentropic fluids if recuperator is used in the cycle. And Saleh et al. (2007) proved that. Now the question is how the thermodynamic performance is, when the mixture is used in the low-temperature solar Rankine cycle.
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Fig. 4. Schematic of Rankine cycle for pure isentropic working fluids.
Fig. 5. Schematic of the Rankine cycle for mixed drying working fluids.
3. Working fluids proposed and its theoretical thermal performance In this section, we propose three zeotropic mixtures based on different mass fractions of R245fa and R152a. They are compared in the low-temperature Rankine cycles under the same working conditions. Beyond that, a theoretical thermodynamic analysis under idealized conditions is given. 3.1. Working fluids proposed The phase change process of zeotropic mixtures is quite different with that of pure working fluids, which has obvious temperature glide during phase change. This characteristic implies that when there is an IHE more heat can be reclaimed inside the system. First, the transferred heat does not need to be supplied from outside, thus some solar collector areas can be saved. At the same time, with an IHE, the average evaporating temperature of the zeotropic will increase while the average condensing temperature will decrease. So, the economical efficiency and thermal efficiency of the low-temperature Rankine cycle will increase. Another advantage of the mixture is that, when a drying fluid and a wetting fluid are mixed, under a certain mass fraction, we can gain the isentropic working fluid. This could greatly extend the range of available working fluids for low-temperature Rankine cycles. (Figs. 5–7) illustrate the theoretical cycle processes of the zeotropic mixtures which are corresponding to (Figs. 2–4). Apparently, with different mass fractions of the components, the mixtures might be drying, wetting or isentropic. At the same time, because of the characteristic of zeotropic mixtures that there is an obvious temperature glide during
Fig. 6. Schematic of Rankine cycle for mixed wetting working fluids.
phase change, the state point 6a of IHE outlet might be in the two-phase region, which is quite is useful because the duty of the condenser is reduced. In order to investigate the thermal performance of the zeotropic mixtures used in the low-temperature Rankine cycles, we take the typical drying fluid R245fa (Fig. 2) and the typical wetting fluid R152a (Fig. 3) as the original components. Both of them have a zero ODP (Ozone Depression Potential) and quite low GWP (Global Warming Potential), so the mixtures can also be environmental friendly and relatively safe. Three typical mass fractions of R245fa/R152a are chosen, which are 0.9/0.1 (Ma),
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3.2. Thermodynamic analysis of the proposed zeotropic mixtures Throughout this investigation, the ideal Rankine cycles using Ma, Mb and Mc as the working fluids are under the same operating conditions and the irreversibilities associated with the heat transfer and compression processes are neglected. At the same time, the expansion efficiency gE in the expander is set as 80%. The theoretical schematic T–S diagrams of the cycles are the same as the graphics shown in Figs. 5–7.
Fig. 7. Schematic of Rankine cycle for mixed isentropic working fluids.
0.65/0.35 (Mb), 0.45/0.55 (Mc). Under these mass fraction conditions, the zeotropic mixtures are respectively drying (Ma), isentropic (Mb) and wetting (Mc). Some properties of the original components are listed in Table 1, and (Fig. 8) shows the T–S diagram of the three zeotropic mixtures. The dashed lines in Fig. 8 are the isobaric lines of 1 MPa. It is clear that with the mass fraction of R245fa increasing, the pressure level of the zeotropic mixture decreases. Table 1 List of the original components Original components
Molecular weight (g/ mol)
TCRIT (°C)
PCRIT (MPa)
Std 34 safety group
ODP
GWP (100 yr)
R152a R245fa
66.05 134.05
113.3 154.1
4.52 4.43
A2 B1
0 0
120 950
All properties come from Calm and Hourahan (2001).
Fig. 8. T–S diagram for the three zeotropic mixtures.
3.2.1. The given operating condition In order to analyze the performance of the working fluids in the ideal cycle, a given operating condition is necessary. In (Figs. 5–7), we set the lowest temperature of the cycle t1 = 25 °C, and the highest temperature t5 = 85 °C. In this temperature range, considering the wetting working fluid Mc might lead to liquid formation in the expander, superheating of the vapor is still considered here. The temperature difference of point 5 and point 4 is set as 5 °C. 3.2.2. Basic equations Basic equations of the cycle : t1 ¼ 25 C p1 ¼ p6 ¼ p60 ¼ p7 ¼ p6a s1 ¼ s2 p2 ¼ p3 ¼ p4 ¼ p5 ¼ p2a t5 ¼ 85 C t4 ¼ t5 5 C ¼ 80 C s5 ¼ s60 gE ¼ ðh5 h6 Þ=ðh5 h60 Þ ¼ 0:8 Solar collector heat inputðwithout IHEÞ : QE ¼ h5 h2 Solar collector heat inputðwith IHEÞ : QE ¼ h5 h2a Expansion work output : W S ¼ h 5 h6 Heat transfer in IHE : QI ¼ h6 h6a ¼ h2a h2 Condenser heat rejectionðwithout IHEÞ : QC ¼ h6 h1 Condenser heat rejectionðwith IHEÞ : QC ¼ h6a h1 Pump work input : W P ¼ h2 h1 Net power output : WN ¼WS WP The Rankine cycle efficiency defined : WN WS WP gR ¼ ¼ QE QE
ð1Þ ð2Þ ð3Þ ð4Þ ð5Þ ð6Þ ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ ð12Þ ð13Þ ð14Þ ð15Þ ð16Þ ð17Þ
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In the study, all the calculations and evaluations of the ideal Rankine cycles are based on unit mass working fluids. To make the analyses simple and clear, some assumptions are made: (1) Flow directions of working fluids in IHE are countercurrent, and leakage of heat in IHE and condenser is ignored; (2) It is considered that the temperature gliding of working fluid distributes linearly along heat exchanger and solar collector; (3) The internal resistances in heat exchanger and solar collector are negligible and the condensation and evaporation pressures of working fluids keep constant respectively; (4) The circulated compositions of the zeotropic mixtures do not change in every process of the cycle.
3.2.3. Cycle thermodynamics and thermal efficiencies of proposed zeotropic mixtures Based on the above basic equations, the results of evaluations are shown in Table 2. All the parameters used in the calculation come from NIST REFPROP 7.0 (Lemmon et al., 2002), which has a sufficient accuracy. In (Table 2), Rankine cycle thermal performances of the proposed zeotropic mixtures between 25 and 85 °C with and without IHE are compared. Some explanations need to be illuminated here. When there is no IHE in the system, it is considered that the exhausted vapor of the expander go directly to the condenser. No heat is reclaimed in the cycle, and the state points 2a and 6a will not appear. On the contrary, when the IHE is added to the system, heat energy h6 h6a will be reclaimed. In that case, in order to make the evaluation simple and clear, the authors consider that inside the IHE, there are equations QI = h6 h6a =
Table 2 Comparison of proposed zeotropic mixtures in Rankine cycle without(IHE) and with internal heat exchanger (+IHE). Components (R245fa/R152a, mass)
R245fa (1/0)
Ma (0.9/0.1)
Mb (0.65/0.35)
Mc (0.45/0.55)
Corresponding schematic diagram
Fig. 2
Fig. 5
Fig. 7
Fig. 6
Evaporation bubble-point temperature t3 (°C) Evaporation dew-point temperature t4 (°C) Evaporation temperature glide t4 t3 (°C) Evaporation pressure p3 (MPa) Condensation bubble-point temperature t1 (°C) Condensation dew-point temperature t7 (°C) Condensation temperature glide t7 t1 (°C) Condensation pressure p1 (MPa) h1 (kJ/kg) t2 (°C) h2 (kJ/kg) h3 (kJ/kg) h4 (kJ/kg) t5 = t4 + 5 (°C) h5 (kJ/kg) t6 (°C) h6 (kJ/kg) h7 (kJ/kg) s4 (kJ/K kg) s7 (kJ/K kg) v5 (m3/kg) v6 (m3/kg) Volume ratio v6/v5 t2a (°C) h2a (kJ/kg) t6a (°C) h6a = h6 + h2 h2a (kJ/kg) Dryness 6a (mol/mol) Expansion work output W1 = h5 h6 (kJ/kg) Pump work input W2 = h2 h1 (kJ/kg) Net power output W = W1 W2 (kJ/kg) Solar collector heat input h5 h2 (kJ/kg)(IEH) Solar collector heat input h5 h2a (kJ/kg)(+IEH) Rankine cycle efficiency gR = W/(h5 h2)(IEH Rankine cycle efficiency gR = W/(h5 h2a)(+IEH) Carnot efficiency gC = 1 T1/T5 Thermodynamics perfection gR/gC (IEH) Thermodynamics perfection gR/gC (+IEH)
80 80 0 0.7888 25 25 0 0.1494 233.2 25.20 233.7 312.8 466.1 85 471.9 48.3 446.62 424.1 1.793 1.756 0.02358 0.1280 5.428 41.36 256.0 25.20 424.3 overheated 25.28 0.5 24.78 238.2 215.9 10.403% 11.478% 16.760% 62.070% 68.482%
72.87 80 7.13 0.9214 25 34.58 9.58 0.2474 234.2 25.16 234.6 305.2 473.7 85 479.7 52.50 458.02 440.1 1.819 1.796 0.02195 0.08465 3.857 52.50 274.1 34.15 418.52 0.8941 21.68 0.4 21.28 245.1 205.6 8.682% 10.350% 16.760% 51.802% 61.755%
70.65 80 9.35 1.296 25 37.31 12.31 0.3955 236.8 25.35 237.5 310.0 493.9 85 500.6 48.09 477.48 465.9 1.882 1.882 0.01837 0.06259 3.407 48.09 272.7 36.12 442.28 0.9013 23.12 0.7 22.42 263.1 227.9 8.521% 9.838% 16.760% 50.841% 58.697%
73.31 80 6.69 1.625 25 34.37 9.37 0.4738 238.9 25.46 239.9 321.8 509.9 85 517.3 40.80 490.98 483.8 1.927 1.946 0.01612 0.05769 3.579 40.80 264.8 33.44 466.08 0.9325 26.32 1 25.32 277.4 252.5 9.128% 10.028% 16.760% 54.463% 59.831%
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h2a h2 and t6 = t2a. Obviously, it is impossible to achieve the equations in the IHE during the real operation, because those call for endless heat transfer time and areas. But it can be acceptable for the theoretically analyses. Just like what mentioned above, it can be easily found in Table 2 that with the increasing mass fraction increasing of R245fa, the pressure level of the zeotropic mixture decreases. Ma possesses the lowest pressure level during evaporating and condensing in the propose temperature range. That implies when the pressures of Rankine cycle are constant, Ma can reach the highest temperatures. However, Mb that is isentropic, possesses the largest temperature glides among the three mixtures, which are 9.35 °C at evaporation and 12.31 °C at condensation. Besides, under the same working condition, t6a of Mb is the highest, which is 36.12 °C. Comparing with the other two mixtures, Mb shows greater potential for heat transfer during phase change. For example, if the system is two-stage, the heat energy between point 6a and 1 could still be utilized by the lower stage. The Rankine cycle efficiencies of the zeotropic mixtures in Table 2, which are also shown in Fig. 9, show quite peculiar trend. It has been known that for pure working fluids a significant increase can be achieved if the Rankine cycle system is combined with an IHE. As zeotropic mixtures, Ma Mb and Mc show the same trend when an IHE is introduced. Comparing with the Rankine cycle system without IHE, when an IHE is used, Rankine cycle efficiencies of Ma, Mb and Mc increase 19.212%, 15.456% and 9.860% respectively. At the same time, further calculation indicates that Rankine cycle efficiency of pure R245fa increases 10.334% (from 10.403% to 11.478%) under the same working conditions (shown in Fig. 9). This result indicates that for zeotropic mixtures introducing an IHE to the system can also significantly increase the thermal efficiencies, and the effect can be more evident than that of pure fluids.
Rankine cycle efficiency %
12 without IHE with IHE
11
10
9
8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
R152a mass fraction Fig. 9. Rankine cycle efficiencies with and without IHE for R245fa, Ma, Mb and Mc.
611
Meanwhile, we can learn from Table 2 and (Fig. 9) that the isentropic zeotropic mixtures Mb possesses a lower Rankine cycle efficiency than drying mixture Ma and wetting mixture Mc. This is quite different from the pure working fluid. Bahaa Saleh, pointed out that, for pure working fluids, the general trend was that with increasing critical temperature, the thermal efficiency increased (Saleh et al., 2007). But the conclusion seems not suitable for zeotropic mixtures. For it is obviously the critical temperature of Mb is higher than Mc. As a consequence, judging by Rankin cycle efficiency, the isentropic zeotropic mixtures might not be the best choice for Rankine cycle systems. In order to make the effect of introducing an IHE to Rankine cycle more evident, thermodynamics perfections of the cycle are also mentioned in Table 2. Obviously, introducing an IHE to the system can greatly increase the thermal performances of the Rankine cycle, especially for drying zeotropic mixtures. For the design of the Rankine cycle low-temperature systems, other two important factors are the volume flow rate at the inlet of the expander and the outlet/inlet volume flow ratio. These factors directly decide the design and expense of the expander which costs almost 30% of the whole system (Stine et al., 1985). So substances with a high thermal efficiency, a low value of volume flow rate and a low value of outlet/inlet volume flow ratio are appreciated. (Table 2) shows the specific volume value v5 at the expander inlet and the volume ratio v6/v5 of the three zeotropic mixtures. When the overall expansion work output Wall is set, it is obviously at the expander inlet the volume flow rate V_ 5 ¼ v5 W all =W 1 :. Further calculations show that V_ 5 of Ma, Mb and Mc follow the same trend of v5 in Table 2. We learn that Mc possesses the lowest value of V_ 5 while Mb possesses the lowest value of v6/v5. Table 2 and Fig. 9 also show the thermal performances of pure R245fa under the prescribed conditions. Obviously, it appears the highest Rankine cycle efficiency is provided with pure R245fa, and the result is independent of the use of an internal heat exchanger. But as what we can see from Table 2, the specific volume value v5 and the volume ratio v6/v5 of pure R245fa are much higher than that of the proposed mixtures. This implies larger dimension and more expensive expander for pure R245fa. Meanwhile, we can also find from Table 2 that, for the mixtures, the exhausted vapor from IHE possesses a relatively high-temperature and dryness. Because of the mixture’s temperature glide during condensing, in the set temperature range, if a heat recovery unit is introduced between the IHE and the condenser, most of the latent heat during condensing process can be reclaimed, and the overall thermal efficiency of the system can be greatly enhanced. On the other hand, without temperature glide, pure R245fa can not utilize its latent heat during condensing process in the same temperature range, and the overall thermal efficiency of the system is limited. From (Figs. 2 to 7), it can be concluded that, when the condensation bubble-point temperature t1 is constant, the cooling water temperature
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at the condenser outlet of zeotropic mixture is definitely higher than that of pure R245fa. This is quite important to those solar Rankine systems which aim at offering power and heat at the same time. It is interesting to consider the Rankine cycle efficiency gR, the volume flow rate V_ 5 and the volume ratio v6/v5 together. For the four researched working fluids, under the prescribed conditions, none of them can possess the highest gR, the lowest V_ 5 and v6/v5 at the same time, whether with or without the IHE. Another interesting and important phenomenon is that from Fig. 9, it is clear that there might be two different mass fractions for the same Rankine cycle efficiency. These also mean more technical and economical evaluations need to make according to the real working conditions, when choosing a zeotropic mixtures for a low-temperature Rankine cycle. 3.2.4. Effect of the overheating in the Rankine cycle In Section 3.2.3, an overheating of 5 °C is proposed in the set working conditions, because Mc is a wetting zeotropic mixture. Here, the effect of the overheating in the Rankine cycle will be scanned. Firstly, the most important effect of eliminating the overheating in the cycle is that most wetting mixtures can’t be used, even in the real operation, or else we will have to face the challenge of wet expansion in the expander. For revealing the effect of overheating, the working conditions proposed in Section 3.2.3 are inherited, but the only difference is that there is no overheating at solar collector outlet. Fig. 10 illustrates the Rankine cycle efficiencies of Ma, Mb, Mc and R245fa without overheating, and shows the compare of with and without overheating. Detailed calculations show that, when there is no overheating, the Rankine cycle efficiencies for R245fa, Ma, Mb and Mc are 10.387%, 8.699%, 8.401% and 9.111% without IHE, while 11.215%, 10.014%, 9.373% and 9.651% with IHE. As shown in Fig. 10, without IHE, the efficiencies for R245fa, Ma and Mc are almost the same whether they 12.0 superheating without IHE superheating with IHE saturation without IHE saturation with IHE
Rankine cycle efficiency %
11.5 11.0 10.5 10.0 9.5 9.0 8.5 8.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
R152a mass fraction Fig. 10. Rankine cycle efficiencies compare with and without overheating.
are overheated or not, and the efficiencies difference for Mb is also small, just 1.428%. Significant increases of the efficiencies come from the introducing of IHE. For example, Ma’s efficiency without overheating but with IHE is 10.014%, even higher than Mb’s efficiency with overheating and IHE which is 9.838%. As a whole, for all the working fluids employed, it is believed that the increase of efficiencies by superheating without IHE is generally small; a more significant increase can be achieved if superheating is combined with IHE. It is necessary to point out that although superheating at the solar collector outlet can increase Rankine cycle efficiencies of the system, it may also lead to uneconomic solar collector areas. The overall heat transfer coefficient of the vapor in the solar collector tube is much lower than that of the liquid. As a result, when the vaporizer surface dries out, more heat transfer area will be required for the desired heat transfer rate. A primary experiment carried out by the authors shows that for pure R245fa used in a plat solar collector, when the vaporizer surface dries out, almost one third of the collector areas are consumed to gain a 5 °C overheating at the collector outlet. It is believed the situations for zeotropic mixtures would be quite similar. This strongly indicates that the economic factors should be considered when the overheating is set. Meanwhile, it was found during the primary experimental that the overheating at the collector outlet or the integral phase change in the solar collector is controlled by the mass flow rate of working fluid and the insolation on the collector surface. A small mass flow rate of working fluids can assure its integral phase change, but at the same time, the overall net work output would be limited. Searching for the optimal mass flow rate for the low-temperature solar Rankine cycle system would be a useful and interesting work. 4. Conclusions and suggestions In the present paper, the authors propose three typical mass fractions of R245fa/R152a, which are 0.9/0.1 (Ma), 0.65/0.35 (Mb), 0.45/0.55 (Mc). In the typical temperature range of low-temperature solar Rankine cycle system operating, they are drying, isentropic and wetting respectively. And the thermal performance investigations of them are carried out in low-temperature Rankine cycles. Because of the characteristic of zeotropic mixtures that there is an obvious temperature glide during phase change, based on the simple low-temperature Rankine cycle system, an internal heat exchanger (IHE) is introduced. Some findings concerning the proposed zeotropic mixtures are interesting. Different from the pure fluids, for the proposed zeotropic mixtures, the isentropic working fluid Mb possesses the lowest Rankine cycle efficiency all the time, comparing with the drying and wetting fluids. Calculation indicates that, under the set working conditions, introducing an IHE to the system can greatly increase the thermal performances of the Rankine cycle,
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especially for drying and isentropic zeotropic mixtures. After transferring the heat to the compressed liquid, the exhaust working fluids still possess relatively high-temperature and dryness. A heat recovery unit is proposed between the IHE and the condenser to reclaim the latent heat during condensing process. This implies the possibility of gaining a higher overall thermal efficiency by utilizing zeotropic mixtures in the solar Rankine cycle system. Under the same pressure conditions, thermal performances of no overheating and an overheating of 5 °C are compared. It indicates that for pure working fluid and zeotropic mixtures the increase of efficiencies by superheating without IHE is generally small while a more significant increase can be achieved if superheating is combined with IHE. At the same time, it is necessary to balance the efficiency factors and the economic factors, when the superheating of working fluid is set. When a working fluid is used in the low-temperature solar Rankine cycle system, one might require a high thermal efficiency gR, a low flow rate V_ 5 and a low value of v6/ v5. But on the whole, for pure fluids, drying fluids usually possess high gR and high values of v6/v5, on the contrary, wetting pure fluids possess low gR and low values of v6/ v5. High value of v6/v5 usually implies high expense of expander or turbine. Hence, the choice ranges of pure fluids for low-temperature solar Rankine cycle systems are usually limited. Meanwhile, it is interesting to find that, utilizing the proposed zeotropic mixtures, there might be two different mass fractions for the same Rankine cycle efficiency. Therefore the choice of mixing pure drying and wetting fluids brings us a wider range when we chose working fluids for lowtemperature solar Rankine cycle. Although the Rankine cycle efficiency using pure R245fa is higher than any of the zeotropic mixtures proposed in this paper, it requires a larger expander dimension. As a result, the cost of the system using pure R245fa might be much higher than the mixtures. Further research in zeotropic mixtures is justified because of the potential that it might reduce the capital cost and improve the overall thermal efficiency of Rankine cycle system. Meanwhile, although none of the three proposed mixtures by the authors can possess the highest gR, the lowest V_ 5 and v6/v5 at the same time, it is believed that when the overall power output demand is set, under the boundary
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