J. Cent. South Univ. (2017) 24: 2829−2841 DOI: https://doi.org/10.1007/s11771-017-3698-z

Thermodynamic optimization and fluid selection of organic driven by a latent source

XU Peng(徐鹏)1, LU Jian(吕建)1, LI Tai-lu(李太禄)1, ZHU Jia-ling(朱家玲 )2

1. School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, China; 2. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, Ministry of Education (Tianjin University), Tianjin 300072, China

© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Abstract: Organic Rankine cycle (ORC) is applicable for the heat-work conversion. Whereas, there also exist a lot issues that influence the efficiency and the cost of the system. In this work, eleven pure working fluids (as categorized into alkanes, and fluorinated alkanes) are investigated based on the first and second law of thermodynamics. The major objective is to obtain the most suitable for the source. The results show that the working fluid is an important factor of the system performance. The heat absorption of the working fluid in the evaporator is inversely proportional to the evaporating temperature, but the thermal and exergetic efficiencies are just the opposite. RC318 has the highest net power output and the lowest outlet temperature of the heat source, but its global warming potential (GWP) value is too high. The cyclohexane shows the highest thermal efficiency among the fluids investigated. Moreover, the figure of merit (FOM) of the isobutane is higher than that of other working fluids. Overall, the cyclohexane shows that the optimal comprehensive performance is more feasible for medium grade heat source in engineering applications.

Key words: organic Rankine cycle; working fluids; thermodynamics; low-temperature; evaporating temperature

PHEs will effectively be smaller than the real example 1 Introduction given, with a consequent reduction in cost. CLEMENTE et al [12] investigated scroll expanders derived from the Renewable energies have attracted much more in the heating, ventilation and air- attention as a result of the shortage of the global energy, conditioning (HVAC) field to recover heat from an such as solar energy [1], [2], the internal engine. WANG et al [13] proposed a [3], ocean thermal energy [4], and wind novel system combining a dual loop ORC with a energy. Among them, the heat-work conversion for low- gasoline engine. LI et al [14] investigated the low and medium-temperature heat source is the most temperature solar thermal electric generation with ORC. frequently studied. Especially, the organic Rankine cycle MAVROU et al [15] proposed a systematic sensitivity (ORC) has attracted much attention due to its simple analysis procedure explicitly considering the impacts of cycle configuration, high reliability and flexibility, and working fluid and ORC design/operating decisions on convenient maintenance in the past few decades [5–8]. the ability of the ORC to operate under conditions Whereas, the thermal efficiency is low, only 8%–12% [9], different from its nominal design settings to select but the economic benefit is poor. working fluid mixtures in view of operating variability in According to the research in recent years, in order solar organic ranking cycles (ORC). HE et al [16] to improve the utilization of the heat source, the proposed a combined ORC system utilizing exhaust optimization of the ORC system has been mostly focused waste as its heat source and liquid natural (LNG) as on, such as the minimization of the system irreversibility its heat sink to provide alternative power for an LNG- loss and the choice of the working fluids. MAGO et al fired vehicle and examined five working fluids at various [10] did an analysis about the destruction and working conditions, and they found that R236fa has the obtained that the exergy destruction in evaporator is highest thermal efficiency. WU et al [17] presented the about 77%, much higher than other cycle configuration. performance of ORC using hot air as heat resource using ZHU et al [11] analyzed the plate heat exchangers (PHE) zeotropic mixture fluids R227ea/R245fa, Butane/R245fa in evaporator and found that by optimizing its design, the and RC318/R245fa as the working fluids. The result

Foundation item: Project(51406130) supported by the National Natural Science Foundation of China Received date: 2016−02−29; Accepted date: 2016−05−17 Corresponding author: LI Tai-lu, Lecturer, PhD; Tel: +86–22–28305107; E-mail: [email protected] 2830 J. Cent. South Univ. (2017) 24: 2829–2841 indicates that better thermal performance can be such as corrosive, toxic, flammable and environmental achieved when the temperature difference of cooling harmful. So the mixed working fluids are a way to solve is near the temperature glide of zeotropic mixture the issues. For example, some hydrocarbons have a very in the condenser. DESAI et al [18] did a thermo- good power performance, but flammable is a problem for economic analysis and selection of working fluid for hydrocarbons working fluids. Therefore, adding a certain solar ORC. proportion of the working fluid which has excellent There are also some scholars focus on the performance and flame retardant, can realize safe and components change of the ORC system for the power efficient application of the working fluids. output and economy of the system, such as the PAPADOPOULOS et al [35] presented that the selection regenerative organic Rankine cycle (RORC), the parallel of the working fluids significantly limited the double-evaporator organic Rankine cycle (PDORC), the opportunities of identifying highly performing options. two-stage series organic Rankine cycle (TSORC) and so CHEN et al [36] indicated that zeotropic mixtures had a on. MAGO et al [19], XI et al [20], PEI et al [21], higher efficiency. LAKEW et al [37] found that the FERNÁNDEZ et al [22], and ROY et al [23] analyzed power output of the R227ea is highest for the heat source RORC and found that the supercritical RORC is temperature range from 80 °C to 160 °C, and the R245fa preferable for high temperatures heat source. The internal gave the highest power output when the temperature is the main factor to system efficiency. LI ranges from 160 °C to 200 °C. PASETTI et al [38] et al [24] proposed and compared PDORC with the ORC presented an improved survey method for the evaluation to show that the irreversible loss of the PDORC is lower of the thermal stability of working fluids for ORCs. LI than that of the ORC. BORSUKIEWICZ-GOZDUR et al et al [39] proposed a novel combined cooling, heating [25] tried to increase the working fluid flow rate as a and power organic Rankine cycle (CCHP-ORC) system kind of method to enhance the power output of installed with heat to select optimal zeotropic geothermal power plant. LI et al [26] constructed and mixtures and determined the component concentration experimentally analyzed the RORC and found that the that gives a better performance. The results showed that thermal load of the condenser and the irreversible loss R141b/R134a, R141b/R152a and R123/152a have a reduced at the same time. Moreover, the thermal higher COP and exergy efficiency than others. efficiency of the RORC is higher than that of the ORC MAVROU et al [40] investigated the performance of by 1.83%. working fluid mixtures for use in solar ORC with heat Besides the cycle parameters and the cycle storage employing flat plate collectors (FPC) configuration, the working fluid has an important and assessed the impact of heat source variability on the influence on the system performance. BADR et al [27] ORC performance for different working fluid mixtures, investigated thermodynamic and thermophysical and a mixture of neopentane-2-fluoromethoxy-2- properties of organic working fluids. HUNG et al [28] methylpropane at 70% neopentane was the most efficient used , benzene, R11, R12, R134a and R113 as in all the considered criteria simultaneously. Besides the the working fluid, respectively, and compared the mentioned above, many factors should be considered for efficiencies of ORCs with each working fluid. SALEH the working fluid choice, such as specific volume, low et al [29] gave a thermodynamic screening of 31 pure , global warming potential (GWP), ozone component working fluids for ORCs, the largest amount depletion potential (ODP), high latent heat of of heat can be transferred to a supercritical fluid and the vaporization, high thermal conductivity and a stable least to a high-boiling subcritical fluid. Based on the first operating pressure. It should be pointed out that a large and second laws of the thermodynamics, YARI [30, 31] number of researchers have focused on the heat-work investigated several dry fluids for ORC, and DESAI et al conversion for low- and medium-grade sensible heat, and [32] presented that the dry fluids were the better working few literatures have been found to discuss the working fluid for ORC utilizing low-grade heat sources. Also, the fluid selection of ORC driven by low- and medium-grade wet fluids were investigated by HUNG et al [33], latent vapor resource resources. showing that the wet fluids with very steep saturated In this work, the saturated vapor was adopted as the vapor curves in the T–s diagram for the -series heat source, which has the latent and sensible heat at the and benzene-series fluids had a higher overall same time, and eleven kinds of working fluids was performance in energy conversion efficiencies than that chosen for comparison. Based on the first and second of dry fluids. LIU et al [34] presented that the thermal laws of thermodynamics, the parameters, such as power efficiency and the total heat recovery efficiency were output, irreversible loss, total thermal conductance, different for various working fluids. exergetic efficiency, and thermal efficiency were For the pure working fluids, their thermodynamic optimized. The ORC with each working fluid was properties may be the issues in engineering applications, identified based on the cycle performance.

J. Cent. South Univ. (2017) 24: 2829–2841 2831

2 System descriptions

Figure 1 shows the system flow chart of the ORC, which can be categorized in three loop circuits according to the working media: the heat source, the working fluid, and the heat sink. As shown in Fig. 1, it can be got that the ORC is made of an evaporator, a turbine, a generator, a condenser, a , a hot water pump, a cooling water pump, and a cooling tower. Fig. 2 T–s schematic diagram of an ORC system

thermodynamics, the energetic and exergetic analysis were carried out for the working fluid researched. For simplicity, the following hypotheses are made: 1) The saturated vapor is supplied in a steady-state condition, at a heat source of 130 °C; 2) Superheated vapor is considered at the evaporator outlet, with a degree of superheat of 5 K. Supercooled liquid is considered at the condenser exit, with a degree of superheat of 5 K; 3) The kinetic and potential energy changes are negligible; 4) Pressure drops throughout the evaporator, the condenser and the pipelines are negligible;

Fig. 1 Schematic diagram of an ORC system 5) The temperature and friction losses are negligible. The heat source is saturated vapor, which comes The mathematical model for ORC is expressed by from metallurgical plant and steel mills. Compared with the following equations: Turbine: geothermal water, there is the latent heat of saturated vapor, which is far greater than the sensible heat under ηt  (h1  h2 ) (h1  h2s ) (1) the condition of unit mass. When the saturated vapor where η and h denote the efficiency and enthalpy, releases heat and flows out of evaporator in the form of respectively; the subscripts t and s represent the turbine water, it can be used in other aspects. and , respectively. The saturated vapor first flows into the evaporator to transfer heat to the working fluid to generate Wt  ηt mwf (h1  h2s )  mwf (h1  h2 ) (2) high-pressure vapor (Figs. 1 and 2, state 1), and it is msv (hsv,in  hsv,2 ) released into the atmosphere. The working fluid absorbs mwf  (3) h1  h4' the heat from the saturated vapor to generate high- pressure in the evaporator, then the vapor flows into the where W and mwf stand for the power output and the turbine and its enthalpy is converted into shaft work to mass flow rate, respectively; the subscript wf means the drive the generator. The vapor existed from the turbine working fluid. (Figs. 1 and 2, state 2) is led to the condenser where it is I t  T0mwf (s2  s1) (4) liquefied by cooling water. The liquid available at the condenser outlet (Figs. 1 and 2, state 3) is pressurized by where I and s represent the irreversible loss and the the pump and flow into the evaporator (Figs. 1 and 2, , respectively; T0 stands for the environment state 4). The ORC can be identified as 1→2→3→4, temperature. shown by black lines. The cooling water goes into the Condenser: condenser driven by the cooling water pump. Then a new Figure 3 shows the T–q diagram of the heat transfer cycle begins. The T–s diagram is shown in Fig. 2. process in the condenser. Clearly, as presented in Fig. 3,

it can be seen that the processes of T2→T2′→T2″→T3 and

3 Modeling Tcw,in→Tcw,1→Tcw,2→Tcw,out represent the temperature variations of the working fluid and the cooling water in Based on the first and second laws of the condenser, respectively. There are superheated vapor

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water pump, Pcw is the pressure loss in the cooling water

circuit and ρcw represents the density for the cooling water; subscripts cw and p stand for the cooling water and the pump, respectively.

p  (h4s  h3 ) (h4  h3 ) (16)

mwf ( pe  pc ) Wp  (17) p wf

I p  T0mwf (s4  s3 ) (18) Fig. 3 T–q diagram for heat transfer in condenser where h4s is specific enthalpy at the pump outlet of the working fluid at the condenser inlet and experiencing an isentropic process. super-cooled fluid at the condenser outlet. The process in Figure 4 shows the temperature difference variation condenser is composed of three parts: super-cooling, between saturated vapor and working fluid in the condensing and pre-cooling, which separately evaporator versus the heat transfer rate q, T–q diagram. represented by I, II and III. Tcw,1 and Tcw,2 are the From Fig. 4, it can be evidently seen that the processes of temperature of cooling water leaving and entering the T4→T4′→T4″→T1 and Tsv,in→Tsv,1→Tsv,2→Tsv,out represent condensing part. the temperature variations of the working fluid and the

saturated vapor in the evaporator, respectively. There are Qc,  mwf (h2''  h3 ) (5) superheated vapor of the working fluid at the condenser Qc,  mwf (h2'  h2'') (6) inlet and super-cooled fluid at the condenser outlet. With condenser, the evaporator also can be divided into three Qc,  mwf (h2  h2' ) (7) sections: preheating, evaporating and vapor superheating Qc  Qc,Ι  Qc,  Qc,ΙΙΙ  mwf (h2  h3 ) (8) sections; which are represented by I, II and III. Tsv,1 and Tsv,2 represent the temperatures of saturated vapor where Q denotes the thermal load; the subscripts c and I, leaving and entering the evaporating section. II, III stand for the three sections of condenser shown in Fig. 3.

Qc, (KA)c,  (9) Tc,

Qc, (KA)c,  (10) Tc,

Qc,ΙΙΙ (KA)c,ΙΙΙ  (11) Tc,ΙΙΙ

(KA)c,total  (KA)c,Ι  (KA)c,ΙΙ  (KA)c,ΙΙΙ (12) Fig. 4 T–q diagram for heat transfer in evaporator where (KA)c,I, (KA)c,II and (KA)c,III are the thermal conductance of sections I, II and III of condenser, Qe,Ι  mwf (h4'  h4 ) (19) respectively; K , A and ∆T stand for the heat transfer Qc,  mwf (h4''  h4' ) (20) coefficient, the heat transfer area, and the logarithm mean temperature difference, respectively. Qc,  mwf (h1  h4'' ) (21)

Ic  T0[mwf (s3  s2 )  mcw (scw,in  scw,out )]Wp,cw Qe  Qe,Ι  Qe,  Qe,ΙΙΙ  mwf (h1  h4 ) (22)

(13) where the subscripts 1 and 4 stand for the outlet and inlet mcw Pcw of the working fluid at evaporator. Wp,cw  (14) p,cw cw Q (KA)  e, (23) e, T mwf (h2  h3 ) e, mcw  (15) cTcw Qe, (KA)e,  (24) where Wp,cw means the power consumption of the cooling Te,

J. Cent. South Univ. (2017) 24: 2829–2841 2833 Q e,ΙΙΙ is: (KA)e,ΙΙΙ  (25) Te,ΙΙΙ Q0  Csv (Tsv,in Tsv,out )  Ccw (Tcw,in T0 ) Wnet (33)

(KA)  (KA)  (KA)  (KA) (26) where Csv and Ccw are the heat capacities of the saturated e,total e,Ι e,ΙΙ e,ΙΙΙ vapor and the cooling water, respectively. where (KA) , (KA) and (KA) are the thermal e,I e,II e,III The volumetric flow rate (VFR, R ) is given as: conductance of Sections I, II and III of evaporator, vf respectively. Rvf  v2 v1 (34)

Ie  T0[mwf (s1  s4 )  msv (ssv,in  ssv,out )]Wp,sv (27) where v1 and v2 stand for the volumetric flow rate of the inlet and outlet at the turbine, respectively. msv Psv Thermal efficiency: Wp,sv  (28) p,sv sv   W Q (35) th net e where Wp,sv, psv, ηp,sv and ρsv are the power consumption The exergy for saturated vapor at inlet and outlet of of saturated vapor pump, the pressure provided by the the evaporator can be expressed as saturated vapor pump, the efficiency of the saturated msv (hsv,in  hsv,out )  mwf (h1  h4 ) (36) vapor pump, and the density for the saturated vapor; the subscripts sv, in and out represent the saturated vapor, the where hsv,in and hsv,out denote the enthalpy of the saturated inlet and outlet of the evaporator for saturated vapor, vapor at the evaporator inlet and outlet. respectively. Total irreversibility: EX sv  msv[(hsv,in  hsv,out ) T0 (ssv,in  ssv,out )] (37)

I  I  I  I  I Exergetic efficiency: total t c p e  Wp,cw Wp,sv T0[mcw (scw,in  scw,out )  ex  Wnet EX sv (38)

msv (ssv,in  ssv,out )] (29) where EX is the exergy input into the cycle provided by sv The total thermal conductance of heat exchangers: saturated vapor.

(KA)total  (KA)c  (KA)e (30) 4 Results and discussion

sg,total  st  sc  sp  se In this work, eleven kinds of pure working fluids  msv (ssv,out  ssv,in )  mcw (scw,out  scw,in ) (31) were used in the subcritical ORC based saturated vapor Net power output: as an example for low- and medium-grade heat source,

and the main physical properties of the working fluids Wnet mgWt Wp Wp,sv Wp,cw (32) are shown in Table 2. Table 3 shows the system where ηm and ηg are the mechanical efficiency and the parameters and ambient conditions used in this work, efficiency of the generator. which is obtained from an existed practical ORC system.

The heat flow rate released to the environment Q0 From Table 2, it can be seen that the GWP of

Table 2 Thermodynamic properties of working fluids Physical data Environmental data Substance Ref. –1 2 M/(g·mol ) Tb/°C Tcri/°C Pcri/MPa ALT/a ODP GWP/10 a R245fa 134.05 14.90 154.05 3.640 7.6 0 1030 [39] R123 152.93 27.82 183.68 3.662 1.3 0.02 77 [40] R141b 116.95 32.05 206.81 4.460 9.3 0.12 725 [41] RC318 200.05 –6.0 115.2 2.78 3200 0 10250 [42] Isobutane 58.12 –11.7 134.7 3.63 0.019 0 ～20 [43] Isopentane 72.15 27.8 187.2 3.38 0.01 0 ～20 [44] n-pentane 72.15 36.1 196.6 3.37 0.01 0 ～20 [44] n-hexane 86.175 68.71 234.67 3.034 — — — [45] n-heptane 100.2 98.38 266.98 2.736 — — — [45] n-decane 142.28 174.12 344.55 2.103 — — — [45] Cyclohexane 84.161 80.736 280.49 4.075 — — — [45]

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Table 3 Data used to simplify calculation in this work Parameter Value Inlet temperature of saturated vapor/°C 130 Inlet temperature of cooling water/°C 25 Outlet temperature of cooling water/°C 30 Pinch point temperature difference/°C 5 Turbine inlet superheated degree/°C 5 Efficiency of feed pump/% 60 Efficiency of hot water pump/% 75 Efficiency of cooling water pump/% 75 Efficiency of turbine/% 75 Efficiency of mechanical/% 96 Fig. 5 Variation of mass flow rate of different working fluids versus evaporating temperature Efficiency of generator/% 95

Environment temperature/°C 20 n-hexane, n-heptane and n-decane are almost the same

Environment pressure/MPa 0.101325 line. From big to small, the total order is mRC318, mR123,

mR245fa, mR141b, misobutane, misopentane, mn-pentane, mn-hexane, working fluid RC318 is 10250, much bigger than other mn-heptane, mn-decane and mcyclohexane in turn. working fluids, which means RC318 has a stronger influence on greenhouse effect. Also the ALT of RC318 4.2 Net power output reaches the maximum value of all working fluid, which Figure 6 demonstrates the variation of the net power represents that it is a long time for RC318 to exist in the output of different working fluids versus the evaporating natural environment without being damaged or break temperature. As shown in Fig. 6, the net power output down. Among the working fluids, the alkanes, including first increases and reaches its maximum, and then isobutane, isopentane, n-pentane, n-hexane, n-pentane, decreases with the increment of the evaporating n-decane and cyclohexane, have the flammable temperature, which applies to all the working fluids. It characteristics. It should be known that the type changing also can be seen that the Wnet corresponding to Te,turning is of the turbine usually leads to the variation of expansion the optimal Wnet for each working fluid, so Te,turning can be efficiency. To simplify the calculation, it is assumed that regarded as the Te,opt. In essence, the two parameters can the isentropic efficiency of the turbine is unchanged. And be deemed as one. From Eq. (32), the net power output, the mass flow rate of saturated vapor is 1 kg/s. Wnet, is proportional to Wt, which is due to that the values

of the power consumptions, Wp, Whp and Wcp, are

4.1 Mass flow rate of working fluids relatively much smaller compared with Wt. The Figure 5 shows the variation of the mass flow rate maximum net power output is 20.67 kW for RC318 of the different working fluids versus the evaporating when the evaporating temperature comes to 38℃, while temperature. It can be seen that the variation trends of the cyclohexane keeps the minimum net power output at mass flow rate of all working fluids are the same. A rise the same evaporating temperature. For net power output, in evaporating temperature decreases the mass flow rate. Based on the law of energy conservation, the mass flow rate is directly inversely proportional to the enthalpy difference of the working fluid between the inlet and outlet of the evaporator with the heat and cold source remaining steady. And the increase of the evaporating temperature decreases the enthalpy of the evaporate outlet, therefore leading to a drop in the mass flow rate of the working fluids. The mass flow rate of RC318 ranges from 2.607 kg/s to 1.982 kg/s with the evaporating temperature change from 75 °C to 95 °C, and the mass flow rate of cyclohexane ranges from 0.5742 kg/s to 0.3592 kg/s, which are the maximum and minimum values at the same evaporating temperature, Fig. 6 Variation of net power output of different working fluids respectively. The variation curves of the n-pentane, versus evaporating temperature

J. Cent. South Univ. (2017) 24: 2829–2841 2835 the performance of the working fluids decreases in the order: RC318, R245fa, isobutane, R123, isopentane, n-pentane, R141b, n-hexane, n-heptane, n-decane and cyclohexane. From the cost of turbine, it can be obtained that a larger mwf will increase the thickness of the wall of turbine, so the cost of turbine will increase. The saturated vapor outlet temperature versus the evaporating temperature for various working fluids is presented in Fig. 7. As shown, the rise of Tsv,out is proportional with Te, and the change rate of Tsv,out to Te is almost the same for all working fluids. The Tsv,out of the RC318 is always lesser than other working fluids at the same evaporating temperature, and it ranges from 42.98 °C for Te=75 °C to 59.31 °C for Te=95 °C, whereas Fig. 8 Influence of evaporating temperature on irreversibility of the Tsv,out of the cyclohexane is greater than the left system for various working fluids working fluids in the same situation, and the range of variation is from 65.93 °C for Te=75 °C to 87.38 °C for changing curve of In-hexane, In-pentane, In-heptane and In-decane is Te=95 °C. The differences between the Tsv,out of alkanes, almost coincident. Combined with Fig. 7, it can be like n-pentane, n-heptane, n-hexane and n-decane, are in obtained that with the heat that working fluids absorbed a small range. In this work, the heat source is saturated from heat source reducing, the irreversible loss of the vapor, which means that there are latent heat and sensible system decreases together. heat existing in the process of heat transfer. From Figure 9 illustrates the entropy generation of the Eq. (22), it can be obtained that with the inlet system with the evaporating temperature for various temperature of the evaporate fixed, the increase of the working fluids. The entropy generation Sg is composed tsv,out decreases the quantity of heat transferred from the of the system Sg,c, Sg,e, Sg,p and Sg,t, in which subscripts c, heat source. e, p and t represent condenser, evaporator, pump and turbine, respectively. Among them, the entropy generation caused by evaporate is greater than other system components for each working fluid. As shown in Fig. 9, the entropy generation of RC318 is the biggest of

all working fluids, whereas Sg,cyclohexane is minimum under

the same te, from 0.1048 kJ/K to 0.08785 kJ/K and 0.08599 kJ/K to 0.05431 kJ/K, respectively. From

Eq. (31), it can be obtained that Sg is related with the mass flow rate of saturated vapor and cooling water and the entropy difference of saturated vapor and cooling water in the inlet and outlet of evaporator and condenser, respectively. Whereas m , S , S and S are sv gw,in cw,out cw,in Fig. 7 Saturated vapor outlet temperature versus evaporating unchanged, so the variation of Sg depends on mcw and temperature for various working fluids

4.3 Irreversible loss Figure 8 demonstrates the influence of the evaporating temperature on the irreversibility of the system for various working fluids. The irreversible loss of the system contains the irreversible loss caused by condenser, evaporator, pump and turbine, respectively. It can be seen from Fig. 8 that the irreversible loss of the system decreases with the increment of evaporating temperature. The irreversible loss of the system of RC318 is the largest in the 11 kinds of working fluids, which ranges from 35.23 kW to 29.39 kW. Whereas, the value Icyclohexane is the least value and its change range is Fig. 9 Entropy generation of system with evaporating from 28.53 kW to 18.16 kW. At the same time, the temperature for various working fluids

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Sgw,out. Combined Fig. 6, it can be obtained that the value constant and is different from each other for all working of mcw is much greater than msv (msv=1 kg/s), and the fluids. From Eq. (12), it can be obtained that KAc is mass flow rate of cooling water plays a decisive role. So proportional to the thermal load in condenser, and is the variation trend of Sg is consistent with that of mcw. inversely proportional to the log mean temperature difference in condenser. From Fig. 3, the rising of Tsv,out

4.4 Mass flow rate of cooling water decreases the thermal load in evaporator, so Qc will also

The variation of the mass flow rate of the cooling diminish as Qe, moreover, ∆Tc is proportional to Te. water versus the evaporating temperature for various fluids is shown in Fig. 10. Evidently, as shown in Fig. 10, the mass flow rate of the cooling water is gradually reduced with the increase of evaporating temperature.

The value of mcw,RC318 is greater than other medium, and its variation range is from 16.2 kg/s to 12.93 kg/s with Te rises from 75 °C to 95 °C, while mcyclohexane varying from 11.71 kg/s to 7.562 kg /s, which is less than other working fluids. From Eq. (15), it can be obtained that mcw is proportional to mwf and the difference between h2 and h3, and it is inversely proportional to c and Tcw. On account of the value of h5, c and Tcw are fixed, so just mwf and h2 are taken in account. Combined with Fig. 5, as Te increases, the mass flow rate of working fluids, mwf, Fig. 11 Thermal conductance of condenser versus evaporating decreases. Whereas the enthalpy of condenser inlet, h2, temperature for different working fluids increases with Te. But the absolute value of mwf to Te is greater than the value of h2 to Te, so the rising in Te leads Figure 12 illustrates the thermal conductance of to the decreasing of mcw. evaporator versus the evaporating temperature for different working fluids. Apparently, it can be got from

Fig. 12 that the maximum value of KAe appeared when

the working fluid is RC318; the minimum value of KAe occurred when cyclohexane was used as working fluid, whereas the shape of the curve is different for different working fluids. The change trend of RC318 first

increases when KAe,RC318 reaches the maximum value

22.44 kW/°C for Te=80 °C, and then decreases with the

increment of Te like a straight line; each change rate of the rest curves in Fig. 8 can be approximately regarded

as constant. From Eq. (26), it can be obtained that KAe is determined by the thermal load in evaporator and the log mean temperature difference in the evaporator. The rising Fig. 10 Variation of mass flow rate of cooling water versus of the Te results in the decrease of the log mean evaporating temperature for various fluids

4.5 Thermal conductance Figure 11 illustrates the thermal conductance of condenser versus the evaporating temperature for different working fluids. Clearly, as presented in Fig. 11, the thermal conductance of condenser decreases with the rising of evaporating temperature for each working fluid.

In all the working fluids, KAc,RC318 is the biggest, which ranges from 178 kW/°C to 128.8 kW/°C; whereas

KAc,n-decane is the smallest, the variation range of which is 136.9 kW/°C to 77.92 kW/°C. By calculating, the change rate of the gap between the working fluids, which is adjacent to each other in Fig. 7, is not very big. The Fig. 12 Thermal conductance of evaporator versus evaporating value of KAc to Te can be approximately regarded as temperature for different working fluids

J. Cent. South Univ. (2017) 24: 2829–2841 2837 temperature difference in the evaporator and the thermal efficiency. From the point of economic, INVERNIZZI load of the evaporator. For RC318, when Te<80 °C, the et al [47] presented that in order to achieve a turbine change rate of ∆T to Te is greater than that when efficiency higher than 80%, the VFR should be lower

Te>80 °C. The variation range of KAe,RC318 is from 22.17 than 50. So the maximum and minimum of the turbine kW/°C to 20.72 kW/°C, and the variation range of efficiency are isobutane and n-decane, respectively. But,

KAe,cyclohexane is from 13.08 kW/°C to 10.28 kW/°C. for all working fluids, the turbine efficiency is higher Figure 13 illustrates the total thermal conductance than 80%. Moreover, it can be got that the length of the of system versus the evaporating temperature for turbine will increase with the increase of the VFR, then different working fluids. Clearly, as presented in Fig. 13, the cost of turbine will also increase. The variation range

KA decreases with the increase of Te, and the change of VFRn-decane is from 12.02 for Te=75 °C to 28.66 for trend of KA is semblable with KAc for all working fluids. Te=95 °C, meanwhile the variation range of VFRisobutene is

From Eq. (30), KA is got by KAc and KAe. It can be from 3.198 for Te=75 °C to 5.121 Te=95 °C. clearly obtained from Figs. 11 and 12 that KAc is much greater than KAe because of the smaller temperature difference in the condenser. So KAc is the key factor which determines the variation trend of KA, and that is the reason why KA and KAc show the similar change rules for every working fluid. Put Figs. 7–9 together, it can be seen that Qc and Qe are both reduced as the Tsv,out increases, and the total KA also decreases with the change of Qc and Qe. The maximum value, KARC318, ranges from 200.2 kW/°C to 149.5 kW/°C, whereas the minimum value, KAn-decane, ranges from 151 kW/°C to 88.78 kW/°C.

Fig. 14 Variation of volumetric flow rate versus evaporating temperature for different working fluids

4.7 Figure of merit Figure 15 shows the variation of the figure of merit

(FOM, Fom) versus the evaporating temperature for different working fluids. The concept of FOM is put forward by MIKIELEWICZ [48], FOM is treated as an important index to evaluate the merits of the working fluids, which is expressed as follows:

0.8 0.1 Tc FJom a  (39) Te Fig. 13 Total thermal conductance of system versus evaporating temperature for different working fluids where Ja is the ratio of cp,e and re, cp,e and re are the

4.6 Volumetric flow rate Figure 14 shows the variation of the volumetric flow rate versus the evaporating temperature for different working fluids. Obviously, as presented in Fig. 14, it can be obtained that the VFR of the n-decane is higher than that of other working fluids, and the VFR of the isobutene is lower than that of the rest working fluids. It also can be known that the system condensing pressure can be regarded as a constant due to the environment condition is unchanged. So Te is the only factor affecting the size of VFR: VFR is proportional to Te. From MACCHI et al [46], there exists an inversely proportional relationship between VFR and turbine Fig. 15 Variation of figure of merit versus evaporating efficiency: lower values of VFR deliver higher turbine temperature for different working fluids

2838 J. Cent. South Univ. (2017) 24: 2829–2841 sensible heat and the latent heat of vaporization of isobutane ranges from 0.5641 for Te=75 °C to 0.4811 for working fluids, respectively. Te=95 °C. The change trend of FOM decreases with the

As shown in Fig. 15, the FOMs of all working increase of Te. According to Ref. [20], a higher value of fluids have the consistent trends which decrease with the SP results in higher turbine efficiency. Then combined increases of te. Among them, FOMisobutane is obviously Fig. 12 and Eq. (40), it can be obtained that the enthalpy higher than that for other working fluids, and FOMR141b difference of inlet and outlet increases with increasing Te; is evidently lower than that for the left working fluids. So at the same time, the mass flow rate of working fluids the performance of the isobutane is excellent than that of increases also. That is the reason why SP becomes others. FOMisobutane ranges from 0.5641 to 0.4811 and smaller with the increase of Te. From the point view of

FOMR141b ranges from 0.5305 to 0.4433, when Te economic, a higher SP will increase the size of turbine, increases from 75 °C to 95 °C. From Eq. (39), it can be so the cost of turbine will also increase. seen that FOM is directly proportional to the sensible heat of the working fluid (cp,e), and is inversely 4.9 System efficiency proportional to the evaporating temperature (Te) and the Figures 17 and 18 show the exergetic efficiency and latent heat of the working fluid (re). Combined Figs. 11, thermal efficiency of system versus the evaporating 13 and 14, there is a rule that FOM is inversely temperature for different working fluids. Evidently, it can proportional to thermal efficiency and exergy efficiency. be seen from Figs. 17 and 18 that ηex and ηth are

proportional to Te for all working fluids. Whereas the

4.8 Size parameter ratio of ηex to Te is not consistent and it becomes smaller As the analysis of working fluids is described from and smaller, but the variation trend is almost unchanged. the point of thermodynamics, the size parameter (SP, Ps) From Eq. (38), it can be seen that ηex is determined by is brought up to measure the turbine efficiency for the Wnet and the exergy at the inlet and outlet of the different working fluids. The parameter SP is defined by evaporator for saturated vapor. From Fig. 7, increasing MACCHI et al [46] as follows: T will result in increasing T , and the difference e sv,out

Vout Ps  (40) 4 mhhwf() 1 2s where Vout stands for volume flow rate of the working fluids at the outlet of the turbine, and h2s is specific enthalpy at the turbine outlet experiencing an isentropic process. Figure 16 shows the variation of the size parameters versus the evaporating temperature for different working fluids. As presented in Fig. 16, it can be clearly seen that

SPn-decane is significantly higher than the values of other working fluids, and SPisobutane is lower than that of other working fluids. The value of n-decane changes from Fig. 17 Exergetic efficiency of system versus evaporating

2.899 for Te=75 °C to 2.408 for Te=95 °C, and the SP of temperature for different working fluids

Fig. 16 Variation of size parameters versus evaporating Fig. 18 Thermal efficiency of system versus evaporating temperature for different working fluids temperature for different working fluids

J. Cent. South Univ. (2017) 24: 2829–2841 2839

Table 1 Validation of numerical model with previous published data [29] for various fluids-based ORC 3 –1 Substance T1/°C T3/°C Pe/MPa Pc/MPa V1/(m ·s ) VFR ηth/% Ref. 40.06 30.00 2.000 1.564 2.878 1.270 2.32 [29] R245fa 40.06 30.00 2.000 1.564 2.834 1.360 2.35 Present work 57.14 30.00 2.000 1.079 1.063 1.667 5.91 [29] R123 57.14 30.00 2.000 1.079 1.049 1.764 5.81 Present work 67.75 30.00 2.000 0.772 0.656 2.357 7.74 [29] R141b 67.75 30.00 2.000 0.772 0.639 2.483 7.48 Present work

between EXsv,in and EXsv,out will reduce with the increase important parameter of the ORC, and the optimal of Tsv,out. From Fig. 6, it can be known that Wnet first evaporating temperature will minimize the irreversible increases and then decreases. That is the reason why the loss and the entropy generation and is different with the variation trends do not keep consistent. For all working working fluid, so it should be optimized to obtain the fluids, the maximal value of the ηex is ηex,cyclohexane, which optimal system performance, especially for the low- and ranges from 32.37% for Te=75 °C to 39.51% for Te= medium-grade heat sources. 95 °C. On the contrary, the ηex,RC318 is the minimum 2) RC318 shows the highest net power output as a value and its range is from 28.75% for Te=75 °C to result of the lowest outlet temperature of the heat source, 33.37% for Te=95 °C. so the corresponding system efficiency is the lowest. From Eq. (37), it can be got that ηth relies on Wnet, Moreover, the high GWP value also limits the utilization mwf and the enthalpy at the inlet and outlet of the of RC318. evaporator for saturated vapor. For all working fluids, the 3) The n-decane has the lowest total thermal maximal value of ηth is ηth,cyclohexane, which ranges from conductance, but its volumetric flow ratio and size 6.914% for Te=75 °C to 9.451% for Te=95 °C; on the parameter are too high to restrict its application. contrary, ηth,RC318 is the minimum value and its range is 4) The cyclohexane suggests the highest thermal from 5.317% at Te=75 °C to 6.856% at Te=95 °C. and exergetic efficiencies, and it shows outstanding From the above analysis, it can be obtained that the overall performances and can be used in engineering evaporating temperature is the most key parameter for applications. the system performance of the ORC and should be The cycle parameters and the working fluid optimized in engineering applications. Furthermore, the selection are the two main aspects that should be optimal working fluid differs with one evaluation index considered for the actual ORC plants, and the system to another. Overall, the cyclohexane has excellent performance must be optimized based on the temperature comprehensive performance. level of the heat source and heat sink.

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Cite this article as: XU Peng, LU Jian, LI Tai-lu, ZHU Jia-ling. Thermodynamic optimization and fluid selection of organic Rankine cycle driven by a latent heat source [J]. Journal of Central South University, 2017, 24(12): 2829–2841. DOI: https://doi.org/10.1007/s11771-017-3698-z.