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Energy Conversion and Management 88 (2014) 267–276

Contents lists available at ScienceDirect

Energy Conversion and Management

journal homepage: www.elsevier.com/locate/enconman

Applicability of entropy, entransy and exergy analyses to the optimization of the Organic Rankine Cycle

Yadong Zhu a, Zhe Hu b, Yaodong Zhou a, Liang Jiang a, Lijun Yu a,?

a b

Institute of Thermal Energy Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Sino-US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai 200030, China

a r t i c l e

i n f o

a b s t r a c t

Based on the theories of entropy, entransy and exergy, the concepts of entropy generation rate, revised entropy generation number, exergy destruction rate, entransy loss rate, entransy dissipation rate and entransy ef?ciency are applied to the optimization of the Organic Rankine Cycle. Cycles operating on R123 and N-pentane have been compared in three common cases which are variable evaporation temperature, hot stream temperature and hot stream mass ?ow rate. The optimization goal is to produce maximum output power. Some numerical analyses and simulations are presented, and the results show that when both the hot and cold stream conditions are ?xed, all the entropy principle, the exergy theory, the entransy loss rate and the entransy ef?ciency are applicable to the optimization of the ORC, while entransy dissipation is not. This conclusion is available no matter what kind of working ?uid is used, nevertheless, the system performances and parameters may be much different. The results also indicate that when the hot stream condition (temperature or mass ?ow rate) varies, the entransy loss rate is the only parameter which always corresponds to the maximum power output. ? 2014 Elsevier Ltd. All rights reserved.

Article history: Received 7 May 2014 Accepted 31 July 2014 Available online 7 September 2014 Keywords: Entropy generation Entransy loss Exergy destruction Organic Rankine Cycle (ORC) Evaporation temperature Mass ?ow rate

1. Introduction Global energy demands escalating at a dramatic speed are contradict with global warming attributed to a large extent, to significant rise in the use of fossil fuels for electricity generation. However, it must be conceded that economic development and energy consumption are closely associated. Up to now over a half of the low or moderate temperature heat sources ($773.15 K), e.g. as solar energy, biomass energy, geothermal energy and waste heat are directly rejected to the environment. How to recovery these parts of low-grade heat attracts large attention for the purpose of energy conservation and thermal pollution reduction. Although heat recovery has huge potential and is around the corner, but the progresses of the technologies still require more research and development. Recovery system based on the ORC (Organic Rankine Cycle) [1–38] with heat input and power output reversing low-grade heat into high-grade electricity with its simplicity and commonly available components has been widely discussed in recent decades. Analyses [33–38] of the ORC are mainly around the ?rst and second law ef?ciency by thermodynamics. In this paper, we

? Corresponding author. Tel./fax: +86 21 3420 6287.

E-mail address: ljyu@sjtu.edu.cn (L. Yu). http://dx.doi.org/10.1016/j.enconman.2014.07.082 0196-8904/? 2014 Elsevier Ltd. All rights reserved.

distinctively consider the applications of some theories, such as entropy generation, exgergy destruction concepts and entransy theory. Entropy generation minimization is always related to the optimal output and minimized irreversibility since it stands for the ability loss of doing work. However, in recent years there are some different voices, the applicability of this theory is challenged. It was found not lead to the maximum system performance all the time unless the refrigeration capacity is prescribed [39,40]. The entransy theory [41–51] was proposed by Guo et al. [41] and developed for optimization design of thermal system and heat transfer. It is a quantity corresponds to the electrical potential energy in a capacitor, and now it is de?ned to describe the ‘‘potential energy of heat’’ in heat exchangers or heat-work conversion systems. It was also investigated to analyses of heat-work conversion processes by Cheng [42–46] as the ‘‘ability to release heat of the system’’. The results show that the increase in output power is corresponding to the increasing entransy loss. Yang et al. [47] applied the entransy theory and ?nite-time thermodynamics theory to research a two-heat-reservoir heat engine model with heat leakage, ?nite heat capacity high-temperature source and in?nite heat capacity low-temperature heat sink. Their results are classi?ed into three different cases. Wang et al. [48] extended the entransy theory to the steam power cycle and proved that it can serve as an approach of optimization. Zhou et al. [49] analyzed

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Nomenclature C c _d E e G* _ G dis _ G f _ G M _ m NRS h P _ Q _ S f _g S _ DS s T _ W heat capacity ?ow rate, kW/K speci?c heat capacity, kJ/(kg K) exergy destruction rate, kW speci?c exergy, kJ/kg entransy ef?ciency entransy dissipation rate, kW K heat entransy ?ow rate, kW K heat entransy loss rate, kW K molar mass, g/mol mass ?ow rate, kg/s revised entropy generation number speci?c enthalpy, kJ/kg Pressure, kPa heat exchange rate, kJ/s entropy ?ow rate, kW/K entropy generation rate, kW/K entropy change rate, kW/K speci?c entropy, kJ/(kg K) temperature, K power output, kW Subscripts 0 environment 1–16 state points of the cycle bp boiling point c cold stream cond condensation cr critical evap evaporation exp expansion fp fusing point H high temperature side h hot stream in ?ow into the system L low temperature side out ?ow out of the system pp pinch point pump working ?uid pump r working ?uid sub subcooling sup superheating total the total system

loss

and optimized Stirling cycle by taking the maximum output work as an objective, and discussed suitability of entransy loss, entransy dissipation, entropy generation, number of entropy generation, and improved number of entropy generation in optimization of system parameters, and the results showed that the consistency of entransy loss was better than others when it was applied to optimize the output power of Stirling cycle. However, the organic Rankine cycle is far different from the steam power cycle with working ?uids, heat stream temperature range and circulation way. For steam Rankine cycle, the suitable working ?uid is only water (wet ?uid), thus not many conditions need to be considered. However, for ORC, dry ?uids or adiabatic ?uids are used to generate. Beyond that, ORC is an approach to recovery the waste heat from the exhaust gas from steam Rankine cycle, therefore the gas inlet temperature of ORC is always lower that of steam Rankine cycle. Besides, steam Rankine cycle usually adopts steam turbine as power machine, however, ORC utilizes screw or scroll expander to replace the turbine. That means the ef?ciencies and ef?ciency correction factors of the power machines are different. Since there are many differences, whether the entransy theory can be applied to any ?uid and temperature range of ORC is need to be veri?ed. The applicability of the entransy theory to ORC still needs further discussions for lack of reports. Mago et al. [8] applied exergy destruction to ORC operating on R113, the result demonstrates that for the ORC the evaporator is the component with the highest exergy loss contribution (77%) followed by the expander with 21.4%. Moreover, he summarized that the total system exergy loss decreases with the evaporator pressure increase in the analyzed case. In this paper, R123 and N-pentane are chosen as working ?uids and compared by different indicators. The concepts of entransy loss and dissipation are applied to the analyses of the ORC. The relationship of the concepts of entropy generation, entransy loss, entransy dissipation, exergy destruction and the output power for ORC are derived and demonstrated under both ?xed and variable hot stream conditions. Different evaporation temperatures, hot stream inlet temperatures and mass ?ow rates are simulated so as to ?nd the variation tendency of the concepts mentioned above. The article ?rstly analyzed the Organic Rankine Cycle and introduced the difference with steam Rankine cycle in Section 2.

And then it expressed the formulas and the derivation processes of the evaluation indicators in Section 3. After that, in Section 4, the global model including hot and cold stream conditions, brief assumptions, and working ?uids properties is given. Finally, 3 typical cases have been taken into consideration to give a crosswise comparison in Section 5. Results prove that the entransy loss rate can be a method to optimize the output power of ORC in all the three cases, which gives us a train of thoughts that when designing the system operating condition, ?nding the maximum entransy loss rate is same to getting the maximum output power. However, other concepts which are widely used not are not suitable for all three cases.

2. Analyses of Organic Rankine Cycle Fig. 1 shows that the elementary con?guration of ORC system contains an evaporator, an expander, a condenser, a working ?uid pump and a cooling cycle. The evaporator and the condenser are both expressed as three-step models by Quoilin et al. [15] and Wei et al. [9]. The thermodynamic processes on the T–S diagram for the ideal ORC system corresponding to the numbers in Fig. 1 are illustrated in Fig. 2 where the tawny curve connecting points 4, 7, 8 and 3 is the saturation curve. The whole system is under equilibrium state and stable, without leakages, mechanical and heat losses. In the following, the quantities Ti, Pi, hi, and si denote the temperature, the pressure, the speci?c enthalpy and the spe_ i;j denote _ i;j and Q ci?c entropy at state point i and the quantities W the speci?c work and heat in the process from state point i to state point j. At state point 1, the working ?uid with pressure P1, temperature T1 = Tevap + Tsup is superheated vapor, then it enters the expander where it undergoes an expansion till it arrives at point 2 with pressure P2, temperature T2, s1 = s2. During the expansion, work _ 1;2 ? m _ r ?h1 ? h2 ? is delivered from the expander. At state point W 2 the working ?uid enters the condenser in which it returns isobarically to subcooled state point 5 by releasing the speci?c heat _ 2;5 to the cold stream. At state point 5 whose temperature and Q pressure are the lowest ones in the ORC, the working ?uid is subcooled liquid at T5 = Tcond ? Tsub and the corresponding vapor

Y. Zhu et al. / Energy Conversion and Management 88 (2014) 267–276

269

Expander 1

Generator

T 7 ? T 8 ? T ev ap T 3 ? T 4 ? T cond

?2? ?3? ?4? ?5?

Hot stream 9 2 16

T 11 ? T 7 ? T pp T 15 ? T 3 ? T pp

Tpp is the pinch point which is ?xed as 5 K in this paper. Through the isobaric lines, Eqs. (6) and (7) can be got

3 Evaporation Condensation 15

Superheating 10 8

Precooling

P6 ? P7 ? P8 ? P1 P5 ? P4 ? P3 ? P2

?6? ?7?

11

7 Preheating Subcooling

4

14

12

6

Pump

5

13 Cold stream

It is assumed that the speci?c heat of the hot stream as constant and the pressure of the hot stream equals the environment pres_ c and tempersure P9 = P0. When given the hot stream ?ow rate m ature Th,in = T9, the energy balance inside the evaporator can be listed as Eqs. (8) and (9).

_ r ?h1 ? h7 ? ? m _ h ?h9 ? h11 ? m _ r ?h1 ? h6 ? ? m _ h ?h9 ? h12 ? m

?8? ?9?

Fig. 1. Schematic diagram for the ORC system.

Thus, when a Tevap is given, we can get the mass ?ow rate of work_ r by Eq. (8) ing ?uid m

pressure is P5 = P2. By adiabatic compression to P6 = P1 which is the highest pressure in the ORC, the state point 6 reaches temperature _ 5;6 ? m _ r ?h6 ? h5 ?. T6, s5 = s6. The compression requires work W From point 6 the liquid ?ows isobarically through the evaporator till it arrives at its overheated temperature at point 1, which is the highest temperature in the ORC. As is known to all, as long as we got two of the four parameters Ti, Pi, hi, and si, of the state point, we can determine the other two. These thermodynamic calculations are carried out by using Engineering Equation Solver [52] Ver. 9. The total power regenerated can be given as Eq. (1)

_r?m _ h ?h9 ? h11 ?=?h1 ? h7 ? m

?10?

and hot stream outlet temperature Th,out = T12. Same analysis method in the condenser, it is assumed that the speci?c heat of the cold stream is constant and the pressure and inlet temperature of the cold stream equals those of the environment P13 = P0, Tc,in = T13 = T0. Meanwhile, the cold stream ?ow rate _ c is ?xed. The energy balances inside the condenser are as given m in Eqs. (11) and (12).

_ r ?h5 ? h3 ? ? m _ c ?h13 ? h15 ? m _ r ?h5 ? h2 ? ? m _ c ?h13 ? h16 ? m

?11? ?12?

_ ev ap ? Q _ cond _ ?W _ 1;2 ? W _ 5;6 ? Q W _ 6;7 ? Q _ 7 ;8 ? Q _ 8;1 ? ? ?Q _ 2;3 ? Q _ 3;4 ? Q _ 4;5 ? ? ?Q ? 1?

To combine Eqs. (3) and (5) with (7), the condensation temperature Tcond and pressure Pcond can be obtained. Hence, all the state points in the T–S diagram can be located. 3. Entropy, entransy and exergy analyses The whole system entropy balance equation is always expressed as

_ 6;7 ; Q _ 7;8 and Q _ 8;1 represent the preheating, evaporating and superQ _ 62;3 ; Q _ 3;4 and Q _ 4;5 represent the precooling, heating sections, whilst Q condensing and subcooling sections respectively. Some other constraints in the evaporation and condensation parts are given in Eqs. (2)–(5) below.

Fig. 2. T–S diagram for the ORC system.

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Y. Zhu et al. / Energy Conversion and Management 88 (2014) 267–276

_g ? S _ f ? DS _ S

?13?

To combine it with Eq. (17), we can get

_ g is the entropy generation rate, S _ f is the entropy ?ow rate where S _ is the entropy change rate with time. However, into the system, DS _ equals to zero when the system is steady state and thus S _ g can be DS changed as

_ loss ? 1 C h ?T h;in ? T 0 ?2 ? 1 C c ?T c;in ? T 0 ?2 ? WT _ 0 G 2 2

?23?

_ g ? ?S _f ? S _ f ;out ? S _ f ;in S Z Z

?14?

_ f ;out ; S _ f ;in are the entropy ?ow out of and into the system. where S

The entransy dissipation is also discussed in this paper for the system optimization, which equals to the difference between the entransy loss and the entransy variation (work entransy) due to heat-work conversion [43]. The total entransy dissipation rate of the ORC system includes three parts,

1 1 _ dis ? 1 C h T 2 ? T 2 Q ?T 6 ? T 7 ?? Q 7;8 T 8 ? Q 1;8 ?T 1 ? T 8 ? G h;in h;out ? 2 2 6;7 2 1 1 2 1 C c T c;out ? T 2 Q 4;5 ?T 4 ? T 5 ?? Q 3;4 T 4 ? Q 2;3 ?T 2 ? T 3 ? ? c;in ? 2 2 2 1 1 2 2 2 2 ? C h T h;out ? T 0 ? C c T c;out ? T 0 ??C h ?T h;out ? T 0 ?T 0 ? C c ?T c;out ? T 0 ?T 0 ? 2 2 ?24?

_ f ;in ? S

T h;in

T0

C h dT ? T

T c;in

T0

C c dT T h;in T c;in ? C h ln ? C c ln T T0 T0

?15?

_ _ f ;out ? Q 0 S T0

_ 0 is the heat ?ow released to the environment In Eq. (16) Q

?16?

_ 0 ? C h ?T h;in ? T 0 ? ? C c ?T c;in ? T 0 ? ? W _ Q

?17?

_ h , and Cc is Ch is the heat capacity ?ow rate of hot stream C h ? ch m _ c. that of the cold stream C c ? cc m Combining Eqs. (15)–(17) with Eq. (14) gives

_ _ g ? C h ln T 0 ? C c ln T 0 ? C h ?T h;in ? T 0 ? ? C c ?T c;in ? T 0 ? ? W S T0 T0 T h;in T c;in

?18?

The concept of entransy loss rate is de?ned by Cheng and Liang [43], which equals to the difference between entransy into and out of the system

the ?rst one is the entransy dissipation rates due to heat transfer between the hot stream and the working ?uid, which is braced as the ?rst part on the right side in Eq. (24). As the same principle goes, the second brace is the entransy dissipation rates resulted from heat transfer between the working ?uid and the cold stream. The last part in the third brace is the entransy dissipation rates caused by dumping the used streams into the environment. The concept of entransy ef?ciency, de?ned by Guo and Huai [53] when they analyzed the chemical heat pump, is also investigated.

G? ?

_ loss ? G _H ?G _L G _ H ? 1 Ch T 2 ? T 2 G h;in 0 2

?19?

Gf ;out GL ? Gf ;in GH

?25?

_ H is the entransy ?ows into the system, in ORC system, where G

In addition, the revised entropy generation number [44,54] is also considered,

?20?

_ g =Q _ out NRS ? T 0 S

?26?

_ L is the entransy ?ows out of the system which can be also G extended in ORC system as

_ L ? 1 Cc T 2 ? T 2 _ G 0 c;in ? Q 0 T 0 2

?21?

where the ?rst term on the right side is the net entransy ?ow rate taken in from the cold stream. The second term is the entransy loss rate due to the heat ?ow released into the environment. Based on Eqs. (20) and (21), Eq. (19) can be changed into

_ d is also utilized for the The concept of exergy destruction rate E system optimization. Exergy is a substitute of available energy (effective energy) in thermodynamics. Analysis of exergy as an energy conversion coef?cient considers not only the quantity, but also the quality of the energy, which can more profoundly reveal the essence of energy conversion and loss than energy analysis does. The exergy destruction rate in the evaporator

_ loss G

1 1 2 2 2 _ ? Ch T 2 h;in ? T 0 ? C c T c;in ? T 0 ? Q 0 T 0 2 2

_ d;ev ap ? m _ r ?e6 ? e1 ? ? m _ h ?e9 ? e12 ? E

The exergy destruction rate in the expander

?27?

?22?

Table 1 Basic thermodynamic and environmental properties of the working ?uids. Working ?uid R123 N-pentane tcr (°C) 183.7 196.5 Pcr (MPa) 3.668 3.364 tfp (°C) ?107.2 ?129.7 tbp (°C) 27.79 35.87 Safety B1 A3 ODP 0.012 0 GWP 120 11 M 152.9 72.15

Table 2 Assumptions for streams and components. Parameter The environment temperature Speci?c heat of the hot stream The temperature of the cold stream The ?ow rate of the cold stream Speci?c heat of the cold stream Degree of superheating Degree of subcooling Minimum heat transfer temperature difference in evaporator Minimum heat transfer temperature difference in condenser Sign T0 ch tc,i _c m cc Tsup Tsub DTevap DTcond Unit K kJ/(kg K) K kg/s kJ/(kg K) K K K K Value 288.15 1.025 288.15 1.8 4.184 5 3 5 5

Y. Zhu et al. / Energy Conversion and Management 88 (2014) 267–276

271

Fig. 3a. Variations of the evaluation parameters with evaporation temperature in the case of prescribed hot and cold streams for R123.

Fig. 4a. Variations of the evaluation parameters with hot stream inlet temperature at evaporation temperature = 353.15 K for R123.

Fig. 3b. Variations of the evaluation parameters with evaporation temperature in the case of prescribed hot and cold streams for N-pentane.

Fig. 4b. Variations of the evaluation parameters with hot stream inlet temperature at evaporation temperature = 383.15 K for R123.

Table 3 Representative thermodynamic and parametric data of R123 and N-pentane at optimized Tevap. R123 Tevap = 403.85 K Th,out (K) Tcond (K) Tc,out (K) _ 1;2 (kW) W _ 5;6 (kW) W _ ev ap (kW) Q _ Q cond (kW) _ (kW) Q _ g (kW/K) S _ G loss (kW K) _ d (kW) E _ G dis (kW K) G* NRS 346.05 303.18 299.59 21.26 0.44 106.95 86.13 20.84 0.05173 20,536 14.59 8083 0.6566 0.1102 N-pentane Tevap = 401.35 K 342.78 303.17 300.02 20.66 0.33 109.7 89.37 20.33 0.05351 20,389 15.1 8800 0.659 0.1136

_ d;exp ? m _ 1;2 _ r ?e1 ? e2 ? ? W E

The exergy destruction rate in the condenser

?28?

Fig. 4c. Variations of the evaluation parameters with hot stream inlet temperature at evaporation temperature = 413.15 K for R123.

_ d;cond ? m _ r ?e2 ? e5 ? ? m _ c ?e13 ? e16 ? E

The exergy destruction rate in the working ?uid pump

?29?

_ d;total ? E _ d;ev ap ? E _ d;exp ? E _ d;cond ? E _ d;pump ? E _ d;dump E

?32?

_ d;pump ? m _ 5;6 _ r ?e5 ? e6 ? ? W E

?30?

4. Global model 4.1. Working ?uid Working ?uids have great in?uence on system safety, environmental protection and economic ef?ciency of ORC system. Numerous researchers have carried out extensive and in-depth working

The exergy destruction rate due to dumping the used streams into the environment

_ d;dump ? m _ h e12 ? m _ c e16 E

Thus, the total exergy destruction rate of the ORC system

?31?

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Y. Zhu et al. / Energy Conversion and Management 88 (2014) 267–276

Fig. 5. Variations of the power output with both hot stream temperature and evaporation temperature for R123.

Fig. 6. Variations of the entropy generation rate with both hot stream temperature and evaporation temperature for R123.

Fig. 7. Variations of the entransy loss rate with both hot stream temperature and evaporation temperature for R123.

medium selection researches [27–29,55–62]. Applicable ?uids with good thermodynamics, chemistry, environmental protection, safety and economic characteristics, such as a ?uid with low liquid speci?c heat, viscosity, toxicity, ?ammability, ozone depletion potential (ODP), global warming potential (GWP) value and price has more potential to be widely recommended and accepted. Based on the previous criteria, two commonly utilized working ?uids – R123 and N-pentane are chosen for comparison in this

paper. Basic thermodynamic and environmental properties of the ?uids selected are shown in Table 1.

4.2. Assumptions While giving the global model, in order to simplify the complicacy and computing, we make some assumptions of unchanged

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273

Fig. 8. Variations of the entransy dissipation rate with both hot stream temperature and evaporation temperature for R123.

Fig. 9. Variations of the exergy destruction rate with both hot stream temperature and evaporation temperature for R123.

Fig. 10. Variations of the entransy ef?ciency with both hot stream temperature and evaporation temperature for R123.

parameters which are not the key points and will not signi?cantly affect the accuracy of the calculation in Table 2. Hot air whose humidity ratio is 4% is used to imitate the hot stream. Water of general environment condition is utilized as the cold stream.

5. Results and discussion In this section, prescribed hot and stream conditions are considered as the ?rst case for both R123 and N-pentane. Through the comparison, the law of the changes and trends for the optimization

274

Y. Zhu et al. / Energy Conversion and Management 88 (2014) 267–276

for the ORC can be got. Next, variable hot stream condition are taken into account, since the results for the two working ?uids are extremely similar under this condition, the research for R123 is only showed as a typical case of ORC. 5.1. Case I: Prescribed hot and cold stream conditions

principle, exergy theory, entransy loss rate and entransy ef?ciency are applicable to the optimization of the ORC, while the entransy dissipation is not. This conclusion is available no matter what working ?uid is used, nevertheless, the system performances and parameters may be much different. 5.2. Case II: Variable hot stream temperature

_ h ? 0:83 kg=s, and This case input data are Th,in = 473.15 K, m _ c ? 1:8 kg=s. Tevap varies from 353.15 K to Tc,in = 288.15 K, m 413.15 K. For the ORC the evaporation temperature is the only free parameter left in this case. This range of Tevap is chosen since it has already shown the change rules of the optimization criteria, meanwhile Tevap must be lower than the critical temperatures Tcr of both working ?uids. _ , entropy genThe calculated variations of the output power W _ _ _ d, eration rate Sg , entransy loss rate Gloss , exergy destruction rate E _ dis , entransy ef?ciency G? and revised entransy dissipation rate G entropy generation number NRS with the evaporation temperature Tevap are shown in Fig. 3a for R123 and Fig. 3b for N-pentane. Fig. 3a indicates that among the seven parameters, the minimum entropy generation rate, exergy destruction rate, entransy ef?ciency, revised entropy generation number and maximum entransy loss rate are corresponding to the maximum output power. However, the minimum entransy dissipation rate does not associate with the output power variation, it can be explained as follow: the entransy dissipation is one part of the entransy loss rate besides entransy variation (work entransy) or does not consider the in?uence of work output on the change of entransy. The similar change laws are demonstrated in Fig. 3b for N-pentane under the same stream conditions. It is worth pointing out that compared to the optimized evaporation temperature for R123, the one for N-pentane appears earlier. 403.85 K and 401.35 K are the optimized temperature for R123 and N-pentane respectively. Other thermodynamic and parametric data at optimized Tevap for both working ?uids of R123 and N-pentane are listed in Table 3. Through Table 3, it can be obtained that R123 has a higher out_ ? 20:84 kW, which is 2.45% more than that of N-penput power W tane. However, the Th,out of N-pentane is 3.27 K lower than the one of R123 means less energy released into the environment. In another word, R132 has better heat-power conversion capacity attributing to less energy was absorbed and more power was outputted in this case. In spite of more outstanding performances of R123, higher Th,out will lead to more serious thermal pollution. For this case where the inlet temperatures, the mass ?ow rates and the heat capacities of the streams are ?xed, all the entropy

In this case, variable hot stream temperature Th,in is taken into account. Since the results for the two working ?uids are extremely similar, we only illustrate the research for R123 as a typical case of _ h ? 0:83 kg=s, and Tc,in = 288.15 K, ORC. It is set that m _ c ? 1:8 kg=s. Tevap varies from 353.2 K to 413.15 K, and Th,in varies m from 473.15 K to 523.15 K. In order to observe the distinctions at different Tevap, the curves at 353.15 K, 383.15 K and 413.15 K are captured equidifferently as Figs. 4a–4c. In Fig. 4a, all the parameters increase with the increasing Th,in besides the entransy ef?ciency G? at Tevap = 353.15 K. This law is continued at Tevap = 383.15 K as shown in Fig. 4b only in addition to some different changing proportions. However, changes occur in Fig. 4c, there _ g, are in?ection point on the curves of the entropy generation rate S _ d and the revised entropy generation the exergy destruction rate E number NRS. As a result, it is summarized that in this case, the _ loss and entransy dissipation rate G _ dis always entransy loss rate G have the same increasing tendency with the output power rate _ , while the entransy ef?ciency G? has the opposite one. W For further discussion, more detailed 3-D coordinates (Figs. 5– 11) are utilized to observe the global variation of parameters with Tevap and Th,in. It is depicted in the 3-D picture that the surface of _ loss in Fig. 7 is similar to that of the power the entransy loss rate G _ output W in Fig. 5, but the entransy ef?ciency G? always has the _g, opposite variation. If Th,in is constant, entropy generation rate S _ d and the revised entropy generation the exergy destruction rate E number NRS will be suitable to the optimized power output as discussed in Case I, however, when it is extended to the 3-D, the result _ dis will not the same. Although the entransy dissipation rate G (Fig. 8) in Case II has the same variation tendency with the power _ , its utilization has already been excluded in Case I. output W 5.3. Case III: Variable hot stream mass ?ow rate _ condition is In this case, a variable hot stream mass ?ow rate m considered. The same as above, the research for R123 is only illustrated since the results for N-pentane are alike. Input data are _ c ? 1:8 kg=s. m _ h varies from Th,in = 473.15 K, and Tc,in = 288.15 K, m 0.7 to 1 kg/s. Three Tevap at 353.15 K, 383.15 K and 413.15 K are

Fig. 11. Variations of the revised entropy generation number with both hot stream temperature and evaporation temperature for R123.

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275

6. Conclusions In the present study, analyses of entropy, entransy and exergy are applied to the optimization of the Organic Rankine Cycle operating on R123 and N-pentane. Three different common cases which are variable evaporation temperature, hot stream temperature and hot stream mass ?ow rate have been taken into account to explore the applicability of the parameters. The investigations are carried out through a computer programming in Engineering Equation Solver Ver. 8 which includes the working ?uids’ properties. The main conclusions can be summarized as follows: (1) The theory of entransy is proposed for Organic Rankine Cycle optimization including entransy loss, entransy dissipation and entransy ef?ciency, as well as the concepts of entropy generation and exergy destruction. The applicabilities of _ g , entransy loss rate G _ loss , the entropy generation rate S ? _ entransy dissipation rate Gdis , entransy ef?ciency G , revised entropy generation number NRS and exergy destruction rate _ d to optimization of the ORC are discussed in three cases. E (2) R123 and N-pentane are selected as the working ?uids, detail comparisons are proceeded under constant Th,in condition. Although the optimal evaporation temperature and optimized output power is different, but the change laws of the parameters are same. Thus the applicability bellow can be veri?ed no matter whatever the working ?uid is used. (3) After comparing prescribed and variable hot stream cases, it can be summarized that larger entransy loss rate invariably corresponds to lager power output. The concept of entransy loss is appropriate for the optimization of the ORC for all the cases discussed in this paper. The concept of entropy and exergy can be only utilized under ?xed stream conditions.

Fig. 12a. Variations of the evaluation parameters with hot stream ?ow rate at evaporation temperature = 353.15 K for R123.

References

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Fig. 12c. Variations of the evaluation parameters with hot stream ?ow rate at evaporation temperature = 413.15 K for R123.

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