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Thermoeconomic multi-objective optimization of an organic Rankine cycle for exhaust waste heat recovery of a diesel engine Fubin Yang a, b, Hongguang Zhang a, b, *, Songsong Song a, b, Chen Bei a, b, Hongjin Wang a, b, Enhua Wang c a b c

College of Environmental and Energy Engineering, Beijing University of Technology, Pingleyuan No. 100, 100124 Beijing, China Collaborative Innovation Center of Electric Vehicles in Beijing, Pingleyuan No. 100, 100124 Beijing, China State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Qinghuayuan, 100084 Beijing, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 June 2015 Received in revised form 20 September 2015 Accepted 24 October 2015 Available online xxx

In this paper, the ORC (Organic Rankine cycle) technology is adopted to recover the exhaust waste heat of diesel engine. The thermodynamic, economic and optimization models of the ORC system are established, respectively. Firstly, the effects of four key parameters, including evaporation pressure, superheat degree, condensation temperature and exhaust temperature at the outlet of the evaporator on the thermodynamic performances and economic indicators of the ORC system are investigated. Subsequently, based on the established optimization model, GA (genetic algorithm) is employed to solve the Pareto solution of the thermodynamic performances and economic indicators for maximizing net power output and minimizing total investment cost under diesel engine various operating conditions using R600, R600a, R601a, R245fa, R1234yf and R1234ze as working ﬂuids. The most suitable working ﬂuid used in the ORC system for diesel engine waste heat recovery is screened out, and then the corresponding optimal parameter regions are analyzed. The results show that thermodynamic performance of the ORC system is improved at the expense of economic performance. Among these working ﬂuids, R245fa is considered as the most suitable working ﬂuid for the ORC waste heat application of the diesel engine with comprehensive consideration of thermoeconomic performances, environmental impacts and safety levels. Under the various operating conditions of the diesel engine, the optimal evaporation pressure is in the range of 1.1 MPae2.1 MPa. In addition, the optimal superheat degree and the exhaust temperature at the outlet of the evaporator are mainly inﬂuenced by the operating conditions of the diesel engine. The optimal condensation temperature keeps a nearly constant value of 298.15 K. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Diesel engine Waste heat recovery Organic Rankine cycle Thermoeconomic analysis Multi-objective optimization

1. Introduction IC (Internal combustion) engines only convert about 40% of the total fuel combustion energy into useful work, and the remaining energy is discharged into environment in the form of waste heat [1,2]. Under the background of energy crisis, how to realize the recovery of the waste heat from the IC engines has received much attention these years. Light-duty passenger vehicle exhaust system operates at gas temperatures from 500 to 900 C, while the heavyduty vehicle exhaust system operates at gas temperatures from 500 to 650 C. These high temperature exhaust gases provide signiﬁcant

* Corresponding author. Beijing University of Technology, Pingleyuan No. 100, 100124 Beijing, China. Tel.: þ86 10 6739 2469; fax: þ86 10 6739 2774. E-mail address: [email protected] (H. Zhang). http://dx.doi.org/10.1016/j.energy.2015.10.117 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

opportunities for waste heat recovery [3]. The exhaust waste heat recovery of IC engines would not just bring huge advantages for improving the fuel consumption, but also increase engine power output, further reducing CO2 and other harmful exhaust gas emissions [4]. If approximately 6% of the exhaust heat could be converted into useful power, it would be possible to reduce the fuel consumption around 10% [5]. ORC (Organic Rankine cycle) system is considered as a promising method due to its simple conﬁguration and high efﬁciency [6e9]. The concept of applying an ORC to IC engines ﬁrst appeared after the 1970 energy crisis [10e12]. Compared with other waste heat recovery technologies, ORC is receiving more and more attention due to its higher thermal efﬁciency, simplicity and ability to operate efﬁciently under low and medium grade heat sources [13]. Another advantage of this technology is the use of widely available and affordable components because of the similarities between ORC

F. Yang et al. / Energy 93 (2015) 2208e2228

and refrigeration cycle [14]. However, it is difﬁcult to control the ORC system due to the transient characteristic of IC engines. Another technical bottleneck is that the ORC system requires a large installation space. In addition, the exhaust backpressure will deteriorate the performance of IC engines. Currently, most of the researches are focused on working ﬂuid selection, parameters optimization, and conﬁguration analysis. The properties of the working ﬂuid have a great inﬂuence on the performance of the ORC system. The working ﬂuid with good properties performs higher system efﬁciency and meets the environmental requirements. Many investigations have been conducted to select the optimal working ﬂuid. Liu et al. presented the inﬂuence of working ﬂuids on the performance of ORC for waste heat recovery. The effects of different types of working ﬂuids, including wet, isentropic and dry ﬂuids on the thermal efﬁciency and the total heat-recovery efﬁciency were evaluated. The results showed that dry or isentropic ﬂuids are considered as appropriate for the ORC applications [15]. Wang et al. investigated the performances of ORC system with nine different pure organic working ﬂuids for engine waste heat recovery. The results revealed that R245fa and R245ca are the most environment-friendly working ﬂuids [16]. Andreasen et al. provided a generic method for ORCs optimization and ﬂuid selection considering pure ﬂuids and mixtures. It was shown that mixed working ﬂuid can increase the net power output of the cycle [17]. Tian et al. conducted ﬂuids selection and parameters optimization for the ORCs used in exhaust heat recovery of ICE (Internal Combustion Engine). The results indicated that R141b, R123 and R245fa present better performance than the other ﬂuids [13]. Roy et al. presented a study of ORC system by using R12, R123, R134a and R717 as working ﬂuid. The results showed that R123 is the most suitable choice for the investigated system [18]. Xu et al. proposed a critical temperature criterion for selection of working ﬂuids for subcritical pressure organic Rankine cycle. In addition, a new method was developed to couple the heat source with the organic ﬂuid, and the integrated-average temperature difference was used to quantify the thermal match in the evaporator. The results showed that the thermal efﬁciencies of the ORC system are well correlated with critical temperature. R245fa and R141b can be used over a wide heat source temperature range [19]. Generally speaking, the selection of working ﬂuid is mainly inﬂuenced by the heat source temperature range. Besides, operating conditions, thermoeconomic performances, environmental impacts and safety levels should also be concerned. Therefore, no single working ﬂuid is best for all ORC applications. Recently, many studies have shown that the critical temperature limits the application range of the working ﬂuid [19,20]. But more comprehensive study needs to be done in the future. In order to achieve the optimal performances of the ORC system, several key parameters including evaporation pressure, superheat degree and condensation temperature need to be optimized. Mago et al. analyzed the effects of turbine inlet parameters on the system performances. The results indicated that the ﬂuid with the highest boiling point has the best thermal efﬁciency [21]. Wang et al. examined the effects of four key thermodynamic parameters, including turbine inlet pressure, turbine inlet temperature, pinch temperature difference and approach temperature difference, on the net power output and surface area of heat exchangers. The results revealed that the thermodynamic parameters have signiﬁcant effects on net power output and heat transfer area of the ORC system [22]. Liu et al. investigated the sensitivity of system parameters, containing working ﬂuid, superheat degree, pinch temperature difference in the heat exchangers, evaporating temperature, the isentropic efﬁciencies of the pump and the pump, to the performance of the ORC system. The results showed that the evaporating temperature has a great inﬂuence on the

2209

thermodynamic and economic performances of the ORC system [23]. Yang et al. analyzed the effects of the turbine inlet and outlet pressures on the net power output, thermal efﬁciency, and total cost of equipments of the ORC system. The results revealed that the thermo-economic performance of the ORC system can be improved by increasing the turbine inlet temperature in superheated state [24]. Miao et al. conducted the experimental researches by adjusting the frequency of the working ﬂuid pump and the shaft torque of the expander. The results showed that the optimal performance of the ORC system can be controlled by these two parameters [25]. In addition, optimization algorithms are widely used in many researches to improve the system performance for ﬁnding the optimal operation parameters. For parametric optimization, optimization algorithms are used to achieve the optimal system performance. Xi et al. examined the performances of three different ORC systems using six kinds of working ﬂuids. The GA (genetic algorithm) is used to optimize the operating conditions and the thermodynamic parameters [26]. Wang et al. presented a working ﬂuid selection and parametric optimization by using simulated annealing algorithm [27]. Rashidi conducted the parametric optimization of regenerative Clausius and ORC system based on artiﬁcial neural network and artiﬁcial bees colony algorithm [28]. Different performance criteria are adopted by scholars for evaluating ORC system. One type is the thermodynamic indicators. Shu et al. presented the thermodynamic analysis of a dual loop ORC system with net power output, thermal efﬁciency, and exergy efﬁciency as the objective functions [29]. Yang et al. studied the performances of zeotropic mixtures of ORC under engine various operating conditions. Variations of net power output, thermal efﬁciency, exergy efﬁciency of the ORC system were investigated [30]. Song et al. examined the waste heat recovery of a marine diesel engine using ORC technology. The maximum power output was adopted as the evaluation criterion to deﬁne the optimal system parameters [31]. Maraver provided optimization guidelines for a wide range of operating conditions and different ORC conﬁgurations in terms of the exergy efﬁciency [32]. In addition, another type is the economic indicators. Imran conducted the thermo-economic optimization of basic ORC and regenerative ORC for waste heat recovery. Thermal efﬁciency and speciﬁc investment cost were considered by using NSGA-II (Nondominated Sorting Genetic Algorithm-II) [33]. Zhang et al. presented an investigation on the parameter optimization and performance comparison of subcritical ORC and transcritical power cycle system for low-temperature geothermal power generation. Thermal efﬁciency, exergy efﬁciency, recovery efﬁciency, heat exchanger area per unit power output and the levelized energy cost were selected as the performance indicators [34]. Li et al. examined the effects of pinch point temperature difference and evaporating temperature on the performance of ORC system for minimizing the electricity production cost [35]. Hajabdollahi et al. optimized the design parameters of the ORC system for diesel engine waste heat recovery. The NSGA-II was applied to maximize the thermal efﬁciency and minimize the total annual cost simultaneously [36]. Based on the aforementioned analysis, ORC technology which is an effective method to recover the low temperature waste heat has been widely studied, especially in working ﬂuid selection and parameters optimization. But most of researches about the ORC are only focused on stationary heat source. Few studies have been conducted for the IC engines with large temperature span, small mass ﬂow rate and variable heat source. In this paper, the exhaust waste heat characteristics of a vehicle diesel engine are analyzed under various operating conditions. The effects of four key parameters, including evaporation pressure, superheat degree, condensation temperature and exhaust temperature at the outlet of

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F. Yang et al. / Energy 93 (2015) 2208e2228

the evaporator on the performances of the ORC system are investigated based on the thermodynamic and economic models. Subsequently, genetic algorithm is employed to solve the Pareto solution of the thermodynamic performances and economic indicators for maximizing net power output and minimizing total investment cost under diesel engine various operating conditions using R600, R600a, R601a, R245fa, R1234yf and R1234ze as working ﬂuids. The most suitable working ﬂuid used in the ORC system for diesel engine waste heat recovery is screened out, and then the corresponding optimal parameter regions are analyzed.

Table 1 The main technical performance parameters of the diesel engine. Items

Parameters

Type Rated power Maximum torque Displacement Cylinder number Speed at maximum torque Stroke and cylinder bore Compression ratio Air intake type Fuel injection system

WP12. 336E40 247 1600 11.596 6 1400 155 126 17.1 Turbocharged and Intercooled High pressure common rail

Units kW Nm L r/min mm

2. Modeling 2.1. System description The schematic diagram of the ORC system for diesel engine waste heat recovery is shown in Fig. 1. The ORC system mainly consists of evaporator, expander, condenser and pump. The working ﬂuid absorbs waste heat from the diesel engine in the evaporator and turns into high temperature and high pressure vapor. Then the high temperature and high pressure vapor ﬂows into the expander to produce power. After that, the low pressure superheated vapor enters the condenser and condenses into liquid state. Finally, the liquid working ﬂuid is pumped back to evaporator and a new cycle begins. In this paper, exhaust gas acts as the high temperature heat source. The heat source is characterized with exhaust mass ﬂow rate and exhaust temperature. Evaporator is the coupling unit between the diesel engine and the ORC system, in which the exhaust gas transfer heat to the ORC system. The exhaust waste heat characteristics of a six-cylinder, in-line, turbocharged, intercooled, direct injection, heavy truck diesel engine were evaluated. The main technical performance parameters of the diesel engine are listed in Table 1. The engine test cell integrated with all the measuring equipments was designed by Weichai Power Co., Ltd. When selecting the most appropriate working ﬂuid for ORC system, many aspects including thermodynamic property,

Diesel engine

environmental impacts, safety levels, and chemical stability need to be taken into account. Considering the strict restriction of the Montreal Protocol, CFCs (chloroﬂuorocarbon) is ﬁrstly excluded due to its high atmospheric lifetime and ODP (ozone depletion potential). Generally, dry and isentropic working ﬂuids are better than wet working ﬂuids as they can avoid the presence of droplet after an expansion process. So this study only investigates the ORC system with dry or isentropic working ﬂuids. For a subcritical ORC system, the critical temperature and pressure of the working ﬂuid limits the application range. The working ﬂuid with low critical temperature and pressure could easily become a supercritical ORC system due to the high exhaust temperature. While the supercritical ORC system would make the condensation process more difﬁcult [37]. In order to avoid the negative pressure in the pipelines, the condensation pressure of the working ﬂuid should be higher than the atmospheric pressure. In addition, non-corrosive, non-ﬂammable, non-toxic and environmental friendly (low ODP and GWP (global warming potential)) working ﬂuids are recommended. It should be noted that HFCs is currently being replaced by HFOs because of its high GWP [38]. Moreover, alkanes are also environmental friendly with null ODP and a relatively low GWP, which has been widely used in ORC application. Considering all the above factors, six different working ﬂuids are selected for thermodynamic and economic analysis. The properties of the selected working ﬂuids are shown in Table 2, and the corresponding Tes diagram is shown in Fig. 2. 2.2. Thermodynamic modeling Similar to the steam Rankine cycle, the ORC mainly includes four thermodynamic processes. The thermodynamic model of the ORC system is established based on the ﬁrst and second laws of thermodynamics. Taking R245fa as an example, the Tes diagram is plotted in Fig. 3 for thermodynamic analysis. To simplify the calculation process, several assumptions are given as follows:

Turbine

Compressor Air intake

Exhaust gas

Texh,out

Texh,in Evaporator

1

5 Pump

Expander

Generator

4

2

Cooling water

Tcool,out

Condenser

Tcool,in

Fig. 1. Schematic diagram of the ORC system.

(1) The whole system is under steady state. (2) There are no pressure drops in the pipes and the components. (3) The heat losses in each component are also neglected. (4) The isentropic efﬁciencies of the expander and the pump are set to 0.7 [39] and 0.65 [33]. For the practical application of the ORC system, the isentropic efﬁciencies of the pump and expander are not as high as the assumptions [25,40]. While this study is principally focused on analyzing the waste heat recovery potential of the ORC system, therefore the isentropic efﬁciencies of the pump and expander are assumed under the optimal condition. Accordingly, the effects of these two values on the ORC system performance will be discussed with the experimental data in the future works.

F. Yang et al. / Energy 93 (2015) 2208e2228

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Table 2 Properties of the selected working ﬂuids. Working ﬂuids

Molar mass

Critical temperature (K)

Critical pressure (MPa)

ODP

GWP(yr)

R600 R600a R601a R1234yf R1234ze R245fa

58.122 58.122 72.149 114.04 114.04 134.05

425.13 407.81 460.35 367.85 382.52 427.16

3.796 3.629 3.378 3.382 3.636 3.651

0 0 0 0 0 0

~20 ~20 ~20 4 6 950

500

I_exp ¼ T0 m_ wf ðs2 s1 Þ

The isentropic efﬁciency of the expander can be expressed as:

450 R245fa

R601a

Temperature (K)

(2)

R600

400 R1234ze

350

300 R1234yf

250 0

0.5

1

1.5

Entropy (kJ/kg.K)

2

h1 h2 h1 h2s

(3)

Process 2e4 (Condenser): For pure working ﬂuid, there is no temperature glide during the condensation process. The temperature variation of the cooling water in the condenser is small. Therefore, the exergy change of the cooling water in the condenser is neglected. The heat transfer rate and exergy destruction rate of the condenser can be determined as:

R600a

-0.5

hise;exp ¼

2.5

Fig. 2. Tes diagram of the six selected working ﬂuids.

Q_ con ¼ m_ wf ðh2 h4 Þ

(4)

I_con ¼ m_ wf ½ðh2 h4 Þ T0 ðs2 s4 Þ

(5)

Process 4e5 (Pump): The power consumed and exergy destruction rate of the pump can be expressed as:

_ p ¼ m_ ðh5 h Þ W 4 wf

(6)

I_p ¼ T0 m_ wf ðs5 s4 Þ

(7)

The isentropic efﬁciency of the pump can be expressed as:

hise;p ¼

h5s h4 h5 h4

(8)

Process 5e1 (Evaporator): The heat transfer rate and exergy destruction rate of the evaporator can be determined as:

Q_ eva ¼ m_ wf ðh1 h5 Þ ¼ m_ exh hexh;in hexh;out

Fig. 3. Tes diagram of the ORC system.

(5) The ambient temperature is set to 291.15 K. (6) When the diesel engine is running, the exhaust temperature is relatively high. The PPTD (pinch point temperature difference) may occur at either the starting point of preheating (state point 5 shown in Fig. 3) or the starting point of vaporization (state point 6 shown in Fig. 3) [37,41]. In this paper, the PPTD in the evaporator is set to be greater than 20 K. The ﬂow chart of the determination of PPTD is shown in Fig. 4. In addition, the PPTD in the condenser occur at state point 3 shown in Fig. 3, whose value is set to 5 K. Process 1e2 (Expander): The power output and exergy destruction rate of the expander can be expressed as:

_ exp ¼ m_ ðh h Þ W 2 wf 1

(1)

(9)

I_eva ¼ m_ exh hexh;in hexh;out T0 sexh;in sexh;out m_ wf ½ðh1 h5 Þ T0 ðs1 s5 Þ

(10)

The net power output and thermal efﬁciency of the ORC system are respectively calculated using the following equations:

_ exp W _p _ net ¼ W W hth ¼

_ net W _ Q

(11)

(12)

eva

2.3. Heat exchanger modeling Heat exchangers contribute a large proportion of the system total cost [42], whereas the cost of the heat exchangers mainly depends on the heat transfer area. The effective heat transfer area of the heat exchanger varies with the heat source temperature and

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F. Yang et al. / Energy 93 (2015) 2208e2228

Start

Parameters optimization

Calculate the temperature difference between exhaust gas and state point 5 ( TDexh,5)

Calculate the temperature difference between exhaust gas and state point 6 ( TDexh,6)

Compare TDexh,5 with TDexh,6 and determine the pinch point temperature difference ( TPPTD)

No

Is

TPPTD greater than 20K? Yes Output optimal solution

End Fig. 4. Flow chart of the determination of PPTD.

mass ﬂow rate. Furthermore, the operating parameters of the ORC system also inﬂuence the effective heat transfer area of the heat exchanger. Therefore, it will be necessary to set up the thermodynamic model of the heat exchanger for the parameters optimization of the ORC system under engine various operating conditions. LMTD (Logarithmic mean temperature difference) method is used in this study. The heat transfer rate between the working ﬂuid and the exhaust gas in each section can be expressed as:

Q_ ¼ KADTLMTD

(13)

1 b db ro 1 þ þ ¼ þ ri b þ Keva ai l h ao h a¼

(15)

lNu d

(16)

For the exhaust gas outside of the tube, Zhukauskas correlation is used to calculate the Nusselt number [44]. When 1000 < Re < 2 105,

The LMTD can be determined as:

DTLMTD ¼ Dt 0

Dt 0 Dt Dt 0 ln Dt 00

Nuexh ¼ 0:35ε

00

(14)

0:2

0:36 Re0:6 exh Prexh

Prexh Prexh;wall

2.3.1. Evaporator modeling The evaporator used in ORC system for IC engines should meet the requirements of thermal stability, low resistance, compact size and high heat transfer efﬁciency. Relevant researches have shown that ﬁn-and-tube evaporator performs better [39,41,43]. In this study, a ﬁn-and-tube evaporator is selected for thermodynamic analysis. The schematic and the geometric dimensions of the ﬁnand-tube evaporator are shown in Fig. 5 and Table 3, respectively. Based on the geometric dimensions of the evaporator and the physical properties of the exhaust gas and the working ﬂuid under engine various operating conditions, the thermodynamic model of the evaporator is established. As shown in Fig. 3, the evaporator is divided into preheated zone (state point 5 e state point 6), evaporation zone (state point 6 e state point 7) and superheated zone (state point 7 e state point 1) based on the working ﬂuid state in the evaporator. The overall heat transfer coefﬁcients for each zone can be calculated using the following equations:

(17)

When Re < 1000,

00

where and Dt are the maximum and minimum temperature differences at the ends of the heat exchangers, respectively.

!0:25

0:36 Nuexh ¼ 0:71Re0:5 exh Prexh

Prexh Prexh;wall

!0:25 (18)

For the single phase working ﬂuid in the tube side, Gnielinski correlation is used to calculate the Nusselt number [45].

Nuwf

" 2=3 # ðf =8Þ Rewf 1000 Prwf d ¼ 1 þ ct pﬃﬃﬃﬃﬃﬃﬃﬃ 2=3 l 1 þ 12:7 f =8 Prwf 1

2 f ¼ 1:82lgRewf 1:64

(19)

(20)

For liquid state,

ct ¼

Prwf Prwall

0:01 ;

For vapor state,

Prwf ¼ 0:05 20 Prwall

(21)

F. Yang et al. / Energy 93 (2015) 2208e2228

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Working fluid outlet

Exhaust inlet Exhaust outlet

Working fluid inlet

Exhaust outlet

Exhaust inlet

Fig. 5. Schematic of the ﬁn-and-tube evaporator.

ct ¼

Twf Twall

0:45

T ; wf ¼ 0:5 1:5 Twall

(22)

Liu and Winterton correlation is applied for the convective heat transfer coefﬁcient in the evaporation zone [46].

htp

rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 Fhfb þ ðShnb Þ2 ¼

(23)

Similar to the evaporator, the condenser is divided into superheated zone (state point 2 e state point 3) and condensation zone (state point 3 e state point 4). The overall heat transfer coefﬁcients for each zone can be determined using the following equations:

1 1 d 1 ¼ þ ri þ þ ro þ Kcon ai l ao

(28)

The forced convective heat transfer enhancement factor is calculated by:

For the single phase working ﬂuid in the superheated zone, the Chisholm and Wanniarachchi correlation is adopted to calculate the Nusselt number [47].

0:35 r F ¼ 1 þ xPrl l 1 rv

(24)

Nusp ¼ 0:724

(25)

Table 3 Geometric dimensions of the ﬁn-and-tube evaporator.

0:646 6b Re0:583 Pr1=3 p

(29)

The suppression factor is given by:

1 S ¼ 1 þ 0:055F 0:1 Re0:16 L

The convective heat transfer coefﬁcient for the ﬁlm boiling is calculated according to Dittus-Boelter equation.

hfb ¼

0:4 0:023ðll =dÞRe0:8 L Prl

(26)

The convective heat transfer coefﬁcient for the nucleate boiling is calculated based on Cooper's pool boiling correlation.

hnb ¼ 55p0:12 q2=3 ð lgpr Þ0:55 M 0:5 r

(27)

2.3.2. Condenser modeling The plate heat exchanger is used as the condenser. The geometric dimensions of the plate condenser are listed in Table 4.

Items

Parameters

Units

Number of tubes in each row Number of tube rows Tube outer diameter Tube inner diameter Tube pitch Row pitch Fin height Fin width Rib effect coefﬁcient Tube row alignment Tube material Fin material Inner heat transfer area Tube length

9 20 25 20 60 100 12 1 3 Staggered type Stainless steel316L Stainless steel316L 9 8.8

e e mm mm mm mm mm mm e e e e m2 m

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F. Yang et al. / Energy 93 (2015) 2208e2228

Table 4 Geometric dimensions of the plate condenser.

CEXP ¼

Items

Parameters

Units

Chevron angle Plate spacing Width of plate Plate thickness

60 2.24 0.119 0.3

degree mm m mm

For the two phase working ﬂuid, Nusselt number is calculated according to Ref. [48]. 1=3 Nutp ¼ 4:118Re0:4 eq Pr

(30)

TIC (Total investment cost) and EPC (electricity production cost) of the ORC system are selected for evaluating the economic performance. The TIC of the ORC system depends mainly on the cost of the four components. Therein, the cost of the heat exchanger is given by Ref. [49]:

CHX

(31)

where CEPCI2001 and CEPCI2013 are the Chemical Engineering Plant 0 is the basic cost of the heat Cost Index for years 2001 and 2013, CHX exchanger, FS is an additional factor for overhead cost, B1;HX and B2;HX are the constants for the heat exchanger type, FM;HX is the material factor of the heat exchanger, and FP;HX is the pressure factor of the heat exchanger. The basic cost of the heat exchanger can be calculated by: 0 lgCHX ¼ K1;HX þ K2;HX lgAHX þ K3;HX ðlgAHX Þ2

(32)

where K1;HX , K2;HX and K3;HX are the constants for heat exchanger type, and AHX is the heat transfer area. The pressure factor of the heat exchanger can be determined by:

lgFP;HX ¼ C1;HX þ C2;HX lgPHX þ C3;HX ðlgPHX Þ2

(33)

where C1;HX , C2;HX and C3;HX are the constants for heat exchanger type, and PHX is the design pressure of the heat exchanger. The cost of the pump is given by:

CPP ¼

CEPCI2013 0 FS CPP B1;PP þ B2;PP FM;PP FP;PP CEPCI2001

(37)

0 where CEXP is the basic cost of the expander, FMP is the additional factor of the expander. The basic cost of the expander is given by:

2 0 _ _ EXP þ K lgCEXP ¼ K1;EXP þ K2;EXP lgW 3;EXP lgW EXP

(38)

where K1;EXP , K2;EXP and K3;EXP are the constants for the expander type, WEXP is the power output of the expander. The system total investment cost is the sum of the cost of each component.

Ctot ¼ CHX þ CPP þ CEXP

2.4. Economic modeling

CEPCI2013 ¼ F C0 B þ B2;HX FM;HX FP;HX CEPCI2001 S HX 1;HX

CEPCI2013 F C0 F CEPCI2001 S EXP MP

(34)

(39)

The CRF (capital recovery factor) can be calculated by Ref. [50]:

CRF ¼

ið1 þ iÞLTpl

(40)

ð1 þ iÞLTpl 1

where i is the interest rate, and LTpl is the plant lifetime. The EPC can be expressed as [13]:

EPC ¼ Ctot

CRF þ fK Wexp Wp hfullload

(41)

where fK is the maintenance and insurance cost factor, and hfullload is the full load operation hours. The values of these constants for the economic model are listed in Table 5. The economic model adopted in this paper is mainly applied to large-power level ORC system. With the commercialization of the small-power level ORC system, the system cost will signiﬁcantly decrease. It will be part of authors' future work to correct the economic model. 2.5. Coupling between ORC and diesel engine This paper focuses mainly on the diesel engine waste heat recovery by using the ORC system. For a variable heat source, it is difﬁcult to achieve the coupling between the ORC system and the engine waste heat. The related researches can be seen in Refs. [20,25,51]. In this research, because m_ exh , Texh;in and Pexh are obtained by engine experiment, the total heat transfer rate of the evaporator can be determined as:

Q_ eva ¼ m_ exh hexh;in hexh;out

(42)

0 is the basic cost of the pump, B where CPP 1;PP and B2;PP are the constants for pump type, FM;PP is the material factor of the pump, and FP;PP is the pressure factor of the pump. The basic cost of the pump is given by:

where, hexh;in and hexh;out are the speciﬁc enthalpies of the exhaust gas at the inlet and the outlet of the evaporator, respectively. The

2 0 _ _ PP þ K lgCPP ¼ K1;PP þ K2;PP lgW 3;PP lgW PP

Table 5 Constants for economic modeling.

(35)

Constant

where K1;PP , K2;PP and K3;PP are constants for the pump type, and WPP is the consumption power of the pump. The pressure factor of the pump is given by:

lgFP;PP ¼ C1;PP þ C2;PP lgPPP þ C3;PP ðlgPPP Þ2

(36)

where C1;PP , C2;PP and C3;PP are the constants for the pump type, PPP is the design pressure of the pump. The cost of the expander is given by:

FS

B1,HX B2,HX FM,HX K1,HX K2,HX K3,HX C1,HX C2,HX C3,HX

Value

Constant

Value

Constant

Value

1.70 0.96 1.21 2.40 4.66 0.1557 0.1547 0 0 0

FM,PP B1,PP B2,PP K1,PP K2,PP K3,PP C1,PP C2,PP C3,PP

2.20 1.89 1.35 3.389 0.536 0.1538 0.3935 0.3957 0.00226 3.5

K1,EXP K2,EXP K3,EXP CEPCI2013 CEPCI2001 i LTpl fK hfull-load

2.2659 1.4398 0.1776 527.7 397 0.1 15 0.0165 7500

FMP

F. Yang et al. / Energy 93 (2015) 2208e2228

values of hexh;in and hexh;out can be determined by h ¼ hðT; PÞ. Therefore, the heat transfer process of the linear curve AC for the exhaust gas shown in Fig. 6 can be expressed as:

Q_ ¼ m_ exh hexh hexh;out

(43)

The optimal performances of the ORC system are obtained by the coordinated variation of the operating parameters. The P7 , T1 , T4 and Texh;out are given the initial values at ﬁrst. Because P1 is equal to P7 , so h1 and h4 can also be obtained by h ¼ hðT; PÞ. In addition, h5s is given by h ¼ hðP; sÞ, and h5 is described as:

h5 ¼ h4 þ

h5s h4 hise;p

(44)

The mass ﬂow rate of the working ﬂuid can be determined using the following equation:

Q_ eva ¼ m_ wf ðh1 h5 Þ

(45)

Based on the thermodynamic and economic models, the ﬁtness function is calculated. Thus the iterative process is conducted to repeat the above procedure, until the ﬁtness function meets the convergence criterion. Therein, the convergence criterion can be expressed as:

jFunction tolerancej < 106

(46)

The entropies of state points 1 and 6 shown in Fig. 3 are obtained by s ¼ sðT; PÞ, and the entropy of state point 5 shown in Fig. 3 is obtained by s ¼ sðP; hÞ. Therefore, the equation for exhaust gas shown in Fig. 3 (Line AC in Fig. 6) can be expressed as:

T¼

Texh:in Texh:out ðs sexh:out Þ þ Texh:out sexh:in sexh:out

(47)

According to Eq. (47), the temperature of state point 8 shown in Fig. 3 can be calculated. A comparison of DTDexh;5 (temperature difference between the state point 5 and exhaust gas at the outlet of the evaporator) and DTDexh;6 (temperature difference between the state point 6 and exhaust gas at state point 8) is conducted to identify the DTPPTD . If the DTPPTD meets the requirement of PPTD, all of the operating parameters are decided. The next step is to evaluate the thermodynamic and economic performances of the ORC system. Otherwise, the above procedure will be repeated.

Fig. 6. The TeQ curve coupling the exhaust gas and organic ﬂuid.

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3. Engine waste heat evaluation When the diesel engine is running, the exhaust energy varies with the operating conditions. As the high temperature heat source of the ORC system, the variation of the exhaust energy has an effect on the operating parameters of the ORC system. Therefore, it is essential to analyze the characteristics of the exhaust waste heat under engine various operating conditions. Fig. 7(a) shows the variation of the power output and BSFC (brake speciﬁc fuel consumption) of the diesel engine under various operating conditions. It can be observed that the power output of the diesel engine increases with the engine speed and engine torque. At engine rated condition, the power output of the diesel engine reaches a maximum value of 247 kW. Furthermore, the diesel engine has better fuel economy at mediumehigh speed and load regions. The exhaust energy of the diesel engine is mainly inﬂuenced by exhaust mass ﬂow rate and exhaust temperature. Fig. 7(b) shows the variation of exhaust temperature under engine various operating conditions. It can be observed that the exhaust temperature is in the range of 606 Ke653 K at mediumehigh load regions. The variation of exhaust mass ﬂow rate with engine operating conditions is shown in Fig. 7(c). It can be seen that the exhaust mass ﬂow rate increases with the engine speed and load. At rated condition, the exhaust mass ﬂow rate reaches a maximum value of 0.36 kg/s. The exhaust temperature at the outlet of the evaporator is set to 393.15 K to avoid the acid corrosion. Thus the available exhaust energy is shown in Fig. 7(d). According to the results presented in Fig. 7(d), the variation of the operating conditions of the diesel engine has a great inﬂuence on the available exhaust energy. In addition, the available exhaust energy increases with the engine speed and load. Over the whole operating range of the diesel engine, the available exhaust energy is in the range of 3 kWe103 kW. Especially in the mediumehigh speed and load regions, the available exhaust energy is relative high.

4. Multi-objective optimization 4.1. Multi-objective optimization solution Analyses of the ORC system is involved in multi-objective optimization of both thermodynamic and economic performances. The objective functions are constrained by decision variables with each other, which mean one objective function performs better at the expense of others'. There exist the Pareto solutions for the multi-objective optimization, which is the mainly different from single-objective optimization. For the practical application of the ORC system, it is essential to select one or several solutions as the optimal choice from the Pareto solutions. The genetic algorithm has been widely used in multi-objective optimization [22,26,33,36]. GA is a random search algorithm based on natural selection and biology evolutionary theory. The GA uses three main types of operators at each step to create the next generation from the current population. Selection operator selects the individuals that contribute to the population at the next generation. Crossover operator combines two parents to form children for the next generation. Mutation operator applies random changes to individual parents to form children [52]. In this study, GA is used to conduct the multi-objective optimization for the ORC system. The net power output and total investment cost are selected as the objective functions with evaporation pressure, superheat degree, condensation temperature and exhaust temperature at the outlet of evaporator as decision variables. The multi-objective optimization model can be described as:

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Fig. 7. Performance map of the diesel engine.

_ net ¼ f P7 ; T ; T ; T max W 1 4 exh;out

(48)

min ðCtot Þ ¼ f P7 ; T1 ; T4 ; Texh;out

(49)

The logical bounds of the decision variables depend on the practical operating conditions of the ORC system. The logical bounds of the decision variables are listed in Table 6. The ﬂow chart of the optimization procedure is shown in Fig. 8.

4.2. Evaluation of the genetic algorithm When GA is used for multi-objective optimization of the ORC system, it is essential to verify the optimization model. The parameters of the GA mainly include population size, tournament size and crossover fraction. Take engine rated condition for example, R245fa is selected as the working ﬂuid for verifying the

optimization model. The Pareto frontier for the optimization model should be well-distributed. Fig. 9 shows the variation of Pareto frontier with the population size. It can be seen that the Pareto frontier presents good consistency under different population size. When the population size is 150 or 200, the Pareto frontier with well-distributed converge in a small area. Furthermore, there is no signiﬁcant difference for the Pareto frontier when the population size increases from 150 to 200, but the optimization model has slower convergence rate with increasing population size. The variation of the Pareto frontier with the tournament size is shown in Fig. 10. It can be observed that the Pareto frontier obtains ideal distribution when the tournament size is 2, 4 or 8. In addition, when the tournament size is 4, the distribution of the Pareto frontier is better than that of others. Fig. 11 shows the variation of Pareto frontier with crossover fraction. It can be concluded that when the crossover fraction is 0.6 or 0.8, the Pareto frontier has ideal distribution. When the crossover fraction increases from 0.6 to 0.8, there is no signiﬁcant improvement for the Pareto frontier.

Table 6 Lower and upper bounds of decision variables. Decision variables

Lower bound

Upper bound

Evaporation pressure (MPa) Superheat degree (K) Condensation temperature (K) Exhaust temperature at the outlet of evaporator (K)

1 0 298.15 393.15

3 20 308.15 418.15

F. Yang et al. / Energy 93 (2015) 2208e2228

Start

Input operating conditions and logical bounds

Initial population

First generation

Calculate fitness function

If meet stopping criteria?

Yes

No

Selection Operator

Crossover Operator

Mutation Operator

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Fig. 12(a). It can be observed that the net power output increases with the evaporation pressure. This is due to the enthalpy of state point 2 shown in Fig. 3 is set as a constant value, the enthalpy of state point 1 increases with the evaporation pressure, which results in an increase in enthalpy difference between the inlet and the outlet of the expander. When the evaporation pressure increases from 1 MPa to 3 MPa, the net power output of the ORC system increases from 9.13 kW to 12.82 kW. Fig. 12(b) shows the variation of the EPC with the evaporation pressure. It can be seen that the EPC decreases with increasing evaporation pressure. According to Eq. (41), the EPC is mainly affected by the TIC and the net power output. Therein, the TIC is primarily determined by the heat transfer area. As can be seen from Fig. 12(d), the heat transfer area also increases with the evaporation pressure. The increment of the net power output is larger than that of the heat transfer area, which results in decreasing the EPC with the evaporation pressure. When the evaporation pressure increases from 1 MPa to 3 MPa, the EPC decreases from 1.13$/kW h to 0.86$/kW h. Fig. 12(c) illustrates the variation of the thermal efﬁciency with the evaporation pressure. From Eqs. (9), (11) and (12), when the heat transfer rate is certain, the thermal efﬁciency of the ORC system increases with the evaporation pressure. When the evaporation pressure increases from 1 MPa to 3 MPa, the thermal efﬁciency of the ORC system increases from 0.09 to 0.13. Furthermore, it can be seen from Fig. 12(d) that the heat transfer area increases from 25.47 m2 to 28.19 m2 with evaporation pressure increases from 1 MPa to 3 MPa.

New population

5.2. Effect of superheat degree

Output optimum solution

End Fig. 8. Flow chart of the optimization procedure.

Based on the above veriﬁcation results of the optimization model, the parameters setting are listed in Table 7. The method of ideal point is introduced to select an optimal solution from the Pareto solutions [53]. 5. Results The operating parameters of the ORC system have a great inﬂuence on the system performance. Therefore, it is necessary to investigate the variation of the system performance with the operating parameters. In addition, the exhaust temperature at the outlet of the evaporator is usually set up to be constant value [1,2,53e56]. However, the exhaust temperature, which is mainly inﬂuenced by the engine operating conditions, varies for the practical application. Take engine rated condition for example, R245fa is selected as the working ﬂuid to explore the potential for recovering the exhaust gas waste heat from a diesel engine. The effects of evaporation pressure, superheat degree, condensation temperature and exhaust temperature at the outlet of the evaporator on the system performance are analyzed. 5.1. Effect of evaporation pressure Fig. 12 shows the effect of the evaporation pressure on the net power output, EPC, thermal efﬁciency and heat transfer area at Tsup ¼ 10 K, Tcon ¼ 303.15 K and Texh;out ¼ 408.15. The variation of the net power output with the evaporation pressure is shown in

Fig. 13 shows the effect of the superheat degree on the system performances at Peva ¼ 2 MPa, Tcon ¼ 303.15 K and Texh;out ¼ 408.15. The variation of the net power output with the superheat degree is presented in Fig. 13(a). As can be seen, the net power output of the ORC system slightly increases with the increment of the superheat degree. When the superheat degree increases from 0 K to 20 K, the enthalpies of state point 1 in Fig. 3 are 485.15 kJ/kg, 493.16 kJ/kg, 500.69 kJ/kg, 507.88 kJ/kg and 514.84 kJ/kg, respectively. Due to the condensation temperature is kept constant at 303.15 K, so the increments of the enthalpy difference between state point 1 and state point 2 in Fig. 3 are 5.01 kJ/kg, 7.53 kJ/kg, 7.19 kJ/kg and 6.97 kJ/kg, respectively. Because of the working ﬂuid mass ﬂow rate is small, which leads to slightly increase in net power output with the superheat degree. When the superheat degree increases from 0 K to 20 K, the net power output of the ORC system shows an increase of 11.63 kWe11.74 kW. Fig. 13(b) illustrates the effect of the superheat degree on the EPC. It can be observed that the superheat degree causes a small decrease in EPC. This is due to the small variation in the net power output and heat transfer area with the increase in superheat degree. When the superheat degree increases from 0 K to 20 K, the EPC decreases from 0.93$/kW h to 0.91$/kW h. The effect of the superheat degree on the thermal efﬁciency is shown in Fig. 13(c). As can be seen, the thermal efﬁciency is almost kept a constant at 0.12. Fig. 13(d) shows the variation of the heat transfer area with the superheat degree. It can be concluded that the heat transfer area shows a decrease of 27.42 m2e27.18 m2. 5.3. Effect of condensation temperature Fig. 14 illustrates the variation of system performances with the condensation temperature at Peva ¼ 2 MPa, Tsup ¼ 10 K and Texh;out ¼ 408.15. The variation of the net power output with the condensation temperature is shown in Fig. 14(a). It can be observed that the net power output decreases obviously with increasing condensation temperature. This is due to the fact that the enthalpy of state point 1 in Fig. 3 is kept a constant value, whereas the

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Fig. 9. Pareto frontier under different population size.

Fig. 10. Pareto frontier under different tournament size.

F. Yang et al. / Energy 93 (2015) 2208e2228

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Fig. 11. Pareto frontier under different crossover fraction.

enthalpy of state point 2 in Fig. 3 increases, which results in increasing the enthalpy difference between the inlet and the outlet of the expander. When the condensation temperature increases from 298.15 K to 308.15 K, the net power output of the ORC system decreases from 12.33 kW to 11.09 kW. Fig. 14(b) shows the effect of the condensation temperature on the EPC. As can be seen, the EPC increases obviously with the condensation temperature. This is because an increase in condensation temperature causes the net power output to decrease while the heat transfer area to increase. When the condensation temperature increases from 298.15 K to 308.15 K, the EPC decreases from 0.87$/kW h to 0.97$/kW h. Fig. 14(c) illustrates the effects of the condensation temperature on the thermal efﬁciency. Similar to the evaporation pressure and superheat degree, the thermal efﬁciency depends mainly on the net power output when the heat transfer rate is certain. It can be seen that the thermal efﬁciency of the ORC system shows a decrease of 0.125 to 0.113 with the condensation temperature. The effect of the condensation temperature on the heat transfer area is evaluated in Fig. 14(d). It can be observed that the heat transfer area increases from 27 m2 to 27.46 m2 with the condensation temperature. Table 7 Parameters setting of genetic algorithm. Parameters

Value

Population size Selection function Tournament size Crossover fraction Mutation function Crossover function Stop generations

150 Tournament 4 0.6 Adaptive feasible Scattered 800

5.4. Effect of exhaust temperature at the outlet of the evaporator Fig. 15 shows the variation of the system performances with the exhaust temperature at the outlet of the evaporator at Peva ¼ 2 MPa, Tsup ¼ 10 K and Tcon ¼ 303.15. The effect of the exhaust temperature at the outlet of the evaporator on the net power output is presented in Fig. 15(a). It is shown that the net power output decreases obviously with increasing exhaust temperature at the outlet of the evaporator. This is due to all state points in Fig. 3 are certain, the net power output is mainly inﬂuenced by the mass ﬂow rate of the working ﬂuid. The heat transfer rate of the evaporator decreases with the increases of the exhaust temperature at the outlet of the evaporator, which will result in a decrease in the mass ﬂow rate of the working ﬂuid. When the exhaust temperature at the outlet of the evaporator increases from 393.15 K to 418.15 K, the net power output of the ORC system decreases from 12.40 kW to 11.24 kW. Fig. 15(b) shows the effect of the exhaust temperature at the outlet of the evaporator on the EPC. As can be seen, the EPC increases with the exhaust temperature at the outlet of the evaporator. This can be explained by the fact that the decrement of the net power output is larger than that of the heat transfer area presented in Fig. 15(d). When the exhaust temperature at the outlet of the evaporator increases from 393.15 K to 418.15 K, the EPC shows an increase of 0.89$/kW h to 0.94$/kW h. The effect of the exhaust temperature at the outlet of the evaporator on the thermal efﬁciency is shown in Fig. 15(c). It can be observed that the exhaust temperature at the outlet of the evaporator has no inﬂuence on the thermal efﬁciency. This is because the thermal efﬁciency of the ORC system depends on the enthalpies of each state point shown in Fig. 3. When all state points in Fig. 3 are certain, the thermal efﬁciency has no change. Under this condition, the thermal efﬁciency of the ORC system is

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Fig. 12. The effects of evaporation pressure on the system performances.

0.12. Fig. 15(d) shows the variation of the heat transfer area with the exhaust temperature at the outlet of the evaporator. It can be concluded that the heat transfer area decreases with increasing exhaust temperature at the outlet of the evaporator, which is mainly caused by decreasing the heat transfer rate. The heat transfer area shows a decrease of 29.86 m2e25.67 m2 with the exhaust temperature at the outlet of the evaporator. It can be seen from the aforementioned analysis that the variation of the operating parameters has a great inﬂuence on the system performance. For the practical application of the ORC system, the optimal operating parameters vary with the engine's operating conditions. Therefore, it will be necessary to investigate the optimal operating parameters under engine various operating conditions. 5.5. Pareto optimization of the ORC system Based on the optimization model established in section 4, the evaporation pressure, superheat degree, condensation temperature and exhaust temperature at the outlet of the evaporator are selected as the decision variables for maximizing net power output and minimizing total investment cost. GA is used to conduct the multi-objective optimization for six different working ﬂuids in the ORC system. Fig. 16 shows the optimization results of the net power output for six different working ﬂuids under various operating conditions of the diesel engine. It can be seen that the optimization results of the net power output for these six different working ﬂuids have the same variation tendency, and all present higher net power output

in high speed and high load region. This is due to the exhaust energy is high when the diesel engine operates in the high speed and high load region, which results in a higher mass ﬂow rate of the working ﬂuid. It can also be observed that the overall variation tendency of the net power output depends on the exhaust energy of the diesel engine other than the types of the working ﬂuids. Although the optimization results of the net power output for these six different working ﬂuids has the same variation tendency, the corresponding values for each working ﬂuid are different. Fig. 16(a) shows the optimization results of the net power output using R600 under various operating conditions of the diesel engine. As can be seen, at the engine's rated condition, the optimized net power output of the ORC system is 11.19 kW. While at idle condition, the optimized net power output of the ORC system is only 0.32 kW. Similarly, Fig. 16(b)e(f) illustrates the optimized net power output of the ORC system using R600a, R601a, R245fa, R1234yf and R1234ze respectively. At the engine's rated condition, the optimized net power outputs of the ORC system for these ﬁve different working ﬂuids are 8.78 kW, 13.19 kW, 11.55 kW, 5.17 kW and 7.05 kW, respectively. It can be concluded that when using R601a, R245fa and R600 as the working ﬂuids, the ORC system shows better thermal performance. In addition, whichever working ﬂuid the ORC system selects, they all have the lowest net power output at idle condition of the diesel engine. At idle condition, the optimized net power outputs of the ORC system for these ﬁve different working ﬂuids are 0.27 kW, 0.45 kW, 0.36 kW, 0.16 kW and 0.21 kW, respectively. Fig. 17 shows the optimization results of the TIC for these six different working ﬂuids under various operating conditions of the

F. Yang et al. / Energy 93 (2015) 2208e2228

2221

Fig. 13. The effects of superheat degree on the system performances.

diesel engine. Similar to the net power output, the TIC is mainly inﬂuenced by the operating conditions of the diesel engine. The net power output of the ORC system increases with the exhaust energy, which results in an increase in cost of power consumption equipment and heat transfer area. Thus, the TIC increases with the cost of power consumption equipment and heat transfer area. That is to say, thermodynamic performance of the ORC system is improved at the expense of economic performance. Fig. 17(a)e(f) illustrates the optimization results of the TIC using R600, R600a, R601a, R245fa, R1234yf and R1234ze, respectively. At the engine's rated condition, the corresponding TIC are 527,000$, 501,930$, 536,990$, 532,710$, 501,930$ and 511,460$. According to the results presented in Figs. 16 and 17, the ORC system using R601a, R245fa and R600 has higher net power output with higher TIC. At idle condition, the optimization results of the TIC for these six different working ﬂuids are 372,900$, 370,750$, 382,900$, 384,930$, 368,890$ and 369,230$. It can be concluded that even if at idle condition, the ORC system also has higher TIC with lower exhaust energy. This is due to the ORC system is not yet common at this stage. For the near future, the TIC will decrease with the development of the ORC technology. It can be seen from the aforementioned analysis that the working ﬂuid with higher net power output also has higher TIC. Therefore, it is essential to investigate other evaluation indicators for the optimal working ﬂuid. EPC is usually used to evaluate the thermoeconomic performance of the ORC system. Fig. 18 shows the normalized results of the EPC for these six different working ﬂuids under full-load characteristic. As can be seen, the ORC system using R601a, R245fa and R600 has smaller polygon area under the eleven operating points of the full-load characteristic. That is to say, the

ORC system using R601a, R245fa and R600 has lower EPC under the same operating condition of the diesel engine. When using R1234yf as working ﬂuid, the ORC system has the largest polygon area with the worst thermoeconomic performance. It also can be seen that the EPC decreases with increasing engine speed. Fig. 19 shows the normalized results of the thermal efﬁciency for these six different working ﬂuids under full-load characteristic. As can be seen, the polygons of the normalized results of the thermal efﬁciency for these six different working ﬂuids are nearly circular, which shows that the thermal efﬁciency remains approximately constant under full-load characteristic of the diesel engine. Furthermore, the polygon areas of the normalized results of the thermal efﬁciency using R601a and R245fa are obviously larger than that of others. According to the optimization results, the effect of critical temperature of these six different working ﬂuids on the system performances when the diesel engine operates at rated condition is shown in Fig. 20. The working ﬂuids with critical temperature in descending order are: R601a, R245fa, R600, R600a, R1234ze and R1234yf. Fig. 20(a) presents the variation of net power output with the critical temperature. It can be seen that the net power output increases with increasing working ﬂuids' critical temperature. R601a with the highest critical temperature has the maximum net power output, while R1234yf with the lowest critical temperature has the minimum net power output. The ﬁgure also shows that the net power output increases from 5.17 kW to 13.19 kW as the critical temperature increases from 367.85 K to 460.35 K. The same behavior is also obtained for the thermal efﬁciency presented in Fig. 20(c). It clearly indicates that the higher the critical

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F. Yang et al. / Energy 93 (2015) 2208e2228

Fig. 14. The effects of condensation temperature on the system performances.

temperature of the working ﬂuid the better the system net power output and thermal efﬁciency. Consistent with other researchers' ﬁndings [19,20,57,58], the critical temperature of the working ﬂuid is a vital decision criteria for the ORC system performances. Fig. 20(b) shows the variation of EPC with the critical temperature. It can be concluded that the EPC decreases with increasing working ﬂuids' critical temperature. When the critical temperature increases from 367.85 K to 460.35 K, the EPC decreases from 1.91$/ kW h to 0.8$/kW h. It means that the working ﬂuids with the higher critical temperature also have better economic performances. Contrary to net power output and thermal efﬁciency, the critical temperature of the working ﬂuid is not the only criteria for TIC as shown in Fig. 20(d). Based on the aforementioned analysis, when using R601a and R245fa as the working ﬂuids, the ORC system presents better thermodynamic and economic performances. For practical application of the ORC system, not only the thermoeconomic performances, but also the environmental impacts, safety levels, toxicity and ﬂammability should be considered. Comparing R601a with R245fa, both working ﬂuids have null ODP and low GWP. R245fa is a non-corrosive, non-ﬂammable, low-toxic and stable working ﬂuid under the atmospheric pressure, which can be applied over a wide heat source temperature range. Although R601a is an environmental friendly working ﬂuids and presents better thermodynamic performances, important point to be noted that it is an extremely volatile and extremely ﬂammable liquid at room temperature and pressure [55,59,60]. Furthermore, R601a may also cause respiratory disease and mild dermatitis due to its irritant effect. Thus, R245fa is selected as the most suitable working ﬂuid for engine waste heat recovery application with overall consideration of thermoeconomic

performances, environmental impacts, safety levels and ﬁtness factors. While many researches of working ﬂuid selections have been done for ORC applications, the general conclusions cannot be reached at this stage [19]. The new contribution of this study is to obtain the optimal operating regions of the ORC system with consideration of working ﬂuid selections and thermoeconomic performances under engine various operating conditions by using optimization algorithm. More detailed mechanism analysis of organic working ﬂuids will be accomplished in the future. Fig. 21 shows the optimization results of evaporation pressure, superheat degree, condensation temperature and exhaust temperature at the outlet of the evaporator using R245fa under engine various operating conditions. Combined with the optimal operating parameters, it can provide a guidance for the control strategy of the ORC system. The optimization result of the evaporation pressure under engine various operating conditions is shown in Fig. 21(a). As can be seen, the optimized evaporation pressure varies in a small range. The variation range of the optimized evaporation pressure is from 1.1 MPa to 2.1 MPa. The evaporation pressure is set from 1 MPa to 3 MPa in the optimization model of section 4. It can thus be seen that the optimized evaporation pressure do not reach the upper limit of the evaporation pressure. Considering the rated pressure of the pump and the pressure capacity of the pipe, the optimized evaporation pressure can meet the requirements of practical engineering application. Fig. 21(b) shows the optimization results of the superheat degree under engine various operating conditions. In general, it can be concluded that the optimized superheat degree is mainly inﬂuenced by the operating conditions of the diesel engine. Over the whole operating range of the diesel engine, the optimized superheat degree is from 0.5 K to 20 K. The optimized condensation

F. Yang et al. / Energy 93 (2015) 2208e2228

2223

Fig. 15. The effects of exhaust temperature at the outlet of the evaporator on the system performances.

temperature under engine various operating conditions is illustrated in Fig. 21(c). It can be observed that the optimized condensation temperature is almost kept a constant at 298.15 K for most of the operating conditions, and only few operating points can reach

up to 300 K. It also indicated that the variation of the operating conditions of the diesel engine has a slight inﬂuence on the optimized condensation temperature in pursuit of the optimal thermoeconomic performance. Considering the lower condensation

Fig. 16. The optimization results of the net power output for the six different working ﬂuids.

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Fig. 17. The optimization results of the total investment cost for the six different working ﬂuids.

temperature of the working ﬂuid, the water cooling method is recommended for the practical application of the ORC system. Meanwhile, the cooling water's temperature varies signiﬁcantly with the seasons. The cooling intensity is controlled by regulating the mass ﬂow rate of the cooling water. The temperature of the low temperature heat source varies within a small range. Therefore, the optimized condensation temperature can also meet the requirements of practical engineering application. Fig. 21(d) shows the optimization results of the exhaust temperature at the outlet of the evaporator under engine various operating conditions. It can be seen that the optimized exhaust temperature at the outlet of the evaporator is mainly inﬂuenced by the engine torque. When the engine torque is above 500 N m, the optimized exhaust temperature at the outlet of the evaporator is in the range of 414 Ke417 K. When the engine torque is from the idle condition to 500 N m, the optimized exhaust temperature at the outlet of the evaporator is in the range of 393 Ke414 K. In addition, the optimized exhaust temperature at the outlet of the evaporator decreases from 414 K to

393 K with decreasing the engine torque. This is due to the fact that the exhaust temperature is low when the engine is operated at low load regions. The exhaust temperature at the outlet of the evaporator should be decreased to ensure higher heat transfer rate. Fig. 22 shows the optimization results of the mass ﬂow rate of the working ﬂuid, heat transfer rate, EPC and thermal efﬁciency using R245fa under engine various operating conditions. The operating parameters of the ORC system is controlled by regulating the mass ﬂow rate of the working ﬂuid during practical operation. The variation of the optimized mass ﬂow rate of the working ﬂuid under engine various operating conditions is shown in Fig. 22(a). As can be seen, although the optimized operating parameters have a big ﬂuctuation, the mass ﬂow rate of the working ﬂuid is mainly inﬂuenced by the exhaust energy. It also can be seen that the mass ﬂow rate of the working ﬂuid increases with the exhaust energy. Over the whole operating range of the diesel engine, the optimized mass ﬂow rate of the working ﬂuid is in the range of 0.01 kg/s to 0.34 kg/s. Fig. 22(b) shows the variation of the heat transfer rate in

Fig. 18. Normalized results of the EPC for the six different working ﬂuids under fullload conditions.

Fig. 19. Normalized results of the thermal efﬁciency for the six different working ﬂuids under full-load conditions.

F. Yang et al. / Energy 93 (2015) 2208e2228

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Fig. 20. The effect of critical temperature of six different working ﬂuids on the system performances.

the evaporator under engine various operating conditions. It can be seen that the variation of the heat transfer rate is very similar to the exhaust energy and the mass ﬂow rate of the working ﬂuid. For the exhaust side, the exhaust mss ﬂow rate and exhaust temperature increases with the engine speed and engine torque, which further increases the exhaust energy and the heat transfer rate of the

evaporator. Over the whole operating range of the diesel engine, the heat transfer rate of the evaporator is in the range of 3.11 kWe94.27 kW. The variation of the EPC under engine various operating conditions is presented in Fig. 22(c). It can be observed that the EPC is mainly inﬂuenced by the engine torque. When the diesel engine operates at the high load regions, the ORC system

Fig. 21. Optimization results of the operating parameters for R245fa.

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Fig. 22. Optimization results of mass ﬂow rate of working ﬂuid, heat transfer rate, EPC and thermal efﬁciency for R245fa.

shows a better economic performance with a lower EPC. At these operating regions of the diesel engine, the EPC is in the range of 0.91$/kW h to 3.19$/kW h. The EPC increases dramatically with decreasing engine torque. This is due to the fact that when the diesel engine operates at the medium-low torque regions, the net power output of the ORC system decreases signiﬁcantly, while the TIC of the ORC system decreases slightly, which results in an increase in EPC obviously. That is to say, when the ORC technology is used to recover the waste heat from the IC engines, it has better thermoeconomic performance at the mediumehigh regions of the IC engines. Fig. 22(d) illustrates the variation of the thermal efﬁciency of the ORC system under engine various operating conditions. It can be seen that the thermal efﬁciency of the ORC system is approximately 0.12 under most of the operating conditions. When the diesel engine operates at the low load regions, the thermal efﬁciency of the ORC system decreases to 0.11. Based on the aforementioned analysis, the optimal operating parameters and their corresponding thermoeconomic indicators using R245fa as working ﬂuid at engine rated condition are listed in Table 8.

6. Conclusions In this paper, the ORC system is used to recover the exhaust waste heat from a diesel engine, the thermodynamic, economic and optimization models of the ORC system are established, respectively. The effects of four key parameters, including evaporation pressure, superheat degree, condensation temperature and exhaust temperature at the outlet of the evaporator on the thermodynamic

Table 8 Optimal operating parameters and the corresponding thermoeconomic indicators of the ORC system at engine rated condition. Item

Value

Item

Value

Item

Value

Peva (MPa) Tsup (K) Tcon (K) Texh;out (K)

1.83 19.98 298.62 417.61

_ net (kW) W Ctot ($) m_ wf (kg/s) EPC($/kW h)

11.55 532,707 0.34 0.91

hth (%) Q_ eva (kW) Aeva (m2) Acon (m2)

12.26 94.27 14.76 10.55

performances and economic indicators of the ORC system are investigated. Furthermore, based on the established optimization model, genetic algorithm is employed to solve the Pareto solution of the thermodynamic performances and economic indicators for maximizing net power output and minimizing total investment cost under diesel engine various operating conditions using R600, R600a, R601a, R245fa, R1234yf and R1234ze as working ﬂuids. The most suitable working ﬂuid used in the ORC system for diesel engine waste heat recovery is screened out, and then the corresponding optimal parameter regions are analyzed. The main conclusions can be summarized as follows: (1) The thermodynamic and economic performance of the ORC system is improved by increasing the evaporation pressure. The superheat degree has a slight inﬂuence on the ORC system. Both thermodynamic and economic performances gradually worsen with increasing the condensation temperature and exhaust temperature at the outlet of the evaporator. (2) Based on the optimization results, the thermodynamic performance of the ORC system is improved at the expense of economic performance. For the selected working ﬂuids, R601a and R245fa show better thermoeconomic performance. At engine rated condition, the net power outputs of the ORC system for these two working ﬂuids are 13.19 kW and 11.55 kW, respectively. The total investment costs of the ORC system for these two working ﬂuids are 536,990$ and 532,710$, respectively. (3) R245fa is the best choice for the engine waste heat recovery application with overall consideration of thermoeconomic performances, environmental impacts and safety levels. (4) When using R245fa as the working ﬂuid, the optimized evaporation pressure varies from 1.1 MPa to 2.1 MPa. The optimized superheat degree is mainly inﬂuenced by the operating conditions of the diesel engine. Over the whole operating range of the diesel engine, the optimized superheat degree is from 0.5 K to 20 K. The optimized condensation temperature is almost kept a constant at 298.15 K for

F. Yang et al. / Energy 93 (2015) 2208e2228

most of the operating conditions. The optimized exhaust temperature at the outlet of the evaporator is mainly inﬂuenced by the engine torque. When the engine torque is above 500 N m, the optimized exhaust temperature at the outlet of the evaporator is in the range of 414 Ke417 K. (5) Both mass ﬂow rate of the working ﬂuid and heat transfer rate of the evaporator increases with the engine speed and torque. The ORC system has better thermoeconomic performance at the mediumehigh regions of the IC engines. The thermal efﬁciency of the ORC system is approximately 0.12 under most of the operating conditions. ORC technology is an effective way to recover the low grade waste heat. Currently, this technology has also been widely applied in engine waste heat recovery. But most of the present researches only focus on the parameters sensitivity analysis, and few of them have considered the multi-objective and multi-parameter optimization by using the optimization algorithm. In addition, the vehicle engine often operates at various operating conditions. Therefore, one important thing is how to deal with the coordinated variation of ORC parameters and engine operating conditions. The main contribution of this paper is to obtain the optimal operating regions of the ORC system with consideration of thermodynamic performances and economic indicators under engine various operating conditions by using genetic algorithm. The optimization results indicate that engine operating conditions have a great inﬂuence on the optimized evaporation pressure, superheat degree and exhaust temperature at the outlet of the evaporator, while the optimized condensation temperature is almost kept a constant value for most of the engine operating conditions. In summary, this research is helpful in determining optimal operating regions and selecting proper working ﬂuids for the diesel engine-ORC combined system. Acknowledgments This work was sponsored by the National Natural Science Foundation of China (Grant No. 51376011), the Beijing Natural Science Foundation Program (Grant No. 3152005), the Scientiﬁc Research Key Program of Beijing Municipal Commission of Education (Grant No. KZ201410005003), and the Key Project of Thirteenth Scientiﬁc Research Foundation for Graduate Students in Beijing University of Technology (Grant No. ykje2014e10708). The authors would like to thank the reviewers for their valuable comments on this research. Nomenclature _ W Q_ m_ h s I_ T P K A Nu d r Re Pr l

power (kW) heat transfer rate (kW) mass ﬂow rate (kg/s) speciﬁc enthalpy (kJ/kg) or convective heat transfer coefﬁcient (W/m2 K) speciﬁc entropy (kJ/kg K) exergy destruction rate (kW) temperature (K) pressure (MPa) overall heat transfer coefﬁcient (W/m2 K) heat transfer area (m2) Nusselt number diameter (m) fouling resistance (m2 K/W) Reynolds number Prandtl number length (m)

ct f F S x pr q M P

2227

temperature difference correction factor resistance coefﬁcient forced convective heat transfer enhancement factor suppression factor quality reduced pressure heat ﬂux (W/m2) molecular weight (kg/kmol) pressure (MPa)

Greek symbols b rib effect coefﬁcient a heat transfer coefﬁcient (W/m2 K) l thermal conductivity (W/m K) h efﬁciency d ﬁn height (m) ε correction factor Subscripts 0 reference state 1e7 state points in the cycle i inner o outer exp expander exh exhaust con condenser wf working ﬂuid tp two phase l liquid v vapor fb ﬁlm boiling nb nucleate boiling L all the mass ﬂow rate taken as liquid eva evaporator eq equivalent th thermal sup superheat degree in inlet out outlet tot total cool cooling water Acronyms ORC organic Rankine cycle PPTD pinch point temperature difference LMTD logarithmic mean temperature difference ODP ozone depletion potential GWP global warming potential References [1] Yang FB, Dong XR, Zhang HG, Wang Z, Yang K, Zhang J, et al. Performance analysis of waste heat recovery with a dual loop organic Rankine cycle (ORC) system for diesel engine under various operating conditions. Energy Convers Manag 2014;80:243e55. [2] Wang EH, Zhang HG, Fan BY, Wu YT. Optimized performances comparison of organic Rankine cycles for low grade waste heat recovery. J Mech Sci Technol 2012;26:2301e12. [3] Hendricks TJ, Lustbader JA. Advanced thermoelectric power system investigations for light-duty and heavy duty applications: part I. In: Proceedings of the 21st international conference on thermoelectrics; 2002. [4] Wang TY, Zhang YJ, Peng ZJ, Shu GQ. A review of researches on thermal exhaust heat recovery with Rankine cycle. Renew Sustain Energy Rev 2011;15:2862e71. [5] Vazaquez J, Zanz-Bobi MA, Palacios R, Arenas A. State of the art of thermoelectric generators based on heat recovered from the exhaust gases of automobiles. In: Proceedings of 7th European workshop on thermoelectrics; 2002.

2228

F. Yang et al. / Energy 93 (2015) 2208e2228

[6] Zhang HG, Wang EH, Fan BY. A performance analysis of a novel system of a dual loop bottoming organic Rankine cycle (ORC) with a light-duty diesel engine. Appl Energy 2013;102:1504e13. [7] Yue C, Han D, Pu WH. Analysis of the integrated characteristics of the CPS (combined power system) of a bottoming organic Rankine cycle and a diesel engine. Energy 2014;72:739e51. [8] Yu GP, Shu GQ, Tian H, Wei HQ, Liu LN. Simulation and thermodynamic analysis of a bottoming organic Rankine cycle (ORC) of diesel engine (DE). Energy 2013;51:281e90. [9] Galindo J, Ruiz S, Dolz V, Royo-Pascual L, Haller R, Nicolas B, et al. Experimental and thermodynamic analysis of a bottoming organic Rankine cycle (ORC) of gasoline engine using swash-plate expander. Energy Convers Manag 2015;103:519e32. [10] Lodwig E. Performance of a 35 HP organic Rankine cycle exhaust gas powered system. 1970. SAE Paper 700160. [11] Leising CJ, Purohit GP, DeGrey SP, Finegold JG. Waste heat recovery in truck engines. 1978. SAE Paper 780686. [12] Doyle E, Dinanno L, Kramer S. Installation of a diesel-organic Rankine compound engine in a class 8 truck for a single vehicle test. 1979. SAE Paper 790646. [13] Tian H, Shu GQ, Wei HQ, Liang XY, Liu LN. Fluids and parameters optimization for the organic Rankine cycles (ORCs) used in exhaust heat recovery of Internal Combustion Engine (ICE). Energy 2012;47:125e36. [14] Sprouse III C, Depcik C. Review of organic Rankine cycles for internal combustion engine exhaust waste heat recovery. Appl Them Eng 2015;75: 1065e75. [15] Liu BT, Chien KH, Wang CC. Effect of working ﬂuids on organic Rankine cycle for waste heat recovery. Energy 2004;29:1207e17. [16] Wang EH, Zhang HG, Fan BY, Ouyang MG, Zhao Y, Mu QH. Study of working ﬂuid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy 2011;36:3406e18. [17] Andreasen JG, Larsen U, Knudsen T, Pierobon L, Haglind F. Selection and optimization of pure and mixed working ﬂuids for low grade heat utilization using organic Rankine cycles. Energy 2014;73:204e13. [18] Roy JP, Mishra MK, Misra A. Performance analysis of an organic Rankine cycle with superheating under different heat source temperature conditions. Appl Energy 2011;88:2995e3004. [19] Xu JL, Yu C. Critical temperature criterion for selection of working ﬂuids for subcritical pressure organic Rankine cycles. Energy 2014;74:719e33. [20] Xu JL, Liu C. Effect of the critical temperature of organic ﬂuids on supercritical pressure organic Rankine cycles. Energy 2013;63:109e22. [21] Mago PJ, Chamra LM, Srinivasan K, Somayaji C. An examination of regenerative organic Rankine cycles using dry ﬂuids. Appl Therm Eng 2008;28: 998e1007. [22] Wang JF, Yan ZQ, Wang M, Ma SL, Dai YP. Thermodynamic analysis and optimization of an (organic Rankine cycle) ORC using low grade heat source. Energy 2013;49:356e65. [23] Liu XM, Wang X, Zhang CH. Sensitivity analysis of system parameters on the performance of the organic Rankine cycle system for binary-cycle geothermal power plants. Appl Therm Eng 2014;71:175e83. [24] Yang MH, Yeh RH. Thermo-economic optimization of an organic Rankine cycle system for large marine diesel engine waste heat recovery. Energy 2015;82: 256e68. [25] Miao Z, Xu JL, Yang XF, Zhou JH. Operation and performance of a low temperature organic Rankine cycle. Appl Therm Eng 2015;75:1065e75. [26] Xi H, Li MJ, Xu C, He YL. Parametric optimization of regenerative organic Rankine cycle (ORC) for low grade waste heat recovery using genetic algorithm. Energy 2013;58:473e82. [27] Wang ZQ, Zhou NJ, Guo J, Wang XY. Fluid selection and parametric optimization of organic Rankine cycle using low temperature waste heat. Energy 2012;40:107e15. [28] Rashidi MM, Galanis N, Nazari F, Basiri Parsa A, Shamekhi L. Parametric analysis and optimization of regenerative Clausius and organic Rankine cycles with two feedwater heaters using artiﬁcial bees colony andartiﬁcial neural network. Energy 2011;36:5728e40. [29] Shu GQ, Liu LN, Tian H, Wei HQ, Yu GP. Parametric and working ﬂuid analysis of a dual-loop organic Rankine cycle (DORC) used in engine waste heat recovery. Appl Energy 2014;113:1188e98. [30] Yang K, Zhang HG, Wang Z, Zhang J, Yang FB, Wang EH, et al. Study of zeotropic mixtures of ORC (organic Rankine cycle) under engine various operating conditions. Energy 2013;58:484e510. [31] Song J, Song Y, Gu CW. Thermodynamic analysis and performance optimization of an organic Rankine cycle (ORC) waste heat recovery system for marine diesel engines. Energy 2015;82:976e85. [32] Maraver D, Royo J, Lemort V, Quoilin S. Systematic optimization of subcritical and transcritical organic Rankine cycles (ORCs) constrained by technical parameters in multiple applications. Appl Energy 2014;117:11e29. [33] Imran M, Park BS, Kim HJ, Lee DH, Usman M, Heo M. Thermo-economic optimization of regenerative organic Rankine cycle for waste heat recovery applications. Energy Convers Manag 2014;87:107e18.

[34] Zhang SJ, Wang HX, Guo T. Performance comparison and parametric optimization of subcritical organic Rankine cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88:2740e54. [35] Li YR, Du MT, Wu CM, Wu SY, Liu C, Xu JL. Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis. Energy 2014;68:238e47. [36] Hajabdollahi Z, Hajabdollahi F, Tehrani M, Hajabdollahi H. Thermo-economic environmental optimization of organic Rankine cycle for diesel waste heat recovery. Energy 2013;63:142e51. [37] Yu HS, Feng X, Wang YF. A new pinch based method for simultaneous selection of working ﬂuid and operating conditions in an ORC (organic Rankine cycle) recovering waste heat. Energy 2015. http://dx.doi.org/10.1016/j.energy. 2015.02.059. [38] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Them Eng 2011;31: 2885e93. [39] Wang TY, Zhang YJ, Zhang J, Peng ZJ, Shu GQ. Comparisons of system beneﬁts and thermo-economics for exhaust energy recovery applied on a heavy-duty diesel engine and a light-duty vehicle gasoline engine. Energy Convers Manag 2014;84:97e107. [40] Yang XF, Xu JL, Miao Z, Zou JH, Yu C. Operation of an organic Rankine cycle dependent on pumping ﬂow rates and expander torques. Energy 2015. http:// dx.doi.org/10.1016/j.energy.2015.07.121. [41] Zhang HG, Wang EH, Fan BY. Heat transfer analysis of a ﬁnned-tube evaporator for engine exhaust heat recovery. Energy Convers Manag 2013;65: 438e47. [42] Papadopoulos AI, Stijepovic M, Linke P. On the systematic design and selection of optimal working ﬂuids for organic Rankine cycles. Appl Therm Eng 2010;30:760e9. [43] Wang EH, Zhang HG, Fan BY, Ouyang MG, Yang K, Yang FY, et al. 3D numerical analysis of exhaust ﬂow inside a ﬁn-and-tube evaporator used in engine waste heat recovery. Energy 2015;82:800e12. [44] Zukauskas A. Heat transfer from tubes in cross ﬂow. Adv. Heat Transfer. New York: Academic Press; 1972. p. 93e106. [45] Gnielinski V. New equations for heat mass transfer in turbulent pipe and channel ﬂows. Int Chem Eng 1976;16:359e68. [46] Liu Z, Winterton RHS. A general correlation for saturated and subcooled ﬂow boiling in tubes and annuli, based on a nucleate pool boiling equation. Int J Heat Mass Tran 1991;34:2759e66. n-Salvador JM, Gonza lvez-Maci [47] García-Cascales JR, Vera-García F, Corbera a J. Assessment of boiling and condensation heat transfer correlations in the modelling of plate heat exchangers. Int J Refrig 2007;30:1029e41. [48] Yan YY, Lio HC, Lin TF. Condensation heat transfer and pressure drop of refrigerant R-134a in a plate heat exchanger. Int J Heat Mass Tran 1999;42: 993e1006. [49] Li MQ, Wang JF, Li SL, Wang XR, He WF, Dai YP. Thermo-economic analysis and comparison of a CO2 transcritical power cycle and an organic Rankine cycle. Geothermics 2014;50:101e11. [50] Nafey AS, Sharaf MA. Combined solar organic Rankine cycle with reverse osmosis desalination process: energy, exergy, and cost evaluations. Renew Energy 2010;35:2571e80. [51] Chen QC, Xu JL, Chen HX. A new design method for organic Rankine cycles with constraint of inlet and outlet heat carrier ﬂuid temperatures coupling with the heat source. Appl Energy 2012;98:562e73. [52] Matlab. Global optimization toolbox user's guide, Matlab R2010a. The MathWorks, Inc; 2010. [53] Wang JF, Yan ZQ, Wang M, Li MQ, Dai YP. Multi-objective optimization of an organic Rankine cycle (ORC) for low grade waste heat recovery using evolutionary algorithm. Energy Convers Manag 2013;71:146e58. [54] Vaja I, Gambarotta A. Internal combustion engine (ICE) bottoming with organic Rankine cycles (ORCs). Energy 2010;35:1084e93. [55] Zhang J, Zhang HG, Yai K, Yang FB, Wang Z, Zhao GY, et al. Performance analysis of regenerative organic Rankine cycle (RORC) using the pure working ﬂuid and the zeotropic mixture over the whole operating range of a diesel engine. Energy Convers Manag 2014;84:282e94. [56] Yang FB, Zhang HG, Bei C, Song SS, Wang EH. Parametric optimization and performance analysis of ORC (organic Rankine cycle) for diesel engine waste heat recovery with a ﬁn-and-tube evaporator. Energy 2015;91:128e41. [57] Rayegan R, Tao YX. A procedure to select working ﬂuids for solar organic Rankine cycles (ORCs). Renew Energy 2011;36:659e70. [58] Aljundi IH. Effect of dry hydrocarbons and critical point temperature on the efﬁciencies of organic Rankine cycle. Renew Energy 2011;36:1196e202. [59] Garg P, Kumar P, Srinivasan K, Dutta P. Evaluation of isopentane, R-245fa and their mixtures as working ﬂuids for organic Rankine cycles. Appl Therm Eng 2013;51:292e300. [60] Shu GQ, Li XN, Tian H, Liang XY, Wei HQ, Wang X. Alkanes as working ﬂuids for high-temperature exhaust heat recovery of diesel engine using organic Rankine cycle. Appl Energy 2014;119:204e17.

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