Thermoeconomic multi-objective optimization of an organic Rankine cycle for exhaust waste heat recovery of a diesel engine

Energy 93 (2015) 2208e2228

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Energy journal homepage: www.elsevier.com/locate/energy

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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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

2213

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

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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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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

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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

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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.

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