Fluids and parameters optimization for the organic Rankine cycles (ORCs) used in exhaust heat recovery of Internal Combustion Engine (ICE)

Fluids and parameters optimization for the organic Rankine cycles (ORCs) used in exhaust heat recovery of Internal Combustion Engine (ICE)

Energy 47 (2012) 125e136 Contents lists available at SciVerse ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Fluids and para...

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Energy 47 (2012) 125e136

Contents lists available at SciVerse ScienceDirect

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

Fluids and parameters optimization for the organic Rankine cycles (ORCs) used in exhaust heat recovery of Internal Combustion Engine (ICE) Hua Tian, Gequn Shu*, Haiqiao Wei, Xingyu Liang, Lina Liu State Key Laboratory of Engines, Tianjin University, No. 92 Weijin Road, Nankai Region, Tianjin 300072, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 October 2011 Received in revised form 20 August 2012 Accepted 8 September 2012 Available online 9 October 2012

An Organic Rankine Cycle (ORC) system used in the Internal Combustion Engine (ICE) exhaust heat recovery was proposed and techno-economically analyzed based on various working fluids. It is significant to recover ICE exhaust heat (about one third of energy generated from the fuel) by ORC system. In this paper, the suitable working fluids have been screened and recommended for the ORC system, among 20 fluids (boiling point temperature range from 51.60 to 32.05  C) analyzed on the rated condition of one popular commercial diesel generator set. The cycle parameters, including the thermal efficiency (hth), the expansion ratio (v2/v1), the net power output per unit mass flow rate of hot exhaust (Pnet), the ratio of total heat transfer area to net power output (A/Wnet), and electricity production cost (Epc), have also been analyzed and optimized. Results show that R141b, R123 and R245fa present the highest hth and Pnet values ranging from 16.60% to 13.30% (hth value), and from 60 to 49 kJ/kg (Pnet value). Meanwhile, the three fluids also express the lowest Epc values ranging from 0.30 to 0.35$/kWh, and lowest A/Wnet values ranging from 0.436 to 0.516 m2/kW. The optimum evaporating pressures for R141b, R123, R245fa are ranging from 2.8 MPa to 3.6 MPa. Research Subject: Waste heat recovery technology in internal combustion engine; The key technology on the improvement of ICE efficiency. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Working fluid Organic Rankine cycle (ORC) Internal Combustion Engine (ICE) Exhaust gas Techno-economy

1. Introduction Energy is an important entity for the economic development of any country. The rapid industrial and economical growth in China where one fourth population of the world is present has increased the need for energy rapidly in the recent years. Considering the environmental protection and also in the context of great uncertainty over future energy supplies, attention is concentrated on the utilization of sustainable energy sources and the energy conservation methodologies. In China, internal combustion engines (ICE) have consumed over 66 percent of overall fuel consumption. Since it is difficult for the maximum efficiency of ICE to be higher than 42% [1], large amount fuel energy is rejected from the engine to the surroundings as waste heat in several forms, with a significant fraction through the exhaust. A recent study [2] estimated in a typical 2L gasoline engine used on passenger cars, 21% of the released energy is wasted through the exhaust at the most common load and speed condition. This increases to 44% at the peak power * Corresponding author. Tel./fax: þ86 (0)22 27409558. E-mail addresses: [email protected], [email protected] (G. Shu). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.09.021

point. On average, about one third of energy generated from the fuel is wasted via exhaust gases. It was predicted by Vazaquez et al. [3] that if only 6% of the heat contained in exhaust gases was converted to electric power, this would mean reduction of fuel consumption by 10% due to the decrease in mechanical losses from the resistance of the alternator drive. In addition, the experimental work conducted by Honda (Endo et al. [4]) with a thermal recovery system showed a maximum thermal cycle efficiency of 13%. At 100 km/h, this yielded a cycle output of 2.5 kW (for an engine output of 19.2 kW), representing an increase in the thermal efficiency of the engine from 28.9% to 32.7%. Organic Rankine Cycle (ORC) could be used to recover waste heat from ICE exhaust gas. Compared to steam Rankine cycle on a same working condition, there are some advantages of ORC as follows. First, higher thermal efficiency and more net power are achieved by ORC. Second, organic fluids often have lower vaporization heat and can follow the heat source to be cooled better than water at the same boiling temperature, thus reducing temperature differences and irreversibility at the evaporator, and therefore downsizing system volume and weight, which is significant for vehicle applications. Finally, turbines for organic cycles can provide higher efficiencies at

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part loads as well and are usually less complex due to the lower enthalpy drop of the fluid. For the ORC system using in ICE waste heat recovery, there are several researches. Kane M et al. [5] presented the retrofit with two different ORC systems rated about 10 kW of a small engine with a power of 200 kW, fueled with biogas. The paper focused on the application of scroll expander for its advantageous when the power of the ORC is limited. The feasibility of the system was supported by field tests conducted on an experimental unit. Ringler et al. [6] considered water and ethanol as working fluids for two kinds of ORC for waste heat recovery of gasoline engines. Danov SN and Gupta AK [7,8] proposed a setup where a low speed two stroke marine turbocharged Diesel engine acted as the topper of a combined cycle, with exhaust gases used for a bottoming cycle based on a Rankine cycle. Vaja I [9] considered the assessment of double cascade ORC designs in conjunction to stationary ICEs, which would be presented in future works. Teng et al. [1,10] proposed a supercritical, reciprocating Rankine expander for waste heat recovery of diesel engines. Diego et al. [11] studied three configurations of Rankine cycle for waste heat recovery in a hybrid vehicle. Srinivasan et al. [12] did the research on Rankin cycle (RC) coupled on an Advanced Injection Low Pilot Ignition Natural Gas (ALPING) engine. It was demonstrated the RC system contributed a fuel conversion efficiency improvement of the order of 10% at half load operation while maintaining the essential low NOx characteristics of ALPING combustion. BMW [13] employed a dual RC system for passenger car applications, with a high temperature steam RC in parallel with a low temperature RC, where expanders were used to produce mechanical work. Yamada and Mohamad [14] proposed a novel waste heat recovery sub-system on a hydrogen internal combustion engine (HICE), where two potential valuable products of combustion with large amount were exploited at the same time, water to be the working fluid for an open-cycle power generation system based on the Rankine cycle, while exhaust waste heat to be used to superheat the fluid. For the working fluids of ORC system, several researches focused on solar energy harnessing, low-grade waste heat recovery, and geothermal energy utilization. Yamamoto et al. [15] estimated the optimum operating conditions of ORC comparing HCFC-123 and water as working fluids. Tchanche et al. [16] comparatively accessed 20 working fluids for use in low temperature solar organic Rankine cycle systems. Hung et al. [17] analyzed ORC efficiency using cryogens such as benzene, ammonia, R11, R12, R134a and R113 as working fluids. Maizza and Maizza [18] investigated the thermodynamic and physical properties of 20 unconventional fluids used in organic Rankine cycles supplied by waste energy sources. Lemort et al. [19] studied ORC system performance with a scroll expander instead of a turbine with R123 as the working fluid. Angelino and Colonna di Paliano [20] evaluated organic fluid mixtures as working media for Rankine power cycles. Chen et al. [21] compared a carbon dioxide, trans-critical power cycle with an organic Rankine cycle with R123 as the working fluid. Saleh et al. [22] investigated 31 pure component working fluids for subcritical and supercritical ORCs for geothermal power plants. Liu et al. [23] examined the influence of working fluids on the performance of ORC for waste heat recovery system. The considered performance parameters were thermal efficiency and total heat recovery efficiency. In this study, an ORC system used in exhaust heat recovery of ICE was proposed and techno-economically analyzed. The suitable working fluids have been screened and recommended for the ORC system, among 20 fluids (boiling point temperature range from 51.6 to 32.05  C) were analyzed on the rated condition of one popular commercial diesel generator set in China (a kind of ICE). The cycle parameters have also been analyzed and optimized. The screening criteria included the thermal efficiency of ORC (hth), the expansion ratio (v2/v1), the net power output per unit mass flow

rate of hot exhaust (Pnet), the ratio of total heat transfer area to net power output (A/Wnet), and electricity production cost (Epc). 2. System description 2.1. Topping ICE system In this study, a commercial diesel generator set is considered as a topping system. The engine is an inline 6 cylinder 4 stroke supercharged diesel oil fired engine: the main parameters of the engine are presented in Table 1. As the aim of this study analysis is to obtain the fluids comparison and parameters optimization for the ORC use in exhaust heat recovery of ICE, we assume the engine to operate at the rated condition. It has been calculated that the air fuel ratio is 19.75 and the excess air coefficient is 1.38 at the nominal condition, under the hypothesis of perfect combustion of diesel oil. By the way, excess air coefficient is defined as the ratio of real air consumption to theoretical value (14.3 for diesel fuel). The composition of the exhaust gases on the basis of mass has been calculated as: CO2 ¼ 15.10%, H2O ¼ 5.37%, N2 ¼ 73.04%, O2 ¼ 6.49%. This composition is used to evaluate the gas properties. 2.2. Bottoming ORC system The proposed bottoming ORC system layout and its corresponding Tes diagram (taking R134a for example) are shown in Figs. 1 and 2, respectively. The system is a subcritical ORC, consisting of turbinegenerator, condenser, refrigerant pump, preheater, evaporator, superheater and other test facilities. The hot exhaust from ICE first rejects heat in superheater, then rejects heat in evaporator and finally in preheater, and then discharges to the atmosphere. The temperature of exhaust decreases from Tg,in to Tg,v, then to Tg,l, and finally to Tg,out. The ORC system can be identified as 1-2-3-4-5-6-1 and described as follows. The generated high pressure superheated vapor (point 1) in the superheater flows into the turbine and its enthalpy is converted into work, and then converted into electricity by generator. The process 1 to 2s means isentropic expansion, which is ideal and impossible. When the turbine efficiency is higher, the point 2 is closer to point 2s, which means the real expansion process in turbine is closer to the isentropic expansion. The low pressure vapor (point 2) exits from the turbine and flows into the condenser where it is liquefied and condensed into saturated liquid (point 3) by supplied cooling water. The saturated liquid available at the condenser outlet is pumped to be high pressure liquid (point 4) by refrigerant pump, and then flows into the preheater where it is heated to be saturated liquid at high pressure (point 5) by the exhaust. The saturated liquid at high pressure flows into the evaporator and be vaporized to be saturated vapor (point 6) by the exhaust, and then flows into the superheater where it is heated to be superheated vapor (point 1) also by the exhaust. The whole cycle is complete as shown in Figs. 1 and 2. 2.3. Consideration of working fluid heating process Fig. 2 can give the heat exchange diagram during the working fluid heating process in preheater, evaporator and superheater. Table 1 Main parameters of the commercial diesel generator set. Parameter Electrical power output (kW) Torque (N m) Exhaust temperature ( C) Smoke intensity (FSN)

Values 235.8 1500 519 0.55

Parameter

Values

Rotate speed (rpm)

1501

Fuel consumption (kg/h) Combustion air mass flow (kg/h) Exhaust mass flow (kg/h)

47.79 943 990.79

H. Tian et al. / Energy 47 (2012) 125e136

Tg,in,Pg

mg

127

1 T1,P1

ICE-

Exhaust

Gen Suph

Internal combustion engine Tur-Turbine

Tur

Gen-Generator

Tg,v

6

T6,P6

Con-Condenser

ICE

T2,P2

M-Mass flowmeter

2

Tcw,in

Evap

Rp-Refrigerant pump Preh-Preheater

mcw

Con Tg,l

5

T5,P5

Evap-Evaporater Suph-Superheater

Tcw,out

Preh Rp

mr 3 M

Tg,out,Pg

4

T4,P4

T3,P3

Fig. 1. Schematic diagram of the bottoming ORC system.

Heat needed to heat, vaporize and superheat the organic working fluid is provided by the ICE exhaust. The gas temperature at ICE exhaust (Tg,in) and mass flow rate (mg) are tested and constant. The highest temperature of working fluid (T1) is assumed to be 250  C. A minimum pinch point temperature difference (Tg,pp) at Pinch Point (PP) to meet the gas fluid heat exchanger performance is considered to be 30  C. The heat exchange between working fluid and exhaust can be considered as follows. Step 1, the PP is assumed at point 5, which means Tg,l ¼ T5þTg,pp, and this allows writing a first energy balance, referring to complete fluid vaporization and superheating:

mr;1 ¼

  mg cpg;inl Tg;in  Tg;l

(1)

h1  h5

wherein, the organic fluid enthalpies are obtained at the evaporating pressure chosen for the ORC and cpg;inl is calculated according to the exhaust gas composition at the average temperature between Tg,in and Tg,l. R134a

Tg,in

500

Tg,v

450

1

Tg,l

T [K]

400 350

5

Tg,out

3 MPa

6

4 0.069 MPa

3 200 0.00

0.25

0.50

0.75

Tg;v ¼ Tg;in 

mr;1 ðh1  h6 Þ mg cpg;inv

Tg;out ¼ Tg;in 

mr;1 ðh1  h4 Þ mg cpg

(2)

wherein, the cpg;inv and cpg are calculated at the average temperature between Tg,in and Tg,v, and between Tg,in and Tg,out respectively. Therefore, four temperature differences at the working fluid heating process can be obtained as follows:

DTin ¼ Tg;in  T1 DTv ¼ Tg;v  T6 DTl ¼ Tg;l  T5 DTout ¼ Tg;out  T4

(3)

Step 3, compare the four temperature differences above and chose the minimum one to be the pinch point temperature difference (Tg,pp), and then repeat establishing energy balances from Equations (1) and (2) to determine the true working fluid mass flow ratio and other parameters. Step 4, if Tg,out calculated with equations above is lower than the minimum allowed temperature for the exhaust gases (Tg,min ¼ 120  C), a procedure modifies the pinch point temperature difference (Tg,pp) and repeats from step 1 to step 4, while Tg,out is above Tg,min.

2 2s

300 250

Step 2, another two energy balances allow to determine the exhaust gas temperature at the superheater outlet (Tg,v) and that at the preheater outlet (Tg,out):

1.00

s [kJ/kg-K] Fig. 2. Tes diagram of the bottoming ORC system.

1.25

3. Mathematical modeling Before establishing the mathematical model of this system, some general assumptions are formulated as follows: (1) Each component is considered as a steady-state steady-flow system, (2) The kinetic and potential energies are neglected, (3) Heat losses in each component and system pipe are also neglected; (4) The plate type heat exchangers are used in the preheater, evaporator, superheater and condenser in this analysis due to their

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compactness and high heat transfer coefficients which result in less heat transfer area than that when using shell and tube heat exchanger [24]. The plate type heat exchangers are supplied by a famous European company, whose heat transfer plate is about 0.5 m length, 0.2 m width and 0.002 m thickness. Moreover, the passage interval of hot gas side is about 0.008 m, with which of others are all 0.006 m. (5) Isentropic turbine efficiency is 0.7; isentropic pump efficiency is 0.8; working fluid temperature at condensation is 35  C; evaporating pressure varies between condensation pressure Pc and critical pressure Pcr. The detailed analysis of the system mathematical model is described as follows.

Table 3 Coefficients in equations evaluating the investment of system components [25].

Wnet ¼ Wt  Wrp

(5)

3.1. Mathematical model of each components

Pnet ¼ Wnet =mg

(6)

The energy balance and investment model of each system components are presented in Table 2.Wherein, Wt means the power output of turbine (kW); mr means the mass flow rate of ORC system (kg/s); h means the specific enthalpy (kJ/kg); ht means the isentropic efficiency of turbine; hrp means the isentropic efficiency of refrigerant pump; P means pressure (MPa); Q means the heat capacity in heat exchanger (kW); U means the overall heat transfer coefficient (kW/m2 K); A means the overall heat transfer area (m2); DTm means the logarithmic mean temperature difference (K); K, C, B, F are the coefficients presented in Table 3. Subscripts t, rp, preh, e, suph and c mean turbine, refrigerant pump, preheater, evaporator, superheater and condenser respectively. Equations for evaluating the investment of system components are obtained by [25], which is widely used for analysis, synthesis and design of chemical processes. 3.2. System performance The thermal efficiency is obtained by Equation (4) as follow.



hth ¼ Wt  Wrp



  Qpreh þ Qe þ Qsuph

(4)

Components K1

K2

Turbine Refrigerant pump Preheater Evaporator Superheater Condenser

K3

0.424 0.424 0.424 0.424

C1

C2

C3

B1

B2

Fm

Fbm

3.514 0.589 0 / / / / / / 3.5 3.579 0.321 0.003 0.168 0.348 0.484 1.80 1.51 1.80 / 3.853 3.853 3.853 3.853

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

1.53 1.53 1.53 1.53

1.27 1.27 1.27 1.27

2.80 2.80 2.80 2.80

/ / / /

Therefore, the total heat transfer area per net power output can be defined as Equation (7).

A=W ¼



Apreh þ Ae þ Asuph þ Ac

. Wnet

(7)

3.3. Heat transfer coefficient The overall heat transfer coefficient (U) at heat exchangers such as preheater, evaporator, superheater and condenser is defined as follow.

1=U ¼ 1=ar þ l=k þ 1=ag ðto preheater; evaporator; superheaterÞ 1=U ¼ 1=ar þ l=k þ 1=acw ðto condenserÞ (8) In the Equation (8), numerical correlations are used to calculate the heat transfer coefficients of working fluids, hot exhaust and cooling water in these heat exchangers. In evaporator, the boiling heat transfer coefficient (ar,e) for all working fluids is calculated using the correlation as follows [26,27].

ar;e ¼ 1:5  55ðPe =Pcr Þð0:120:2 gRpÞ ð  1gðPe =Pcr ÞÞ0:55 q0:67 M0:5 (9)

The net power output can be obtained by Equation (5). Therefore, the net power output per unit mass flow rate of hot exhaust can be defined as Equation (6). Wherein, mg means the mass flow rate of hot exhaust in ICE (kg/s).

wherein, Pcr means the critical pressure of working fluid (MPa); Rp means the mean asperity height (mm), which is the mean roughness between peak and valley at surface. According to the supplied plate

Table 2 Energy balance and investment model of each components. Components

Energy balance model

Investment model

Turbine

Wt ¼ mr ðh1  h2 Þ ht ¼ ðh1  h2 Þ=ðh1  h2s Þ

lgCp;t ¼ K1;t þ K2;t lgWt þ K3;t ðlgWt Þ Cbm;t ¼ Cp;t Fbm;t

Refrigerant pump (work fluid pump)

Wrp ¼ mr ðh4  h3 Þ hrp ¼ ðh4s  h3 Þ=ðh4  h3 Þ

lgCp;rp ¼ K1;rp þ K2;rp lgWrp þ K3;rp ðlgWrp Þ2

Preheater

Qpreh ¼ mr ðh5  h4 Þ Apreh ¼ Qpreh =ðUpreh DTm;preh Þ

Evaporator

Superheater

Condenser

Qe ¼ mr ðh6  h5 Þ Ae ¼ Qe =ðUe DTm;e Þ

Qsuph ¼ mr ðh1  h6 Þ Asuph ¼ Qsuph =ðUsuph DTm;suph Þ

Qc ¼ mr ðh2  h3 Þ Ac ¼ Qc =ðUc DTm;c Þ

Fp;rp ¼ C1;rp þ C2;rp lgPrp þ C3 ðlgPrp Þ2 Cbm;rp ¼ Cp;rp Fbm;rp ¼ Cp;rp ðB1;rp þ B2;rp Fm;rp Fp;rp Þ lgCp;preh ¼ K1;preh þ K2;preh lgApreh þ K3;preh ðlgApreh Þ2 lgFp;preh ¼ C1;preh þ C2;preh lgPpreh þ C3;preh ðlgPpreh Þ2 Cbm;preh ¼ Cp;preh Fbm;preh ¼ Cp;preh ðB1;preh þ B2;preh Fm;preh Fp;preh Þ lgCp;e ¼ K1;e þ K2;e lgAe þ K3;e ðlgAe Þ2 lgFp;e ¼ C1;e þ C2;e lgPe þ C3;e ðlgPe Þ2 Cbm;e ¼ Cp;e Fbm;e ¼ Cp;e ðB1;e þ B2;e Fm;e Fp;e Þ lgCp;suph ¼ K1;suph þ K2;suph lgAsuph þ K3;suph ðlgAsuph Þ2 lgFp;suph ¼ C1;suph þ C2;suph lgPsuph þ C3;suph ðlgPsuph Þ2 Cbm;suph ¼ Cp;suph Fbm;suph ¼ Cp;suph ðB1;suph þ B2;suph Fm;suph Fp;suph Þ lgCp;c ¼ K1;c þ K2;c lgAc þ K3;c ðlgAc Þ2 lgFp;c ¼ C1;c þ C2;c lgPc þ C3;c ðlgPc Þ2 Cbm;c ¼ Cp;c Fbm;c ¼ Cp;c ðB1;c þ B2;c Fm;c Fp;c Þ

H. Tian et al. / Energy 47 (2012) 125e136 Table 4 Equivalent diameter of each channel. Components

Hot exhaust side (m)

Working fluid side (m)

Components

Cooling water side (m)

Working fluid side (m)

Preheater Evaporator Superheater

0.016 0.016 0.016

0.012 0.012 0.012

Condenser

0.012

0.012

129

In superheater, the heat transfer coefficient (ar,suph) of gas phase in working fluid side can be calculated using the correlation as follows [29].

Rev ¼ rv nv Deq;r =mv Prv ¼ cpv mv =kv 1=f 0:5 ¼ cos b=ð0:18tan b þ 0:36sin b þ f0 =cos bÞ

The dates in Table 4 are obtained by plate type heat exchanger products from a European company.

0:5

þð1  cos bÞ=ð3:8f1 Þ0:5

(11)

When Rev < 2000; f0 ¼ 64=Rev f1 ¼ 579=Rev þ 3:85 type heat exchangers by a European company, the value of Rp is 0.3 in this calculation; q means the heat flux (W/m2), which is evaluated by assuming initial wall temperature, and then using the iterative method; M means the molar mass of working fluid (kg/kmol). In preheater, the heat transfer coefficient (ar,preh) of liquid phase in working fluid side can be calculated using the correlation as follows [28].

Rel ¼ rl nl Deq;r =ml Prl ¼ cpl ml =kl ð0:1892bþ0:6398Þ

Nul ¼ ð0:0154b þ 0:1298ÞRel

When Rev  2000; f0 ¼ ð1:8lgRev  1:5Þ2 f1 ¼ 39=Re0:289 v 1=3

Nuv ¼ 0:122Prv

ðmv =mwall Þ1=6 ðfRe2v sin 2bÞ

ar;suph ¼ Nuv kv =Deq;r wherein, subscript v means the properties on the gas phase condition. Deq,r in Equation (11) should be the equivalent diameter of superheater channel. In condenser, the condensation heat transfer coefficient (ar,c) of all working fluid can be calculated using the correlation as follows [30,31].



Prl0:35 ðml =mwall Þ0:14

ar;preh ¼ Nul kl =Deq;r (10) wherein, Re, Pr, Nu mean the Reynolds number, Prandtl number and Nusselt number respectively; r means the density of working fluid (kg/m3); n means the velocity (m/s); Deq,r means the equivalent diameter of channel (m), which is defined as Deq ¼ 4A=Ch ¼ 4$d$l=2$l ¼ 2d, twice the passage interval to plate type heat exchangers. According to the supplied data, Table 4 gives the equivalent diameter of each channel; m means the viscosity (Pa s); cp means the specific heat at constant pressure (kJ/kg K); k means the conductivity of working fluid (kW/m K); b means the chevron angle of plate type heat exchanger (radian); Subscripts l and wall mean the properties on the liquid phase condition and wall temperature condition respectively.

0:374



ar;l ¼ 0:2092 kl =Deq;r Re0:78 Prl0:33 ðm=mwall Þ0:14 l Co ¼ ðrv =rl Þð1=x  1Þ0:8   r2l gDeq;r Frl ¼ G2

(12)

Bo ¼ q=G$ifg   ar;c ¼ ar;l 0:25Co0:45 Frl0:25 þ 75Bo0:75 wherein, x means the vapor quality; G means the working fluid mass flux (kg/m2 s); g means the acceleration due to gravity (m/s2); ifg means the enthalpy of vaporization (kJ/kg). The cooling water side heat transfer coefficient (acw) is evaluated by the same model as that of gas phase in working fluid side [29]. The hot exhaust side heat transfer coefficient (ag) is obtained by the follow equations [32].

Table 5 Physical and environmental data of working fluids (sorted by normal boiling point) [35e50]. Substance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a

Environmental propertiesa

Physical data

R32 R125 R1270 R143a R290 R22 R218 R717 R1234yf R134a R152a R124 R142b RC318 R600 R114 R245fa R11 R123 R141b

Fluid type

M (kg/kmol)

Tb ( C)

Tcr ( C)

Pcr (MPa)

ALT (yr)

ODP

GWP (100yr)

52.02 120 42.08 84.04 44.10 86.47 188.02 17.03 114.04 102.03 66.05 136.48 100.50 200.03 58.12 170.92 134.05 137.37 152.93 116.95

51.60 49.00 47.69 47.24 42.09 40.81 36.83 33.33 29.45 26.07 24.02 11.96 9.15 5.98 0.55 3.59 14.90 23.71 27.82 32.05

78.10 66.05 92.42 72.71 96.68 96.15 71.95 132.25 94.70 101.06 113.26 122.28 137.11 115.23 151.98 145.68 154.05 197.96 183.68 206.81

5.780 3.592 4.665 3.761 4.247 4.990 2.671 11.333 3.382 4.059 4.517 3.624 4.070 2.778 3.796 3.257 3.640 4.408 3.662 4.460

4.9 29 ~0 52 0.04 12 2600 0.01 0.03 14 1.4 5.8 17.9 3200 0.02 300 7.6 45 1.3 9.3

0 0 0 0 0 0.05 0 0 0 0 0 0.02 0.07 0 0 1 0 1 0.02 0.12

675 2800 ~20 4470 ~20 1810 8830 <1 4 1430 124 609 2310 10,250 ~20 10,040 1030 4750 77 725

Safety and environmental data of R1234yf were obtained by [49] while others refer to [50].

Wet Isentropic Wet Isentropic Wet Wet Isentropic Wet Isentropic Isentropic Wet Isentropic Isentropic Isentropic Isentropic Isentropic Isentropic Isentropic Isentropic Isentropic

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H. Tian et al. / Energy 47 (2012) 125e136

Table 6 Validation of the numerical model with the previously published data [51] for the various fluids-based ORC.

Benzene R11 R134a

Porc [kW]

horc [e]

Pcond [kPa]

Pvap [kPa]

Tvap [K]

mf [kg/s]

V3 [m3/s]

v2/v1 [e]

Dh21 [kJ/kg]

Source

349.3 334.1 290.3 291.4 147.5 159.7

0.199 0.198 0.166 0.155 0.085 0.079

19.6 19.6 147.9 147.2 883.3 883.8

2000 1998 3835.9 3810 3723.4 3723

494.5 494.5 461 461 369.9 369.9

2.737 2.56 7.487 7.483 8.967 9.917

0.052 0.049 0.030 0.027 0.041 0.034

107 107.3 32 35 5 6.2

130.5 130.5 41.9 38.9 19.4 16.1

[51] Present [51] Present [51] Present

 2 fg ¼ 1:82lgReg  1:64

AN;K ¼ Cost2008 CRF

When Reg >10; 000 or When Reg < 5  106; h   0:5   Nug ¼ fg =8 Reg  1000 Prg 12:7 fg =8

The electricity production cost (Epc) can be obtained by Equation (18).

2=3

ðPrg When Re 10; 000;h  g <  0:5 12:7 fg =8 fg =8 Reg Prg

Nug ¼

2=3

ðPrg

i  1Þ þ 1:07

i  1Þ þ 1:07

ag ¼ Nug kg =Deq;g

(13)

wherein, fg is the friction factor; subscript g means the hot exhaust.

  EPC ¼ AN;K þ fK Cost2008

(17)

 

  Wt  Wrp  hfullload

(18)

wherein, i is the interest rate, whose value is 5%; time is the economic life time, whose value is 15 years; fK is the maintenance and insurance cost factor, whose value is 1.65%; hfull-load is the full load operation hours, whose value is 7500 h. These values are referred from references [33] and [34], in which there are almost the same components as that in our system. The values are all reasonable and obtained by statistic of related products.

3.4. Economic analysis The electricity production cost (Epc) is defined and obtained by the follow equations referred from [33,34]. The system cost based on the price of year 2008 is obtained by Equations (14) and (15).

Cost1996 ¼Cbm;t þCbm;rp þCbm;preh þCbm;e þCbm;suph þCbm;c

(14)

Cost2008 ¼ Cost1996 CEPCI2008 =CEPCI1996

(15)

wherein, CEPCI1996 ¼ 382, CEPCI2008 ¼ 575.4 (CEPCI means Chemical Engineering Plant Cost Index). The capital recovery cost (CRF) is estimated based on the following equation.

CRF ¼ ið1 þ iÞtime



 ð1 þ iÞtime 1

(16)

The annuity of the investment can be obtained using Equation (17).

0.11 0.10

4. Working fluid choice Organic working fluids used for ORC system may have different characteristics in the Tes diagram and the saturation lines may be bell shaped, nearly isentropic or overhanging depending on the fluid molecule complexity. Typically, fluids with simpler molecules are characterized by bell shaped vapor lines and lower critical temperatures and fluids with more complex molecules display an overhanging vapor line and higher critical temperatures. According to the slope of saturated vapor curve in the Tes diagram, Organic working fluids can be classified as the dry one, isentropic one and wet one. Types of working fluids can be predicted by z ¼ ds/dTH, which is the slope of saturated vapor curve. The organic fluid is a dry type with z > 0, an isentropic type with z ¼ 0, and a wet type with z < 0 [23]. Meanwhile, there are several general criteria while recommending the proper working fluids. Stability, non-fouling, non-corrosiveness, non-toxicity and non-flammability are a few preferable physical and chemical characteristics. However, in a cycle design, not all the desired general requirements can be satisfied. Table 5 shows physical property and environmental data of fluids considered in this study and the predicted fluid types.

0.09 0.08

0.14

0.07

0.12

0.06

R32 R125 R1270 R143a R290 R22 R218

0.05 0.04 0.03 0.02 0.01 0.00

0.10 0.08 0.06 0.04 0.02

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Evaporating pressure(MPa) Fig. 3. Variation of thermal efficiency with evaporating pressure (Group 1).

R717 R1234yf R134a R152a R124 R142b RC318

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 Evaporating pressure(MPa) Fig. 4. Variation of thermal efficiency with evaporating pressure (Group 2).

H. Tian et al. / Energy 47 (2012) 125e136

0.18

9

0.16

8

0.14

Thermal efficiency (

131

7

0.12

6

0.10

5

R600 R114 R245fa R11 R123 R141b

0.08 0.06 0.04

4 3 2 1

0.02 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5

Evaporating pressure(MPa) Fig. 5. Variation of thermal efficiency with evaporating pressure (Group 3).

5. Validation Numerical calculated solution is validated with the results of Iacopo Vaja et al. [51] for the ICE bottoming with various fluidsbased ORC and for the same operating conditions listed as follows. The cycle in Ref. [51] was using the exhaust gases of a 12 cylinder 4 stroke cogeneration engine with 470  C available temperature and 15,673 kg/h mass flow rate. The condensation temperature was 35  C, the isentropic turbine efficiency was 0.7, and the isentropic pump efficiency was 0.8. Evaporating pressure varied between condensation pressure Pc and critical pressure Pcr. The pinch point temperature difference was 30  C. As shown in Table 5, the comparison shows a very good agreement between present solution and the results of Iacopo Vaja et al. [51]. The discrepancies of different parameters showed in Table 6 mainly derive from the choosing of fluid property evaluation software that the REFPROP database was selected in Ref. [51] while the EES (Equation Evaluation Solution) database is chosen in the present study.

6. Calculated results and discussion The exhaust gases conditions of a real engine are given in Table 1 and the calculated conditions of ORC system along with the characteristics of the turbine, pump, etc. are expressed in section 2. In

3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0

Fig. 7. Variation of expansion ratio with evaporating pressure (Group 2).

the following paragraphs we present the results of a comparative study for different working fluids-based ORC system based on the model previously described. The thermodynamic properties of fluids and system performance are evaluated with EES (Equation Evaluation Solution), which has a sufficient accuracy. The investigated 20 fluids are divided into three groups according to their normal boiling point temperatures ranging from 51.6  C to 32.05  C. They are listed as follows, Group 1, Tb < 35  C; Group 2, 35  C < Tb < 5  C; Group 3,Tb > 5  C. Figs. 3e17 show performances of different working fluids investigated for the based bottoming ORC system on five different screening criteria, including hth, v2/v1, Pnet, A/Wnet and Epc in this analysis. 6.1. Thermal efficiency hth In Figs. 3e5, the cycle thermal efficiency is plotted for the considered working fluids in the range of evaporating pressure between condensing pressure Pcond and critical pressure of each working fluid Pcrit. As the Pcrit of each working fluid is different and varies from 2.7 MPa (R218) to 11 MPa (R717), working fluids have different horizontal axis values in these figs. Higher hth value means that more power output can be obtained with the same heat capacity recovered from exhaust gases. As shown in Figs. 3e5, the curves are monotonic and increasing as the increase of evaporating pressures for all fluids. The increase trend of various working fluids

40

R600 R114 R245fa R11 R123 R141b

35 30 25 20 15 10 5 1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Evaporating pressure(MPa) Fig. 6. Variation of expansion ratio with evaporating pressure (Group 1).

Fig. 8. Variation of expansion ratio with evaporating pressure (Group 3).

132

H. Tian et al. / Energy 47 (2012) 125e136

40 35

Pnet(kJ/kg)

30 25 20

Pnet(kJ/kg)

R32 R125 R1270 R143a R290 R22 R218

15 10 5 0 1.0

1.5

2.0

2.5 3.0 3.5 4.0 4.5 Evaporating pressure(MPa)

5.0

is obvious at low evaporating pressures and becomes smooth near critical pressure. The curve patterns in Group 3 are more obvious. In Group 1, R22 and R290 outstand among. R142b shows the largest hth value in Group 2. Meanwhile, R717 can achieve a high hth but at a high evaporating pressure. R141b, R11 and R123 outstand among Group 3. Comparing the highest hth value presented by each fluid, R141b is the highest one of about 16.6% at evaporating pressure 3.6 MPa, and the top high ones are as follows: R141b(16.6%,3.6 MPa)>R123(15.7%,3.4 MPa)>R11(14.2%,1.6 MPa)> R245fa(13.3%,3.6 MPa)>R717(13.2%,7 MPa)>R142b(13%,4 MPa)> R600(12.9%,3.6 MPa)>R152a(11.8%,4.5 MPa). If considering the environmental characteristics (ODP value <0.20, GWP value < 1500), the top three fluids presenting higher hth values are R141b, R123 and R245fa ranging from 16.6% to 13.3%.

Figs. 6e8 report, for each fluid, the curves referring to the expansion ratio, which is the turbine outlet/inlet volume flow ratio (v2/v1). The expansion ratio is particularly significant as it shows how much the fluid volume increases through the expansion process. As shown in Figs. 6e8, the curves are linear and increasing as the increase of evaporating pressures for all fluids. In Group 1,

50

Pnet(kJ/kg)

15 10

1.5 2.0 2.5 3.0 3.5 Evaporating pressure(MPa)

4.0

4.5

Fig. 11. Variation of net power output per unit mass flow rate with evaporating pressure (Group 3).

R218 and R290 outstand among. R142b, RC318 and R124 show larger v2/v1 value in Group 2. R141b and R123 outstand among Group 3. Fluids in Group 1 show the lowest v2/v1 value and that in Group 3 present the highest values. R141b presents the highest v2/v1 value of about 41. The top three fluids presenting higher v2/v1 values are R141b, R123 and R245fa of 41, 29 and 18 respectively. It should be noted that the expansion ratio v2/v1 can change significantly depending on the characteristics of the working fluid, for example several fluids can achieve values up to 550, but some other’s value are smaller than 50. However, the high expansion ratio is bad for a single stage turbine design. The pre-research [52] indicated that when the expansion ratio is smaller than 50, a single stage axial turbine can be easy designed and achieve an expansion efficiencies higher than 0.8.

Figs. 9e11 present variation of Pnet values for Group 1e3 working fluids with various evaporating pressures. Higher Pnet value means that more power output can be obtained with the same mass flow rate of exhaust gases. As shown in Figs. 9e11, Pnet value is increasing as the increase of evaporating pressures. The increase trend of various working fluids is obvious at low evaporating pressures and becomes smooth near critical pressure except

R32 R125 R1270 R143a R290 R22 R218

6

40

20

1.0

7

45

25

0.5

6.3. Net power output per unit mass flow rate Pnet

6.2. Expansion ratio v2/v1

30

R600 R114 R245fa R11 R123 R141b

0.0

5.5

Fig. 9. Variation of net power output per unit mass flow rate with evaporating pressure (Group 1).

35

65 60 55 50 45 40 35 30 25 20 15 10 5

R717 R1234yf R134a R152a R124 R142b RC318

5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 Evaporating pressure(MPa) Fig. 10. Variation of net power output per unit mass flow rate with evaporating pressure (Group 2).

5 4 3 2 1 0

1.5

2.0

2.5 3.0 3.5 4.0 4.5 Evaporating pressure(MPa)

5.0

5.5

Fig. 12. Variation of total heat transfer area per net power output with evaporating pressure (Group 1).

3.6 3.2 R717 R1234yf R134a R152a R124 R142b RC318

2

A/Wnet(m /kW)

2.8 2.4 2.0 1.6 1.2 0.8 0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Evaporating pressure(MPa)

Electricity production cost(Epc)(dollar/kWh)

H. Tian et al. / Energy 47 (2012) 125e136

133

3.6

R32 R125 R1270 R143a R290 R22 R218

3.2 2.8 2.4 2.0 1.6 1.2 0.8 0.4 1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Evaporating pressure(MPa) Fig. 13. Variation of total heat transfer area per net power output with evaporating pressure (Group 2).

Electricity production cost(Epc)(dollar/kWh)

R141b which decreases near critical pressure. In Group 1, R22 and R290 outstand among. R124 shows larger Pnet value in Group 2. Meanwhile, R717 can achieve a high Pnet but at a high evaporating pressure. R141b, R11 and R123 outstand among Group 3. Fluids in Group 1 show the lowest Pnet values except R22 and R290 which present the highest Pnet values of about 37 kJ/kg and 30 kJ/kg respectively. Among all the considered working fluids, R141b presents the highest Pnet value of about 60 kJ/kg at evaporating pressure 3.6 MPa. R123 also presents higher Pnet value of about 58 kJ/kg at evaporating pressure 3.4 MPa, which is only 3.3% lower than R141b. Moreover, R11 and R245fa also present high Pnet values of about 52 kJ/kg (at 1.6 MPa) and 49 kJ/kg (at 3.6 MPa), which are 13.3% and 18.3% lower than R141b respectively. Also considering the environmental characteristics (ODP value <0.20, GWP value < 1500), the top three fluids presenting higher Pnet values are R141b, R123 and R245fa ranging from 60 to 49 kJ/kg.

Fig. 15. Variation of EPC with evaporating pressure (Group 1).

1.6 R600 R114 R245fa R11 R123 R141b

2

A/Wnet(m /kW)

1.0 0.8 0.6 0.4 0.2 0.0

0.5

1.0

1.5 2.0 2.5 3.0 3.5 Evaporating pressure(MPa)

4.0

R717 R1234yf R134a R152a R124 R142b RC318

1.6 1.4 1.2 1.0 0.8 0.6 0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Evaporating pressure(MPa)

4.5

Fig. 14. Variation total heat transfer area of per net power output with evaporating pressure (Group 3).

investment in some aspect. As shown in Figs. 12e14, the curves are decreasing rapidly first and then going to smooth, finally rising slightly especially for working fluids in Group 2 and Group 3. In Group 1, R22 and R290 show the lowest values. R142b and R152a show lower A/Wnet value in Group 2. Moreover, R141b, R11 and R123 show the lowest values among Group 3. The minimum A/Wnet

Electricity production cost(Epc)(dollar/kWh)

Figs. 12e14 report, for each fluid in Group 1e3, the curves referring to the total heat transfer area per net power output A/Wnet values with various evaporating pressures. It is noted that lower A/Wnet value expresses that smaller total heat transfer areas would be needed in order to achieve the same net power output which can indicate the heat transfer performance and reduce the system

1.2

1.8

Fig. 16. Variation of EPC with evaporating pressure (Group 2).

6.4. Total heat transfer area per net power output A/Wnet

1.4

2.0

1.1 1.0

R600 R114 R245fa R11 R123 R141b

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.0

0.5

1.0 1.5 2.0 2.5 3.0 Evaporating pressure(MPa)

3.5

4.0

Fig. 17. Variation of EPC with evaporating pressure (Group 3).

4.5

134

H. Tian et al. / Energy 47 (2012) 125e136

Table 7 Performance sequence of fluids-based on four different screening criteria 1e4.

hth

Pe/MPa

Dev1

Pnet

Pe/MPa

Dev2

A/Wnet

Pe/MPa

Dev3

Epc

Pe/MPa

Dev4

R141b R123 R245fa R717 R600 R152a R124 R134a R290 R32 R1270 R1234yf

3.6 3.4 3.6 7 3.6 4.5 3.6 4 4.1 5.4 4 2.8

0 5.2 19.9 20.7 22.5 29.0 34.2 42.5 47.8 49.0 52.4 61.1

R141b R123 R245fa R717 R600 R152a R124 R134a R290 R32 R1270 R1234yf

3.6 3.4 3.6 7 3.6 4.5 3.6 4 4.1 5.4 4 2.8

0 4.3 19.2 20.0 21.9 28.5 33.4 42.0 47.5 48.7 52.1 60.8

R717 R123 R141b R245fa R600 R152a R124 R134a R32 R290 R1270 R1234yf

7 2.8 3 3.2 3.4 4.2 3.2 3.8 5.4 4.1 4 2.8

0 1.0 11.5 13.0 19.6 32.6 48.5 67.3 80.0 84.5 118.4 150.0

R141b R123 R717 R245fa R600 R152a R124 R134a R32 R290 R1270 R1234yf

3.2 3.4 7 3.6 3.6 4.5 3.6 4 5.4 4.1 4 2.8

0 2.2 14.2 16.7 20.3 27.8 36.5 50.7 63.1 63.0 91.3 108.5

values for R141b, R123, R245fa, R11, R142b and R152a are 0.481, 0.436, 0.487, 0.439, 0.641 and 0.572 m2/kW corresponding with the optimum evaporating pressure of 3, 2.8, 3.2, 1.6, 3.6 and 4.2 MPa respectively. Fluids with better environmental characteristics presenting lower A/Wnet values are R141b, R123, R245fa and R152a ranging from 0.436 to 0.572 m2/kW. 6.5. Electricity production cost Epc Figs. 15e17 present variation of the electricity production cost Epc values for Group 1e3 working fluids with various evaporating pressure. It is noted that smaller Epc values means that it can leads to higher system techno-economy. As shown in Figs. 15e17, Epc value is decreasing first rapidly and then going to smooth, even increase for several fluids like R141b. Fluids in Group 1 present the largest Epc values ranging from 0.43 to 3.5 $/kWh, in which R22 shows the lowest value of about 0.43$/kWh. R412b, R152a and R717 show higher economical efficiency among Group 2. In Group 3, R141b, R123, R245fa, R11 and R600 show smaller Epc values. Among all the fluids, the lower ones are as follows: R141b(0.300$/kWh,3.2 MPa) is lower than R123(0.307$/ kWh,3.4 MPa), and then R11(0.325$/kWh,1.6 MPa), R717(0.343$/ kWh,7 MPa), R245fa(0.350$/kWh,3.6 MPa), R142b(0.358$/ kWh,4 MPa), R600(0.361$/kWh,3.6 MPa) and R152a(0.384$/ kWh,4.5 MPa). If considering the environmental characteristics (ODP value <0.20, GWP value < 1500), the top four fluids presenting lower Epc values are R141b, R123, R717 and R245fa ranging from 0.300 to 0.350$/kWh. 6.6. Performance sequence of fluids If under the restriction of the environmental characteristics (ODP value < 0.20, GWP value < 1500), the performance sequence of fluids studied in this analysis based on four different screening criteria is listed in Table 7 along with the deviation values which are defined as follows:

  Dev1 ¼ hth  hth;max hth;max  100%   Dev2 ¼ Pnet  Pnet;max Pnet;max  100%   Dev3 ¼ ðA=Wnet Þ  ðA=Wnet Þmin ðA=Wnet Þmin  100%

(19)

Dev4 ¼ ðEpc  Epcmin Þ=Epcmin  100% As shown in Table 7, each fluid has large discrepancy for the four different screening criteria. However, R141b, R123, R245fa always show the better performance than the other fluids and small discrepancy with each other. R141b shows largest hth and Pnet values, and lowest Epc value. The optimum evaporating pressures for R141b, R123, R245fa are ranging from 2.8 MPa to 3.6 MPa.

7. Conclusions In this study, an ORC system use in exhaust heat recovery of ICE is proposed and techno-economically analyzed. The suitable working fluids have been screened and recommended for the ORC system, among 20 fluids (boiling point temperature range from 51.6 to 32.05  C) which are analyzed on the rated condition of one popular commercial diesel generator set in China (a kind of ICE). The cycle parameters have also been analyzed and optimized. The screening criteria include the thermal efficiency of ORC (hth), the expansion ratio (v2/v1), the net power output per unit mass flow rate of hot exhaust (Pnet), the ratio of total heat transfer area to net power output (A/Wnet), and electricity production cost (Epc). Each fluid is evaluated at the given condition. The main results are as follows: (1) When evaporating pressure varies from condensation pressure Pcond to critical pressure of each working fluid Pcrit, the curves of hth, v2/v1 and Pnet are monotonic and increasing. The top three fluids presenting higher hth and Pnet values are R141b, R123 and R245fa ranging from 16.6% to 13.3% (hth value), and from 60 to 49 kJ/kg (Pnet value). However, R141b, R123 and R245fa present the top three higher v2/v1 values of 41, 29 and 18 respectively. It can be observed that v2/v1 values are always smaller than 50, which would allow the use of simple expanders such as single stage turbines. (2) The curves of A/Wnet and Epc are decreasing rapidly first and then going to smooth. Fluids with better environmental characteristics presenting lower A/Wnet values are R141b, R123, R245fa and R152a ranging from 0.436 to 0.572 m2/kW. The top four fluids presenting higher Epc values are R141b, R123, R717 and R245fa ranging from 0.300 to 0.350$/kWh. (3) R141b, R123, R245fa always shows better performance than the other fluids and small discrepancy with each other. R141b shows largest hth and Pnet values, and lowest Epc value. The optimum evaporating pressures for R141b, R123, R245fa are ranging from 2.8 MPa to 3.6 MPa. Moreover, further ORC cycle solutions will be analyzed in future works as well as dynamical model will be introduced to evaluate the behavior of the system in off-design conditions. Also a detailed exergy analysis will numerically quantify the entity of losses in ORC system used in exhaust heat recovery of ICE.

Acknowledgments This work was supported by a grant from the National Basic Research Program of China (973 Program) (No. 2011CB707201), and the Natural Science Foundation of Tianjin (No. 12JCQNJC04400).

H. Tian et al. / Energy 47 (2012) 125e136

Nomenclature A B,C,K Bo cp Co cost Deq Dev Epc fg fK Fbm Fr GWP G g hfull-load h ifg i k l M m Nu ODP P Pr q Q Rp Re time T DTm U V

n W x

overall heat transfer area (m2) coefficients in equations for evaluating the investment of system components Boiling number (dimensionless) specific heat capacity at average temperature (kJ/kg  C) Convection number (dimensionless) investment of system components ($) equivalent diameter of channel (m) deviation (%) electricity production cost ($/kWh) friction factor (dimensionless) maintenance and insurance cost factor (%) bare module factor (dimensionless) Froude number (dimensionless) global warming potential working fluid mass flux (kg/m2 s) acceleration due to gravity (m/s2) full load operation hours (h) specific enthalpy (kJ/kg) enthalpy of vaporization (kJ/kg) interest rate (%) thermal conductivity (W/m K) thickness of the plate (m) molar mass of working fluid (kg/kmol) mass flow ratio (kg/s) Nusselt number (dimensionless) ozone depletion potential pressure (MPa) Prandtl number (dimensionless) heat flux (W/m2) heat injected or rejected (kW) asperity height (mm) Reynolds number (dimensionless) economic life time (yr) temperature ( C) logarithmic mean temperature difference (K) overall heat transfer coefficient (kW/m2 K) volume flow rate (m3/s) velocity (m/s) power output (kW) vapor quality (dimensionless)

Greek symbols a heat transfer coefficient (W/m2 K) b chevron angle (radian) r density of working fluid (kg/m3) m viscosity (Pa s) h efficiency (dimensionless) Subscripts b boiling cw cooling water cr critical c,cond condenser e,vap evaporator t turbine g exhaust gas l liquid phase net net orc organic Rankine cycle preh preheater rp refrigerant pump r working fluid

suph v wall 1-6, 2s

135

superheater gas phase wall state points

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