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Thermoeconomic multi-objective optimization of a dual loop organic Rankine cycle (ORC) for CNG engine waste heat recovery ⁎

MARK

⁎

Fubin Yanga,b,c, Heejin Chob, , Hongguang Zhanga,c, , Jian Zhangb a b c

College of Environmental and Energy Engineering, Beijing University of Technology, Pingleyuan No. 100, Beijing 100124, China Department of Mechanical Engineering, Mississippi State University, 210 Carpenter Engineering Building, P.O. Box 9552, Mississippi State, MS 39762, USA Collaborative Innovation Center of Electric Vehicles in Beijing, Pingleyuan No. 100, Beijing 100124, China

H I G H L I G H T S dual loop ORC system is used to recover the waste heat of a CNG engine. • ASensitivity analysis of the decision variables is performed. • Thermoeconomic optimization of dual loop ORC system is conducted. • Genetic algorithmmulti-objective is employed to solve the multi-objective optimization problem. • The optimal operating regions of the decision variables are obtained. •

A R T I C L E I N F O

A S B T R A C T

Keywords: CNG engine Waste heat recovery Dual loop organic Rankine cycle Thermoeconomic analysis Multi-objective optimization

In this paper, a thermoeconomic model of a dual loop organic Rankine cycle (ORC) system has been developed to analyze both the thermodynamic and economic performance of several working ﬂuid groups for the purpose of compressed natural gas (CNG) engine waste heat recovery. The eﬀects of six key parameters on the thermoeconomic indicators of the dual loop ORC system are investigated. Furthermore, a multi-objective genetic algorithm (GA) is employed to solve the Pareto optimal solutions from the viewpoints of maximizing net power output and minimizing total investment cost over the whole operating range of the CNG engine. The most suitable working ﬂuid group is screened out, then the optimal parameter regions are determined. The results show that a higher evaporation pressure and a lower condensation temperature exhibit a positive eﬀect on the thermoeconomic performances of the dual loop ORC system while the eﬀects of variation in superheat degree and exhaust outlet temperature on the thermoeconomic performances are not obvious. The optimal evaporation pressure of the high temperature loop ORC (HT cycle) is always above 2.5 MPa. The optimal condensation temperature of the HT cycle, optimal evaporation temperature and condensation temperature of the low temperature loop ORC (LT cycle) are all kept almost constants. In addition, the optimal exhaust outlet temperature is mainly inﬂuenced by the engine speed. At the rated condition, the dual loop ORC system has the maximum net power output of 23.62 kW and the minimum electricity production cost (EPC) of 0.41 $/kW h. The thermal eﬃciency of the dual loop ORC system is in the range of 8.97–10.19% over the whole operating range.

1. Introduction Due to the substantially increase of fossil fuel consumption, the energy saving and emission reduction of internal combustion (IC) engines have received more and more attention. As one of the main prime movers used in transportation industry, engineering machinery and farm machinery, the maximum thermal eﬃciency of the IC engines is usually less than 40% [1]. Considering increasingly stringent emission

regulations, clean alternative fuels are considered to be a good choice for the spark ignition engines. Among various alternative fuels, compressed natural gas (CNG) has been regarded as one of the best substitutions because of its abundant reserves and environmental beneﬁts [2,3]. Overall energy eﬃciency and fuel consumption can be greatly improved by recovering waste heat from the CNG engines [4,5]. In the current literatures, organic Rankine cycle (ORC) is considered to be one of the most advantageous technologies for the engine waste heat

⁎ Corresponding authors at: Department of Mechanical Engineering, Mississippi State University, Mississippi State, MS 39762, USA (H. Cho), College of Environmental and Energy Engineering, Beijing University of Technology, Pingleyuan No. 100, Beijing 100124, China (H. Zhang). E-mail addresses: [email protected] (H. Cho), [email protected] (H. Zhang).

http://dx.doi.org/10.1016/j.apenergy.2017.08.127 Received 17 April 2017; Received in revised form 30 June 2017; Accepted 12 August 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.

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Nomenclature

Ẇ Q̇ ṁ h s T P K A Nu d r Re Pr l ct f F S x pr q M i fg ″ qwall G w D N b Bo

p1 eva1 exh a−d exp2 L L1−L8 in out con p2 int eva2 cool tot th max min ft wf l v tp fb nb pla h eq out

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) 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) 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) enthalpy of vaporization (J/kg) imposed wall heat ﬂux (W/m2) mass velocity (kg/m2 s) channel width (m) port diameter (m) number channel spacing (m) boiling number

Acronyms

ORC CNG GA HT LT HT ODP GWP CFCs HCFCs LMTD MCT BSFC TOPSIS

Greek symbols

β α λ η δ ε ρ

rib eﬀect coeﬃcient or chevron angle heat transfer coeﬃcient (W/m2 K) thermal conductivity (W/m K) eﬃciency ﬁn height (m) correction factor or eﬀectiveness of the heat exchanger density (kg/m3)

Subscripts

exp1 H H1−H7 ise pre

pump 1 evaporator 1 exhaust state points in exhaust gas expander 2 low temperature or all the mass ﬂow rate taken as liquid state points in LT cycle inner outer condenser pump 2 intercooler evaporator 2 coolant total thermal maximum minimum ﬁn-and-tube working ﬂuid liquid vapor two-phase ﬁlm boiling nucleate boiling plate hydraulic equivalent outlet

expander 1 high temperature state points in HT cycle isentropic preheater

CEPCI EPC TIC CRF

organic Rankine cycle compressed natural gas genetic algorithm high temperature low temperature internal combustion ozone depletion potential global warming potential chloroﬂuorocarbon hydrochloroﬂuorocarbons logarithmic mean temperature diﬀerence module costing technique brake speciﬁc fuel consumption Technique for Order Preference by Similarity to an Ideal Solution Chemical Engineering Plant Cost Index electricity production cost total investment cost capital recovery factor

examined the eﬀects of eight diﬀerent zeotropic mixtures on the ORC system under engine various operating conditions [13]. Amicabile et al. introduced a systematic method to screen out the candidate working ﬂuids considering thermodynamic, environmental and safety criteria [14]. Ethanol, pentane and R245fa were used in their research. Various ORC system conﬁgurations have been proposed by many researchers to improve the system performance and eﬃciency. A dual loop ORC system including a high temperature loop and a low temperature loop was proposed by Zhang et al. to recover the waste heat from a light-duty diesel engine [15]. Song and Gu designed a dual loop ORC system to utilize the waste heat of a diesel engine and analyzed the

recovery applications [6–10]. Currently, studies of the ORC system mainly focus on working ﬂuid selection, conﬁguration improvement, parametric optimization, and thermoeconomic analysis. Many investigations have been conducted to select the favorable working ﬂuids for ORC applications. Wang et al. adopted an ORC system to recover exhaust waste heat from an IC engines and evaluated nine diﬀerent organic working ﬂuids based on the thermodynamic properties [11]. Shu et al. discussed the feasibility of alkanes as working ﬂuid for diesel engine waste heat recovery based on ORC system [12]. They studied thermodynamic and economic aspects and made a comparison with the traditional steam cycle. Yang et al.

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the exhaust waste heat characteristics of a large marine diesel engine [28]. Yu et al. proposed a transcritical cascade-ORC system to recover multi-grade waste heat from a diesel engine [29]. The objective of their research was mainly to minimize the electricity production cost and payback period. Hajabdollahi et al. adopted an ORC system for recovering the waste heat of a diesel engine and used a genetic algorithm to achieve the maximum thermal eﬃciency and minimum total annual cost [30]. Wang et al. compared the thermoeconomic performance for an ORC exhaust waste heat recovery system applied on a heavy duty diesel engine and a light duty gasoline engine [31]. Yang et al. investigated the eﬀects of four key operating parameters on the thermoeconomic performance of an ORC system for the exhaust waste heat recovery of a diesel engine [32]. From the aforementioned literature reviews, it is shown that the dual loop ORC system for IC engine’s waste heat recovery has been widely investigated. However, very few studies have been devoted to the multi-objective optimization of a dual loop ORC system using an evolutionary algorithm considering both thermodynamic and economic performance. Furthermore, the coordinated variation of key parameters for the dual loop ORC system under various operating conditions of the IC engine is seldom considered. The aim of this study is to investigate the thermoeconomic multi-objective optimization of a dual loop ORC system for CNG engine waste heat recovery from both thermodynamic and economic points of views. The thermodynamic, economic and optimization models of the dual loop ORC system are established. The eﬀects of the key ORC parameters on the thermoeconomic performance of the dual loop ORC system are investigated. Those parameters include the evaporation pressure, superheat degree and condensation temperature of high temperature loop organic Rankine cycle (HT cycle), evaporation and condensation temperatures of low temperature loop organic Rankine cycle (LT cycle), and exhaust temperature at the outlet of HT cycle evaporator. R245fa and R600 are selected as the candidate working ﬂuids for HT cycle, while R245fa, R600, R1234yf and R1234ze are considered for LT cycle. Subsequently, the optimal parameter regions of the dual loop ORC system for maximizing net power output and minimizing total investment cost are obtained using a genetic algorithm. As one of the eﬀective evolutionary algorithms, the genetic algorithm has been widely applied in the ﬁelds of thermal energy and ORC applications. Table 1 gives the applications of genetic algorithm within these ﬁelds [33–53]. The optimization results of this study can provide a useful guidance for the coordinated control of the dual loop ORC system under various operating conditions of IC engines.

performance of the ORC system with wet steam expansion in the high temperature loop [16]. Shu et al. also developed a dual loop ORC system for a turbocharged diesel engine, which is mainly deﬁned as a subcritical-subcritical system or subcritical-transcritical system [17]. They evaluated the thermodynamic performance of the dual loop ORC system with diﬀerent working ﬂuids and operating loads. Wang et al. analyzed ﬁve diﬀerent ORC conﬁgurations based on the ﬁrst and second laws of thermodynamics and used a genetic algorithm to obtain the maximum thermal eﬃciency for each ORC conﬁguration [18]. Zhang et al. presented the performance analysis of a regenerative ORC system using pure working ﬂuid R245fa and zeotropic mixture isopentane/R245fa over the whole operating range of a diesel engine [19]. Yue et al. compared the thermodynamic performance between a transcritical ORC system and a Kalina cycle for the IC engine exhaust waste heat recovery under various working conditions [20]. Kim et al. proposed a novel single loop ORC system for engine waste heat recovery that can simultaneously utilize waste heat from both engine coolant and exhaust gas [21]. Their results showed that 20% additional power output can be achieved by using their proposed novel single loop ORC system under target engine conditions. The parametric optimization has been widely discussed in several studies. For instance, Yang et al. presented a parametric optimization of an ORC system for the exhaust waste heat recovery of a diesel engine [22]. The evaporation pressure, superheat degree and condensation temperature were optimized simultaneously under various operating conditions in their study. Vaja et al. conducted a parametric analysis of a simple ORC system to achieve the optimal evaporation pressures for three diﬀerent organic ﬂuids [23]. Shu et al. analyzed the inﬂuence of evaporation temperatures of high temperature and low temperature cycles on the thermodynamic performances of a dual loop ORC system [24]. Dolz et al. applied the bottoming Rankine cycle to the waste heat recovery system of heavy duty diesel engines and investigated the effects of the evaporation temperature and maximum cycle temperature on the bottoming cycle [25,26]. Wang et al. evaluated the eﬀects of three key parameters, including the expander isentropic eﬃciency, evaporation pressure of high temperature loop and condensation temperature of low temperature loop on the thermodynamic performances of a dual loop ORC system for the diesel engine waste heat recovery [27]. The thermoeconomic analysis was performed in many studies in the ORC community. Yang et al. performed the thermodynamic optimization of an ORC system to evaluate the economic performance based on

Table 1 Application of genetic algorithm in thermal energy and ORC systems. Application description

Objective functions

Variable numbers

Optimization type

Steam RC system, air bottoming cycle and ORC system [33] Transcritical CO2 cycle and ORC system [34] Flash-binary geothermal power system [35] Supercritical CO2 Brayton cycle [36] Basic ORC system [37] Basic ORC system [38] Basic, single-stage and double-stage regenerative ORC systems [39] Basic, recuperated and regenerative ORC systems [40] Basic ORC system [41] Basic, parallel two-stage and series two-stage ORC systems [42] Basic and regenerative ORC systems [43] Organic split-cycle system [44] ORC system [45] Ice thermal energy storage system [46] Gas turbine cycle [47] Ice thermal energy storage system [48] Combine cooling, heating and power solar generation system [49] Ice thermal energy storage system [50] Hybrid ORC system [51] Dual loop ORC system [52] Basic ORC system [53]

CO2 emissions, total module weight and net present value Exergy eﬃciency and total product unit cost Exergy eﬃciency First law eﬃciency, exit pressure and net work output Exergy eﬃciency and overall capital cost Ratio of net power output to total heat transfer area Exergy eﬃciency Speciﬁc investment cost and exergy eﬃciency Total annualized cost Net power output and turbine size parameter Exergy eﬃciency and heat transfer area per unit net power output Net power output Net power output Exergy eﬃciency and total cost rate Exergy eﬃciency and payback time Exergy eﬃciency and total cost rate Net annual beneﬁt and exergy eﬃciency Exergy eﬃciency and total cost rate First and second law eﬃciencies and levelized energy cost Net power output and total heat transfer area Exergy eﬃciency and levelized energy cost

16 7 3 4 5 4 3 3 2 4 5 5 6 5 8 7 5 8 4 6 5

Multi-objective Multi-objective Single-objective Multi-objective Multi-objective Single-objective Single-objective Multi-objective Single-objective Multi-objective Multi-objective Single-objective Single-objective Multi-objective Multi-objective Multi-objective Multi-objective Multi-objective Multi-objective Multi-objective Multi-objective

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2. Dual loop ORC system

2.3. Thermodynamic modeling

2.1. System description

2.3.1. HT cycle process Taking R245fa as an example, the T-s diagram of the HT cycle is shown in Fig. 3 and the each process is described below.

In this study, a six-cylinder, in-line, turbocharged, intercooled CNG engine is chosen as the topping cycle. The main performance parameters of the CNG engine are listed in Table 2. The schematic diagram of the dual loop ORC system including a HT cycle and a LT cycle is shown in Fig. 1. The HT cycle is designed to recover the exhaust energy, while the LT cycle is used to recover the waste heat from the coolant, intercooler heat rejection, and the released heat from the condensation process of the HT cycle. These two cycles are connected by a preheater. In the HT cycle, the working ﬂuid is pumped to a high pressure liquid state using pump 1. Then it enters evaporator 1 and is heated to a superheated vapor state. Afterwards, the superheated vapor enters expander 1, where it expands and produces work. Finally, the working ﬂuid leaves the expander 1 as a low pressure vapor and is condensed to a saturated liquid state in the preheater. The working principle of the LT cycle is similar to that of the HT cycle. The main diﬀerence between both cycles is that the LT cycle recovers the waste heat from the coolant system, intercooler and the condensation process of the HT cycle. Therefore, there are four heat exchangers in the LT cycle. During the heating process, the working ﬂuid is ﬁrst heated to a subcooled liquid state by the intercooler. Then the working ﬂuid absorbs heat in the preheater and turns into a two phase (vapor-liquid) state. Subsequently, it is heated to a saturated vapor state in evaporator 2.

Process H1–H2 (Expander 1): The power output and isentropic eﬃciency of the expander 1 are given by:

̇ Wexp1 = ṁ H (hH1−hH2) ηise,exp1 =

hH1−hH2 hH1−hH2s

The heat transfer rate of the preheater can be expressed as:

Q̇H,pre = ṁ H (hH2−hH4 )

The power consumption and isentropic eﬃciency of the pump 1 can be expressed as:

ηise,p1 =

The selection of the working ﬂuid plays a key role in designing an ORC system. To recover low grade waste heat from the IC engines, the working ﬂuid with a low boiling temperature is preferred. Refrigerants and hydrocarbons are two commonly recommended components. Considering the safety and environmental impacts, the working ﬂuid should be non-corrosive, non-ﬂammable, and non-toxic. Thus, CFCs (chloroﬂuorocarbons) and HCFCs (hydrochloroﬂuorocarbons) are ﬁrst excluded due to their high GWP (global warming potential) and ODP (ozone depletion potential) values. The presence of liquid droplets in the expansion process can cause blade erosion, so the wet working ﬂuid is not considered in this study. The heat source temperature of the HT cycle is relatively high, so the working ﬂuid with high critical point properties is preferred for the HT cycle. During the last few years, extensive researches have indicated that R245fa [1,9–11,24,28,32,39,40] and R600 [12,24,28] were widely adopted in ORC applications. Furthermore, the traditional refrigerants are currently being replaced by HFOs (hydroﬂuorooleﬁns). HFOs are new and environmentally friendly refrigerants with null ODP and a relatively low GWP. Considering all the factors mentioned above, four working ﬂuids are selected for the thermoeconomic analysis in this study. The thermodynamic properties of these four working ﬂuids are shown in Table 3, and the corresponding T-s diagram is shown in Fig. 2.

In-line 6 Turbocharged and Intercooled Port fuel injection Spark ignition 210 8.8 1120 114 × 144

hH5s−hH4 hH5−hH4

(4)

(5)

Process H5–H1 (Evaporator 1): The heat transfer rate of the evaporator 1 is given by:

̇ Qeva1 = ṁ H (hH1−hH5) = ṁ exh (h exh,a−h exh,d )

(6)

2.3.2. LT cycle process Also taking R245fa as an example, the T-s diagram of the LT cycle is shown in Fig. 4 and the each process is described below. Process L1–L2 (Expander 2): The power output and isentropic eﬃciency of the expander 2 can be expressed as:

̇ Wexp2 = ṁ L (hL1−hL2)

ηise,exp2 =

hL1−hL2 hL1−hL2s

(7) (8)

Process L2–L4 (Condenser): The heat transfer rate of the condenser can be determined as:

Table 2 Main technical performance parameters of the CNG engine.

Cylinder arrangement Cylinder number Air intake type Fuel supply Ignition type Rated power Displacement Maximum torque Stroke and cylinder bore

(3)

Process H4–H5 (Pump 1):

2.2. Working ﬂuid selection

Parameters

(2)

Process H2–H4 (Preheater):

̇ = ṁ H (hH5−hH4 ) Wp1

Items

(1)

̇ = ṁ L (hL2−hL4 ) Qcon

(9)

Units

Process L4–L5 (Pump 2): The power consumption and isentropic eﬃciency of the pump 2 can be calculated as:

̇ = ṁ L (hL5−hL4 ) Wp2

kW L Nm mm

ηise,p2 =

1103

hL5s−hL4 hL5−hL4

(10) (11)

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Fig. 1. Schematic diagram of the dual loop ORC system.

500

Table 3 Thermodynamic properties of selected working ﬂuids. Critical temperature (K)

Critical pressure (MPa)

ODP

GWP (yr)

R245fa R600 R1234yf R1234ze

427.16 425.13 367.85 382.52

3.651 3.796 3.382 3.636

0 0 0 0

950 ∼20 4 6

450

Temperature (K)

Working ﬂuids

Process L5–L6 (Intercooler): The heat transfer rate of the intercooler can be determined as:

Q̇int = ṁ L (hL6−hL5) = ṁ air (hair,e−hair,f )

R245fa

400

R600

R1234ze

350

300

(12)

R1234yf

Process L6–L8 (Preheater):

250

The heat transfer rate of the preheater can be expressed as:

Q̇L,pre = ṁ L (hL8−hL6) = εpre Q̇H,pre

0

0.5

1

1.5

2

2.5

Entropy (kJ/kg·K)

(13)

Fig. 2. T-s diagram of selected working ﬂuids.

Process L8–L1 (Evaporator 2): include net power output and thermal eﬃciency. The net power output of the HT cycle is given by:

The heat transfer rate of the evaporator 2 can be determined as:

̇ Qeva2 = ṁ L (hL1−hL8) = εeva2 ṁ cool (h cool,g−h cool,h )

̇ −Wp1 ̇ ẆH,net = Wexp1

(14)

(15)

The net power output of the LT cycle can be determined as: 2.3.3. Thermodynamic indicators and assumptions of the dual loop ORC system The thermodynamic indicators of the dual loop ORC system mainly

̇ −Wp2 ̇ ẆL,net = Wexp2

(16)

The total net power output of the dual loop ORC system can be 1104

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(1) (2) (3) (4)

The whole system operates under a steady state condition. Pressure drops in heat exchangers and pipelines are neglected. The isentropic eﬃciency of the expander is set to 0.65 [1,22,32]. The isentropic eﬃciency of the pump is set to 0.7 [1,14,22,32,35,38–40,42]. (5) The eﬀectiveness of the heat exchanger is set to 0.5 [22]. 2.4. Heat transfer modeling Considering the waste heat characteristics of the IC engines, two diﬀerent types of heat exchangers are considered in this study. The ﬁnand-tube heat exchanger is selected as the evaporator 1 due to the high exhaust temperature, whereas the plate heat exchanger is used as the intercooler, condenser, preheater and evaporator 2. The heat transfer modeling is established on the basis of logarithmic mean temperature diﬀerence (LMTD) method. The heat transfer rate is given by:

Q̇ = UAΔTLMTD

(19)

The LMTD can be expressed as:

Fig. 3. T–s diagram of the HT cycle.

ΔTLMTD =

Δtmax−Δtmin Δt

ln Δtmax

(20)

min

2.4.1. Fin-and-tube heat exchanger modeling As shown in Fig. 3, the ﬁn-and-tube heat exchanger is divided into three zones: the single phase liquid zone (state H5–state H6), the liquid and vapor phase zone (state H6–state H7), and the single phase vapor zone (state H7–state H1). The working ﬂuid inside the tube absorbs heat from the exhaust gas. The schematic and geometric dimensions of the ﬁn-and-tube heat exchanger are presented in Fig. 5 and Table 4, respectively. The overall heat transfer coeﬃcient in each section is given by:

δβ β 1 r 1 = + rin β + + out + λ η hout η Uft h in Fig. 4. T–s diagram of the LT cycle.

h= expressed as:

̇ Wtot,net = ẆH,net + ẆL,net

̇ Wtot,net ̇ ̇ Qeva1 + Q̇int + Qeva2

(22)

The Nusselt number for the exhaust gas is given by the Zhukauskas correlation [54]. When 1000 < Re < 2 × 105,

(17)

The thermal eﬃciency of the dual loop ORC system is given by:

ηth =

λNu d

(21)

0.6 0.36 Nuexh = 0.35ε 0.2Reexh Prexh

(18)

For the thermodynamic modeling of the dual loop ORC system, the following assumptions are adopted to simplify the calculation:

0.25 Pr ⎛ exh ⎞ ⎜ Prexh,wall ⎟ ⎝ ⎠

(23)

When Re < 1000, Fig. 5. Schematic of the ﬁn-and-tube heat exchanger.

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Table 4 Geometric dimensions of the ﬁn-and-tube evaporator. 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 steel 316 L Stainless steel 316 L 9 8.8

– – mm mm mm mm mm mm – – – – m2 m

0.5 0.36 ⎛ Prexh ⎞ Nuexh = 0.71Reexh Prexh ⎜ ⎟ ⎝ Prexh,wall ⎠

0.25

(24)

The Nusselt number for the single phase working ﬂuid can be determined using the Gnielinski correlation [55].

Nu wf

(f /8)(Re wf −1000) Prwf ⎡ d 2/3 1 + ⎛ ⎞ ⎤ ct = 2/3 ⎢ 1 + 12.7 f /8 (Prwf −1) ⎣ ⎝l⎠ ⎥ ⎦

f = (1.82 log Re wf −1.64)−2

Fig. 6. Schematic of the plate heat exchanger.

(25)

Table 5 Geometric dimensions of the plate heat exchanger.

(26) Items

Parameters

Units

Chevron angle Corrugation depth Corrugation width Plate thickness Plate length Plate width

65 3 4 0.35 0.536 0.123

deg mm mm mm m m

In the single phase liquid zone,

Pr ct = ⎛ wf ⎞ Pr ⎝ wall ⎠ ⎜

0.01

,

⎟

Prwf = 0.05 ∼ 20 Prwall

(27)

In the single phase vapor zone,

T ct = ⎛ wf ⎞ ⎝ Twall ⎠ ⎜

⎟

0.45

,

Twf = 0.5 ∼ 1.5 Twall

(28)

1 1 δ 1 = + rin + + rout + Upla h in λ hout

For the liquid and vapor phase zone inside the tube, the heat exchanger is discretized and divided into N parts. The thermodynamic properties of the working ﬂuid in each part can be assumed as constant [37,40]. The convective heat transfer coeﬃcient is given by the Liu and Winterton correlation [56].

htp,i =

(Fi h fb,i

)2

+ (Si h nb,i

)2

The Nusselt number for the single phase working ﬂuid can be expressed using the Chisholm and Wanniarachchi correlation [57].

6β 0.646 0.583 1/3 Re Pr Nu = 0.724 ⎛ ⎞ ⎝π⎠

(29)

GD h μ

Re =

0.35

Si = (1 +

G=

h fb,i =

Dh =

(37)

4wb 2(w + b)

(38)

The two-phase heat transfer zone of the plate heat exchanger is also discretized and divided into N parts, which is similar to that of the ﬁnand-tube heat exchanger mentioned above. The Nusselt number for the condensation process is given by [58]:

(32)

The convective heat transfer coeﬃcient for the nucleate boiling is given by the Cooper’s pool boiling correlation.

h nb,i = 55pr0.12 qi2/3 (−log pr )−0.55 M−0.5

m N ·w·b

The hydraulic diameter of the ﬂow channel can be expressed as:

(31)

The convective heat transfer coeﬃcient for the ﬁlm boiling can be calculated using the Dittus–Boelter equation. 0.8 0.023(λl / d ) ReL,i Prl0.4

(36)

The mass ﬂux can be expressed as:

(30)

The suppression factor is given by: 0.16 −1 0.055Fi0.1ReL,i )

(35)

The Reynolds number is given by:

The forced convective heat transfer enhancement factor can be determined as:

⎛ ρl ⎞ ⎤ Fi = ⎡ ⎢1 + x i Pr l ⎜ ρ −1⎟ ⎥ ⎝ v ⎠⎦ ⎣

(34)

(33)

0.4 Nu i = 4.118Reeq,i Prl1/3

(39)

The Nusselt number for the evaporation process is given [59]:

2.4.2. Plate heat exchanger modeling The schematic and geometric dimensions of the plate heat exchanger are presented in Fig. 6 and Table 5, respectively. The overall heat transfer coeﬃcient of the plate heat exchanger can be determined as [32,52]:

0.5

ρ ⎡ ⎤ 0.3 Rei0.5 ⎢1−x i + x i ⎛⎜ l ⎟⎞ ⎥ Nu i = 1.926Prl1/3 Boeq,i ρ ⎝ v⎠ ⎦ ⎣ The equivalent Reynolds number can be determined as: 1106

(40)

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Reeq,i =

Geq,i D h μl

where K1,EXP , K2,EXP and K3,EXP are the constants depending on the expander type, and ẆEXP is the power output of the expander. The system total investment cost (TIC) is the sum of the cost of each component, which can be determined as:

(41)

The equivalent boiling number can be expressed as:

Boeq,i =

″ qwall (42)

The capital recovery factor (CRF) is given by [61]:

where,

CRF =

0.5

ρ ⎡ ⎤ Geq,i = G ⎢1−x i + x i ⎛⎜ l ⎞⎟ ⎥ ρ ⎝ v⎠ ⎦ ⎣

EPC = Ctot

The dual loop ORC system consists of many diﬀerent components. All direct and overhead costs need to be considered for each component. The module costing technique (MCT) is a commonly used method to estimate the bare module cost for chemical plants [60]. Based on the MCT, the capital cost of the heat exchanger can be calculated using the following equation:

CEPCI2014 0 = FS CHX (B1,HX + B2,HX FM,HX FP,HX ) CEPCI2001

(44)

CEPCI2014 0 FS CPP (B1,PP + B2,PP FM,PP FP,PP ) CEPCI2001

(45)

(46)

(47)

0 CPP

where is the bare module cost of the pump, B1,PP and B2,PP are the constants depending on the pump type, and FM,PP and FP,PP are the material and pressure factors, respectively. The bare module cost of the pump is given by: 0 logCPP = K1,PP + K2,PP logẆPP + K3,PP (logẆPP )2

(48)

where K1,PP , K2,PP and K3,PP are constants depending on the pump type, and ẆPP is the power consumption of the pump.

Table 6 Constants for economic modeling.

The pressure factor of the pump can be determined as:

logFP,PP = C1,PP + C2,PP logPPP + C3,PP (logPPP )2

(49)

where C1,PP , C2,PP and C3,PP are the constants depending on the pump type, and PPP is the design pressure of the pump. The capital cost of the expander can be expressed:

CEXP =

CEPCI2014 0 FS CEXP FMP CEPCI2001

(50)

0 CEXP

where is the bare module cost of the expander, and FMP is the additional factor of the expander. The bare module cost of the expander is given by: 0 logCEXP = K1,EXP + K2,EXP logẆEXP + K3,EXP (logẆEXP )2

(54)

Before analyzing the thermoeconomic performance of the dual loop ORC system, the waste heat characteristics of the CNG engine tested on an experimental bench were evaluated. The operating characteristics of the IC engine over its whole speed and load range are plotted as shown in Fig. 7 based on the experimental data. As shown in Fig. 7(a), the engine speed has minor eﬀect on the brake speciﬁc fuel consumption (BSFC) at low torques while the CNG engine has better fuel economy at high torques. It can also be seen that the CNG engine reaches a maximum power output of 210 kW near the rated conditions. The eﬀect of the speed and torque on the eﬀective thermal eﬃciency of the CNG engine is shown in Fig. 7(b). Similar to the BSFC, a higher eﬀective thermal eﬃciency can be achieved at a higher engine torque. The CNG engine achieves eﬀective thermal eﬃciency values of 16.91–41.11% over the whole operating range. Fig. 7(c) shows the variation in the exhaust temperature with respect to the engine speed and torque. Over the whole operating range of the CNG engine, the exhaust temperature is above 720.75 K. The variation in the exhaust mass ﬂow rate is shown in Fig. 7(d). The exhaust mass ﬂow rate increases as the engine speed and torque increase. Near the rated conditions, the exhaust mass ﬂow rate reaches a maximum value of 0.31 kg/s. A turbocharger is used to increase the power output of this CNG engine. The temperature and pressure of the intake air increase dramatically when passing through the compressor. The turbocharged IC engine often uses an intercooler to reduce the charge air temperature [62]. So the charge air is treated as the waste heat that can preheat the working ﬂuid in the ORC system. Fig. 8(a) shows the variation in charge air temperature at the inlet of the intercooler. It shows that the charge

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

CPP =

CRF + fK (Wexp−Wp) h full − load

3. Waste heat evaluation of the CNG engine

where K1,HX , K2,HX and K3,HX are the constants depending on the heat exchanger type, and AHX is the heat transfer area. The pressure factor of the heat exchanger can be expressed as:

logFP,HX = C1,HX + C2,HX logPHX + C3,HX (logPHX )2

(53)

where fK is the maintenance and insurance cost factor, and h full − load is the full load operation hours. Table 6 lists all the constant values mentioned in this section for the economic modeling.

where the Chemical Engineering Plant Cost Index (CEPCI) is used to adjust the speciﬁc plant cost for diﬀerent years. CEPCI2001 and CEPCI2014 are the Chemical Engineering Plant Cost Index for years 2001 and 2014, 0 respectively, CHX is the bare module cost of the heat exchanger, FS is the construction overhead cost factor, B1,HX and B2,HX are the constants depending on the heat exchanger type, and FM,HX and FP,HX are the material and pressure factors, respectively. The bare module cost of the heat exchanger is given by: 0 logCHX = K1,HX + K2,HX logAHX + K3,HX (logAHX )2

i (1 + i) LTpl (1 + i) LTpl−1

where i is the interest rate, and LTpl is the plant lifetime. The electricity production cost (EPC) can be expressed as:

(43)

2.5. Economic modeling

CHX

(52)

Ctot = CHX + CPP + CEXP

Geq,i·i fg

Constant

Value

Constant

Value

Constant

Value

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

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 FMP

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 CEPCI2014 CEPCI2001 i LTpl fK hfull-load

2.2659 1.4398 −0.1776 586.77 397 0.1 15 0.0165 7500

Note that all values are obtained from [59] except the CEPCI values that are obtained from [28].

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Fig. 7. Performance map of the CNG engine.

intercooler varies within a small range of 298–323 K. Fig. 8(c) shows the variation in the intake air mass ﬂow rate with respect to the engine speed and torque. Similar to the charge air at the inlet of the intercooler, the intake air mass ﬂow rate increases with increasing engine speed and torque. Near the rated conditions, the intake air mass ﬂow rate achieves a maximum value of 0.29 kg/s. Fig. 8(d) shows the

air temperature at the inlet of the intercooler increases gradually from 308 to 410 K as the engine speed and torque increase. Fig. 8(b) shows the variation in the charge air temperature at the outlet of the intercooler. The charge air temperature at the outlet of the intercooler shows a complicated trend over the whole operating range of the CNG engine. It can be seen that the charge air temperature at the outlet of the

Fig. 8. Waste heat characteristics of intercooler.

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variation in the available waste heat of intake air over the whole operating range. It shows that the waste heat of intake air can be above 10 kW when the engine speed and torque exceed the midpoint of the rated conditions. The waste heat characteristics of the coolant are shown in Fig. 9. The coolant temperature at the outlet of the IC engine is below 363.15 K. Fig. 9(a) shows the variation in the coolant temperature at the inlet of the CNG engine from 350 to 360 K. Fig. 9(b) shows the variation in the coolant temperature at the outlet of the CNG engine. It shows that the coolant temperature at the outlet of the CNG engine is mostly below 365.15 K. Fig. 9(c) shows the variation in the coolant mass ﬂow rate, and it demonstrates that the engine torque has little eﬀect on the coolant mass ﬂow rate. It also indicate that the coolant mass ﬂow rate increases linearly as the engine speed varies from 1.55 to 3.37 kg/s. Fig. 9(d) shows the variation in the available waste heat of the coolant. On the whole, the waste heat of the coolant increases with the engine speed and torque. Near the rated conditions, the maximum waste heat of the coolant can reach up to 88 kW. Although the temperature of the coolant is lower than that of the charge air (also see Fig. 8), the coolant has a larger quantity of the waste heat source compared to the charge air.

Table 7 Logical bounds of decision variables. Decision variables

Lower bound

Upper bound

PH7 (MPa) TH1 (K) TH4 (K) TL1 (K) TL4 (K) Texh,out (K)

1 0 350.15 323.15 298.15 393.15

3 20 360.15 343.15 318.15 423.15

•T •T

L4 :

Condensation temperature of the LT cycle (K) Exhaust temperature at the outlet of evaporator 1 (K)

exh,out :

The thermoeconomic multi-objective optimization model for the dual loop ORC system can be expressed as follows:

̇ ) = f1 (PH7,TH1,TH4,TL1,TL4,Texh,out ) max(Wnet

(55)

min(Ctot ) = f2 (PH7,TH1,TH4,TL1,TL4,Texh,out )

(56)

The logical bounds of the aforementioned decision parameters are listed in Table 7.

4. Multi-objective optimization

4.2. Evaluation of the genetic algorithm

4.1. Objective functions and decision parameters

Unlike single-objective optimization problems, the multi-objective optimization algorithm forms a Pareto optimal set. Each solution in the Pareto optimal set represents a trade-oﬀ solution to the multi-objective function. The Pareto optimal set points should be evenly distributed and closely spaced in a small region. The optimization model is evaluated to obtain appropriate ranges of control parameters to achieve an adequate qualify of Pareto solution. Taking the rated condition as an example, Fig. 10 shows the variation in the Pareto frontier under different control parameters. These parameters include population size, tournament size, crossover function, and crossover fraction. The eﬀect of the population size on the distribution of the Pareto frontier is shown in Fig. 10(a). It demonstrates that when the population size is 600, the

In the present study, two conﬂict objectives of maximizing the net power output and minimizing the total investment cost of the dual loop ORC system are considered in the proposed multi-objective optimization framework. The following decision parameters are selected for the thermoeconomic optimization of the dual loop ORC system:

•P •T •T •T

H7 :

Evaporation pressure of the HT cycle (MPa) Superheat degree of the HT cycle (K) H4 : Condensation temperature of the HT cycle (K) L1: Evaporation temperature of the LT cycle (K) H1:

Fig. 9. Waste heat characteristics of coolant.

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Pareto frontier is distributed more evenly than others. As to the tournament size, crossover function and crossover fraction, the best parameter values are determined in the similar way. The parameter settings of the optimization model are listed in Table 8.

Table 8 Parameter settings of the genetic algorithm.

4.3. Decision-making in multi-objective optimization This study involves multi-objective optimization of the dual loop ORC system, so a suitable multi-criteria decision analysis method should be employed to obtain a ﬁnal optimal solution from the Pareto frontier. The TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) is commonly used to this end. The core concept of the TOPSIS method is to identify an alternative that will have the shortest geometric distance from the positive ideal point and the longest geometric distance from the negative ideal point. The positive ideal point is the solution with the best value for each objective function, while the negative ideal point has the worst value for each objective function in a Pareto optimal set. The TOPSIS method is adopted to select the ﬁnal optimal solution in the present study. Considering the dimension of each objective function may be diﬀerent, the objective functions are non-dimensionalized by Euclidian non-dimensionalization method before decision making process [47]. For the TOPSIS method, the spatial distance between each solution and the positive ideal solution on the Pareto frontier is deﬁned as:

d i+ =

Multi-objective optimization problems involve multiple conﬂicting objectives and multiple decision parameters. Each decision parameter has a great inﬂuence on the thermoeconomic performances of the dual loop ORC system in this study. First of all, the eﬀects of decision parameters and working ﬂuids on the thermoeconomic performances of the dual loop ORC system are investigated. In this part, the CNG engine operates at the rated condition. The value of each considered parameter is within their logical bound and is set as the median value of the logical bounds (as shown in Table 7).

(57)

n

5.1.1. Eﬀect of the evaporation pressure of the HT cycle The variations in the thermoeconomic performances of the six working ﬂuid groups with the evaporation pressure of the HT cycle (PHT,ep ) are shown in Fig. 12. On the whole, no matter which working ̇ ), total investment ﬂuid group is adopted, the net power output (Wtot,net cost (TIC), and total heat transfer area ( Atot ) all increase with PHT,ep , while the electricity product cost (EPC) shows a opposite tendency. As can be seen in Fig. 12(a), the working ﬂuid group of R245fa+R245fa ̇ presents the highest Wtot,net with increasing PHT,ep . When PHT,ep varies

(58)

where Fjnon-ideal is the negative ideal solution. The closeness coeﬃcient can be deﬁned as:

Ci =

d i− d i+ + d i−

600 Tournament 6 0.6 Adaptive feasible Scattered 1200

5.1. Sensitivity analysis and working ﬂuids comparison

is the positive ideal solution. where The spatial distance between each solution and the negative ideal solution on the Pareto frontier is deﬁned as:

∑j=1 (Fij−Fjnon−ideal )2

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

5. Results and discussion

Fjideal

d i− =

Value

condition of the CNG engine as an example, the decision-making process for selecting the ﬁnal optimal solution on the Pareto frontier is illustrated in Fig. 11.

n

∑j=1 (Fij−Fjideal )2

Parameters

(59)

In the TOPSIS decision-making process, a solution corresponding to a maximum Ci is selected as the ﬁnal optimal solution. Taking the rated

Fig. 10. Pareto frontier under diﬀerent population size.

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results in little change in enthalpy at state H1 presented in Fig. 3. As shown in Fig. 13(a) and (c), the working ﬂuid group of R245fa+R245fa ̇ generates the highest Wtot,net and lowest EPC with increasing THT,sd . ̇ is almost kept a constant at near 16.55 kW, while EPC remains at Wtot,net about 0.55 $/kW h. Furthermore, the working ﬂuid group of R245fa +R1234yf has the largest TIC and Atot with increasing THT,sd . 5.1.3. Eﬀect of the condensation temperature of the HT cycle Fig. 14 shows the variations in the thermoeconomic performances of the six working ﬂuid groups with the condensation temperature of the ̇ HT cycle (THT,ct ). It is seen that Wtot,net and TIC decrease with increasing THT,ct for all working ﬂuid groups. This is because the enthalpy diﬀerence between the inlet and outlet of expander decreases with THT,ct , ̇ ̇ . The maximum Wtot,net is achieved which causes the reduction in Wtot,net by the working ﬂuid group of R245fa+R245fa. When THT,ct varies from ̇ decreases from 17.63 to 15.47 kW. The 350.15 to 360.15 K, Wtot,net working ﬂuid group of R600+R600 shows the lowest TIC under the given operating conditions. As seen in Fig. 14(c) and (d), EPC and Atot increase with increasing THT,ct . The increase in THT,ct leads to the dė , which results in the increase in EPC. The working ﬂuid crease in Wtot,net group of R245fa+R245fa has the lowest EPC among all working ﬂuid groups while the working ﬂuid group of R600+R600 exhibits the smallest Atot .

Fig. 11. Pareto frontier for multi-objective optimization.

̇ from 1 to 3 MPa, Wtot,net increases from 9.66 kW to its maximum value of 19.36 kW. The working ﬂuid group of R600+R600 shows a relative low TIC when PHT,ep is below 2.5 MPa as shown in Fig. 12(b). When PHT,ep is between 2.5 and 3 MPa, the working ﬂuid group of R245fa +R245fa has the lowest TIC. The working ﬂuid group of R245fa +R245fa exhibits the lowest EPC with the increment of PHT,ep as dė among all working ﬂuid picted in Fig. 12(c) because of its highest Wtot,net groups. When PHT,ep is 3 MPa, the working ﬂuid group of R245fa +R245fa achieves the minimum EPC of 0.49 $/kW h. As indicated in Fig. 12(d), the working ﬂuid groups of R245fa+R1234yf and R600+R600 require the largest and smallest Atot , respectively.

5.1.4. Eﬀect of the evaporation temperature of the LT cycle Fig. 15 shows the variations in the thermoeconomic performances of the six working ﬂuid groups with the evaporation temperature of the LT ̇ cycle (TLT,et ). Similar to the eﬀect of PHT,ep , Wtot,net , TIC, and Atot increase with the increase of TLT,et , while EPC presents the opposite trend. The increase of TLT,et results in an increase of the enthalpy diﬀerence between the inlet and the outlet of expander 2, which increases ẆLT,net . The heat transfer area during the evaporation process in the LT cycle also increases with TLT,et . Due to the increase in equipment costs of the expander 2 and heat exchanger, TIC increases accordingly as TLT,et increases. As shown in Fig. 15(a) and (b), the working ﬂuid group of ̇ R245fa+R245fa presents the highest Wtot,net and relatively low TIC. ̇ increases from 13.98 When TLT,et varies from 323.15 to 343.15 K, Wtot,net

5.1.2. Eﬀect of the superheat degree of the HT cycle The variations in the thermoeconomic performances of the six working ﬂuid groups with the superheat degree of the HT cycle (THT,sd ) as depicted in Fig. 13 are examined in this section. It shows that THT,sd ̇ has nearly no aﬀect on Wtot,net , TIC, and EPC while THT,sd leads to a small ̇ , this is due to the fact that increasing THT,sd increase in Atot . For Wtot,net

Fig. 12. Eﬀect of the evaporation pressure of the HT cycle on the thermoeconomic performances.

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Fig. 13. Eﬀect of the superheat degree of the HT cycle on the thermoeconomic performances.

Fig. 14. Eﬀect of the condensation temperature of the HT cycle on the thermoeconomic performances.

to 18.79 kW. The reason for the decrease of EPC in Fig. 15(c) is that the ̇ eﬀect of the increasing Wtot,net is greater than that of the increasing TIC. As seen in Fig. 15(c), the working ﬂuid group of R245fa+R245fa exhibits the lowest EPC with increasing TLT,et .

Fig. 16 are discussed in this section. It is seen that TLT,ct has the similar eﬀect with THT,ct on the thermoeconomic performances. For each ̇ and TIC decrease as TLT,ct increase while working ﬂuid group, Wtot,net EPC and Atot show an opposite trend. The reason for this is similar to the discussion presented in Section 5.1.3. The working ﬂuid group of ̇ R245fa+R245fa shows the highest Wtot,net and lowest EPC. When TLT,ct ̇ varies from 298.15 to 318.15 K, Wtot,net decreases from 19.19 to ̇ 13.81 kW. It is worthwhile to note that TIC is directly related to Wtot,net

5.1.5. Eﬀect of the condensation temperature of the LT cycle The thermoeconomic performances of the six working ﬂuid groups with the condensation temperature of the LT cycle (TLT,ct ) as shown in 1112

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Fig. 15. Eﬀect of the evaporation temperature of the LT cycle on the thermoeconomic performances.

performances. Fig. 17 shows the variations in the thermoeconomic performances of the six working ﬂuid groups with the exhaust temperature at the outlet of evaporator 1 (Texh,out ). As shown in Fig. 17(a), ̇ decreases as Texh,out increases. When Texh,out varies from 393.15 to Wtot,net ̇ decreases from 16.95 to 16.16 kW. This can be ex423.15 K, Wtot,net plained by the fact that the heat recovery rate decreases with increasing Texh,out resulting a decreased mass ﬂow rate of the working ﬂuid in the HT cycle. It can be seen from Fig. 17(d) that the increase of Texh,out also

rather than Atot . It is because the eﬀect of expander cost is greater than that of heat exchanger cost. 5.1.6. Eﬀect of the exhaust temperature at the outlet of evaporator 1 The IC engines usually operate under various conditions, which cause a large variation in the exhaust temperature. As a high temperature heat source of the dual loop ORC system, the exhaust temperature has a signiﬁcant inﬂuence on the thermoeconomic

Fig. 16. Eﬀect of the condensation temperature of the LT cycle on the thermoeconomic performances.

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respectively. Fig. 19 shows the optimization results for the operating parameters of the dual loop ORC system. Each optimal operating parameter corresponds to the optimization result presented in Fig. 18. As indicated in Fig. 19(a), the optimal PHT,ep is above 2.5 MPa over the whole operating range of the CNG engine. To fully utilize the waste heat of the IC engines, a higher PHT,ep will be beneﬁcial to achieve a larger temperature ̇ . diﬀerence between the LT and HT cycles resulting an increased Wtot,net Furthermore, the optimal PHT,ep is between 2.7 and 2.9 MPa under most conditions. The optimal THT,sd is shown in Fig. 19(b). It can be seen that the optimal THT,sd ﬂuctuates with the engine’s operating conditions. The ﬁrst main reason is that the exhaust energy of the CNG engine is unstable as the operating condition varies. In addition, the optimal THT,sd is directly related to the PHT,ep and ṁ H . The results shown in Fig. 19(c)–(e) illustrate that the optimal operating parameters (i.e., THT,ct , TLT,et , and TLT,ct ) are remaining near constant over the entire engine operating range. Fig. 19(f) shows the optimal Texh,out over the whole operating range of the CNG engine. It points out that the optimal Texh,out is mainly inﬂuenced by the engine speed. When the engine speed varies from 800 to 2200 r/min, the optimal Texh,out increases from 402.03 to 422.88 K. The optimal Texh,out is all above 400 K, resulting in a higher heat transfer rate in evaporator 1, which leads to an increase in the net power output of the dual loop ORC system. Based on the optimal operating parameters discussed above, other thermoeconomic indicators including EPC, thermal eﬃciency, heat transfer area, and heat transfer rate are also determined and depicted in Fig. 20. As seen in Fig. 20(a), EPC increases dramatically as the engine speed and torque decrease. This is because the eﬀect of the decreasing ̇ TIC is less than that of the decreasing Wtot,net . The EPC varies from 0.41 to 3.17 $/kW h over the whole operating range. The EPC level is generally acceptable, since the IC engines usually operate at the high speed and load conditions. The thermal eﬃciency of the dual loop ORC system is illustrated in Fig. 20(b). It shows that the thermal eﬃciency of the dual loop ORC system is mainly determined by the engine load. When the engine torque is above 500 N m, the dual loop ORC system exhibits higher thermal eﬃciencies. The thermal eﬃciency of the dual loop ORC system is in the range of 8.97–10.19% over the whole

lead to a reduction in Atot . On the whole, TIC exhibits a decrease trend with the increase of Texh,out as shown in Fig. 17(b). Furthermore, EPC is almost kept a constant value with increasing Texh,out as presented in Fig. 17(c). For the working ﬂuid group of R245fa+R245fa, EPC is about 0.55 $/kW h. 5.2. Multi-objective optimization of the dual loop ORC system Based on the aforementioned sensitivity analysis, it can be concluded that the operating parameters of the dual loop ORC system have great inﬂuences on the thermoeconomic performances. Furthermore, the working ﬂuid group of R245fa+R245fa performs better than any others from the view point of economics and thermodynamics. To maximize the net power output and minimize the TIC for the working ﬂuid group of R245fa+R245fa, the multi-objective optimization algorithm is adopted to determine the Pareto solutions under various conditions of the CNG engine. The optimization results for each engine operating condition are obtained based on the aforementioned TOPSIS decision-making method. Fig. 18 shows the optimization results for the maximum net power output and minimum total investment cost. It shows that the net power output increases with increasing engine speed and torque. Generally, the waste heat of the CNG engine shows an increase trend with the increase of the engine speed and torque, resulting in the increase in the heat transfer rate and mass ﬂow rate, which leads to the increment of the net power output. The optimized net power output of the dual loop ORC system varies from 1.84 to 23.62 kW over the whole operating range of the CNG engine. A conclusion can be drawn that no matter how the thermoeconomic performances of the dual loop ORC system is optimized, the net power output is mainly inﬂuenced by the waste heat quantity. Furthermore, the thermodynamic performances of the vapor power cycles are improved at the expense of economy. Therefore, the total investment cost exhibits a same trend as that of the net power output as shown in Fig. 18(b). The total investment cost increases gradually with the operating engine speed and torque over the whole operating range of the CNG engine. At the idle and rated conditions, the optimized total investment costs are $ 419,182 and $ 667,962,

Fig. 17. Eﬀect of the exhaust temperature at the outlet of evaporator 1 on the thermoeconomic performances.

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Fig. 18. Optimization results for the maximum net power output and the minimum total investment cost.

Fig. 19. Optimization results of the operating parameters of the dual loop ORC system.

Fig. 20. Optimization results of (a) EPC, (b) thermal eﬃciency, (c) heat transfer area, and (d) heat transfer rate.

1115

1116

0.27 9.5 34 2001 and 2014 16 7500 0.0165 0.7 Cascade-ORC system Yu et al. [29]

0.8

20 7500 0.2 0.8 Single loop ORC Li et al. [68]

0.8

– – Single loop ORC

Shu et al. [66]

Zhang et al. [67]

0.75

0.8

0.015

15 7500 0.0165 0.8 0.7

20 7500 0.0165 0.8

Single loop ORC with superheater Single loop ORC Neto et al. [65]

0.8

20 8000 0.015 0.8 Single loop ORC Feng et al. [64]

0.8

20 8000 0.015 0.8 Regenerative ORC Feng et al. [63]

0.8

20 8000 0.015 0.8 Single loop ORC Feng et al. [53]

0.8

–

Higher isentropic eﬃciencies of the pump and expander are assumed Similar with this study – 30

23

0.288

Higher investment cost is required 0.055 – 129 and

0.079 and

300.3

–

1846000

Higher isentropic eﬃciencies of the pump and expander are assumed Higher investment cost is required 602803 0.091 6 165.5 and

All factors are higher than this study – – and

–

0.093

All factors are higher than this study – – – and

– and

–

0.142

667962 0.41 10.19 23.62 and

2001 2014 1996 2011 1996 2011 1996 2011 2001 2014 2001 2014 2001 2014 – 15 7500 0.0165 0.7 Dual loop ORC This study

0.65

fK

ηexp

ηp

In this paper, a thermoeconomic model of a dual loop ORC system is developed to analyze both the thermodynamic and the economic performances of several working ﬂuid groups for the purpose of CNG engine waste heat recovery. The eﬀects of six key parameters on the thermoeconomic indicators of the dual loop ORC system are investigated. Furthermore, a multi-objective genetic algorithm is employed to obtain the Pareto optimal solutions from the viewpoints of maximizing net power output and minimizing total investment cost over the whole operating range of the CNG engine. The most suitable working ﬂuid group is screened out, and the optimal parameter regions are determined. The main originality of this paper lies in the multiobjective optimization study of the dual loop ORC system using a genetic algorithm to investigate the optimal operating regions with consideration of thermodynamic performances and economic factors under various operating conditions of a CNG engine. This research is helpful in determining optimal operating regions and selecting proper working ﬂuids for the IC engine-dual loop ORC combined system. The same method can also be used to other waste heat recovery systems. The main conclusions can be summarized as follows:

Conﬁgurations

6. Conclusions

Authors

Table 9 Summary of the thermoeconomic comparison for various ORC conﬁgurations.

hfull-load

LTpl (years)

CEPCI (years)

Power output (kW)

ηth (%)

Optimal EPC ($/kW h)

TIC ($)

Remarks

A selective summary of the thermoeconomic comparison for various ORC conﬁgurations is listed in Table 9. It should be noted that most existing studies of ORC thermoeconomic performance is focused on the single loop ORC system and it is reﬂected in Table 9. To the best of our knowledge, this study is the ﬁrst work showing the thermoeconomic performance of a dual loop ORC system. Table 9 shows that the EPC obtained in this study is relatively high compared with that from other studies. One of the reasons for this is that higher isentropic eﬃciencies of the pump and expander are adopted in other studies. Yu et al. pointed out that high eﬃciency expander leads to a cost reduction of the ORC system [29]. The previous studies have shown that the actual isentropic eﬃciencies of the pump and expander are far below the theoretical values [69,70]. In this study, more realistic isentropic eﬃciency values are assumed for the pump and expander, resulting in a higher EPC compared to other studies. Another reason is that the initial coeﬃcients of the economic modeling are diﬀerent, e.g., CEPCI, maintenance cost factor (fK), full load operation hours (hfull-load), and plant lifetime (LTpl). It is seen from various analyses that older CEPCI coeﬃcients, lower maintenance cost factor, higher plant lifetime and longer full load operation hours can result in a decrease of EPC [60,65]. In addition, there are two other main contributors to the ﬁnal EPC: the thermal eﬃciency and TIC of ORC system. The dual loop ORC systems tend to have higher thermal eﬃciency and TIC compared to the single loop ORC systems. This may result higher or lower EPC for the dual loop ORC systems than the single loop systems depending on the system performance and overall investment costs. Without performing a detailed thermoeconomic analysis, it cannot be easily determined which system would provide better economic performance (i.e., a lower EPC). It is realized that only a few literatures reported the thermal eﬃciency and TIC as shown in Table 9. Therefore, a direct comparison of EPCs between the dual loop ORC system and other systems may not be valid and reasonable comparisons among EPCs from diﬀerent ORC conﬁgurations cannot be made. The information in Table 9 is provided because it can provide an indication how the optimal EPC value found in this study is roughly comparable with that from literature.

0.188

5.3. Thermoeconomic comparison of various ORC conﬁgurations

–

All factors are higher than this study

operating range. From the results presented in Fig. 20(c) and (d), Atot and total heat transfer rate have the similar variation trend under the entire operating conditions of the CNG engine. It is expected to see that they all increase due to the increase in the waste heat recovery from the CNG engine as the engine speed and torque increase. The total heat transfer rate can reach up to 238.56 kW at the rated condition.

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(1) A higher evaporation pressure (evaporation temperature) and a lower condensation temperature (condensation pressure), no matter in the HT cycle or LT cycle, exhibit a positive eﬀect on the thermoeconomic performances of the dual loop ORC system. While the eﬀects of the variation in the superheat degree and exhaust outlet temperature on the thermoeconomic performances are not obvious. (2) With the overall consideration of the thermoeconomic indicators, the working ﬂuid group of R245fa+R245fa performs better than any other ﬂuid group examined in this study for the dual loop ORC system. (3) The thermodynamic performances of the dual loop ORC system are improved at the expense of part of economy. Both the net power output and total investment cost increase with the engine speed and torque in the entire operating range. The net power output can reach up to the maximum of 23.62 kW at the rated condition. (4) Based on the optimization results, the optimal PHT,ep is always above 2.5 MPa. The optimal THT,ct and TLT,ct are kept almost constants, and both close to their lower bounds. The optimal TLT,et is close to its upper bound under most operating conditions. In addition, the optimal Texh,out is mainly inﬂuenced by the engine speed. (5) The EPC increases dramatically with the decrease of the engine speed and torque. At the rated condition, the EPC has the minimum value of 0.41 $/kW h. The thermal eﬃciency of the dual loop ORC system is in the range of 8.97–10.19% over the whole operating range.

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[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

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This paper only presents a thermoeconomic multi-objective optimization of a dual loop ORC system for CNG engine waste heat recovery from both thermodynamic and economic points of views. It is a very meaningful work to make a comparative study of the thermoeconomic performance between the single and dual loop ORC systems. That will be part of authors' future work.

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Acknowledgments

[24]

This work was sponsored by the National Natural Science Foundation of China (Grant No. 51376011), the China Scholarship Council (CSC), the Beijing Natural Science Foundation Program (Grant No. 3152005), the Projects of International Cooperation and Exchanges NSFC (Grant No. 51611130193), and the Scientiﬁc Research Key Program of Beijing Municipal Commission of Education (Grant No. KZ201410005003). The authors would like to thank the reviewers for their valuable comments on this research.

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