Parametric analysis and optimization of transcritical-subcritical dual-loop organic Rankine cycle using zeotropic mixtures for engine waste heat recovery

Parametric analysis and optimization of transcritical-subcritical dual-loop organic Rankine cycle using zeotropic mixtures for engine waste heat recovery

Energy Conversion and Management 195 (2019) 770–787 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www...

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Energy Conversion and Management 195 (2019) 770–787

Contents lists available at ScienceDirect

Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Parametric analysis and optimization of transcritical-subcritical dual-loop organic Rankine cycle using zeotropic mixtures for engine waste heat recovery

T

Liang-Hui Zhia, Peng Hua, , Long-Xiang Chenb, Gang Zhaoa,c, ⁎



a

Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230027, China Quanzhou Institute of Equipment Manufacturing, Haixi Institutes, Chinese Academy of Sciences, Jinjiang 362200, China c Centre for Biomedical Engineering, Department of Electronic Science & Technology, University of Science and Technology of China, Hefei 230027, China b

ARTICLE INFO

ABSTRACT

Keywords: Dual-loop organic Rankine cycle Transcritical-subcritical Regenerator Parametric analysis and optimization Zeotropic mixtures

Dual-loop organic Rankine cycle is a great potential technology to recover engine waste heat for energy saving. Transcritical cycle can improve exergy efficiency of heat transfer process in the evaporator, and zeotropic mixtures furtherly can improve thermal match with heat source and sink. Thus, a transcritical-subcritical dualloop organic Rankine cycle system using zeotropic mixtures is adopted for engine waste heat recovery, and system without and with regenerator is considered. The whole system is assumed in the steady state, R600a/ R601a and R134a/R245fa mixtures are used as working fluid of transcritical and subcritical cycle, respectively. Parametric analysis and optimization about turbine inlet temperature and pressure of high-temperature loop, evaporation temperature of low-temperature loop are carried out. According to the results, the designed parameters have great effect on performance of system, and for the system without and with regenerator, the optimal turbine inlet temperature, pressure and evaporation temperature are 260 °C, 11 MPa, 85 °C and 250 °C, 10 MPa, 85 °C respectively. Moreover, the effects of components of mixtures on the performance of system are analyzed. The results demonstrate that system with zeotropic mixtures can significantly improve the performance of system. The system without regenerator using R600a/R601a (0.2/0.8) and R134a/R245fa (0.4/0.6) shows the maximum power output of 97.49 kW which is higher 5.48–20.00% than pure fluids, and system with regenerator using R600a/R601a (0.3/0.7) and R134a/R245fa (0.4/0.6) achieves the maximum power output of 97.95 kW, increment of 6.52–19.78% compared with using pure fluids. And the power output of engine can be improved by 9.79% and 9.83% for the system without and with regenerator, respectively. Furthermore, the exergy destruction analysis demonstrates that zeotropic mixtures can reduce heat transfer exergy destruction and total exergy destruction of system.

1. Introduction Nowadays, facing environment and energy issues including global warming and shortage of fossil fuels, energy saving has attracted more and more attention, and great efforts have been carried out by different organizations including government, research institutes, companies and colleges. In a typical industrial country, internal combustion engines (ICEs), as the power source of industrial machineries, are the primary consumers of fossil fuel. However, in an ICE, about 55–70% of fuel heat is not utilized and wasted through exhaust and engine coolant [1]. Thus, it is a promising way to recover the waste heat of ICE to save energy. Many thermodynamic cycles including organic Rankine cycle

(ORC) [2], Kalina cycle [3] and Brayton cycle [4] have been considered as efficient methods to recover waste heat. Among them, ORC has attracted much interest due to its safety, high efficiency, high reliability and flexibility, low costs and easy maintenance [5]. Many researchers have adopted ORC to recover waste heat from engine exhaust and coolant. In terms of configurations, single loop ORC was firstly studied to recover engine waste heat [6]. Due to a large temperature difference between engine exhaust and coolant, only a small amount of the engine coolant heat could be utilized by single loop ORC. A typical work was carried out by Vaja and Gambarotta [7] by analyzing and comparing three different structures. The results showed that the ORCs with

⁎ Corresponding authors at: Centre for Biomedical Engineering, Department of Electronic Science & Technology, University of Science and Technology of China, Hefei 230027, China. E-mail addresses: [email protected] (P. Hu), [email protected] (G. Zhao).

https://doi.org/10.1016/j.enconman.2019.05.062 Received 19 April 2019; Received in revised form 16 May 2019; Accepted 19 May 2019 0196-8904/ © 2019 Published by Elsevier Ltd.

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Nomenclature

Subscripts

M T m h Q W s I E

cri pp gl g w i o c 0 p t r ex

molecular mass (kg/kmol) temperature (°C) mass flow rate (kg/s) enthalpy (J/kg) heat transfer rate (kW) work transfer rate (kW) entropy (J/kg K) irreversibility rate (kW) exergy transfer rate (kW)

Abbreviations ORC DORC HT LT ATL ODP GWP

organic Rankine cycle dual-loop organic Rankine cycle high-temperature low-temperature all life time ozone depletion potential global warming potential

critical point pinch point gas–liquid engine exhaust cooling water inlet outlet engine coolant atmospheric state pump turbine regenerator exergy

Greek letters

ex

T

utilization of both exhaust and coolant heat of engine as heat source had more power output than utilization of only exhaust heat of engine as heat source, and the regenerator would not come into effect when expander efficiency was relatively high. However, only 9.5–26.1% of engine coolant heat could be released to the ORC. Yu et al. [8] conducted a thermodynamic analysis of a single loop ORC for diesel engine exhaust and coolant waste heat recovery. The results showed that the ORC system achieved net power output of 14.5 kW, recovery efficiency of 9.2%, and 6.1% of increment in thermal efficiency of diesel engine. However, only 9.5% of waste heat was recovered from engine coolant. In view of this situation, for the single loop ORC systems, researchers mainly only focused on the recovery of engine exhaust [9]. For example, Srinivasan et al. [10] investigated the single loop ORC exhaust heat recovery potential of the fuel conversion efficiency, nitrogen oxide (NOx ) and carbon dioxide (CO2 ) emissions for a single cylinder research engine. The results demonstrated that the average fuel conversion efficiency was improved by 7%, NOx and CO2 emissions were reduced by an average of 18%. Zhao et al. [11] proposed performance evaluation of a single loop ORC for exhaust waste heat recovery from 6-cylinder 4stroke turbocharged diesel engine. The results indicated that engine with ORC system achieved the net power output increment of 4.13 kW, fuel consumption reduction of 3.61 g/(kW h) and thermal efficiency improvement of 0.66%. However, two problems exist: after being expanded in the turbine, the working fluid is still in a high-temperature state which contains much heat; and the engine coolant also contains great heat which is released into atmosphere, causing severe energy wasting. Aim at these issues, another configuration named dual-loop organic Rankine cycle (DORC) has been proposed to recover waste heat of engine exhaust and coolant by many researchers in recent years. DORC consists of high-temperature (HT) loop and low-temperature (LT) loop which are adopted to recover waste heat from engine exhaust and engine coolant respectively. Shu et al. [12] investigated the energy utilization rate of DORC, and found that the utilization rate of engine exhaust and coolant waste heat could reach to 100% and 88.97% respectively in the DORC. Yang et al. [13] adopted a DORC to recover exhaust and coolant heat of six-cylinder diesel engine, the results showed that the dual loop could achieve the maximum power output of 27.86 kW and the fuel consumption could be reduced by 4%. Sung and Kim [14] designed a ORC to recover engine waste heat and liquid natural gas cold, and found that the ORC system could produce power output of 729.1 kW and the original thermal efficiency of engine was improved by 4.15%. Song et al. [15] conducted a performance analysis

energy efficiency exergy efficiency temperature difference

of DORC for engine waste heat recovery, and water was used as the working fluid of HT loop, the results indicated that the dryness fraction of 0.2 of water entering the expander could maximize the power output of DORC and the maximum power output reached to 115.1 kW. Wang et al. [16] studied the performance of DORC for engine exhaust and coolant waste heat recovery under five different engine working conditions, the results demonstrated that the DORC could improve the efficiency of engine quite well for different engine working conditions, and showing great working conditions adaptability. Yang et al. [17] conducted a parametric optimization of DORC for compressed natural gas engine waste heat recovery. The results indicated that the optimal pressure and superheat degree were mainly related with the engine operating condition, and the maximum power output reached to 23.62 kW. In addition, some studies focused on the structure of DORC. Huang et al. [18] compared the performance of two different DORCs called as S1 and S2 for engine waste heat recovery, and showing that methanol-based DORC S2 performed better. Shu et al. [19] investigated the effect of thermofluidic feed pump on performance of DORC for engine waste heat recovery and indicated that thermofluidic feed pump could achieve the maximal mass flow rate with a smaller volume and less pressure fluctuation, and R1234ze was considered as the best working fluid. Wang et al. [20] considered a regenerative supercriticalsubcritical DORC for engine waste heat recovery and demonstrated that the proposed system showed better performance than other DORCs. Furthermore, other analysis like thermo-economic [21] also has been carried out. In terms of types of working fluid, pure fluid was easily and mostly considered as working fluid of ORC for engine waste heat recovery. Wang et al. [22] proposed a single loop ORC for engine exhaust waste heat recovery, and nine pure fluids were considered as candidate working fluids. The results indicated that R11, R141b, R113 and R123 had little better performance than other pure fluids, but R245fa and R245ca showed better environmental-friendly characteristic. Tian et al. [23] designed a regenerative transcritical-transcritical DORC for engine exhaust and coolant waste heat recovery, six pure fluid were selected and analyzed in the HT loop, and R134a was used in LT loop. The results showed that toluene could produce the maximum power output of 42.46 kW. However, the pure fluid has an isothermal phase-change line that can’t match with heat source and sink lines well, and thus leading a large irreversibility and exergy destruction. Unlike pure fluid, zeotropic mixtures show non-isothermal phase-change characteristic that can improve performance of system significantly. Shu et al. [24] studied the 771

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characteristic of zeotropic mixture used in the single loop ORC for engine waste heat recovery. Cyclopentane, cyclohexane, benzene and R11, R123 were selected for combination. The results demonstrated that zeotropic mixtures had a better performance than pure fluids, and mixture benzene/R11 (0.7/0.3) could achieve efficiency growth 7.12–9.72%. Song and Gu [25] adopt a single loop ORC with the zeotropic mixtures for engine waste heat recovery, hydrocarbons and R141b, R11 were considered to form zeotropic mixtures. The results concluded that cyclohexane/R141b (0.5/0.5) was the optimal zeotropic mixture for the engine waste heat recovery with increasing power output of system by 13% compared to pure cyclohexane. In addition, Ge et al. [26] proposed zeotropic mixture as the working fluid in the subcritical-subcritical DORC for engine waste heat recovery, and found that the power output of DORC system using zeotropic mixtures was improved by 2.5–9.0% compared with using the corresponding pure fluids. Generally, transcritical ORC has a higher power output than subcritical ORC [27]. Unlike subcritical ORC where the working fluid is heated to subcritical state in the evaporator, the working fluid in the evaporator of transcritical ORC is heated directly to supercritical state, bypassing two-phase region, which leads a better thermal match for the working fluid and heat source, and resulting in a less exergy destruction and a higher exergy efficiency [27]. Yağlı et al. [28] compared the performance of transcritical and subcritical ORCs for the engine waste heat recovery. The results demonstrated that transcritical ORC showed better performance than subcritical ORC, and the maximum power output were 81.52 kW and 79.23 kW in the transcritical and subcritical ORCs, respectively. Baik et al. [29] investigated the potential of transcritical ORC using zeotropic mixture by comparing with subcritical ORC using pure fluid for engine waste heat recovery, and pressure drop was considered. The results indicated that R125-R245fa mixture transcritical ORC produced 11% more power output than R134a subcritical ORC under the fixed conditions. Radulovic and Beleno [30] also compared the performance between transcritical ORC with zeotropic mixture and subcritical ORC with pure fluid and showed that transcritical ORC with R134a/R124 (0.7/0.3) mixture achieved 15% higher cycle efficiency than subcritical ORC with pure R134a under the same operational conditions. Based on the review of previous studies, due to better performance, researchers has replaced single-loop ORC with DORC for engine waste heat recovery. However, up to now, a few researcher introduced a transcritical ORC to DORC system for engine waste heat recovery. As mentioned above, transcritical ORC can achieve a higher power output than subcritical ORC. And due to no limitation for pressure and temperature, transcritical ORC shows a better characteristic of designing, which is hardly discussed in the previous study. In addition, the zeotropic mixtures used in subcritical ORC shows a better performance than pure fluids. Whether the performance of transcritical-subcritical DORC system can be improved when the zeotropic mixtures are used, which also needs to be made sure. Therefore, in this paper, a model of transcritical-subcritical DORC with zeotropic mixture for engine waste heat recovery is established, and the system with or without regenerator is analyzed and compared. Zeotropic mixtures R600a/R601a and R134a/R245fa are used as the working fluid of HT and LT loops, respectively. The energy and exergy analyses are carried out, designed parameters including turbine inlet temperature and pressure of HT loop, evaporation temperature of LT loop are analyzed and optimized. Moreover, the effects of components of zeotropic mixtures on the performance of system are studied. Furthermore, the exergy destruction rate analysis of each components and total system are also considered.

Table 1 Properties of pure working fluid. fluids

M (kg/kmol)

Tcri (°C)

Pcri (MPa)

ALT (yr)

ODP

GWP (100 yr)

R600a R601a R134a R245fa

58.12 72.15 102.03 134.05

134.66 187.20 101.06 154.01

3.63 3.38 4.06 3.65

0.02 0.01 7.20 13.80

0 0 0 0

∼20 ∼20 950 1300

Table 2 Engine parameters. Parameters

Value

Electrical power output Rotation speed Torque Exhaust gas temperature Exhaust pressure Exhaust gas mass flow rate Engine coolant temperature Engine coolant mass flow rate

996 kW 1500 r/min 6340 Nm 300 °C 0.1 MPa 1.98 kg/s 65/90 °C 1.91 kg/s

Considering good thermodynamic properties and suitable critical point, zeotropic mixtures R600a/R601a [31] and R134a/R245fa [32] are used as the working fluid of transcritical ORC and subcritical ORC, respectively. The properties of pure R600a, R601a, R134a and R245fa are listed in Table 1. The detailed information of system is introduced in the following sections. 2.1. Engine parameters An inline 6-cylinder turbocharged engine manufactured by Hudong Heavy Machinery Co. is selected as the topping engine. The main parameters of the engine is given in Tables 2, and 3 lists the composition of the engine exhaust. In general, the exhaust final outlet temperature should be above 105 °C to avoid acid dew point [15]. 2.2. Dual loop organic Rankine cycle Dual loop organic Rankine cycle (DORC) consists of a high-temperature (HT) transcritical ORC and a low-temperature (LT) subcritical ORC. The schematic diagram of DORC is showed in Fig. 1, it is worth mentioning that the exhaust waste heat is utilized by HT and LT loops successively. Fig. 1(a) displayed the structure of DORC without regenerator. For transcritical ORC: the saturated liquid working fluid from condenser exit enters pump and is pressurized to high pressure state above its critical pressure (process 1–2, 3); the high pressure liquid working fluid enters evaporator and is heated directly to the supercritical state by the exhaust waste heat source, bypassing two-phase region, which can lead a better thermal match for working fluid and exhaust waste heat source (process 3–4); and then the supercritical working fluid enters expander and expands to produce mechanical power (process 4–5, 6); finally, the expanded vapor enters the condenser and is condensed into saturated liquid state (process 6–1), it is worth noting that the working fluid of HT loop releases heat to the working fluid of LT loop in this process, and the HT cycle is completed. Table 3 The main composition of engine exhaust.

2. System description The proposed engine exhaust and coolant waste heat recovery system consists of transcritical HT-ORC and subcritical LT-ORC. 772

Exhaust composition

Fraction (%)

Carbon dioxide Water Nitrogen Oxygen

4.36 6.20 74.61 14.83

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subcritical DORC, several assumptions and conditions are given as following: (1) The whole system is in the steady state, pressure drop and heat loss in all pipes and heat exchangers are negligible, and kinetic and potential are ignored in the system. (2) The isentropic efficiency of turbines and pumps are set as 80% [15]. (3) The condensation dew point temperature of HT and LT loops are set as 100 °C and 30 °C for keeping the condensation pressure higher than atmospheric pressure [26]. (4) The pinch point temperatures for gas–liquid and liquid–liquid heat exchangers are set to 30 °C and 5 °C respectively [19]. (5) The ambient temperature and pressure are assumed to be 15 °C and 0.1 MPa, and ambient state is assumed as the dead state. In addition, the range of three designed parameters are listed in Table 4. In view of the temperature of engine exhaust and critical temperature of R600a and R601a, the turbine inlet temperature of HT loop is set as 200–260 °C. In order to observe the effect of turbine inlet pressure of HT loop on performance of system, a wide pressure range of 4–15 MPa above the critical pressure of R600a and R601a is considered. For the evaporation temperature of LT loop, the acid dew point temperature of engine exhaust and the condensation temperature of HT loop need to be considered. Thus, a range of 70–85 °C is selected.

(a) DORC without regenerator

3. Thermodynamic analysis For the HT transcritical ORC, when the working fluid changes from liquid state to supercritical state, the thermophysical properties of working fluid will vary highly with temperature, the specific heat of working fluid can’t be considered as constant. That is to say, the temperature of working fluid does not vary linearly with absorbed heat. Therefore, the location of pinch point of evaporator in transcritical cycle should be considered carefully, which is essential for decision of mass flow of working fluid. A method by dividing the heat transfer process into n sections with equal heat interval as shown in Fig. 3 (in this study, n is set to 200, which is enough accurate). There are four known parameters in the evaporator: inlet temperature and mass flow rate of engine exhaust, inlet and outlet temperature of working fluid. According to the energy balance in the evaporator as shown in Eq. (1), the mass flow rate of working fluid can be calculated after the outlet enthalpy (temperature) of exhaust is defined. Thus, an iteration process can be given as follows: initially assume a value for the outlet temperature of exhaust, calculate the mass flow rate of working fluid by Eq. (1). Then divide the total transferred heat Q into n sections, and successively calculate the enthalpy (temperature) of kth node for engine exhaust and working fluid by Eqs. (2) and (3). And then calculate the temperature difference of each node, chose the minimum temperature difference Tmin . If Tmin equals to pinch point temperature of gas–liquid heat exchanger Tpp, gl (30 °C), end the calculation and output the results. If not, repeat the iteration process until Tmin equals to Tpp, gl .

(b) DORC with regenerator. Fig. 1. Structure of DORC: (a) without regenerator, (b) with regenerator.

For subcritical ORC: the saturated liquid working fluid is compressed by the pump (process 7–8); then the compressed working fluid successively absorbs heat into saturated vapor state from engine coolant (evaporator 1), working fluid of HT loop (evaporator 2) and engine exhaust from evaporator exit of HT loop (evaporator 3) (process 8–9, 9–10, 10–11); and the saturated vapor working fluid expands to produce power in the turbine (process 11–12); finally, the working fluid exhaust enters condenser and is condensed to saturated liquid state by cooling water, and the LT cycle is completed. The schematic diagram of DORC with regenerator is displayed in Fig. 1(b), there is a regenerator located between turbine and pump of HT loop, the pressurized working fluid is preheated by the high temperature working fluid exhaust from turbine exit, which can lead a less exergy destruction and a higher efficiency under given conditions. The temperature-entropy schematic diagram of transcritical-subcritical DORC is displayed in Fig. 2. The lines with the same color as in Fig. 1 represent the same processes. Due to the utilization of zeotropic mixtures, the non-isothermal phase-change line can be observed in the Fig. 2.

mg (h g, i1

h g, i2) = m w,HT (h4

mg h g , k = mg h g, k

1

h3)

+ Q/ n k = 1, 2, 3 . .. n

m w,HT h 4, k = m w,HT h4, k

1

+ Q/n k = 1, 2, 3 . .. n

(1) (2) (3)

where hg,0 and h4,0 (k = 1) represents the enthalpy of exhaust outlet and working fluid inlet in the evaporator, respectively. Finally, a right value of outlet temperature of exhaust meeting the requirement of pinch point temperature difference will be outputted. And the mass flow rate of can be calculated by Eq. (4). The iteration method also can be used in the LT subcritical ORC for the calculation of mass flow rates of working fluid and cooling water, then the mass flow rates are given by Eqs. (5) and (6), respectively.

2.3. Assumptions and conditions Before the establishment of mathematical model of transcritical773

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(a) HT loop without regenerator

(b) HT loop with regenerator

(c) LT loop Fig. 2. Temperature-entropy schematic diagram of transcritical-subcritical DORC with zeotropic mixture: (a) HT loop without regenerator, (b) HT loop with regenerator, (c) LT loop.

power output and energy efficiency are the final output results. The energy analysis for HT-ORC and LT-ORC are carried out, respectively. For each process, the energy equations are given as follows.

Table 4 The range of three designed parameters. Designed parameters

range

turbine inlet temperature of HT loop turbine inlet pressure of HT loop evaporation temperature of LT loop

200–260 °C 4–15 MPa 70–85 °C

mHT =

mLT =

m g ( h g , i1 (h 4

mc ( h c , i

3.1.1. High-temperature organic Rankine cycle For the pump (process 1–2):

h2 = h1 + (h2, is

h g , i2 )

hc , o) + mHT (h6

m (h h 7) m w = LT 12 h w, o h w , i

Wp,HT = mHT (h2

(4)

h3)

(h11

h1) + mg (hg , i2 h8 )

h1)/

(7)

p

(8)

h1)

For the regenerator (process 2–3, 5–6):

hg , o)

mHT (h5

(5)

h6) = mHT (h3

h2 )

(9)

For the evaporator (process 3–4):

Qi,HT = mHT (h4

(6)

(10)

h3)

For the turbine (process 4–5):

h5 = h4

3.1. Energy analysis

(h 4

Wt,HT = mHT (h4

The energy analysis is based on the first thermodynamic law. The 774

h5, is ) ×

h5)

t

(11) (12)

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(26)

Wtot = WHT + WLT Qi, tot = mg (h g, i1 tot

=

h g , o ) + m c (h c , i

h c, o )

Wtot Qi, tot

(27) (28)

3.2. Exergy analysis The basis of exergy analysis is the second thermodynamic law, the final output result is exergy efficiency. In order to observe the exergy destruction rate of each component, the irreversibility of each process is calculated, and the equations for HT and LT loops are given as follows. 3.2.1. High-temperature organic Rankine cycle For the pump (process 1–2):

Ip,HT = mHT T0 (s2

For the regenerator (process 2–3, 5–6):

Fig. 3. Schematic diagram of pinch point in the evaporator of transcritical ORC.

Ir = mHT T0 [(s3

(13)

h1)

Ie,HT = T0 [mHT (s4

HT

It,HT = mHT T0 (s5

(14)

Wp,HT

W = HT Qi,HT

Ic,HT = T0 [mLT (s10

Wp,LT = mLT (h8

h 7)

Ei,HT = mg [(hg , i1

(16)

p

(17)

Eo,HT = mLT [(h10

ex ,HT

For the evaporator 2 (process 9–10):

Qi2,LT = mLT (h10

(19)

h 9)

(20)

h10)

(h11

Wt,LT = mLT (h11

h12, is ) ×

t

h12)

h7)

LT

=

Qi1,LT

Wp,LT

WLT + Qi2,LT + Qi3,LT

s9 )

mHT (s6

s1)]

h g , i2 )

T0 (sg , i1

sg, i2)]

h9 )

T0 (s10

(33)

(34) (35)

s9)]

WHT Ei,HT Eo,HT

Ie1,LT = T0 [mLT (s9

(22)

(36)

(37)

s7 )

s8)

mc (sc, i

sc , o)]

(38)

For the evaporator 2 (process 9–10): (39)

Ie2,LT = Ic,HT (23)

For the evaporator 3 (process 10–11):

Thus, the power output and energy efficiency of LT-ORC can be obtained by:

WLT = Wt ,LT

(32)

s4 )

For the evaporator 1 (process 8–9):

(21)

For the condenser (process 12–7):

Qo,LT = mLT (h12

=

Ip,LT = mLT T0 (s8

For the turbine (process 11–12):

h12 = h11

(31)

3.2.2. Low-temperature organic Rankine cycle For the pump (process 7–8):

For the evaporator 3 (process 10–11):

Qi3,LT = mLT (h11

sg, i2)]

Then the exergy efficiency of HT-ORC is calculated by: (18)

h8 )

mg (sg , i1

Output of exergy of HT loop:

For the evaporator 1 (process 8–9):

Qi1,LT = mLT (h9

s3)

And the input and output of exergy of HT loop in the evaporator and condenser are given, respectively. Input of exergy of HT loop:

3.1.2. Low-temperature organic Rankine cycle For the pump (process 7–8):

h7)/

(30)

s6)]

For the condenser (process 6–1):

(15)

h8 = h7 + (h8, is

(s5

For the turbine (process 4–5):

Hence, the power output and energy efficiency of HT-ORC can be calculated by:

WHT = Wt ,HT

s2 )

For the evaporator (process 3–4):

For the condenser (process 6–1):

Qo,HT = mHT (h6

(29)

s1)

Ie3,LT = T0 [mLT (s11

s10)

m g (s g , i 2

sg , o)]

(40)

For the turbine (process 11–12):

(24)

It,LT = mLT T0 (s12

(41)

s11)

For the condenser (process 12–7):

(25)

Ic,LT = T0 [m w (sw, o

Finally, the total power output and energy efficiency of transcriticalsubcritical DORC can be expressed by:

sw, i)

mLT (s12

Input of exergy of LT loop: 775

s7)]

(42)

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hc , o) T0 (sc , i + mg [(hg , i2

sc, o)] + mHT [(h6 h1) hg , o) T0 (sg , i2 sg , o)]

T0 (s6

s1)]

Exhaust outlet temperature from HT loop (°C)

Ei,LT = mc [(hc, i

(43) Output of exergy of LT loop:

Eo,LT = m w [(h w, o

h w, i )

T0 (sw, o

(44)

sw, i)]

And the exergy efficiency of LT-ORC is obtained by: ex ,LT

=

WLT Ei,LT Eo,LT

(45)

And then the total input and output of exergy of the whole system are given by Eqs. (46) and (47), respectively.

Ei, tot = mg [(hg , i1

hg , o)

T0 (sg , i1

(46)

sg , o )]

(47)

Eo, tot = Eo,LT

134

132

130

128

126

124

122

Hence, the total exergy efficiency of transcritical-subcritical DORC can be expressed as: ex , tot

=

Wtot Ei, tot Eo, tot

Eo, tot = Wtot +

6

8

10

12

14

16

Fig. 4. Variation of exhaust outlet temperature from evaporator of HT loop with turbine inlet pressure of HT loop at different turbine inlet temperature while the evaporation temperature of LT loop is 70 °C, mass fractions of R600a/ R601a and R134a/R245fa are 0.5/0.5 and 0.5/0.5 respectively.

(48)

I

4

Turbine inlet pressure of HT loop (MPa)

In addition, the exergy balance equation of the whole system is given by Eq. (49), which can be used to verify the correctness of abovegiven calculation of exergy destruction rate [27].

Ei, tot

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

from evaporator with the turbine inlet temperature and pressure. As shown, for turbine inlet temperature in the range 200–220 °C, the exhaust outlet temperature varies linearly with turbine inlet pressure, for turbine inlet temperature in the range 230–260 °C, some points are also in the straight line. Actually, the values of exhaust outlet temperature points in the straight line are exactly 30 °C higher than the temperature of point 3 of working fluid, which implies that the pinch point exactly locates in the inlet of evaporator (point 3 shown in Fig. 1(a)). The detailed values of exhaust outlet temperature from evaporator and the temperature of point 3 of working fluid are given in Appendix A. It can be observed that the outlet temperature of exhaust is nearly 40 °C higher than the temperature of point 3 of working fluid under the turbine inlet temperature of 260 °C and pressure of 4 MPa, and that indicates that the location of pinch point has shifted from the inlet of evaporator (point 3). In addition, the phenomenon of pinch point shifting also can be observed under some different turbine inlet temperature and pressure. Therefore, the results demonstrate that the thermodynamic properties of working fluids will highly vary with temperature in the supercritical state, and the method mentioned in Section 3 has the ability to deal with the problem.

(49)

It is worth noting that the exergy destruction rate of condenser of HT loop which was also used as the evaporator of LT loop only can be summed once by Eq. (49). 4. Model validation MATLAB R2015b is used to simulate the thermodynamic model of transcritical-subcritical DORC. And the thermodynamic properties of R600a/R601a and R134a/R245fa are obtained by REFPROP version 9.1 [33]. In order to ensure accuracy of simulation code, the ORC model in literature [7] is selected to verify the correctness of calculation. The same boundary conditions are set, and the results comparison are showed in Table 5. As shown, the present code has a good agreement with literature [7]. Thus, the present simulation code has enough accuracy for the simulation of the current study. 5. Results and discussion

5.1. Mass flow rate of working fluid

For the heat transfer in the evaporator of transcritical ORC, if the specific heat is considered as constant, the line representing the heat transfer process 3–4 shown in Fig. 2(a) will be straight, which implies that the location of pinch point must be in the inlet or outlet of evaporator. However, as mentioned in Section 3, when the working fluid changes from liquid state to supercritical state, the thermophysical properties of working fluid will highly vary with temperature, the specific heat of working fluid can’t be considered as constant. That is to say, the pinch point may not be in inlet or outlet of evaporator. In order to observe the phenomenon, the outlet temperature of exhaust from evaporator of HT loop of transcritical-subcritical DORC system is analyzed. Fig. 4 shows the variation of the outlet temperature of exhaust

The variations of mass flow rates of HT and LT loops with turbine inlet temperature and pressure of HT loop is displayed in Fig. 5. Fig. 5(a) shows the variation of mass flow rate of HT loop of transcritical-subcritical DORC without regenerator. According to Eq. (4), the mass flow rate of HT loop is defined by the ratio of heat released by engine exhaust heat to enthalpy difference between point 3 and point 4 of working fluid shown in Fig. 1(a). For a given turbine inlet pressure, to be specific, the temperature of point 3 of working fluid shown in Fig. 1(a) is fixed, with the increase of turbine inlet temperature, the enthalpy difference between point 3 and 4 of working fluid increases,

Table 5 Results comparison between present study and literature [7]. working fluid

PORC (kW)

Benzene [7] Benzene Relative deviation (%)

349.3 346.6 0.78%

ORC

0.1986 0.1981 0.27%

Pcond (kPa)

Pvap (kPa)

Tvap (K)

mf (kg/s)

V3 (m3/s )

v4/v3

19.6 19.659 0.3%

2000 2000 0

494.5 494.57 0.01%

2.737 2.715 0.78%

0.052 0.0514 0.58%

107 107.779 0.72%

776

h3

4 (kJ/kg)

130.5 130.491 0

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1.2

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

1.3

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

Mass flow rate of HT loop (kg/s)

Mass flow rate of HT loop (kg/s)

1.4

1.0

0.8

0.6

1.2 1.1 1.0 0.9 0.8 0.7 0.6

4

6

8

10

12

14

16

4

Turbine inlet pressure of HT loop (MPa)

(a) HT loop without regenerator

10

12

14

16

2.69

2.67 2.66 2.65

Mass flow rate of LT loop (kg/s)

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

2.68

Mass flow rate of LT loop (kg/s)

8

(b) HT loop with regenerator

2.69

2.64 2.63 2.62 2.61 2.60

6

Turbine inlet pressure of HT loop (MPa)

4

6

8

10

12

14

2.67 2.66 2.65 2.64 2.63 2.62

16

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

2.68

4

6

8

10

12

14

Turbine inlet pressure of HT loop (MPa)

Turbine inlet pressure of HT loop (MPa)

(c) LT loop without regenerator

(d) LT loop with regenerator

16

Fig. 5. Variations of mass flow rates of HT and LT loops with turbine inlet temperature at different turbine inlet pressure while the evaporation temperature of LT loop is 70 °C, mass fractions of R600a/R601a and R134a/R245fa are 0.5/0.5 and 0.5/0.5, respectively.

according to Eq. (4), then the mass flow rate of working fluid will decrease as shown in Fig. 5(a). Moreover, it can be observed from Fig. 5(a) that the mass flow rate of working fluid increases with turbine inlet pressure. When the turbine inlet pressure increases, the pump will consume more work, which leads to a higher outlet temperature of working fluid from the pump and results in a smaller enthalpy difference between point 3 and 4 for the working fluid. Meanwhile, the exhaust outlet temperature from evaporator increases with the turbine inlet pressure, causing a smaller enthalpy difference between inlet and outlet of exhaust, and then less heat is released to working fluid from engine exhaust. However, the enthalpy difference of working fluid decreases faster than exhaust does, which finally leads to the increase of mass flow rate of working fluid. Fig. 5(b) indicates the variation of mass flow rate of HT loop for the transcritical-subcritical DORC with regenerator. As shown in Fig. 5(b), when the turbine inlet pressure is relatively lower, the mass flow rate of working fluid is significantly bigger than the value of transcritical-subcritical without regenerator shown in Fig. 5(a) under the same turbine inlet temperature especially for a higher turbine inlet temperature. However, with the increase of turbine inlet pressure, both values gradually tends to be uniform. When the lower the turbine inlet pressure is, the smaller the pressure ratio is, the less the work consumed by pump is, and less the work produced by turbine is, the temperature of point 2 and 5 of working fluid shown in

Fig. 1(b) will decreases and rises respectively, resulting in a bigger temperature difference between point 2 and 5 of working fluid especially for higher turbine inlet temperature, then a bigger regenerative effect can be made by regenerator and a bigger mass flow rate can be obtained. And with the increase of turbine inlet pressure, the temperature difference between point 2 and 5 of working fluid will be shorten, and then the effect of regenerator is weakened, which makes that the mass flow rate values tends to be uniform. Fig. 5(c) and (d) display the variation of mass flow rate of LT loop for transcriticalsubcritical DORC without and with regenerator, respectively. According to the Eq. (5), for a given evaporation temperature, the mass flow rate of working fluid of LT loop is mainly affected by the heat released by HT loop and engine exhaust which lead a fluctuation of the value. Comparing the DORC without and with regenerator, the mass flow rate for DORC with regenerator is a little bigger than the DORC without regenerator. 5.2. Effects of designed parameters on performance of system The effects of turbine inlet temperature and pressure of HT loop on power out, energy and exergy efficiencies are showed in Figs. 6, 7 and 8, respectively. The variations of power output of HT loop, LT loop and whole 777

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40

Power output of HT loop (kW)

Power output of HT loop (kW)

40

35

30

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

25

20

4

6

8

10

12

14

35

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

30

25

20

16

4

Turbine inlet pressure of HT loop (MPa)

(a) Power output of HT loop without regenerator

10

12

14

16

52.0

51.8

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

51.6 51.4 51.2

Power output of LT loop (kW)

Power output of LT loop (kW)

8

(b) Power output of HT loop with regenerator

52.0

51.0 50.8 50.6 50.4

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

51.8 51.6 51.4 51.2 51.0 50.8

4

6

8

10

12

14

16

4

Turbine inlet pressure of HT loop (MPa)

90

88

88

Total power output (kW)

92

90

86 84 82 200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

78 76 74 4

6

8

10

12

14

16

(d) Power output of LT loop with regenerator

92

80

6

Turbine inlet pressure of HT loop (MPa)

(c) Power output of LT loop without regenerator

Total power output (kW)

6

Turbine inlet pressure of HT loop (MPa)

86 84 82

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

80 78 76 74

8

10

12

14

16

4

Turbine inlet pressure of HT loop (MPa)

6

8

10

12

14

16

Turbine inlet pressure of HT loop (MPa)

(f) Total power output with regenerator

(e) Total power output without regenerator

Fig. 6. Variation of power output of HT loop, LT loop and whole system with turbine inlet pressure at different turbine inlet temperature while the evaporation temperature of LT loop is 70 °C, mass fractions of R600a/R601a and R134a/R245fa are 0.5/0.5 and 0.5/0.5, respectively.

system with turbine inlet temperature and pressure of HT loop are shown in Fig. 6. Fig. 6(a) displays the variation of power output of HT loop for the transcritical-subcritical DORC without regenerator. As shown, for a given turbine inlet temperature, with the increase of

turbine inlet pressure, the power output firstly increases and then decreases. That is to say, there is an optimal turbine inlet pressure to maximize the power output of HT loop. And it is worth noting that the higher the turbine inlet temperature is, the bigger the optimal turbine 778

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Energy efficiency of HT loop (%)

Energy efficiency of HT loop (%)

11

10

9 200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

8

7

6

4

6

16 14 12 10

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

8 6

8

10

12

14

4

16

(a) Energy efficiency of HT loop without regenerator

9.5 9.0 8.5 8.0 7.5

5

14

16

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

10.0 9.5 9.0 8.5 8.0 7.5

10

5

15

(c) Energy efficiency of LT loop without regenerator

14.5

14.5

Total energy efficiency (%)

15.0

14.0

13.5 200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

12.5

14.0

13.5

6

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

13.0

12.5

12.0 4

8

10

12

14

15

(d) Energy efficiency of LT loop with regenerator

15.0

13.0

10

Turbine inlet pressure of HT loop (MPa)

Turbine inlet pressure of HT loop (MPa)

Total energy efficiency (%)

12

7.0

7.0

12.0

10

10.5

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

10.0

8

(b) Energy efficiency of HT loop with regenerator

Energy efficiency of LT loop (%)

Energy efficiency of LT loop (%)

10.5

6

Turbine inlet pressure of HT loop (MPa)

Turbine inlet pressure of HT loop (MPa)

16

4

6

8

10

12

14

16

Turbine inlet pressure of HT loop (MPa)

Turbine inlet pressure of HT loop (MPa)

(e) Total energy efficiency without regenerator

(f) Total energy efficiency with regenerator

Fig. 7. Variation of energy efficiency of HT loop, LT loop and whole system with turbine inlet pressure at different turbine inlet temperature while the evaporation temperature of LT loop is 70 °C, mass fractions of R600a/R601a and R134a/R245fa are 0.5/0.5 and 0.5/0.5, respectively.

inlet pressure is. Moreover, it can be observed that when the turbine inlet pressure is relatively lower such as 4 and 5 MPa, the higher the turbine inlet temperature is, the less the power output is. However, when the turbine inlet pressure is relatively higher such as 14 and 15 MPa, the power output increases with turbine inlet temperature. That is because the lower the turbine inlet pressure is, the smaller pressure ratio of turbine is, that leads a bad match with relatively higher turbine inlet temperature and results in a less power output

shown in Fig. 6(a). Contrarily, a high turbine inlet pressure has a good match with a high turbine inlet temperature, which results in a more mechanical work produced by turbine. Fig. 6(b) indicates the variation of power output of HT loop for the transcritical-subcritical DORC with regenerator. Comparing with the system without regenerator shown in Fig. 6(a), it can be observed that the power output has a significant improvement under the relatively lower turbine inlet pressure such as 4 and 5 MPa, especially for higher turbine inlet temperature. As 779

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Exergy efficiency of HT loop (%)

Exergy efficiency of HT loop (%)

55 40

35 200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

30

25

4

6

50 45 40 200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

35 30 25

8

10

12

14

4

16

48

48

47

47

46 45 44 200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

42 41 40 4

6

8

10

12

14

43 200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

42 41

39

16

4

Total exergy efficiency (%)

Total exergy efficiency (%)

46

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

12

14

10

12

14

16

46

16

200 °C 210 °C 220 °C 230 °C 240 °C 250 °C 260 °C

44

42

40 10

8

(d) Exergy efficiency of LT loop with regenerator

48

8

6

Turbine inlet pressure of HT loop (MPa)

48

6

16

44

50

4

14

45

50

40

12

40

(c) Exergy efficiency of LT loop without regenerator

42

10

46

Turbine inlet pressure of HT loop (MPa)

44

8

(b) Exergy efficiency of HT loop with regenerator

Exergy efficiency of LT loop (%)

Exergy efficiency of LT loop (%)

(a) Exergy efficiency of HT loop without regenerator

43

6

Turbine inlet pressure of HT loop (MPa)

Turbine inlet pressure of HT loop (MPa)

4

6

8

10

12

14

16

Turbine inlet pressure of HT loop (MPa)

Turbine inlet pressure of HT loop (MPa)

(f) Total exergy efficiency with regenerator

(e) Total exergy efficiency without regenerator

Fig. 8. Variation of exergy efficiency of HT loop, LT loop and whole system with turbine inlet pressure at different turbine inlet temperature while the evaporation temperature of LT loop is 70 °C, mass fractions of R600a/R601a and R134a/R245fa are 0.5/0.5 and 0.5/0.5, respectively.

mentioned in Section 5.1, when the turbine inlet pressure is relatively lower, the regenerator will come into effect significantly especially for higher turbine inlet temperature, which leads a better utilization of heat and a more power output. And with the increase of turbine inlet pressure, the effect of regenerator is weakened. Hence, the power output is hardly improved for the transcritical-subcritical DORC with regenerator

under higher turbine inlet pressure. Fig. 6(c) and 6(d) show the power output of LT loop for transcritical-subcritical DORC without and with regenerator, respectively. According to the energy analysis shown in Section 3.1 and the Eq. (24), for a given evaporation temperature of LT loop, the power output of LT loop is absolutely defined by the mass flow rate of LT loop. Thus, it can be observed the variation tendency of 780

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power output of LT loop shown in Fig. 6(c) and (d) are same as the variation of mass flow rate of LT loop shown in Fig. 5(c) and (d). Fig. 6(e) and (f) display the variation of total power output of transcritical-subcritical DORC without and with regenerator, respectively. As shown in Fig. 6(e) and (f), for each turbine inlet temperature, there is

an optimal turbine inlet pressure to maximize the total power output, and the optimal turbine inlet pressure increases with turbine inlet temperature. Moreover, comparing Fig. 6(f) with (e), it can be observed when the turbine inlet pressure is relatively lower, due to the significant regenerative effect, the total power output of system with regenerator is

92

94 70 °C 75 °C 80 °C 85 °C

88

70 °C 75 °C 80 °C 85 °C

92

Total power output (kW)

Total power output (kW)

90

86 84 82 80 78 76

90 88 86 84 82 80 78 76

74

74 4

6

8

10

12

14

16

4

Turbine inlet pressure of HT loop (MPa)

16.0

10

12

14

16

16.5 16.0

15.0

Total energy efficiency (%)

70 °C 75 °C 80 °C 85 °C

15.5

Total energy efficiency (%)

8

(b) Total power output with regenerator

(a) Total power output without regenerator

14.5 14.0 13.5 13.0 12.5 12.0

6

Turbine inlet pressure of HT loop (MPa)

70 °C 75 °C 80 °C 85 °C

15.5 15.0 14.5 14.0 13.5 13.0 12.5

4

6

8

10

12

14

12.0

16

4

Turbine inlet pressure of HT loop (MPa)

6

8

10

12

14

16

Turbine inlet pressure of HT loop (MPa)

(d) Total energy efficiency with regenerator

(c) Total energy efficiency without regenerator

54 70 °C 75 °C 80 °C 85 °C

50 48 46 44 42 40

70 °C 75 °C 80 °C 85 °C

52

Total exergy efficiency (%)

Total exergy efficiency (%)

52

50 48 46 44 42 40

4

6

8

10

12

14

16

4

6

8

10

12

14

16

Turbine inlet pressure of HT loop (MPa)

Turbine inlet pressure of HT loop (MPa)

(e) Total exergy efficiency without regenerator

(f) Total exergy efficiency with regenerator

Fig. 9. Effect of evaporation temperature of LT loop on the performance of system while the turbine inlet temperature of HT loop is 200 °C, mass fractions of R600a/ R601a and R134a/R245fa are 0.5/0.5 and 0.5/0.5 respectively. 781

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significantly more than without regenerator. Therefore, if the HT loop needs to be operated at lower pressure, the transcritical-subcritical DORC system with regenerator is preferred to recover the engine exhaust and coolant waste heat. Otherwise, the system without regenerator will be more suitable. Figs. 7 and 8 indicate the variation of energy, exergy efficiency of HT loop, LT loop and whole system with turbine inlet temperature and pressure of HT loop. Due to the adoption of regenerator, the utilization rate of engine exhaust waste heat in HT loop can be improved, which results in a higher energy and exergy efficiencies for HT loop with regenerator than without regenerator, that can be observed by comparing Fig. 7(a) and (b) with Fig. 8(a) and (b). According to the energy analysis shown in Section 3.1 and Eq. (25), it can be inferred that the energy efficiency of LT loop is only affected by the evaporation temperature of LT loop. Hence, it can be observed the energy efficiency is a constant of 8.77% regardless of the variation of turbine inlet temperature and pressure as shown in Fig. 7(c) and (d). However, for the exergy efficiency of LT loop shown in Fig. 8(c) and (d), the higher the turbine inlet temperature of HT loop is, the higher the outlet temperature of working fluid from turbine is, leading a bigger heat transfer temperature difference in the evaporator 2 (process 9–10) shown in Fig. 2, then resulting in a bigger exergy destruction and a lower exergy efficiency of LT loop. On the contrary, when the turbine inlet pressure of HT loop is relatively higher, the pressure ratio of turbine of HT loop will be bigger, after expanding in the turbine, the outlet temperature of working fluid from turbine will be lower, and then a higher exergy efficiency can be observed. Fig. 7(e) and (f) and Fig. 8(e), (f) show the variation of total energy and exergy efficiencies, respectively. According to Eqs. (28) and (48), the total power output is the main parameter affecting energy and exergy efficiencies. Thus, it can be observed that the variation tendency of total energy and exergy efficiencies is nearly same as the total power output shown in Fig. 6. Fig. 9 indicates the effect of evaporation temperature of LT loop on the performance of transcritical-subcritical DORC without and with regenerator. As shown, the higher the evaporation temperature of LT loop is, the better the performance of system is. With the increase of evaporation temperature of LT loop, the heat transfer temperature difference between working fluids in the evaporation 2 and 3 (process 9–10 and 10–11) will decrease, and the evaporation pressure will increase, then the expansion ratio of turbine will increase, which leads to a less exergy destruction and a more power output, and then resulting in a better performance of system.

5.3. Optimization of designed parameters Fig. 10 demonstrates the variations of optimal turbine inlet pressure of HT loop and optimal evaporation temperature of LT loop with turbine inlet temperature of HT loop for transcritical-subcritical DORC without and with regenerator. As mentioned in Section 5.2, for a given turbine inlet temperature of HT loop, there is an optimal turbine inlet pressure to optimize the performance of system, and the optimal turbine inlet pressure increases with turbine inlet temperature, that can be observed from Fig. 10(a) and (b). Moreover, it can be observed that the maximum evaporation temperature of 85 °C is the optimal parameter to optimize the performance regardless of the variation of turbine inlet temperature of HT loop. That is also uniform with the results shown in Fig. 9: the higher the evaporation temperature of LT loop is, the better the performance of system is. Fig. 11 shows the maximum total power output, energy and exergy efficiencies corresponding with the optimal turbine inlet pressure of HT loop and evaporation temperature of LT loop at different turbine inlet temperature of HT loop. As shown, when the turbine inlet temperature is relatively lower, the corresponding optimal turbine inlet pressure is also relatively lower (see Fig. 10), the maximum total power output, energy and exergy efficiencies of transcritical-subcritical DORC with regenerator are higher than without regenerator. And with the increase of turbine inlet temperature, the corresponding optimal turbine inlet pressure also increases, the performance difference between transcritical-subcritical DORC without and with regenerator gradually decreases. Thus, if the HT loop needs to operate at lower temperature and pressure, the transcritical-subcritical DORC with regenerator is preferred to recover engine waste heat. Otherwise, the system without regenerator will be more suitable. Moreover, it can be observed that turbine inlet temperature of 260 °C, corresponding optimal turbine inlet pressure of HT loop and evaporation temperature of LT loop of 11 MPa and 85 °C (see Fig. 10), can maximize the total power output, energy and exergy efficiencies of transcritical-subcritical DORC without regenerator. And for the transcritical-subcritical DORC with regenerator, turbine inlet temperature of 250 °C, corresponding optimal turbine inlet pressure of HT loop and evaporation temperature of LT loop of 10 MPa and 85 °C (see Fig. 10), can maximize the total power output, energy and exergy efficiencies. 5.4. Effects of components of mixtures on performance of system Based on the optimization of designed parameters, the effects of components of zeotropic mixtures on performance of system are

90

9 8

85

7 80

6 5 200

210

220

230

240

250

260

Optimal turbine inlet pressure of HT loop (MPa)

10

Optimal evaporation temperature of LT loop (°C)

Optimal turbine inlet pressure of HT loop (MPa)

Optimal turbine inlet pressure of HT loop Optimal evaporation temperature of LT loop

75

11

Optimal turbine inlet pressure of HT loop Optimal evaporation temperature of LT loop

10

90

9 8

85

7 80

6 5 200

210

220

230

240

250

260

Optimal evaporation temperature of LT loop (°C)

95

95 11

75

Turbine inlet temperature of HT loop (°C)

Turbine inlet temperature of HT loop (°C)

(b) With regenerator

(a) Without regenerator

Fig. 10. Variations of optimal turbine inlet pressure of HT loop and evaporation temperature of LT loop with turbine inlet temperature of HT loop for transcriticalsubcritical DORC without and with regenerator. 782

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97

Maximum total energy efficiency (%)

Maximum total power output (kW)

98

96 95 94 93 92 91 90

200

210

220

230

240

250

Without regenerator With regenerator

16.4

16.2

16.0

15.8

15.6

260

200

Turbine inlet temperature of HT loop ( °C)

210

220

230

240

250

260

Turbine inlet temperature of HT loop ( °C)

(b) Energy efficiency

(a) Power output

Maximum total exergy efficiency (%)

55.0 Without regenerator With regenerator

54.5 54.0 53.5 53.0 52.5 52.0 51.5

200

210

220

230

240

250

260

Turbine inlet temperature of HT loop ( °C)

(c) Exergy efficiency Fig. 11. The maximum total power output, energy and exergy efficiencies corresponding with the optimal turbine inlet pressure of HT loop and evaporation temperature of LT loop at different turbine inlet temperature of HT loop.

investigated furtherly. Fig. 12 shows the effects of components of mixtures on the performance of system. The R600a/R601 and R134a/ R245fa zeotropic mixtures are the working fluids of HT and LT loops, respectively. It can be observed that the system using zeotropic mixtures has a significant improvement on the power output, energy and exergy efficiencies compared with using pure fluids. For the system without regenerator shown in Fig. 12(a), (c) and (e), the mass fractions of R600a/R601a (0.2/0.8) and R134a/R245fa (0.4/0.6) are the optimal ratio to achieve the maximum power output of 97.49 kW, energy efficiency of 16.77% and exergy efficiency of 55.58%. Comparing with the system using pure fluids in the HT and LT loops, the system using R600a/R601a (0.2/0.8) and R134a/R245fa (0.4/0.6) achieve the power output increment of 5.48–20.00%, the energy and exergy efficiencies improvement of 9.10–24.13% and 7.89–23.53%, respectively. Furthermore, it can be observed that zeotropic mixture (R134a/R245fa) used in LT loop has more improvement than zeotropic mixture (R600a/ R601a) used in HT loop. As mentioned in Section 1, zeotropic mixtures show non-isothermal phase-change characteristic that can improve the thermal match with heat source and sink, and leading a less exergy destruction and a higher energy efficiency. However, for the transcritical ORC, the working fluid is heated directly from liquid to supercritical state, bypassing two-phase region, which also leads a better thermal match for the working fluid and heat source, then leading a

better performance. Therefore, the zeotropic mixture used in transcritical HT loop can furtherly improve the thermal match with heat sink, but the zeotropic mixture used in subcritical LT loop can furtherly improve the thermal match with both heat source and sink, which leads to the results that zeotropic mixture used in LT loop shows more improvement than used in HT loop. It is worth mentioning that the transcritical ORC itself shows better performance than subcritical ORC [27]. As for the system with regenerator shown in Fig. 12(b), (d) and (f), the system with R600a/R601a (0.3/0.7) and R134a/R245fa (0.4/ 0.6) achieve the maximum power output of 97.95 kW, energy and exergy efficiencies of 16.67% and 55.34%. And comparing with the system using pure fluids, the system using R600a/R601a (0.3/0.7) and R134a/R245fa (0.4/0.6) achieve the power output increment of 6.52–19.78%, the energy and exergy efficiencies improvement of 9.02–22.57% and 8.17–22.43%, respectively. Moreover, when the optimal transcritical-subcritical DORC with and without regenerator are used to recover the engine exhaust and coolant waste heat, the power output of engine can be improved by 9.79% and 9.83%, respectively. Fig. 13 indicates the comparison of exergy destruction between using optimal zeotropic mixtures and pure fluids for transcritical-subcritical DORC without and with regenerator. Comparing Fig. 13(a) and (b), it can be observed that the system using zeotropic mixture has significant less total exergy destruction than using pure fluids. For the 783

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98

98

96

R134a/R245fa

94

Total power output (kW)

Total power output (kW)

96

0/1 0.1/0.9 0.2/0.8 0.3/0.7 0.4/0.6 0.5/0.5 0.6/0.4 0.7/0.3 0.8/0.2 0.9/0.1 1/0

92 90 88 86 84

92 90 88 86

82 0.0

0.2

0.4

0.6

0.8

0.0

1.0

0.2

0.4

0.6

0.8

1.0

Mass fraction of R600a (R600a/R601a)

Mass fraction of R600a (R600a/R601a)

(a) Total power output without regenerator

(b) Total power output with regenerator

17.0

17.0

16.5

16.5

R134a/R245fa

16.0

0/1 0.1/0.9 0.2/0.8 0.3/0.7 0.4/0.6 0.5/0.5 0.6/0.4 0.7/0.3 0.8/0.2 0.9/0.1 1/0

15.5 15.0 14.5 14.0

Total energy efficiency (%)

Total energy efficiency (%)

0/1 0.1/0.9 0.2/0.8 0.3/0.7 0.4/0.6 0.5/0.5 0.6/0.4 0.7/0.3 0.8/0.2 0.9/0.1 1/0

84

82 80

R134a/R245fa

94

R134a/R245fa 16.0

0/1 0.1/0.9 0.2/0.8 0.3/0.7 0.4/0.6 0.5/0.5 0.6/0.4 0.7/0.3 0.8/0.2 0.9/0.1 1/0

15.5 15.0 14.5 14.0

13.5 13.5 0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Mass fraction of R600a (R600a/R601a)

Mass fraction of R600a (R600a/R601a)

(c) Total energy efficiency without regenerator

(d) Total energy efficiency with regenerator 56

56

54

R134a/R245fa

Total exergy efficiency (%)

Total exergy efficiency (%)

54

0/1 0.1/0.9 0.2/0.8 0.3/0.7 0.4/0.6 0.5/0.5 0.6/0.4 0.7/0.3 0.8/0.2 0.9/0.1 1/0

52

50

48

0/1 0.1/0.9 0.2/0.8 0.3/0.7 0.4/0.6 0.5/0.5 0.6/0.4 0.7/0.3 0.8/0.2 0.9/0.1 1/0

52

50

48

46

46

44

R134a/R245fa

44 0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Mass fraction of R600a (R600a/R601a)

Mass fraction of R600a (R600a/R601a)

(e) Total exergy efficiency without regenerator

(f) Total exergy efficiency with regenerator

Fig. 12. Effects of components of mixtures on performance of system without and with regenerator while the evaporation temperature of LT loop is 85 °C, the turbine inlet temperature and pressure of HT loop for without and with regenerator are 260 °C, 11 MPa and 250 °C, 10 MPa, respectively.

system with zeotropic mixture, the exergy destruction ratio of all heat exchangers to total exergy destruction is 65.30%, which is 5.92% less ratio than the system with pure fluids. The similar results can be found in in Fig. 13(c) and (d) for the transcritical-subcritical DORC with regenerator system. That is to say, the transcritical-subcritical DORC system with zeotropic mixture has less total exergy destruction and less heat transfer exergy destruction rate than with pure fluids. The results

demonstrate that the zeotropic mixture can improve the thermal match with heat source and sink and lead a less exergy destruction and higher exergy efficiency. 6. Conclusion In this study, the transcritical-subcritical DORC system with and 784

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Itot= 77.92 kW 15.77%

1.21% 17.72%

17.75%

HT evaporator HT turbine HT pump LT evaporator 1 LT evaporator 2 LT evaporator 3 LT turbine LT pump LT condensor

4.64%

14%

17.91%

0.36%

22.94%

0.84% 10.25%

3.56%

HT evaporator HT turbine HT pump LT evaporator 1 LT evaporator 2 LT evaporator 3 LT turbine LT pump LT condensor

Itot= 87.32 kW

8.44% 3.18%

12.58%

17.3%

11.24%

20.33%

(a) R600a/R601a (0.2/0.8) and R134a/R245fa (0.4/0.6)

(b) Pure R601a and R245fa without regenerator

without regenerator Itot= 79.05 kW 13.61%

17.68%

5.39%

HT evaporator HT turbine HT pump LT evaporator 1 LT evaporator 2 LT evaporator 3 LT turbine LT pump LT condensor Regenerator

0.84%

17.72%

Itot= 87.78 kW 13.62%

10.23% 12.4%

0.36%

22.85%

9.55%

8.4% 3.09%

2.03%

3.41%

13.94%

16.69%

(c) R600a/R601a (0.3/0.7) and R134a/R245fa (0.4/0.6) with

HT evaporator HT turbine HT pump LT evaporator 1 LT evaporator 2 LT evaporator 3 LT turbine LT pump LT condensor Regenerator

1.09% 11.26%

15.85%

(d) Pure R601a and R245fa with regenerator

regenerator Fig. 13. Comparison of exergy destruction between using optimal zeotropic mixtures and pure fluids for transcritical-subcritical DORC without and with regenerator.

without regenerator is proposed to recover engine exhaust and coolant waste heat. Zeotropic mixtures R600a/R601a and R134a/R245a are used as the working fluid of HT-ORC and LT-ORC, respectively. The thermodynamic analysis including energy and exergy analyses are considered. And then the effects of designed parameters including turbine inlet temperature and pressure of HT loop and evaporation temperature of LT on the system performance are studied. Furthermore, the components of zeotropic mixtures are analyzed and optimized. And an exergy destruction analysis is also considered. Based on the analysis above, several main conclusions are summarized as following:

will be more suitable. 3. System with zeotropic mixtures can significantly improve the performance of system. If regenerator isn’t adopted, system using R600a/R601a (0.2/0.8) and R134a/R245fa (0.4/0.6) will be preferred and shows the maximum power output of 97.49 kW which is higher 5.48–20.00% than pure fluids. And if regenerator is adopted, system using R600a/R601a (0.3/0.7) and R134a/R245fa (0.4/0.6) is preferred and achieves the maximum power output of 97.95 kW, increment of 6.52–19.78% compared with using pure fluids. And the power output of engine can be improved by 9.79% and 9.83% for the system without and with regenerator, respectively. 4. According the exergy analysis, system with zeotropic mixtures has less total exergy destruction and less heat transfer exergy destruction than with pure fluids. That is to say, zeotropic mixture used in proposed system can improve the thermal match with heat source and sink furtherly.

1. For a given turbine inlet temperature of HT loop, system performance firstly increases and then decrease with turbine inlet pressure. That is to say, there is an optimal pressure to maximize the system performance, and the optimal pressure increases as temperature increases. And the higher the evaporation temperature of LT loop is, the better the system performance is. For the system without and with regenerator, the optimal turbine inlet temperature, pressure and evaporation temperature are 260 °C, 11 MPa, 85 °C and 250 °C, 10 MPa, 85 °C respectively. 2. When the turbine inlet pressure of HT loop is relatively lower, the performance of system with regenerator is significant higher than without regenerator, and with the increasing of the pressure, the performance difference between them is gradually shorten. Thus, if the HT loop needs to be operated at lower pressure, the system with regenerator is preferred. Otherwise, the system without regenerator

Declaration of Competing Interest None. Acknowledgment This work is supported by the National Natural Science Foundation of China (Grant No.: 51706221 and 51576187). 785

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Appendix A Detailed values of exhaust outlet temperature from evaporator of HT loop and the temperature of point 3 of working fluid (Tables A1 and A2).

Table A1 The outlet temperature of exhaust from evaporator under different given turbine inlet temperature and pressure. Turbine inlet pressure (MPa)

Turbine inlet temperature (°C) 200

210

220

230

240

250

260

4 5 6 7 8 9 10 11 12 13 14 15

123.71 124.63 125.54 126.41 127.26 128.09 128.90 129.69 130.46 131.22 131.97 132.69

123.71 124.63 125.54 126.41 127.26 128.09 128.90 129.69 130.46 131.22 131.97 132.69

123.71 124.63 125.54 126.41 127.26 128.09 128.90 129.69 130.46 131.22 131.97 132.69

124.21 124.63 125.54 126.41 127.26 128.09 128.90 129.69 130.46 131.22 131.97 132.69

126.21 126.13 126.04 126.41 127.26 128.09 128.90 129.69 130.46 131.22 131.97 132.69

128.71 129.13 129.04 128.41 128.26 128.09 128.90 129.69 130.46 131.22 131.97 132.69

131.21 132.63 133.54 133.41 132.76 132.59 131.90 131.69 131.96 132.22 132.47 133.19

Table A2 The temperature of point 3 of working fluid under different given turbine inlet temperature and pressure. Turbine inlet pressure (MPa)

Turbine inlet temperature (°C) 200

210

220

230

240

250

260

4 5 6 7 8 9 10 11 12 13 14 15

93.71 94.63 95.54 96.41 97.26 98.09 98.90 99.69 100.46 101.22 101.97 102.69

93.71 94.63 95.54 96.41 97.26 98.09 98.90 99.69 100.46 101.22 101.97 102.69

93.71 94.63 95.54 96.41 97.26 98.09 98.90 99.69 100.46 101.22 101.97 102.69

93.71 94.63 95.54 96.41 97.26 98.09 98.90 99.69 100.46 101.22 101.97 102.69

93.71 94.63 95.54 96.41 97.26 98.09 98.90 99.69 100.46 101.22 101.97 102.69

93.71 94.63 95.54 96.41 97.26 98.09 98.90 99.69 100.46 101.22 101.97 102.69

93.71 94.63 95.54 96.41 97.26 98.09 98.90 99.69 100.46 101.22 101.97 102.69

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