Comparative analysis of a bottoming transcritical ORC and a Kalina cycle for engine exhaust heat recovery

Energy Conversion and Management 89 (2015) 764–774

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Comparative analysis of a bottoming transcritical ORC and a Kalina cycle for engine exhaust heat recovery Chen Yue ⇑, Dong Han, Wenhao Pu, Weifeng He Nanjing University of Aeronautics and Astronautics, Jiangsu Province Key Laboratory of Aerospace Power Systems, Nanjing 210016, China

a r t i c l e

i n f o

Article history: Received 30 May 2014 Accepted 11 October 2014

Keywords: Internal combustion engine Organic Rankine cycle Waste heat recovery (WHR) Kalina cycle Thermal match

a b s t r a c t A performance comparison of two types of bottoming cycles, including a Kalina cycle and a transcritical organic Rankine cycle (ORC) using working fluids with sliding-temperature boiling characteristics, is conducted in order to analyze energy saving of the sensible exhaust waste heat recovery (WHR) under various internal combustion engine (ICE) working conditions. Through quantitatively analyzing the relation between exhaust waste-heat behaviors and the ICE load of a commercial ICE, two bottoming subsystems models, including a transcritical ORC using some several Alkanes and a Kalina cycle using NH3–H2O as working fluids, are build under the same ICE various-temperature exhaust heat-source and air heat-sink conditions. Compared to Kalina cycle, the transcritical ORC shows prominent advantages on the overall thermal efficiency, low operation pressure and simple components configuration at the ICE load with exhaust temperature over 491 K. The optimal thermal performance of the transcritical ORC appears at the ICE load with the certain exhaust temperature of 569–618 K. However, thermodynamic performance of the bottoming transcritical ORC is worsened considerably at the ICE load with the exhaust temperature over or under the certain value. Moreover, the extremely high turbine expansion ratio requires a complex multi-stage turbine design and big turbine dimensions for the bottoming transcritical ORC using Alkanes-based working fluid. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Internal combustion engine (ICE) is a primary driving technology for power generation and transportation presently. The average thermal efficiency of either the spark-ignition ICE or the compression-ignition ICE is approximately 40% [1]. Except for energy conversion to power, approximately 60% of fuel chemical energy is emitted into the ambient as sensible heat, e.g., via exhaust, coolant and lubricant, considering the energy balance of ICE [2–4]. In recent years, rising liquid fuel consumption and stringent environmental emission regulations, motivation is growing for developing the low-grade waste heat recovery (WHR) to improve the energy efficiency of the ICE. Organic Rankine cycle (ORC) and Kalina cycle are two eligible thermal to mechanical power technologies, those can be used to recover waste heat from ICE for power generation [5–9]. The coupling of the bottoming ORC with the topping ICE allows utilization of the ICE waste heat, and generates extra power ⇑ Corresponding author at: College of Energy & Power Engineering, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing 210016, China. Tel./fax: +86 02584892201. E-mail address: [email protected] (C. Yue). http://dx.doi.org/10.1016/j.enconman.2014.10.029 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved.

without consuming extra fuel, and the specific pollutant emissions of the ICE is also reduced. Some recent studies on the use of the bottoming ORC for the engine low-grade WHR can be found in [10–16]. Dai et al. [10] conducted a parametric optimization and comparative study of the bottoming subcritical ORC using different working fluids under the same waste heat condition. Wei et al. [11] performed a thermodynamic analysis for a bottoming subcritical ORC using R123 as working fluid, to recover exhaust heat from a heavy-duty diesel ICE. Gewald et al. [12] presented an integrated approach to optimize overall system efficiency of a combined cycle, including a topping ICE and a bottoming ORC, and evaluated thermodynamic performance of the combined cycle. Fu et al. [13] conducted a thermodynamic analysis for ICE WHR, via the mapping characteristics of a natural aspirated engine. Kostowski and Uson [14] proposed a novel exergy recovery system for natural gas expansion based on the integration of a topping ICE and a bottoming ORC, and found an exergy efficiency of 52.6% can be achieved by the analyzed system. Wang et al. [15] conducted a thermo-economic performance comparison of two bottoming ORC based several working fluids for exhaust WHR between a diesel and a gasoline ICE. It is known from above that overall thermal efficiency of the ICE is improved by 2–6% via exhaust WHR ORC technologies. However,

C. Yue et al. / Energy Conversion and Management 89 (2015) 764–774

765

Nomenclature cp Ex h H I j m n p P Q0 Q1 Q2 Q3 Q4 qLHV T s v V x

specific heat capacity, kJ/(kg K) exergy, kW specific enthalpy, kJ/kg enthalpy, kJ irreversibility, kW component number mass flow rate, kg/s the carbon atom numbers pressure, kPa power output, kW overall heating value of fuel, kW coolant waste heat, kW exhaust waste heat, kW exhaust heat recovered, kW discharged heat of the condenser, kW lower heating value of fuel, kJ/kg temperature, K specific entropy, kJ/(kg K) specific volume, m3/kg volume flow rate, m3/s NH3 mass fraction in mixtures

Symbols

g Dt Dt1 Dt2 DtHE1 DtHE2 Dtc

efficiency, % minimal temperature difference, K the minimal temperature difference in the evaporator, K the minimal temperature difference in the condenser, K the minimal temperature difference in HE1, K the minimal temperature difference in HE2, K the temperature increase of the working fluid in evaporator, K

there still exists a big exergy recovery potential in the evaporator of the bottoming subcritical ORC during the sensible WHR process. Yue et al. [16] analyzed the integrated characteristics of a topping ICE and a bottoming exhaust WHR ORC, and found the exergy loss in the exhaust WHR evaporator accounts for 32% of the overall fuel exergy input. Thus, in order to decrease thermal irreversibilities in the heat-transfer processes, particularly between the exhaust heat source and the working fluid, some advanced ORCs are put forward, e.g. the ORC using the zeotropic mixture [17,18], dual-loop ORC [1,19,20], trilateral cycle [21,22] and transcritical ORC [23– 25], in order to improve thermal match of the temperature profile between the working fluid and sensible heat source. Zhang et al. [17] designed a regenerative subcritical ORC system to recover the diesel engine exhaust heat, and studied the influences of working fluids selection on overall thermodynamic performance of the proposed system, and found that the ORC using zeotropic mixture of isopentane/R245fa (in a 0.7/0.3 mol fraction) as working fluids, performs better than the pure R245fa. Zhao and Bao [18] studied influence of the composition shift on ORC using zeotropic mixture as working fluids, and found there exists a maximal power output value of ORC using zeotropic mixture at a certain composition fraction. Yang et al. [1] conducted a performance analysis of a subcritical dual-loop ORC for the ICE WHR under various operation conditions, and found thermal efficiency of the ICE can be improved by 13%. Wang et al. [19] proposed a novel system, combining a gasoline engine with a dual-loop subcritical ORC to recover the ICE exhaust heat, and found the absolute thermal efficiency of the ICE was improved by 3–6% throughout the engine’s operational region. Tian et al. [20] proposed a novel

Dth

p

the temperature decrease of the exhaust in evaporator, K compression ratio of the bottoming cycle pump

Subscripts 0, 1, 2. . . state point a pinch point c cooling source eg exhaust gases en endothermic ex exergetic energy exo exothermic eva evaporator fuel fuel h heat source HE1 HE1 HE2 HE2 Heat_transfer heat-transfer process ICE internal combustion engine LHV lower heating value Loss thermal energy loss ORC organic Rankine cycle p pump t turbine th thermal energy wf working fluid WHR WHR bottoming cycle Abbreviations AHTTD average heat-transfer temperature difference ICE internal combustion engine ORC organic Rankine cycle WHR waste heat recovery

regenerative transcritical dual-loop ORC, and conducted a theoretical research on working fluid selection for ICE WHR. Zamfirescu and Dincer [21] assessed the thermodynamic performance of a NH3–H2O trilateral cycle that uses no boiler, but rather the saturated liquid is flashed by a positive displacement expander, and found the thermal efficiency of the trilateral cycle is 7% higher than that of the steam Rankine cycle. Fischer [22] performed a comparison of the trilateral cycle and ORC, and found the exergy efficiency of the power output of the trilateral cycle is 14–29% higher than that of the ORC. Through comparing to the subcritical ORC, Chen et al. [23] studied the transcritical ORC using CO2 as working fluid, and found that the CO2-based transcritical ORC gives a high power output than a R123-based subcritical ORC. Guo et al. [24] conducted a comparative analysis of CO2-based and R245fabased subcritical ORC, and proved that the CO2-based ORC presented high net power and reduced the dimension of turbine design. Chen et al. [25] conducted a comparative studied on transcritical ORC using CH2F2 (R32) and CO2 as the working fluids, respectively, and then performed an exergy analysis for the transcritical ORC, in order to conceive an ‘‘ideal’’ working fluids for transcritical ORC. Analyzing above advanced ORC cycles, though the dual-loop and dual-pressure ORCs show better thermodynamic performance than a simple subcritical ORC, there still exists a high thermal mismatch in the evaporator of the topping ORC loop. The subcritical ORC using zeotropic mixture shows only a small improvement on overall thermal performance due to the small temperature slide during the isobarically evaporating and condensing processes [25,26], and it is not suitable for the ICE sensible exhaust WHR

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with several-hundred temperature decrease. A positive displacement expander is necessary for the trilateral cycle, considering the wet steam characteristics during the expansion process. The transcritical ORC shows good overall thermodynamic performance, due to the good thermal match in heat introduction process between the exhaust waste heat source and working fluid. Besides the transcritical ORC, Kalina cycle using the zeotropic mixtures as working fluids, indicates good thermal match during the various-temperature heat-transfer processes in the evaporator and condenser, and some Kalina cycles with different configurations have been studied [8,9,27–31]. Kalina [27] proposed a novel absorption thermodynamic cycle using zeotropic mixtures, e.g. NH3–H2O as working fluids, which proved to produce more power than that of the conventional subcritical ORC using pure working fluid [9]. Larsen et al. [28] proposed and investigated a Kalina split-cycle, which shows better thermal performance than the conventional Kalina cycle. He et al. [29] designed a novel bottoming combined cycle for an engine WHR, including a Kalina cycle to recover coolant waste heat and an ORC to recover exhaust and lubricant waste heats, and found that a maximal thermal efficiency of 21% for the bottoming combined cycle can be achieved when using suitable working fluids. Yu et al. [30] proposed and investigated thermal performance of a cooling and power combined cycle, integrating a Kalina cycle and an absorption refrigeration cycle. Through using the specific exergy costing methodology, Singh and Kaushik [31] conducted a thermoeconomic analysis and optimization of Brayton–Rankine–Kalina combined system. Bombarda et al. [9] conducted a thermodynamic comparison between a Kalina and a subcritical ORC for diesel engine WHR, and found the Kalina cycle can produce about 45% and 25% more power than a single and a dual pressure ORC, respectively. In a brief, a review of the literature shows that both the transcritical ORC and Kalina cycle achieve prominent thermal performance, and indicates better thermal match than the subcritical ORC using pure working fluid with constant-temperature boiling characteristics under given sensible heat source conditions. The actual ICE working conditions are various due to the external various power demands, consequently, the exhaust temperature and the available waste heat are various under different ICE working conditions. It raises the question of which is better for the transcritical ORC and Kalina cycle for the same ICE sensible varioustemperature exhaust WHR under different engine working conditions. The present paper focuses on the thermal performance comparison of two eligible bottoming cycles for ICE exhaust WHR under different working conditions. The two types of the ICE exhaust WHR bottoming cycle models, including a Kalina cycle using NH3–H2O and a transcritical ORC using some several Alkane as working fluids, are build under the hypothesis of operating at the same various-temperature exhaust waste heat source and ambient air heat sink. Through quantitatively analyzing the relation between the exhaust waste heat characteristics and load of a commercial ICE under different working conditions, thermodynamic performances of the two bottoming cycles are investigated, and the influences from internal operation parameters of the two bottoming cycles on overall thermal performance are also analyzed.

2. System description The bottoming transcritical ORC with the topping ICE is shown in Fig. 1. The pure working fluid from liquid tank is pumped above its critical pressure (6–7), and then heated isobarically from liquid state into the supercritical state through HE1 and evaporator (7–8– 3). The supercritical vapor is expanded in the turbine to extract mechanical power (3–4). After expansion, the hot gaseous working

fluid flows through HE1 (4–5) to preheat the cold liquid working fluid (7–8), finally the gaseous working fluid discharging HE1 is condensed (5–6) by dissipating heat to ambient air and completes the transcritical thermodynamic Rankine cycle. The bottoming Kalina cycle with the topping ICE is shown in Fig. 2. The primary zeotropic liquid mixtures with a certain concentration from liquid tank is used as working fluids and firstly pumped to a fixed pressure (6–7), then is preheated by the turbine exhaust in HE1 (7–9), and then preheated by the weak concentration solution in HE2 (9–8), and further heated into the vapor– liquid state with high steam dryness by the engine exhaust in the evaporator (8–10) and finally sent to the separator, where the gas–liquid mixtures are separated into the strong concentration vapor (3) and the weak concentration solution (11). The strong concentration vapor is expanded in the turbine to extract mechanical power (3–4). After expanding, the hot gaseous working fluids are used to preheat the cold liquid mixtures in HE1 (4–14); the weak concentration solution is used to preheat the liquid mixtures in HE2 (11–12). The weak concentration solution out of HE2 is throttled through the valve (12–13), the strong concentration vapor and the weak concentration solution are mixed (14, 13–5) and then condensed in the condenser (5–6), finally send to the liquid tank. 3. Calculation model 3.1. Assumptions The following are the main assumptions used to derive the mathematical models. – The system works at steady-state conditions. – The non-equilibrium allowance is ignored. – The pressure drop in the evaporator and condenser of the ORC loop is ignored. – The constant specific heat capacities are assumed for the ICE exhaust and the ambient air. 3.2. Problem statement This study focuses on the comparison of two types of bottoming cycles, using working fluids with various-temperature evaporation characteristics for the ICE exhaust WHR, and thermodynamic performances of the two bottoming cycles are discussed based the exhaust waste heat data of a commercial ICE under different working conditions, considering the relation between the exhaust behaviors and the ICE load. Under the same ambient temperature (T0), pressure (p0), exhaust temperature (T1, T2), exhaust pressure (p1, p2), and assumptions of the minimal heat-transfer temperature difference requirements (Dt1, Dt2, DtHE1 and DtHE2) in all heat-exchangers, the ICE exhaust is used as waste heat-source and the ambient air is used as heat-sink, the bottoming transcritical ORC and a Kalina cycle are simulated via the simulation platform of Aspen PlusÒ. The NRTL-RK physical properties method is used to calculate the basic state point parameters of the two bottoming WHR subsystems. Then, after quantitatively analyzing the various-temperature exhaust influences on the thermal match during heat introduction in evaporation, the influence of the ICE load on thermal performance indices of the two bottoming cycles, e.g. gth and Dgth are discussed, in light of the relation between exhaust characteristics and the ICE load. Finally, the influences from the internal parameters of the bottoming Kalina cycle, including primary solution mass fraction (x6)

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ICE subsystem

ORC subsystem

Air

1

0

Radiator

Liquid tank

Condenser

15

T

6

3

Pump

7

5 HE1

Pump

4

8

4

ICE

Exhaust end

Suction end

Turbine

2 Δt1

Flue gas Silencer device

2

Mechanical power

6

Δt2

a

Catalytic purificaiton

Air 0

5

7

Evaporator

1

8

3

15

0

T0

Power transfer device

(a)

S

(b)

Fig. 1. The bottoming transcritical ORC with the topping ICE. (a) Flow diagram. (b) T–S diagram.

ICE subsystem

Kalina cycle subsystem

Air

Liquid tank

0

Radiator

6 Pump Condenser 5 14 13 Valve Pump

4

9 HE2

Exhaust end

Suction end

3

ICE

Separator 10

Silencer 2 device

1 Air 0

1

Turbine

12

Flue gas

T

7

HE1

15

10

8

3

11

11

2 8

12

Δt1

5

14

4

13 9

Evaporator

Catalytic purificaiton

7 15

Mechanical power

Power transfer device

(a)

6

Δt2 T0

0

(b)

S

Fig. 2. The bottoming Kalina cycle with the topping ICE. (a) Flow diagram. (b) T–S diagram.

and the pressure ratio (p = p7/p6), on overall thermal performance of the WHR bottoming Kalina cycle are analyzed under given ICE working conditions. 3.3. Energetic analysis The energy balance of the topping ICE subsystem is expressed as

PICE þ Q loss þ Q 2 þ Q 1 ¼ Q 0 ¼ mfuel  qLHV

ð1Þ

where mfuel is the mass flow rate of diesel. In view of the steam vapor latent in exhaust could not be recovered, the lower heating value of diesel fuel is used. qLHV is the lower heating value of diesel, 42.805 MJ/kg [32]. Q0 is the overall fuel heating value entry during the combustion process. Q1 is the cooling heat taken away by the coolant and lubricant, and Q2 is waste heat of the exhaust exiting

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the topping ICE subsystem. Qloss is the heat loss of the engine thermodynamic cycle. PICE is the net power output of the ICE subsystem. For the WHR process in the evaporator of the transcritical ORC, the exhaust waste heat recovered of Q3 is calculated by

Q 3 ¼ meg  cpeg  ðT 1  T 2 Þ ¼ m6  ðh3  h8 Þ

ð2Þ

where meg is the mass flow rate of exhaust, and m6 is the mass flow rate of the working fluid in the transcritical ORC loop. T1 and T2 are the exhaust heat source inlet and outlet temperature of the WHR evaporator, respectively. The specific heat capacity of the exhaust, cpeg is assumed a constant during the heat-transfer process. For the WHR process in the evaporator of Kalina cycle, the exhaust waste heat recovered is calculated by

Q 3 ¼ meg  cpeg  ðT 1  T 2 Þ ¼ m8  ðh10  h8 Þ

ð3Þ

Expanding work of the turbine in the bottoming cycle is expressed as

Pt ¼ gt  m3  ðh3  h4 Þ

ð4Þ

the pumping process and the expanding process) is not considered in the research. The exergy of each stream in ORC subsystem is calculated by

Exj ¼ mj  ½ðhj  h0 Þ  T 0 ðsj  s0 Þ

Irreversibility is the main cause of inefficiency and exergy destruction in four processes of ORC subsystem. The irreversibility in the heat exchangers of the bottoming WHR subsystem is calculated by

IHeat

1

gp

 m6  ðh6  h7 Þ

ð5Þ

ð7Þ

Thermal efficiency of the bottoming WHR cycle is calculated by

gWHR

PWHR ¼ 100% Q3

ð8Þ

Ieva ¼

where Dt1 is the minimal temperature difference in the evaporator. For the transcritical ORC, the minimal temperature of the working fluids exiting condenser is expressed as

ð10Þ

where Dt2 is the minimal temperature difference in the condenser. For Kalina cycle, the minimal temperature of the working fluids exiting condenser is calculated by

T 6 ¼ Dt 2 þ T 0

ð11Þ

Thermal efficiency of the ICE-ORC system is calculated by

P þ PICE gth ¼ WHR 100% Q0

Dgth ¼

gth  P ICE Q0

100%

 mh mc dQ  T exo T en

ð15Þ

ð16Þ

ðT 1  T 2 Þ Dt h ¼ T1 þ 2 2

ð17Þ

Ten in the bottoming transcritical ORC is calculated by

T en ¼ T 8 þ

ðT 3  T 8 Þ Dt c ¼ T8 þ 2 2

ð18Þ

Ten in Kalina cycle is calculated by

T en ¼ T 8 þ

ðT 10  T 8 Þ Dt c ¼ T8 þ 2 2

ð19Þ

When Dt1 is located at the evaporator inlet, the irreversibility in the exhaust WHR evaporator is expressed as

Ieva

" # m2wf T exo T0Q 3 ¼ meg  Q3 T exo mwf ðT 2  Dt 1 Þ þ 2cp

ð20Þ

When Dt1 is located at the evaporator outlet, the irreversibility in the exhaust WHR evaporator is expressed as

Ieva

" # m2wf T exo T0Q 3 ¼ meg  Q3 T exo mwf ðT 1  Dt 1 Þ  2cp

ð12Þ

ð21Þ

wf

The exergetic efficiency of the exhaust WHR evaporator in the transcritical ORC is calculated by

gex eva ¼

Ex3  Ex8 100% Ex1  Ex2

ð22Þ

The exergetic efficiency of the exhaust WHR evaporator in Kalina cycle is calculated by

gex eva ¼

Improvement of the thermal efficiency of the topping ICE subsystem is calculated by PICE Q0



  T0Q 3 mwf T exo meg  T exo T en

T exo ¼ T 1 þ

ð9Þ

T 6 ¼ Dt 2 þ T a

Q

wf

The minimal temperature of working fluids flowing into the evaporator is calculated by

T 8 ¼ T 2  Dt 1

Z

where Texo is the average exothermic temperature, Ten is the average endothermic temperature. The irreversibility in the evaporator of the two bottoming WHR subsystems is calculated by

ð6Þ

where mc is the cooling air flow rate, kg/s. Net work output of the bottoming WHR cycle is expressed as

PWHR ¼ Pt  Pp

¼ T0 

Texo is calculated by

where gp is the pump efficiency. The heat discharged to ambient air by condenser is calculated by

Q 4 ¼ m6  ðh5  h6 Þ ¼ mc  ðh15  h0 Þ

transfer

0

where gt is the turbine efficiency. The work consumption of the pump is calculated by

Pp ¼

ð14Þ

Ex10  Ex8 100% Ex1  Ex2

ð23Þ

Overall exergetic efficiency of the bottoming WHR subsystem is calculated by

gex ¼

PWHR 100% Ex1  Ex2

ð24Þ

ð13Þ 4. Results and discussion

3.4. Exergetic analysis

4.1. Operation parameter and working fluids selection

Only the exergy loss caused by the heat-transfer processes are analyzed, and the exergy loss caused by the flow process (including

The main input parameters of the two bottoming WHR cycles are given in Table 1. The ICE exhaust waste heat parameters at

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C. Yue et al. / Energy Conversion and Management 89 (2015) 764–774 Table 1 Main input parameters of the two bottoming WHR cycles. Parameter

Value

Range

Source

gp (%) gt (%)

75 75 2.87 0.37 712 443a 10 8 5.3 4.0 101 293 10 10

– – 1.29–2.87 0–1 419–712 443–712 10–200 5–20 – – – – – –

[33] [34] – [33] – – [35] [35] – – – – [33] [33]

m1 (kg/s) x6 T1 (K) T2 (K) Dt1 (K) Dt2 (K) p7 in Kalina cycle (MPa) p7 in transcritical ORC (MPa) p0 (kPa) T0 (K) DtHE1 (K) DtHE2 (K)

a Refers the minimum allowable exhaust temperature, when T8 + Dt1 is over 443 K, T2 is equal to T8 + Dt1.

different working conditions are calculated according to the Appendix Table A1. The choice of working fluid is important for the ICE bottoming ORC. Alkanes are considered as good candidates for high-temperature ICE exhaust WHR, and shows prominent advantages in ORC of the lowgrade heat into mechanical power [35,36]. Some several Alkanes have been selected as the working fluids for the transcritical ORC system, and shown in Table 2. It can be seen from Table 2 that the critical temperature of Tcrit in Alkanes increases as the number of carbon atoms of n is increased, and the critical pressure of pcrit decreases as n is increased. The ammonia–water (NH3–H2O) mixtures are selected as the zeotropic working fluids for Kalina cycle. It should be noted that this study is mainly focused on the thermal performance comparison of two types of sliding-temperature bottoming exhaust WHR cycles under various-temperature exhaust conditions, and working fluids selected for the two bottoming WHR cycles are not the optimized. 4.2. Thermal performance analysis for the two bottoming cycles The results shown in Tables 3–5 are obtained based on the exhaust parameters at the ICE’s rated working point of 2000 kW. Tables 3 and 4 give the parameter of every state point in the bottoming transcritical ORC using some several Alkanes and Kalina cycle using NH3–H2O as working fluids, respectively. Table 5 gives the main thermodynamic performance indices for the two types of bottoming WHR cycles. It is seen from Table 5 that the transcritical ORC shows prominent thermodynamic performance advantages at the ICE rated load condition in this study. Compared to the bottoming Kalina cycle, PWHR of the transcritical ORC using different Alkanes-based working fluid is increased by 106–145 kW, gWHR is increased by 9.3– 12.7%, and gex is improved by 18.8–25.8%. Above results can be explained that Alkanes possess a low specific heat capacity during transcritical process. When Alkanes is heated directly from the liquid state into supercritical vapor state, the significant temperature increase of 133–171 K is obtained for the working fluid at cold

Table 2 Thermal physical characteristics of some several Alkanes [36]. Name

n

Tcrit (K)

pcrit (kPa)

M (kg/kmol)

n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane

5 6 7 8 9 10

469.7 507.8 540.1 569.3 594.6 617.7

3370 3034 2736 2497 2281 2103

72.149 86.175 100.2 114.23 128.26 142.28

Table 3 The parameter of every state point in the bottoming transcritical ORC using n-pentane as working fluid. State

p (kPa)

T (K)

v (m3/kg)

m (kg/s)

0 1 2 3 4 5 6 7 8 15

101 101 101 4000 81 81 81 4000 4000 101

293 712 443 566 485 315 303 305 433 295

0.833 2.76 1.26 0.0262 1.46 0.0035 0.0035 0.0035 0.0036 0.839

– 3.99 3.99 2.155 2.155 2.155 2.155 2.155 2.155 386

Table 4 The parameter of every state point in the bottoming Kalina cycle using NH3–H2O as working fluids. State

P (kPa)

T (K)

v (m3/kg)

m (kg/s)

x (NH3 mass fraction)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

101 101 101 5300 397 397 397 5300 5300 5300 5300 5300 5300 397 397 101

293 712 443 494 381 334 301 302 433 370 494 494 380 345 311 326

0.833 2.76 1.26 0.0389 0.414 0.108 0.00121 0.00121 0.00154 0.00134 0.0137 0.00163 0.00128 0.0681 0.180 0.927

– 3.99 3.99 0.668 0.668 2.06 2.06 2.06 2.06 2.06 2.06 1.39 1.39 1.39 0.668 27.78

– – – 0.616 0.616 0.370 0.370 0.370 0.370 0.370 0.370 0.252 0.252 0.252 0.596 –

side in the evaporator, which causes the average heat-transfer temperature difference (AHTTD) in the evaporator of the transcritical ORC is significantly lower than the Kalina cycle (with a temperature increase of 61 K), resulting in a good thermal match between temperature profiles of the working fluids and the exhaust in evaporator, and thus thermal efficiency and exergetic efficiency of the bottoming transcritical ORC are high. For the bottoming Kalina cycle, besides the heat-transfer exergy loss in the evaporator, the heat-transfer processes in HE1 and HE2 also contribute to high exergy losses, due to the big heat transferred and high AHTTD during recovering the sensible heat of the effluents. It is also observed from Table 5, the overall thermal efficiency of the transcritical ORC of gWHR increases as the critical temperature of the Alkane-based working fluid is increased. However, the turbine expansion ratio is increased considerably in the transcritical ORC. The turbine expansion ratio in the transcritical ORC is increased from 49.4 to 15,878 when using different Alkanes-based working fluids, and is much higher than the Kalina cycle, which means a multi-stage turbine is requirement correspondingly, resulting in a complex and big dimension turbine design, and probably a high turbine cost. Table 5 also shows Q3 in the transcritical ORC using n-nonane is only of 1134 kW, which is a little lower than 1151 kW with exhaust temperature of 443 K. It is because of that the exhaust temperature is increased from 443 K to 448 K in order to keep the minimal heattransfer temperature difference in each of the heat exchangers, and thus, the waste heat recovered of Q3 is decreased. 4.3. Impact of the ICE load T2 and m2 are two key exhaust parameters those influence thermodynamic performance of the bottoming WHR cycles

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Table 5 The main thermodynamic performance indices of the two bottoming cycles. Performance index

Transcritical ORC

Q3 (kW) Q4 (kW) QHE1 (kW) QHE2 (kW) Dth (K) Dtc (K) cpeg (kJ/(kg K)) cpwf (kJ/(kg K)) Ieva (kW) IHE1 (kW) IHE2 (kW) T3 (K) p3 (kPa) p6 (kPa) p3/p4 V3 (m3/s) m3 (kg/s) Pp (kW) Pt (kW) PWHR (kW) PWHR/m3 (kW/kg) PWHR/V3 (kW/m3)

gex_eva gWHR gex

Kalina cycle

n-Pentane

n-Hexane

n-Heptane

n-Octane

n-Nonane

n-Decane

1151 827.7 777 – 269 133 0.965 4.02 91.2 47.8 – 566 4000 81 49.4 0.0262 2.16 18.2 342 323 150 12,337 83.9% 28.1% 57.0%

1151 816 726 – 269 138 0.965 3.95 87.8 40.0 – 571 4000 25 160 0.0178 2.11 17.2 359 341 162 19,238 84.5% 29.6% 60.2%

1151 806 695 – 269 148 0.965 3.73 80.5 35.7 – 581 4000 7.3 728 0.0107 2.09 16.4 368 345 168 32,697 85.8% 30.5% 62.0%

1151 786 676 – 269 156 0.965 3.54 76.0 34.7 – 589 4000 2.44 1636 0.00743 2.09 15.9 373 357 171 48,055 86.6% 31.0% 63.0%

1134 774 676 – 265 158 0.965 3.50 70.6 31.8 – 595 4000 0.780 7175 0.0064 2.05 15.8 375 359 175 56,181 87.4% 31.7% 64.1%

1151 788 662 – 269 171 0.965 3.20 66.4 30.2 – 604 4000 0.252 15,878 0.00572 2.10 15.5 378 362 170 63,480 88.3% 31.5% 64.0%

1151 935 688 737 269 61 0.965 9.16a 144 18.2 43.7 494 5300 400 13.4 0.0260 0.669 16.3 233 217 324 8333 74.7% 18.8% 38.2%

a It refers the equivalent specific heat capacity of the zeotropic mixtures working fluids, since it includes latent heat and sensible heat of the working fluids during the sliding-temperature evaporation process at fixed pressure.

significantly. Impact of the ICE load on the bottoming WHR subsystem is investigated, due to the mass flow rate and temperature of the ICE exhaust are functions of the topping ICE load. The relation between gex_eva and the ICE percentage load is shown in Fig. 3. For the bottoming Kalina cycle, gex_eva increases and then decreases as the ICE percentage load is increased, and the maximal value of gex_eva is obtained at 25% ICE load with the exhaust temperature of 514 K. gex_eva of Kalina cycle is decreased considerably when the ICE load is over 25% of the ICE load, due to increase rate of the average exothermic temperature of the exhaust gases (Texo) is significant, and the average endothermic temperature of the working fluid (Ten) in evaporator is fixed as the ICE load is increased, which results in the high AHTTD and the correspondingly high heat-transfer exergy loss in the evaporator at high ICE load. Fig. 3 also indicates gex_eva of the transcritical ORC increases and then decreases as the ICE load is increased. gex-eva reaches its maximal value at 40–60% of the ICE load with T1 of 569–618 K, and the maximal gex_eva value of the transcritical ORC using working fluid

with low critical temperature appears at ICE load with low exhaust temperature when using Alkanes-based working fluid. The transcritical ORC using n-pentane reaches its maximal gex-eva at 40% of the ICE load with T1 of 569 K, and n-decane appears at 60% of the ICE load with T1 of 618 K. gex-eva decreases considerably at the ICE load with T1 over 618 K or under 569 K. This can be explained Texo increases as the ICE load is increased, and Ten is near Texo  Dt1 at the ICE load with T1 of 569–618 K, which results in the low AHTTD and the correspondingly high exergetic efficiency of the evaporator. However, at the ICE load with T1 under 569 K, T1 is decreased considerably. In order to satisfy minimal heat-transfer temperature of Dt1 in the evaporator, T3 is decreased and is equal to T1  Dt1, which causes T8 is decreased significantly at the low ICE load, and thus results in the low Ten and high AHTTD in the evaporator, the consequent gex_eva is decreased. gex_eva in the transcritical ORC is even lower than the Kalina cycle under 30% of the ICE load. At the ICE load with T1 over 618 K, Texo increases significantly, and Ten is fixed during the heat-transfer process in evaporator, thus the AHTTD in evaporator is increased, and thus gex_eva is decreased.

100

96

94

ORC(n-pentane) ORC(n-hexane) ORC(n-heptane) ORC(n-octane) ORC(n-nonane) ORC(n-decane) Kalina cycle

92

90

ORC(n-pentane) ORC(n-hexane) ORC(n-heptane) ORC(n-octane) ORC(n-nonane) ORC(n-decane) Kalina cycle

300

PWHR (kW)

ex_eva (%)

98

20

40

60

200

100

80

100

ICE percentage load (%) Fig. 3. The relation between gex_eva and the ICE percentage load.

0

20

40

60

80

100

ICE percentage load (%) Fig. 4. The relation between PWHR and the ICE percentage load.

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70 65 60 ex(%)

The relation between PWHR of the bottoming WHR cycles and the ICE percentage load is shown in Fig. 4. It is seen that PWHR in both of the WHR bottoming cycles increases as the ICE percentage load is increased, and the increase rate of the transcritical ORC using Alkanes-based working fluid is more prominent at high ICE load, compared to the bottoming Kalina cycle. It is also seen from Fig. 4 that PWHR of the transcritical ORC is near Kalina cycle under 20% of the ICE load with T1 under 491 K. The relation between gWHR and the ICE percentage load is illustrated in Fig. 5. It is evident that gWHR of Kalina cycle almost keeps a constant at different ICE percentage load, due to although Q3 decreases as the ICE load is decreased, state parameters of Kalina cycle, e.g. turbine inlet temperature of T3 and Ten in evaporator are kept constants, and thus the thermal efficiency of Kalina cycle is fixed at 18.8% according to the second law of thermodynamics. It is also seen from Fig. 5 that gWHR of the transcritical ORC keeps a constant when the ICE load is over 60% due to the fixed T3 and compositions out of evaporator, and decreases considerably at the ICE percentage load with T1 under 569 K, due to the significant decrease of T3. gWHR of the transcritical ORC using n-nonane is even lower than Kalina cycle at the ICE percentage load with T1 under 491 K. The relation between gex and ICE percentage load is illustrated in Fig. 6. The curves shown in Fig. 6 indicate the similar trends to Fig. 3, because the exergetic loss in the evaporator accounts for a big fraction of the exhaust available energy in both of the bottoming WHR cycles. It is seen from Fig. 6 that exergetic efficiency of the bottoming Kalina cycle decreases as the ICE percentage load is increased, gex of the Kalina cycle is decreased from 48.5% to 36.7% with the ICE load increased from 20% to 100%. For the bottoming transcritical ORC using n-octane, a maximal exergetic efficiency of 71.1% is obtained at 50% ICE load with T1 of 596 K, due to the AHTTD in evaporator nearly reaches its minimal value of 10 K, resulting in an optimal thermal match between temperature profiles of the exhaust and working fluid in the evaporator. It is also known from Figs. 3 and 6 that the ICE load influences the thermal match between the working fluid and exhaust temperature for both of the bottoming WHR cycles importantly, in light of the relation between exhaust behaviors and the ICE percentage load. For the transcritical ORC using Alkanes-based working fluids, there exists an optimal thermal match between the temperature profiles of the working fluid and exhaust at 40–60% of the ICE load with T1 of 569–618 K, and the thermodynamic performance of the bottoming transcritical ORC is worsened significant at the ICE load with T1 under 569 K or over 618 K. Combined the results on high-temperature ORC using Alkanes as working fluids [36], it is known from Figs. 3 and 6 that the bottoming transcritical ORC using a pure Alkane-based working fluid

50 45 40 35

15

40

60

80

80

100

4.4. Impact analysis of the operation parameters on the bottoming Kalina cycle Impact of the turbine inlet parameters on overall thermodynamic performance of the bottoming Kalina cycle are discussed in this section. Since the turbine inlet parameters, including p3, T3 and m3, are functions of p7/p6 and x6, the influences of p7/p6 and x6 on overall thermodynamic performance of Kalina cycle are analyzed, respectively. Considering the requirements of the minimal heat-transfer temperature difference in each heat exchanger in Kalina cycle and exhaust temperature of T2 exiting the evaporator, the influence of pressure ratio of the pump (p7/p6) in the range

35

ORC(n-pentane) ORC(n-hexane) ORC(n-heptane) ORC(n-octane) ORC(n-nontane) ORC(n-decane) Kalina cycle

30

25 20

60

is suitable at some ICE load with a certain exhaust temperature. gex of the bottoming ORC is worsened considerably at the ICE load with exhaust temperature over or under the certain value. Thus, both the ICE load and the correspondingly operation time at each load should be considered when selecting the optimal working fluid of bottoming transcritical ORC for the ICE various-temperature exhaust WHR. The relation between gth, Dgth and the ICE percentage load are shown in Figs. 7 and 8, respectively. It is seen that gth of the two ICE-WHR combined cycle systems increases as the ICE percentage load is increased, and gth of the ICE with bottoming transcritical ORC is much higher than that of the ICE with bottoming Kalina cycle at high ICE load, due to increase rates of Ten and T3 in evaporator of the transcritical ORC are higher than Kalina cycle. Compared to the ICE with bottoming Kalina cycle, Dgth of the ICE with transcritical ORC using n-decane is increased from 0.45% to 7.7% when the ICE load is increased from 20% to 100%.

th(%)

WHR (%)

20

40

Fig. 6. The relation between gex and the ICE percentage load.

40

ORC(n-pentane) ORC(n-hexane) ORC(n-heptane) ORC(n-octane) ORC(n-nonane) ORC(n-decane) Kalina cycle

20

ICE pencentage load (%)

30

25

ORC(n-pentane) ORC(n-hexane) ORC(n-heptane) ORC(n-octane) ORC(n-nontane) ORC(n-decane) Kalina cycle

55

100

ICE percentage load (%) Fig. 5. The relation between gWHR and the ICE percentage load.

20

40

60

80

100

ICE pencentage load (%) Fig. 7. The relation between gth and the ICE percentage load.

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20 ORC(n-pentane) ORC(n-hexane) ORC(n-heptane) ORC(n-octane) ORC(n-nontane) ORC(n-decane) Kalina cycle

tc

520

100 80

500

K

60

10

480

K

th (%)

15

120

T3

540

40

460

20

5 20

40

60

80

440 10

100

12

14

16

20

22

24

Fig. 10. The relation between T3, Dtc and p7/p6.

Fig. 8. The relation between Dgth and the ICE percentage load.

25

250

20

200

15

kW

150

PWHR

100

10

(%) WHR 5

50

0 10

12

14

16

18

20

22

24

Fig. 11. The relation between PWHR, gWHR and p7/p6.

40

10

m6 m3/m10

8

0.65

kg/s

4

30

20

50

0.60

m3

0.55 0.50

10

0.1 0.2 0.3 0.4 0.5 0.6

x6

0 0.1

0.2

0.3

x6

0.4

0.5

0.6

Fig. 12. The relation between m6, m3/m10 and x6.

40

12 0.6

kg/s

kg/s

16

60

%

kg/s

6

2

m6 m3/m10

0 26

p7/p6

70 20

0 26

p7 /p6

ICE pencentage load (%)

of 11 and 25 (p3 is varied from 4.3 MPa to 9.7 MPa) and x6 in the range of 0.15–0.6 are investigated. The results shown in Figs. 9– 11 are obtained based on the exhaust parameters at rated load and x6 of 0.37. The results shown in Figs. 12–14 are obtained based the exhaust parameters at rated load and p7/p6 of 13.4. The relations between m6, m3/m10 and p7/p6 are illustrated in Fig. 9. It is seen that m6 decreases as p7/p6 is increased, and the vapor fraction out the evaporator of m3/m10 increases as p7/p6 is increased. Combined results of above two aspects cause m3 increases considerably and then decreases flatly as p7/p6 is increased, and the maximal value of m3 is of 0.68 at p7/p6 of 13. The relations between T3, Dtc and p7/p6 are illustrated in Fig. 10. It is seen that both T3 and Dtc increase as p7/p6 is increased due to the thermal matches during HE1 and HE2 are improved at high m3/m10. The relation between PWHR, gWHR of the bottoming Kalina cycle and the pressure ratio of the pump (NH3–H2O) is demonstrated in Fig. 11. It is evident that both PWHR and gWHR increase as p7/p6 is increased. Combined the results shown in Figs. 9 and 10, it is known despite m3 increases considerably and then decreases flatly as p7/p6 is increased, T3 increases significant as p7/p6 is increased, which results in PWHR and the consequent gWHR are high at high p7/p6. Fig. 12 shows the relation between m6, m3/m10 and x6. It is seen m6 decreases flatly and then increases significantly as x6 is increased, and the minimal value of m6 is of 1.64 kg/s at x6 of 0.25. However, the vapor fraction out of evaporator of m3/m10 increases and then decreases as x6 is increased, and the maximal value of m3/m10 is of 0.37 at x7 of 0.3. Combined results from above two aspects, m3 increases and then decreases as x6 is increased, and the maximal value of m3 is of 0.66 at x6 of 0.35.

18

8

30

m3

0.4

20

0.2

4

12

0 10

12

14

16

18

16

20

p7 /p6

20

22

24

10

24

p7 /p6 Fig. 9. The relation between m6, m3/m10 and p7/p6.

0 26

The relation between T3, Dtc and x6 is demonstrated in Fig. 13. It is evident both T3 and Dtc increase and then decrease as x6 is increased, and the maximal values of T3 and Dtc are of 495 K and 62 K at x6 of 0.35, respectively. The relation between net power output of PWHR, gWHR and x6 is presented in Fig. 14. It is seen that both PWHR and gWHR increase and then decrease as x6 is increased, due to the combined results from the relations between m3, T3 and x6 shown in Figs. 12 and 13. PWHR and gWHR reach their maximum values of 216 kW and 18.8% at x6 of 0.35, respectively.

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C. Yue et al. / Energy Conversion and Management 89 (2015) 764–774

70

500

580

T3 tc

490

60

29.0

Temperature Efficiency

575

28.5

K

T3(K)

50

480

28.0 565 27.5

40

470

WHR (%)

K

570

560 27.0 30

460 0.1

0.2

0.3

x6

0.4

0.5

555 35

0.6

40

45

50

55

60

65

70

75

p7 /p6

Fig. 13. The relation between T3, Dtc and x6.

Fig. A1. The relation between T3, gWHR and p7/p6 for the transcritical ORC subsystem using n-pentane.

20 200

PWHR

Acknowledgements 15

WHR

10

100

%

kW

150

The work described in this paper is fully supported by a Project Funded by the Youth Natural Science Foundation of Jiangsu Province of China (BK20130799), the Priority Academic Program Development of the Jiangsu Higher Education Institutions (PAPD) and China Scholarship Council.

5

50

Appendix A 0

0 0.1

0.2

0.3

0.4

0.5

0.6

x6 Fig. 14. The relation between PWHR, gWHR and x6.

5. Conclusions We conducted a steady-state thermodynamic performance comparison of a transcritical ORC using some several Alkanes and a Kalina cycle using zeotropic mixtures as working fluids for the ICE exhaust waste heat recovery under different working conditions. The next conclusions are obtained: 1. Compared to Kalina cycle using zeotropic NH3–H2O mixtures, the transcritical ORC using Alkanes-based working fluids shows advantages on the overall WHR efficiency, low operation pressure and simple system components configuration at the ICE load with exhaust temperature over 491 K. However, the turbine expansion ratio in the transcritical ORC is much higher than the Kalina cycle, which requires a complex multi-stage turbine design and big turbine dimensions. 2. For the transcritical ORC using fixed working fluid, there exists an optimal thermal match between the temperature profile of the working fluid and exhaust at some ICE percentage load with a certain exhaust temperature, and the thermodynamic performance of the transcritical ORC subsystem is worsened significantly at the ICE load with exhaust temperature over or under the certain value. Both the ICE load and the actual operation time at this ICE load should be considered when selecting the working fluid for the ICE various-temperature exhaust WHR transcritical ORC. 3. Transcritical ORC is suitable for recovering the sensible heat from a high-temperature heat source fluid with a low specific heat capacity. The optimal thermal match of transcritical ORC using Alkanes-based working fluid is obtained at 40–60% ICE load with exhaust temperature of 569–618 K.

Fig. A1 gives the relation between T3, gWHR and p7/p6 for the transcritical ORC subsystem using n-pentane. It is seen that T3 is only increased by 20 K when the pressure ratio of the pump is increased from 37 to 74, which causes turbine inlet pressure of p3 is increased from 3 MPa to 6 MPa, but only a 1.9% improvement of the thermal efficiency of the transcritical ORC is obtained, the main reason can be explained as follows. When n-pentane is heated isobarically, it changes from liquid into supercritical vapor nearly alone the saturated liquid curve of n-pentane at different supercritical pressure, the AHTTD in the evaporator changes a little. Table A1 gives the waste exhaust operation parameter at different ICE percentage load for the 3516CDITA ICE. In light of the exhaust temperature is only of 419 K at 10% ICE load, which is much lower than 443 K, and no waste heat can be recovered from exhaust waste-heat source at this working condition. Therefore, the two bottoming cycles’ thermodynamic performance at 10% ICE load is not investigated in this research.

Table A1 The waste exhaust operation parameter at different ICE load (p1 = 101 kPa). ICE load percentage

Fuel total heating value Q0 (MW)

Power output PICE (kW)

Exhaust gases volume flow rate V1 (m3/s)

Exhaust gases temperature T1 (K)

100 90 80 75 70 60 50 40 30 25 20 10

5.59 5.05 4.56 4.33 4.11 3.64 3.12 2.58 2.05 1.81 1.56 1.06

2000 1800 1600 1500 1400 1200 1000 800 600 500 400 200

7.20 6.70 6.28 6.08 5.87 5.41 4.81 4.07 3.37 3.05 2.75 2.16

712 683 660 649 638 618 596 569 535 514 491 419

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