Simulation and thermodynamic analysis of a bottoming Organic Rankine Cycle (ORC) of diesel engine (DE)

Energy 51 (2013) 281e290

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

Simulation and thermodynamic analysis of a bottoming Organic Rankine Cycle (ORC) of diesel engine (DE) Guopeng Yu, Gequn Shu*, Hua Tian, Haiqiao Wei, Lina Liu State Key Laboratory of Engines, Tianjin University, No. 92, Weijin Road, Nankai Region, Tianjin 300072, People’s Republic of China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 August 2012 Received in revised form 28 October 2012 Accepted 29 October 2012 Available online 30 November 2012

This paper presents a simulation model based on an actual Organic Rankine Cycle (ORC) bottoming system of a diesel engine. The ORC system is built to recover waste heat both from engine exhaust gas and jacket water using R245fa as working fluid. Simulations and thermodynamic analyses are conducted to observe the influence of evaporating pressure and diesel engine (DE) conditions on system performance. Comprehensive evaluations are carried out on waste heat absorbing, expansion power, system efficiency, exergy loss and exergy efficiency. The combined system of diesel engine with bottoming ORC (DE-ORC) is finally investigated. Results indicate that, approximately 75% and 9.5% of waste heat from exhaust gas and from jacket water respectively can be recovered under the engine conditions ranging from high load to low load. The ORC system performances well under the rated engine condition with expansion power up to 14.5 kW, recovery efficiency up to 9.2% and exergy efficiency up to 21.7%. Combined with bottoming ORC system, thermal efficiency of diesel engine can be improved up to 6.1%. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Bottoming Organic Rankine Cycle (ORC) Diesel engine (DE) Waste heat recovery Simulation Thermodynamic analysis

1. Introduction In a typical diesel engine, less than 45% of fuel energy might be converted into useful work output from crankshaft, and the remaining energy is mainly lost through exhaust gas and jacket water [1]. If the waste heat contained in exhaust gas and in jacket water could be efficiently recovered and utilized, the efficiency of the original diesel engine would be significantly improved without adding any fuel. Among all the existed waste heat recovery technologies, the Organic Rankine Cycle (ORC) is getting increasing attention with high efficiency, reliability and flexibility [14]. As one of the promising technologies of converting low-grade waste heat into electricity, the ORC system has been studied from different aspects. Working fluids researches [2e4] mainly focus on diverse screening and assessment criteria for dozens of organic fluid on performance of ORC system; performance analysis [5e8] focus on usable percentage of heat, output expansion power, recovery efficiency and exergy efficiency et al; System designs [9e 11,30] based on scroll expanders, vapor injectors and dual loop ORCs; optimizations [12e15] on parameters of turbine inlet pressure, evaporating temperature, pinch point temperature, heat transfer area et al. And the ORC technique has also been explored in

* Corresponding author. Tel.: þ86 022 27409558 E-mail addresses: [email protected], [email protected] (G. Shu). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.10.054

the engine field: Bianchi M and Pascale [16] revealed that the ORC technology results as the most performing and well proven solution, in order to exploit low/medium temperature heat sources such as ICEs. Tchanche et al. [17] presented existing applications of ORC and analyzes their maturity, including in car and engine field. Velez et al. [18] did a technical, economical and market review of ORC for waste heat recovery in ICEs as a part of their work. Bombarda et al. [19] simulated and compared performances of ORC and Kalina cycle on recovery of waste heat in exhaust gases from two diesel engines, although obtained useful powers were actually equal, the Kalina cycle was less suitable than ORC because its complicated plant scheme, large surface heat exchangers, high pressure resistant and no-corrosion materials. Srinivasan et al. [20] examined the exhaust waste heat recovery potential of a dual fuel low temperature combustion engine using an ORC. With hot EGR and ORC turbocompounding, the fuel conversion efficiency improved by an average of 7 percentage points for all injection timings and loads while NOx and CO2 emissions recorded an 18 percent (average) decrease. Teng et al. [21,22] simulated an ORCWHR system to recover heat in exhaust gas, charge air cooler and EGR cooler. The case study showed up to 20% increase in engine power. They also proposed a system recovering waste heat from only EGR (EGR-WHR system). The composite fuel savings over the ESC 13-mode test is up to 5%. Vaja and Gambarotta [23] studied three configurations of ORC system for a 12-cylinder natural gas engine. Best fluid and configuration were selected and the

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maximum efficiency increase was about 12.5%. Boretti [24,25] explored the recovery of waste heat from exhaust gases and the coolant of a H2ICE and a naturally aspirated gasoline engine in succession. Hountalas and co-workers [26,27] researched on heavy-duty truck diesel engines using Rankine bottoming cycles. When exhaust heat and EGR heat were recovered, the improvement of brake specific fuel consumption (bsfc) ranged between 6% and 7.5% depending on engine loads. When CAC (Charge Air cooler) heat was also taken into account, maximum improvement in bsfc was 11.3% with Organic Rankine Cycle and 9% with steam rankine cycle. Kane et al. [28] integrated solar energy with a combined cycle of a biodiesel engine with two ORCs in cascade in a small pilot plant (10e25 kW), achieving overall efficiency of 41%. So far, most researches on waste heat recovery of the engine using ORC are theoretical researches and simulations [16e23], and only a few experiments are developed, especially in engine field [24,25]. What’s more, most simulations are based on simple thermodynamic models, i.e., ignoring detailed structures and operating characteristics of system components including heat exchangers and expanders. So models like that are too ideal to precisely reflect the real performance of the ORC. The system model proposed in this paper is built up based on an actual experimental ORC set built in our lab which serves as the bottoming system of a typical diesel engine. Main components are detailed modeled according to real products. The experimental ORC set contains an expander, two pumps, seven heat exchangers and several accessory equipments. It is built to investigate the feasibility of waste-heat-recovery from a high duty diesel engine (DE). If proven in high practicability, it can be adopted by generation sets in power plants and ICEs in ships, where the requirement for compactness is low, and waste heat are in high grade and quantity. After optimizations and downsizing, it is also expected to be used in vehicles in the future. After validating from different angles, the model is rather close to the real system, and the simulation results are more reliable to predict the system performance. Besides, five typical DE conditions are investigated to reveal how the variable condition of the engine affects the bottoming ORC system. Simulations and thermodynamic analyses are conducted to evaluate waste heat absorbing, expansion power, system efficiency, exergy loss and exergy efficiency of the ORC. The combined system of DE with bottoming ORC (DE-ORC) is finally analyzed to show its maximal working potential. 2. Description of systems

Table 1 Five typical conditions of the diesel engine. Parameters

Condition Condition Condition Condition Condition 1 2 3 4 5

Power output [kW] Fuel consumption rate [kg/h] Temperature of exhaust gas [K] Mass flow of exhaust gas [kg/s] Output temperature of jacket water [K] Mass flow of jacket water [kg/s]

258.3 53.22

235.8 47.79

211.6 42.81

176.2 35.43

117.7 23.91

808.15

792.15

771.15

747.15

693.15

0.2981

0.2752

0.2586

0.2235

0.1697

366.15

365.65

365.25

364.65

363.75

2.1

2.1

2.1

2.1

2.1

water pump is driven by the engine crankshaft, whose speed is constant. So the pump rotates uniformly and the flow of the jacket water is basically unchanged at about 2.1 kg/s. 2.2. Description of ORC as the bottoming system Figs. 1 and 2 show the principle schematic diagram and the Tes diagram of the bottoming ORC for the diesel engine. As shown in these two figures, the deep red line represents the exhaust gas flow from behind the engine to reject heat to the ORC system. The light red loop circuit besides the engine is the cooling water circuit. The green loop represents the ORC circuit. A thermal-oil circuit (in black line) is used between exhaust gas and ORC circuit to prevent decomposition of working fluid R245fa. The whole system operates as follows: hot exhaust gas from engine rejects heat to thermal-oil circuit and then is discharged to atmosphere; working fluid R245fa under low pressure in liquid state (point 5) is firstly pumped into high pressure state (point 1), and then is preheated by engine jacket water (point 2); after that, working fluid evaporates and is superheated by hot thermal oil, thus working vapor under high pressure and temperature is generated (point 3); the vapor (point 3) flows into the turbine, and its enthalpy is converted into expansion power; low pressure vapor (point 4) exits from turbine and flows into condenser where it is liquefied and condensed into saturated liquid (point 5) by cooling water. Thus a whole cycle completes. Cycles run in this way to generate continuative power. The actual ORC system contains an expander, an oil pump and a working fluid pump, a pre-heater, a gaseoil heat exchanger,

2.1. Description of diesel engine as the topping system The diesel engine selected as topping system is an inline sixcylinder turbocharged engine used in a generator set. As a power plant used engine, its speed is constant (1500 rpm) while its load varies under different conditions. Five important conditions of the engine are picked out in Table 1, and it generally runs under rated condition (condition 2). The thermal balance of the diesel engine is firstly analyzed according to data from engine tests, as listed in Table 1. Under these five conditions of Table 1, the temperatures of the exhaust gas are within 690e810 K, and that of jacket water are within 363e366 K. Approximately 30e46% of the fuel energy is contained in exhaust gas and 15% in jacket water. It is further confirmed that, heat recovery of the two resources will significantly reduce fuel consumption and improve engine efficiency. It has been calculated that the air fuel ratio is 19.7 under the rated condition. Under the hypothesis of perfect combustion of diesel fuel, the composition of the exhaust gas on mass basis has been calculated at: CO2 ¼ 15.1%, H2O ¼ 5.5%, N2 ¼ 71.6%, O2 ¼ 7.8%. This composition is used to evaluate gas properties. Without considering trace additives, the jacket water is simulated as pure water. It should be noted that the

Fig. 1. Schematic diagram of the bottoming ORC.

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our lab. The experimental ORC set is built to investigate the feasibility of waste-heat-recovery from a high duty DE described above. According to the actual ORC bottoming system, the ORC model is constructed by integration of ASPEN PLUS and ASPEN EDR (Exchanger Design & Rating) software from Aspen Technology, Inc. [29]. Modeling of heat exchangers is based on detailed structural parameters listed in Table 2 which are provided by manufactures. By importing these reliable data and inlet values of working fluid, parameters like outlet values of working fluid, heat loads, heat transfer coefficients (HTCs) of heat exchangers are calculated out by ASPEN EDR software. After validations, models of heat exchanger are quite reliable. Modeling of expander is based on its performance curves as listed in Table 3, ignoring the internal structure of this component. The expansion power (Pexp) can be calculated based on Eqs. (1) and (2) below, combing with isentropic efficiency (hexp) and compression ratio (Rp) values in Table 3 tested by manufactures:

_ Pexp ¼ m*ðh 3  h4 Þ

(1)

hexp ¼ ðh3  h4 Þ=ðh3  h4s Þ

(2)

_ is mass flow of the working fluid. The number wherein, m subscripts used above are all illustrated in Fig. 2. By importing the Rpen curve and hexpen of the actual expander, the model of the expander is supposed to run as the real expander does. As for the two pumps contained e the oil pump and working fluid pump e they are simply modeled, because their power consumptions are so small that they have little effect on system performance, and their efficiencies are set the same, at 0.8. The components modeled above are connected by thermal-oil stream and R245fa stream correctly and the ORC system model is then completed.

Fig. 2. Tes diagram of the bottoming ORC.

condensing devices and oil-working fluid heat exchangers. As shown in the two diagrams, oil-working fluid heat exchangers are three exchangers connected in series (HE1, HE2, HE3). HE1 heats working fluid to saturated state, i.e. from point 2 to (2e3)a; HE2 evaporates the working fluid from point (2e3)a to (2e3)b; HE3 superheats working fluid from point (2e3)b to 3. Similarly, condensing process is also completed by two connected exchangers (CON1 and CON2). All the seven heat exchangers are plate counterflow exchangers modeled in detail according to actual exchanger components. Main practical parameters of the exchangers are listed in Table 2. The exchangers are selected under the rated condition of diesel engine, and the designed evaporating pressure is supposed to be 30 bar. The expander is selected based on its actual performance curves, including the compression ratioevolume flow curve (Rpen) and the efficiencyevolume flow (hexpen) curve. Main performance parameters of the expander are listed in Table 3. R245fa is the working medium of the ORC system, and it is a nonchlorinated hydro fluorocarbon, non-ozone depleting liquid with low global warming potential, good heat transfer ability, excellent thermal stability and low viscosity, and it is rather an appropriate working fluid for the ORC system [15].

3.2. Modeling for ORC thermodynamic analysis Firstly, a proper system model should be in good energy balance. Namely, energy output should match well with energy input, as demonstrated in Eq. (3).

jQin  Qout j ¼ 0

(3)

Qin is the total energy that enters ORC system, while Qout is that leaves the system. Neglecting the energy loss in actual components, pipes and oil pump, energy balance can be extended to be Eq. (4).

Qexh þ Qjw þ Pwf  Qcond  Pexp ¼ 0

3. Modeling

(4)

Qexh and Qjw are the waste heats absorbed from exhaust gas and from jacket water; Pwf is the electric energy consumed by working fluid pump. Qcond is the heat released from working vapor to cooling water in condensation. Pexp is the output expansion power.

3.1. Modeling of the ORC system The system model proposed in this paper is built up based upon an actual experimental ORC set which is now under construction in

Table 2 Main parameters of plate exchangers in the ORC system. Parameters

Unit

Total heat transfer area Overall H T C. Number of plates Dimension of plates

m2

Pre-heater 1.06 2

Length Width Thickness

W/m K e mm mm mm

1380 40 287 117 2.3

Gaseoil heat exchanger 35 30 38 2000 500 2

HE1 1.45 1280 25 526 119 2.2

HE2 1.76 520 30 526 119 2.2

HE3 5.28 180 50 316 316 1.2

CON1 1.10 882 40 287 117 2.3

CON2 4.08 2430 70 526 119 2.2

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G. Yu et al. / Energy 51 (2013) 281e290

Table 3 Main performance parameters of the expander in the ORC system.

n e Volume flow [103 cum/s] hexp e isentropic efficiency [/] Rp e compression ratio [/]

4.5 0.45 10.30

3.9 0.5 10.90

3.7 0.54 11.40

3.5 0.55 11.60

The recovery efficiency is generally regarded as the 1st law efficiency, i.e. the ratio of expansion power to the heat absorbed by the ORC system from the heat resources.

h1st ¼

Pexp Qexh þ Qjw

(5)

Efficiency of the DE-ORC combined system (ha) is the ratio of total output mechanical power to total fuel energy. Total output mechanical power is the sum of the original diesel engine power (Po) and the ORC expansion power (Pexp).

P þ Po ha ¼ exp Qfuel

(6)

The 2nd law analysis is then carried out to explore the exergy utilization and exergy loss within the ORC system [5]. The subscripts used below are all illustrated in Fig. 2. Eq. (7) shows how to calculate the exergy flow change of a certain material stream (stream i) when it flows through a certain component. Among _ i is them, E_ i is the exergy rate of stream i under a certain state and m the mass flow of this stream. In the following analysis, the dead state temperature is assumed to be 290 K (T0).

_i E_ i ¼ E_ iIN  E_ iOUT ¼ ½ðhiIN  hiOUT Þ  T0 ðsiIN  siOUT Þ$m (7)

3.3 0.60 11.70

2.9 0.51 11.68

2.7 0.50 11.67

1.9 0.48 11.63

1.5 0.48 11.63

1.0 0.47 11.62

0.4 0.46 11.60

The exergy loss in the preheat process between jacket water and working fluid I_ PREHE :

I_PREHE ¼

   E_ JWIN  E_ JWOUT  E_ 2  E_ 1



(13)

Exergy losses that are carried out through output cooling water I_ CW :

I_CW ¼ E_ CW _ CW ¼ ½ðhCWOUT  hCWIN Þ  T0 ðsCWOUT  sCWIN Þ$m (14) Exergy losses due to non-isentropic vapor expansion in the expander I_ EXP :

I_EXP ¼



   _ E_ 3  E_ 4  H_ 3  H_ 4 ¼ T0 ðs4  s3 Þ$m

(15)

Exergy losses due to non-isentropic compression of working fluid pump I_P :

_ I_P ¼ T0 ðs1  s5 Þ$m

(16)

_ is defined In summary, total exergy that leaves the ORC system ðIÞ as Eq. (17):

I_ ¼ I_EXHF þ I_PREHE þ I_EXP þ I_COND þ I_CW þ I_P

(17)

The net exergy rate of the exhaust gas entering the system is E_ EXH

The second-law efficiency of the power cycle, also referred to as exergy efficiency (h2nd ), can be defined as follows:

E_ EXH ¼ E_ EXHIN  E_ EXHOUT

h2nd ¼

_ EXH ¼ ½ðhEXHIN  hEXHOUT Þ  T0 ðsEXHIN  sEXHOUT Þ$m (8) The net exergy rate of the jacket water entering the system is E_ JW

E_ JW ¼ E_ JWIN  E_ JWOUT 

 _ JW ¼ hJWIN  hJWOUT  T0 sJWIN  sJWOUT $m

(9)

The total exergy rate entering the system is E_ A

E_ A ¼ E_ EXH þ E_ JW þ Pwf

(10)

Neglecting small amount of exergy loss around the oil pump, the exergy loss in the heat exchanging process between exhaust gas and working fluid ðI_ EXHF Þ is considered to be the sum of exergy losses in the following four heat exchangers: Gaseoil heat exhchanger, HE1, HE2 and HE3.

I_EXHF ¼

    E_ EXHIN  E_ EXHOUT  E_ 3  E_ 2

(11)

Similarly, exergy loss in the condensing process between working fluid and cooling water ðI_ COND Þ is considered to be the sum of exergy losses in the following two heat exchangers: COND1 and COND2.

I_COND ¼



   E_ 4  E_ 5  E_ CWOUT  E_ CWIN

(12)

Pexp 

(18)

EA 4. Model validations 4.1. Mass-balance and energy-balance validation No leakage is considered in the system model. All the mass flows of materials contained remain unchanged, and the mass of the system is thus in good balance. The energy-balance validation is reflected in the Eq. (4). Under the rated engine condition, system energy-balance calculations within 25e33 bar evaporation pressure ranges are listed in Table 4. Energy budget under the 9 pressures all fit Eq. (4) quite well, and maximum deviation is only 0.23 kW. Additionally, energy budget of the other four engine conditions are calculated, revealing that the energy of the system is well balanced. 4.2. Model validated with heat exchanger products The heat exchanger products in the real ORC system are selected and bought under the hypothesis that, the diesel engine runs under the rated condition, and evaporating pressure is 30 bar, the mass flow of working fluid is 0.34 kg/s. With the same assumption, simulation is conducted on the basis of detailed modeling, and simulating results (temperatures and pressures) are compared with product parameters supplied by heat exchanger manufacturers. These product parameters are design data of the exchangers which are enough reliable. As shown in Fig.3, the comparison revels that

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Table 4 Validation of energy balance of the WHR system under rated engine condition.

Qexhaust [kW] Qjacket-water [kW] Ppump [kW] Qcondens [kW] Pexpansion [kW] jEin  Eoutj [kW]

25 bar

26 bar

27 bar

28 bar

29 bar

30 bar

31 bar

32 bar

33 bar

118.23 28.17 0.72 135.94 11.07 0.11

118.12 28.59 0.75 135.52 11.80 0.16

118.09 28.57 0.78 134.42 12.80 0.23

118.06 28.93 0.81 134.60 13.25 0.03

118.04 29.14 0.84 134.43 13.47 0.13

118.02 29.36 0.87 133.70 14.45 0.11

118.02 29.47 0.89 133.96 14.48 0.05

118.03 29.60 0.92 134.67 13.75 0.14

118.03 29.61 0.95 135.53 13.07 0.01

two sets of data are in good agreement at these main points. The tick labels in X-axis of Fig. 3 are inlet or outlet points of exchangers in the ORC system, as pointed out in Figs. 1 and 2. Maximum temperature deviation is in point 1, where the simulated temperature is 11.7 K lower than that of the actual pre-heater exchanger, and the absolute deviation is about 3.8%. Maximum pressure deviation is at point CW-OUT, where the simulated pressure is 0.01 bar lower than that of COND1 exchanger, and the absolute deviation is about 3.1%. The exchangers are thus well validated. The entire ORC system model is now proven reliable and accurate. 5. Results and discussion 5.1. Waste heat absorbing In the proposed ORC system, waste heat is absorbed from both the exhaust gas and the jacket water of the diesel engine. As is

a 800 Simulating results Parameters of heat exchangers from manufacturers

600

500

400

300

1

2

3

4

5

CW-IN CW-MID CW-OUT JW-IN JW-OUT EXH-IN EXH-OUT

Main points in the ORC sytem

b

149

30 Simulating results Parameters of heat exchangers from manufacturers

20

148 147 146 145

119.0

31

Heat recovered from jacket water[KW]

15

10

5

0

118.5

30 29

118.0

28

117.5 27

117.0

26

24 1

2

3

4

5

CW-IN CW-MID CW-OUT JW-IN JW-OUT EXH-IN EXH-OUT

Heat recovered from exhaust gas[KW]

Pressure[bar]

25

Total amount of heat recovered by the ORC system [KW]

Temperature[K]

700

shown in Fig. 4, the total heat absorbed by the ORC, and the heat recovered from exhaust gas and from jacket water all vary not much with changing of evaporating pressure. The highest fluctuation is less than 2 kW. So it is sensible to replace these three items of heat with their average values within the variation of evaporating pressure. Then it is calculated that, under the rated engine condition, the average amount of total heat absorbed is about 147 kW, the heats absorbed from exhaust gas and from jacket water are 118.1 kW and 29 kW, accounting for 4/5 and 1/5 of the total amount respectively. In order to further clarify heat recovery capability of the ORC system, the concept of waste heat utilization rate (UR) is proposed. The waste heat UR is the ratio of heat absorbed from a certain source by the ORC system to maximum heat available in this heat source. As for the two heat sources involved in this paper, two URs are concerned, i.e. waste heat URs of exhaust gas and of jacket water. It should be noted that, the maximum heat available in exhaust gas is the heat rejected under the hypothesis that the gas is cooled to 298 K, and 333 K is set for jacket water. Then the URs of exhaust gas and of jacket water are 73.7% and 9.3% under the rated engine condition. Similar calculations are done for all five engine conditions. The results are listed in Table 5. The reduction of the engine load (from condition 1 to condition 5) surely results in the reduction in temperature and in mass flow of the heat resources e exhaust gas and jacket water. With these reductions, total heat absorbed by the ORC decreases significantly, as shown in the 1st column in Table 5. From the 2nd and the 3rd columns, the average ratio of heat recovered from exhaust gas keeps falling, while that of jacket water keeps rising. The reason can be found from Table 1. It shows that with the reduction of engine load, the temperature and mass flow of exhaust gas decrease greatly, but those of jacket water decrease only slightly. That is to say, the heat of exhaust gas decreases much faster than the heat in jacket water does. It then causes similar changes in the heat absorbed. But in general, heat absorbed from

26

28

30

32

34

Evaporating Pressure[bar]

Main points in the ORC sytem Fig. 3. Comparison between simulating results and heat exchangers’ real parameters on (a) temperatures and (b) pressures.

Fig. 4. Variation of heat absorbed from exhaust gas and from jacket water, and total heat absorbed by the ORC system with evaporating pressure under the rated DE condition.

286

G. Yu et al. / Energy 51 (2013) 281e290

Table 5 Waste heat recovery of the ORC system under different engine conditions.

Condition Condition Condition Condition Condition

1 2 3 4 5

Total heat recovered of the ORC system [kW]

The average ratio of heat recovered from jacket water [%]

The average ratio of heat recovered from exhaust gas [%]

The average UR for waste heat in jacket water [%]

The average UR for waste heat in exhaust gas [%]

159.38 147.12 136.51 117.42 88.00

18.40 19.74 21.77 25.66 33.29

81.60 80.26 78.23 74.34 66.71

9.25 9.29 9.61 9.92 9.90

72.29 73.68 74.46 74.64 76.19

exhaust gas is all the time much more than that from jacket water. Because high grade heat in exhaust gas is definitely easier to be recovered than low grade heat in jacket water. From the last two columns in Table 5, URs of waste heat in exhaust gas and in jacket water all change slightly, the value of the former is around 75%, and that of the later is about 9.5%. It can be concluded that, the ORC system can recover heat in exhaust gas effectively, but can’t behave well in absorbing waste heat in jacket water. 5.2. Expansion power and recovery efficiency As shown in Fig. 5, the expansion power and recovery efficiency change in the same way, because heat absorbed by the ORC system is almost constant under certain engine condition, thus the changing regularity of expansion power determines that of the system efficiency. Both of them appear to increase first and then decrease with increasing evaporating pressure. The maximum expansion power and recovery efficiency are gained under the pressure of around 31 bar and are about 14.5 kW and 9.2%. This regularity is explained as follows: when the evaporating pressure increases from 25 bar to 33 bar, the volume flow of inlet stream (stream3) of expander reduces gradually from 4.5e3 cum/s to 4.0e4 cum/s. When the evaporating pressure is around 31 bar, the volume flow is about 3.3e3 cum/s. From Table 3, the pressure ratio of expander (the ratio of inlet pressure to outlet pressure) reaches its maximum value of about 11.7, meanwhile the isentropic efficiency is as high as 0.6. That means, enthalpy difference between inlet stream and outlet stream of the expander is maximal, and exergy loss is relatively low, so maximum expansion power is output. When evaporating pressure is below 30 bar, pressure ratio of expander is smaller, the enthalpy difference is smaller and thus expansion power is reduced. When evaporating pressure is above

31 bar, though expander’s pressure ratio is still high, its isentropic efficiency is as low as only 0.46, which means the exergy loss increases and the expansion power is also reduced. It can be concluded from Fig. 6 that peak value of expansion power under each engine condition moves to the left side (low pressure direction) gradually with decreasing of engine load (from condition 1 to condition 5). Under the condition 5 and condition 4, expansion power decreases constantly with the increase of evaporating pressure, and the maximum power they get are only 7.2 kW and 11.3 kW. The reason is that the quantity and quality of the heat within heat resources are quite low under these two conditions; under condition 3 and condition 2, expansion power appears to increase firstly and then decrease with the increase of evaporating pressure. The maximum power of condition 3 is gained when evaporating pressure is 28 bar, which is about 13.7 kW. While for condition 2 with a higher load, maximum power is obtained when evaporating pressure is about 30 bar, which is about 14.5 kW; when diesel engine runs under condition 1 with high load, the expansion power increases constantly with the increase of evaporating pressure and it is up to 15.5 kW when the evaporating pressure is 33 bar. The reasons of these regularities are the same with that is explained for Fig. 5. Namely, they are all decided by the combined effect of the pressure ratio and isentropic efficiency of the expander. As for the recovery efficiencies in Fig. 7, they change similarly with corresponding expansion power. With the decreasing of engine load from condition 1 to condition 5, maximum values are 9.1%, 9.2%, 9.4%, 9.1% and 7.4% successively. They do not reduce gradually as the peaks of expansion power do. Take condition 2 and condition 3 for instance, their peak expansion power are lower than that of condition 1, but their peak recovery efficiencies are higher

16 15.0

10.0

14.5

9.0

13.0 12.5

8.5

12.0 8.0

11.5 11.0

Recovery Efficiency[%]

13.5

7.5

10.5

Expansion Power [ KW]

14 9.5

14.0

Expansion Power[KW]

Condition 1 Condition 2 Condition 3 Condition 4 Condition 5

15

13 12 11 10 9 8 7

10.0

7.0 24

26

28

30

32

34

Evaporating Pressure[bar] Fig. 5. Variation of expansion power and recovery efficiency with evaporating pressure under the rated DE condition.

24

26

28

30

32

Evaporating Pressure[KW] Fig. 6. Variation of expansion power with evaporating pressure under five DE conditions.

G. Yu et al. / Energy 51 (2013) 281e290

Fig. 7. Variation of recovery efficiency with evaporating pressure under five DE conditions.

than that of condition 1, since recovered heat under these two conditions are much less. Overall, the ORC system gets relative high expansion power and recovery efficiencies under conditions 1, 2 and 3. 5.3. Exergy flow losses and exergy efficiency An appropriate exergy analysis will give a better understanding of the irreversibility of the ORC system, and is indispensable for a complete evaluation of the whole ORC system. Six items of exergy flow losses of the ORC system under the rated engine condition is plotted in Fig. 8. Orderly, they are (1) exergy flow losses in the heat exchanging process between exhaust gas and working fluid I_EXHF ; (2) exergy flow losses in the preheating process between jacket water and working fluid I_PREHE ; (3) exergy flow losses due to non-isentropic vapor expansion in the expander I_ EXP ; (4) exergy flow losses in the condensing process between working fluid and cooling water I_ COND ; (5) exergy flow losses that are carried out through output cooling water I_CW ; (6) exergy flow losses due to non-isentropic compression of working fluid pump I_ P . Among the six items of exergy flow losses, I_EXHF is

287

Fig. 9. Influence of DE conditions on exergy flow losses of the ORC system.

the highest. One reason is that four heat exchangers (gaseoil heat exchanger, HE1, HE2 and HE3) are included in the heat exchanging process between exhaust gas and working fluid, and the sum of their exergy flow losses is surely high. On the other hand, temperature differences in this process are rather great, resulting in severe irreversibility. The second and the third highest exergy flow losses are I_COND and I_ EXP . The other three items of exergy flow losses are as low as below 10 kW. Besides, under the other four engine conditions, the rankings are the same as under the rated condition. So it is critical to reduce these first three items of exergy losses to lower the irreversibility of the ORC system. After exergy calculations of all the five engine conditions, it shows that, each item of exergy flow loss does not change much with increasing of evaporating pressure, just as shown in Fig. 8 under the rated condition. So the average values are calculated to replace the items of exergy flow losses correspondingly. For example, the above six items of exergy flow losses of the ORC system under the rated engine condition are replaced with the average value 20.6 kW, 2.7 kW, 6.6 kW, 19.0 kW, 4.1 kW and 0.2 kW respectively. Then average values under each engine condition are gathered in Fig. 9, showing the influence of engine conditions on average exergy flow losses of the ORC system. Overall, the reduction of

40

Exergy Flow Losses under The Rated Condition [KW]

35 30

EXH-F PRE-HE EXPANDER CONDENSE CW PUMP

25 20 15 10 5 0 24

26

28

30

32

34

Evaporating Pressure[bar] Fig. 8. Exergy flow losses of the ORC system under the rated DE condition.

Fig. 10. Variation of exergy efficiency with evaporating pressure under five DE conditions.

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Fig. 11. Increment of thermal efficiency by integrating the bottoming ORC system to DE.

engine load (from condition 1 to condition 5) results in downgrading of waste heat of exhaust gas and of jacket water (especially of the exhaust gas), and thus exergy from the heat resources falls, and total exergy flow loss of the ORC system drops consequently. As is shown in Fig. 9, obvious drops occur in I_EXHF , I_COND and I_CW . Because of the reduction of engine load, the temperature difference between the exhaust gas and the working fluid decreases, and therefore I_EXHF decreases. On the other hand, with downgrading of waste heat, the highest temperature e the inlet temperature in front of the expander e of the working vapor falls and then the temperature after expansion falls. Then the temperature difference between the working vapor and the cooling water decreases, therefore the I_COND decreases. Decreases of I_EXHF and I_COND are the main reasons for the drops of the total exergy flow loss. Besides, since less heat is condensed and the outlet temperature of the

cooling water is lower, the I_ CW also drops a lot. As for I_PREHE, it almost keeps constant, since the temperature of outlet jacket water does not change much, and heat exchanging within the pre-heater is stable. Also, I_EXP and I_P do not vary much, because their entropy differences between inlet and outlet steams are very small as seen from the calculating results. As explained above, heat absorbed by the ORC system is almost constant under certain engine condition, so is exergy. Therefore, the changing regularity of expansion power determines the changing trends of both the recovery efficiency and the exergy efficiency, so the regularities of the expansion power, recovery efficiency and exergy efficiency are quite similar under certain engine condition by comparing Figs. 6, 7 and 10. But the difference occurs at the peak values, and with decreasing of engine load from condition 1 to condition 5, peak values of exergy efficiencies are 20.9%, 21.7%, 22.9%, 23.2% and 22.3% successively, as shown in Fig. 10. Under condition 4 and condition 5, the expansion power and recovery efficiencies are not high, but their exergy efficiencies are quite high, because waste heats under these conditions are not much and the exergy entered the system are low, which are only 49 kW and 33 kW, thus high exergy efficiencies are obtained. Oppositely, in condition 1, the expansion power and recovery efficiency are rather high, but its exergy efficiency is low, because large amount of exergy (about 74 kW) is absorbed into the system. Besides, exergy efficiencies of condition 2 and condition 3 are still high. In a word, by analyzing Figs. 6e8, the overall performance of the ORC system including its expansion power, recovery efficiency and exergy efficiency are relatively higher in condition 2 and condition 3 than that in other three conditions. 5.4. Performance of the DE-ORC combined system Performance of the combined DE-ORC system is firstly showed in Fig. 11 by variation of increments in thermal efficiency of the combined system to the original diesel engine. With the increase of

Fig. 12. Energy distribution of the DE and the DE-ORC combined system.

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evaporating pressure, increments appear to rise constantly in condition 1, increase firstly and then decrease in condition 2 and in condition 3, and decrease constantly in condition 4 and condition 5. Maximal efficiencies under each condition are pointed out and connected to show the greatest working potential of the ORC system. They are, 5.7% of the increment in condition 1 under 33 bar, 5.8% in condition 2 under 30 bar and 31 bar, 6.1% in condition 3 under 28 bar, 6.0% in condition 4 under 25 bar and 5.5% in condition 5 under 25 bar. Besides, average values of increment under each condition are calculated and noted, they are 4.8%, 5.2%, 5.5%, 5.3%, 5.2% from conditions 1 to 5. Fig. 12 reveals the energy distribution before and after the integration of the bottoming ORC to the DE by gathering the average value of each item within the range 25e33 bar. The pump power and other secondary energy losses are ignored. As marked in the left side, the DE power accounts for only around 40% of the fuel energy in the five conditions. Most fuel energy is lost through exhaust gas and jacket water, especially in low load condition. As marked in the right side, the integration of the bottoming ORC modifies the original energy distribution. Expansion power gained by the ORC increase the useful power without adding fuel, and the thermal efficiency is thus uplifted. It is very meaningful in this bottleneck period of the engine efficiency lifting. As shown in the figure, heat recovery of exhaust gas is much more efficient than that of the jacket water. More suitable system should be explored in the future work to recover more low-grade heat from jacket water, for example the dual loop ORC [30]. It also shows that only a little energy of the heat absorbed converts into expansion power, the remaining is lost mainly through condensing. So the ORC system should be optimized to be more efficient in the future. 6. Conclusions A detailed ORC system is modeled and validated for a diesel engine to recover waste heat in exhaust gas and in jacket water. Comprehensive thermodynamic analyses are conducted and main conclusions can be drawn as follows: (1) The ORC system can recover heat in exhaust gas effectively, but behaves badly in recovering heat in jacket water. URs for waste heat in exhaust gas and in jacket water are about 75% and 9.5%. (2) Expansion power and recovery efficiency change similarly under each engine condition. The ORC system gets relatively high power (15.5 kW, 14.5 kW and 13.7 kW) and efficiencies (9.1%, 9.2% and 9.4%) under conditions 1, 2 and 3. (3) The first three exergy losses occur in the heat exchanging process between exhaust gas and working fluid, in the condensing process between working fluid and cooling water and in the non-isentropic vapor expansion in the expander. (4) The overall performance of the ORC system including its expansion power, recovery efficiency and the exergy efficiency are relatively higher in condition 2 and condition 3 than that in the other three conditions left. (5) Up to 6.1% of increment in thermal efficiency can be obtained by the combined DE-ORC system. If given the rated condition (condition 2), up to 5.8% of increment can be acquired by setting the evaporating pressure at 30 bar or 31 bar. Acknowledgements This work was supported by a grant from the National Natural Science Foundation of China (No. 51206117), and the National Basic Research Program of China (973 Program) (No. 2011CB707201).

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Nomenclature

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