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A novel cascade organic Rankine cycle (ORC) system for waste heat recovery of truck diesel engines
Energy Conversion and Management 138 (2017) 210–223
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
A novel cascade organic Rankine cycle (ORC) system for waste heat recovery of truck diesel engines Tao Chen a, Weilin Zhuge a,b, Yangjun Zhang a,b,⇑, Lei Zhang a a b
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China Collaborative Innovation Center of Electric Vehicles in Beijing, China
a r t i c l e
i n f o
Article history: Received 22 October 2016 Received in revised form 28 December 2016 Accepted 22 January 2017
Keywords: Waste heat recovery Organic Rankine cycle (ORC) Diesel engine Cascade expansion
a b s t r a c t Waste heat recovery (WHR) of engines has attracted increasingly more concerns recently, as it can improve engine thermal efficiency and help truck manufacturers meet the restrictions of CO2 emission. The organic Rankine cycle (ORC) has been considered as the most potential technology of WHR. To take full advantage of waste heat energy, the waste heat in both exhaust gases and the coolant need to be recovered; however, conventional multi-source ORC systems are too complex for vehicle applications. This paper proposed a confluent cascade expansion ORC (CCE-ORC) system for engine waste heat recovery, which has simpler architecture, a smaller volume and higher efficiency compared with conventional dual-loop ORC systems. Cyclopentane is analyzed to be regarded as the most suitable working fluid for this novel system. A thermodynamic simulation method is established for this system, and off-design performance of main components and the working fluid side pressure drop in the condenser have been taken into consideration. System performance simulations under full engine operating conditions are conducted for the application of this system on a heavy-duty truck diesel engine. Results show that the engine peak thermal efficiency can be improved from 45.3% to 49.5% where the brake specific fuel consumption (BSFC) decreases from 185.6 g/(kW h) to 169.9 g/(kW h). The average BSFC in the frequently operating region can decrease by 9.2% from 187.9 g/(kW h) to 172.2 g/(kW h). Compared with the conventional dual-loop ORC system, the CCE-ORC system can generate 8% more net power, while the total volume of heat exchangers is 18% less. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The interests in truck diesel engine waste heat recovery (WHR) has grown dramatically recently as the CO2 emission regulation becomes stricter. Many researchers [1–5] believe that the WHR is the most potential technology to improve the engine thermal efficiency since more than half of the fuel energy is dissipated as waste heat. For a conventional diesel engine [6], the peak efficiency can be up to 43%, while about 27%, 20%, 7% of the fuel energy is taken away by exhaust gases, coolant and the intercooler respectively; furthermore, a higher proportion of fuel energy will be dissipated as waste heat when engines operate under partial engine load conditions. Several technologies have been researched to recover the waste heat of truck diesel engines, such as the thermoelectric generators (TEG), the turbo-compound system and the ORC system. The TEG ⇑ Corresponding author at: State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China. E-mail address: [email protected] (Y. Zhang). http://dx.doi.org/10.1016/j.enconman.2017.01.056 0196-8904/Ó 2017 Elsevier Ltd. All rights reserved.
system seems to be the simplest one among these technologies but it has the disadvantage of lowest efficiency (<4%) [7]. Hence, it cannot be a good choice until high efficiency thermoelectric materials are available. The turbo-compound system will cause higher engine backpressure and cannot utilize all the waste heat of engines, such as coolant waste heat, though this system is simple to be applied and can improve the engine efficiency by 8% under certain conditions [4]. Compared with other technologies, the ORC system has the highest potential overall efficiency [8] with a suitable size for trucks, and it is able to recover the waste heat energy in exhaust gases, coolant and the intercooler. Some studies [9–12] have been done on the ORC systems which only recover the waste heat in exhaust gases. In these studies, the working fluid selection and system performance analysis have been researched. With the purpose of recovering more waste energy and further improving engine efficiency, some researchers turned to the multi-heat-source ORC system which can recover both exhaust gases and the coolant. The preheating ORC system and the dual-loop ORC system are two main types of multi-heatsource ORC systems currently.
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Nomenclature Acronyms CCE confluent cascade expansion EGR exhaust gas recirculation GWP global warming potential HT high temperature LT low temperature NBP normal boiling point ODP ozone depletion potential ORC organic Rankine cycle WHR waste heat recovery TEG thermos-electric generator Latin and Greek symbols A area [m2] Cp isobaric heat capacity [kJ/(kg °C)] Cs isentropic velocity [m/s] dp pressure drop [kPa] D diameter [m] Ds specific diameter [mm] h enthalpy [kJ/kg] I exergy loss [kW] k specific heat ratio [–] m mass flow rate [kg/s] M Mach number [–] N rotating speed [r/min] p pressure [kPa] P power [kW] Q heat energy [kW] R gas constant [J/(kg °C)] s entropy [kJ/(kg °C)] SR blade speed [–]
In the preheating ORC system (Fig. 1), working fluid is preheated by the coolant, and then it absorbs the waste heat in exhaust gases. Arias et al. [13] and Yu et al. [14] studied the preheating ORC system and showed that only 5% of the coolant waste heat can be absorbed if evaporating temperature of ORC system is higher than coolant temperature. Ringler et al. [15] have studied the preheating ORC system on their test bench, and their results showed that the gasoline engine power output could be improved
Fig. 1. Structure of a typical preheating ORC system.
T DT U UA v V y
g
temperature [°C] temperature difference [°C] rotor tip velocity [m/s] heat transfer rate [W/°C] velocity [m/s] volume flow rate [m3/s] pump head [kJ/kg] efficiency [–]
Subscripts and superscripts a refers to ambient con refers to condensers cool refers to coolant eff refers to effective ev refers to evaporators g refers to gas HT refers to high temperature in refers to inlet l refers to liquid LT refers to low temperature h net refers to net power out refers to outlet ph refers to two-phase region pump refers to pump s refers to an isentropic process tot refers to total tur refers to turbines n refers to nominal nozzle refers to nozzle 0 refers to total 1–8 refers to locations of CCE-ORC
by 10% with this ORC system. Vaja and Gambarotta [16] analyzed the preheating ORC system and gave the conclusion that the working fluids with low critical temperatures as well as bell shaped vapor lines were suitable for the preheating ORC system. Kim et al. [17] designed a preheating ORC system with regenerators and it improved ORC net power output by 35.6% compared with a conventional preheating ORC system. In order to utilize the coolant waste heat effectively, the cascade ORC system was developed. Fig. 2 shows a typical cascade ORC system for engine waste heat recovery. There are two ORC loops recovering the waste heat in coolant and exhaust gases respectively; meanwhile, the condenser of high-temperature (HT) loop is used as one of the evaporators in the low-temperature (LT) loop. Shu et al. [18] studied a cascade ORC system applied on a vehicle diesel engine, using water as the working fluid for HT loop. Their results showed that R1234yf was the best working fluid for LT loop and it could output 36.77 kW net power in theory when the engine power was 235.8 kW. Song and Gu [19,20] studied a cascade ORC system applied on a heavy-duty diesel engine, and they conducted that R236fa was the best choice for the LT loop while cyclohexane and water were the proper working fluids for the HT loop. This system can improve engine power by 11.2–11.6%. Huang et al. [21] compared the typical cascade ORC system with another system, in which waste energy in exhaust gases was absorbed by HT loop and LT loop in turn, and the results showed that the performance of typical cascade ORC system was slightly better. Kulkarni and Sood [22] used R245fa and R236fa for HT loop and LT loop respectively, and they analyzed the system performance under different engine operating conditions. The results showed that the cascade ORC system can output 7.26–14.16 kW net power and its overall thermal efficiency was about 10%. Wang, Zhang et al. [23,24] pro-
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on a heavy-duty truck diesel engine under both the system design condition and full engine operation conditions. Finally, the CCEORC system performance is compared with the conventional dual-loop ORC system. 2. CCE-ORC system description
Fig. 2. Structure of a dual-loop ORC system.
posed a cascade ORC system, in which LT loop working fluid absorbed heat from intercooler, HT loop condenser and coolant successively. This system can improve the power of a light-duty diesel engine by 19–22% and promote the power of a gasoline engine by 14–16% when heat transfer loss is assumed to be minimum. Yang et al. [25] proposed a modified system, in which a regenerator was applied in the HT loop, based on the system proposed by Wang and Zhang [23,24]. This system can achieve the largest net power of 27.85 kW and reduce the BSFC by 4%. The conventional dual-loop ORC systems are too complex for vehicle engine applications, since plenty of space is needed to place four heat exchangers and two complete loops. This paper proposed a novel confluent cascade expansion ORC (CCE-ORC) system [26] for recovering multi-source waste heat of a truck engine. It has a simpler architecture and only one kind of working fluid is needed. Firstly, thermodynamic models including component off-design performance models for the CCE-ORC system are established. And then, the system performance and the improvement on the engine fuel efficiency are analyzed for the application of the system
The cycle configuration and T-S diagram of the CCE-ORC system are shown in Fig. 3. There are two branches (high-temperature branch and low-temperature branch) to recover waste heat of exhaust gases and coolant respectively. In the HT branch, a part of working fluid is compressed to higher pressure so that high evaporating temperature can be achieved to match the exhaust temperature. Then this part of working fluid is heated into superheated state by exhaust gases and flows to the HT turbine. In the LT branch, the other part of the working fluid is pumped to lower pressure so that the evaporating temperature in this branch is lower than coolant temperature, then the compressed working fluid absorbs all the waste heat energy of coolant and evaporates to saturated vapor phase state in the LT evaporator. The working fluid after the LT evaporator and that after the HT turbine mix together, and then the fluid flows into the LT turbine. After that the working fluid flows into the condenser and is condensed into saturated liquid phase state by air. Only one kind of working fluid, one reservoir and three heat exchangers are needed in this system, so this system is compact enough for a multi-source ORC system. Compared with conventional dual-loop ORC system, the intermediate heat exchanger is not needed in this system and the reservoir for HT loop is also not needed while the volumes of other components maintains the same level, so the total volume of CCE-ORC system can be smaller. The HT branch can absorb more energy from the exhaust gases than the HT loop in dual-loop ORC systems, and the exergy loss in the mixing process is less than that in the intermediate heat exchanging process; as a result, CCE-ORC system can output more net power. Meanwhile, the LT branch can recover all the waste heat in coolant so the original coolant radiator can be replaced. It means that the ORC condenser can be laid at the position where the original coolant radiator used to be, and the working fluid can be cooled by air directly. Radial-inflow turbines are used in this system, because this type of expander has the advantages of light weight, small size, mature manufacturability and high efficiency [27]. Although the high
Fig. 3. Cycle layout and T-S diagram of the confluent cascade expansion (CCE) ORC system.
T. Chen et al. / Energy Conversion and Management 138 (2017) 210–223
rotating speed is usually considered as a disadvantage, it has been conducted that a low specific speed turbine can be designed to reduce the rotating speed [28].
3. Performance simulation methods The energy and exergy analysis [29] and off-design performance of components [30,31] are important while analyzing system performance. The full operating condition performance simulation method consists of two steps, including calculating design point performance and predicting off-design performance under full operating conditions. The flow diagram of this method is shown in Fig. 4. Step 1: calculating the inlet and outlet conditions of each component at design point to determine main design parameters of each component, such as effective throat areas of turbines and
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heat transfer rates of evaporators. In this step, pinch point temperature different (PPTD) of evaporators and efficiency of pumps as well as turbines are given, and mass flow rate is calculated by system thermodynamic model. All the given parameters at design point are shown in Table 1. Step 2: calculating component performance at off-design points and simulating the system full operating condition performance. In this step, flow characteristics of pumps and turbines are used to determine mass flow rate, and then pump efficiency, turbine efficiency and heat transfer quantity are calculated by off-design models of components to evaluate the system performance. The system net power output and exergy loss are calculated by system thermal model (in Section 3.1) when the heat transfer quantity of each evaporator, efficiency and flow characteristic of pumps and turbines have been calculated by component offdesign models (in Section 3.2).
Fig. 4. Flow diagram of system performance simulation method.
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Table 1 The value of all the given parameters at design point.
gpump;HT ¼
Parameter
Value
PPTD of HT evaporator PPTD of LT evaporator Superheating temperature of HT branch Superheating temperature of LT branch Condensing temperature Turbine efficiency Pump efficiency Pressure drop in each heat exchanger
30 °C 10 °C 20 °C 0 °C 50 °C 80% 50% 10 kPa
The assumptions in models are given below: (1) Kinetic energy of working fluids is ignored; (2) Heat loss and pressure drop in all pipes are ignored; (3) Mixing process is an isobaric process following the energy conservation law with no heat loss; (4) Condensing temperature is a constant value: 50 °C. These models are established in the Matlab environment, and the working fluid properties reference the REFPROP database. 3.1. System thermal model The thermodynamic model of the whole system is established, and the pressure drop is taken into consideration. Working fluid side pressure drop of the condenser has a negative effect on system performance because it will influence turbine expansion ratio and pump pressure ratio. This effect will become more significant when condensing pressure lowers. Under the same condensing temperature, the working fluid with high critical temperature usually has a lower condensing pressure. The total mass flow rate equals to the summation of that in two branches (Eq. (1)), and the mass flow rate of each branch is calculated by the energy conservation equation of each evaporator, after the enthalpy difference between evaporator inlet and outlet of the working fluid and the heat transfer quantity calculated.
mtot ¼ mHT þ mLT
ð1Þ
In the HT branch: The isentropic efficiency of the pump is given and the performance of the pump is calculated by the equations below:
h4s h1 h4 h1
ð2Þ
P pump;HT ¼ mHT ðh4 h1 Þ
ð3Þ
Ipump;HT ¼ mHT T a ðs4 s1 Þ
ð4Þ
The evaporator model with consideration of pressure drop is shown in Fig. 5. It is assumed that all the pressure drop of heat exchangers occurs at the inlet of heat exchangers and it is an isenthalpic process. So the assumptive process in the heat exchanger consists of two steps: 4–40 is an isenthalpic process where pressure goes down; 40 –5 is an isobaric process where working fluids absorb heat from exhaust gases. The mathematic model is shown below:
p40 ¼ p4 dpeV;HT
ð5Þ
h40 ¼ h4
ð6Þ
p40 ¼ p5
ð7Þ
Q eV;HT ¼ mHT ðh5 h40 Þ ¼ mexh Cpexh ðT exh;in T exh;out Þ
ð8Þ
IeV;HT ¼ mHT T a ðs5 s4 Þ mexh T a ðsexh;in sexh;out Þ
ð9Þ
The isentropic efficiency of the turbine is given and the performance of the high-temperature turbine is calculated by equations below:
gtur;HT ¼
h5 h6 h5 h6s
ð10Þ
P tur;HT ¼ mHT ðh5 h6 Þ
ð11Þ
Itur;HT ¼ mHT T a ðs5 s6 Þ
ð12Þ
In the LT branch, the models of components are shown here:
gpump;LT ¼
h2s h1 h2 h1
ð13Þ
Ppump;LT ¼ mLT ðh2 h1 Þ
ð14Þ
Ipump;LT ¼ mLT T a ðs2 s1 Þ
ð15Þ
p20 ¼ p2 dpeV;LT
ð16Þ
Fig. 5. Evaporator model with the consideration of working fluid side pressure drop.
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h20 ¼ h2
ð17Þ
p20 ¼ p3
ð18Þ
Q eV;LT ¼ mLT ðh3 h20 Þ ¼ mcool Cpcool ðT cool;in T cool;out Þ
ð19Þ
IeV;LT ¼ mLT T a ðs3 s2 Þ mcool T a ðscool;in scool;out Þ
ð20Þ
where y0;n is the pump head at nominal rotating speed when no flow rate is allowed, yn is the pump head under design point condition, N pump;n is nominal rotating speed. The off-design pump efficiency defined as function of flow rate and rotating speed is shown in Eq. (37).
gpump ¼
gpump;n V 2pump Npump;n
The model for the LT turbine is shown here:
V 2pump;n
Npump
2
þ2
gpump;n V pump Npump;n V pump;n
Npump
ð37Þ
p3 ¼ p6 ¼ p7
ð24Þ
where gpump;n is the pump nominal efficiency which is also the design efficiency. The evaporator model is based on Logarithmic Temperature Mean Difference (LMTD) method, LTMD is defined in Eq. (38) and exchanging heat quantity is defined as function of LTMD, as shown in Eq. (39) [33]. The whole evaporator model consists of three parts (Eq. (40)), liquid phase state part, two-phase state part and gas phase state part, and heat capacity of working fluid in each part is assumed to be constant. The condenser model is simpler than evaporator model and condensing temperature is assumed to be constant as adequate cooling air is available.
mHT h6 þ mLT h3 ¼ mtot h7
ð25Þ
DT LTMD ¼
Imix ¼ mHT T a ðs7 s6 Þ þ mLT T a ðs7 s3 Þ
ð26Þ
gtur;LT ¼
h7 h8 h7 h8s
ð21Þ
Ptur;LT ¼ mtot ðh7 h8 Þ
ð22Þ
Itur;LT ¼ mtot T a ðs7 s8 Þ
ð23Þ
The mixing process of working fluids obeys the energy conservation law:
The condenser model is shown below:
DT max DT min lnðDT max =DT min Þ
ð38Þ
where DT min is the minimum one of the temperature differences at heat exchanger inlet and outlet, and DT max is the other one.
Q¼
X
UADT LTMD
ð39Þ
p70 ¼ p7 dpcon
ð27Þ
h70 ¼ h7
ð28Þ
UA ¼ UAl þ UAph þ UAg
p70 ¼ p8
ð29Þ
The pressure drop of these heat exchangers is proportional to the square of the working fluid mass flow rate.
Q con ¼ mtot ðh7 h8 Þ
ð30Þ
dp ¼ dpn ðm=mn Þ2
Icon ¼ Q con þ mtot T a ðs1 s8 Þ
ð31Þ
The effective throat area of the nozzle (Aeff ;nozzle ) is taken into consideration in the turbine model [34], and off-design efficiency is defined as a function of blade speed ratio (SR), as shown in Eq. (42) [35],
The net power of this ORC system is calculated by the equation follow:
Pnet ¼ Ptur;1 þ Ptur;2 P pump;HT Ppump;LT
ð32Þ
The total exergy loss consists of the eight parts mentioned above and another part of exergy loss in the exhaust gas discharged to the atmosphere (defined in Eq. (33)):
Iexh;out ¼ Q exh;out þ mexh T a ðsexh;out sT0 Þ Itot ¼
9 X I
ð41Þ
ð42Þ
ð33Þ ð34Þ
SR ¼
The turbine efficiency and pump efficiency at design point are given, and heat transfer quantity at design point is calculated when PPTD of each evaporator is given. The component off-design performance is calculated by the off-design models introduced in this section. Flow rate characteristics and efficiency characteristics are considered in this off-design pump model [32]. The pump head is defined in Eq. (35) and the function of flow rate, rotating speed and pump head is shown in Eq. (36)
2 V 2pump Npump;n 2 Npump;n y ¼ 2 ðyn y0;n Þ þ yo;n Npump V pump;n N pump
gtur ¼ gtur;n
2 ! 2SR SR SRn SRn
ð40Þ
where SRn is the nominal blade speed. The blade speed ratio is defined as the rotor tip velocity (U) divided by the isentropic velocity (C S ).
3.2. Component models
y ¼ hpump;out hpump;in
where UA is heat transfer rate of heat exchangers.
ð35Þ ð36Þ
U pNtur D=60 ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cs k1 2cp T 0;in 1 ðpout =p0;in Þ k
ð43Þ
The flow rate characteristics of two turbines are different as the HT turbine is a transonic turbine (the working fluid flow speed equals to the speed of sound at the nozzle throat) and the LT turbine is a subsonic turbine (the working fluid flow maintains lower than the speed of sound in the entire turbine) normally. For the transonic turbine, if effective throat area of the nozzle (Aeff ;nozzle ) is designed, mass flow rate can be solved by turbine inlet and outlet condition but not affected by the rotating speed [36], and Mach number at nozzle throat is almost a constant (M ¼ 1).
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kþ1 m RT 0;in =k k 1 2 2ðk1Þ M ¼M 1þ 2 Aeff ;nozzle p0;in
ð44Þ
For the subsonic turbine, rotating speed can influence turbine mass flow rate [34], because it will influence nozzle pressure ratio pnozzle . p0;in
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Table 2 Comparison of the present simulated results with Ref. [20]. Parameter
Table 3 Main parameters of the diesel engine.
Present results
Reference result [20]
Deviation (%)
HT loop Working fluid Evaporating temperature (°C) Absorbed heat load (kW) Mass flow rate (kg/s) Net power output (kW) Thermal efficiency
Cyclohexane 207.2 429.1 0.77 63.5 14.8%
Cyclohexane 207.2 432.2 0.8 64 14.8%
0.72 3.90 0.79 0.01
LT loop Working fluid Evaporating temperature (°C) Absorbed heat load (kW) Mass flow rate (kg/s) Net power output (kW) Thermal efficiency
R245fa 75.9 566.0 2.66 45.8 8.1%
R245fa 75.9 568.1 2.7 47.2 8.3%
0.37 1.50 3.06 2.57
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u !2 !kþ1 3 u 2k p2 k k u p p 0;in nozzle nozzle 4 5 m ¼ Aeff ;nozzle t ðk 1ÞRT 0;in p0;in p0;in k 2 0 !k1 13k1 k g 2 1 pnozzle 4 p out tur @1 A5 ¼ 1 p0;in 2SR gnozzle p0;in
Parameter
Value
Cylinder number Displacement Compression ratio Stroke Cylinder bore Rated power (speed) Peak torque (speed)
6 11 L 16.4 156 mm 123 mm 306 kW (1900 rpm) 2045 N m (1100 rpm)
Table 4 Engine test data at the ORC system design point conditions.
ð45Þ
Parameters
Value
Engine load [%] Engine speed [rpm] Engine torque [N m] Fuel consumption rate [g/kW h] Engine power [kW] Exhaust energy [kW] Coolant energy [kW] Exhaust mass flow rate [kg/s] Exhaust temperature [°C] Coolant temperature (inlet) [°C] Coolant temperature (outlet) [°C]
90 1400 1765.5 190.14 258.9 157.7 115.2 0.388 405 80 88
ð46Þ
where gnozzle is the nozzle isentropic efficiency. It has to be mentioned that if mtot is larger than maximum flow capacity of the LT turbine, a part of working fluid will be bypassed. 3.3. Model validation The validation of system model was done by using the equations to calculate a dual-loop ORC system in Ref. [20] and comparing the calculated results with reference results, because this system consists of all the components in CCE-ORC system and these components are simulated by the same mathematic models. That system is applied on a diesel engine whose power output is 996 kW, exhaust gas temperature is 300 °C, exhaust gas mass flow rate is 7139 kg/h, outlet coolant temperature is 90 °C, inlet coolant temperature is 65 °C, whose coolant mass flow rate is 6876 kg/h. The deviation of the present results compared with the reference results is less than 4% (shown in Table 2). It can be recognized that the thermodynamic models of those components in the CCE-ORC system are accurate enough to evaluate the system performance. 4. Results and discussions The performance of CCE-ORC system designed for a heavy-duty diesel engine is discussed in this section. Working fluid selection is discussed, and system performance at design point and full operating condition are simulated and analyzed.
4.1. Parameters of the diesel engine The studied truck diesel engine in this paper is a turbocharged and intercooled diesel engine without exhaust gas recirculation (EGR), and main parameters of this engine are shown in Table 3. The rated power is 306 kW at 1900 rpm, while the full-load engine torque is about 2000 N m in the range 1100–1400 rpm. The exhaust gas temperature is in the range 250–450 °C, and high temperature region is the high engine load region. The coolant outlet temperature is about 88 °C in all the conditions, while the coolant inlet temperature is in the range 78–86 °C. The exhaust mass flow rate is in the range 0.1–0.47 kg/s, and it is nearly proportional to the engine power. While the coolant mass flow rate is in the range 2–5 kg/s, and it is also proportional to the engine speed. The minimum BSFC is 185.6 g/(kW h) under the working condition (1200 rpm/1500 N m) where the engine efficiency is about 45%. Frequently working condition area of this engine is in the range, where rotating speeds are 1100–1400 rpm and engine loads are within 50–90%, and maximum engine power condition in this area is chosen as the design point condition (shown in Table 4). If the heat transfer capacity of heat exchangers and the flow capacity of turbines can meet the demand of the design point, the system can operate well in the engine frequently working condition areas and the maximum pressure will also be kept in the acceptable range. Working fluid is selected based on the design point condition.
Table 5 Properties of the working fluids. Name
Chemical formula
Molecular NBP Critical Critical Thermal stability GWP ASHRAE std Slope mass (g/mol) temperature (°C) temperature (°C) pressure (MPa) temperature (°C) (100 yr) 34 safety class
R134a [37,38] Butane [37,39] R245fa [37,40] R1233zd-e [39,41] Pentane [37,42] Cyclopentane [37,40]
CH2FCF3 CH3CH2CH2CH3 CF3CH2CHF2 CF2CH@CHCl CH3CH2CH2CH2CH3 A(CH2)5A
102.03 58.12 134.05 130.5 72.15 70.13
26.1 0.5 15.1 18.0 36.1 49.4
101.1 152.0 154.0 165.6 196.6 238.6
NBP: normal boiling point; GWP: global warming potential (for 100 years’ integration).
4.06 3.8 3.65 3.57 3.37 4.51
368 310 250 200 280 275
1370 20 1050 7 20 11
A1 A3 B1 A1 A3 –
Wet Dry Dry Dry Dry Dry
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4.2. Working fluid selection Working fluid selection should follow the criteria below: (1) The ozone depletion potential (ODP) index of the working fluid must be zero; (2) The critical temperature should be higher than 100 °C to achieve high evaporating temperature and high efficiency; (3) The normal boiling point (NBP) temperature should be below 50 °C, to make sure that the ORC system operating pressures are always higher than atmosphere. It has to be mentioned that combustible fluids are also taken into consideration in this study. As a result, six organic fluids, whose properties are shown in Table 5, are selected as candidates among the working fluids mentioned in Ref. [37]. Since there is a mixing process after the LT evaporator, the superheating temperature of working fluid at the inlet of LT turbine is high enough to make sure that the turbine works safely even for the wet fluid R134a. The most suitable one would be determined by comparing these fluids in term of the net power output. System performance of these six working fluids is calculated and the system net power output as a function of hightemperature branch evaporating temperature is shown in Fig. 6 (a). The net power output increases as the evaporating temperature increases because of the exergy loss decreasing in
high-temperature evaporator (Fig. 6(b)). It means that critical temperature is an important parameter for working fluid, because it limits the maximum evaporating temperature of a subcritical ORC system. As a result, cyclopentane is considered as the most suitable working fluid for this ORC system, since it has the highest critical temperature and can output the maximum net power.
Table 6 The ORC system performance at design point. Parameter
Value
Mass flow rate in HT branch Mass flow rate in LT branch Net power output Total exergy loss Thermal efficiency Exergy efficiency HT turbine power output LT turbine power output HT pump power input LT pump power input HT evaporator heat transfer quantity LT evaporator heat transfer quantity Condenser heat transfer quantity Condensing pressure HT turbine pressure ratio LT turbine pressure ratio
0.21 kg/s 0.28 kg/s 29.0 kW 46.1 kW 11.65% 38.62% 21.9 kW 9.0 kW 1.9 kW 0.1 kW 133.4 kW 115.2 kW 219.7 kW 113.8 kPa 16.84 1.72
Fig. 6. ORC system net power output and exergy loss in high-temperature evaporator as function of evaporating temperature of high-temperature branch.
Fig. 7. Exergy loss distribution at design point.
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Table 7 Sensitivity analysis of main design parameters at design point. Parameter
Variation considered in the parameter
Resulting variation in system net power output
HT evaporating temperature PPTD of HT evaporator PPTD of LT evaporator Condensing temperature Condenser pressure drop HT pump isentropic efficiency LT pump isentropic efficiency HT turbine isentropic efficiency LT turbine isentropic efficiency
±5 °C ±5 °C ±5 °C ±5 °C ±10 kPa ±10%
±0.54% 1.27% 3.86% 7.75% 4.81% ±2.34%
±10% ±10%
±0.11% ±8.50%
±10%
±4.77%
4.3. Performance at design point This ORC system performance at design point is calculated by the simulation method and the design parameters have been given in Table 1, and cyclopentane is chosen as the working fluid. The LT evaporating temperature is calculated by the simulation method. As the LT evaporator has to absorb all the waste heat in coolant and do not influence the coolant inlet temperature, the LT
evaporating temperature can be calculated when the PPTD in the LT evaporator and the working fluid superheating temperature at evaporator outlet have been given. High-temperature branch evaporating temperature is set at 215 °C, so the maximum pressure under all the operating conditions can be kept under the critical pressure (4.5 MPa), to make sure that the system operates safely and functions well. The system performance and component operating condition at the design point are shown in Table 6. The net power output is 29.0 kW and the total exergy loss is 46.1 kW. The thermal efficiency of this system is 11.65% and the exergy efficiency is 38.62%. The HT turbine pressure ratio is 16.84 so a transonic turbine should be applied in this position, while the LT turbine pressure ratio is 1.72 and a subsonic turbine should be applied. The mass flow rate of HT turbine is about half of that of the LT turbine while the HT turbine generates much more power than the LT turbine. The power consumed by the HT pump is 1.9 kW, but the LT pump consumes much fewer. The condenser heat transfer quantity is 219.7 kW, which is about twice of the quantity for the original engine coolant radiator, so a condenser with a larger frontal area than that of the original radiator should be placed to take away the heat. The volume of ORC condenser is estimated by the condenser volume evaluation model [43]. It is 53.8 L while the original coolant radiator volume is 28.1 L. The frontal area of the condenser could be increased from
Fig. 8. Evaporating temperature, evaporating pressure and mass flow rate in high-temperature branch.
T. Chen et al. / Energy Conversion and Management 138 (2017) 210–223
the original radiator area 0.56 m2 to 0.8 m2. The thickness of the condenser would increase 34% compared to the radiator. The exergy loss distribution is shown in Fig. 7. It shows that most of the exergy loss occurs in the condenser (20.2 kW) and more than 3/4 of the exergy loss occurs in three heat exchangers. The exergy loss in turbines is larger than that in pumps, while more exergy loss occurs in HT turbine and HT pump than in LT turbine and LT pump. The mixing process causes 1.2 kW exergy loss because of the temperature different between the working fluid from two branches. There are also 2.1 kW exergy which is taken away by engine exhaust gases since the exhaust gas temperature cannot be cooled to ambient temperature. All the main design parameter sensitivity analysis results are summarized in Table 7. It has to be mentioned that a 10 kPa increase in the condenser fluid side pressure drop will cause a 4.81% decrease in the system net power output. The reason is that the working fluid side pressure drop in condenser will influence the turbine expansion ratio and increase the exergy loss in condenser. In this ORC system with cyclopentane, the condensing pressure is only 114 kPa so the pressure drop can influence the turbine expansion ratio significantly. 4.4. Performance under full operating conditions The system is fixed in its designed components when analyzing the off-design system performance. The component off-design
219
performance is calculated by off-design models. Under off-design conditions, mean temperature difference in heat exchangers is variable because of the fixed heat transfer area. Since the flow rate characteristics of turbine are fixed, the evaporating pressure and mass flow rate will be changed together under different conditions. The thermodynamic analysis of parameter variation in this system is also conducted in this section. The ORC evaporating temperature, evaporating pressure and mass flow rate in the HT branch under full operating conditions are shown in Fig. 8. These three parameters will increase when the engine speed and engine load rise. The trend is caused by the HT turbine flow characteristic. Waste heat energy in the exhaust is larger in the high-load and high-speed region, so the mass flow rate of working fluid should be larger in that region to absorb the exhaust waste heat, and it asks for higher turbine inlet pressure due to the transonic turbine flow characteristic (Eq. (44)). It means that the evaporating pressure has to be higher as the mass flow rate increasing and a changeless evaporating pressure, which is beneficial to the system, cannot be achieved around the full operating conditions. In the frequently operating region (engine speed/engine load: 1100–1400 rpm/50–90%), the evaporating temperatures in the HT branch are 170–220 °C, the pressures are 2–3.5 MPa and the mass flow rates are 0.11–0.2 kg/s. At 100% engine load and 1900 rpm point, the working fluid in the HT branch will be closed to the critical state since the exhaust gas has not been bypassed in these cases.
Fig. 9. Evaporating temperature, evaporating pressure and mass flow rate in low-temperature branch.
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The ORC evaporating temperature, evaporating pressure and mass flow rate in the LT branch are shown in Fig. 9. The mass flow rate increases as the engine load and speed increase. Since there is more coolant waste heat in high engine load region, more working fluid should be pumped to absorb all that energy and meet the engine cooling requirement. However, the evaporating temperature and evaporating pressure decrease as the engine load and speed increase. The reason is that the return coolant temperature is lower in high-speed high-load region, so the evaporating temperature should also be lower in that region (shown in Fig. 10) because of the LT evaporator heat transfer ability. In the frequently operating region (engine speed/engine load: 1100–1400 rpm/50–90%), the evaporating temperatures in the LT branch are 72–78 °C, the pressures are 190–240 kPa and the mass flow rates are 0.15–0.3 kg/s. The mass flow rate in the LT branch is higher than that in the HT branch slightly. The evaporating temperature and pressure variation range in the LT branch is much smaller than that in the HT branch. The power outputs of two turbines are shown in Fig. 11. The HT turbine power output increases as the engine load increases, while the LT turbine power increases first then decreases. The reason is that a part of working fluid should be bypassed in the high-speed high-load region because of the limitation of the LT turbine maximum flow capacity. The net power output of the ORC system is shown in Fig. 12. It is assumed that 90% of the net power output of the ORC system can
be transformed to the engine shaft power. The new engine MAP is shown in Fig. 13. The peak thermal efficiency can be improved from 45.3% to 49.5%, where the minimum fuel consumption decreases from 185.6 g/(kW h) to 169.9 g/(kW h). The average fuel consumption in the frequently operating region decreases by about 9.2% from 187.9 g/(kW h) to 172.2 g/(kW h).
Fig. 10. Evaporating temperature in low-temperature branch under different engine load conditions.
Fig. 13. Comparison of engine thermal efficiency and fuel consumption between engine with and without the CCE-ORC system.
Fig. 12. The ORC system net power output under full operating conditions.
Fig. 11. Power output of two turbines under full operating conditions.
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Fig. 14. Dual-loop ORC system net power output and heat transfer rate of intermediate heat exchanger versus the PPTD of intermediate heat exchanger.
Table 8 Comparison between the CCE-ORC system and the dual-loop ORC system. Parameter
The CCE-ORC system
The dual-loop ORC system
Net power output (kW) Total thermal efficiency (%) Total exergy efficiency (%) UA of HT evaporator (W/°C) UA of LT evaporator (W/°C) UA of condenser (W/°C) UA of intermediate heat exchanger (W/°C) Q of HT evaporator (kW) Q of LT evaporator (kW) Q of condenser (kW) Q of intermediate heat exchanger (kW) HT evaporating temperature (°C) LT evaporating temperature (°C) HT evaporating pressure (kPa) LT evaporating pressure (kPa) HT turbine pressure ratio LT turbine pressure ratio HT turbine mass flow rate (kg/s) LT turbine mass flow rate (kg/s)
29.0 11.67 38.62 2142 8445 8290 – 133.4 115.2 219.7 – 215 70.8 3292.5 195.6 16.8 1.7 0.210 0.488
26.8 11.39 35.72 1790 8323 8151 8803 120.0 115.2 208.4 102.7 215 72.3 3292.5 648.6 11.8 1.83 0.223 1.083
Table 9 Comparison between the CCE-ORC system and the dual-loop ORC system in term of main component parameters. Parameter Heat exchanger volume (L)
Pump parameters
Turbine parameters
The CCE-ORC system
The dual-loop ORC system
13.7 21.1 –
11.4 20.8 22.4
53.8 88.6
53.1 107.6
HT pump head (kPa) HT pump volume flow rate (L/min) LT pump head (kPa) LT pump volume flow rate (L/min)
3198.7 17.6
3034.5 19.6
101.7 23.4
324.5 51.3
HT turbine volume expansion ratio HT turbine rotor diameter (mm) LT turbine volume expansion ratio LT turbine rotor diameter (mm)
20.9
15.7
42.3
37.7
1.5
1.86
121.7
82.7
HT evaporator LT evaporator Intermediate heat exchanger Condenser Total
5. Comparison between dual-loop ORC system and CCE-ORC system The performance and compactness between the CCE-ORC system and dual-loop ORC system have been compared in this section. A dual-loop ORC system is designed for the engine mentioned in Section 4.1, and cyclopentane and R245fa are used as working fluids for the HT loop and the LT loop respectively. All the design parameters are the same as those of the CCE-ORC system except the PPTD of intermediate heat exchanger. The system net power and compactness have a trade-off relationship under different intermediate heat exchanger PPTD. If that PPTD increases, the system net power output decreases (shown in Fig. 14(a)), while the UA of intermediate heat exchanger also decreases, which means that the volume of that heat exchanger decreases (shown in Fig. 14(b)). The comparison between the CCE-ORC system and the dual-loop ORC system is shown in Table 8, when intermediate heat exchanger PPTD is set at 10 °C. The heat transfer rate of each heat exchanger in each system is approximately the same, while the CCE-ORC system does not have an intermediate heat exchanger. The volumes of heat exchangers in these two systems are evaluated by the condenser volume evaluation model [43], and the comparison result is shown in Table 9. The total heat exchanger
Fig. 15. Comparison of exergy loss between the CCE-ORC system and the dual-loop ORC system.
volume of the CCE-ORC system is 21 L (18%) less than that of the dual-loop ORC system. The pump characteristic parameters are compared in Table 9. It shows that the volume flow rates of the pumps, especially the LT pump, in the CCE-ORC system are smaller, so the pumps of the CCE-ORC system have smaller volumes.
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Fig. 16. Comparison of net power output between the CCE-ORC system and the dual-loop ORC system.
The turbine characteristic parameters are shown in Table 9. The turbine rotor diameter is calculated by Eq. (47) [44]. Although turbine rotor diameters of the CCE-ORC system are larger than that of the dual-loop ORC system, the volume difference between turbines is not remarkable, because the turbine volume only makes up a small proportion of the total system volume. Overall, considering the difference in each main component as well as one less reservoir, the CCE-ORC system can be recognized more compact than the dual-loop ORC system.
pffiffiffiffiffiffiffiffiffi 1=4 Drotor ¼ Ds V out =Dh
ð47Þ
where Ds is the specific diameter; V out is the volume flow rate at turbine outlet; Dh is the enthalpy drop in the turbine. The CCE-ORC system generates 8% more power than the dualloop ORC system at the design point. The main reason is that this system can absorb more waste heat from the exhaust gases since working fluid temperature at HT evaporator inlet is lower in the CCE-ORC system. The comparison of exergy loss distribution (Fig. 15) shows that more exergy is dissipated in the condenser and the HT evaporator of the CCE-ORC system than in that of the dual-loop ORC system, while less exergy is lost in the unused exhaust gases of the CCE-ORC system. It has to be mentioned that the mixing process in the CCE-ORC system leads to only about 1.2 kW exergy loss, while the intermediate heat exchanger in the dual-loop ORC system causes about 4 kW exergy loss. That is why the CCE-ORC system total thermal efficiency (11.67%) is slightly higher than the dual-loop ORC system thermal efficiency (11.39%). The comparison of these two system in term of net power output under full operating conditions is shown in Fig. 16. The net power output of the CCE-ORC system is larger under all the conditions, while the relative difference of the net power between these two systems is larger in lower engine rotating speed and lower engine load region. Compared with the dual-loop ORC system, the CCE-ORC system can output 7.94% more net power in frequently operating region on average.
is used. This system can also replace the original coolant radiator, since it can recover all the waste heat in coolant. Cyclopentane is the most suitable working fluid for this CCEORC system among six candidates following the working fluid selection criteria. The net power of the system with cyclopentane is the highest, following by that for pentane and R1233-zd-e. The working fluid side pressure drop in condenser has a negative impact on system net power output, because it will decrease the turbine expansion ratio, thereby leading to a less net power output. This effect is significant in the system with cyclopentane, whose normal boiling point (NBP) is high, which means the condensing pressure is normally quite low. The result shows that if this pressure drop increases by 10 kPa, the system net power output will be reduced by 4.8%. System performance under full operating conditions is simulated. The result shows that the peak thermal efficiency can be improved from 45.3% to 49.5%, where the minimum BSFC decreases from 185.6 g/(kW h) to 169.9 g/(kW h). The average BSFC in the frequently operating region (engine rotating speed: 1100–1400 rpm; engine load: 50–90%) decreases by about 9.2% from 187.9 g/(kW h) to 172.2 g/(kW h). Compared with the dual-loop ORC system, the CCE-ORC system can generate 7.94% more net power in frequently operating conditions in average, because it can recover more waste heat from exhaust gases and the mixing process dissipate less exergy than the intermediate heat exchanger. The CCE-ORC system is also more compact since the intermediate heat exchanger can be removed and the total volume of heat exchangers can be reduced by 21 L (18%). The pump volumes can also be reduced, while the volumes of other components are approximately the same. Acknowledgements The authors would like to thank the National Natural Science Foundation of China [No. 51636005] for the support. References
6. Conclusions In this paper, a CCE-ORC system is proposed to recover the waste heat in both exhaust gases and coolant. This ORC system uses only single loop to recover both the high temperature and low temperature waste heat in two branches respectively. The system structure is simple and only one kind of working fluid
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Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
A novel cascade organic Rankine cycle (ORC) system for waste heat recovery of truck diesel engines Tao Chen a, Weilin Zhuge a,b, Yangjun Zhang a,b,⇑, Lei Zhang a a b
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China Collaborative Innovation Center of Electric Vehicles in Beijing, China
a r t i c l e
i n f o
Article history: Received 22 October 2016 Received in revised form 28 December 2016 Accepted 22 January 2017
Keywords: Waste heat recovery Organic Rankine cycle (ORC) Diesel engine Cascade expansion
a b s t r a c t Waste heat recovery (WHR) of engines has attracted increasingly more concerns recently, as it can improve engine thermal efficiency and help truck manufacturers meet the restrictions of CO2 emission. The organic Rankine cycle (ORC) has been considered as the most potential technology of WHR. To take full advantage of waste heat energy, the waste heat in both exhaust gases and the coolant need to be recovered; however, conventional multi-source ORC systems are too complex for vehicle applications. This paper proposed a confluent cascade expansion ORC (CCE-ORC) system for engine waste heat recovery, which has simpler architecture, a smaller volume and higher efficiency compared with conventional dual-loop ORC systems. Cyclopentane is analyzed to be regarded as the most suitable working fluid for this novel system. A thermodynamic simulation method is established for this system, and off-design performance of main components and the working fluid side pressure drop in the condenser have been taken into consideration. System performance simulations under full engine operating conditions are conducted for the application of this system on a heavy-duty truck diesel engine. Results show that the engine peak thermal efficiency can be improved from 45.3% to 49.5% where the brake specific fuel consumption (BSFC) decreases from 185.6 g/(kW h) to 169.9 g/(kW h). The average BSFC in the frequently operating region can decrease by 9.2% from 187.9 g/(kW h) to 172.2 g/(kW h). Compared with the conventional dual-loop ORC system, the CCE-ORC system can generate 8% more net power, while the total volume of heat exchangers is 18% less. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The interests in truck diesel engine waste heat recovery (WHR) has grown dramatically recently as the CO2 emission regulation becomes stricter. Many researchers [1–5] believe that the WHR is the most potential technology to improve the engine thermal efficiency since more than half of the fuel energy is dissipated as waste heat. For a conventional diesel engine [6], the peak efficiency can be up to 43%, while about 27%, 20%, 7% of the fuel energy is taken away by exhaust gases, coolant and the intercooler respectively; furthermore, a higher proportion of fuel energy will be dissipated as waste heat when engines operate under partial engine load conditions. Several technologies have been researched to recover the waste heat of truck diesel engines, such as the thermoelectric generators (TEG), the turbo-compound system and the ORC system. The TEG ⇑ Corresponding author at: State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China. E-mail address: [email protected] (Y. Zhang). http://dx.doi.org/10.1016/j.enconman.2017.01.056 0196-8904/Ó 2017 Elsevier Ltd. All rights reserved.
system seems to be the simplest one among these technologies but it has the disadvantage of lowest efficiency (<4%) [7]. Hence, it cannot be a good choice until high efficiency thermoelectric materials are available. The turbo-compound system will cause higher engine backpressure and cannot utilize all the waste heat of engines, such as coolant waste heat, though this system is simple to be applied and can improve the engine efficiency by 8% under certain conditions [4]. Compared with other technologies, the ORC system has the highest potential overall efficiency [8] with a suitable size for trucks, and it is able to recover the waste heat energy in exhaust gases, coolant and the intercooler. Some studies [9–12] have been done on the ORC systems which only recover the waste heat in exhaust gases. In these studies, the working fluid selection and system performance analysis have been researched. With the purpose of recovering more waste energy and further improving engine efficiency, some researchers turned to the multi-heat-source ORC system which can recover both exhaust gases and the coolant. The preheating ORC system and the dual-loop ORC system are two main types of multi-heatsource ORC systems currently.
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Nomenclature Acronyms CCE confluent cascade expansion EGR exhaust gas recirculation GWP global warming potential HT high temperature LT low temperature NBP normal boiling point ODP ozone depletion potential ORC organic Rankine cycle WHR waste heat recovery TEG thermos-electric generator Latin and Greek symbols A area [m2] Cp isobaric heat capacity [kJ/(kg °C)] Cs isentropic velocity [m/s] dp pressure drop [kPa] D diameter [m] Ds specific diameter [mm] h enthalpy [kJ/kg] I exergy loss [kW] k specific heat ratio [–] m mass flow rate [kg/s] M Mach number [–] N rotating speed [r/min] p pressure [kPa] P power [kW] Q heat energy [kW] R gas constant [J/(kg °C)] s entropy [kJ/(kg °C)] SR blade speed [–]
In the preheating ORC system (Fig. 1), working fluid is preheated by the coolant, and then it absorbs the waste heat in exhaust gases. Arias et al. [13] and Yu et al. [14] studied the preheating ORC system and showed that only 5% of the coolant waste heat can be absorbed if evaporating temperature of ORC system is higher than coolant temperature. Ringler et al. [15] have studied the preheating ORC system on their test bench, and their results showed that the gasoline engine power output could be improved
Fig. 1. Structure of a typical preheating ORC system.
T DT U UA v V y
g
temperature [°C] temperature difference [°C] rotor tip velocity [m/s] heat transfer rate [W/°C] velocity [m/s] volume flow rate [m3/s] pump head [kJ/kg] efficiency [–]
Subscripts and superscripts a refers to ambient con refers to condensers cool refers to coolant eff refers to effective ev refers to evaporators g refers to gas HT refers to high temperature in refers to inlet l refers to liquid LT refers to low temperature h net refers to net power out refers to outlet ph refers to two-phase region pump refers to pump s refers to an isentropic process tot refers to total tur refers to turbines n refers to nominal nozzle refers to nozzle 0 refers to total 1–8 refers to locations of CCE-ORC
by 10% with this ORC system. Vaja and Gambarotta [16] analyzed the preheating ORC system and gave the conclusion that the working fluids with low critical temperatures as well as bell shaped vapor lines were suitable for the preheating ORC system. Kim et al. [17] designed a preheating ORC system with regenerators and it improved ORC net power output by 35.6% compared with a conventional preheating ORC system. In order to utilize the coolant waste heat effectively, the cascade ORC system was developed. Fig. 2 shows a typical cascade ORC system for engine waste heat recovery. There are two ORC loops recovering the waste heat in coolant and exhaust gases respectively; meanwhile, the condenser of high-temperature (HT) loop is used as one of the evaporators in the low-temperature (LT) loop. Shu et al. [18] studied a cascade ORC system applied on a vehicle diesel engine, using water as the working fluid for HT loop. Their results showed that R1234yf was the best working fluid for LT loop and it could output 36.77 kW net power in theory when the engine power was 235.8 kW. Song and Gu [19,20] studied a cascade ORC system applied on a heavy-duty diesel engine, and they conducted that R236fa was the best choice for the LT loop while cyclohexane and water were the proper working fluids for the HT loop. This system can improve engine power by 11.2–11.6%. Huang et al. [21] compared the typical cascade ORC system with another system, in which waste energy in exhaust gases was absorbed by HT loop and LT loop in turn, and the results showed that the performance of typical cascade ORC system was slightly better. Kulkarni and Sood [22] used R245fa and R236fa for HT loop and LT loop respectively, and they analyzed the system performance under different engine operating conditions. The results showed that the cascade ORC system can output 7.26–14.16 kW net power and its overall thermal efficiency was about 10%. Wang, Zhang et al. [23,24] pro-
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on a heavy-duty truck diesel engine under both the system design condition and full engine operation conditions. Finally, the CCEORC system performance is compared with the conventional dual-loop ORC system. 2. CCE-ORC system description
Fig. 2. Structure of a dual-loop ORC system.
posed a cascade ORC system, in which LT loop working fluid absorbed heat from intercooler, HT loop condenser and coolant successively. This system can improve the power of a light-duty diesel engine by 19–22% and promote the power of a gasoline engine by 14–16% when heat transfer loss is assumed to be minimum. Yang et al. [25] proposed a modified system, in which a regenerator was applied in the HT loop, based on the system proposed by Wang and Zhang [23,24]. This system can achieve the largest net power of 27.85 kW and reduce the BSFC by 4%. The conventional dual-loop ORC systems are too complex for vehicle engine applications, since plenty of space is needed to place four heat exchangers and two complete loops. This paper proposed a novel confluent cascade expansion ORC (CCE-ORC) system [26] for recovering multi-source waste heat of a truck engine. It has a simpler architecture and only one kind of working fluid is needed. Firstly, thermodynamic models including component off-design performance models for the CCE-ORC system are established. And then, the system performance and the improvement on the engine fuel efficiency are analyzed for the application of the system
The cycle configuration and T-S diagram of the CCE-ORC system are shown in Fig. 3. There are two branches (high-temperature branch and low-temperature branch) to recover waste heat of exhaust gases and coolant respectively. In the HT branch, a part of working fluid is compressed to higher pressure so that high evaporating temperature can be achieved to match the exhaust temperature. Then this part of working fluid is heated into superheated state by exhaust gases and flows to the HT turbine. In the LT branch, the other part of the working fluid is pumped to lower pressure so that the evaporating temperature in this branch is lower than coolant temperature, then the compressed working fluid absorbs all the waste heat energy of coolant and evaporates to saturated vapor phase state in the LT evaporator. The working fluid after the LT evaporator and that after the HT turbine mix together, and then the fluid flows into the LT turbine. After that the working fluid flows into the condenser and is condensed into saturated liquid phase state by air. Only one kind of working fluid, one reservoir and three heat exchangers are needed in this system, so this system is compact enough for a multi-source ORC system. Compared with conventional dual-loop ORC system, the intermediate heat exchanger is not needed in this system and the reservoir for HT loop is also not needed while the volumes of other components maintains the same level, so the total volume of CCE-ORC system can be smaller. The HT branch can absorb more energy from the exhaust gases than the HT loop in dual-loop ORC systems, and the exergy loss in the mixing process is less than that in the intermediate heat exchanging process; as a result, CCE-ORC system can output more net power. Meanwhile, the LT branch can recover all the waste heat in coolant so the original coolant radiator can be replaced. It means that the ORC condenser can be laid at the position where the original coolant radiator used to be, and the working fluid can be cooled by air directly. Radial-inflow turbines are used in this system, because this type of expander has the advantages of light weight, small size, mature manufacturability and high efficiency [27]. Although the high
Fig. 3. Cycle layout and T-S diagram of the confluent cascade expansion (CCE) ORC system.
T. Chen et al. / Energy Conversion and Management 138 (2017) 210–223
rotating speed is usually considered as a disadvantage, it has been conducted that a low specific speed turbine can be designed to reduce the rotating speed [28].
3. Performance simulation methods The energy and exergy analysis [29] and off-design performance of components [30,31] are important while analyzing system performance. The full operating condition performance simulation method consists of two steps, including calculating design point performance and predicting off-design performance under full operating conditions. The flow diagram of this method is shown in Fig. 4. Step 1: calculating the inlet and outlet conditions of each component at design point to determine main design parameters of each component, such as effective throat areas of turbines and
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heat transfer rates of evaporators. In this step, pinch point temperature different (PPTD) of evaporators and efficiency of pumps as well as turbines are given, and mass flow rate is calculated by system thermodynamic model. All the given parameters at design point are shown in Table 1. Step 2: calculating component performance at off-design points and simulating the system full operating condition performance. In this step, flow characteristics of pumps and turbines are used to determine mass flow rate, and then pump efficiency, turbine efficiency and heat transfer quantity are calculated by off-design models of components to evaluate the system performance. The system net power output and exergy loss are calculated by system thermal model (in Section 3.1) when the heat transfer quantity of each evaporator, efficiency and flow characteristic of pumps and turbines have been calculated by component offdesign models (in Section 3.2).
Fig. 4. Flow diagram of system performance simulation method.
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Table 1 The value of all the given parameters at design point.
gpump;HT ¼
Parameter
Value
PPTD of HT evaporator PPTD of LT evaporator Superheating temperature of HT branch Superheating temperature of LT branch Condensing temperature Turbine efficiency Pump efficiency Pressure drop in each heat exchanger
30 °C 10 °C 20 °C 0 °C 50 °C 80% 50% 10 kPa
The assumptions in models are given below: (1) Kinetic energy of working fluids is ignored; (2) Heat loss and pressure drop in all pipes are ignored; (3) Mixing process is an isobaric process following the energy conservation law with no heat loss; (4) Condensing temperature is a constant value: 50 °C. These models are established in the Matlab environment, and the working fluid properties reference the REFPROP database. 3.1. System thermal model The thermodynamic model of the whole system is established, and the pressure drop is taken into consideration. Working fluid side pressure drop of the condenser has a negative effect on system performance because it will influence turbine expansion ratio and pump pressure ratio. This effect will become more significant when condensing pressure lowers. Under the same condensing temperature, the working fluid with high critical temperature usually has a lower condensing pressure. The total mass flow rate equals to the summation of that in two branches (Eq. (1)), and the mass flow rate of each branch is calculated by the energy conservation equation of each evaporator, after the enthalpy difference between evaporator inlet and outlet of the working fluid and the heat transfer quantity calculated.
mtot ¼ mHT þ mLT
ð1Þ
In the HT branch: The isentropic efficiency of the pump is given and the performance of the pump is calculated by the equations below:
h4s h1 h4 h1
ð2Þ
P pump;HT ¼ mHT ðh4 h1 Þ
ð3Þ
Ipump;HT ¼ mHT T a ðs4 s1 Þ
ð4Þ
The evaporator model with consideration of pressure drop is shown in Fig. 5. It is assumed that all the pressure drop of heat exchangers occurs at the inlet of heat exchangers and it is an isenthalpic process. So the assumptive process in the heat exchanger consists of two steps: 4–40 is an isenthalpic process where pressure goes down; 40 –5 is an isobaric process where working fluids absorb heat from exhaust gases. The mathematic model is shown below:
p40 ¼ p4 dpeV;HT
ð5Þ
h40 ¼ h4
ð6Þ
p40 ¼ p5
ð7Þ
Q eV;HT ¼ mHT ðh5 h40 Þ ¼ mexh Cpexh ðT exh;in T exh;out Þ
ð8Þ
IeV;HT ¼ mHT T a ðs5 s4 Þ mexh T a ðsexh;in sexh;out Þ
ð9Þ
The isentropic efficiency of the turbine is given and the performance of the high-temperature turbine is calculated by equations below:
gtur;HT ¼
h5 h6 h5 h6s
ð10Þ
P tur;HT ¼ mHT ðh5 h6 Þ
ð11Þ
Itur;HT ¼ mHT T a ðs5 s6 Þ
ð12Þ
In the LT branch, the models of components are shown here:
gpump;LT ¼
h2s h1 h2 h1
ð13Þ
Ppump;LT ¼ mLT ðh2 h1 Þ
ð14Þ
Ipump;LT ¼ mLT T a ðs2 s1 Þ
ð15Þ
p20 ¼ p2 dpeV;LT
ð16Þ
Fig. 5. Evaporator model with the consideration of working fluid side pressure drop.
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h20 ¼ h2
ð17Þ
p20 ¼ p3
ð18Þ
Q eV;LT ¼ mLT ðh3 h20 Þ ¼ mcool Cpcool ðT cool;in T cool;out Þ
ð19Þ
IeV;LT ¼ mLT T a ðs3 s2 Þ mcool T a ðscool;in scool;out Þ
ð20Þ
where y0;n is the pump head at nominal rotating speed when no flow rate is allowed, yn is the pump head under design point condition, N pump;n is nominal rotating speed. The off-design pump efficiency defined as function of flow rate and rotating speed is shown in Eq. (37).
gpump ¼
gpump;n V 2pump Npump;n
The model for the LT turbine is shown here:
V 2pump;n
Npump
2
þ2
gpump;n V pump Npump;n V pump;n
Npump
ð37Þ
p3 ¼ p6 ¼ p7
ð24Þ
where gpump;n is the pump nominal efficiency which is also the design efficiency. The evaporator model is based on Logarithmic Temperature Mean Difference (LMTD) method, LTMD is defined in Eq. (38) and exchanging heat quantity is defined as function of LTMD, as shown in Eq. (39) [33]. The whole evaporator model consists of three parts (Eq. (40)), liquid phase state part, two-phase state part and gas phase state part, and heat capacity of working fluid in each part is assumed to be constant. The condenser model is simpler than evaporator model and condensing temperature is assumed to be constant as adequate cooling air is available.
mHT h6 þ mLT h3 ¼ mtot h7
ð25Þ
DT LTMD ¼
Imix ¼ mHT T a ðs7 s6 Þ þ mLT T a ðs7 s3 Þ
ð26Þ
gtur;LT ¼
h7 h8 h7 h8s
ð21Þ
Ptur;LT ¼ mtot ðh7 h8 Þ
ð22Þ
Itur;LT ¼ mtot T a ðs7 s8 Þ
ð23Þ
The mixing process of working fluids obeys the energy conservation law:
The condenser model is shown below:
DT max DT min lnðDT max =DT min Þ
ð38Þ
where DT min is the minimum one of the temperature differences at heat exchanger inlet and outlet, and DT max is the other one.
Q¼
X
UADT LTMD
ð39Þ
p70 ¼ p7 dpcon
ð27Þ
h70 ¼ h7
ð28Þ
UA ¼ UAl þ UAph þ UAg
p70 ¼ p8
ð29Þ
The pressure drop of these heat exchangers is proportional to the square of the working fluid mass flow rate.
Q con ¼ mtot ðh7 h8 Þ
ð30Þ
dp ¼ dpn ðm=mn Þ2
Icon ¼ Q con þ mtot T a ðs1 s8 Þ
ð31Þ
The effective throat area of the nozzle (Aeff ;nozzle ) is taken into consideration in the turbine model [34], and off-design efficiency is defined as a function of blade speed ratio (SR), as shown in Eq. (42) [35],
The net power of this ORC system is calculated by the equation follow:
Pnet ¼ Ptur;1 þ Ptur;2 P pump;HT Ppump;LT
ð32Þ
The total exergy loss consists of the eight parts mentioned above and another part of exergy loss in the exhaust gas discharged to the atmosphere (defined in Eq. (33)):
Iexh;out ¼ Q exh;out þ mexh T a ðsexh;out sT0 Þ Itot ¼
9 X I
ð41Þ
ð42Þ
ð33Þ ð34Þ
SR ¼
The turbine efficiency and pump efficiency at design point are given, and heat transfer quantity at design point is calculated when PPTD of each evaporator is given. The component off-design performance is calculated by the off-design models introduced in this section. Flow rate characteristics and efficiency characteristics are considered in this off-design pump model [32]. The pump head is defined in Eq. (35) and the function of flow rate, rotating speed and pump head is shown in Eq. (36)
2 V 2pump Npump;n 2 Npump;n y ¼ 2 ðyn y0;n Þ þ yo;n Npump V pump;n N pump
gtur ¼ gtur;n
2 ! 2SR SR SRn SRn
ð40Þ
where SRn is the nominal blade speed. The blade speed ratio is defined as the rotor tip velocity (U) divided by the isentropic velocity (C S ).
3.2. Component models
y ¼ hpump;out hpump;in
where UA is heat transfer rate of heat exchangers.
ð35Þ ð36Þ
U pNtur D=60 ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cs k1 2cp T 0;in 1 ðpout =p0;in Þ k
ð43Þ
The flow rate characteristics of two turbines are different as the HT turbine is a transonic turbine (the working fluid flow speed equals to the speed of sound at the nozzle throat) and the LT turbine is a subsonic turbine (the working fluid flow maintains lower than the speed of sound in the entire turbine) normally. For the transonic turbine, if effective throat area of the nozzle (Aeff ;nozzle ) is designed, mass flow rate can be solved by turbine inlet and outlet condition but not affected by the rotating speed [36], and Mach number at nozzle throat is almost a constant (M ¼ 1).
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kþ1 m RT 0;in =k k 1 2 2ðk1Þ M ¼M 1þ 2 Aeff ;nozzle p0;in
ð44Þ
For the subsonic turbine, rotating speed can influence turbine mass flow rate [34], because it will influence nozzle pressure ratio pnozzle . p0;in
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Table 2 Comparison of the present simulated results with Ref. [20]. Parameter
Table 3 Main parameters of the diesel engine.
Present results
Reference result [20]
Deviation (%)
HT loop Working fluid Evaporating temperature (°C) Absorbed heat load (kW) Mass flow rate (kg/s) Net power output (kW) Thermal efficiency
Cyclohexane 207.2 429.1 0.77 63.5 14.8%
Cyclohexane 207.2 432.2 0.8 64 14.8%
0.72 3.90 0.79 0.01
LT loop Working fluid Evaporating temperature (°C) Absorbed heat load (kW) Mass flow rate (kg/s) Net power output (kW) Thermal efficiency
R245fa 75.9 566.0 2.66 45.8 8.1%
R245fa 75.9 568.1 2.7 47.2 8.3%
0.37 1.50 3.06 2.57
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 u !2 !kþ1 3 u 2k p2 k k u p p 0;in nozzle nozzle 4 5 m ¼ Aeff ;nozzle t ðk 1ÞRT 0;in p0;in p0;in k 2 0 !k1 13k1 k g 2 1 pnozzle 4 p out tur @1 A5 ¼ 1 p0;in 2SR gnozzle p0;in
Parameter
Value
Cylinder number Displacement Compression ratio Stroke Cylinder bore Rated power (speed) Peak torque (speed)
6 11 L 16.4 156 mm 123 mm 306 kW (1900 rpm) 2045 N m (1100 rpm)
Table 4 Engine test data at the ORC system design point conditions.
ð45Þ
Parameters
Value
Engine load [%] Engine speed [rpm] Engine torque [N m] Fuel consumption rate [g/kW h] Engine power [kW] Exhaust energy [kW] Coolant energy [kW] Exhaust mass flow rate [kg/s] Exhaust temperature [°C] Coolant temperature (inlet) [°C] Coolant temperature (outlet) [°C]
90 1400 1765.5 190.14 258.9 157.7 115.2 0.388 405 80 88
ð46Þ
where gnozzle is the nozzle isentropic efficiency. It has to be mentioned that if mtot is larger than maximum flow capacity of the LT turbine, a part of working fluid will be bypassed. 3.3. Model validation The validation of system model was done by using the equations to calculate a dual-loop ORC system in Ref. [20] and comparing the calculated results with reference results, because this system consists of all the components in CCE-ORC system and these components are simulated by the same mathematic models. That system is applied on a diesel engine whose power output is 996 kW, exhaust gas temperature is 300 °C, exhaust gas mass flow rate is 7139 kg/h, outlet coolant temperature is 90 °C, inlet coolant temperature is 65 °C, whose coolant mass flow rate is 6876 kg/h. The deviation of the present results compared with the reference results is less than 4% (shown in Table 2). It can be recognized that the thermodynamic models of those components in the CCE-ORC system are accurate enough to evaluate the system performance. 4. Results and discussions The performance of CCE-ORC system designed for a heavy-duty diesel engine is discussed in this section. Working fluid selection is discussed, and system performance at design point and full operating condition are simulated and analyzed.
4.1. Parameters of the diesel engine The studied truck diesel engine in this paper is a turbocharged and intercooled diesel engine without exhaust gas recirculation (EGR), and main parameters of this engine are shown in Table 3. The rated power is 306 kW at 1900 rpm, while the full-load engine torque is about 2000 N m in the range 1100–1400 rpm. The exhaust gas temperature is in the range 250–450 °C, and high temperature region is the high engine load region. The coolant outlet temperature is about 88 °C in all the conditions, while the coolant inlet temperature is in the range 78–86 °C. The exhaust mass flow rate is in the range 0.1–0.47 kg/s, and it is nearly proportional to the engine power. While the coolant mass flow rate is in the range 2–5 kg/s, and it is also proportional to the engine speed. The minimum BSFC is 185.6 g/(kW h) under the working condition (1200 rpm/1500 N m) where the engine efficiency is about 45%. Frequently working condition area of this engine is in the range, where rotating speeds are 1100–1400 rpm and engine loads are within 50–90%, and maximum engine power condition in this area is chosen as the design point condition (shown in Table 4). If the heat transfer capacity of heat exchangers and the flow capacity of turbines can meet the demand of the design point, the system can operate well in the engine frequently working condition areas and the maximum pressure will also be kept in the acceptable range. Working fluid is selected based on the design point condition.
Table 5 Properties of the working fluids. Name
Chemical formula
Molecular NBP Critical Critical Thermal stability GWP ASHRAE std Slope mass (g/mol) temperature (°C) temperature (°C) pressure (MPa) temperature (°C) (100 yr) 34 safety class
R134a [37,38] Butane [37,39] R245fa [37,40] R1233zd-e [39,41] Pentane [37,42] Cyclopentane [37,40]
CH2FCF3 CH3CH2CH2CH3 CF3CH2CHF2 CF2CH@CHCl CH3CH2CH2CH2CH3 A(CH2)5A
102.03 58.12 134.05 130.5 72.15 70.13
26.1 0.5 15.1 18.0 36.1 49.4
101.1 152.0 154.0 165.6 196.6 238.6
NBP: normal boiling point; GWP: global warming potential (for 100 years’ integration).
4.06 3.8 3.65 3.57 3.37 4.51
368 310 250 200 280 275
1370 20 1050 7 20 11
A1 A3 B1 A1 A3 –
Wet Dry Dry Dry Dry Dry
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4.2. Working fluid selection Working fluid selection should follow the criteria below: (1) The ozone depletion potential (ODP) index of the working fluid must be zero; (2) The critical temperature should be higher than 100 °C to achieve high evaporating temperature and high efficiency; (3) The normal boiling point (NBP) temperature should be below 50 °C, to make sure that the ORC system operating pressures are always higher than atmosphere. It has to be mentioned that combustible fluids are also taken into consideration in this study. As a result, six organic fluids, whose properties are shown in Table 5, are selected as candidates among the working fluids mentioned in Ref. [37]. Since there is a mixing process after the LT evaporator, the superheating temperature of working fluid at the inlet of LT turbine is high enough to make sure that the turbine works safely even for the wet fluid R134a. The most suitable one would be determined by comparing these fluids in term of the net power output. System performance of these six working fluids is calculated and the system net power output as a function of hightemperature branch evaporating temperature is shown in Fig. 6 (a). The net power output increases as the evaporating temperature increases because of the exergy loss decreasing in
high-temperature evaporator (Fig. 6(b)). It means that critical temperature is an important parameter for working fluid, because it limits the maximum evaporating temperature of a subcritical ORC system. As a result, cyclopentane is considered as the most suitable working fluid for this ORC system, since it has the highest critical temperature and can output the maximum net power.
Table 6 The ORC system performance at design point. Parameter
Value
Mass flow rate in HT branch Mass flow rate in LT branch Net power output Total exergy loss Thermal efficiency Exergy efficiency HT turbine power output LT turbine power output HT pump power input LT pump power input HT evaporator heat transfer quantity LT evaporator heat transfer quantity Condenser heat transfer quantity Condensing pressure HT turbine pressure ratio LT turbine pressure ratio
0.21 kg/s 0.28 kg/s 29.0 kW 46.1 kW 11.65% 38.62% 21.9 kW 9.0 kW 1.9 kW 0.1 kW 133.4 kW 115.2 kW 219.7 kW 113.8 kPa 16.84 1.72
Fig. 6. ORC system net power output and exergy loss in high-temperature evaporator as function of evaporating temperature of high-temperature branch.
Fig. 7. Exergy loss distribution at design point.
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Table 7 Sensitivity analysis of main design parameters at design point. Parameter
Variation considered in the parameter
Resulting variation in system net power output
HT evaporating temperature PPTD of HT evaporator PPTD of LT evaporator Condensing temperature Condenser pressure drop HT pump isentropic efficiency LT pump isentropic efficiency HT turbine isentropic efficiency LT turbine isentropic efficiency
±5 °C ±5 °C ±5 °C ±5 °C ±10 kPa ±10%
±0.54% 1.27% 3.86% 7.75% 4.81% ±2.34%
±10% ±10%
±0.11% ±8.50%
±10%
±4.77%
4.3. Performance at design point This ORC system performance at design point is calculated by the simulation method and the design parameters have been given in Table 1, and cyclopentane is chosen as the working fluid. The LT evaporating temperature is calculated by the simulation method. As the LT evaporator has to absorb all the waste heat in coolant and do not influence the coolant inlet temperature, the LT
evaporating temperature can be calculated when the PPTD in the LT evaporator and the working fluid superheating temperature at evaporator outlet have been given. High-temperature branch evaporating temperature is set at 215 °C, so the maximum pressure under all the operating conditions can be kept under the critical pressure (4.5 MPa), to make sure that the system operates safely and functions well. The system performance and component operating condition at the design point are shown in Table 6. The net power output is 29.0 kW and the total exergy loss is 46.1 kW. The thermal efficiency of this system is 11.65% and the exergy efficiency is 38.62%. The HT turbine pressure ratio is 16.84 so a transonic turbine should be applied in this position, while the LT turbine pressure ratio is 1.72 and a subsonic turbine should be applied. The mass flow rate of HT turbine is about half of that of the LT turbine while the HT turbine generates much more power than the LT turbine. The power consumed by the HT pump is 1.9 kW, but the LT pump consumes much fewer. The condenser heat transfer quantity is 219.7 kW, which is about twice of the quantity for the original engine coolant radiator, so a condenser with a larger frontal area than that of the original radiator should be placed to take away the heat. The volume of ORC condenser is estimated by the condenser volume evaluation model [43]. It is 53.8 L while the original coolant radiator volume is 28.1 L. The frontal area of the condenser could be increased from
Fig. 8. Evaporating temperature, evaporating pressure and mass flow rate in high-temperature branch.
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the original radiator area 0.56 m2 to 0.8 m2. The thickness of the condenser would increase 34% compared to the radiator. The exergy loss distribution is shown in Fig. 7. It shows that most of the exergy loss occurs in the condenser (20.2 kW) and more than 3/4 of the exergy loss occurs in three heat exchangers. The exergy loss in turbines is larger than that in pumps, while more exergy loss occurs in HT turbine and HT pump than in LT turbine and LT pump. The mixing process causes 1.2 kW exergy loss because of the temperature different between the working fluid from two branches. There are also 2.1 kW exergy which is taken away by engine exhaust gases since the exhaust gas temperature cannot be cooled to ambient temperature. All the main design parameter sensitivity analysis results are summarized in Table 7. It has to be mentioned that a 10 kPa increase in the condenser fluid side pressure drop will cause a 4.81% decrease in the system net power output. The reason is that the working fluid side pressure drop in condenser will influence the turbine expansion ratio and increase the exergy loss in condenser. In this ORC system with cyclopentane, the condensing pressure is only 114 kPa so the pressure drop can influence the turbine expansion ratio significantly. 4.4. Performance under full operating conditions The system is fixed in its designed components when analyzing the off-design system performance. The component off-design
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performance is calculated by off-design models. Under off-design conditions, mean temperature difference in heat exchangers is variable because of the fixed heat transfer area. Since the flow rate characteristics of turbine are fixed, the evaporating pressure and mass flow rate will be changed together under different conditions. The thermodynamic analysis of parameter variation in this system is also conducted in this section. The ORC evaporating temperature, evaporating pressure and mass flow rate in the HT branch under full operating conditions are shown in Fig. 8. These three parameters will increase when the engine speed and engine load rise. The trend is caused by the HT turbine flow characteristic. Waste heat energy in the exhaust is larger in the high-load and high-speed region, so the mass flow rate of working fluid should be larger in that region to absorb the exhaust waste heat, and it asks for higher turbine inlet pressure due to the transonic turbine flow characteristic (Eq. (44)). It means that the evaporating pressure has to be higher as the mass flow rate increasing and a changeless evaporating pressure, which is beneficial to the system, cannot be achieved around the full operating conditions. In the frequently operating region (engine speed/engine load: 1100–1400 rpm/50–90%), the evaporating temperatures in the HT branch are 170–220 °C, the pressures are 2–3.5 MPa and the mass flow rates are 0.11–0.2 kg/s. At 100% engine load and 1900 rpm point, the working fluid in the HT branch will be closed to the critical state since the exhaust gas has not been bypassed in these cases.
Fig. 9. Evaporating temperature, evaporating pressure and mass flow rate in low-temperature branch.
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The ORC evaporating temperature, evaporating pressure and mass flow rate in the LT branch are shown in Fig. 9. The mass flow rate increases as the engine load and speed increase. Since there is more coolant waste heat in high engine load region, more working fluid should be pumped to absorb all that energy and meet the engine cooling requirement. However, the evaporating temperature and evaporating pressure decrease as the engine load and speed increase. The reason is that the return coolant temperature is lower in high-speed high-load region, so the evaporating temperature should also be lower in that region (shown in Fig. 10) because of the LT evaporator heat transfer ability. In the frequently operating region (engine speed/engine load: 1100–1400 rpm/50–90%), the evaporating temperatures in the LT branch are 72–78 °C, the pressures are 190–240 kPa and the mass flow rates are 0.15–0.3 kg/s. The mass flow rate in the LT branch is higher than that in the HT branch slightly. The evaporating temperature and pressure variation range in the LT branch is much smaller than that in the HT branch. The power outputs of two turbines are shown in Fig. 11. The HT turbine power output increases as the engine load increases, while the LT turbine power increases first then decreases. The reason is that a part of working fluid should be bypassed in the high-speed high-load region because of the limitation of the LT turbine maximum flow capacity. The net power output of the ORC system is shown in Fig. 12. It is assumed that 90% of the net power output of the ORC system can
be transformed to the engine shaft power. The new engine MAP is shown in Fig. 13. The peak thermal efficiency can be improved from 45.3% to 49.5%, where the minimum fuel consumption decreases from 185.6 g/(kW h) to 169.9 g/(kW h). The average fuel consumption in the frequently operating region decreases by about 9.2% from 187.9 g/(kW h) to 172.2 g/(kW h).
Fig. 10. Evaporating temperature in low-temperature branch under different engine load conditions.
Fig. 13. Comparison of engine thermal efficiency and fuel consumption between engine with and without the CCE-ORC system.
Fig. 12. The ORC system net power output under full operating conditions.
Fig. 11. Power output of two turbines under full operating conditions.
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Fig. 14. Dual-loop ORC system net power output and heat transfer rate of intermediate heat exchanger versus the PPTD of intermediate heat exchanger.
Table 8 Comparison between the CCE-ORC system and the dual-loop ORC system. Parameter
The CCE-ORC system
The dual-loop ORC system
Net power output (kW) Total thermal efficiency (%) Total exergy efficiency (%) UA of HT evaporator (W/°C) UA of LT evaporator (W/°C) UA of condenser (W/°C) UA of intermediate heat exchanger (W/°C) Q of HT evaporator (kW) Q of LT evaporator (kW) Q of condenser (kW) Q of intermediate heat exchanger (kW) HT evaporating temperature (°C) LT evaporating temperature (°C) HT evaporating pressure (kPa) LT evaporating pressure (kPa) HT turbine pressure ratio LT turbine pressure ratio HT turbine mass flow rate (kg/s) LT turbine mass flow rate (kg/s)
29.0 11.67 38.62 2142 8445 8290 – 133.4 115.2 219.7 – 215 70.8 3292.5 195.6 16.8 1.7 0.210 0.488
26.8 11.39 35.72 1790 8323 8151 8803 120.0 115.2 208.4 102.7 215 72.3 3292.5 648.6 11.8 1.83 0.223 1.083
Table 9 Comparison between the CCE-ORC system and the dual-loop ORC system in term of main component parameters. Parameter Heat exchanger volume (L)
Pump parameters
Turbine parameters
The CCE-ORC system
The dual-loop ORC system
13.7 21.1 –
11.4 20.8 22.4
53.8 88.6
53.1 107.6
HT pump head (kPa) HT pump volume flow rate (L/min) LT pump head (kPa) LT pump volume flow rate (L/min)
3198.7 17.6
3034.5 19.6
101.7 23.4
324.5 51.3
HT turbine volume expansion ratio HT turbine rotor diameter (mm) LT turbine volume expansion ratio LT turbine rotor diameter (mm)
20.9
15.7
42.3
37.7
1.5
1.86
121.7
82.7
HT evaporator LT evaporator Intermediate heat exchanger Condenser Total
5. Comparison between dual-loop ORC system and CCE-ORC system The performance and compactness between the CCE-ORC system and dual-loop ORC system have been compared in this section. A dual-loop ORC system is designed for the engine mentioned in Section 4.1, and cyclopentane and R245fa are used as working fluids for the HT loop and the LT loop respectively. All the design parameters are the same as those of the CCE-ORC system except the PPTD of intermediate heat exchanger. The system net power and compactness have a trade-off relationship under different intermediate heat exchanger PPTD. If that PPTD increases, the system net power output decreases (shown in Fig. 14(a)), while the UA of intermediate heat exchanger also decreases, which means that the volume of that heat exchanger decreases (shown in Fig. 14(b)). The comparison between the CCE-ORC system and the dual-loop ORC system is shown in Table 8, when intermediate heat exchanger PPTD is set at 10 °C. The heat transfer rate of each heat exchanger in each system is approximately the same, while the CCE-ORC system does not have an intermediate heat exchanger. The volumes of heat exchangers in these two systems are evaluated by the condenser volume evaluation model [43], and the comparison result is shown in Table 9. The total heat exchanger
Fig. 15. Comparison of exergy loss between the CCE-ORC system and the dual-loop ORC system.
volume of the CCE-ORC system is 21 L (18%) less than that of the dual-loop ORC system. The pump characteristic parameters are compared in Table 9. It shows that the volume flow rates of the pumps, especially the LT pump, in the CCE-ORC system are smaller, so the pumps of the CCE-ORC system have smaller volumes.
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Fig. 16. Comparison of net power output between the CCE-ORC system and the dual-loop ORC system.
The turbine characteristic parameters are shown in Table 9. The turbine rotor diameter is calculated by Eq. (47) [44]. Although turbine rotor diameters of the CCE-ORC system are larger than that of the dual-loop ORC system, the volume difference between turbines is not remarkable, because the turbine volume only makes up a small proportion of the total system volume. Overall, considering the difference in each main component as well as one less reservoir, the CCE-ORC system can be recognized more compact than the dual-loop ORC system.
pffiffiffiffiffiffiffiffiffi 1=4 Drotor ¼ Ds V out =Dh
ð47Þ
where Ds is the specific diameter; V out is the volume flow rate at turbine outlet; Dh is the enthalpy drop in the turbine. The CCE-ORC system generates 8% more power than the dualloop ORC system at the design point. The main reason is that this system can absorb more waste heat from the exhaust gases since working fluid temperature at HT evaporator inlet is lower in the CCE-ORC system. The comparison of exergy loss distribution (Fig. 15) shows that more exergy is dissipated in the condenser and the HT evaporator of the CCE-ORC system than in that of the dual-loop ORC system, while less exergy is lost in the unused exhaust gases of the CCE-ORC system. It has to be mentioned that the mixing process in the CCE-ORC system leads to only about 1.2 kW exergy loss, while the intermediate heat exchanger in the dual-loop ORC system causes about 4 kW exergy loss. That is why the CCE-ORC system total thermal efficiency (11.67%) is slightly higher than the dual-loop ORC system thermal efficiency (11.39%). The comparison of these two system in term of net power output under full operating conditions is shown in Fig. 16. The net power output of the CCE-ORC system is larger under all the conditions, while the relative difference of the net power between these two systems is larger in lower engine rotating speed and lower engine load region. Compared with the dual-loop ORC system, the CCE-ORC system can output 7.94% more net power in frequently operating region on average.
is used. This system can also replace the original coolant radiator, since it can recover all the waste heat in coolant. Cyclopentane is the most suitable working fluid for this CCEORC system among six candidates following the working fluid selection criteria. The net power of the system with cyclopentane is the highest, following by that for pentane and R1233-zd-e. The working fluid side pressure drop in condenser has a negative impact on system net power output, because it will decrease the turbine expansion ratio, thereby leading to a less net power output. This effect is significant in the system with cyclopentane, whose normal boiling point (NBP) is high, which means the condensing pressure is normally quite low. The result shows that if this pressure drop increases by 10 kPa, the system net power output will be reduced by 4.8%. System performance under full operating conditions is simulated. The result shows that the peak thermal efficiency can be improved from 45.3% to 49.5%, where the minimum BSFC decreases from 185.6 g/(kW h) to 169.9 g/(kW h). The average BSFC in the frequently operating region (engine rotating speed: 1100–1400 rpm; engine load: 50–90%) decreases by about 9.2% from 187.9 g/(kW h) to 172.2 g/(kW h). Compared with the dual-loop ORC system, the CCE-ORC system can generate 7.94% more net power in frequently operating conditions in average, because it can recover more waste heat from exhaust gases and the mixing process dissipate less exergy than the intermediate heat exchanger. The CCE-ORC system is also more compact since the intermediate heat exchanger can be removed and the total volume of heat exchangers can be reduced by 21 L (18%). The pump volumes can also be reduced, while the volumes of other components are approximately the same. Acknowledgements The authors would like to thank the National Natural Science Foundation of China [No. 51636005] for the support. References
6. Conclusions In this paper, a CCE-ORC system is proposed to recover the waste heat in both exhaust gases and coolant. This ORC system uses only single loop to recover both the high temperature and low temperature waste heat in two branches respectively. The system structure is simple and only one kind of working fluid
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