A supercritical or transcritical Rankine cycle with ejector using low-grade heat

Energy Conversion and Management 78 (2014) 551–558

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A supercritical or transcritical Rankine cycle with ejector using low-grade heat Xinguo Li ⇑, Haijun Huang, Wenjing Zhao Department of Thermal Engineering, School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China

a r t i c l e

i n f o

Article history: Received 20 August 2013 Accepted 14 November 2013 Available online 10 December 2013 Keywords: Supercritical or transcritical Rankine cycle (SRC TRC) Supercritical or transcritical Rankine cycle with ejector (ESRC ETRC) Ejector Thermodynamic analysis

a b s t r a c t A supercritical or transcritical Rankine cycle with ejector (ESRC, ETRC) based on the basic supercritical or transcritical Rankine cycle (SRC, TRC) are proposed for the conversion of low-grade heat to power in this paper. The thermodynamic comparative analyses on the SRC, TRC and ESRC, ETRC are conducted on the power output and thermal efficiency of the cycles. The carbon dioxide is chosen as the working fluid for the cycles. Water is chosen as the fluid of the low-grade heat. The water temperature is selected in a range of 60–90 °C, a typical water temperature is 80 °C, and the mass flow rate is 1 kg/s. The same temperature and mass flow rate of the water is the standard condition for the comparative analysis of the thermodynamic performance. Results show that the net power output of the cycles could be ranked from high to low: ESRC > ETRC > SRC > TRC, and the thermal efficiency could be ranked from high to low: TRC > SRC > ESRC > ETRC. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The low-grade heat, such as solar energy, geothermal energy, biomass energy, and waste heat from various thermal processes, exists in the world extensively. Especially, the low-grade heat with temperature range of 60–100 °C is larger amount and more easily acquired. The utilization and conversion of this kind of energy will be more practical and significant. The organic Rankine cycle (ORC) and supercritical or transcritical Rankine cycle (SRC, TRC) are the promising processes for the conversion of low-grade heat to power. However, the isothermal boiling process in the conventional ORC results in a mismatch between the working fluid and the heat source, which would further causes a relatively irreversibility destruction of this process [1,2]. A supercritical or transcritical Rankine cycle, on the other hand, could avoid this problem preferably. Gu and Sato [3] studied a supercritical power cycle with a regenerative process to reach the maximum thermal efficiency by choice of an appropriate working fluid and optimization of the condensing temperature or pressure. Vetter et al. [4] compared the sub- and supercritical processes using propane, carbon dioxide (CO2) and 10 other refrigerants and showed that propane or R143a can increase specific net power output more than 40% at a geothermal temperature of 150 °C. Chen et al. [5] conducted a comparative study of CO2 transcritical power cycle compared with R123’s ORC in waste heat recovery and found that CO2 transcritical power ⇑ Corresponding author. E-mail address: [email protected] (X. Li). 0196-8904/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.enconman.2013.11.020

cycle has a better performance than the ORC. Zhang et al. [6] presented that R123 in subcritical ORC system yields the highest thermal efficiency and exergy efficiency, while for transcritical ORC, R125 has a higher thermal and exergy efficiency than that of R123 in ORC. Chen et al. [7] studied the transcritcal Rankine cycle using R32 and CO2. The energy and exergy analyses showed that the R32 based transcritical Rankine cycle can achieve 12.6–18.7% higher thermal efficiency and works at much lower pressures. Baik et al. [8] compared the power output of the CO2 and R125 transcritical cycle for a low-grade heat source of about 100 °C and showed that R125 transcritical cycle produced 14% more power than that of the CO2. Baik et al. [9] compared the R125 transcritical cycle with the subcritical ORCs using R134a, R245fa and R152a and showed that the power output of the R125 transcritical cycle was greater than that of subcritical ORCs when a total overall conductance was higher than 35 kW/K. Kim et al. [10] proposed a transcritical-CO2 Rankine cycles or fully cooled supercritical-CO2 cycles using both the low and high temperature heat sources which can maximize the power output of the CO2 power cycle with the given high temperature heat sources. Wang et al. [11] and Cayer et al. [12] conducted parametric studies on the thermodynamic performance and exergy destruction in a CO2-based transcritical Rankine cycle to find that parameters such as turbine inlet pressure and temperature have significant effects on the exergy efficiency of the supercritical CO2 power cycle. Vélez et al. [13] conducted an energy and exergy analysis on the CO2 transcritical power cycle. Results indicated an increase up to 25% for the exergy efficiency, and up to 300% for the energy efficiency when the inlet temperature to the turbine is risen

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X. Li et al. / Energy Conversion and Management 78 (2014) 551–558

Nomenclature h m Q s P T u W

specific enthalpy (J kg1) mass flow rate (kg s1) heat transfer (W) specific entropy (J kg1 K1) pressure (bar) temperature (K) entrainment ratio of ejector or mass flow ratio in firststage heater power (W)

Greek symbols g efficiency (%) Subscripts dry dry fluid (expansion) cool (c) cooling cr critical

from 60 to 150 °C. Bıyıkog˘lu and Yalçınkaya [14] investigated a geothermal power cycle using CO2 at supercritical condition, and a parametric study was performed to test the proposed system under different reservoir conditions. Schuster et al. [15] conducted an exergy analysis and comparison and indicated that the system efficiency could improve approximately 8% for the supercritical parameters because of the better exergetical efficiency. Sarkar and Bhattacharyya [16] analyzed the effects of different operating conditions and cycle performance on the optimized supercritical CO2 recompression cycle. In nuclear reactors, solar energy collectors and coal-fired plant adapted CO2 capture process et al., the supercritical CO2 power cycle attracted more and more interests recently [17–20]. Zhang et al. [21,22] investigated the performance of a solar supercritical Rankine system using CO2 and showed that heat collection efficiency for the CO2-based solar collector is measured at 8.78– 9.45% which presents a potential future for the solar powered CO2 Rankine system. Song et al. [23] analyzed a transcritical CO2 power cycle driven by solar energy and showed that there is an optimum turbine inlet pressure where the net power output and the system efficiency both reach maximum values. In addition, the condensation temperature has a significant impact on the system performance. Halimi and Suh [24] developed a optimized supercritical cycle analysis code to analyze the design of a supercritical CO2 driven Brayton cycle for a fusion reactor. Carbon dioxide (CO2) with the advantages of abundant in nature, non-toxic, non-flammable and inexpensive has been extensively studied as the working fluid in the supercritical or transcritical Rankine cycles. However, the low critical temperature of 31.18 °C might be a disadvantage for the condensation process. Both the ORC and supercritical or transcritical Rankine cycle (SRC and TRC) have their own advantages. Although the SRC and TRC can obtain a better thermal match than the ORC, the SRC and TRC normally needs high pressure that may lead to difficulties in operation and a safety concern. From brief review of the literatures above, the researches on the supercritical or transcritical Rankine cycles are mainly focused on the temperature of low-grade heat in medium to high (>100 °C) conditions. But, most of the temperature is lower than 100 °C which is larger amount and more easily acquired, as solar energy, low temperature geothermal and waste heat from various thermal processes et al. To use this kind of energy, especially to increase the

exp expander heat (h) heating in inlet max maximum oc environment opt optimum out outlet net net output pp pinch point r reduced parameter sum sum th thermal w water wet wet fluid (expansion) wf working fluid 1–7 state points

power output from this low temperature energy by power cycles will be more practical and significant to the research and application. In view of this consideration, a supercritical or transcritical Rankine cycle with ejector is proposed in this paper. With the ejector, the power output of the cycle could be increased compared to the basic supercritical or transcritical Rankine cycle. 2. Principle of the supercritical or transcritical Rankine cycle with ejector Fig. 1 shows the process of the supercritical or transcritical Rankine cycle (SRC, TRC) in the T–S diagram. The major difference between the supercritical and transcritical Rankine cycle is whether the cooling process takes place at a pressure below the critical pressure. As shown in Fig. 1a, the working fluid in the supercritical Rankine cycle (SRC) processes is found entirely above its critical pressure. While, in transcritical Rankine cycle (TRC), the cooling process goes through the two-phase region below the critical pressure, as shown in Fig. 1b. Based on the basic SRC and TRC, an ejector and a second-stage heater are introduced to the SRC and TRC to form the supercritical or transcritical Rankine cycle with ejector (ESRC, ETRC), as shown in Figs. 2 and 3. In the ETRC and ESRC, the supercritical fluid from the second-stage heater works as the primary fluid in the ejector to entrain the exhaust from the expander so as to decrease the expander’s backpressure and increase the pressure difference in

T

T Ph Ph Pc Pc

s

(a) SRC

s

(b) TRC

Fig. 1. T–S diagram of supercritical and transcritical Rankine cycle (SRC and TRC).

X. Li et al. / Energy Conversion and Management 78 (2014) 551–558

LGHS

(Ph2) primary fluid (state 2) from second-stage heater in the ESRC or ETRC expands in the motive nozzle where its internal energy converts to kinetic energy. This high speed primary fluid entrains a low pressure (P3) secondary fluid (state 3) from the expander in the suction nozzle. Both fluids enter the mixing section where they exchange momentum, kinetic and internal energies and become a mixed fluid (state 4) outlet from the ejector and inlet to the cooler or condenser with a middle pressure (Pc). The result of the ejection process is that the outlet pressure from the expander (P3) as the secondary fluid is lower than the cooling or condensation pressure (Pc) of the mixed fluid. It means that the expander’s backpressure of P3 in the ESRC or ETRC is decreased compared to the basic cycle of SRC or TRC in which the backpressure is Pc that results in an increase of the power output in the ETRC and ESRC compared to the TRC and SRC.

Expander

1 First-stage heater

6 Second-stage heater

3

2

7

Fluid pump

Cooler or condenser

4

5

Ejector

Fig. 2. Configuration and processes of supercritical and transcritical Rankine cycle with ejector (ESRC and ETRC).

T

T

1

1

Ph1 Ph1

2 6 7

Ph2 Pc

4

6

3

5

Ph2 Pc

7 5 s

(a) ESRC

553

2

4 3 s

(b) ETRC

Fig. 3. T–S diagram of the ESRC and ETRC.

the expander that results in an increase of the power output of the cycles. 2.1. Process and principle of the ESRC and ETRC (1) The first cycle 5–6–1–3–4–5: One part of subcooled (or saturated) liquid from the cooler (or condenser) is pumped to the first-stage heater in process 5–6, and then heated to the supercritical state in process 6–1; the supercritical fluid expands in the expander, generating power in process 1–3; the exhaust fluid from the expander (state 3) will work as the secondary fluid of the ejector to the ejection process. (2) The second cycle 5–7–2–4–5: The other part of subcooled (or saturated) liquid from the cooler (or condenser) is pumped to the second-stage heater in process 5–7, and heated to the supercritical state (or superheated vapor in the ETRC) in process 7–2; the supercritical fluid (or superheated vapor) (state 2) will work as the primary fluid of the ejector to the ejection process. (3) The primary fluid (state 2) and the secondary fluid (state 3) are mixed and diffused in the ejector to form the mixed fluid (state 4). The mixed fluid (state 4) from the ejector enters to the cooler (or condenser) to be cooled to the subcooled (or saturated) fluid (state 5); then pumped to the two heaters by the fluid pumps in process 5–6 and process 5–7 respectively, completed the cycle. 2.2. Process and principle of the ejector Fig. 4 shows the configuration and process of the ejector. A typical ejector consists of a motive nozzle, a suction nozzle or receiving chamber, a mixing section and a diffuser. A high pressure

3. Thermodynamic analysis of the cycle 3.1. Specifications and conditions for calculations 1. The carbon dioxide CO2 is chosen as the working fluid for the supercritical or transcritical Rankine cycles (SRC, TRC, ESRC and ETRC). 2. Water is chosen as the fluid of the low-grade heat. The water temperature is selected in a range of 60–90 °C, a typical water temperature is 80 °C, and the mass flow rate is 1 kg/s. The same temperature and mass flow rate of the water is the standard condition for the comparative analysis of the thermodynamic performance. 3. A pinch point temperature difference (DT_pp) between the heat source water and the working fluid is set to 8 °C. The maximum outlet and inlet temperature of the CO2 in the heater of the cycles is set to lower than the inlet and outlet temperature of the water by DT_pp respectively in the calculation. 4. In the SRC and ESRC, the outlet temperature of the CO2 from the cooler is set to 30 °C. In the TRC and ETRC, the outlet of CO2 from the condenser is set as saturated liquid, and the bubble temperature of CO2 is set the same as 30 °C. 5. Carbon dioxide CO2 is a wet fluid. A wet expansion can be transferred to dry expansion with the outlet of the expander shifted to the saturated (or super heat) vapor, and the inlet to the expander will be shifted to the super heat state. 6. In the ETRC and ESRC, the outlet pressure from the expander (P3), i.e., the pressure of the second fluid in the ejector, is set to 0.95 or 0.9 times the cooling pressure (Pc), and a pressure drop ratio (c) is defined as c = P3/Pc = 0.95 or 0.9. 7. In consideration of the comparability, a reduced parameter of the pressure (Pr = P/Pcr) is used to illustrate the cycle’s thermodynamic performance of the working fluids. 8. The environment state is set to: Poc = 101.325 kPa, Toc = 298.15 K. 3.2. The simulation of the ejector In consideration of the calculation load and to simplify the calculation process, an idealized thermodynamic process of the ejector in the ESRC and ETRC is assumed and considered as the enthalpy balance and the entropy balance in the ejection process of the ejector, as follows:

h4 ¼ ðh3  u þ h2 Þ=ð1 þ uÞ

ð1Þ

S4 ¼ ðs3  u þ s2 Þ=ð1 þ uÞ

ð2Þ

The entrainment ratio (u) of the ejector, i.e., the mass flow ratio in the first-stage heater, is:

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B

C

D

Primary fluid from second-stage heater (Ph2) Mixed fluid to cooler (Pc)

A Secondary fluid from expander (P3) Ph2

Pc P3

Fig. 4. Configuration and process of ejector.

u ¼ mwf 1 =mwf

ð3Þ

2

The total mass flow ratio (mwf) in the cycle is:

mwf ¼ mwf

1

þ mwf

ð4Þ

2

In the ejection process of the ejector, there should exist the pressure losses and irreversible processes to cause the increase of entropy in the ejection process. For the unsound theory and model of the ejection process for the supercritical fluid, this problem will be necessary for a further study in the future. 3.3. Thermodynamic performance of the cycle The thermodynamic analyses and comparisons between the ESRC, ETRC and the basic SRC, TRC will be conducted. And the emphasis will be on the thermodynamic performance at the maximum net power output (Wnet_max) of the cycles. The calculated thermodynamic performance includes: heating load (Qheat), power output from the expander (Wout), pumping power (Wpump), net power output (Wnet), thermal efficiency (gth), and the operating condition parameters. The simulation procedures for the cycle’s thermodynamic performance are built based on the refrigerant’s physical properties by REFPROP from NIST [25] on Matlab. Fig. 5 shows the flow chart of the simulation procedure for the ESRC. An idealized thermodynamic process of the cycles is assumed and considered as no pressure loss, no heat loss, and isentropic processes are assumed for the expander and the pump. The heating load (Qheat) from heat source water in the heater is:

Q heat ¼ mwf  ðhheat

out

 hheat

in Þ

ð5Þ

The cooling load (Qcool) in the cooler (or condenser) is:

Q cool ¼ mwf  ðhcool

in

 hcool

out Þ

Fig. 5. Flow chart of the simulation procedure for the ESRC.

ð6Þ 4. Results and discussion

The power output (Wout) from the expander is:

W out ¼ mwf  ðhexp

in

 hexp

out Þ

ð7Þ

The pumping power (Wpump) by the pump is:

W pump ¼ mwf  ðhpump

out

 hpump in Þ

ð8Þ

The net power output (Wnet) of the cycle is:

W net ¼ W out  W pump

ð9Þ

The thermal efficiency (gth) of the cycle is:

gth ¼ W net =Q heat

ð10Þ

For different working fluids have different pressure in the heating or cooling processes in the cycle, a reduced parameter of the pressure (Pr = P/Pcr) will be used to illustrate the thermodynamic performance of the cycles. This reduced parameter of the pressure will be more intuitive and comparable to the evaluation of thermodynamic performance of different working fluids. Figs. 6–12 present the thermodynamic performance of the basic supercritical or transcritical Rankine cycle (SRC, TRC) and the supercritical or transcritical Rankine cycle with ejector (ESRC, ETRC) with working fluid of CO2.

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Heating pressure of Pr1 (=Ph1/Pcr)

Net power output (kW)

11

9

7 ESRC ETRC_wet

5

ETRC_dry SRC

3

TRC_wet TRC_dry

1 1

1.5

2

2.5

3

3.5

8 ESRC SRC

6

4

2

0

4

1

1.2

Heating pressure of Pr1 (=Ph1/Pcr)

1.4

1.6

1.8

2

Cooling pressure of Prc (=Pc /Pcr)

Fig. 6. Net power output of cycles with CO2 with the heating pressure of Ph1 at water temperature of 80 °C.

Fig. 10. Heating pressure of Ph1 with cooling pressure of Pc at water temperature of 80 °C for SRC and ESRC with CO2.

10

16

Maximum net power output (kW)

Thermal efficiency (%)

12

TRC_wet TRC_dry

8

SRC ESRC

6

ETRC_wet ETRC_dry

4

2 1

1.5

2

2.5

3

3.5

4

Heating pressure of Pr1 (=Ph1/Pcr)

ESRC

14

ETRC

12 SRC

10

TRC

8 6 4 2

Fig. 7. Thermal efficiency of cycles with CO2 with Ph1 at water temperature of 80 °C.

60

65

70

75

80

85

90

Water temperature (ºC) Fig. 11. The maximum net power output (Wnet_max) with water temperature.

180

ETRC_Qh_sum ESRC_Qh_sum ETRC_Qh2

120

ESRC_Qh2 90

10

SRC_Qh or Qh1

TRC

TRC_Qh or Qh1

60

9

30 0 1

1.5

2

2.5

3

3.5

4

Heating pressure of Pr1 (=Ph1/Pcr) Fig. 8. Heating load of cycles with CO2 with Ph1 at water temperature of 80 °C.

Thermal efficiency (%)

Heating load (kW)

150

SRC ESRC

8

ETRC

7 6 5 4

13

11

3

ESRC_Wnet

60

9

11

SRC_η ESRC_η

7

9

5

7

3

5

Thermal efficiency (%)

Net power output (kW)

SRC_Wnet

3

1 1

1.2

1.4

1.6

1.8

2

Cooling pressure of Prc (=Pc /Pcr) Fig. 9. Net power output and thermal efficiency with cooling pressure of Pc at water temperature of 80 °C for SRC and ESRC with CO2.

65

70

75

80

85

90

Water temperature (ºC) Fig. 12. Thermal efficiency with water temperature at the Wnet_max.

It is found that the variation of the net power output (Wnet) in the dry expansion and wet expansion is the same in most range of the operation conditions. In the calculation of the dry expansion, the outlet of the expansion will be shifted manually to the saturated vapor if it falls into the two-phase region to avoid the wet expansion. So the outlet temperature of the CO2 from the heater will be increased until it reaches the maximum which is lower than the inlet water temperature by DT_pp of 8 °C, and the calculation will be terminated.

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In the optimum calculation, the outlet temperature of the CO2 from the heater in those four cycles always reaches the maximum of 72 °C which is lower than the water temperature of 80 °C by DT_pp of 8 °C.

reduced parameter of pressure (Pr1) is 1.67, 1.74, 1.69 and 1.78. The Wnet of the cycles can be ranked from high to low: ESRC > ETRC > SRC > TRC. 4.2. Thermal efficiency (gth)

4.1. Net power output (Wnet) As shown in Fig. 6, the net power output (Wnet) of the TRC, SRC, ETRC and ESRC with CO2 at water temperature of 80 °C increases and then decreases with the first-stage heating pressure (Ph1), and exists the maximum net power output (Wnet_max). The Wnet_max is 9.25 kW, 9.45 kW, 10.19 kW, 10.32 kW for TRC, SRC, ETRC, ESRC respectively at the pressure drop ratio (c = P3/Pc) of 0.95 in ETRC and ESRC, as shown in Table 1. And the increases of the Wnet_max in the SRC, ETRC, ESRC is 2.14%, 10.18% and 11.60% compared to the TRC respectively. The corresponding optimum first-stage heating pressure (Ph1_opt) is 122.91 bar, 128.58 bar, 124.74 bar and 131.34 bar for TRC, SRC, ETRC and ESRC respectively, or the

As shown in Fig. 7, the thermal efficiency (gth) of the TRC and SRC increases with the Ph1 throughout. But the gth of the ETRC and ESRC increases and then decreases with the Ph1, and exists the maximum of gth (gth_max). The gth_max is 6.41% for ETRC and 6.37% for ESRC, and the corresponding Ph1 is 117.51 bar, 124.17 bar respectively at the pressure drop ratio (c = P3/Pc) of 0.95 in ETRC and ESRC. But this condition of the maximum of gth (gth_max) is different to the condition of the maximum net power output (Wnet_max). In the condition of the Wnet_max, the gth of the TRC, SRC, ETRC and ESRC is 8.19%, 7.88%, 6.23%, and 6.30%. Different to the increase of the Wnet_max, the gth of the SRC, ETRC and ESRC is 3.89%,

Table 1 Performance comparison among the cycles at different expander’s outlet pressure in the condition of the maximum net power output (Wnet_max) and water temperature of 80 °C and flow rate of 1 kg/s. Cycle

TRC

SRC

ETRC

1. Pressure drop ratio c(P3/Pc) in expander in ETRC and ESRC

/

/

/

0.95

0.9_wet 0.9_dry 0.95

0.9_wet 0.9_dry

2. Water temperature outlet from heater First-stage heater Second-stage heater

°C °C

53.05 /

51.36 /

53.48 40.94

55.36 44.14

54.55 44.91

51.89 40.88

54.29 43.44

52.15 44.26

Pressure (Ph1) Pressure ratio of Pr1 (Ph1/Pcr) Inlet temperature (T6) Outlet temperature (T1) Mass flow rate (mwf1) Heating load (Qh1)

bar /

122.91 128.58 124.74 1.67 1.74 1.69

133.25 1.81

129.54 1.76

131.34 1.78

144.17 1.95

132.66 1.80

°C °C kg/s kW

45.05 72 1.02 112.88

43.36 72 1.07 119.97

45.47 72 1.03 111.10

47.36 72 1.10 103.21

46.55 72 1.07 106.60

43.89 72 1.10 117.72

46.29 72 1.21 107.70

44.15 72 1.11 116.65

Pressure (Ph2) Pressure ratio of Pr2 (Ph2/Pcr) Inlet temperature (T7) Outlet temperature (T2) Mass flow rate (mwf2) Heating load (Qh2)

bar /

/ /

/ /

79.72 1.08

89.34 1.21

91.85 1.25

83.30 1.13

92.86 1.26

96.09 1.30

°C °C kg/s kW

/ / / /

/ / / /

32.94 45.48 0.44 52.43

36.14 47.36 0.48 46.92

36.91 46.55 0.48 40.30

32.88 43.89 0.41 46.03

35.44 46.29 0.51 45.35

36.26 44.15 0.57 33.00

Pressure (Pc) Pressure ratio of Prc (Pc/Pcr) Inlet temperature (T4) Outlet temperature (T5) Mass flow rate (mwf) Cooling load (Qcool)

bar /

72.14 73.78 72.14 0.9778 1.0001 0.9778

72.14 0.9778

72.14 0.9778

73.78 1.0001

73.78 1.0001

73.78 1.0001

°C °C kg/s kW

34.08 30 1.02 103.63

34.01 30 1.07 110.52

34.65 30 1.48 153.33

31.90 30 1.58 139.46

31.88 30 1.54 136.27

33.86 30 1.50 153.42

31.79 30 1.71 142.43

31.79 30 1.67 139.14

Pressure (Ph2) Temperature (T2) Pressure (P3) Pressure ratio of Pr3 (P3/Pcr) Temperature (T3) Quality Pressure (Pc) Temperature (T4)

bar °C bar /

/ / / /

/ / / /

79.72 45.48 68.53 0.92891

89.34 47.36 64.92 0.88002

91.85 46.55 64.92 0.88002

83.30 43.89 70.09 0.950095

92.86 46.29 66.40 0.90009

96.09 44.15 66.40 0.90009

Entrainment ratio (u) Pressure ratio (inlet/outlet) in expander

°C kg/kg bar °C / /

/ / / / / /

/ / / / / /

30.01 sup-heat 72.14 34.65 2.34 1.82

25.39 0.96 72.14 31.90 2.28 2.05

25.39 sat. vap 72.14 31.88 2.25 2.00

30.05 sup-heat 73.78 33.86 2.68 1.87

26.37 0.86 73.78 31.79 2.38 2.17

26.37 sat. vap 73.78 31.79 1.95 2.00

5. Performance of the cycles Total heating load (Qh_sum = Qh1 + Qh2) Power output from expander (Wout) Pumping power (Wpump) Maximum net power output (Wnet_max) Thermal efficiency (gth)

kW kW kW kW %

112.88 17.41 8.16 9.25 8.19

119.97 18.11 8.67 9.45 7.88

163.52 19.28 9.09 10.19 6.23

150.13 22.44 11.77 10.67 7.11

146.91 21.73 11.09 10.64 7.24

163.75 20.19 9.86 10.32 6.30

153.04 24.47 13.86 10.62 6.94

149.65 21.99 11.48 10.51 7.02

6. Increase of the performance compared to TRC Increase of the Wnet_max Increase of the gth

% %

/ /

2.14 10.18 3.89 23.94

3. Cycle parameters of working fluid CO2 First-stage heater

Second-stage heater

Cooler or condenser

4. Parameters in ejection Primary fluid (state 2) Second fluid (state 3)

Mixed fluid (state 4)

ESRC

15.34 15.03 11.60 13.27 11.62 23.07

14.78 13.64 15.34 14.28

X. Li et al. / Energy Conversion and Management 78 (2014) 551–558

23.94% and 23.07% lower than that of the TRC respectively, as shown in Table 1. 4.3. Heating load (Qh) Fig. 8 presents the variation of the heating load (Qh) with the first-stage heating pressure (Ph1). At the same Ph1, the heating load in the first-stage (Qh1) of the ETRC and ESRC is the same as the heating load in the TRC and SRC respectively, and the Qh1 decreases with the Ph1. But the heating load in the second-stage (Qh2) of the ETRC and ESRC increases with the Ph1, and the total heating load (Qh_sum = Qh1 + Qh2) in the ETRC and ESRC increases with Ph1. There exists the maximum of the thermal efficiency (gth_max) in the ETRC and ESRC which is different from the TRC and SRC, as shown in Fig. 7. The reason is that the Qh in TRC and SRC is decreasing throughout but the Qh_sum in ETRC and ESRC is increasing due to the Qh2. With the Ph1 higher than the optimum Ph1_opt which is 122.91 bar, 128.58 bar, 124.74 bar, 131.34 bar for TRC, SRC, ETRC and ESRC, as present in Section 3.1, the Wnet decreases. But the negative slope or the decreased tendency of the Qh is higher than that of the Wnet in the TRC and SRC that the gth of the TRC and SRC does not decrease, but increase. On the contrary, due to the increase of the Qh_sum throughout in the ETRC and ESRC, the gth will decrease after the increase that the maximum of the thermal efficiency (gth_max) comes out, as shown in Fig. 7. 4.4. Comparison of the maximum net power output (Wnet_max) The performance of the ETRC and ESRC in the condition of the maximum net power output (Wnet_max) is calculated with different outlet pressure (P3) of the expander (the pressure drop ratio c at 0.95 and 0.9), as shown in Table 1. The lower the P3 (or the c) is, the higher the Wnet_max and gth of the ETRC and ESRC is. For example, the Wnet_max at c of 0.9 is 4.68% in wet expansion and 4.40% in dry expansion higher than the Wnet_max at c of 0.95 in the ETRC. But the lower the P3 (or the c) is, the more possibility the wet expansion will occur for the wet working fluid of the CO2. In summary, an ejector is introduced to the basic cycles of the TRC and SRC to form the ETRC and ESRC. The outlet pressure of the expander in the ETRC and ESRC is decreased or the pressure difference in the expander is increased by the ejector that results in an increase of the net power output of the cycle. The net power output is higher in the ETRC and ESRC compared to the TRC and SRC.

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arly. The thermal performance and the analyses of the cycles at different water temperature are similar to the outcomes at water temperature of 80 °C. The net power output of the cycles could be ranked from high to low: ESRC > ETRC > SRC > TRC; and the thermal efficiency could be ranked from high to low: TRC > SRC > ESRC > ETRC in the water temperature range of 60– 90 °C. 5. Conclusions An ejector is introduced to the basic supercritical or transcritical Rankine cycle (SRC, TRC) to form the supercritical or transcritical Rankine cycle with ejector (ESRC, ETRC). The outlet pressure of the expander in the ETRC and ESRC is decreased or the pressure difference in the expander is increased by the ejector that results in an increase of the net power output of the cycle. 1. The net power output (Wnet) of the cycles could be ranked from high to low: ESRC > ETRC > SRC > TRC, and the thermal efficiency (gth) could be ranked from high to low: TRC > SRC > ESRC > ETRC with working fluid of CO2 at the pressure drop ratio (c = outlet pressure of expander (P3)/cooling pressure (Pc)) of 0.95 in ETRC and ESRC in water temperature range of 60–90 °C. 2. The increases of the maximum net power output (Wnet_max) in the SRC, ETRC, ESRC is 2.14%, 10.18% and 11.60% compared to the TRC, but the corresponding gth of the SRC, ETRC and ESRC is 3.89%, 23.94% and 23.07% lower than that of the TRC respectively at c of 0.95 in ETRC and ESRC. 3. The lower the outlet pressure (P3) of the expander is, the higher the Wnet_max and gth of the ETRC and ESRC is. In the ETRC, the Wnet_max at c of 0.9 is 4.68% in wet expansion and 4.40% in dry expansion higher than the Wnet_max at c of 0.95. 4. The cooling pressure in the SRC and ESRC by the optimum calculation demonstrates to be as lower as possible to near the critical pressure of the CO2.

Acknowledgement The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51276122). References

4.5. Effect of the cooling pressure It is well known that the lower the condensation condition (i.e., the condensation pressure or condensation temperature) is, the higher the thermal performance of the power cycle will be. The optimum calculation reveals that the cooling pressure (Pc) in the SRC and ESRC is as lower as possible to close to the critical pressure of the CO2. The Pc had to be set to a definite value as the reduced parameter of the cooling pressure (Prc) is set to 1.0001, as shown in Table 1. The lower the cooling pressure (Prc) is, the higher the thermal performance of the Wnet and gth is, as shown in Fig. 9. But the heating pressure (Ph1) will increase with the Prc in the SRC and ESRC, as shown in Fig. 10. 4.6. Performance (Wnet_max and gth) with water temperature Figs. 11 and 12 present the maximum net power output (Wnet_max) and the corresponding thermal efficiency (gth) of the TRC, SRC, ETRC and ESRC with CO2 at pressure drop ratio (c) of 0.95 in water temperature range of 60–90 °C. The Wnet_max and gth of the cycles increase with the water temperature almost line-

[1] Chen HJ, Goswami DY, Stefanakos EK. A review of thermodynamic cycles and working fluids for the conversion of low-grade heat. Renew Sust Energy Rev 2010;14(9):3059–67. [2] Chen HJ, Goswami DY, Stefanakos EK, Rahman MM. A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power. Energy 2011;36(1):549–55. [3] Gu ZL, Sato H. Optimization of cyclic parameters of a supercritical cycle for geothermal power generation. Energy Convers Manage 2001;42(12):1409–16. [4] Vetter C, Wiemer HJ, Kuhn D. Comparison of sub-and supercritical Organic Rankine Cycle for power generation from low-temperature/low-enthalpy geothermal wells, considering specific net power output and efficiency. Appl Therm Eng 2013;51(1–2):871–9. [5] Chen Y, Lundqvist P, Johansson A, Platell P. A comparative study of the carbon dioxide transcritical power cycle compared with an organic rankine cycle with R123 as working fluid in waste heat recovery. Appl Therm Eng 2006;26(17– 18):2142–7. [6] Zhang SJ, Wang HX, Guo T. Performance comparison and parametric optimization of subcritical organic Rankine cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88(8):2740–54. [7] Chen HJ, Goswami DY, Rahman MM, Stefanakos EK. Energetic and exergetic analysis of CO2- and R32-based transcritical Rankine cycles for low-grade heat conversion. Appl Energy 2011;88(8):2802–8. [8] Baik YJ, Kim MS, Chang KC, Kim SJ. Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source. Appl Energy 2011;88(3):892–8.

558

X. Li et al. / Energy Conversion and Management 78 (2014) 551–558

[9] Baik YJ, Kim MS, Chang KC, Lee YS, Yoon HK. A comparative study of power optimization in low-temperature geothermal heat source driven R125 transcritical cycle and HFC organic Rankine cycles. Renew Energy 2012;54:78–84. [10] Kim YM, Kim CG, Favrat D. Transcritical or supercritical CO2 cycles using both low- and high-temperature heat sources. Energy 2012;43(1):402–15. [11] Wang JF, Sun ZX, Dai YP, Ma SL. Parametric optimization design for supercritical CO2 power cycle using genetic algorithm and artificial neural network. Appl Energy 2010;87(4):1317–24. [12] Cayer E, Galanis N, Nesreddine H. Parametric study and optimization of a transcritical power cycle using a low temperature source. Appl Energy 2012;87(4):1349–57. [13] Vélez F, Chejne F, Antolin G, Quijano A. Theoretical analysis of a transcritical power cycle for power generation from waste energy at low temperature heat source. Energy Convers Manage 2012;60:188–95. [14] Bıyıkog˘lu A, Yalçınkaya R. Effects of different reservoir conditions on carbon dioxide power cycle. Energy Convers Manage 2013;72:125–33. [15] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical oranic Rankine cycle. Energy 2010;35(2):1033–9. [16] Sarkar J, Bhattacharyya S. Optimization of recompression supercritical-CO2 power cycle with reheating. Energy Convers Manage 2009;50(8):1939–45. [17] Le Moullec Yann. Conceptual study of a high efficiency coal-fired power plant with CO2 capture using a supercritical CO2 Brayton cycle. Energy 2013;49(1):32–46.

[18] Sarkar J. Second law analysis of supercritical CO2 recompression Brayton cycle. Energy 2009;34(9):1172–8. [19] Singh R, Miller SA, Rowlands AS, Jacobs PA. Dynamic characteristics of a directheated supercritical carbon-dioxide Brayton cycle in a solar thermal power plant. Energy 2013;50(1):194–204. [20] Singh R, Rowlands AS, Miller SA. Effects of relative volume-ratios on dynamic performance of a direct-heated supercritical carbon-dioxide closed Brayton cycle in a solar-thermal power plant. Energy 2013;55(15):1025–32. [21] Zhang XR, Yamaguchi H, Uneno D, Fujima K, Enomoto M, Sawada N. Analysis of a novel solar energy-powered Rankine cycle for combined power and heat generation using supercritical carbon dioxide. Renew Energy 2006;31(12):1839–54. [22] Zhang XR, Yamaguchi H, Fujima K, Enomoto M, Sawada N. Theoretical analysis of a thermodynamic cycle for power and heat production using supercritical carbon dioxide. Energy 2007;32(4):591–9. [23] Song YH, Wang JF, Dai YP, Zhou EM. Thermodynamic analysis of a transcritical CO2 power cycle driven by solar energy with liquefied natural gas as its heat sink. Appl Energy 2012;92:194–203. [24] Halimi B, Suh KY. Computational analysis of supercritical CO2 Brayton cycle power conversion system for fusion reactor. Energy Convers Manage 2012;63:38–43. [25] Lemmon EW, Huber ML, McLinden MO. NIST reference fluid thermodynamic and transport properties REFPROP 8. In: NIST Standard Reference Database. vol. 23; 2007.