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

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 20August 2013Accepted 14November 2013

Available online 10December 2013Keywords:

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 ef?ciency of the cycles.The carbon dioxide is chosen as the working ?uid for the cycles.Water is chosen as the ?uid 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 ?ow rate is 1kg/s.The same tem-perature and mass ?ow 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 ef?ciency could be ranked from high to low:TRC >SRC >ESRC >ETRC.

ó2013Elsevier 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 signi?cant.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 ?uid 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 ef?ciency by choice of an appropriate working ?uid and optimization of the condensing temperature or pressure.Vetter et al.[4]compared the sub-and supercritical processes using propane,carbon dioxide (CO 2)and 10other refrigerants and showed that propane or R143a can increase speci?c net power output more than 40%at a geother-mal temperature of 150°C.Chen et al.[5]conducted a comparative study of CO 2transcritical power cycle compared with R123’s ORC in waste heat recovery and found that CO 2transcritical power cycle has a better performance than the ORC.Zhang et al.[6]pre-sented that R123in subcritical ORC system yields the highest ther-mal ef?ciency and exergy ef?ciency,while for transcritical ORC,R125has a higher thermal and exergy ef?ciency than that of R123in ORC.Chen et al.[7]studied the transcritcal Rankine cycle using R32and CO 2.The energy and exergy analyses showed that the R32based transcritical Rankine cycle can achieve 12.6–18.7%higher thermal ef?ciency and works at much lower pressures.Baik et al.[8]compared the power output of the CO 2and R125transcrit-ical cycle for a low-grade heat source of about 100°C and showed that R125transcritical cycle produced 14%more power than that of the CO 2.Baik et al.[9]compared the R125transcritical cycle with the subcritical ORCs using R134a,R245fa and R152a and showed that the power output of the R125transcritical cycle was greater than that of subcritical ORCs when a total overall conduc-tance was higher than 35kW/K.Kim et al.[10]proposed a trans-critical-CO 2Rankine cycles or fully cooled supercritical-CO 2cycles using both the low and high temperature heat sources which can maximize the power output of the CO 2power 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 destruc-tion in a CO 2-based transcritical Rankine cycle to ?nd that param-eters such as turbine inlet pressure and temperature have signi?cant effects on the exergy ef?ciency of the supercritical CO 2power cycle.Vélez et al.[13]conducted an energy and exergy analysis on the CO 2transcritical power cycle.Results indicated an increase up to 25%for the exergy ef?ciency,and up to 300%for the energy ef?ciency when the inlet temperature to the turbine is risen

0196-8904/$-see front matter ó2013Elsevier Ltd.All rights reserved.https://www.360docs.net/doc/4e6661917.html,/10.1016/j.enconman.2013.11.020

Corresponding author.

E-mail address:xgli@https://www.360docs.net/doc/4e6661917.html, (X.Li).

from60to150°C.B?y?kog?lu and Yal??nkaya[14]investigated a geothermal power cycle using CO2at supercritical condition,and a parametric study was performed to test the proposed system un-der different reservoir conditions.Schuster et al.[15]conducted an exergy analysis and comparison and indicated that the system ef?-ciency could improve approximately8%for the supercritical parameters because of the better exergetical ef?ciency.Sarkar and Bhattacharyya[16]analyzed the effects of different operating conditions and cycle performance on the optimized supercritical CO2recompression cycle.

In nuclear reactors,solar energy collectors and coal-?red plant adapted CO2capture process et al.,the supercritical CO2power cy-cle attracted more and more interests recently[17–20].Zhang et al. [21,22]investigated the performance of a solar supercritical Rankine system using CO2and showed that heat collection ef?ciency for the CO2-based solar collector is measured at8.78–9.45%which presents a potential future for the solar powered CO2Rankine 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 ef?ciency both reach maximum values.In addition, the condensation temperature has a signi?cant impact on the sys-tem performance.Halimi and Suh[24]developed a optimized supercritical cycle analysis code to analyze the design of a super-critical CO2driven Brayton cycle for a fusion reactor.

Carbon dioxide(CO2)with the advantages of abundant in nature,non-toxic,non-?ammable and inexpensive has been exten-sively studied as the working?uid in the supercritical or transcrit-ical 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 dif?culties 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 than100°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 power output from this low temperature energy by power cycles will be more practical and signi?cant 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.1shows 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?uid 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 crit-ical 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.2and3.In the ETRC and ESRC,the supercritical?uid from the second-stage heater works as the primary?uid in the ejector to entrain the exhaust from the expander so as to decrease the expander’s backpressure and increase the pressure difference in

Nomenclature

h speci?c enthalpy(J kgà1)

m mass?ow rate(kg sà1)

Q heat transfer(W)

s speci?c entropy(J kgà1Kà1)

P pressure(bar)

T temperature(K)

u entrainment ratio of ejector or mass?ow ratio in?rst-stage heater

W power(W)

Greek symbols

g ef?ciency(%)

Subscripts

dry dry?uid(expansion)

cool(c)cooling

cr critical 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?uid(expansion) wf working?uid

1–7state points

552X.Li et al./Energy Conversion and Management78(2014)551–558

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?rst cycle5–6–1–3–4–5:One part of subcooled(or sat-

urated)liquid from the cooler(or condenser)is pumped to the?rst-stage heater in process5–6,and then heated to the supercritical state in process6–1;the supercritical?uid expands in the expander,generating power in process1–3;

the exhaust?uid from the expander(state3)will work as the secondary?uid of the ejector to the ejection process.

(2)The second cycle5–7–2–4–5:The other part of subcooled

(or saturated)liquid from the cooler(or condenser)is pumped to the second-stage heater in process5–7,and heated to the supercritical state(or superheated vapor in the ETRC)in process7–2;the supercritical?uid(or super-heated vapor)(state2)will work as the primary?uid of the ejector to the ejection process.

(3)The primary?uid(state2)and the secondary?uid(state3)

are mixed and diffused in the ejector to form the mixed?uid (state4).The mixed?uid(state4)from the ejector enters to the cooler(or condenser)to be cooled to the subcooled(or saturated)?uid(state5);then pumped to the two heaters by the?uid pumps in process5–6and process5–7respec-tively,completed the cycle.

2.2.Process and principle of the ejector

Fig.4shows the con?guration 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 (P h2)primary?uid(state2)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?uid entrains a low pressure(P3)secondary?uid(state3)from the expander in the suction nozzle.Both?uids enter the mixing section where they exchange momentum,kinetic and internal energies and become a mixed?uid(state4)outlet from the ejector and inlet to the cooler or condenser with a middle pressure(P c).

The result of the ejection process is that the outlet pressure from the expander(P3)as the secondary?uid is lower than the cooling or condensation pressure(P c)of the mixed?uid.It means that the expander’s backpressure of P3in 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.

3.Thermodynamic analysis of the cycle

3.1.Speci?cations and conditions for calculations

1.The carbon dioxide CO2is chosen as the working?uid for the

supercritical or transcritical Rankine cycles(SRC,TRC,ESRC and ETRC).

2.Water is chosen as the?uid of the low-grade heat.The water

temperature is selected in a range of60–90°C,a typical water temperature is80°C,and the mass?ow rate is1kg/s.The same temperature and mass?ow rate of the water is the standard condition for the comparative analysis of the thermodynamic performance.

3.A pinch point temperature difference(D T_pp)between the heat

source water and the working?uid is set to8°C.The maximum outlet and inlet temperature of the CO2in the heater of the cycles is set to lower than the inlet and outlet temperature of the water by D T_pp respectively in the calculation.

4.In the SRC and ESRC,the outlet temperature of the CO2from the

cooler is set to30°C.In the TRC and ETRC,the outlet of CO2 from the condenser is set as saturated liquid,and the bubble temperature of CO2is set the same as30°C.

5.Carbon dioxide CO2is a wet?uid.A wet expansion can be trans-

ferred 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?uid in the ejector,is set to0.95or0.9times the cooling pressure(P c),and a pressure drop ratio(c)is de?ned as c=P3/P c=0.95or0.9.

7.In consideration of the comparability,a reduced parameter of

the pressure(P r=P/P cr)is used to illustrate the cycle’s thermo-dynamic performance of the working?uids.

8.The environment state is set to:P oc=101.325kPa,

T oc=298.15K.

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?eh3?uth2T=e1tuTe1TS4?es3?uts2T=e1tuTe2TThe entrainment ratio(u)of the ejector,i.e.,the mass?ow ratio in the?rst-stage heater,is:

X.Li et al./Energy Conversion and Management78(2014)551–558553

u?m wf1=m wf2e3TThe total mass?ow ratio(m wf)in the cycle is:

m wf?m wf1tm wf2e4TIn 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?uid,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 max-imum net power output(W net_max)of the cycles.The calculated thermodynamic performance includes:heating load(Q heat),power output from the expander(W out),pumping power(W pump),net power output(W net),thermal ef?ciency(g th),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?ow 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(Q heat)from heat source water in the heater is: Q heat?m wf?eh heat outàh heat inTe5TThe cooling load(Q cool)in the cooler(or condenser)is:

Q cool?m wf?eh cool inàh cool outTe6TThe power output(W out)from the expander is:

W out?m wf?eh exp inàh exp outTe7TThe pumping power(W pump)by the pump is:

W pump?m wf?eh pump outàh pump inTe8TThe net power output(W net)of the cycle is:

W net?W outàW pumpe9TThe thermal ef?ciency(g th)of the cycle is:

g th ?W net=Q heate10T

4.Results and discussion

For different working?uids have different pressure in the heat-

ing or cooling processes in the cycle,a reduced parameter of the

pressure(P r=P/P cr)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 thermo-

dynamic performance of different working?uids.

Figs.6–12present 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?uid of CO2.

Fig.5.Flow chart of the simulation procedure for the ESRC. 554X.Li et al./Energy Conversion and Management78(2014)551–558

It is found that the variation of the net power output (W net )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 satu-rated vapor if it falls into the two-phase region to avoid the wet expansion.So the outlet temperature of the CO 2from the heater will be increased until it reaches the maximum which is lower than the inlet water temperature by D T _pp of 8°C,and the calculation will be terminated.

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

555

In the optimum calculation,the outlet temperature of the CO2 from the heater in those four cycles always reaches the maximum of72°C which is lower than the water temperature of80°C by

D T_pp of8°C.

https://www.360docs.net/doc/4e6661917.html, power output(W net)

As shown in Fig.6,the net power output(W net)of the TRC,SRC, ETRC and ESRC with CO2at water temperature of80°C increases and then decreases with the?rst-stage heating pressure(P h1), and exists the maximum net power output(W net_max).The W net_max is9.25kW,9.45kW,10.19kW,10.32kW for TRC,SRC,ETRC,ESRC respectively at the pressure drop ratio(c=P3/P c)of0.95in ETRC and ESRC,as shown in Table1.And the increases of the W net_max in the SRC,ETRC,ESRC is2.14%,10.18%and11.60%compared to the TRC respectively.The corresponding optimum?rst-stage heat-ing pressure(P h1_opt)is122.91bar,128.58bar,124.74bar and 131.34bar for TRC,SRC,ETRC and ESRC respectively,or the reduced parameter of pressure(P r1)is1.67,1.74,1.69and1.78. The W net of the cycles can be ranked from high to low: ESRC>ETRC>SRC>TRC.

4.2.Thermal ef?ciency(g th)

As shown in Fig.7,the thermal ef?ciency(g th)of the TRC and SRC increases with the P h1throughout.But the g th of the ETRC and ESRC increases and then decreases with the P h1,and exists the maximum of g th(g th_max).The g th_max is6.41%for ETRC and 6.37%for ESRC,and the corresponding P h1is117.51bar, 124.17bar respectively at the pressure drop ratio(c=P3/P c)of

0.95in ETRC and ESRC.But this condition of the maximum of g th

(g th_max)is different to the condition of the maximum net power output(W net_max).

In the condition of the W net_max,the g th of the TRC,SRC,ETRC and ESRC is8.19%,7.88%,6.23%,and6.30%.Different to the increase of the W net_max,the g th of the SRC,ETRC and ESRC isà3.89%,

Table1

Performance comparison among the cycles at different expander’s outlet pressure in the condition of the maximum net power output(W net_max)and water temperature of80°C and?ow rate of1kg/s.

Cycle TRC SRC ETRC ESRC

1.Pressure drop ratio c(P3/P c)in expander in ETRC and ESRC///0.950.9_wet0.9_dry0.950.9_wet0.9_dry

2.Water temperature outlet from heater

First-stage heater°C53.0551.3653.4855.3654.5551.8954.2952.15 Second-stage heater°C//40.9444.1444.9140.8843.4444.26

3.Cycle parameters of working?uid CO2

First-stage heater Pressure(P h1)bar122.91128.58124.74133.25129.54131.34144.17132.66

Pressure ratio of

P r1(P h1/P cr)

/ 1.67 1.74 1.69 1.81 1.76 1.78 1.95 1.80

Inlet temperature(T6)°C45.0543.3645.4747.3646.5543.8946.2944.15

Outlet temperature(T1)°C7272727272727272

Mass?ow rate(m wf1)kg/s 1.02 1.07 1.03 1.10 1.07 1.10 1.21 1.11

Heating load(Q h1)kW112.88119.97111.10103.21106.60117.72107.70116.65 Second-stage heater Pressure(P h2)bar//79.7289.3491.8583.3092.8696.09

Pressure ratio of

P r2(P h2/P cr)

/// 1.08 1.21 1.25 1.13 1.26 1.30

Inlet temperature(T7)°C//32.9436.1436.9132.8835.4436.26

Outlet temperature(T2)°C//45.4847.3646.5543.8946.2944.15

Mass?ow rate(m wf2)kg/s//0.440.480.480.410.510.57

Heating load(Q h2)kW//52.4346.9240.3046.0345.3533.00 Cooler or condenser Pressure(P c)bar72.1473.7872.1472.1472.1473.7873.7873.78

Pressure ratio of P rc

(P c/P cr)

/0.9778 1.00010.97780.97780.9778 1.0001 1.0001 1.0001

Inlet temperature(T4)°C34.0834.0134.6531.9031.8833.8631.7931.79

Outlet temperature(T5)°C3030303030303030

Mass?ow rate(m wf)kg/s 1.02 1.07 1.48 1.58 1.54 1.50 1.71 1.67

Cooling load(Q cool)kW103.63110.52153.33139.46136.27153.42142.43139.14

4.Parameters in ejection

Primary?uid(state2)Pressure(P h2)bar//79.7289.3491.8583.3092.8696.09

Temperature(T2)°C//45.4847.3646.5543.8946.2944.15 Second?uid(state3)Pressure(P3)bar//68.5364.9264.9270.0966.4066.40

Pressure ratio of

P r3(P3/P cr)

///0.928910.880020.880020.9500950.900090.90009

Temperature(T3)°C//30.0125.3925.3930.0526.3726.37

Quality kg/kg//sup-heat0.96sat.vap sup-heat0.86sat.vap Mixed?uid(state4)Pressure(P c)bar//72.1472.1472.1473.7873.7873.78

Temperature(T4)°C//34.6531.9031.8833.8631.7931.79 Entrainment ratio(u)/// 2.34 2.28 2.25 2.68 2.38 1.95 Pressure ratio(inlet/outlet)in expander/// 1.82 2.05 2.00 1.87 2.17 2.00

5.Performance of the cycles

Total heating load(Q h_sum=Q h1+Q h2)kW112.88119.97163.52150.13146.91163.75153.04149.65 Power output from expander(W out)kW17.4118.1119.2822.4421.7320.1924.4721.99 Pumping power(W pump)kW8.168.679.0911.7711.099.8613.8611.48 Maximum net power output(W net_max)kW9.259.4510.1910.6710.6410.3210.6210.51 Thermal ef?ciency(g th)%8.197.88 6.237.117.24 6.30 6.947.02

6.Increase of the performance compared to TRC

Increase of the W net_max%/ 2.1410.1815.3415.0311.6014.7813.64 Increase of the g th%/à3.89à23.94à13.27à11.62à23.07à15.34à14.28 556X.Li et al./Energy Conversion and Management78(2014)551–558

à23.94%andà23.07%lower than that of the TRC respectively,as shown in Table1.

4.3.Heating load(Q h)

Fig.8presents the variation of the heating load(Q h)with the ?rst-stage heating pressure(P h1).At the same P h1,the heating load in the?rst-stage(Q h1)of the ETRC and ESRC is the same as the heating load in the TRC and SRC respectively,and the Q h1decreases with the P h1.But the heating load in the second-stage(Q h2)of the ETRC and ESRC increases with the P h1,and the total heating load (Q h_sum=Q h1+Q h2)in the ETRC and ESRC increases with P h1.

There exists the maximum of the thermal ef?ciency(g th_max)in the ETRC and ESRC which is different from the TRC and SRC,as shown in Fig.7.The reason is that the Q h in TRC and SRC is decreas-ing throughout but the Q h_sum in ETRC and ESRC is increasing due to the Q h2.With the P h1higher than the optimum P h1_opt which is 122.91bar,128.58bar,124.74bar,131.34bar for TRC,SRC,ETRC and ESRC,as present in Section3.1,the W net decreases.But the negative slope or the decreased tendency of the Q h is higher than that of the W net in the TRC and SRC that the g th of the TRC and SRC does not decrease,but increase.On the contrary,due to the in-crease of the Q h_sum throughout in the ETRC and ESRC,the g th will decrease after the increase that the maximum of the thermal ef?ciency(g th_max)comes out,as shown in Fig.7.

https://www.360docs.net/doc/4e6661917.html,parison of the maximum net power output(W net_max)

The performance of the ETRC and ESRC in the condition of the maximum net power output(W net_max)is calculated with different outlet pressure(P3)of the expander(the pressure drop ratio c at 0.95and0.9),as shown in Table1.The lower the P3(or the c)is, the higher the W net_max and g th of the ETRC and ESRC is.For exam-ple,the W net_max at c of0.9is4.68%in wet expansion and4.40%in dry expansion higher than the W net_max at c of0.95in the ETRC.But the lower the P3(or the c)is,the more possibility the wet expan-sion will occur for the wet working?uid 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 dif-ference 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.

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(P c)in the SRC and ESRC is as lower as possible to close to the critical pressure of the CO2.The P c had to be set to a de?nite value as the reduced parameter of the cooling pressure(P rc)is set to1.0001,as shown in Table1.The lower the cooling pressure(P rc)is,the higher the thermal performance of the W net and g th is,as shown in Fig.9. But the heating pressure(P h1)will increase with the P rc in the SRC and ESRC,as shown in Fig.10.

4.6.Performance(W net_max and g th)with water temperature

Figs.11and12present the maximum net power output (W net_max)and the corresponding thermal ef?ciency(g th)of the TRC,SRC,ETRC and ESRC with CO2at pressure drop ratio(c)of

0.95in water temperature range of60–90°C.The W net_max and

g th of the cycles increase with the water temperature almost line-arly.The thermal performance and the analyses of the cycles at dif-ferent water temperature are similar to the outcomes at water temperature of80°C.The net power output of the cycles could be ranked from high to low:ESRC>ETRC>SRC>TRC;and the thermal ef?ciency could be ranked from high to low: TRC>SRC>ESRC>ETRC in the water temperature range of60–90°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 dif-ference 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(W net)of the cycles could be ranked from

high to low:ESRC>ETRC>SRC>TRC,and the thermal ef?-ciency(g th)could be ranked from high to low:TRC>SRC>ESR-

C>ETRC with working?uid of CO2at the pressure drop ratio

(c=outlet pressure of expander(P3)/cooling pressure(P c))of

0.95in ETRC and ESRC in water temperature range of60–90°C.

2.The increases of the maximum net power output(W net_max)in

the SRC,ETRC,ESRC is2.14%,10.18%and11.60%compared to the TRC,but the corresponding g th of the SRC,ETRC and ESRC isà3.89%,à23.94%andà23.07%lower than that of the TRC respectively at c of0.95in ETRC and ESRC.

3.The lower the outlet pressure(P3)of the expander is,the higher

the W net_max and g th of the ETRC and ESRC is.In the ETRC,the W net_max at c of0.9is4.68%in wet expansion and4.40%in dry expansion higher than the W net_max at c of0.95.

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?nancial support from the National Natural Science Foundation of China(Grant No. 51276122).

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