The net power output of ideal supercritical organic Rankine cycle with different flow arrangement evaporators

The net power output of ideal supercritical organic Rankine cycle with different flowarrangement evaporatorsChao He, Chao Liu, Hong Gao, Hui Xie, Yourong Li, and Shuangying Wu

Citation: Journal of Renewable and Sustainable Energy 6, 033117 (2014); doi: 10.1063/1.4880212 View online: http://dx.doi.org/10.1063/1.4880212 View Table of Contents: http://scitation.aip.org/content/aip/journal/jrse/6/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A concept of power generator using wind turbine, hydrodynamic retarder, and organic Rankine cycle drive J. Renewable Sustainable Energy 5, 023123 (2013); 10.1063/1.4798314 Thermodynamic analysis of performance improvement by reheat on the CO2 transcritical power cycle AIP Conf. Proc. 1440, 499 (2012); 10.1063/1.4704255 The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phaseseparations, and the conditions for heat flow from lower to higher temperatures J. Chem. Phys. 122, 224111 (2005); 10.1063/1.1901658 Heat capacity of an ideal gas along an elliptical PV cycle Am. J. Phys. 70, 1044 (2002); 10.1119/1.1495408 Unsteady heat transfer from a sphere in a uniform cross-flow Phys. Fluids 13, 3714 (2001); 10.1063/1.1416886

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The net power output of ideal supercritical organic Rankinecycle with different flow arrangement evaporators

Chao He,1,2 Chao Liu,1,a) Hong Gao,1 Hui Xie,1 Yourong Li,1

and Shuangying Wu1

1Key Laboratory of Low-Grade Energy Utilization Technologies and Systems of Ministryof Education, College of Power Engineering, Chongqing University, Chongqing 400030,China2Key Laboratory of New Materials and Facilities for Rural Renewable Energy,Ministry of Agriculture, College of Mechanical and Electrical Engineering,Henan Agricultural University, Zhengzhou 450002, China

(Received 10 November 2013; accepted 16 May 2014; published online 27 May 2014)

The theoretical models of net power output for ideal supercritical ORC (organic

Rankine cycle) with the evaporator of counter flow, parallel flow, and cross flow

are, respectively, proposed. The effects of the ratio of heat capacity rates of heat

source and working fluid, the number of heat transfer unit, and the ratio of the

cycle high and low temperatures on the net power output of ideal supercritical

ORC are addressed. The numerical simulation results of ideal supercritical ORC

elucidate that the larger rate difference between the heat capacity of working

fluids and heat source will help to improve the net power output. The net power

output will be kept constant when the number of heat transfer unit reaches a

certain value. In addition, supercritical ORC with counter flow evaporator exhibits

the largest net power output while one with parallel flow evaporator does the

lowest. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4880212]

I. INTRODUCTION

For the low-to-medium temperature heat source, the ORC (organic Rankine cycle) performs

better than the conventional steam power cycle in converting the heat energy into power.1–4 In

the past few decades, the research on the ORC has become a hot topic, and ORC shows its

great potential both in using renewable energy and recovering the low-grade waste heat.

ORC possesses the capability to couple with different forms of low-grade heat sources to

generate power. Some researchers5–7 revolved about the ORC for agricultural residues and

biomass-based power generation and some8–13 focused on the ORC using solar energy. Besides,

there were some others14–17 conducted the study on the ORC for low-temperature geothermal

power generation. Additionally, some others2,18–29 showed their interest in the ORC for the

low-grade waste heat recovery.

The appropriate working fluids are of key importance in the ORC. For subcritical ORC, much

research has been done in terms of working fluid selection. According to the slope of saturation

steam curve of working fluids in T-s diagram, the working fluids can be grouped into three catego-

ries: dry, isentropic, and wet fluids corresponding to the positive, infinite, and negative slopes of

saturation curve, respectively.27,30 Mago et al.31 presented the second law analysis of ORC with

dry and wet fluids. Their work showed that dry fluids exhibited better performance than wet fluids.

Hung et al.32,33 investigated the effect of dry, isentropic, and wet fluids on the system efficiency

and indicated that the wet fluids were easy to form droplets during the vapor expansion in the

expander, the dry fluids were usually superheated vapor at the expander exit, making the net power

output reduced, and the isentropic or nearly isentropic fluids avoided the disadvantages of dry and

wet fluids and they were regarded as the most suitable working fluids for low-grade heat source.

a)Author to whom correspondence should be addressed. Electronic mail: [email protected]. Tel./Fax: þ86 023 65112469.

1941-7012/2014/6(3)/033117/12/$30.00 VC 2014 AIP Publishing LLC6, 033117-1

JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 6, 033117 (2014)

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For the subcritical ORC with pure working fluids, the amount of exergy destruction in the

evaporator is usually the greatest among the key components.12,21,34–36 Because the constant

temperature evaporation behavior leads to the pinch point and the unmatched temperature pro-

files between the working fluid and heat source, this makes the significant irreversible losses

during evaporation process.37 In order to reduce the irreversibility in the evaporator, supercriti-

cal ORC is proposed. Different from the subcritical ORC, working fluids in supercritical ORC

bypass the two phase regions and directly transform from liquid state into the supercritical state.

Hence, supercritical ORC improves the thermal match between the working fluid and heat

source.

Many researchers are interested in the supercritical ORC and have conducted numerical

simulation about supercritical ORC with the specific working fluids. Schuster et al.38 investi-

gated the efficiency optimization potential in supercritical ORC. Their results demonstrated that

the exergy efficiency of system will improve by 8% for supercritical ORC compared to subcriti-

cal ORC. Baik et al.17,39 carried out the power output analysis of supercritical ORC and indi-

cated that the output power of supercritical ORC with R125 was more than that of subcritical

ORC with HFC (hydrofluorocarbon). Cayer et al.40,41 considered the effect of regenerator on

the supercritical Rankine cycle with carbon dioxide and compared the net power output and

thermal efficiency of supercritical ORC with ethane, R125, and carbon dioxide. It was difficult

to decide the role of introducing the regenerator and supercritical ORC with R125 exhibited the

lowest cost. Vetter et al.42 made a comparison of specific net power output and efficiency

between the subcritical and supercritical ORCs with pure working fluids and pointed out that

the net power output of supercritical ORC could be improved by 30% compared to subcritical

ORC. Zhang et al.43 evaluated the performance of subcritical and supercritical ORCs with dif-

ferent pure fluids from the aspects of efficiency, net power output, and cost. Their results

showed that supercritical ORC with R125 was cost effective for the low-temperature geother-

mal ORC system. Chen et al.37,44 compared the supercritical Rankine cycle with carbon dioxide

and R32 based on the thermal efficiency and exergy efficiency of system and proposed the

supercritical ORC with zeotropic mixtures.

There exist a few technologies that can compete with the supercritical ORC in an attempt

to better match the temperatures between working fluids and heat source. One alternative is the

triangular cycle, which has been proposed by Smith.45 The working fluid in this cycle is single

phase which makes absorb process of the working fluid match the temperature profile of heat

source in a perfect manner. Some researchers have been interested in this triangular cycle.

DiPippo46 analyzed the efficiency of triangular cycle and made a comparison to Carnot cycle

efficiency. Zamfirescu and Dincer47 did a thermodynamic analysis of trilateral cycle with

ammonia-water under the specific heat source conditions. Fischer48 completed the optimization

of maximum water temperature for trilateral cycle and compared the exergy efficiencies of

trilateral cycle and ORC under the condition of different heat source inlet temperatures. Steffen

et al.49 mainly researched the isentropic efficiency of expansion unit in a triangle cycle with

water.

Supercritical ORC is similar to the triangular cycle if the pumping process is neglected.

From the brief reviews above, the specific working fluids are usually adopted to research the

characteristics of supercritical ORC and triangular cycle. Few researchers contributed to analyze

the characteristics of supercritical ORC and triangular cycle theoretically. In order to obtain a

comprehensive conclusion, supercritical ORC is modeled as a triangular cycle and the ideal the-

oretical model for supercritical ORC is proposed. The net power output of ideal supercritical

ORC is discussed in this paper. This also helps to further understand the characteristics of the

triangular cycle in utilization of low-grade heat source.

II. THEORETICAL MODEL AND ANALYSIS

During the process of waste heat recovery, supercritical ORC is an effective way of reduc-

ing the irreversibility of system. When a supercritical ORC couples with the low-grade heat

source, the characteristics of heat source, working fluids, and the cycle parameters are the key

033117-2 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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points to analyze the performance of the cycle. In order to obtain a comprehensive conclusion,

the ideal theoretical model for the supercritical ORC is proposed. The ideal supercritical ORC

is a triangular reversible cycle. The diagram of ORC system is shown in Fig. 1. The pumping

process is not shown in Fig. 1 because the power consumed by the pump is ignored. The mass

flow rate and inlet temperature of a sensible heat source are given. The organic substance with

low boiling points such as R32, R125, R143a, and so on could be used as the working fluid for

this ORC system.

For the ideal supercritical ORC, the specific net power output yields

xnet ¼1

2DsðT1 � T2Þ: (1)

The energy balance in the evaporator can be written as

_mwf qwf ¼ Cph _mhðT5 � T6Þ: (2)

The heat input per mass flow rate of working fluid can be expressed as

qwf ¼1

2DsðT1 þ T2Þ: (3)

The net power output of the ideal supercritical ORC is defined as

_Wnet ¼ _mwf xnet: (4)

Substituting Eqs. (1)–(3) into Eq. (4), the net power output of the ideal supercritical ORC

can be obtained as follows:

_Wnet ¼Cph _mhðT5 � T6Þ

1þ 2

T1

T2

� 1

: (5)

The effectiveness of the evaporator is defined as

e ¼ T5 � T6

T5 � T2

: (6)

The ratio of heat capacity rates of heat source and working fluid could be given by

FIG. 1. The diagram of ORC system (a) schematic diagram for general ORC and (b) T-s diagram for the ideal supercritical

ORC.

033117-3 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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R ¼ ðCp _mÞmin

ðCp _mÞmax

: (7)

The number of heat transfer unit, NTU, of the evaporator can be expressed as

NTU ¼ KA

ðCp _mÞmin

: (8)

For the evaporator, the relation among the number of heat transfer unit, the effectiveness,

and the ratio of heat capacity rates depends on the flow arrangement of the evaporator. Here,

three kinds of flow arrangement evaporators are considered: counter flow, parallel flow, and

cross flow.

For the counter flow evaporator, the effectiveness can be rewritten as

e ¼ 1� exp ð�NTUÞð1� RÞ½ �1� R exp ð�NTUÞð1� RÞ½ � R 6¼ 1ð Þ; (9)

e ¼ NTU

1þ NTUR ¼ 1ð Þ: (10)

Substituting Eqs. (6), (9), and (10) into Eq. (5), the net power output yields

_Wnet ¼1� exp ð�NTUÞð1� RÞ½ �� �

Cph _mhðT5 � T2Þ� �

1� R exp ð�NTUÞð1� RÞ½ �� �

1þ 2

T1

T2

� 1

0@

1A

R 6¼ 1ð Þ; (11)

_Wnet ¼Cph _mhðT5 � T2Þ

1þ 1

NTU

� �1þ 2

T1

T2

� 1

0@

1A

R ¼ 1ð Þ: (12)

By dividing Eqs. (11) and (12) with the potentially maximum heat absorbed by the working

fluid, i.e., _Qmax ¼ Cph _mhðT5 � T2Þ, the dimensionless net power output aW of the cycle with the

counter flow evaporator can be written as

aW ¼

1� exp ð�NTUÞð1� RÞ½ �

1� R exp ð�NTUÞð1� RÞ½ �� �

1þ 2

h� 1

� R 6¼ 1ð Þ

1

1þ 1

NTU

� �1þ 2

h� 1

� � R ¼ 1ð Þ;

8>>>>>>><>>>>>>>:

(13)

where h denotes the ratio of the cycle high and low temperatures,

h ¼ T1

T2

: (14)

For the parallel flow evaporator, the effectiveness can be rewritten as

e ¼ 1� exp ð�NTUÞð1þ RÞ½ �1þ R

R 6¼ 1ð Þ; (15)

e ¼ 1� expð�2NTUÞ2

R ¼ 1ð Þ: (16)

033117-4 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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Similar to the counter flow evaporator, combining Eqs. (6), (15), and (16) with Eq. (5),

the dimensionless net power output of the cycle with the parallel flow evaporator can be

expressed as

aW ¼

1� exp ð�NTUÞð1þ RÞ½ �

1þ Rð Þ 1þ 2

h� 1

� R 6¼ 1ð Þ

1� exp �2NTUð Þ

2 1þ 2

h� 1

� � R ¼ 1ð Þ:

8>>>>>>><>>>>>>>:

(17)

For the cross flow evaporator, the effectiveness can be rewritten as

e ¼ 1

R1� exp½�Rð1� expð�NTUÞÞ�� �

: (18)

Analogous to the counter flow and parallel flow evaporators, by combining Eqs. (6) and

(18) with Eq. (5), the dimensionless net power output of the cycle with the cross flow evapora-

tor yields

aW ¼1� exp �R 1� exp �NTUð Þ

� �� �R 1þ 2

h� 1

� � : (19)

For the ideal supercritical ORC with three kinds of flow arrangement evaporators, the

dimensionless net power output is related to the ratio of heat capacity rates of heat source and

working fluid (R), the NTU, and the ratio of the cycle high and low temperatures (h). The influ-

ence of R, NTU, and h on aW will be addressed by the numerical computation.

III. SIMULATED RESULTS AND DISCUSSION

When the inlet temperature and mass flow rate of the heat source are known, the maximum

net power output in the supercritical ORC is expected. According to Eqs. (13), (17), and (19),

the dimensionless net power output aW in the ideal supercritical ORC is related to R, NTU, and

h. In order to get general conclusions, the specific working fluids are not selected and the influ-

ences of R, NTU, and h on the net power output are discussed. For all the investigated situations,

the ranges of R, NTU, and h are from 0.1 to 1, 1 to 10, and 1.1 to 1.8, respectively.

Fig. 2 presents the variation of aW with the NTU and R when h is equal to 1.2 for the coun-

ter flow evaporator. From Fig. 2(a), aW first increases with the increase of NTU and then will

FIG. 2. The variation of aW with NTU and R for counter flow evaporator (h¼ 1.2).

033117-5 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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reach a stable value when the ratio of heat capacity rates R is fixed. This implies that there

exists a critical value (NTU) to make aW maximum. The increase of NTU means the increase

of heat exchanger area, thus the heat source will release much more heat to the working fluid

and more net power output will be obtained when other conditions remain unchanged.

However, under the conditions of the given heat source and environment, the heat released by

the heat source is limited and the heat absorbed by working fluid will reach the maximum with

the increase of NTU. In this case, the increase of NTU will not help to improve the absorption

heat of working fluid. Therefore, aW will not be improved. From Fig. 2(b), it is obvious that aW

decreases with the increase of the ratio of heat capacity rates R at the fixed NTU. This indicates

that the greater difference rate between the heat capacity of working fluid and heat source helps

to produce the larger net power output.

Fig. 3 depicts the variation of aW with h and R when NTU is equal to 4 for counter flow

evaporator. Fig. 3(a) shows that aW obviously increases with the increase of h when R is given.

The increase of h represents the increase of the expander inlet temperature relative to condensa-

tion temperature, thus the heat absorbed by working fluid will be improved and the net power

output will increase. From Fig. 3(b), aW decreases with the increase of R when h is given. This

implies that the greater rate difference between the heat capacity of working fluid and heat

source helps to produce the larger net power output under the fixed h.

Fig. 4 illustrates the variation of aW with NTU and h when R is equal to 0.4 for the counter

flow evaporator. As shown in Fig. 4(a), aW increases with the increase of NTU for the fixed h.

After the NTU exceeds a certain value, aW will not increase and remain unchanged. Fig. 4(b)

shows that aW increases with the increase of h for the given NTU.

Fig. 5 shows the variation of aW with the NTU and R when h is equal to 1.2 for the parallel

flow evaporator. aW gets first increased and then keeps constant for each ratio of heat capacity

FIG. 3. The variation of aW with h and R for counter flow evaporator (NTU¼ 4).

FIG. 4. The variation of aW with NTU and h for counter flow evaporator (R¼ 0.4).

033117-6 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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rates R as shown in Fig. 5(a). The reason for this is similar to the situation of counter flow

evaporator. At the same NTU, the more aW will be obtained for the smaller ratio of heat

capacity rates R. Fig. 5(b) describes this phenomenon in detail. At the lower value of NTU, the

higher NTU, the larger net power output will be gotten for the same ratio of heat capacity rates

R. However, at the higher value of NTU, the difference of net power output between the differ-

ent numbers of heat transfer units is very small for the same ratio of heat capacity rates R.

Fig. 6 depicts the variation of aW with h and R when NTU is equal to 4 for parallel flow

evaporator. For the same R, aW increases linearly with the increase of h as shown in Fig. 6(a).

From Fig. 6(b), aW decreases with the rise of R for the same h. Additionally, the decrement of

aW increases with the increase of R at the higher values of h.

Fig. 7 illustrates the variation of aW with NTU and h when R is equal to 0.4 for the parallel

flow evaporator. From Fig. 7(a), aW gets first increased and then keeps constant for each h. For

each NTU, aW increases with the rise of h as shown in Fig. 7(b).

For the cross flow evaporator, the effects of number of heat transfer unit NTU, the ratio of

the cycle high and low temperatures h, and the ratio of heat capacity rates of heat source and

working fluid R on aW have similar law with the results of the parallel flow evaporator that pre-

sented in Figs. 5–7. For simplicity, the results of the cross flow evaporator are given in Figs.

8–10 and are not described in detail.

In summary, for all the three kinds of flow arrangement evaporators, the effects of NTU, R,

and h on the performance of supercritical ORC are analogous. The net power output for the

supercritical ORC will increase with the increase of NTU but it will keep constant when NTUincreases to a certain degree. Also, the increase of h will help to improve the net power output.

The increase of R will lead to the reduction of the net power output.

FIG. 5. The variation of aW with NTU and R for parallel flow evaporator (h¼ 1.2).

FIG. 6. The variation of aW with h and R for parallel flow evaporator (NTU¼ 4).

033117-7 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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In order to compare the performance of supercritical ORC with three kinds of flow arrange-

ment evaporators, Fig. 11 gives the variation of aW with NTU, R, and h for the counter flow,

parallel flow, and cross flow evaporators. As shown in Fig. 11(a), for the three kinds of flow

arrangement evaporators, aW increases with the increase of NTU and then reaches a steady

value when R and h are equal to 0.4 and 1.2, respectively. However, these steady values of aW

are different. It is the largest for the counter flow, while it is the lowest for parallel flow. When

NTU and h are equal to 4 and 1.2, respectively, aW decreases with the increase of R for the

three kinds of flow arrangement evaporators from Fig. 11(b). At the same R, supercritical ORC

FIG. 7. The variation of aW with NTU and h for parallel flow evaporator (R¼ 0.4).

FIG. 8. The variation of aW with NTU and R for cross flow evaporator (h¼ 1.2).

FIG. 9. The variation of aW with h and R for cross flow evaporator (NTU¼ 4).

033117-8 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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with the counter flow evaporator exhibits the greatest aW, while one with the parallel flow evap-

orator does the lowest aW. Fig. 11(c) displays that aW increases with the increase of h at NTUand R are equal to 4 and 0.4, respectively. The supercritical ORC with the counter flow evapo-

rator still possesses the greatest aW, while the parallel flow evaporator does the lowest aW.

From the above discussion, it can be noted that the effects of NTU, R, and h on aW of

supercritical ORC are different. In order to improve the net power output of supercritical ORC,

three methods can be adopted: increasing NTU and h, respectively, and reducing R. However, it

is limited to improve the net power output by increasing NTU and h. For a given heat source,

aW will not increase any more when the NTU increases to a certain degree. Usually, improving

h is restricted by the actual conditions. Consequently, reducing R is the best way to improve

FIG. 11. Comparison of the three kinds of flow arrangement evaporators.

FIG. 10. The variation of aW with NTU and h for cross flow evaporator (R¼ 0.4).

033117-9 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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the net power output of supercritical ORC. This means the greater difference rates between the

heat capacity of working fluids and the heat source are expected in supercritical ORC.

IV. CONCLUSIONS

The model of the ideal supercritical ORC was proposed. The effects of the NTU, the ratio

of heat capacity rates of heat source and working fluid (R), and the ratio of the cycle high and

low temperatures (h) on the net power output were investigated. The main conclusions can be

made as following:

(1) For the supercritical ORC, the improvement of the net power output can rely on the increase

of NTU and h and the decrease of R. However, it is limited to increase the net power output by

increasing NTU and h. The net power output will not increase any more when NTU increases

to a certain value. The increase of h is restricted by the actual conditions. Reducing R is the

best way to improve the net power output of supercritical ORC. This means the greater rate

difference between the heat capacity of working fluids and the heat source is expected in

supercritical ORC.

(2) The supercritical ORC with counter flow evaporator exhibits the greatest net power output,

while one with the parallel flow evaporator does the lowest at the same conditions.

ACKNOWLEDGMENTS

This work was supported by National Basic Research Program of China (973 Program) under

Grant No. 2011CB710701.

NOMENCLATURE

A heat transfer area (m2)

Cp fluid specific heat capacity (kJ kg�1 K�1)

K heat transfer coefficient (W m�2 K�1)

_m mass flow rate (kg s�1)

NTU number of heat transfer unit (dimensionless)

q heat absorption per mass flow rate (kJ kg�1)_Q the heat rate injected (kW)

R ratio of heat capacity rates (dimensionless)

s specific entropy (kJ kg�1 K�1)

T temperature (K)

w specific work (kJ kg�1)_W power output or input (kW)

Ds unit entropy change (kJ kg�1 K�1)

Greek symbols

aW dimensionless power output

h ratio of high and low temperature

Subscripts

evp evaporator

h waste heat source

l liquid

max maximal

min minimal

net net

033117-10 He et al. J. Renewable Sustainable Energy 6, 033117 (2014)

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p pump

wf working fluid

1-6 state points

2s, 4s stat points for the ideal case

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