Thermodynamic study of main compression intercooling effects on supercritical CO2 recompression Brayton cycle

Accepted Manuscript Thermodynamic study of main compression intercooling effects on Supercritical CO2 recompression Brayton cycle

Yuegeng Ma, Ming Liu, Junjie Yan, Jiping Liu PII:

S0360-5442(17)31403-2

DOI:

10.1016/j.energy.2017.08.027

Reference:

EGY 11396

To appear in:

Energy

Received Date:

21 March 2017

Revised Date:

04 August 2017

Accepted Date:

07 August 2017

Please cite this article as: Yuegeng Ma, Ming Liu, Junjie Yan, Jiping Liu, Thermodynamic study of main compression intercooling effects on Supercritical CO2 recompression Brayton cycle, Energy (2017), doi: 10.1016/j.energy.2017.08.027

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ACCEPTED MANUSCRIPT

Thermodynamic study of main compression intercooling effects on Supercritical CO2 recompression Brayton cycle Yuegeng Maa, Ming Liub, Junjie Yanb, Jiping Liua* a

MOE Key Laboratory of Thermal Fluid Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China b State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China *Corresponding author, [email protected], Tel.: +86 29 82665742; fax: +86 29 82665741.

ABSTRACT Supercritical CO2 recompression Brayton cycle has emerged as a promising power cycle for various types of power conversion systems. In order to seek further performance improvement of supercritical CO2 recompression Brayton cycle, thermodynamic effects of main compression intercooling (MCIC) are investigated in this work. Mathematical models were developed for Supercritical CO2 recompression Brayton cycle with MCIC. Two key variable parameters, i.e., compressor pressure ratio and pressure ratio distribution between two main compression stages (represented with RPRMC,1) , were optimized. Effects of working conditions on MCIC effects and the optimized parameters were investigated. A comprehensive comparison between cycles with and without MCIC was performed in four typical conditions from both design and off-design viewpoints. Results show that RPRMC,1 is more predominant to cycle efficiency than compressor pressure ratio. 2.65% efficiency improvement can be obtained by the integration of MCIC in the reference conditions. The variations of working conditions impact MCIC effects on cycle efficiencies. The optimized results of compressor pressure ratio and RPRMC,1 are affected by the variation of minimum temperature, maximum temperature and maximum pressure. In addition to cycle efficiency improvement, the integration of MCIC also shows potentials in costs saving and cycle robustness improvement. KEY WORDS Supercritical Carbon Dioxide; Recompression Brayton cycle; Intercooling; Parameters optimization; Efficiency improvement Nomenclature Cp

specific heat at constant pressure,(kJ/kg/K)

Greek symbols

h

enthalpy,(kJ/kg)

π

pressure ratio

HTR

high temperature recuperator

ηis

isentropic efficiency, (%)

LTR

low temperature recuperator

ε

effectiveness, (%)

m

mass flow rate,(kg/s)

ΔP

pressure losses, (%)

MC

main compressor

ΔT

MCIC

main compression intercooling

pinch point temperature difference, (K,℃)

p

pressure,( MPa)

Subscript

ACCEPTED MANUSCRIPT PHX

primary heat exchanger

0

ambient conditions

Q

energy, (W)

1,2...

RC

recompression compressor

state points; compression stages of main compressor

RPR

ratio of pressure ratio

c

CO2

SR

split ratio

ht

high temperature side

S-CO2

supercritical carbon dioxide

lt

low temperature side

T

temperature, (K,℃)

min

minimum value

W

power,(kW)

max

maximum value

w

specific power,(kW/kg)

is

isentropic process

ηth

thermal efficiency,(%)

r

reactor

1. Introduction Supercritical CO2(S-CO2) Brayton cycle was proposed by Feher [1] in 1960s and was regarded as a promising choice for power generation application according to the preliminary thermodynamic analysis. However, due to the lack of suitable heat source and technical limitations of the crucial components, such as turbo-machinery and heat exchanger, the S-CO2 Brayton cycle has not been deployed in practice. Recently, owing to the renewed attention to high temperature gas-cooled and medium temperature liquid metal or molten salt reactors [2, 3], as well as the significant developments in turbo-machinery [4, 5] and compact heat exchanger [6, 7], the researches about S-CO2 Brayton cycle began to revive among many countries on nuclear energy application. Dostal [8] and Carstens [9] successively conducted studies on the S-CO2 cycle thermodynamic and techno-economic analysis and control strategies development for Gen IV nuclear reactors in Massachusetts Institute of Technology. Pham et al [10] reported a mapping of the thermodynamic performance of different S-CO2 cycle configurations for small modular reactor and sodium-cooled fast reactor. Ishiyama et al [11] and Linares et al [12] presented exploratory analyses of the suitability of SCO2 Brayton power cycles for fusion reactors. Besides, owing to the high thermal efficiency, smaller components and simpler cycle layouts, S-CO2 Brayton cycle has also shown great potentials in a wider spectrum of energy industries including concentrated solar power and fossil fuel power in recent years. Belmonte et al [13] optimized a S-CO2 recompression Brayton cycle for an innovative receiver solar power plant. Iverson et al. [14] established a transient model for S-CO2 cycle and compared the obtained data with the experimental results in order to investigate the effects of transient nature of solar energy on S-CO2 cycle performance. Wang and He [15] performed thermodynamic analysis and optimization of a molten salt solar power tower integrated with a S-CO2 recompression Brayton cycle based on integrated modeling. Milani et al. [16] conducted a comparative study of solar heliostat assisted S-CO2 recompression Brayton cycles, and developed the corresponding dynamic modeling and controlling strategies. Le Moullec et al. [17, 18] conducted a conceptual study of a high efficiency coal-fired power plant with CO2 capture using S-CO2 Brayton cycle, and further investigated the thermodynamic performance of S-CO2 Brayton cycle from thermodynamic consideration and within realistic industrial

ACCEPTED MANUSCRIPT modeling hypotheses. Hanak et al. [19] proposed a concept which use the S-CO2 cycle instead of the conventional steam cycle in the calcium loop for decarbonization of the coal-fired plant. Numerous S-CO2 cycle layouts have been proposed and compared in previous studies. Among all the proposed S-CO2 Brayton cycle layouts, the S-CO2 recompression Brayton cycle was regarded as one of the most optimal layouts with respect to cycle efficiency, simplicity and cost, and hence gained much attention among numerous researchers. Dostal and Kulhanek [8, 20] conducted thermodynamic and techno-economic analyses and comparisons on different S-CO2 cycle layouts, and indicated that S-CO2 recompression Brayton cycle layout was the most potential one for next generation nuclear reactor. Ahn et al [21] compared various S-CO2 cycle layouts, and indicated that S-CO2 recompression Brayton cycle showed the best efficiency and was suitable for next generation nuclear reactor. Fahad and Maimoon [22] compared different S-CO2 Brayton cycles integrated with a solar power tower, and concluded that the recompression cycle reached the highest thermal efficiency and the highest net power output at peak hours. Sarkar [23, 24] optimized the compressor pressure ratio and intermediate pressure to gain maximum thermal efficiency of the reheating S-CO2 recompression Brayton cycle and conducted exergetic analysis on the S-CO2 recompression Brayton cycle to study the effect of operating parameters on the optimum pressure ratio, energetic and exergetic efficiencies and component irreversibilities. Some efforts have been made for further improvement of the S-CO2 recompression Brayton cycle performance by layouts modifications and parameters optimizations. Padilla et al. [25] performed a comprehensive thermodynamic analysis and a multi-objective optimization on three S-CO2 cycles assisted by an ejector, and indicated that by the integrating of the ejector the cycle can achieve higher efficiency than the referenced steam Rankine cycles and reduce the manufacturing costs of the solar receiver and extended its operational life. Yari et al. [26] examined the performance of a novel S-CO2 recompression Brayton cycle of nuclear power plant with pre-cooler exergy utilization, which used a trans-critical CO2 bottom cycle to enhance the performance of this new cycle. Akbari and Mahmoudi [27] performed thermo-economic analysis and optimization of a combined S-CO2 recompression Brayton Organic Rankine cycle and concluded that higher exergy efficiency and lower total product unit cost would be obtained for the proposed cycle. Serrano et al. [28, 29] and Linares et al. [30, 31] proposed and compared several cycle layouts, based on S-CO2 recompression Brayton cycle for energy conversion, in order to make better use the heat sources at different temperatures in future fusion reactors with dual coolant lithium lead blanket and helium cooled lithium lead blanket. Intercooling is a traditional way to improve cycle efficiency by lowering the compressor power in the gas Brayton cycle. Some attempts have been made to apply intercooling between compressor stages to S-CO2 cycle for efficiency improvement. Dostal[8] performed thermodynamic analysis on a S-CO2 simple Brayton cycle with intercooling and indicated that the optimum pressure ratio distribution of compressor in S-CO2 cycle may differ from that of ideal gas Brayton cycle due to the real gas properties near critical point. Kato [32] carried out cycle efficiency between partial cooling S-CO2 Brayton cycle with and without intercoolers and indicated that more than three stages with two intercoolers could not be justified economically. For S-CO2 recompression Brayton cycle, main compression intercooling (MCIC, intercooling between main compressor stages) has been proposed by some researchers

ACCEPTED MANUSCRIPT for cycle performance improvement. However, the conclusions about MCIC effects on cycle efficiency were not consistent among different researches. Moisseytsev and Sienicki [33] investigated several alternative layouts for the S-CO2 Brayton cycle including recompression Brayton cycle with MCIC. Their results showed that no benefits could be achieved by the introduction of MCIC. Turchi et al [34] conducted thermodynamic study of advanced S-CO2 Brayton cycle, and indicated that recompression cycle with MCIC could achieve thermal efficiency greater than 50% accommodating dry cooling. But in their study, the integration of MCIC did not show effects in efficiency improvement when turbine inlet temperature is lower than 700℃. Ricardo et al [35] performed exergetic analysis of S-CO2 Brayton cycles integrated with solar central receivers and indicated that recompression with MCIC had the best thermal and exergetic performance among all the studied cycle layouts. From the above studies, we can conclude that though some attentions have been paid to MCIC integration in S-CO2 recompression Brayton cycle, the conclusions about the MCIC effects on S-CO2 recompression Brayton cycle are still controversial. Moreover, very little research has been devoted to the optimizations of cycle parameters and analyses of the effects of cycle working conditions on the performance of S-CO2 recompression Brayton cycle with MCIC, both of which are essential for the evaluation of MCIC effects. In this work, in order to clarify the thermodynamic effects of MCIC on the S-CO2 recompression Brayton cycle and investigate the feasibility of integrating MCIC in S-CO2 recompression Brayton cycle in various power conversion systems under different operating conditions, detailed parametric analyses and optimization works have been performed in a wide parameters range. Thermodynamic models for S-CO2 recompression Brayton cycle with MCIC have been established and verified. On this basis, two crucial parameters, i.e. the compressor pressure ratio and pressure ratio distribution between two main compressor stages have been optimized in the reference conditions. Then, the effects of working conditions on MCIC effects have been investigated. Optimization results of four typical conditions with different turbine inlet parameters or cooling methods have been chosen to further evaluate the thermodynamic effects of MCIC under different conditions. Finally, a comprehensive comparison between S-CO2 recompression Brayton cycle with and without MCIC has been performed in four typical design conditions and the corresponding off-design conditions with deviated pressure ratio in order to illustrate the MCIC effects on cycle performance from perspectives of not only cycle efficiency but also cost savings and performance robustness.

2. Model development 2.1 Cycle layout The layout of S-CO2 recompression Brayton cycle with MCIC is shown in Fig.1, the corresponding T-S diagram is shown in Fig.2. The low pressure flow after the low temperature recuperator (LTR) is split upstream of the precooler (state 10). The first stream is cooled in the precooler, and compressed to high pressure by main compressor (MC) with intercooler, and then heated through LTR. The second stream is compressed in the recompressor (RC), and mixed with the first stream exiting from LTR (state 5) upstream of the high temperature recuperator (HTR). Then the stream is

ACCEPTED MANUSCRIPT heated in the HTR and PHX in sequence, and then enters the turbine to expand, after exiting from the turbine, the flow finally enters the exothermic sides of HTR and LTR in turn to complete the cycle.

Fig. 1 layout of S-CO2 recompression Brayton cycle with intercooling

Fig. 2 T-s diagram of S-CO2 recompression Brayton cycle with MCIC

2.2 Mathematical models To investigate the performance of S-CO2 recompression Brayton cycle with MCIC, mathematical models are established for the whole cycle system and each component.

ACCEPTED MANUSCRIPT For turbine in the cycle, the calculations of the outlet conditions are based on the inlet conditions and isentropic efficiency. P8  P7 /  tur (1)

h8  h7   h7  h8 s  is,tur

(2)

wtur  h7  h8 (3) Wtur  mc  wtur  mc  (h7  h8 ) (4) For main compressor and recompressor in the cycle, split ratio (SR) is defined as the mass flow rate ratio through main compressor. The calculations of the outlet conditions are based on the inlet conditions and isentropic efficiencies of MC and RC. m (5) SR  1 mc (6) P2   MC,1  P1

h2  h1   h2 s - h1  / is,MC,1 P4   MC,2  P3

(7) (8)

h4  h3   h4 s  h3  / is,MC,2

(9)

wMC  SR   (h2  h1 )  (h4  h3 )

(10)

WMC  mc  wMC  SR  mc   (h2  h1 )  (h4  h3 )

(11)

P5   RC  P10

(12)

h5  h10   h5 s  h10  / is,RC

(13)

wRC  (1  SR)  (h5  h10 ) (14) WRC  mc  wRC  (1  SR)  mc  (h5  h10 ) (15) Meantime, to quantify the distribution of compressor pressure ratio between two compression stages of main compressor, the ratio of pressure ratio for the compression stage i of main compressor, represented with RPRMC,1, is defined in equation (16): Ln( MC,i ) RPRMC,i  , i  1, 2... (16) Ln( MC ) In the present work, the number of main compression stages is 2, which means only one RPRMC,1 is variable to determine the distribution of pressure ratio. In the following discussion, RPRMC,1 is used to represent the pressure ratio distribution between two compression stages of the main compressor. For LTR and HTR, energy conservation should be satisfied during heat transferring. mc  (h8  h9 )  mc  (h6  h5 ) (17) mc  ( h9  h10 )  SR  mc  ( h5  h4 ) (18) And the effectiveness of LTR and HTR are defined by the following equations [36]: T T (19)  HTR  8 9 T8  T5

 LTR

 T9 - T10  T - T , if mCp LTR,ht  mCp LTR,lt  9 4   T5 - T4 , if mCp  mCp LTR,ht LTR,lt  T9 - T4

















(20)

ACCEPTED MANUSCRIPT For heat sink in the cycle, energy conservation should be satisfied in calculations. QPrecooler  SR  mc  (h10  h1 ) (21)

QIntercooler  SR  mc  (h2  h3 ) (22) Heat source in the cycle is assumed to be a reactor with constant temperature [23, 37], and the energy conservation is specified for PHX as: QPHX  mc  (h7  h6 ) (23) The pinch point temperature in PHX is defined as: (24) TPHX =Tr -T7 The cycle efficiency can be evaluated as: W  WMC  WRC  Q  QIntercooler (25) th  tur =1  Precooler QPHX QPHX On the basis of established mathematical models, a cycle analysis code was developed in Matlab R2010b to carry out thermodynamic analysis on the S-CO2 cycle integrated with MCIC. REFPROP 8.1[38] was called to evaluate the CO2 thermal properties during calculation. The following assumptions have been made to complete the modeling calculation:  changes in kinetic and potential energies of fluids are neglected;  heat transfer with ambient are neglected for all the components;  identical inlet temperatures are assumed for two main compression stages;  pressure losses are neglected in all the heat exchangers and pipes, unless otherwise indicated;

2.3 Model verification To validate the proposed mathematical models, the results of modeling calculation have been compared with the results from literature [39] for the S-CO2 recompression Brayton cycle in four different operating conditions. It turns out that the calculated πopt and SR and cycle efficiencies ηth show good coherence with the results reported in the literature [39] in all the operating conditions. results in literature [39]

operating conditions

present results

Tmin [℃]

Tmax [℃]

Pmax [MPa]

πopt [-]

SR [%]

ηth [%]

πopt [-]

SR [%]

ηth [%]

32

550

20

2.64

66.6

41.18

2.640

66.62

41.178

32

750

30

3.94

71.9

49.83

3.940

71.88

49.830

50

550

20

2.4

81.6

36.71

2.389

81.62

36.705

50

750

30

3.08

82.5

45.28

3.081

82.51

45.280

Table 1 comparisons between calculated results and literature results

3. Parameters optimization The initial parameters for reference conditions are listed in the Table 2. The ambient temperature and reactor temperature are assumed to be 25℃ and 850℃, respectively. The working conditions, isentropic efficiencies of turbine machines and effectiveness of recuperators are referred from the published literatures [8, 40, 41] .

ACCEPTED MANUSCRIPT Parameters value 25 T0 [℃] 850 Tr [℃] 35a Tmin [℃] 650a Tmax [℃] Pmax [MPa] 20a ηis,MC [%] 89b ηis,RC [%] 89b ηis,tur [%] 90b εLTR [%] 95c εHTR [%] 95c a:Ref[8],b:Ref[40],c:Ref[41] Table 2 Initial parameters for reference conditions

3.1 Optimization of compressor pressure ratio The optimization of compressor pressure ratio πMC is performed in the range of 2.6-4 with RPRMC,1 =0.22 and other initial parameters specified in Table 2. Fig.3 (a) illustrates the variations of works of compressors and turbine with πMC. As observed from Fig.3 (a), in the pressure ratio range of about 3.15-3.3, the total compressor works increase more apparently with the rise of πMC due to the surges of the compressibility factor of working fluids in the MC and RC. And when πMC is outside this range, the increase of total compressor works is less steep as πMC rises due to the less significant increase of compressibility factor of working fluids in MC and RC. Besides the variations of compressibility, the change of CpLTR,lt with πMC also affects the compressor works. When πMC is beyond 3.2, due to the deviation from pseudocritical temperature as πMC rises, CpLTR,lt suffers an abrupt degradation. This results in the increase of the split ratio(SR) in the MC and corresponding decrease of the split ratio (1-SR) in the RC, leading to the apparent difference of variation tendencies between MC and RC works as observed from Fig.3 (a). On the other hand, the working fluids in turbine can be approximately treated as ideal gas. The turbine work improves almost linearly in the whole studied range of πMC. The variation of net output power is shown in Fig.3 (b). As the combined results of variations of compressors and turbine works, when πMC rises in the range except for about 3.15 to 3.3, the net output power increases monotonously due to the diverging nature of isobars with temperature. In the range of about 3.15 to 3.3, the net output power decreases due to the drastic increase of compressor works. The optimal πMC to maximize the cycle efficiency is obtained at πMC =3.2. The cycle efficiency improves as a result of increased net output power when πMC is less than the optimal value. However, when πMC is beyond its optimal value, the increase of net output power is less apparent, while due to the abrupt degradation of CpLTR,lt in higher πMC, SR and hence the cold source loss increases apparently. Therefore the cycle efficiency decreases with further rise of πMC.

ACCEPTED MANUSCRIPT

(a) variations of works of compressors and turbine

(b) variations of net output power, cold source loss and cycle efficiency Fig. 3 Optimization of compressor pressure ratio

3.2 Optimization of compressor pressure ratio distribution in MC The optimization of RPRMC,1 is performed in the range of 0 to 0.7 in the reference conditions with πMC =3.2. As Fig.4 (a) shows, an optimum RPRMC,1 =0.3 minimizes the compressor works. It should be noted that this optimum value apparently deviates from 0.5, which is the optimum value for the intercooled compressor with ideal gas as working fluids under the same conditions [42]. This can be mainly attributed to the effect of real gas properties on compressibility factor of the compressed fluids near the critical point. The reverse change of MC works and RC work before RPRMC,1 reaches 0.2 can be explained by the abrupt decrease of SR in the MC side and corresponding increase of (1-SR) in RC side because of the apparent improvement of

ACCEPTED MANUSCRIPT CpLTR,lt near pseudocritical temperature. The work of turbine is independent of

RPRMC,1 and hence stays constant. Therefore, as shown in Fig.4 (b), the maximum of net output power is obtained when RPRMC,1 =0.3, in which value the compressor works are minimized. The optimal RPRMC,1 to maximize the cycle efficiency is obtained at RPRMC,1=0.22. Before attaining the optimal RPRMC,1, the cold source loss is relatively stable due to the combined results of increased enthalpy differences and decreased SR across the precooler and intercooler. Therefore, the cycle efficiency improves due to the increased net output power as RPRMC,1 rises However, with further increase of RPRMC,1, the net output power starts to decrease. And cold source loss starts to increase because SR becomes stable while enthalpy differences across the precooler and intercooler keep increasing with further rise of RPRMC,1. Therefore, the cycle efficiency begins to decrease when RPRMC,1 is beyond the optimal value.

(a) variations of compressor works

(b) variations of net output power, cold source loss and cycle efficiency Fig. 4 Optimization of compressor pressure ratio distribution in MC

ACCEPTED MANUSCRIPT

3.3 Optimization results Fig.5 shows the simultaneous optimization results of πMC and RPRMC,1 in the reference conditions. As displayed in Fig.5, the cycle efficiency is more sensitive to the change of RPRMC,1 than πMC due to more abrupt change of cold source loss and output power with RPRMC,1. Therefore RPRMC,1 is more predominant to determine the cycle performance for recompression S-CO2 cycle with MCIC. Table 3 displays the thermodynamic states and performance parameters of the optimal cycle. According to the optimized results, in the reference conditions, the maximum cycle efficiency can be reached is 50.05% while the optimal cycle efficiency for recompression cycle without MCIC (i.e. the case of RPRMC,1=0) is 48.76%. Hence, 2.65% relative efficiency improvement is obtained with the integration of MCIC in the reference conditions.

Fig. 5 Optimization of πMC and RPRMC,1 state point

T/K

P/kPa

Performance parameter

Unit

Value

1

308.15

2

328.53

6250

πMC

\

3.2

8072.59

RPRMC,1

\

0.22

3

308.15

8072.59

ηth

%

50.05

4

347.96

20000

SR

%

64.70

5

469.35

20000

wtur

kJ/kg

169.36

6

733.46

20000

wMC

kJ/kg

22.31

7

923.15

20000

wRC

kJ/kg

29.10

8

776.56

6250

wnet

kJ/kg

117.94

9 10

484.71 354.80

6250 6250

Table 3 Thermodynamic states and performance parameters of the optimized cycle

4. Effects of working conditions on MCIC effects In this section, effects of different working conditions (including cycle minimum temperature, cycle maximum temperature, cycle maximum pressure and pressure

ACCEPTED MANUSCRIPT losses) on MCIC effects and the optimized variables are discussed in this section. Four parameters are selected in this section to represent the effects of working conditions, including two optimized variables, i.e., πMC and RPRMC,1, as well as two parameters regarding MCIC effects on cycle efficiency, i.e., the cycle efficiency and relative efficiency improvement..

4.1 Effects of cycle minimum temperature The effects of cycle minimum temperature Tmin on MCIC effects are investigated at 650℃ cycle maximum temperature and 20MPa cycle maximum pressure. As Fig.6 shows, the optimum πMC decreases as Tmin increases. One reason for this result is the dramatic increase of compressibility factor when compressor inlet temperature deviates from the critical region. And higher πMC tends to amplify the effect of compressor works on cycle performance. Therefore, the optimal πMC tends to reduce as Tmin rises. Besides, this can also be explained from the point of cold source loss. In lower Tmin conditions, the working fluids temperature in the compressor is relatively close to the critical temperature, the decrease of pressure and the increase of temperature in the high temperature side of LTR with the rise of πMC will lead to the reduction of CpLTR,lt, which will reduce SR and hence alleviate the cold source loss in the precooler and intercooler. While in higher Tmin conditions, the temperature of high temperature side is far away from the pseudocritical temperature, therefore the variation of πMC will not apparently affect CpLTR,lt, and SR even increases as πMC rises due to the degradation of CpLTR,lt. Hence the cold source loss enhances with the increase of πMC in higher Tmin conditions. Fig.6 also shows that the optimum RPRMC,1 increases with Tmin. This can also be explained from the point of both cold source loss and compressor work. Due to the expansion of isobars with temperature, the temperature in low temperature side of LTR dramatically increases and deviates from the pseudocritical temperature with the rise of Tmin. As a result, CpLTR,lt will dramatically decrease, and hence SR and cold source loss tend to increase in higher Tmin. On the other hand, the temperature reduction of working fluids in LTR becomes more significant as RPRMC,1 rises. Therefore, the optimum RPRMC,1 increases in higher Tmin to reduce the fluids temperature in the low temperature side of LTR, and hence to reduce SR and cold source loss. Besides, the optimum RPRMC,1 to obtain minimum compressor works also increases with the increase of Tmin due to the weakened real gas effects of working fluids in compressors when Tmin rises. Fig.7 illustrates the variations of cycle efficiency of MCIC recompression cycle and the efficiency improvement by integrating MCIC in different Tmin. As Fig.7 shows, the optimum cycle efficiency decreases monotonously as Tmin increases while the efficiency improvement increases as Tmin increases. This can be attributed to the increase of compressor work and cold source loss with Tmin and hence the more apparent effects of MCIC in reducing compressor work and cold source loss in higher Tmin conditions. In general, the integration of MCIC will provide apparent efficiency improvement (over 2%) in the studied range of Tmin, and the effects will be even more significant in Tmin high conditions. As shown in Fig.7, more than 3.2% cycle efficiency improvement can be obtained by the integration of MCIC when Tmin =50℃.

ACCEPTED MANUSCRIPT

Fig. 6 Effect of cycle minimum temperature on optimum πMC and RPRMC,1

Fig. 7 Effect of cycle minimum temperature on optimum cycle efficiency and efficiency improvement

4.2 Effects of cycle maximum temperature The effects of maximum temperature Tmax on cycle performance are investigated at 35℃ cycle minimum temperature and 20MPa maximum pressure. Fig.8 displays the effect of cycle Tmax on optimum πMC and RPRMC,1. Both of the optimum πMC and RPRMC,1 increase as Tmax rises. The increase of optimum πMC can be attributed to the increasing tendency of the net output work improvement due to the expansion nature of isobars with temperature. The increase of RPRMC,1 with Tmax can be mainly attributed to the increase of temperature in the LTR low temperature side, which will reduce CpLTR,ltand increase SR and hence the cold source loss. Therefore, higher RPRMC,1 is needed to reduce the working fluids temperature and SR to alleviate the augmentation of cold source loss in higher Tmax conditions.

ACCEPTED MANUSCRIPT Fig.9 illustrates the effect of Tmax on the optimum cycle efficiency and the efficiency improvement. The cycle efficiency improves as Tmax increases due to the enhancement of net output power on account of the expasion of isobars with temperature. The cycle efficiency improvement also enhances with the rise of Tmax mainly due to the more apparent effect of MCIC on alleviating cold source loss in higher Tmax. Therefore, the integration of MCIC will be an attractive option for the advanced parameters design cycle with high turbine inlet temperature, while its effects of efficiency improvement on the low Tmax recompression S-CO2 Brayton cycles may be less significant.

Fig. 8 Effect of cycle maximum temperature on optimum πMC and RPRMC,1

Fig. 9 Effect of cycle maximum temperature on optimum cycle efficiency and efficiency improvement

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4.3 Effects of cycle maximum pressure The effects of cycle maximum pressure on cycle performance are investigated at 35℃ cycle maximum temperature and 650℃ cycle maximum temperature. Fig.10 shows the effects of cycle maximum pressure Pmax on optimum πMC and RPRMC,1. The optimum πMC increases as Pmax rises. This can be explained from the variations of compressor works and cold source loss with Pmax. For one thing, the compressor works sharply decrease due to the abrupt reduction of compressibility factor as the compressors inlet pressures shifts from subcritical to supercritical with the rise of Pmax. For another thing, in high Pmax conditions, the cold source loss is relatively stable due to the weakened pseudocritical temperature effect on heat capacity in the low temperature side of LTR. The optimum RPRMC,1 decreases monotonously as Pmax rises as Fig.10 shows. One reason for this is the more apparent effects of real gas properties when the inlet pressure of compressors increases and becomes closer to critical point in higher Pmax. Besides, this can also be explained from the point of cold source loss. In the case of high Pmax, the CpLTR,lt is insensitive to the change of temperature due to the weakened pseudocritical temperature effect as aforementioned. Therefore, the effect of RPRMC,1 on SR in the low temperature side is reasonably negligible. On the contrary, the rise of RPRMC,1 which leads to the increase of enthalpy difference across the precooler and intercooler, will augment the cold source loss. In the case of low Pmax, the pseudocritical temperature effect is relatively apparent on the heat capacity of working fluids in low temperature side of LTR. And the average working temperature is higher than the pseudocritical temperature in the low temperature side of LTR in low Pmax condition. Therefore, the increase of RPRMC,1, which tends to lower the working temperature in the low temperature side of LTR, will reduce SR due to the enhanced CpLTR,lt when approaching pseudocritical temperature. As shown in Fig.11, the optimal cycle efficiency improves as Pmax rises due to the expansion of isobars with temperature and hence the apparent increase of net output power in higher Pmax. The cycle efficiency improvement brought by MCIC decreases in higher Pmax. This can be mainly attributed to the increased cold source loss due to the weakened pseudocritical point effect in higher Pmax as aforementioned. Therefore, the effect of MCIC on cycle performance is less significant in high Pmax conditions. As illustrated in Fig.11, the efficiency brought by MCIC will decrease to less than 1% when Pmax =28MPa. However, in the range of 16-26MPa, 1.2-3.4% cycle efficiency improvement can be obtained. Therefore, it is still an effective method to integrate MCIC in the recompression S-CO2 Brayton cycles in most of the application range of Pmax .

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Fig. 10 Effect of cycle maximum pressure on optimum πMC and RPRMC,1

Fig. 11 Effect of cycle maximum pressure on optimum cycle efficiency and efficiency improvement

4.4 Effects of pressure losses Effects of pressure losses in different heat exchangers on the cycle efficiency in the reference conditions are shown in Fig.12 .Results show that the pressure losses impair the cycle performance in different degrees. And the pressure losses in the PHX and HTR are more significant to the cycle performance than those in other heat exchangers. Therefore, the pressure losses and the consequent efficiency penalties should be taken into consideration during the heat exchanger type selection and design, especially for PHX and HTR. For example, compact heat exchanger such as Printed heat exchanger (PCHE) is usually recommended for the S-CO2 cycle due to the superior heat transfer performance and small overall footprint. However, it may entail higher pressure loss and thus severer consequent efficiency penalty relative to

ACCEPTED MANUSCRIPT the conventional heat exchanger in the meantime. Therefore, the optimization design on hydraulic characteristics of PCHE is necessary to reduce the pressure losses in the heat exchangers [43]. Fig.13 shows the cycle efficiency improvement with the integration of MCIC in different pressure losses conditions in different heat exchangers. Since no intercooler is in the recompression cycle without MCIC, the efficiency improvement brought by the integration of MCIC decreases with the increase of pressure losses in the intercooler as expected. However, cycle efficiency can still be improved with MCIC even when the pressure loss in intercooler is up to 3%. For other heat exchangers, the maximum efficiency improvements are obtained when pressure losses is about 0.5%1%. The pressure losses effects on the optimum πMC and RPRMC,1 are negligible for the proposed cycle.

Fig. 12 Effects of pressure losses on cycle efficiency

Fig. 13 Effects of pressure losses on cycle efficiency improvement

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5 Cycle comparison with and without MCIC In order to perform a comprehensive comparison between cycles with and without MCIC, four typical design conditions with different turbine inlet temperatures or different cooling methods are investigated in this section. The related parameters of four operating conditions are specified in the Table 4. The comparison will be performed in both design conditions and the corresponding off-design conditions. Tmin [℃]

Tmax [℃]

Pmax [MPa]

low turbine inlet parameters

wet cooling

35

500

20

dry cooling

50

500

20

high turbine inlet parameters

wet cooling

35

800

25

dry cooling

50

800

25

Table 4 Design conditions for comparisons

5.1 Cycle comparison in the design conditions In the design conditions, cycle efficiency and temperature difference across the PHX, which is a key factor to determine the cost of PHX [44, 45], are compared to investigate the effects of MCIC from perspectives of both performance improvements and cost savings. Table 5 shows the cycle efficiency comparisons with and without MCIC in four design conditions. It can be concluded that the efficiency improvements brought by the introduction of MCIC are more apparent in the operating conditions of high turbine inlet parameters and dry cooling. The maximum efficiency improvement exceeds 3.8% for the cycle with high turbine inlet temperature and dry cooling. Besides, the temperature difference increases for all operating conditions when MCIC is introduced, especially in the high turbine inlet parameters and dry cooling conditions. The increase of temperature difference will facilitate the reduction of PHX volume and hence leads to cost savings due to the improved heat transfer capacity of working fluids in PHX. cycle efficiency[%]

PHX temperature difference[℃]

Without MCIC

With MCIC

Without MCIC

With MCIC

Low turbine inlet parameters

Wet cooling

43.08

43.74

145.45

157.10

Dry cooling

39.59

40.82

215.40

241.36

High turbine inlet parameters

Wet cooling

54.58

55.68

121.38

138.27

Dry cooling

51.59

53.24

191.61

224.38

Table 5 Cycle comparisons with and without MCIC

5.2 Cycle comparison in the off-design conditions Fig.14 illustrates the cycle efficiency in different off-design conditions with deviated pressure ratio. As shown in Fig.14, the cycle efficiency of recompression cycle without MCIC is sensitive to the deviation of pressure ratio, especially when pressure ratio decreases from the optimum pressure ratio in wet cooling and low turbine inlet parameters conditions. With the integration of MCIC, the cycle

ACCEPTED MANUSCRIPT efficiency is less sensitive to the deviation from optimum pressure ratio for all the selected operating conditions. Therefore, the integration of MCIC may be beneficial for the load control in off-design operating conditions due to the better robustness of cycle efficiency.

Fig. 14 Comparison of cycle efficiency in the off-design conditions with deviated pressure ratio

6. Conclusions Mathematical models for the S-CO2 recompression cycle with MCIC have been established in the present work. A new parameter RPRMC,1 is introduced in the model to represent the compressor pressure ratio distribution between two main compression stages. On this basis, a detailed optimization work of compressor pressure ratio and RPRMC,1 has been performed. Results show that the optimization of compressor pressure ratio and RPRMC,1 is mainly dominated by the real gas properties effects near critical region, which lead to drastic changes of compressibility factor and heat capacity of working fluids. The compressor pressure ratio and RPRMC,1 both affect the cycle efficiency and the latter is more dominant to determine the optimum cycle efficiency due to higher sensitivity of cold source loss and output power to RPRMC,1 change. The optimization results show that 2.65% efficiency improvement can be obtained by the integration of MCIC in the reference conditions. Moreover, effects of working conditions on the optimized parameters and MCIC effects have been investigated. The results show that the working conditions have significant effects on the optimized parameters. The optimum compressor pressure ratio tends to increase with decreasing cycle minimum temperature, increasing cycle maximum temperature and increasing cycle maximum pressure while the optimum RPRMC,1 tends to increase with increasing cycle minimum temperature, increasing cycle maximum temperature and decreasing cycle maximum pressure. The effects of pressure losses in heat exchangers on the optimum pressure ratio and RPRMC,1 are negligible. Besides, the effects of MCIC on cycle efficiency show different variation tendencies with the change of different working conditions. The cycle efficiency will be improved in lower cycle minimum temperature, higher maximum temperature and higher maximum pressure while the efficiency improvement will be more apparent in higher cycle minimum temperature, higher maximum temperature and lower

ACCEPTED MANUSCRIPT maximum pressure. Therefore, the integration of MCIC can bring efficiency improvement in the whole studied range of operating conditions. And S-CO2 recompression Brayton cycles featuring high cycle minimum temperature or high cycle maximum temperature are recommended to be integrated with MCIC due to the relative significant efficiency improvement. High cycle maximum pressure will weaken the MCIC effects. But in most of the typical application ranges of cycle maximum pressure, integrating MCIC is still an effective method for cycle performance improvement. Pressure losses in heat exchangers lead to cycle efficiency decline, especially the pressure losses in HTR and PHX. Cycle efficiency improvement is maximized when pressure losses is 0.5%-1% for each heat exchangers except the intercooler. A comprehensive comparison work has been performed between S-CO2 recompression Brayton cycles with and without MCIC in four typical design conditions with different turbine inlet parameters or cooling methods and the corresponding off-design conditions with deviated compressor pressure ratio. In the design conditions, the integration of MCIC can not only improves the cycle efficiency, but also reduces the temperature difference across the PHX, which tends to bring cost savings for the PHX. In the off-design conditions, the integration of MCIC improves the robustness of cycle performance to the deviation of pressure ratio, which may benefit the loads control in part-load conditions.

Acknowledgement This work is supported by the National Natural Science Foundation of China [Grant No.51436006]; and the Joint Funds of the Equipment department and Education Ministry for Young Talents of China [Grant No.6141A02033501].

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Thermodynamic analyses were conducted on effects of main compression intercooling



Compressor pressure ratio distribution has great influence on cycle performance



Working conditions significantly affect main compression intercooling effects



The performance of cycle with main compression intercooling is more robust