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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (2): 404-414    DOI: 10.3785/j.issn.1008-973X.2023.02.019
    
Performance analysis and optimization of supercritical CO2 Brayton cycle waste heat recovery system
Ting-fang YU(),Ling SONG
School of Advanced Manufacturing, Nanchang University, Nanchang 330031, China
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Abstract  

The Kalina cycle (KC) and the organic Rankine cycle (ORC) were used and modeled as the bottom cycles, to economically and efficiently recover the waste heat of the supercritical carbon dioxide Brayton cycle (SCBC). Parametric analysis was conducted and the NSGA-II multi-objective genetic algorithm was performed for these combined systems to optimize the parameters. The optimization results were compared with the SCBC system performance to display the benefits of combined cycles. Parametric analysis results showed that there was an optimal pressure ratio for the thermodynamic performances of both integrated cycle schemes. The thermodynamic performances of the two schemes were improved by raising the turbo expansion ratio of bottom cycles, and the exergoeconomic performances of the systems were promoted by upping the inlet temperature of the bottom cycle turbine. Comparison results showed that the optimized SCBC/KC system’s thermal efficiency and exergy efficiency increased by 9.27% and 8.69% respectively compared with that of the pre-optimized SCBC system, and its exergoeconomic cost increased by 0.92%. The thermal efficiency and exergy efficiency of SCBC/ORC system increased by 10.73% and 10.08% respectively, and the exergoeconomic cost increased by 1.87%. Comparative analysis showed that the SCBC/KC system was more exergy economical, while SCBC/ORC system was more energy efficient.

Key words： supercritical carbon dioxide Brayton cycle      exergy economics      organic Rankine cycle      Kalina cycle      waste heat recovery technology      performance comparison      multi-objective optimization     
Received: 24 June 2022      Published: 28 February 2023
CLC:  TK 11  
Fund:  国家自然科学基金资助项目(22068024)；江西省重点研发计划资助项目（2017ACG70012）
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Ting-fang YU
Ling SONG
Cite this article:

Ting-fang YU,Ling SONG. Performance analysis and optimization of supercritical CO2 Brayton cycle waste heat recovery system. Journal of ZheJiang University (Engineering Science), 2023, 57(2): 404-414.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.02.019     OR     https://www.zjujournals.com/eng/Y2023/V57/I2/404


超临界CO2布雷顿循环余热回收系统性能分析与优化

为了经济高效地回收超临界CO2布雷顿循环（SCBC）的余热，分别采用卡琳娜循环（KC）和有机朗肯循环（ORC）作为底循环，设计了SCBC/KC及SCBC/ORC这2种系统方案. 对2种方案系统进行参数分析并利用NSGA-Ⅱ多目标遗传算法对联合循环系统进行多目标优化计算，将优化结果与SCBC系统性能进行比较，突出联合循环系统的性能优势. 参数分析结果表明：2种联合循环系统热力性能均存在最佳压比；升高底循环膨胀比有助于提升系统热力性能；提高底循环涡轮机进口温度有助于改善系统?经济性能. 对比结果表明：优化后的SCBC/KC系统热效率和?效率较优化前SCBC系统分别升高了9.27%和8.69%，?经济成本仅升高了0.92%；SCBC/ORC系统热效率和?效率较优化前SCBC系统分别升高10.73%和10.08%，?经济成本升高了1.87%. 通过比较分析可知，SCBC/KC系统更经济，而SCBC/ORC系统更节能.


关键词： 超临界CO2布雷顿循环,  ?经济,  有机朗肯循环,  卡琳娜循环,  余热回收技术,  性能比较,  多目标优化 
Fig.1 Schematic diagram of combined supercritical CO2 Brayton cycle with Kalina cycle
Fig.2 Schematic diagram of combined supercritical CO2 Brayton cycle with organic Rankine cycle
Fig.3 Temperature entropy diagram of top cycle SCBC and bottom cycle KC and ORC
部件 能量守恒方程 ?守恒方程
吸热器 ${\varPhi_{ {\text{ER} } } } = {q_{m,{\text{s} } } }({h_{\text{5} } } - {h_{\text{4} } })$ ${E_{\text{4} } }+{E_{{\text{q, ER} } } } = {E_{\text{5} } }+{E_{ {\text{d,ER} } } }$
透平 ${P_{\text{T} } } = {q_{m,{\text{s} } } }({h_{\text{5} } } - {h_{\text{6} } })$ ${E_{\text{5} } } = {E_{\text{6} } }+{P_{\text{T} } }+{E_{ {\text{d,T} } } }$
主压缩机 ${P_{ {\text{MC} } } } = ({q_{m,{\text{s} } } } - {q_{m,{\text{r} } } })({h_{\text{2} } } - {h_{\text{1} } })$ ${E_{\text{1} } }+{P_{ {\text{MC} } } } = {E_{\text{2} } }+{E_{ {\text{d,MC} } } }$
再压缩机 ${P_{ {\text{RC} } } } = {q_{m,{\text{r} } } }({h_{\text{3} } } - {h_{\text{8} } })$ ${E_{\text{8} } }+{P_{ {\text{RC} } } } = {E_{\text{3} } }+{E_{ {\text{d,RC} } } }$
高温回热器 $ {q_{m,{\text{s}}}}({h_{\text{6}}} - {h_{\text{7}}}) = {q_{m,{\text{s}}}}({h_{\text{4}}} - {h_{\text{3}}}) $ $ {E_{\text{6}}}+{E_{\text{3}}} = {E_{\text{7}}}+{E_{\text{4}}}+{E_{{\text{d,HTR}}}} $
低温回热器 $ {q_{m,{\text{s}}}}({h_{\text{7}}} - {h_{\text{8}}}) = ({q_{m,{\text{s}}}} - {q_{m,{\text{r}}}})({h_{\text{3}}} - {h_{\text{2}}}) $ $ {E_{\text{7}}}+{E_{\text{2}}} = {E_{\text{8}}}+{E_{\text{3}}}+{E_{{\text{d,LTR}}}} $
蒸发器 $ ({q_{m,{\text{s}}}} - {q_{m,{\text{r}}}})({h_{\text{8}}} - {h_{\text{9}}}) = {q_{m,{\text{v}}}}{h_{{\text{01}}}}+{q_{m,{\text{l}}}}{h_{{\text{03}}}} - {q_{m,{\text{k}}}}{h_{{\text{08}}}} $ $ {E_{\text{8}}}+{E_{{\text{08}}}} = {E_{\text{9}}}+{E_{{\text{01}}}}+{E_{{\text{03}}}}+{E_{{\text{d,GK}}}} $
涡轮机 ${P_{ {\text{TK} } } } = {q_{m,{\text{k} } } }({h_{ {\text{01} } } } - {h_{ {\text{02} } } })$ ${E_{ {\text{01} } } } = {E_{ {\text{02} } } }+{P_{ {\text{TK} } } }+{E_{ {\text{d,TK} } } }$
预热器 $ {q_{m,{\text{l}}}}({h_{{\text{03}}}} - {h_{{\text{04}}}}) = {q_{m,{\text{k}}}}({h_{{\text{08}}}} - {h_{{\text{07}}}}) $ $ {E_{{\text{03}}}}+{E_{{\text{07}}}} = {E_{{\text{08}}}}+{E_{{\text{04}}}}+{E_{{\text{d,PHK}}}} $
节流阀 $ {q_{m,{\text{l}}}}{h_{{\text{04v}}}} = {q_{m,{\text{l}}}}{h_{{\text{04a}}}} $ $ {E_{{\text{04}}}} = {E_{{\text{04v}}}}+{E_{{\text{d,VK}}}} $
混合器 $ {q_{m,{\text{v}}}}{h_{{\text{02}}}}+{q_{m,{\text{l}}}}{h_{{\text{04v}}}} = {q_{m,{\text{k}}}}{h_{{\text{05}}}} $ $ {E_{{\text{02}}}}+{E_{{\text{04v}}}} = {E_{{\text{05}}}}+{E_{{\text{d,MK}}}} $
次冷却器 ${\varPhi_{ {\text{CK} } } } = {q_{m,{\text{k} } } }({h_{ {\text{05} } } } - {h_{ {\text{06} } } })$ ${E_{ {\text{05} } } } = {E_{ {\text{06} } } }+{E_{ {\text{q,CK} } } }+{E_{ {\text{d,CK} } } }$
泵 ${P_{ {\text{PK} } } } = {q_{m,{\text{k} } } }({h_{ {\text{07} } } } - {h_{ {\text{06} } } })$ ${E_{ {\text{06} } } }+{P_{ {\text{PK} } } } = {E_{ {\text{07} } } }+{E_{ {\text{d,PK} } } }$
主冷却器 ${\varPhi_{ {\text{CS} } } } = ({q_{m,{\text{s} } } } - {q_{m,{\text{r} } } })({h_{\text{9} } } - {h_{\text{1} } })$ ${E_{\text{9} } } = {E_{\text{1} } }+{E_{ {\text{q,CS} } } }+{E_{ {\text{d,CS} } } }$
Tab.1 Energy and exergy balance expressions for each component in SCBC/KC system
部件 能量守恒方程 ?守恒方程
吸热器 ${\varPhi_{ {\text{ER} } } } = {q_{m,{\text{s} } } }({h_{\text{5} } } - {h_{\text{4} } })$ ${E_{\text{4} } }+{E_{\text{q, ER} } } = {E_{\text{5} } }+{E_{ {\text{d,ER} } } }$
透平 $ {P_{\text{T}}} = {q_{m,{\text{s}}}}({h_{\text{5}}} - {h_{\text{6}}}) $ $ {E_{\text{5}}} = {E_{\text{6}}}+{P_{\text{T}}}+{E_{{\text{d,T}}}} $
主压缩机 $ {P_{{\text{MC}}}} = ({q_{m,{\text{s}}}} - {q_{m,{\text{r}}}})({h_{\text{2}}} - {h_{\text{1}}}) $ $ {E_{\text{1}}}+{P_{{\text{MC}}}} = {E_{\text{2}}}+{E_{{\text{d,MC}}}} $
再压缩机 $ {P_{{\text{RC}}}} = {q_{m,{\text{r}}}}({h_{\text{3}}} - {h_{\text{8}}}) $ $ {E_{\text{8}}}+{P_{{\text{RC}}}} = {E_{\text{3}}}+{E_{{\text{d,RC}}}} $
高温回热器 $ {q_{m,{\text{s}}}}({h_{\text{6}}} - {h_{\text{7}}}) = {q_{m,{\text{s}}}}({h_{\text{4}}} - {h_{\text{3}}}) $ $ {E_{\text{6}}}+{E_{\text{3}}} = {E_{\text{7}}}+{E_{\text{4}}}+{E_{{\text{d,HTR}}}} $
低温回热器 $ {q_{m,{\text{s}}}}({h_{\text{7}}} - {h_{\text{8}}}) = ({q_{m,{\text{s}}}} - {q_{m,{\text{r}}}})({h_{\text{3}}} - {h_{\text{2}}}) $ $ {E_{\text{7}}}+{E_{\text{2}}} = {E_{\text{8}}}+{E_{\text{3}}}+{E_{{\text{d,LTR}}}} $
蒸发器 $ ({q_{m,{\text{s}}}} - {q_{m,{\text{r}}}})({h_{\text{8}}} - {h_{\text{9}}}) = {q_{m,{\text{o}}}}({h_{{\text{09}}}} - {h_{{\text{012}}}}) $ $ {E_{\text{8}}}+{E_{{\text{012}}}} = {E_{\text{9}}}+{E_{09}}+{E_{{\text{d,GO}}}} $
涡轮机 $ {P_{{\text{TO}}}} = {q_{m,{\text{o}}}}({h_{{\text{09}}}} - {h_{{\text{010}}}}) $ $ {E_{{\text{09}}}} = {E_{{\text{010}}}}+{P_{{\text{TO}}}}+{E_{{\text{d,TO}}}} $
次冷却器 ${\varPhi_{ {\text{CO} } } } = {q_{m,{\text{o} } } }({h_{ {\text{010} } } } - {h_{ {\text{011} } } })$ ${E_{ {\text{010} } } } = {E_{ {\text{011} } } }+{E_{ {\text{q,CO} } } }+{E_{ {\text{d,CO} } } }$
泵 $ {P_{{\text{PO}}}} = {q_{m,{\text{o}}}}({h_{{\text{012}}}} - {h_{{\text{011}}}}) $ $ {E_{{\text{011}}}}+{P_{{\text{PO}}}} = {E_{{\text{012}}}}+{E_{{\text{d,PO}}}} $
主冷却器 ${\varPhi_{ {\text{CS} } } } = ({q_{m,{\text{s} } } } - {q_{m,{\text{r} } } })({h_{\text{9} } } - {h_{\text{1} } })$ ${E_{\text{9} } } = {E_{\text{1} } }+{E_{ {\text{q,CS} } } }+{E_{ {\text{d,CS} } } }$
Tab.2 Energy and exergy balance expressions for each component in SCBC/ORC system
部件 ?经济守恒方程
吸热器 $ {C_{\text{4}}}+{C_{\text{q}}}+{Z_{{\text{ER}}}} = {C_{\text{5}}} $
透平 $ {C_{\text{5}}}+{Z_{\text{T}}} = {C_{\text{6}}}+{C_{\text{W}}}_{{\text{,T}}} $
主压缩机 $ {C_{\text{1}}}+{C_{\text{W}}}_{{\text{,MC}}}+{Z_{{\text{MC}}}} = {C_{\text{2}}} $
再压缩机 $ {C_{\text{8}}}+{C_{\text{W}}}_{{\text{,RC}}}+{Z_{{\text{RC}}}} = {C_{\text{3}}} $
高温回热器 $ {C_{\text{6}}}+{C_{\text{3}}}+{Z_{{\text{HTR}}}} = {C_{\text{7}}}+{C_{\text{4}}} $
低温回热器 $ {C_{\text{7}}}+{C_{\text{2}}}+{Z_{{\text{LTR}}}} = {C_{\text{8}}}+{C_{\text{3}}} $
蒸发器 $ {C_{\text{8}}}+{C_{{\text{08}}}}+{Z_{{\text{GK}}}} = {C_{\text{9}}}+{C_{{\text{01}}}}+{C_{{\text{03}}}} $
涡轮机 $ {C_{{\text{01}}}}+{Z_{{\text{TK}}}} = {C_{{\text{02}}}}+{C_{\text{W}}}_{{\text{,TK}}} $
预热器 $ {C_{{\text{03}}}}+{C_{{\text{07}}}}+{Z_{{\text{PHK}}}} = {C_{{\text{08}}}}+{C_{{\text{04}}}} $
节流阀 $ {C_{{\text{04}}}}+{Z_{{\text{VK}}}} = {C_{{\text{04v}}}} $
混合器 $ {C_{{\text{02}}}}+{C_{{\text{04v}}}}+{Z_{{\text{MK}}}} = {C_{{\text{05}}}} $
次冷却器 ${C_{ {\text{05} } } }+{Z_{ {\text{CK} } } } = {C_{ {\text{06} } } }+{C_{ {\text{q,CK} } } }$
泵 $ {C_{{\text{06}}}}+{C_{\text{W}}}_{{\text{,PK}}}+{Z_{{\text{PK}}}} = {C_{{\text{07}}}} $
主冷却器 $ {C_{\text{9}}}+{Z_{{\text{CS}}}} = {C_{\text{1}}}+{C_{{\text{Q,CS}}}} $
Tab.3 Exergoeconomic balance equations for each components in SCBC/KC system
部件 ?经济守恒方程
吸热器 $ {C_{\text{4}}}+{C_{\text{q}}}+{Z_{{\text{ER}}}} = {C_{\text{5}}} $
透平 $ {C_{\text{5}}}+{Z_{\text{T}}} = {C_{\text{6}}}+{C_{\text{W}}}_{{\text{,T}}} $
主压缩机 $ {C_{\text{1}}}+{C_{\text{W}}}_{{\text{,MC}}}+{Z_{{\text{MC}}}} = {C_{\text{2}}} $
再压缩机 $ {C_{\text{8}}}+{C_{\text{W}}}_{{\text{,RC}}}+{Z_{{\text{RC}}}} = {C_{\text{3}}} $
高温回热器 $ {C_{\text{6}}}+{C_{\text{3}}}+{Z_{{\text{HTR}}}} = {C_{\text{7}}}+{C_{\text{4}}} $
低温回热器 $ {C_{\text{7}}}+{C_{\text{2}}}+{Z_{{\text{LTR}}}} = {C_{\text{8}}}+{C_{\text{3}}} $
蒸发器 $ {C_{\text{8}}}+{C_{{\text{012}}}}+{Z_{{\text{GO}}}} = {C_{\text{9}}}+{C_{{\text{09}}}} $
涡轮机 $ {C_{{\text{09}}}}+{Z_{{\text{TO}}}} = {C_{{\text{010}}}}+{C_{\text{W}}}_{{\text{,TO}}} $
次冷却器 ${C_{ {\text{010} } } }+{Z_{ {\text{CO} } } } = {C_{ {\text{011} } } }+{C_{ {\text{q,CO} } } }$
泵 $ {C_{{\text{011}}}}+{C_{\text{W}}}_{{\text{,PO}}}+{Z_{{\text{PO}}}} = {C_{{\text{012}}}} $
主冷却器 ${C_{\text{9} } }+{Z_{ {\text{CS} } } } = {C_{\text{1} } }+{C_{ {\text{q,CS} } } }$
Tab.4 Exergoeconomic balance equations for each components in SCBC/ORC system
Fig.4 Program design flowchart for SCBC/KC and SCBC/ORC systems
循环 设定参数 不同工况 ηtr/% ηt/% Δ/%
KC[4] wk=0.5，
p05=681 kPa 		θw=100 ℃，pg=1 767 kPa 6.60 6.41 2.88
θw=120 ℃，pg=2 411 kPa 8.87 8.80 0.79
θw=140 ℃，pg=3 161 kPa 10.05 10.64 5.87
ORC[19] R245fa θw=119.80 ℃，p010=178.00 kPa 13.68 13.63 0.37
R601 θw=125.50 ℃，p010=82.00 kPa 14.59 14.57 0.14
SCBC[4] PR=3，
p1=7 400 kPa，
θ5=550 ℃ 		— 39.61 39.60 0.03
SCBC/KC[4] wk=0.5，
θw=120 ℃，pg=1 200 kPa，
p05=410 kPa 		— 41.29 41.26 0.07
Tab.5 Model validation of SCBC and SCBC/KC and bottom cycle KC and ORC
循环参数 数值 循环参数 数值
p1/kPa 7400 pr 3
θ1/℃ 35 ηT ,ηTK 0.9
θ5/℃ 550 ηC 0.85
PR 3 ηTO 0.8
ΦER/MW 600 ηH、ηL 0.86
wk 0.45 cQ/($·MW?1·h?1) 7.4
θw/℃ 120 CI,p/CI,o[19] 1.26
pg/kPa 1500 — —
Tab.6 Setting parameter values of SCBC/KC and SCBC/ORC combined cycle systems
决策变量 设定边界范围
θ5/℃ 500~600
PR 2.2~4.0
θw/℃ 100~130
pr 2.2~4.0
Tab.7 Scope boundaries of decision variables for multi-objective optimization
Fig.5 Variation in thermodynamic performances and outputs of SCBC/KC and SCBC/ORC combined cycle systems with top cycle pressure ratio
Fig.6 Variation in exergoeconomic costs of SCBC/KC and SCBC/ORC combined cycle systems with top cycle pressure ratio
Fig.7 Variation in thermodynamic performances of SCBC/KC and SCBC/ORC combined cycle systems with turbine expansion ratio
Fig.8 Variation in exergoeconomic costs of SCBC/KC and SCBC/ORC combined cycle systems with turbine expansion ratio
Fig.9 Optimal Pareto front sets of multi-objective optimization in SCBC/KC and SCBC/ORC combined cycle systems
系统 SCBC/KC SCBC/ORC
PR 3.34 3.27
θ5 /℃ 593.93 599.85
θw /℃ 128.97 127.76
pr 3.39 3.37
ηt/% 43.27 43.85
ηe/% 64.51 65.33
c /($·GJ?1) 10.82 10.92
Tab.8 Multi-objective optimization results for SCBC/KC and SCBC/ORC combined cycle systems
状态点 p/kPa θ /℃ h /(kJ·kg?1) s/(kJ·kg?1·K?1) e/(kJ·kg?1) qm /(kg·s?1)
1 7400.00 35.00 402.40 1.66 200.84 1931.28
2 24716.00 123.33 454.58 1.68 247.39 1931.28
3 24716.00 286.70 701.68 2.21 344.94 2646.26
4 24716.00 412.52 860.45 2.47 431.27 2646.26
5 24716.00 593.93 1087.18 2.76 575.00 2646.26
6 7400.00 447.25 923.27 2.79 403.85 2646.26
7 7400.00 309.18 764.49 2.54 314.27 2646.26
8 7400.00 149.35 584.16 2.18 236.44 1931.28
9 7400.00 100.82 525.47 2.03 219.65 1931.28
01 1500.00 128.97 1884.81 6.35 398.67 60.31
02 442.48 40.37 1705.02 6.42 200.61 60.31
03 1500.00 128.97 478.31 1.98 81.42 175.50
04 1500.00 53.05 130.70 1.02 4.60 175.50
04v 442.48 53.24 130.70 1.03 3.56 175.50
05 442.48 67.93 533.33 2.42 61.77 235.81
06 442.48 42.37 97.06 1.09 2.56 235.81
07 1500.00 42.86 98.69 1.09 3.88 235.81
08 1500.00 90.52 357.40 1.84 48.65 235.81
Tab.9 Thermodynamic state point parameters for SCBC/KC system under optimized operation conditions
状态点 p/kPa θ /℃ h /(kJ·kg?1) s/(kJ·kg?1·K?1) e/(kJ·kg?1) qm /(kg·s?1)
1 7400.00 35.00 402.40 1.66 200.84 1945.09
2 24198.00 121.73 453.36 1.68 246.29 1945.09
3 24198.00 281.92 696.46 2.21 341.30 2641.42
4 24198.00 417.94 867.76 2.48 434.43 2641.42
5 24198.00 599.85 1094.91 2.77 579.03 2641.42
6 7400.00 455.03 932.38 2.80 409.40 2641.42
7 7400.00 306.16 761.08 2.54 312.52 2641.42
8 7400.00 147.55 582.06 2.17 235.75 1945.09
9 7400.00 84.26 503.44 1.97 214.69 1945.09
09 1500.00 127.76 505.35 1.86 61.21 677.22
010 445.10 94.67 485.51 1.88 37.52 677.22
011 445.10 58.66 278.39 1.26 5.40 677.22
012 1500.00 59.37 279.52 1.26 6.29 677.22
Tab.10 Thermodynamic state point parameters for SCBC/ORC system under optimized operation conditions
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