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SCIENCE CHINA Technological Sciences, Volume 61 , Issue 12 : 1802-1813(2018) https://doi.org/10.1007/s11431-018-9331-9

Shift-characteristics and bounds of thermal performance of organic Rankine cycle based on trapezoidal model

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  • ReceivedJun 24, 2018
  • AcceptedJul 25, 2018
  • PublishedNov 21, 2018

Abstract

In consideration of the constraints of actual working fluids on theoretical study of organic Rankine cycle (ORC), a trapezoidal cycle (TPC) with theoretical model to simulate ORC was proposed in previous works. In this study, mathematical models of working fluids including model of simulated saturation curve (MSSC) and model of linear saturation lines (MLSL) are proposed and built. Combining mathematical models of working fluids and TPC, the thermodynamic characteristics and principles of TPC (or ORC) can be studied or predicted theoretically. There exists a shift-curve of net power output with corresponding shift-temperature of heating fluid for working fluids, which indicates the shift of net power output from having optimum condition of maximum power to monotonic increase with evaporation temperature. This shift-characteristic is significant to working fluid selection and evaluation of cycle performance, for it indicates that cycle without optimum condition can yield higher net power output than the cycle with optimum condition. Equations to calculate the shift-temperature in ORC (or TPC) are derived; and equations to calculate the highest optimal evaporation temperature and highest maximum power as the highest optimum condition at this shift-temperature are obtained. Based on TPC and its theoretical model, the lower and upper bounds of thermal performance (maximum power and corresponding thermal efficiency) of TPC (or ORC) can be demonstrated and acquired. TPC can develop to Carnot cycle or trilateral cycle that it is significant to use TPC as a generalized cycle to study the general principles and characteristics of the cycles.


Funded by

the National Natural Science Foundation of China(Grant,No.,51276122)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant No. 51276122).


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  • Figure 1

    (Color online) Organic Rankine cycle and trapezoidal cycle in T-s diagram.

  • Figure 2

    (Color online) Vertex temperature (Tm), slope (kl, kv) of saturation curve and tangent intersection temperature (Tcr′) in working fluid model.

  • Figure 3

    (Color online) Range of slopes (kl, kv) of working fluids.

  • Figure 4

    (Color online) Model of simulated saturation curve of working fluids (MSSC) in T-s diagram.

  • Figure 5

    (Color online) Model of linear saturation lines of working fluids (MLSL) in T-s diagram.

  • Figure 6

    (Color online) Characteristic curves of net power output and corresponding temperature of water as heating fluid for R227ea in ORC.

  • Figure 7

    (Color online) Trapezoidal cycle developed to Carnot cycle or TLC.

  • Figure 8

    (Color online) Comparison of net output power with evaporation temperature between TPC and Carnot cycle.

  • Figure 9

    (Color online) Comparison between Teq,1 and Te,opt in TPC with MLSL.

  • Figure 10

    (Color online) Comparison between Teq,1 and Te,opt in ORC with actual working fluids.

  • Figure 11

    (Color online) Comparison between Teq,2 and Te,opt in TPC with MLSL.

  • Figure 12

    (Color online) Comparison between Teq,2 and Te,opt in ORC with R245fa.

  • Figure 13

    (Color online) Distributions of thermal efficiency at maximum power in TPC and ORC.

  • Table 1   Slopes (, ) of saturation curve and tangent intersection temperature (′) of working fluids at evaporation temperature 67°C

    Working fluids

    Optimal evaporation temperature

    Te,opt (°C)

    Slope of saturated liquid line

    kl(K2 kg/J)

    Slope of saturated vapor curve

    kv(K2 kg/J)

    Tangent intersection temperature

    Tcr (°C)

    Critical temperature

    Tcr (°C)

    Type of working fluids

    R143a

    67.44

    0.11

    –0.15

    80.03

    72.71

    Wet

    R1270

    68.78

    0.1

    –0.31

    117.84

    91.06

    Wet

    R1234yf

    68.76

    0.21

    –2.69

    123.74

    94.7

    Isentropic

    R22

    67.44

    0.22

    –0.53

    126.5

    96.15

    Wet

    R290

    67.97

    0.1

    –0.55

    127.79

    96.74

    Wet

    R134a

    67.44

    0.2

    –1.3

    134.28

    101.06

    Wet

    R227ea

    68.18

    0.25

    2.06

    135.97

    101.75

    Dry

    R1234ze

    67.05

    0.22

    –36.03

    147.74

    109.37

    Isentropic

    R152a

    66.29

    0.17

    –0.74

    153.52

    113.26

    Wet

    RC318

    67.21

    0.28

    1.08

    156.31

    115.23

    Dry

    R236fa

    66.61

    0.25

    1.64

    166.37

    124.92

    Dry

    ammonia

    65.16

    0.07

    –0.1

    176.04

    132.25

    Wet

    Isobutan

    65.23

    0.12

    0.95

    182.93

    134.66

    Dry

    R236ea

    66.12

    0.25

    1.29

    155.86

    139.29

    Dry

    R600

    65.76

    0.13

    0.85

    202.9

    151.98

    Dry

    R245fa

    65.78

    0.24

    1.68

    200.28

    154.01

    Dry

    R245ca

    65.58

    0.24

    1.36

    216.37

    174.42

    Dry

    R123

    65.36

    0.32

    2.72

    228.11

    183.68

    Isentropic

    Pentane

    65.13

    0.13

    0.55

    261.51

    196.55

    Dry

    Hexane

    64.59

    0.14

    0.48

    261.5

    234.67

    Dry

    benzene

    64.98

    0.18

    –7.37

    278.64

    288.87

    Isentropic

    decane

    64.16

    0.14

    0.41

    288.24

    344.55

    Dry

  • Table 2   Fitting factors , , of for conventional working fluids

    Type of working fluids

    Working fluids

    a

    b

    c

    Wet

    R143a

    –0.0888

    55.444

    –6997.1

    R32

    –0.1250

    76.186

    –9594.4

    Propylen

    –0.0893

    56.375

    –6589.5

    Propane

    –0.0646

    41.356

    –4281.2

    R134a

    –0.0328

    21.200

    –1710.7

    R152a

    –0.0321

    20.270

    –1130.9

    Dry

    R227ea

    –0.0177

    12.344

    –645.1

    RC318

    –0.0130

    9.6703

    –298.8

    R236fa

    –0.0142

    10.215

    –203.3

    Isobutan

    –0.0189

    13.956

    –200.6

    R236ea

    –0.0055

    4.517

    761.6

    Butane

    –0.0136

    10.591

    437.7

    R245fa

    –0.0076

    5.915

    647.9

    Isentropic

    Propane

    –0.0646

    41.356

    –4281.2

    R1234yf

    –0.0307

    20.182

    –2558.9

    R1234ze

    –0.0266

    15.127

    –1755.7

  • Table 3   Water shift-temperature for working fluids in ORC (=35°C, Δ=5°C)

    Working fluids

    Critical temperature Tcr (°C)

    TH_shift in ORC (°C)

    TH_shift by eq. (17) (°C)

    Relative deviation (%)

    R143a

    72.71

    86.20

    87.45

    1.45

    R32

    78.11

    93.87

    93.44

    –0.46

    R1270

    91.06

    108.29

    107.80

    –0.45

    R1234yf

    94.70

    111.59

    111.84

    0.22

    R290

    96.74

    114.45

    114.11

    –0.30

    R134a

    101.06

    119.77

    118.90

    –0.73

    R227ea

    101.75

    118.82

    119.66

    0.71

    R1234ze

    109.37

    128.95

    128.12

    –0.65

    R152a

    113.26

    135.37

    132.43

    –2.17

    RC318

    115.23

    133.20

    134.62

    1.06

    R236fa

    124.92

    143.15

    145.37

    1.55

    R600a

    134.66

    156.96

    156.17

    –0.50

    R236ea

    139.29

    165.56

    161.31

    –2.57

    R600

    151.98

    176.90

    175.39

    –0.85

    R245fa

    154.01

    179.35

    177.64

    –0.95

    R245ca

    174.42

    198.50

    200.28

    0.90

  • Table 4   Shift-temperature and corresponding maximum optimum conditions with slope ratio in MLSL (=150°C, Δ=5°C)

    Slope ratio rk

    TH,shiftWFLSL in MLSL (°C)

    TH,shiftWFLSL by eq. (18) or (19) (°C)

    Maximum optimum condition

    Te,opt_M (°C)

    Wmax_M (kW)

    –2

    166.95

    166.42

    117.8

    57.42

    –1.5

    163.88

    163.48

    118.3

    56.56

    –1

    160.58

    160.49

    120.8

    56.37

    –0.5

    157.25

    157.44

    124.8

    58.14

    0

    155.06

    155.0

    140.0

    68.76

    0.1

    155.01

    155.0

    149.5

    76.11

    0.2

    154.98

    155.0

    149.5

    76.77

    0.35

    154.97

    155.0

    149.5

    76.73

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