Results and discussion

The parameters for simulation are listed in table 2. The collectors and turbine are key issues of the low temperature solar thermal power system and the performance is proposed according to market available product [20, 21, 22]. The second-stage heat storage medium appropriate for the low temperature solar thermal electric system could be erythritol, which has melting point 120°C and heat of fusion 339.8 kJ/kg. Magnesium chloride hexahydrate (MgCl2 • 6H2O) would be appropriate as well, which has melting point 117°C, heat of fusion 168.6 kJ/kg and thermal conductivity 0.694 W / m • K (solid). The evaporation temperature considered in this paper is 120°C, which would be well correlated with the above PCMs.

1.3 Comparison of ORC efficiencies

The global efficiency of the proposed system is determined by both heat collection and power conversion processes. In this section, influences of working fluids on the ORC
efficiency are investigated. Performance of working fluids in the ORC is compared in table 3. The environment temperature is 20°C. In order to obtain the same dryness of 1.0 at the evaporator outlet, the collector area for each fluid is different. The state points are referred to as those in the thermodynamic cycle (figure 2). (h – h2′) / (h4 – h2′) represents the ratio of heat required in the sub-cooled heating process to the total heat absorbed by fluid in the ORC process. The relationship between this ratio and optimal FPC proportion will be analyzed in Section 5.3.

Table 3 shows that in the case of dry fluids, the regenerator can significantly warm working fluids from the condenser and complement the heat supplied from outside. The temperature arisen in the regenerator for R123, R113, R245fa, pentane or butane is 14.7°C, 23.3°C, 14.2°C, 25.5°C or 15.3°C respectively. The ORC efficiencies of the fluids are close, though R113 has a maximum value of 0.161 and butane has a minimum value of 0.147.

State point

R123

R113

R245fa

pentane

butane

1

t /°C

25

25

25

25

25

h kJ/kg

225.14

222.67

232.46

-25.93

259.46

2s

t /°C

25.38

25.19

25.60

25.28

25.85

h kJ/kg

225.89

223.07

233.78

-24.58

262.90

2

t /°C

25.62

25.33

25.93

25.47

26.32

h kJ/kg

226.14

223.20

234.22

-24.13

264.05

2′

t /°C

40.34

48.46

40.61

50.96

41.58

h kJ/kg

241.25

244.67

253.79

36.41

301.81

4

t /°C

120

120

120

120

120

h kJ/kg

449.67

431.71

484.39

490.59

740.69

5s

t /°C

38.52

50.99

40.20

54.81

40.68

h kJ/kg

406.00

391.45

437.25

392.84

649.49

5

t /°C

50.78

62.71

50.09

65.42

50.48

h kJ/kg

414.73

399.50

446.68

412.39

667.73

6 assumed

t /°C

25.62

25.33

25.93

25.47

26.32

h kJ/kg

396.95

374.24

423.66

341.16

623.31

6 real

t /°C

29.46

31.06

29.55

31.69

30.00

h kJ/kg

399.62

378.03

427.11

351.84

629.97

(hi – hr)/(h

‘4 – h2’ )

0.422

0.377

0.515

0.403

0.514

ORC efficiency

0.154

0.161

0.148

0.160

0.147

Note: hl is the enthalpy of saturation liquid at 120°C.

Table 3. Comparison of working fluids performance in the ORC 5.2 Heat collection efficiency of single-stage collectors

For the purpose of a better understanding of the advantage of two-stage collectors on heat collection efficiency, a prior study on single-stage collectors is necessary. The collectors in single-stage system and the second stage collectors in two-stage system are CPC collectors connected with evaporator. And single-stage collectors could be interpreted as a special case of two-stage collectors with FPC proportion equal to 0. Heat transfer in the evaporator is simulated in order to establish the relationship between ORC operation temperature and

CPC efficiency. The organic fluid is heated from sub-cooled to binary phase conditions in the evaporator.

Table 4 shows the single-stage collectors efficiency and the specific distribution of thermodynamic parameters. The subscript of f or h represents organic fluid or conduction oil respectively. Xf o is the dryness of organic fluid at evaporator outlet. Tf {is the organic fluid inlet temperature. The evaporator inlet temperatures of the working fluids are different due to the use of regenerator. Since the fluids and conduction oil flow in a contrary direction, the inlet of fluids means location next to the outlet of conduction oil. In order to heat the organic fluid from sub-cooled to saturation vapor state in the evaporator, heat transfer irreversibility between the conduction oil and fluids is large. The average operating temperature of CPC collectors is higher than ORC evaporation temperature, regardless of the much lower inlet temperature of working fluid in the evaporator. A smaller mass flow rate mh can reduce the outlet temperature of conduction oil T o, but T, will be increased. The reason is that the fluid temperature is constant in the binary phase region and heat is required for evaporation. A smaller mh would lead to a larger difference between inlet oil temperature and ORC evaporation temperature according to the law of conservation of energy. As collector efficiency declines more steeply at higher operating temperature, small mh is not preferable.

The heat collection efficiency of single-stage collectors on condition of irradiation 750 W / m2 for R123, R113, R245fa, pentane or butane is 46.47%, 46.05%, 47.02%, 46.37% or 47.01% respectively.

parameter

Organic fluid

R123

R113

R245fa

pentane

butane

mf kg/s

1.23

1.38

1.12

0.57

0.59

mh kg/s

7.00

7.00

7.00

7.00

7.00

U

0

40.34

48.46

40.61

50.96

41.58

Xf, o

1.0

1.0

1.0

1.0

1.0

о

0

n

116.94

118.61

114.51

117.21

114.43

0

n

133.37

135.15

131.16

133.94

131.32

n %

46.47

46.05

47.02

46.37

47.01

Table 4. Heat collection efficiency of single-stage collectors

Note: irradiation is 750 W / m2

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