Category Photovoltaics for Rural Development in Latin America: A Quarter Century of Lessons Learned

Influences of working fluids on two-stage collectors

Economical and technological performances as well as collector efficiency have to be taken into consideration to evaluate the low temperature solar thermal power system with two – stage collectors. However, this work is concerned about influences of working fluids on heat collection and power conversion efficiency. In addition to key factors such as irradiation and environmental temperature that affect the efficiency of single-stage collectors, the proportion of FPC area to the total collector area plays an important role in both the overall heat collection efficiency and cost-effectiveness of the two-stage collectors...

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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...

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Calculation of frictional resistance

Viscosity of the oil is generally larger as compared with that of working fluid or water. For precise simulation, flow frictional resistance of oil should be evaluated.

With N lines of the parallel concentric tubes, the required pump power is obtained by the following [17]:

Y 2

1.2 Overall thermal efficiency

Net electricity output W is obtained by subtracting oil pump power from net output of the ORC.

w = Wore – Woil (21)

image695 Подпись: (22)

Global electricity efficiency is defined by the proportion of net electricity output to the total irradiation as follows:

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Binary-phase region of working fluid

Energy balance of the conduction oil remains to be controlled by Eq.17. However, energy balance (dryness) of organic fluid is controlled by the following:

= П (T – Tf) (19)

dY mf(hf, v – hf tl)

Convection heat transfer coefficient of two-phase flow can be obtained in Rohsenow’s handbook [19].

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Liquid-phase region of working fluid

The controlling equations for the energy balance of working fluid and conduction oil are as follows:


UnDi (Th – Tf)



mfCp, f

T =

UnDi (Th – Tf)



mhCp, h

Total heat transfer coefficient is calculated by the following:

Подпись: (18)U = 1 (i + ±

hi K


The convectional heat transfer coefficient can be calculated using the Dittus-Boelter equation [17]. When flow of the outer fluid is laminar, the concentric tube is considered isothermal at the inner annulus of the cross-section; it is insulated at the outer annulus, thus obtaining the heat transfer coefficient, according to the Handbook of Heat Transfer [18].

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Heat transfer between conduction oil and working fluid

Thermal efficiency of FPCs can be calculated directly by the inlet and outlet temperatures of working fluid, according to Eq.14. On the other hand, thermal efficiency of CPC collectors is determined by the heat transfer process in the evaporator. The temperature relationship between working fluid and conduction oil must be established.

This section focuses on heat transfer in the evaporator, and the developed equations can easily be extended to the case of the condenser. Counter-current concentric tubes are adopted, and the parameters are listed in Table 2.

Подпись: Parameters Value Parameters Value Outer diameter Do mm 45 Generator efficiency є g 0.95 Inner diameter Di mm 25 Regenerator efficiency ЄГ 0.85 Turbine efficiency st 0.80 Pump efficiency Єp 0.75 Optical conversion of CPC n0 0.644 Optical conversion of FPC n0 0.857 First heat loss coefficient of collectors of CPC A wjm1 oC 0.749 First heat loss coefficient of collectors of FPC A Wjm2 oC 3.157 Second heat loss coefficient of collectors of CPC B W/m1 oC2 0.005 Second heat loss coefficient of collectors of FPC B Wjm1 oC2 0.014 Table 2. Specifications of the proposed low-temperature solar thermal electricity system

The following preconditions are assumed: 1) the influence of pressure drop on the saturated temperature arising from flow resistance in the evaporator is negligible; and 2) the two – phase flow is one-dimensional, that is, all pa...

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Equations developed for total thermal efficiency of the collector system

The FPC or CPC collector module available in the market has an effective area of approximately 2.0 m2 . Its thermal efficiency can be expressed by the following equation:

П = П -|(T – T“) –B(T – Ta)2 (7)

Solar thermal electric generation system may demand tens or hundreds of collectors in series, and the temperature differences between neighboring collectors will be small. Thus, it is reasonable to assume the following: 1) the average operating temperature of the collector changes continuously from one module to anther module; and 2) the function of the simulated area of the collector system is integrable.

With inlet temperature T and outlet temperature To, the required solar collection area is obtained by the following [12]:

Подпись: (8)L°mCv (T)

: f P dT T n(T)G

Temperature of conduction oil in...

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. Thermodynamics and heat transfer

1.1 Calculation of thermodynamic cycle

Figure 2 presents the scheme of thermodynamic cycle of a typical dry fluid. Point 1 illustrates the state of fluid at the condenser outlet; Point 2 at the Pump 1 outlet; Point 2′ at the regenerator outlet; Point 3 at the FPC collectors outlet; Point 4 at the evaporator outlet (on the normal condition of irradiation); and Point 5 at the turbine outlet. The points being referred to in Fig. 2 are placed in Fig. 1 with circles outside the numbers (with the exception of 2′). The reversible process of pressurization or expansion are described by 2 s or 5s respectively. Formulas for heat transfer and power conversion are developed below. Enthalpy at Point 2′ is calculated by the following:

h2′ = h2 + [h5 -(T6 =t2 )] • Er (1)

Where er is the regenerator eff...

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