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Thermal Energy Storage for Solar Powered ORC Engines where ηORC ≡ W ̇ net/Q ̇ORC,in (2) is the thermal efficiency of the ORC system. W ̇ net = W ̇ turb − W ̇ aux is the electrical power output of the plant, decreased of the power consumption for auxiliaries; W ̇ net is constrained to be the same for all the simulated cases. W ̇ aux is obtained by summing the power consumption of all the pumps (subscripts P in eq. 3) and the fans in the system and it is therefore evaluated as W ̇aux =W ̇PORC −W ̇PSF −W ̇Pflash −W ̇Fan. (3) W ̇ Pflash in eq. 3 is zero for both the EC and the FC systems (in this last case by virtue of assumption 2), since no liquid drains from the flash are present. Q ̇ORC,in is the thermal power supplied to the ORC system and, for the FC, it reads Q ̇ORC−FC,in =m ̇vap ·(hc −hb′)+m ̇liq ·(hc −hd′ ). (4) ls Here the 2nd term in the right-hand side vanishes because of assumption (2). In the EC case, equation 4 becomes Q ̇ O R C − E C , i n = m ̇ · ( h g − h b ′ ) . ( 5 ) The global efficiency of the solar field is ηSF,glob = Q ̇ORC,in/Q ̇av, (6) and it accounts for the optical and thermal efficiency. The thermal power made available by the direct radiation of the sun at the given design point is given by Q ̇ a v = D N I d e s · A S F . ( 7 ) The area of the solar field ASF can be evaluated as ASF = W ̇ net/[ηORC(q ̇abs − q ̇hl − q ̇piping)] (8) All the terms of the denominator in eq. 8 represent thermal power specific to the m2 of SF aperture area. q ̇abs = DNIdes · ηopt is the thermal power absorbed by the collectors. Having assumed a null incidence angle for design calculations, the optical efficiency ηopt is equal to the peak value ηopt,p [66]. q ̇ accounts for thermal losses in the piping subsystem of the SF, and a value of 10 W/m2 piping is assumed here [67]. q ̇hl = F (Tin,SF, Tout,SF, θinc, Vwind) accounts for the thermal efficiency of the solar absorbers, and is evaluated according to the detailed procedure presented in Ref. [49]1. Figure 7a shows ηSYS,glob (eq. 1) as a function of Tmax. In order to better compare different working fluids, reduced temperatures are used (TR,max). As a consequence of the critical temperature increase with molecular weight (table 4.1), and being the condensing temperature the same for all the simulated cycles, more complex fluids attain higher efficiencies for a given TR,max. As expected, being throttling a purely dissipative process, the FC efficiency for a given TR,max is always lower than that of the corresponding EC for the same working fluid. For all the fluids this penalty decreases for increasingly higher TR,max, and tends to vanish with larger molecular complexity of the fluid. It can thus be concluded that, if siloxanes are adopted as high temperature working fluids, and if the maximum cycle temperature is close to the fluid’s critical temperature, the flash cycle configuration does not imply severe efficiency losses with respect to the traditional evaporative cycle solution. 1The coefficients adopted in the correlation proposed in the reference have been slightly modi- fied, as a consequence of the different fluids and flow regimes, as discussed in Ref. [46]. 107PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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