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Energies 2020, 13, 4014 6 of 18 arrangements are described, for example, in [15,17,26]. In the following, we concentrate our attention on the transcritical Rankine cycles using organic fluids. 3. Recuperative Cycles with Organic Working Fluids Dealing with heat sources with finite heat capacity, the total efficiency in Equation (1) can be optimized adopting an ideal “triangular” cycle. These conditions can be approximated by resorting to working fluids with a critical temperature close to that of the maximum heat source [27,28]. On the other hand, when the critical temperature of the working fluid is much lower than the maximum temperature of the heat source, the ideal thermodynamic cycle approaches the transcritical conditions. In addition to an adequate critical temperature, another important parameter to consider in the selection of the working fluid is a relatively low molecular complexity to avoid superheating during the adiabatic expansion. Nonetheless, excessively low molecular complexity is still not recommended as it results in an adiabatic expansion in the two-phase region. The molecular complexity of a working fluid can be quantified, for example, by the molecular complexity parameter σ = Tc (dS/dT) [29] (p. 109). In general, working fluids with σ ≈ 0 R Tr=0.7,dew show (for reasonable pressure expansion ratios and for a starting point corresponding to the saturated vapor) an adiabatic expansion ending near the upper limit curve (the dew line). As the molecular complexity is strictly correlated to the isentropic exponent (γ−1)/γ, workingfluids with a small molecular complexity (a relatively large negative value of σ) experience a substantial cooling during an adiabatic expansion (with a fixed pressure expansion ratio [29]; see Section 2.5). On the other hand, the molecular weight of the fluid directly affects the enthalpy variations: the higher the molecular weight, the lower the number of the turbine stages, and for a fixed input thermal power, the higher the mass low rate. Both if these results have positive effects on the component design. According to the previous considerations, the fluids listed in Table 2 were chosen. Carbon dioxide is shown in the table as a reference. Water is extensively and successfully used in the traditional Rankine cycles in plants with a high power size (of hundreds of MW). Refrigerant R-134a (1,1,1,2-tetrafluoroethane, CH2FCF3) is a well known refrigerant and together with propane represents a working fluid with a medium molecular complexity (σ ≈ −2). Hydrogen sulphide has a critical temperature similar to that of R-134a and of propane, but it has a smaller molecular complexity (σ ≈ −7); on the contrary, perfluorobutane represents a fluid with a relatively high molecular complexity (σ ≈ 13). Ammonia and chloromethane have a similar critical temperature and similar molecular complexity. Methanol and dichloromethane represent two fluids with the same critical temperature but with an appreciably different molecular complexity. Table 2. Some thermodynamic data for the considered working fluids. Fluid Carbon dioxide Perfluorobutane R134a Propane (R-290) Water Hydrogen sulphide Ammonia Chloromethane (R-40) Dichloromethane (R-30) Methanol (a) σ= Tc (dS/dT) R 73.83 44.01 - 23.23 238.0 13.37 40.56 102.0 −2.346 42.48 42.48 −2.409 220.6 18.01 −10.38 89.63 34.08 −7.416 112.8 17.03 −9.231 66.80 66.8 −7.115 60.8 84.93 −4.793 80.84 32.04 −10.63 Critical Temperature (◦C) 31.06 113.2 101.0 96.68 373.9 100.4 132.5 143.1 236.8 239.3 Tr=0.7,dew Critical Molecular Pressure (bar) Weight Parameter of Molecular Complexity (a) Isentropic Exponent (b) 0.2232 0.04524 0.09730 0.1129 0.2476 0.2432 0.2338 0.2018 0.1622 0.1889 ,see[29](p.109).(b) (γ−1)/γwithγ=C /C foridealgasat25◦C. P VPDF Image | CO2 Mixtures as Working Fluid for High-Temperature Heat Recovery
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