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3.4 Degrees of freedom and constraints When it comes to optimize an ORC, choosing the constraints and defining the degrees of freedom is of special importance. For this work, the simple cycle had 6 degrees of freedom, while the recuperated one had 7. These degrees of freedom were defined as dimensionless parameters related to the cycle variables which have maximum and minimum values, and take values between 0 and 1. 𝑥1 Heat source outlet temperature 𝑥2 Condenser temperature jump 𝑥3 Pressure at the inlet of the turbine 𝑥4 Pressure at the outlet of the turbine 𝑥5 Enthalpy at the inlet of the turbine 𝑥6 Enthalpy at the inlet of the primary heat exchanger 𝑥7 Enthalpy at the outlet of the condenser (only for the recuperated cycle Regarding the constraints, they are the same for the simple and the recuperated cycles. These are: 𝑐1 The working fluid has to be subcooled at the inlet of the pump to avoid cavitation 𝑐2 If the pressure is subcritical, the working fluid has to be subcooled at the inlet of the evaporator to avoid the phase change in the recuperator 𝑐3 If the pressure is subcritical, the working fluid has to be saturated or superheated at the outlet of the evaporator (avoid trilateral and partial evaporation cycles) 𝑐4 The working fluid has to be saturated or superheated at the outlet of the expander (avoid vapour qualities lower than 1) 𝑐5 The pinch point in the evaporator has to be higher than the minimum temperature difference specified to avoid temperature crossing 𝑐6 The pinch point in the condenser has to be higher than the minimum temperature difference specified to avoid temperature crossing 𝑐7 The pinch point in the recuperator has to be higher than the minimum temperature difference specified to avoid temperature crossing 4 Results and discussion 4.1 Thermodynamic analysis Some of the obtained results can be found in Table 3, which includes the working fluid mass flow, turbine and pump powers, net power output and first and second law efficiencies for the plant. The best obtained results for each different working fluid family have been included. Figure 3 shows the results of the thermodynamic optimization as a function of the ratio of the critical temperature to the highest temperature of the cycle (hot source inlet temperature). Results show that those cycles with Tcrit/Thot,in between 0.93 and 1.02 are giving the best plant second law efficiencies (between 31.33% and 33.46%). For values of Tcrit/Thot,in lower than 0.9, the second law efficiency considerably drops, reaching values down to 21%, which correspond to fluids such as R41, CO2 or ethane, whose best cycle configuration is the transcritical one. The reason for this is that, when the Thot,in is above the critical temperature, the best match between the hot source and the working fluid in the primary heat exchanger is found when the working fluid operates above its critical pressure. This is consistent with the conclusions from (Hærvig, 2016; Xu and Liu, 2013). The rest of the working fluids show their best performance at subcritical conditions, except for propylene and R1234yf. For Tcrit/Thot,in values higher than 1.02, the performance of the cycle is slightly worse than the one found for the most optimal working fluids, although the difference found for the second law efficiency is not large. The working fluids showing the worst performance for the analyzed range were ammonia (recuperated) and methanol. The reason for this is that they are wet fluids and, in case of the ammonia, it has no potential for heat recovery (what is more, the recuperator would decrease the temperature at the inlet of the evaporator and the cycle efficiency). For the rest of the working fluids, the efficiencies are all above 31%, showing a better performance when the recuperator unit is installed. DOI: 10.3384/ecp17138251 Proceedings of the 58th SIMS 256 September 25th - 27th, Reykjavik, Iceland Figure 3. Influence of the relationship between the working fluid critical temperature and the highest cycle temperature on the plant second law efficiency As it happens when the H2O is used as the working fluid, some wet fluids require superheating to prevent condensation during the expansion (Bao and Zhao, 2013). For example, ammonia, H2O, and ethanol (wetPDF Image | ORC for Power Generation Low Temperature Geothermal Heat Source
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