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Energies 2020, 13, 370 13 of 31 approach, introduced in [36], to explore the potential of the advanced s-CO2 power cycle layouts in both converting heat into power and extracting heat from the heat source. The response surfaces of ηth, φ, and ηTOT were explored in a wide range of decision variables to verify the flatness of the objective function in the neighborhood of the optimum and the main reasons behind the trend of ηTOT. 2.2.2. Decision Variables and Main Assumptions The heat source is composed of flue gases having an inlet temperature of 600 ◦C and a specific heat typical of the exhausts from a gas turbine [38] or an internal combustion engine [39]. The assumption of a constant specific heat makes the application of the results obtained to different waste heat sources straightforward. For each cycle layout, the decision variables in the optimization of ηTOT are the mass flow fraction (x) in the splitter at the outlet of the compressor and the maximum cycle temperature (TIT), shown within the green labels in Figures 1, 3 and 5. There are three other cycle parameters with a significant impact on the final performance, namely the maximum cycle pressure, limited to 20 MPa, and the minimum cycle pressure and temperature that were taken to equal 7.63 MPa and 32 ◦C, respectively, following [12,36]. Furthermore, the performance of the equipment (heat exchangers, turbomachinery, etc.) strongly affects the performance of the overall system and was set carefully to ultimately obtain a reliable performance prediction and comparison. Following the literature, the effectiveness of the recuperator/s was fixed at 95% (see, e.g., [7]). Shiferaw et al. [40] discussed the design features of printed circuit heat exchangers’ (PCHEs) recuperators and the relationship between the effectiveness and cost in the search for an efficient power cycle and cost-effective design. They showed that a heat exchanger with an effectiveness of up to 95% provides a significant gain in cycle efficiency at a moderate cost. Also, the compact recuperator based on a different design based on the microchannel technology tested in [41] reached values of effectiveness of up to 97%. The minimum temperature difference between the heat source and the CO2 in the heater/s (∆Tmin) was fixed at 50 ◦C as suggested in the design of gas-to-gas heat exchangers [42]. The new heat exchanger between waste gases and supercritical CO2 based on the plate-type design, rather than on the more common finned tube design, built and tested in [43] reached an effectiveness in the range 77%–87%, which is consistent with the assumed temperature difference assumed in this study. The pressure losses in all heaters and recuperators were neglected for an easier comparison against other studies on s-CO2 power cycles, or different waste heat-to-power technologies, where pressure losses are often neglected at the conceptual stage of the design. The reader is referred to a previous study of the first current author [36] for the impact of pressure losses on the performance of s-CO2 power cycles. The isentropic efficiencies of the compressor and turbine/s were fixed at 80% and 85%, respectively, taking into account both the small size of the system (which implies higher losses and lower efficiencies) and the recent advancements in the design of CO2 turbomachinery. Cich et al. [44] report a design turbine efficiency of 85% and compressor efficiencies of 78% to 82% for a 10 MW recompression s-CO2 cycle. A maximum total-to-static efficiency of about 70% was measured for a 50 kW radial compressor tested at Sandia National Laboratories [45], which, however, was designed starting from traditional design tools adjusted for the real gas behavior of CO2. Noall and Pasch [46] estimated a realistically achievable compressor isentropic efficiency of 83% to 85% for a 50 MW plant. The total-to-static efficiency of the 1.16 MW s-CO2 turbine modelled in [47] was 85.4%, which is consistent with the size and efficiency of the present study. The partial heating layout includes a single larger CO2 turbine rather than two smaller turbines, which is beneficial in terms of the turbine efficiency. However, a detailed evaluation of the turbine efficiency that considers the impact of the turbine architecture (radial, single axial, multistage axial, etc. [48]), size, and expansion ratio [49] is left to a further stage of the design process.PDF Image | Novel Supercritical CO2 Power Cycles for Waste Heat Recovery
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