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Energies 2020, 13, 370 15 of 31 recuperated layout (orange process in Figure 6) was not added at the denominator of Equation (5), being treated in the same way as a regenerative heat transfer. The achievement of high thermal efficiencies in both elementary cycles is a prerequisite to reach a high ηTOT, but not sufficient. Indeed, it must be accompanied by a high heat recovery from the external heat source (which is quantified by φ) and a high heat recovery from the turbine exhausts of both elementary cycles. While the heat of the turbine exhaust of the first elementary cycle is recovered by the second elementary cycle, the heat of the turbine exhaust of the latter is recovered by internal regeneration within the elementary cycle itself (single flow split with dual expansion and partial heating layouts) or heat transfer back to the first elementary cycle (dual recuperated layout). Energies 2020, 13, x 15 of 31 3. Results 3.1. Single Flow Split with Dual Expansion s-CO2 Power Cycle 3.1. Single Flow Split with Dual Expansion s-CO2 Power Cycle Figure 7 shows the variation of η for the single flow split with dual expansion cycle in a wide Figure 7 shows the variation of ηTOT for the single flow split with dual expansion cycle in a wide range of variation of the decision variables. The trend of variation of η (not shown for brevity) is the range of variation of the decision variables. The trend of variation of ηth (not shown for brevity) is the TOT the same as η , but its values are just scaled up by the reciprocal of φ, with the latter being constant same as η (φφ = 0..8377) over the entire domain of the decision variables. The maximum ηTOT (22.3%) is obtained 450 ◦ TOT C and x in the range 0.32–0.5 that is asymmetrical to the optimum. Note that a wider domain of x , but its values are just scaled up by the reciprocal of φ, with the latter being constant TOTTOT ◦ at the maximum TIT of 550 °C and x = 0.35. However, a region of high ηTOT occurs at TIT higher than 450 °C and x in the range 0.32–0.5 that is asymmetrical to the optimum. Note that a wider domain of was considered compared to [36] to explore the rapid decay of η at low x values. x was considered compared to [36] to explore the rapid decay ofTηOT TOT Figure 7. Variation of ηTOT with TIT and x for the single ffllow split with a dual expansion cycle. TOT Table 2 shows the values of the performance metrics and cycle parameters at the optimum point Table 2 shows the values of the performance metrics and cycle parameters at the optimum point and at four sub-optimum points forming a parallelogram on the left of the optimum. At the optimum and at four sub-optimum points forming a parallelogram on the left of the optimum. At the optimum point, the temperature at the inlet of the LTT (T7) is moderately high, the temperatures of the two point, the temperature at the inlet of the LTT (T7) is moderately high, the temperatures of the two streams at the mixing point are similar (T5 ≈ T8), and the heat at the exhaust from both the HTT and streams at the mixing point are similar (T5 ≈ T8), and the heat at the exhaust from both the HTT and the LTT is fully recovered (i.e., T →T ). However, it must be noted that the temperature at the inlet of 10 2 the LTT is fully recovered (i.e., T10→T2). However, it must be noted that the temperature at the inlet the LTT is much lower than the temperature at the exhaust of the HTT (T7 << T4) due to a mismatch of the LTT is much lower than the temperature at the exhaust of the HTT (T7 << T4) due to a mismatch between the mass flow rates and the thermal flow capacities in the HTR, inherent to this cycle layout. between the mass flow rates and the thermal flow capacities in the HTR, inherent to this cycle layout. Table 2. Performance metrics and cycle parameters at the optimum and four sub-optimum points the single flow split with a dual expansion cycle. All temperatures are in °C. for Tout 114.1 114.1 114.1 114.1 114.1 TIT x ηTOT ηth φ T2 T4 T5 T6 T7 T8 T9 T10 550 1 0.35 1 500 0.30 500 0.50 400 0.40 400 0.60 22.30 26.62 14.18 16.93 18.76 22.39 16.33 19.50 15.76 18.82 324.9 232.7 233.9 73.8 131.9 55.3 62.1 62.1 379.2 283.3 278.9 124.6 178.3 95.5 99.7 65.9 298.6 208.0 229.7 128.0 83.77 64.1 441.4 236.2 225.4 83.77 64.1 395.3 80.7 64.1 83.77 64.1 395.3 274.5 268.2 83.77 64.1 302.6 106.2 95.9 83.77 64.1 302.6 244.1 221.4 1 Optimum values of the decision variables. th at low x values.PDF Image | Novel Supercritical CO2 Power Cycles for Waste Heat Recovery
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