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Energies 2020, 13, 370 19 of 31 At the optimum ηTOT, the temperature of the two parallel branches entering the mixing point is aElnmerogisets 2e0q2u0,a1l3(,ix.e., T3 ≈ T4), the outlet temperature of the heat source is the minimum allowed, an1d9 otfh3e1 exhaust heat at the outlet of the CO2 turbine is fully recovered (T8 → T2). The increase of the mass flow fraction above the optimum point (x = 0.5) results in a marked The increase of the mass flow fraction above the optimum point (x = 0.5) results in a marked decrease of the outlet temperature in the upper branch (T3), a temperature mismatch at the mixing decrease of the outlet temperature in the upper branch (T3), a temperature mismatch at the mixing point (T4 >> T3), and the incomplete recovery of the turbine exhaust (T8 >> T2). On the other hand, the point (T4 >> T3), and the incomplete recovery of the turbine exhaust (T8 >> T2). On the other hand, decrease of the mass flow fraction below the optimum point (x = 0.1) implies an incomplete utilization the decrease of the mass flow fraction below the optimum point (x = 0.1) implies an incomplete of the external heat source, which leaves the plant at a temperature much higher than the minimum utilization of the external heat source, which leaves the plant at a temperature much higher than the allowed. The former sub-optimum condition (high x) results in a marked decrease of η and unvaried minimum allowed. The former sub-optimum condition (high x) results in a marked decrease of η unvaried φ, whereas the latter (low x) results in a marked decrease of φ and almost unvaried η . and unvaried φ, whereas the latter (low x) results in a marked decrease of φ and almost unvaried η ◦ . TheiinccrreeaasseeooffTTITITaabboovveeththeeoopptitmimuummpopionitn(te(.eg.g, .5,05000C°CininTaTbalebl4e) 4im) ipmlipelsieasmaamrkaerdkeindcirnecarseaosfe tohfethCeOCOte2mtepmepraetruarteuraetathtethienlientleotfohfehaetaerte2r(2T(T)5a)nadndththeeinincocommppleleteteuutitliilzizaatitoionnoofftthheeeexxtteerrnallheatt 25 sourrcce.. In addition,, the exhaustt temperratturreeattttheouttlleettoffttherecupeerraattoorr((T8) turns out to be higher tthanththeemmininmimumum. T.hTuhsu,tsh,ethmeodmeoradteriamteprimovpermovenemtinenηt inisηtotalilsytovtaerllcyomoveebrycothmeembayrktehdedmecarrekaesed th in φ. Instead, a decrease of TIT below the optimum (e.g., 300 ◦C) results in a poor η dictated by the th decrease in φ. Instead, a decrease of TIT below the optimum (e.g., 300 °C) results in athpoor ηth dictated low maximum cycle temperature. dictated by the low maximum cycle temperature. Figure 11 shows the T-s diagram of the partial heating cycle at the optimum point. The power Figure 11 shows the T-s diagram of the partial heating cycle at the optimum point. The power cycle is actually composed of two superimposed Brayton cycles operating between the same minimum cycle is actually composed of two superimposed Brayton cycles operating between the same and maximum temperatures. The thermal efficiency of the first elementary cycle (Figure 4a) is the ratio minimum and maximum temperatures. The thermal efficiency of the first elementary cycle (Figure between the net power output obtained by the mass flow rate, m , and heat input from the external 4a) is the ratio between the net power output obtained by the mass flow rate, m1, and heat input from heat source in heaters 1 and 2 needed to heat CO from the compressor outlet to the turbine inlet the external heat source in heaters 1 and 2 needed to heat CO2 from the compressor outlet to the (as per Equation (5)). The thermal efficiency of the second elementary cycle (Figure 4b) is the ratio turbine inlet (as per Equation (5)). The thermal efficiency of the second elementary cycle (Figure 4b) between the net power output obtained by m and the sum of the heat recovered from the exhaust is the ratio between the net power output obta2ined by m2 and the sum of the heat recovered from the of elementary cycle 1 and heat input from the external heat source in heater 2, (i.e., the term Q in exhaust of elementary cycle 1 and heat input from the external heat source in heater 2, (i.e., thehst,e2rm Equation 6 is added). The thermal efficiency of elementary cycle 2 is approximately two times higher Qhs,2 in Equation 6 is added). The thermal efficiency of elementary cycle 2 is approximately two times than that of elementary cycle 1 due to the recuperated layout (Table 5). The elementary cycle 1 enables higher than that of elementary cycle 1 due to the recuperated layout (Table 5). The elementary cycle an effective heat extraction from the heat source (φ = 83.77%), whereas the elementary cycle 2 enables 1 enables an effective heat extraction from the heat source (φ = 83.77%), whereas the elementary cycle aneffectiveheatrecoveryfromtheexhaustoftheCO turbine. 2 enables an effective heat recovery from the exhaust2of the CO2 turbine. Figure 11. Partial heating layout: T–s diagram of the optimum thermodynamic cycle maximizing η . Figure 11. Partial heating layout: T–s diagram of the optimum thermodynamic cycle maximizTiOnTg 2 1 8 th th th th The cooling profile of the heat source is superimposed. ηTOT. The cooling profile of the heat source is superimposed.PDF Image | Novel Supercritical CO2 Power Cycles for Waste Heat Recovery
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