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Energies 2020, 13, 2259 7 of 24 To calculate the working fluid exergy as a function of the ambient conditions, Equation (3) is used. ei = hi −h0 +T0s0 −T0si (3) For each device of the cycle, the exergy destruction can be determined with the exergy balance described in Equation (4) E.D = E.D −E.D +m. ·e −m. ·e (4) di Qi Wi in in out out . where EDdi is the exergy destruction rate for components (i), the exergy rate by work and heat .. movementovertheboundaryisEDxWi andEDxQi,andtheinletandoutletrelatedexergyratesare exin and exout. The exergy rate by heat transfer is determined with Equation (5) . .T0 EDxQi =Qi·1−T (5) s where T0 is the atmospheric temperature, and Ts is the source temperature if the heat is produced and the temperature decreases when the heat is lost in the system. Also, Equation (6) is often used to . quantify the exergy destruction rate by component (EDdi) E.D =T.·s. (6) di 0 gen.i is the rate of entropy production, which is calculated with the general entropy balance where s. with Equation (7), as shown as follows: gen.i I,ORC .. . s. =m.·s−m.·s−Q (7) out out in in T The net power of the Brayton cycle (Wnet,Brayton S−CO2 ) is calculated based on Equation (8), from the gen.i . power of the main turbine (T1), the secondary turbine (T2) and the compressor (C1). .. ... Wnet, Brayton S−CO2 = WT1 + WT2 − WC1 (8) . Equation (9) determines the net power of the ORC cycle (Wnet,ORC), based on the power of the turbine (T3) and pumps (P1 and P2). . ... Wnet,ORC = WT3 − WP1 − WP2 (9) The ORC thermal efficiency (ηI,ORC) can be written based on Equation (10). η . = Wnet,ORC (10) . QITC1 where Wnet,ORC is the net power of the ORC, and QITC1 is the heat collected from the heat exchanger. Equation (11) is used to calculate the thermal performance of the Brayton cycle as a function of . the net power of the Brayton cycle and the heat received from the thermal source (QRH). . η = Wnet,Brayton S−CO2 (11) I,Brayton S−CO2 . QRHPDF Image | S-CO2 Brayton Cycle Coupled with ORC as Bottoming Cycle
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