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Appl. Sci. 2020, 10, 9060 22 of 25 even if the capital, operating, and maintenance costs for this component increase [41]. For the turbofan engine, the CC had a low exergoeconomic factor (fP,CC = 0.0147 or 1.47%); therefore, the component performance could be improved, although this would be limited by the combustion process. An exergoeconomic factor close to unity indicates a low irreversibility cost compared with the component cost; therefore, it is not advisable to attempt to improve the efficiency of the process. In other words, this factor suggests decreasing the investment cost in that component at the expense of its exergetic efficiency [41]. The exergoeconomic indicators of fr, fZ, and fp constitute a useful and simple tool for determining possible improvements in an energy system. However, they do not consider the effects induced by changes in the irreversibility of a component on other components. Table A3. Product exergoeconomic cost decomposition: ΠP = ΠeP + ΠrP + ΠZP . Π ̇ P Π ̇ e Π ̇ r = h S Π ̇ r = c S Π ̇ r = c h S Π ̇ Z PPPPP (USD/h) f r = c S 0.15 0.16 0.16 0.01 0.00 0.01 0.01 0.01 0.14 f Z f P 97.95 100 1.20 5.59 1.38 2.85 f r = h S 1.90 GE90 26,754.28 16,331.89 8847.75 37.66 876.32 660.65 33.07 f r = c h S (%) 0 3.31 3.31 2.78 4.20 3.39 3.39 3.36 3.28 D 42.24 0 0.80 0.06 0 41.38 F 25,682.73 15,691 8569.71 41.71 842 538.15 33.50 FN 22,982.24 13,998 7645.71 37.27 751 550.10 33.44 C 40,954.65 20,977 18,119.13 3.52 1126 729.62 44.36 CC 33,096.83 25,927 5663.10 0 1391 115.86 17.11 HPT 33,457.49 20,977 10,804.03 3.52 1126 547.56 32.36 LPT 25,014.96 15,691 8081.70 2.63 842 397.47 32.36 N 3772.04 2334 1202.03 0.39 125 110.55 32.11 1.02 0.20 1.47 0.94 0.91 9.24 1.69 2.47 47.48 30.69 12.17 13.80 Appendix D. Equations of FPR and PFR Symbolic Representations Table A4. FPR and PFR symbolic representations (adapted from [13,17,42]). K ⟨KP⟩ = {κij = E ̇ij/P ̇j}n×n = ⟨PF⟩KD ⟨KR⟩ = {θ = R ̇ /P ̇ } = ⟨PR⟩P−1F ̇r FPR representation In terms of external resources Distribution coefficients Coefficients PFR representation In terms of final products Recirculation coefficients ⟨FP⟩={y =E ̇ /P ̇} =P ⟨KP⟩tP−1 ij ji j n×n D D ⟨PF⟩={r =E ̇ /F ̇} , ∑n r =1 ij ij j n×n i=0 ij n ⟨PR⟩={ρ =R ̇ /F ̇r} , ∑ρ =1 ⟨RP⟩={ψ =R ̇ /P ̇} =P ⟨KR⟩tP−1 ij ji j n×n D ∑n (yij+ψij)=1 i=0 Diagonal matrices = Diag(κ) and P = Diag(P) D ij ij n×n i=1 ij Unitexergyconsumptioncoefficients DD ijijjn×nD F = P+I F = Fe +⟨FP⟩P R = ⟨RP⟩P I = F − P Exergy flows P = Ps +⟨PF⟩F+⟨PR⟩F ̇r (rows of the FPR table) P = Ps +⟨KP⟩P+⟨KR⟩P R = PD⟨KR⟩tu I = PD(KD − UD)u P = ⟨P∣Fe, ⟨P∣ = (KD −⟨FP⟩)−1 F = ⟨F∣Fe, ⟨F∣ = KD⟨P∣ R = ⟨R∣Fe, ⟨R∣ = ⟨RP⟩⟨P∣ I = ⟨I∣Fe, ⟨I∣ = (KD −UD)⟨P∣ F ̇T = utFe P ̇T = yt0⟨P∣Fe, yt0 = {y0j = E ̇j0/P ̇j}1×n ∣P⟩ = (UD −⟨KP⟩−⟨KR⟩)−1 P = ∣P⟩Ps, F = ∣F⟩Ps, ∣F⟩ = KD∣P⟩ R = ∣R⟩Ps, ∣R⟩ = ⟨KR⟩∣P⟩ I = ∣I⟩Ps, ∣I⟩ = (KD −UD)∣P⟩ F ̇T = rt0F = κteP P ̇T = utPsPDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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