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Appl. Sci. 2020, 10, 9060 8 of 25 resources of cS and hS, respectively. The exergy associated with the heat transferred from the air and exhaust gases to the environment (E ̇ Q ̇ c and E ̇ Q ̇ h ) are the residues of these dissipative components. The chemical exergy of the exhausted combustion gases is the fuel and residue of the chemical stack. The exergy of these three residues is destroyed in the environment, which closes the open cycle, but causes harm to the environment. For aircraft engines, the exergy of residues cannot be reused; therefore, the residues can be considered as exergy losses. The productive structure indicates the productive components participating in the formation of the turbofan product E ̇K and residual exergy flow E ̇PH: PcS = {D, F}. The formation of the product E ̇K 887 and residual exergy E ̇ P H is given by P = {D, F, C, CC}. Finally, the chemical exergy of the exhausted 7 hS combustion gases (E ̇CH) forms only in the CC: P = {CC}. 7 chS 4.3. Exergy Balance Equations Table 3 presents the exergy balances of the turbofan components that belong to the bypass (cold-air side) and two-shaft Brayton cycle (hot-air side) sections. Table 3. Resources, products, residues, and irreversibilities of the turbofan components. Component F ̇ P ̇ R ̇ I ̇ Cold-air side (Bypass section) βE ̇K βE ̇PH β(S ̇ −S ̇a) D a t1 0T01 1+β 1+β 1+β β W ̇ β ( E ̇ P H − E ̇ P H ) β ( S ̇ − S ̇ ) F F t2t10T21 1+β 1+β 01+β βE ̇PH −(1+β)E ̇PH (1+β)S ̇ −βS ̇ FN t2 8 E ̇K 0 T 8 2 1+β801+β P H cS E ̇8 Q ̇ 0c T0 (⟨T⟩cSt −S ̇8) E ̇Q ̇c D a t1 0 T01 Hot-gas side (Core engine) E ̇K E ̇PH S ̇ −S ̇a 1+β 1+β 1+β W ̇ E ̇ P H − E ̇ P H S ̇ − S ̇ F F t2t10T21 1+β 1+β 01+β E ̇PH−E ̇PH (1+β)S ̇ −S ̇ C W ̇ t3t20T32 CC HPT LPT N hS chS C1+β01+β E ̇ f E ̇ t4 − E ̇ t3 0 T 0 ( S ̇ 4 − S ̇ 3 ) E ̇PH −E ̇PH W ̇ 0 T(S ̇−S ̇) t4t5 HPT 054 E ̇PH −E ̇PH W ̇ 0 T(S ̇−S ̇) t5t6 LPT 065 E ̇ 7K E ̇ t 6 − E ̇ 7 PH 0 T0(S ̇7−S ̇6) ⎛Q ̇0h ⎞ E ̇7 CH E ̇Q ̇h T0 ⎝⟨T⟩hS −S ̇7⎠ CH ⎛Q ̇0h ⎞ E ̇7 E ̇7 T0 ⎝⟨T⟩hSt −S ̇7⎠ The exergy balances for the productive components are based on the resource–product definition: F ̇i = P ̇i + I ̇i, where F ̇i and P ̇i are the resource and product exergy flows, respectively, and I ̇i is the irreversibility exergy flow. The exergy efficiency of the ith productive component quantifies its useful exergy and is defined as ηex,i = P ̇i/F ̇i. The reciprocal of the exergy efficiency is the unit exergy consumption κi = 1/ηex,i and is the resource required to generate one unit exergy of the product. 4.4. Fuel–Product–Residue Table Table 4 corresponds to the FPR table of the turbofan, which is a mathematical representation of the thermoeconomic model and represents the distribution of resources and products throughout thePDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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