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Appl. Sci. 2020, 10, 9060 6 of 25 The physical exergy is the maximum work obtainable by taking the substance through reversible physical processes from its initial state to the state determined by T0 and P0 [23]. It is defined as dEPH = dH − T0(dH/T − V/TdP) and for a mixture of ideal gases yields: ̇ ⎡⎢⎛ T⎞ P⎤⎥ EPH =m ̇ ⎢cPm⎝T−T0−T0lnT0⎠+RmT0lnP0⎥ (8) ⎣⎦ where cPm is the heat capacity at a constant pressure and Rm is the specific gas constant of the mixture. The chemical exergy is the work that can be obtained by taking a substance at T0 and P0 to chemical equilibrium with the environment [23]. The molar chemical exergy of a mixture of ideal gases can be determined from the knowledge of the standard molar chemical exergies (εCH) and molar compositions 0,i (xi) of the species in the mixture: [24]. εCH = ∑ x εCH + R T ∑ x ln x (9) For a unit mass, the specific chemical exergy of a liquid fuel is determined from the fuel exergy grade function [3]. ξ = f = 1.0401 + 0.01728 eCH LHV H O S⎛ H⎞ + 0.0432 + 0.2196 1 + 2.0628 (10) i0,i u0 i i C C C⎝ C⎠ where H, C, O, and S are the mass fractions of their respective elements. Sulfur is neglected for kerosene fuel [25]; thus, the exergy flow rate of jet fuel is given as: E ̇ =m ̇ eCH=m ̇ ξLHV (11) ffff The exergy of a system can be increased or decreased by the transfer of exergy corresponding to either work or heat. The exergy of mechanical work (E ̇W ̇ ) is identical to that of mechanical work (W ̇ ): E ̇W ̇ =W ̇ (12) Theexergyassociatedwithcombustionheattransfer(Q ̇b =m ̇fηbLHV=ηbE ̇f/ξ)attemperature Tt4 is: E ̇ ̇ =Q ̇b⎛1−T0⎞ (13) Qb ⎝ Tt4⎠ The exergies associated with the heat transfer from the exhausted combustion gases (E ̇ Q ̇ h ) and air (E ̇Q ̇c) into the environment at T7 and T8, respectively, can be approximated by neglecting the irreversibility within the fluid and assuming the specific heat capacity to be constant [26]. E ̇ ̇ =Q ̇h⎛1− T0 lnT7⎞andE ̇ ̇ =Q ̇c⎛1− T0 lnT8⎞ (14) Qh ⎝ T7 − T0 T0⎠ Qc ⎝ T8 − T0 T0⎠ where Q ̇ h = H ̇ 7 and Q ̇ c = H ̇ 8 are the transferred heat from the exhaust gases and air into the environment. 4.2. Productive Structure A productive structure is a graphical representation of the costs for the formations of the product and residues. It explains the distribution of resources and internal products throughout an energy system by using a physical model as a reference [13]. The products of each component fuel otherPDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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