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Appl. Sci. 2020, 10, 9060 12 of 25 (internal irreversibility ∆I), exergy delivered to the environment (external irreversibility ∆R), and total production (∆Ps). ∆FT =ut(∆I+∆R+∆Ps) (22) The variation in internal and external irreversibilities (∆I + ∆R) on the right side of Equation (22) is known as the exergy technical savings and represents the irreversibility attributed to improper operation of the components that can be avoided. The fuel impact defined by Equation (22) can be expressed in terms of malfunctions and dysfunctions. ∆F ̇T = ut (MFte +MFt +MRt +DFK +DF∆Ps) (23) Malfunctions are the endogenous irreversibility variations and can be divided into internal and external malfunctions. The internal malfunction of a component is an irreversibility variation in such a component due to the variation of the exergy unit consumption of resources coming from the environment (MFte = (∆KD − ∆⟨KP⟩) P(x0)) or from other productive components of the energy system (MFt = ∆⟨KP⟩P(x0)) [38]. External malfunction is due to the yielding variations of residues in each component (MRt = ∆⟨KR⟩P(x0)). Dysfunctions are exogenous irreversibility variations in a component. They are induced by the malfunctions of other components, which force the component to consume more or less resources in order to satisfy its local production (DFK = [∣I⟩(x) + ∣R⟩(x)] (MFt + MRt)) and the total production of theenergysystem(DF∆Ps =[UD+∣I⟩(x)+∣R⟩(x)]∆Ps).Thedysfunctionofacomponentdependson its position in the system and can be reduced only if the malfunction is reduced. The fuel impact can also be conceived of as the sum of the cost of the total malfunctions; see Equation (24). The malfunction cost of a component is the sum of the malfunction and the dysfunctionsthatitinduces: MF∗t =MFt,MF∗t =MFt+∣I⟩(x)(MFt+MRt),MR∗t =MRt+ ∣R⟩(x) (MFt + MRt). ∆F ̇ = ut (MF∗t +MF∗t +MR∗t +DF ) (24) Te ∆Ps The fuel impact can also be conceived of as the sum of the cost of the total malfunctions. The cost of each malfunction represents the additional fuel plant consumption due to the existence of an intrinsic malfunction, such as the inefficiency of the corresponding component that forces the rest of the plant components to adapt their operating conditions and provoking induced malfunctions [39]. For a turbofan engine, the combination of the vehicle model and mission profile provides a thrust requirement that depends on the total exergy production given in Equation (4). Because all the equations presented in this section include the variation in the total production, they indicate that, in the presence of a malfunction, the production of an aircraft engine should also be adjusted to satisfy the thrust requirement. 6.2. Fuel Impact Expressed as an Exergoeconomic Cost The fuel impact can be expressed as an economic cost related to a change in operating conditions and corresponds to a variation in the exergoeconomic cost of external resources (∆Πe = Πe(x) − Πe(x0)) [18]. Table A4 indicates that Πe = PDceP, and therefore, the economic cost of the fuel impact can be divided into exergoeconomic costs due to variations between the actual and reference conditions in the cost of external resources, malfunctions, and final product: eePDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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