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Appl. Sci. 2020, 10, 9060 11 of 25 5.2. Production Costs In this study, the symbolic thermoeconomic methodology [17] was used to calculate the production costs. The FPR table (Table 4) was used as the starting point to numerically calculate the costs of the system flows. This methodology is derived from the application of the extended cost propositions of the ECT, one of which is that the cost of residues is generated by the productive components from which they originate [10,13]. • The costs of the external resources are known: Π ̇ E ̇ f = cf E ̇ f and Π ̇ E ̇a = caE ̇a. • The production cost of the ith productive component (Π ̇ P ̇i ) is the sum of the cost of resources required to obtain it (Π ̇ F ̇i ), the formation cost of residues allocated to this component (Π ̇ F ̇ Ri ) (Equation(18)),andthepurchasecostofthecomponent(Z ̇i).Π ̇P ̇i =Π ̇F ̇i+Π ̇F ̇Ri+Z ̇i,i∈P. • If a component has a product comprising several flows, the same unit exergoeconomic cost is assigned to them. In fact, even if two or more products can be identified in the same component, their formation processes are inseparable at the considered level of aggregation. Symbolic thermoeconomics has two ways to determine the production costs of a system, including the effects of residues: the PFR and FPR models (see Table A4). In the PFR model, the thermoeconomic variables are functions of the recirculation coefficients, system products, and unit consumption of the components. This is commonly applied when the total production is fixed and the resource consumption varies. The FPR model is the most suitable for numerically calculating the production costs because it relates any exergoeconomic production cost with the external resources through a linear function of the distribution coefficients: ΠP = ⟨P∗∣(Πe + Z), where ⟨P∗∣ = (UD − ⟨FP⟩ − ⟨RP⟩)−1 ΠF = Πe + ⟨FP⟩ΠP (20a) (20b) (20c) respectivelybyyij =E ̇ji/P ̇j andψrj =R ̇jr/P ̇j andsatisfy ∑ (yij+ψij)=1.Thismodelcandecompose i∈P the exergoeconomic cost of products into three contributions: energy resources (ΠeP), component costs (ΠZP), and residue costs (ΠrP) (Equation (21)). ΠP = ⟨P∗∗∣(Πe +Z+ΠR) =ΠeP +ΠZP +ΠrP (21) Here, ⟨P∗∗∣ = (UD − ⟨FP⟩)−1 indicates the proportion at which the cost increases owing to the internal and external irreversibilities of each component. The most important application of calculating the costs of internal streams is to assess the impact of the additional fuel to compensate component malfunctions (inefficiences). 6. Operational Diagnosis of the Fuel Impact 6.1. Fuel Impact in Terms of Malfunctions and Dysfunctions A thermoeconomic diagnosis is based on a comparison of two operating conditions of a process: the actual and reference conditions denoted by the states x and x0, respectively. The reference condition is commonly the design condition, the state of the plant after an overhaul, or the state after an acceptance test [36]. However, the reference condition can also be associated with a change in the environmental conditions, a change in fuel quality, operation at partial load, or intervention from the control system. The objective of the diagnosis is to identify and quantify the additional resource consumption (∆F ̇T = F ̇(x) − F ̇(x0)) caused by the increases in component irreversibilities (∆I ̇T) [19,37]. The fuel impact is the sum of the variations in the exergy destroyed by each component ΠFR =⟨RP⟩ΠP where ⟨FP⟩ and ⟨RP⟩ are square matrices of n × n. Their elements are distribution coefficients definedPDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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