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Appl. Sci. 2020, 10, 9060 10 of 25 resources, and whose abatement costs are charged to the productive components. The exergoeconomic cost of a residue (Π ̇ R ̇ r ) has three contributions: the residue formation cost that corresponds to the exergy in a residual exergy flow, which is the resource of a dissipative component (Π ̇ F ̇r ); the cost of additional exergetic resources employed for its elimination (Π ̇ F ̇ar ); the non-exergetic abatement costs required for its elimination (Z ̇r). The cost balance for the rth dissipative component takes the form [13]: Π ̇R ̇r =Π ̇F ̇r+Π ̇F ̇ar+Z ̇r,r∈D (15) The residues of the turbofan engine are exergy losses because they leave the stacks without any furtheruse,sotheirexergyandexergoeconomiccostsarezero.Foralltheflightphases,Π ̇R ̇r =0=R ̇∗r for all r ∈ D. Because the stacks are imaginary dissipative components, there are no abatement costs for these losses (i.e., Z ̇ r = 0 for all r ∈ D ). The aircraft losses come from the residual physical exergies of the air and exhaust gases (F ̇cS = E ̇PH and F ̇hS = E ̇PH) formed in the productive components of PcS 87 Π ̇ F ̇r =−Π ̇ F ̇ar >0, r∈D ={cS,hS,chS} (16) In this case study, the dissipative components were not part of the energy system. If it is desired that these components are charged with the elimination costs, Equation (16) indicates that a negative value must be allocated to the cost of F ̇r as an output stream of the system [31]. This is only a case of internalizing the costs taking place downstream of the main process. These costs must be allocated to the productive components involved in the formation cost of each residue. In this manner, the formation cost of a residue (Π ̇ F ̇r ) is decomposed into several costs corresponding to the originating components. Π ̇ F ̇r = ∑ Π ̇ F ̇ri , r ∈ D (17) i∈Pr where Pr is the set of productive components that generate the residue dissipated in the rth dissipative component(PcS,PhS,andPchS)andΠ ̇F ̇ri istheformationcostoftheresiduedissipatedintherth component that has been generated by the ith productive component. The formation cost of the residues charged to the ith productive component is given by: Π ̇ F ̇Ri = Π ̇ F ̇cS,i + Π ̇ F ̇hS,i + Π ̇ F ̇chS,i (18) To determine the values of Π ̇ F ̇ri , thermoeconomics defines the residue cost allocation ratios. For a given residue dissipated in the rth dissipative component, the residue cost allocation ratio associated with the ith productive component (μri ) is the fraction of the residue cost allocated to this component. Π ̇ F ̇ri = μri Π ̇ F ̇r , with ∑ μri = 1, r ∈ D (19) i∈Pr These ratios determine how the cost of a residue should be decomposed into several costs. However, there is no definitive method to determine them. A frequently used criterion is to allocate the cost of residues proportionally to entropy changes during the process [32,33]. The criterion used in this work was proposed by Valero et al. [13] to make the residue cost allocation ratios proportional to the exergy flow produced in the ith component that is processed and dissipated in the rth component according to the productive structure of the plant. According to the thermoeconomic theory, these ratios are known as recirculation coefficients. They can be obtained directly from the information provided by the productive structure and FPR table [34,35]. For the turbofan engine, they are defined in Table 4. and P , whereas the chemical exergy of the exhaust gases forms only in the CC (F ̇ = E ̇CH = E ̇CH). hS chS 7 According to Equation (15), the cost balance for the cold, hot, and chemical stacks is: 4PDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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