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Appl. Sci. 2020, 10, 9060 2 of 25 unavoidable formation of residues (i.e., waste heat dissipated from the engine and the chemical exergy of combustion gases). For these energy systems, residues are considered an exergy loss because they cannot be reused and they contribute to environmental pollution. Thermoeconomics is a powerful analytical tool for cost accounting that is based on exergy cost theory (ECT), which combines the second law of thermodynamics and economics [10]. It provides a rationale for assessing the production cost of energy systems in terms of the consumption of natural resources and their impact on the environment, money, and system irreversibilities [11]. Thermoeconomics can be used to help design, diagnose, and optimize complex energy systems. More precisely, it can help to determine how energy and resources degrade, identify which systems work better, improve the design to reduce consumption, and prevent residues from damaging the environment [12]. Exergy cost theory offers a procedure for determining the production costs of productive components of a system. This theory has been extended to dissipative components, but does not present a general procedure for identifying residue formation costs and their effect on the production costs [10]. The best residue distribution criteria among possible alternatives are still an open question [13–16]. Valero et al. proposed an exergoeconomic methodology known as symbolic thermoeconomics to determine the process cost of functional products and residues and establish a mathematical basis for the production cost assessment. It develops a productive scheme (i.e., productive structure) of the exergy flow distribution throughout the system and its interaction with the environment, which are obtained from its physical structure [10,17]. This methodology formulates two alternative representations for the productive structure of a system: fuel-product-residue (FPR) and product-fuel-residue (PFR). These respectively use the external resources and plant product of the system as known information. Both approaches lead to the same results in terms of costs. The FPR representation is mainly adopted for cost accounting, whereas the PFR representation is highly useful for thermoeconomic diagnosis [18]. Thermoeconomic diagnosis is focused on identifying and interpreting anomalously functioning components and evaluating the effect of each component on additional fuel consumption. Symbolic thermoeconomics also includes the identification of malfunctions and dysfunctions to account for the impact of anomalies on fuel consumption [19,20]. The main motivation of this study is to address the lack of exergoeconomic analysis on the contribution of residue formation to the production cost of turbofan engines. This paper is organized into six different sections. In Section 2, a brief description of a turbofan is presented. Section 3 contains the model, derived from the energy balances of the turbofan and its components, to predict the thermodynamics states of the aircraft engine. Section 4 presents the turbofan productive structure, the exergy balance equations of its components, and the fuel-product-residue table. Section 5 exposes a summary of the mathematical basis for the cost assessment and the formation process of residues. Section 6 presents a summary of thermoeconomic diagnosis theory based on the malfunction and dysfunction analysis. Section 7 deals with the application of the aforementioned methodologies to a GE90-115B aircraft engine at takeoff condition and a thrust requirement of 510 kN, and the malfunction analysis is performed to quantify the effects of a decrease in compressor efficiency (malfunction) in the other components of the¡ engine. Finally, the main contributions of the paper and the discussions on the results are summarized in Section 8. 2. System Description 2.1. General Description of the Engine Operation Turbofan engines with a high bypass ratio are used in considerably large commercial and military transport aircraft. Particularly in modern aircraft, this part of the engine generates 75–80% of the total thrust. Figure 1 shows a schematic of a turbofan engine. From far upstream, where the air velocity relative to the engine is given by the flight velocity (w), the air is brought to the diffuser (D), which decreases its velocity in the flow direction. The air mass flow rate (m ̇ a) is carried to the fan (F); a fraction of thePDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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