# Residue Cost Formation of a High Bypass Turbofan Engine
## 4 Exergy Analysis
### 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 other components to form the main product, byproducts, or residues [27]. As shown in Figure 2, the external resources of the turbofan engine are the total exergy of air and aviation fuel. The products are the kinetic exergy of air and combustion gases in States 7 and 8, which provide the thrust to sustain flight. The residual exergy streams are the chemical exergy of the exhaust gases and the physical exergy of the air and combustion gases leaving their respective nozzles.The products and residues of an energy system are formed within their productive components, and the residues are released to the environment through dissipative components. The productive components provide resources to other components to form the final products and residual streams of an energy system. The set of the productive components of a turbofan engine is \(\mathcal{P}=\{\)D, F, FN, C, CC, HPT, LPT, N\(\}\). The state at the entrance of the D (state _a_) corresponds to the dead state. Therefore, the total air exergy flow is equal to its kinetic exergy (\(\dot{E}_{a}=\dot{E}_{a}^{K}\)). In the D, the air kinetic energy is converted into pressure energy, and the air reaches the stagnation state 01. The productive objective of the F and C is to increase the physical exergy of the air (\(\dot{m}_{a}\) and \(\dot{m}_{h}\)) by increasing the air pressure using the fan and compression power, respectively, as resources. In the CC, the exothermic reaction between air and fuel is used to convert the chemical exergy of JET-A1 into the exergy associated with the combustion heat (\(\dot{E}_{Q_{b}}\)). Simultaneously, the chemical exergy of the combustion gases is formed. Subsequently, \(\dot{E}_{Q_{b}}\) produces a physical exergy change between States 04 and 03. The products of the high and low expansion turbines are the power generated to mechanically drive the C and F. They use the differences between the physical exergies of their corresponding exiting and entering combustion gases as resources. Finally, the productive purposes of the FN and N are to accelerate and exhaust cold air and combustion gases, respectively. Their products are the kinetic exergies in States 7 and 8. The resource of each nozzle is the difference between the stagnant physical exergy at the entrance and the static physical exergy at the exit of each of the productive components. Figure 2 shows the productive structure. The set of dissipative components conforms to cold, hot, and chemical stacks: \(\mathcal{D}=\{\)CS, hS, chS\(\}\). These components do not generate any product; their purpose is to expel the residual exergy flows created during the production process to the environment [13; 28; 29]. The physical exergies of the exhausted air and combustion gases are the  
Figure 2: Productive structure of a turbofan engine. hS, hot stack. resources of cS and hS, respectively. The exergy associated with the heat transferred from the air and exhaust gases to the environment (\(\dot{E}_{\dot{Q}_{c}}\) and \(\dot{E}_{\dot{Q}_{b}}\)) are the residues of these dissipative components. The chemical exergy of the exhausted combustion gases is the fuel and residue of the chemical stack. The exergy of these three residues is destroyed in the environment, which closes the open cycle, but causes harm to the environment. For aircraft engines, the exergy of residues cannot be reused; therefore, the residues can be considered as exergy losses. The productive structure indicates the productive components participating in the formation of the turbofan product \(\dot{E}_{8}^{K}\) and residual exergy flow \(\dot{E}_{8}^{PH}\): \(\mathcal{P}_{cS}=\{\)D, F\(\}\).