# Residue Cost Formation of a High Bypass Turbofan Engine
## 4 Exergy Analysis
### Fuel-Product-Residue Table  
Table 4 corresponds to the FPR table of the turbofan, which is a mathematical representation of the thermoeconomic model and represents the distribution of resources and products throughout the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & \(\dot{F}\) & \(\dot{P}\) & \(\dot{R}\) & \(\dot{I}\) \\ \hline \multicolumn{5}{c}{Cold-air side (Bypass section)} \\ D & \(\frac{\beta E_{8}^{K}}{1+\beta}\) & \(\frac{\beta E_{11}^{PH}}{1+\beta}\) & 0 & \(T_{0}\frac{\beta(\dot{S}_{1}-\dot{S}_{a})}{1+\beta}\) \\ F & \(\frac{\beta\dot{W}_{F}}{1+\beta}\) & \(\frac{\beta(E_{12}^{PH}-E_{11}^{PH})}{1+\beta}\) & 0 & \(T_{0}\frac{\beta(\dot{S}_{2}-\dot{S}_{1})}{1+\beta}\) \\ FN & \(\frac{\beta E_{2}^{PH}-(1+\beta)\dot{E}_{8}^{PH}}{1+\beta}\) & \(\dot{E}_{8}^{K}\) & 0 & \(T_{0}\frac{(1+\beta)\dot{S}_{8}-\beta\dot{S}_{2}}{1+\beta}\) \\ cS & \(\dot{E}_{8}^{PH}\) & & \(\dot{E}_{\dot{Q}_{c}}\) & \(T_{0}\left(\frac{\dot{Q}_{0}^{c}}{(T)_{cSt}}-\dot{S}_{8}\right)\) \\ \hline \multicolumn{5}{c}{Hot-gas side (Core engine)} \\ D & \(\frac{\dot{E}_{a}^{K}}{1+\beta}\) & \(\frac{\dot{E}_{11}^{PH}}{1+\beta}\) & 0 & \(T_{0}\frac{\dot{S}_{1}-\dot{S}_{a}}{1+\beta}\) \\ F & \(\frac{\dot{W}_{F}}{1+\beta}\) & \(\frac{\dot{E}_{2}^{PH}-\dot{E}_{11}^{PH}}{1+\beta}\) & 0 & \(T_{0}\frac{\dot{S}_{2}-\dot{S}_{1}}{1+\beta}\) \\ C & \(\dot{W}_{C}\) & \(\frac{\dot{E}_{3}^{PH}-\dot{E}_{21}^{PH}}{1+\beta}\) & 0 & \(T_{0}\frac{(1+\beta)\dot{S}_{3}-\dot{S}_{2}}{1+\beta}\) \\ CC & \(\dot{E}_{f}\) & \(\dot{E}_{4}-\dot{E}_{3}\) & 0 & \(T_{0}(\dot{S}_{4}-\dot{S}_{3})\) \\ HPT & \(\dot{E}_{44}^{PH}-\dot{E}_{5H}^{PH}\) & \(\dot{W}_{HPT}\) & 0 & \(T_{0}(\dot{S}_{5}-\dot{S}_{4})\) \\ LPT & \(\dot{E}_{5}^{PH}-\dot{E}_{16}^{PH}\) & \(\dot{W}_{LPT}\) & 0 & \(T_{0}(\dot{S}_{6}-\dot{S}_{5})\) \\ N & \(\dot{E}_{16}-\dot{E}_{7}\) & \(\dot{E}_{7}^{K}\) & 0 & \(T_{0}(\dot{S}_{7}-\dot{S}_{6})\) \\ hS & \(\dot{E}_{7}^{PH}\) & & \(\dot{E}_{\dot{Q}_{b}}\) & \(T_{0}\left(\frac{\dot{Q}_{0}^{b}}{(T)_{hS}}-\dot{S}_{7}\right)\) \\ chS & \(\dot{E}_{7}^{CH}\) & & \(\dot{E}_{7}^{CH}\) & \(T_{0}\left(\frac{\dot{Q}_{0}^{b}}{(T)_{hSt}}-\dot{S}_{7}\right)\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Resources, products, residues, and irreversibilities of the turbofan components.  
engine according to its productive structure. It gives the values of flows in the productive structure shown in Figure 2 as a combination of the flows of the physical structure depicted in Figure 1 [30].  
The first column of Table 4 represents the product exergy flow obtained from each productive component, and the first row represents the external resources entering the system [27]. Each column associated with the productive components represents how the resource of a given component comes from other components or from the environment [30]. The \(i\)th element of each column of dissipative components corresponds to the portion of the resource (i.e., residue) responsible for treating and eliminating it, which originates from and is allocated to the \(i\)th component. The rows represent the destinations of the products of each component as resources of other components, the primary product of the system, or residual exergy flows of the system corresponding to the resources of dissipative components [27]. Each row illustrates two chains in the production process: the formation of the final product and, in the opposite direction, the formation and allocation of residues generated during the production process.