# Residue Cost Formation of a High Bypass Turbofan Engine
## 6 Operational Diagnosis of the Fuel Impact
### Malfunction Analysis  
A malfunction analysis was performed on the turbofan engine by decreasing the compressor isentropic efficiency by 1% at a constant thrust requirement of \(\tau=501\) kN. The decrease in compressor efficiency had a fuel impact of \(\Delta\dot{T}_{T}=0.49\) MW, a kinetic exergy production impact of \(\Delta\dot{P}_{T}=-0.77\) MW, an irreversibility impact of \(\Delta\dot{I}_{T}=0.80\) MW, and a residue formation impact of \(\Delta\dot{R}=0.45\) MW. Table 7 presents the contributions to the fuel impact caused by the compressor degradation according to the decompositions given by Equations (22)-(24). The last column of this table shows the contribution of each component to the fuel impact and reveals that the highest additional fuel engine consumption was assessed for compressor (0.87 MW), which was the component where the inefficiency occurred. The first three columns of Table 7 correspond to the decomposition of the fuel impact in terms of the component variations of irreversibility, residues, and products. This part of the mentioned table shows that the anomaly in the compressor made it the component that contributed the most to the fuel impact of irreversibility and residues (0.50 MW and 0.38 MW, respectively). This means that the compressor malfunction increased its irreversibility by 62.1% and the residues allocated to this component by 83.1%. The compressor inefficiency modified the engine operation such that the FN produced more kinetic exergy (\(\Delta\dot{P}_{FN}=0.81\) MW) and N reduced its kinetic energy production (\(\Delta\dot{P}_{FN}=-1.58\) MW). The compressor degradation propagated the anomalies by increasing the irreversibility in all components except for the D and N of the core engine and by increasing the  
energy of the residues allocated to the CC (\(\Delta\dot{R}_{CC}=0.06\) MW). The compressor anomaly not only caused an increase of the resource consumption, but it also caused an increase of the residue generation. According to Equation (23), Table 7 exhibits the diagnosis based on the fuel impact decomposition in terms of malfunctions and dysfunctions. Columns 5 to 7 present the malfunctions due to external resource consumption variation (\(\textbf{MF}_{e}^{t}\)), component energy consumption variation (\(\textbf{MF}^{t}\)), and the variation of component residue generation (\(\textbf{MR}^{t}\)). Since the compressor is only fueled by the power provided by the HPT and its internal malfunction was \(MF_{C}=0.94\) MW, the compressor required then more power to compensate its degradation and satisfy the thrust requirement. Furthermore, the combustion chamber presented a negative malfunction, \(MF_{e,CC}+MF_{CC}+MR_{CC}=0.75-0.9-0.03=-0.18\) MW, indicating that this component did not contribute globally to increase the irreversibility of the component itself. However, it presented a dysfunction of \(DF_{k,CC}+DF_{\Delta\textbf{P}_{s},CC}=0.97-0.07=0.9\) MW. In the context of the loss of compressor performance, the combustion chamber increases the propagation of the irreversibility. All the dysfunctions related to the variation in the local production of components (\(\textbf{DF}_{k}\); see Column 9 of Table 7) were positive or null. A positive dysfunction indicates an increment in the component irreversibility of each component due to the variation of its local production caused by the malfunction of other components. All the components, except those of the bypass section, had negative dysfunctions related to final production variation dysfunctions (see Column 10 of Table 7). These kind of irreversibilities variations do not have a negative impact by themselves, as they are associated with a variation of the overall production. Columns 10 and 11 of Table 7 correspond to the terms of the fuel impact formula given by Equation (24).