## 3 Calculation Results and Discussion
### Hybrid System Off-Design Performance Evaluation under Variable Operation Parameters
#### 3.3.3 Effect of Variable AS-Ratio on Hybrid System Performance  
The HPC outlet air flow is distributed into three fractions, denoted as AS-ratio, directed towards the reformer (AS-reformer), SOFC cathode (AS-cathode), and combustor (AS-combustor). Figure 11 graphically depicts this ratio. While a singular optimal ratio suffices for stationary applications to yield constant output power, the dynamic operational conditions of mobile applications, such as aircraft, necessitate a varying ratio due to fluctuations in the engine inlet air mass flow rate associated with altitude changes during flight. The engine power settings (throttle setting) influence engine inlet flow rate, subsequently influencing AS-ratio. Therefore, this prompts the importance of understanding system performance when the AS-ratio is varied. This variability in the AS-ratio has a profound impact on the overall performance of the hybrid system. At design point, an AS-ratio was optimally selected to yield optimal performance. To discern the extent of influence this parameter exerts on system performance under off-design analysis, individual fractions within the AS-ratio are subjected to perturbations. Altering one fraction inherently induces changes in the remaining two fractions. The analytical approach to AS-ratio perturbations involves selecting a specific fraction for analysis and assigning values to it. The assigned value exhibits the most substantial skew, whether an increase or decrease, from the designated design point fraction. Concurrently, the other two unassigned AS-ratio fractions are adjusted in accordance with Equation (55), ensuring a proportional variation from the design point AS-ratio. This systematic perturbation analysis provides insights into the sensitivity and interdependence of the AS-ratio fractions, offering a nuanced understanding of their role in influencing the hybrid system's performance. Essentially, this is an analysis of the response of the hybrid system performance with variable AS-ratios that are skewed towards one fraction of the ratio. Such investigations are essential for optimizing the AS-ratio under dynamic operational conditions, particularly in mobile applications, to maintain optimal performance throughout varying flight profiles. \[AS_{ratio-unassigned}=\beta_{DP}*\left(1-n_{assigned}\right) \tag{55}\]  
where \(AS_{ratio-unassigned}\) is value of either one of the unassigned AS-ratio fractions; \(\beta_{DP}\) is the ratio of the unassigned fractions at design point; and \(n_{assigned}\) is value of the assigned AS-ratio fraction. In Tables 6-8, the perturbed fraction in AS-ratio is highlighted in blue. AS-Reformer Variation and Its Effect on Hybrid System Performance  
The reformer fraction at the design point is set at 0.00475 of the total HPC outlet air fraction, allocated for reforming reactions in the CPOx process. The shaded region in  
Figure 11: The HPC outlet air split ratio to the reformer, cathode, and combustor. Table 6 includes the design point area, representing the bound where optimal performance is achieved. Throughout this analysis, key parameters are held constant: the O/C ratio is maintained at a steady value of 0.85, current density is fixed at 5000 Am\({}^{-2}\), HX-\(\xi\), remains constant at 23%, HPC outlet air temperature is compressed and consistently maintained at 850.22 K, GT FAR is sustained at 0.02715, and the total engine inlet air flow remains unaltered. The sole parameter subjected to variation is the AS-ratio, with specific attention given to the perturbations of the AS-reformer in this section, as detailed in Table 6. Each instance in the table corresponds to a unique AS-reformer fraction value, and the remaining fractions of the AS-ratio are determined using Equation (55) to ensure a proportional adjustment consistent with the design point AS-ratio. The ensuing graphical representation in Figures 12 and 13 illustrates the variations in hybrid system performance resulting from the perturbations in the AS-reformer fraction.