## 3 Calculation Results and Discussion
### Hybrid System Off-Design Performance Evaluation under Variable Operation Parameters
#### 3.3.2 Effect of Variable SOFC Fuel Utilization (FU) on Hybrid System Performance  
Another critical parameter that greatly influences the performance of the SOFC/GT is the SOFC fuel utilization calculated in Equation (54). As observed earlier, the FU can be a dependent parameter influenced by the anode inlet conditions (H\({}_{2}\) inlet flow rate). However, independently, the FU of the stack can be varied for constant anode inlet conditions. This analysis varies the FU from 60% to 95% by inducing a variable current density (\(j\)) with everything else held constant and then aims to evaluate its influence on the electric generation capabilities of the hybrid system as well as the effect that may be observed on the thrust generation capabilities of the hybrid system. The _SOFC FU_ is calculated as follows:  
\[SOFC~{}FU=\frac{(j\cdot N_{cells}\cdot A)/(n_{e}~{}F)}{H_{2 inlet}}\times 100\% \tag{54}\]  
where \(N_{cells}\) is the number of fuel cells in a stack, \(A\) is the area of the fuel cell, \(n_{e}\) is the number of electron transfer, \(j\) is the current density and \(F\) is the Faraday constant.  
Figure 9 shows the hybrid system performance under off-design conditions. As noted earlier, the safe region of the FU is 75 \(\pm\) 10% for optimal system performance. It is observed in Figure 9A that as the FU increases, the stack power also increases, as expected, making the stack more efficient. There is also an effect on the stack temperature, which changes with change in FU, with the FU between 70 and 85% showing the best performance of the stack. At the design point, the desired stack output power is 100 kW. If the inlet fuel conditions and air flow conditions into the stack are kept constant, an SOFC FU of approximately 75% will yield this desired power. Therefore, if only the SOFC FU is the variable condition and every other parameter is kept constant, the power demand will determine the stack efficiency obtained. The shaded region \"P\" shows the range acceptable for SOFC FU.  
The influence of the SOFC FU on the GT is analyzed, and performance variation is shown in Figures 9B and 10. Since a variable FU means that the SOFC anode outlet conditions are different, the SOFC outlet flow (including unreacted fuel) is recycled in the combustor. This therefore means that the combustor outlet temperature characteristics need to change. The combustor FAR is held constant at 0.02715 for this analysis. For a variable FU from 60% to 95%, the combustor outlet temperature (T\({}_{combustor}\)) changes from 1761 to 1755 K. This is an expected variation, as a high FU means less recycled unused fuel in the combustor, reducing the combustor temperature. As the cathode inlet temperature (T\({}_{atthole}\)) is influenced by the T\({}_{combustor}\), its variation displays the same trend as the T\({}_{combustor}\), changing modestly from 1052.6 to 1051.3 K, a very slight difference for the FU change. As such, the turbine inlet temperature (TIT) follows the same variation trend for the same FU change, reducing, however, from 1558 to 1554 K. These variations are graphically represented in Figure 10.  
The GT performance parameters, i.e., thrust, TSFC and overall efficiency, are assessed for performance variation as shown in Figure 9B. The thrust generated reduced from 7.907 to 7.887 kN, a very slight difference attributed to the slight variation in TIT variation. As the overall efficiency is dependent on the thrust generated, its performance variation follows the same general trend, decreasing with the increase in SOFC FU. The TSFC of the GT increases very slightly from 309 to 309.8 mg/s/N. It is therefore concluded that the SOFC FU does not yield substantial performance variations in the GT; however, it has a great influence on the electric power generation capabilities of the hybrid system.  
Figure 10: Temperature variations relative to variable SOFC FU.  
Figure 9: SOFC fuel utilization effects the SOFC and GT performance.