## 3 Results and Discussions
### Exergy Estimation  
The exergy estimation was done for a performance parameter at altitude 0 m, as shown in Tables 2 and 3. The total inlet exergy of the turbofan engine is calculated from the summation of the fuel's chemical exergy and the air entering the engine, as shown in Figure 4. From the assessment, the exergy of LH\({}_{2}\) is obtained as 134.595 MJ/kg, aligned with the work of [PERSON] et al. [49], and the exergy rate at 1.61 kg/s fuel flow rate, fuel temperature of 25 \({}^{\circ}\)C and pressure 101.325 kPa, is obtained. The ambient conditions T\({}_{0}\) and P\({}_{0}\) are given as 15 \({}^{\circ}\)C and 101.325 kPa, respectively. Hence, the LH\({}_{2}\) fuel exergy rate was calculated as 78,058 kW, and the jet fuel exergy rate is 73,877 kW. The inlet air exergy based on the inlet conditions and mass flow rate is calculated as 623 kW. Therefore, the turbofan engine's total inlet exergy is obtained as 78,681 kW and 74,500 kW for LH\({}_{2}\) and kerosene, respectively. Where the specific heat value (C\({}_{\text{p}}\)) for LH\({}_{2}\) and jet fuel were obtained using Equations (29) and (30) [3]:  
\[C_{pLH2}=1.06029+\left(1.177\times 10^{-5}T\right)+\left(2.51\times 10^{-7} \right)T^{2}-\left(9.308\times 10^{-11}\right)T^{3} \tag{29}\]  
\[C_{pjet}=0.98847+\left(1.163\times 10^{-4}T\right)+\left(1.529\times 10^{-7} \right)T^{2}-\left(6.675\times 10^{-11}\right)T^{3} \tag{30}\]  
Since the assessment was at 0 m altitude, the system thrust for both cases is 123 kW, and the fan inlet mass velocity is calculated using the flow equation \(\dot{m}=\rho AV\) as 154 m/s. The total thrust exergy (useful exergy) is obtained as 18,942 kW. The total exergy waste for LH\({}_{2}\) and jet fuel becomes 59,739 kW and 55,558 kW, respectively. The total exergy waste is calculated by subtracting the total thrust exergy from the exergy input. The waste exergy ratio is calculated as the total waste exergy ratio to the total exergy input. Table 6 summarizes the exergy assessment, showing exergy efficiency of 24.1% and 25.4%, respectively. The turbofan engine's exergy efficiency is calculated from the ratio of the thrust exergy to the total exergy input, represented by Equation (19). Table 7 shows the exergy destruction factor, environmental effect factor and sustainability index. The exergy destruction factor is the ratio of the exergy destruction to the total exergy input, which indicates the decrease of a positive effect of the system on exergy sustainability. The destruction factor will be proportional to the waste ratio if exergy losses are neglected. The environmental effect factor (EFF) is also a measure of sustainability, to measure the engine's potential adverse effect on its surroundings due to its total waste exergy. The EFF is calculated as the ratio of the waste exergy ratio to the exergy efficiency, and the exergy sustainability index is the ratio of 1 to the environmental effect factor. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{2}{c}{**Exergy Efficiency (\%)**} & \multicolumn{2}{c}{**Exergy Input (kW)**} & \multicolumn{2}{c}{**Waste Exergy (kW)**} & \multicolumn{2}{c}{**Waste Exergy Ratio**} \\ \cline{2-7}  & **LH\({}_{2}\)** & **Jet Fuel** & **LH\({}_{2}\)** & **Jet Fuel** & **LH\({}_{2}\)** & **Jet Fuel** & **LH\({}_{2}\)** & **Jet Fuel** \\ \hline Whole Engine & 24.1 & 25.4 & 78,681 & 74,500 & 59,739 & 55,558 & 0.76 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Exergy assessment and comparison for LH\({}_{2}\) and jet fuel. These parameters measure the level of environmental impact and sustainability [50]. The relationship of these parameters has been highlighted in other research works [29; 30; 50; 51]. The exergy assessment goal is to compare each fuel's impact on the overall engine system; hence, there is no need to report the exergy at the component level since the compressor's variation does not differ greatly.