## 2 Materials and Methods
### Exergy Assessment  
Exergy is a valuable tool for understanding the energy conversion quality in an engine, and improving the efficiency of a process or system and its environmental and economic performance [42; 43]. The methodology relies on the conservation of energy and a measure of irreversibility, which is proportional to the entropy increase. The turbofan engine is an internal combustion engine that uses a mixture of air and fuel to convert chemical energy to mechanical energy. Exergy assessment on the turbofan engine has been performed, based on thermodynamic parameters at each component's inlet and exit. The laws of thermodynamics are applied to draw the fundamental equations for mass-energy conservation. The steady-state system and flow process use the mass, energy and exergy balance equations to find the heat, work and enthalpy interactions. The exergy is calculated as exergy destruction within the component, exergy efficiency, rate of exergy decrease, and irreversibility. The exergy assessment compares the impact of LH\({}_{2}\) and jet fuel on the turbofan engine. Figure 3 shows the schematic of the turbofan engine. The exergy assessment considered the following assumptions:  
* Engine operations under steady-state and ideal gas mixture combustion. * The combustion reaction is assumed to be completed. * The LHV of hydrogen and jet fuel were taken as 120 MJ/kg and 43.1 MJ/kg, respectively, based on the estimated chemical property and reactants of the fuels [44]
* Component systems assumed an adiabatic process. * Kinetic energy and exergy changes are neglected as this is assumed to be negligible since the velocity of the air mass flow at the inlet is at a static condition with reference to the environment. * The ambient pressure and temperature for the exergy calculation assume a sea-level static condition of 15 \({}^{\circ}\)C and 101.352 kPa. The mass, energy and exergy balance of the engine with reference to the environmental condition is shown in Figure 4. In the system shown in Figure 4, the exergy entering the system is equal to the sum of exergy leaving, exergy destroyed and exergy losses. The exergy values in this paper were obtained using Equations (13)-(18) [31; 42; 43; 45; 46]. The total specific exergy (\(\hat{\epsilon}_{T}\)) of the system is the sum of the physical, chemical, kinetic and potential exergies:  
\[\hat{\epsilon}_{T}=\dot{m}(\hat{\epsilon}_{k}+\dot{\epsilon}_{p}+\dot{\epsilon }_{ph}+\dot{\epsilon}_{c}) \tag{13}\]  
where \(\dot{\epsilon}_{k}\), \(\dot{\epsilon}_{p}\), \(\dot{\epsilon}_{ph}\), \(\dot{\epsilon}_{c}\) represents kinetic, potential, physical and chemical exergy, respectively. The assessment assumes the potential exergy component is neglected because, as the evaluation was done under sea-level static (SLS) conditions, there is no elevation variation  
Figure 3: Schematic of the turbofan engine. between the inlet and outlet engine conditions to account for potential exergy. The specific physical exergy is given as [43; 46]:  
\[\dot{\epsilon}_{ph}=\dot{m}C_{p}\bigg{[}(T-T_{0})-T_{0}\ln\bigg{(}\frac{T}{T_{0} }\bigg{)}\bigg{]}+RT_{0}\ln\bigg{(}\frac{P}{P_{0}}\bigg{)} \tag{14}\]  
The kinetic and chemical exergy is given as [43; 46]:  
\[\dot{\epsilon}_{k}=\dot{m}\ \frac{V^{2}}{2} \tag{15}\]  
\[\dot{\epsilon}_{c}=\dot{m}\ LHV\xi \tag{16}\]  
where \(\xi\) is the liquid fuel-grade function given as [3; 46]:  
\[\xi=1.0422+0.011925\frac{b}{a}-\frac{0.042}{a} \tag{17}\]  
The system fuel flow exergy (\(\dot{\epsilon}_{f}\)) is given as:  
\[\dot{\epsilon}_{f}=\dot{\epsilon}_{c}+\dot{\epsilon}_{ph} \tag{18}\]  
The system exergy efficiency at sea-level conditions is given as the ratio of total exergy output to the exergy input:  
\[\eta_{ex}=\frac{\dot{\epsilon}_{out}}{\dot{\epsilon}_{in}} \tag{19}\]  
The exergy destruction rate for the steady-state process is the difference between the total exergy output (\(\dot{\epsilon}_{out}\)) and input (\(\dot{\epsilon}_{in}\)). Calculating the exergy at component levels have been fully described by [PERSON] et al.