## 2 Materials and Methods
### Creep Life Assessment  
Creep is a continuous deformation of a material under constant mechanical and thermal load at elevated temperatures [32; 47; 34]. The top-level assessment aims to understand the impact of LH\({}_{2}\) compared to jet fuel on the rate of creep damage to the blade. The HPT blade and nozzle guide vane (NGV) are usually exposed to very high temperatures from the combustion section. The mechanical and thermal stresses on the HPT can be estimated  
Figure 4: Exergy boundary condition. using the turbofan thermodynamic performance and a physics-based model. The thermal and stress calculations are then used as input for the lifting model. The value of TET for the different fuels simulated at constant thrust will have a varying impact on the turbine blade. The HPT performance characteristics are used to estimate the sizing and blade geometry in order to obtain the thermal and stress load. Table 4 summarizes the HPT configuration and blade geometry. The assessment assumes the same HPT materials for both fuels. The thermal model estimates the blade metal temperature (\(T_{m}\)), given as:  
\[T_{m}=T_{g}-\epsilon\big{(}T_{g}-T_{c}\big{)} \tag{21}\]  
where \(T_{g}\) is the mean gas temperature, \(T_{c}\) is the coolant inlet temperature and \(\epsilon\) is the overall cooling effectiveness, which is assumed to be constant across the blade height [47, 48]. Taking the radial temperature distribution approach, since the blade will experience temperature variation in the radial plane, gives a more realistic assessment of the thermal load specified by [PERSON] et al. [48], and by [PERSON] and [PERSON] [41]. Hence, the maximum and minimum mean gas temperature for a given radial temperature distribution factor (RTDF) is given as [35,48]. \[T_{max}=T_{int}+(\Delta T_{combuster}\times RTDF) \tag{22}\]  
\[T_{min}=\frac{(5T_{in}-2T_{max})}{3} \tag{23}\]  
Equation (20) assumes that the maximum gas temperature will occur around 75% of the blade distance from the root, since the blade rotation shifts the gas peak temperature from the mid-span toward the blade tip. The stress model calculates the total stress acting on the blade due to the centrifugal load caused by engine rotation and stress, due to gas bending momentum [41]. The stress model assumes a constant axial velocity along the blade's span, with the centrifugal load acting at the blade center of gravity. As the stress prediction varies along the blade span and chord, the blade is divided into sections, with the centrifugal force (CF) and stress value (\(\sigma\)) at each section given as [33]:  
\[\text{CF}=\rho A_{av}h\omega^{2}d \tag{24}\]  
\[\sigma=\frac{CF}{A} \tag{25}\]  
The bending moment stress due to static pressure differential force on the blade is given as:  
\[\sigma_{BM}=\text{PF}\times d \tag{26}\]  
where PF is given as:  
\[PF=\frac{A_{av}\Delta P_{av}}{N_{b}} \tag{27}\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Description**} & \multicolumn{3}{c}{**Value**} \\ \cline{2-3}  & \(\mathbf{LH_{2}}\) & **Jet Fuel** \\ \hline TET (\({}^{\circ}\)C) & 1119 & 1125 \\ Number of stages & 1 & 1 \\ Blade height (m) & 0.094 & 0.094 \\ Hub to tip ratio (m) & 0.75 & 0.75 \\ Hub diameter (m) & 0.63 & 0.63 \\ Tip diameter (m) & 0.759 & 0.759 \\ Axial velocity & 120 & 120 \\ Inlet Axial Mach no & 0.18 & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: HPT geometry and configuration. The Larson Miller Parameter (LMP) is used to evaluate the creep life. The blade creep life varied at each blade section, due to changes in blade temperature and stresses across the blade span. The blade life is the lowest creep life of any individual blade section considered. The LMP equation is given as:  
\[\text{LMP}=\frac{T}{1000}(\log t_{f}+C) \tag{28}\]  
where \(T\) is the temperature of the material in Kelvin, \(t_{f}\) is the time to creep failure in hours, and C is the material constant. Creep life will vary at the different blade sections, because stress varies at the different points along the blade span.