## 4 Results and Discussion
The thermophysical properties of oxygen, methane, and propane for the liquid, saturated, and vapor phases were acquired from the NIST database. The inlet pressures and inlet temperatures of all coolants were set to 37 bar and 105 K, respectively. Here, it should be noted that both engines have the same thrust chamber profile, which is as depicted in the following figures. The performances of both fuel and oxidizer as the coolant for both engines under the effect of coolant phase change were compared. Results of the gas side wall temperature are given in Figure 8. As the results suggest, oxygen cooling, which results in a maximum wall temperature around 980 K, provides the best cooling performance for both engines under the specific conditions considered. Although methane cooling results in a lower wall temperature compared to propane cooling, cooling with neither propane nor methane can enable a maximum wall temperature under 1000 K according to the analyses. A remark here is that the maximum temperature near the throat is probably over-estimated, and the minimum temperature towards the nozzle exit is probably under-estimated. One reason for this is the fact that the axial conduction in the engine wall is neglected. Figure 7: Comparison of the temperature and the pressure of the methane coolant results with the reference study [39]. Oxygen coolant in the LOX/LC3H8 engine is examined closer in Figure 9 as an example. In the figure, the pressure, temperature, and vapor fraction of the coolant along the cooling channels throughout the thrust chamber are presented. It can be observed that the coolant experiences phase change. As can be seen, the coolant temperature does not increase in the course of phase change, as would be expected. In addition, near the phase change, or saturation, region, the rate of change of temperature is lower, indicating an increase in coolant heat capacity. The coolant pressure, on the other hand, drops steadily in the diverging nozzle section due to the moderate minor loss coefficient, \(K_{L}\), which stems from the radius gradient. After the coolant completely changes its phase into vapor, on the other hand, its pressure drops more rapidly, independently of the radius gradient. This stems from the fact that the vapor density is significantly lower, resulting in the domination of major pressure loss due to the increasing velocity, as resulted from Equation (15). The phase change phenomenon is inspected in Figure 10 as well. In the figure, the evolution of coolant states inside the cooling channels is given on a P-T diagram. Thin lines represent the saturation lines of propane, methane, and oxygen. The initial state of the coolants is at the upper left corner. Up to the saturation line, coolant temperatures rise and coolant pressures drop as expected. When a coolant state encounters its corresponding saturation line, on the other hand, it follows the saturation line until the vapor fraction \begin{table}
\begin{tabular}{l l} \hline
**Input Parameter** & **Value** \\ \hline Ambient pressure, \(P_{a}\) & 0.5 bar \\ \hline Wall thermal conductivity, \(k_{\mathrm{w}}\) & 365 W/mK \\ \hline Channel wall roughness, \(\epsilon\) & 6.3 μm \\ \hline Number of cooling channels, \(N\) & 90 \\ \hline Cooling channel height, \(\delta\) & 6 mm \\ \hline Cooling channel width, \(w\) & 1 mm \\ \hline Engine wall thickness, \(t\) & 5 mm \\ \hline Engine characteristic length, \(L^{*}\) & 0.3 μm \\ \hline Nozzle inflection angle, \(\theta_{n}\) & 45\({}^{\circ}\) \\ \hline Nozzle exit angle, \(\theta_{e}\) & 15\({}^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Input values used in the analysis. Figure 8: Wall temperature comparison of the two engines each assumed to be cooled either with the oxidizer or with the fuel. becomes unity. Meanwhile, the coolant pressure keeps dropping due to major and minor losses.