## 3 Description of the Tool
### Algorithm of the coolant Phase and Thermophysical Properties  
In ODREC, the phase of the coolant at a section is determined using the so-called interpolated temperature, which is found as follows:  
\[T_{\text{int}}=T_{\text{sat},l}+(T_{\text{sat},u}-T_{\text{sat},l})\frac{P_{ \text{sat},u}-P_{c}}{P_{\text{sat},u}-P_{\text{sat},l}} \tag{17}\]  
where \(T_{\text{sat}}\) and \(P_{\text{sat}}\) are the temperature and the pressure values on the saturation line, respectively, which are read from the saturation thermophysical property table. Subscripts \(u\) and \(l\) denote _upper_ and _lower_, respectively, indicating that the coolant pressure at the particular section is in between these values. If the coolant pressure at the particular section is greater than the highest pressure value on the saturation line, then the interpolated temperature becomes the highest temperature value on the saturation line. The interpolation process is visualized in Figure 5. In this figure, there are three example states labeled as 1, 2, and 3, for which the interpolated temperatures are projected onto the horizontal axis. After the interpolated temperature is obtained, the phase of the coolant is found as follows: (i) if the coolant temperature is lower than the interpolated temperature, the coolant is in  
Figure 4: Discretized sections on the thrust chamber contour. the liquid phase; (ii) if the coolant temperature is equal to the interpolated temperature, it is in the saturated phase; (iii) if the coolant temperature is higher than the interpolated temperature, it may be in the vapor or supercritical phase. In Figure 5, State 1 is liquid, State 2 is vapor, and State 3 is supercritical fluid. If the coolant temperature turns out to be greater than the interpolated temperature at a section but it was lower than the interpolated temperature at the previous section, then the coolant has started changing phase. Therefore, its actual temperature equals the interpolated temperature evaluated at its pressure value at the section it occupies until the phase change is completed. Thermophysical properties of the coolant along the channels are determined by interpolations, with the values in the tables provided by the user, using the pressure and temperature values of the coolant. In the liquid phase, the thermophysical property table is provided for a range of temperatures without using any pressure value since the thermophysical properties of liquids are almost invariant of pressure due to the negligible compressibility. On the other hand, the table for the saturation phase should include both the pressure and the temperature values on the saturation curve besides the corresponding saturated liquid and saturated vapor thermophysical properties. The provided properties should also include the specific enthalpy in this phase. At the moment that the phase change begins, the specific enthalpy of the coolant is equal to the saturated liquid's specific enthalpy. As the phase changing coolant flows through the channels, its pressure drops at the same time its specific enthalpy rises due to the absorbed heat. The coolant state will stay on the saturation line until the phase change is completed; therefore, the coolant temperature will drop in the course of the phase change even if the enthalpy rises. In the course of this phase, specific enthalpy, \(h\), of the coolant is updated as follows:  
\[h_{c}^{j+1}=h_{c}^{j}+\frac{\pi d_{i}^{j}Lq^{j}}{Nm_{c}} \tag{18}\]  
Vapor fraction, \(x_{g}\), on the other hand, is calculated at each section as follows:  
\[x_{g}=\frac{h_{g,\text{int}}-h_{c}}{h_{g,\text{int}}-h_{f,\text{int}}} \tag{19}\]  
where \(h_{f,\text{int}}\) and \(h_{g,\text{int}}\) are saturated liquid and saturated vapor enthalpies, respectively, which are interpolated using the coolant state parameters.