## 5 Conclusions  
This study presents the application of a 1-D analysis on the regenerative cooling of liquid propellant rocket engines. An analysis tool, ODREC (One-Dimensional Regenerative Cooling), was developed using object oriented programming in MATLAB (MathWorks, Natick, MA, USA). ODREC carries out a combustion analysis based on a MATLAB implementation of the NASA CEA program. Gas side heat transfer was approximated using isentropic and adiabatic flow assumptions, along with appropriate heat transfer correlations. On the coolant side, heat transfer correlations are utilized considering the fin effect, and the thermodynamics of the coolant was included. A thermal resistance approach was used to calculate the radial heat transfer, and a 1-D hydraulic analysis was conducted to calculate the pressure of the coolant. Results of a study from the literature are reproduced using ODREC. Though ODREC over-predicts the engine wall temperatures, it captures the overall trends in the reference study. One of the primary benefits of ODREC is that complex phenomena such as phase change can be resolved with ease, and a solution takes  
Figure 12: Comparison of the heat capacities of different coolants throughout the cooling channels.  
Figure 13: Comparison of the fin heat transfer coefficients of different coolants throughout the cooling channels.  
only a few seconds. Therefore, it is an excellent candidate for use in optimization studies. In addition, the analysis was carried out compactly without needing other software for combustion analysis and engine sizing. ODREC also provides the flexibility to externally assign the thrust chamber profile as well as the ability to generate it within the program.  
In this study, the regenerative cooling of two small-scale rocket engines, a LOX/LCH4 engine and a LOX/LC3H8 engine, was investigated using ODREC. All coolants were designated to experience phase change. Results show that oxygen cooling provides the lower wall temperature overall for both cases. This stems from the fact that both the heat capacity and heat transfer coefficient of the oxidizer flow are superior for both cases, since the oxidizer mass flow rate is greater than the fuel mass flow rate. In a real engineering application, however, the oxidation of the channel surface due to the coolant oxidizer could be a concern. The thermophysical properties of methane were superior to those of propane in terms of heat transfer, but the temperatures of both propane-cooled and methane-cooled engines still exceeded 1000 K. This might require the additional use of film cooling for the specific engines considered. Furthermore, the pressure drop of the methane and propane coolants was much smaller compared to oxygen. Modifying the channel parameters might have enabled improved cooling at the expense of an increasing pressure drop. However, the channel width was set to 1 mm, and the number of channels was kept constant for both engines in the course of the analysis. Channel parameter optimization utilizing ODREC could be a topic of future study.  
Conceptualization, Y.M.K. and M.C.; methodology, Y.M.K.; formal analysis, Y.M.K.; writing--original draft preparation, M.C. and Y.M.K.; writing--review and editing, Y.M.K. and M.C.; supervision, M.C.; funding acquisition, M.C. All authors have read and agreed to the published version of the manuscript.  
This research is funded by the Turkish Scientific and Technological Research Council (TUBITAK) under project number 214M572 and the Department of Scientific Research of Bogazici University (BAP) under project 18224.  
Not applicable.  
The data presented in this study are available in article.  
The authors declare no conflict of interest.