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Mathematical modeling of transpiration cooling in cylindrical domain

This research reports on the development of a mathematical modeling to simulate the transpiration cooling in a rocket thrust chamber. The transpiration cooling is a process used to protect the thrust chamber wall of a liquid rocket engine so that the coolant can mitigate the large amount of heat transfer by getting preheated prior to entering the thrust chamber. The mathematical model for the porous layer is developed in cylindrical coordinate system, and the results are validated by the experimental results available in open literature. Also, a numerical method is developed to solve the equations of hot gases which are flowing through the nozzle in order to provide the hot boundary condition of the porous layer. The flow equations within the porous medium are solved separately to analyze the important parameters affecting the transpiration cooling process. A parametric study is performed to investigate the effect of coolant mass flow rate, hot face boundary condition, gas type, and porous layer thickness. Moreover, the internal convective heat transfer between solid structure and the coolant flow is studied. The porous solver code is then coupled with the gas solver code to examine the cooling process more realistically. The results show the variation of gas properties through the nozzle and the effect of transpiration cooling on them. The paper concludes with a demonstration of a sample method of controlling the nozzle wall temperature.