The nozzle extension is a critical component of liquid rocket engines for vacuum applications, ensuring the correct gas expansion needed to achieve both the thrust and the specific impulse required by the mission. Although, typically, in space applications rocket nozzles are cooled through regenerative cooling, in this case, due to the prohibitive dimensions of nozzle extensions, a more efficient alternative is employed: film cooling, a thin layer of refrigerant injected tangentially to the wall. This thesis, conducted for The Exploration Company, is focused on their LOX/LCH4 liquid bipropellant engine, Huracán, where supersonic gaseous film cooling is adopted to ensure acceptable temperature ranges in the nozzle extension's walls.