A great effort has been made by the European space industry to ensure an innovative and independent progress in space technology. In this context The Exploration Company, which supported the present work, is rapidly developing new technologies for future space transportation systems, including a new LOX/CH4 liquid rocket engine named Huracán that will equip their future space module and lunar lander Nyx Moon. This thesis focuses on the nozzle extension of the Huracán engine. The nozzle extension is a vital component for a rocket engine with in-space applications. Its purpose is, indeed, to get the most thrust possible from the expansion of the hot gases in a near-vacuum environment.