Plume Shaping for Altitude Compensating Rocket Nozzles : Theory and Experimental Validation of Cosine Loss Cancellation

Altitude-compensating rocket nozzles can improve mission cost efficiency due to lower reliance on multi-stage rockets, presenting a use case for single stage rockets (SSTO’s). Multi-stage rockets are more expensive as they have higher complexity, containing extra engines and mechanisms. Multi-stage rocket engines are designed with different engines and nozzles to optimize performance for certain altitudes. Due to varying atmospheric pressure during the ascent of a rocket, a simple bell nozzle loses efficiency as altitude increases. This study investigates a novel approach to mitigate such cosine losses of a single nozzle through a process termed cosine loss cancellation. In this process, auxiliary channels surrounding the main plume with higher pressure induce controlled contraction of the main plume. Various nozzle concepts were designed using Onshape and SolidWorks. Ansys fluent was used to mesh the geometry, and CFD simulations were performed using OpenFOAM. The k-Epsilon turbulence model was used to model the plume dynamics and combustion for each nozzle, with the boundary conditions fixed for all nozzle designs. Simulation results were used to validate the cosine loss cancellation theory. Physical models of the nozzles were 3D printed and subjected to subsonic flow with pressure sensors as a physical representation of the pressure difference between the auxiliary channel flow and main plume outlet pressure. This research offers a more efficient and versatile generation of SSTO rockets.