Demand for hypersonic aircraft has been increasing in recent years, highlighting the importance of research and development in this aerospace sector. A single expansion ramp Nozzle (SERN) was designed and investigated. An algorithm based on the method of characteristics (MOC) was developed, which generated the optimized contour of a 2D supersonic calorically perfect minimum-length nozzle,
for ideal shock-free flow expansion, and calculated various flow-field properties. An optimized SERN geometry was designed using the algorithm, and truncated for viable integration into a vehicle, without
significant loss in thrust. Numerical simulations at design and off-design conditions were conducted,
evaluating nozzle performance and flow-field phenomena. Overexpanded flow and complex shock-wave patterns were observed, such as the restricted shock separation (RSS) pattern, including separation and reattachment of the main jet to the ramp and formation of a separation bubble, a large recirculation region on the flap, Mach disks, λ-shock structures, and shock trains.