A design method for single expansion ramp nozzle based on three-dimensional characteristic method

Abstract To enhance the aerodynamic performance of hypersonic nozzles, a three-dimensional method of characteristics (3D MOC) is proposed for designing single expansion ramp nozzles (SERN). The flowfield structures and aerodynamic performances of nozzles designed using the 3D and conventional two-dimensional (2D) MOC approaches are compared through three-dimensional numerical simulations. Results indicate that the major geometric differences occur along the circumferential wall. Under typical flight conditions, the nozzle designed by 3D MOC achieves over 0.45% higher axial thrust coefficient and more than 8% higher lift coefficient than the 2D MOC design. Furthermore, based on the 3D MOC, both rectangular nozzle (RN) and circular nozzle (CN) configurations are designed and analysed. The CN exhibits slightly superior aerodynamic performance compared with the RN. By further modifying the upper and lower wall infill surfaces of the RN, three new nozzle variants are obtained. Comparative results show that these geometric infills have a pronounced influence on lift and pitching moment, while the axial thrust coefficient remains nearly constant. Finally, the effect of the tracing radius on the RN and CN configurations is examined. Increasing the tracing radius notably reduces the lift coefficient but has minimal impact on the thrust and pitching moment. These findings highlight the potential of the 3D MOC-based design method to flexibly balance aerodynamic moment and lift in hypersonic nozzle optimisation.