Details

This study presents a comparative analysis of three supersonic nozzle geometries: the conical nozzle, the Rao Thrust-Optimized Parabolic (TOP) bell nozzle, and a Method of Characteristics (MOC) contour. All three were evaluated under identical sea-level ambient conditions (Pamb = 101,325 Pa), placing each in an over-expanded operating state. The conical nozzle serves as the aerodynamic baseline, with a divergence loss of 1.7% at a 15° half-angle. The MOC contour was generated using a custom MATLAB solver incorporating the Prandtl-Meyer function and Riemann invariants (K+, K⁻), producing theoretically shock-free exit flow that represents the inviscid performance ceiling. The Rao bell nozzle recovers most of this performance advantage at roughly 80% of the equivalent conical length. High-fidelity CFD simulations were conducted using a 2D axisymmetric density-based solver with the k-ω SST turbulence model. The MOC nozzle achieves the highest thrust coefficient, followed by the Rao nozzle. At NPR = 100 and ε = 13.42, the Rao nozzle yields CF = 1.5174 against CF = 1.5048 for the conical baseline. Boundary-layer analysis reveals an approximate 3% Mach deficit at the MOC nozzle exit, highlighting the importance of viscous corrections in accurate performance prediction.