Shock‐Assisted Flow Control System in Convergent‐Divergent Nozzle: A Numerical Study on Unconventional Protuberance With Different Geometry

ABSTRACT Thrust Vector Control (TVC) serves as a vital means of flight control, particularly applicable during the initial launch stages or when navigating through rarefied atmospheres. Among diverse TVC techniques, shock control utilizing protuberances stands out. This study investigates the effect of cubic, hemispherical, cylindrical, and conical wall‐mounted protuberances on the exhaust jet of a Mach‐2 convergent–divergent nozzle. A three‐dimensional steady Reynolds Averaged Navier–Stokes (RANS) numerical approach is employed, using the Re‐Normalization Group (RNG) k–ε turbulence model for closure. The analysis examines nozzle‐wall pressure, thrust, and transverse forces to elucidate the underlying flow physics. The results show that the cubic protuberance produces the largest jet deflection, approximately 2.0° (1.995° numerically), in close agreement with the experimental value of 2.1° reported in Ref. [16]. Larger protuberance volumes generate stronger shocks that can interact with the opposite wall; accordingly, cubic and cylindrical protuberances tend to drive shocks toward the opposing wall, whereas hemispherical and conical protuberances produce shocks that exit near the nozzle lip without wall impingement. Across the investigated cases, the axial‐force penalty remains small (≤ 1%), indicating that the thrust reduction is negligible relative to the achieved jet deflection.