Numerical investigation on effects of divergent section expansion ratio on flow characteristics of multi-stream serpentine nozzle under various offset ratios

Multi-stream serpentine nozzles enhance adaptive-cycle engine compatibility and aircraft stealth performance. However, their complex geometry induces severe flow interactions and losses, necessitating a deep understanding of how key geometric parameters affect the flow characteristics. This study numerically investigates 30 nozzle configurations with offset ratios ranging from 0.25 to 0.65 and divergent section expansion ratios ranging from 1.10 to 1.50. Results show increasing offset ratio promotes shock wave coalescence and mainstream over-expansion at lower expansion ratios, forming λ-shaped or normal shocks. Vorticity analysis reveals offset ratio intensifies corner vortices in the transition section, while expansion ratio amplifies upper-wall vortices. Analysis of turbulent kinetic energy identifies distinct jet regions, demonstrating that larger offset ratios accelerate attenuation of the upper tertiary stream core length, with this shortening occurring at progressively lower expansion ratios. Reduced core length shifts the complete mixing location further upstream. Total pressure recovery declines with both parameters (maximum drop 9.915 %). The main discharge coefficient decreases with offset but increases with expansion, whereas the tertiary discharge coefficient varies non-monotonically (maximum deviation 18.919 %). Optimal expansion ratio for peak thrust shifts lower as offset increases. These findings elucidate the individual and superimposed roles of offset ratio and expansion ratio in modulating flow distortion, shock-system evolution, and mixing enhancement, thereby providing a framework for managing aerodynamic losses and optimizing performance in multi-stream serpentine nozzle design. Abbreviations: Δy/D, offset ratio; A_m,e/A_th, divergent section expansion ratio; p_a, ambient pressure; T_a, ambient temperature; NPR, nozzle pressure ratio; TPR, tertiary pressure ratio; T_in^*, inlet total temperature; FPG, favorable pressure gradient; APG, adverse pressure gradient; ES, expansion-shock structure; OS, oblique shock wave; TS, transmitted shock wave; NS, normal shock wave; θ_th, total pressure loss coefficient at the throat of the main stream section; TKE, turbulent kinetic energy; σ_e, total pressure recovery coefficient; C_D,m, discharge coefficient of the main stream; C_D,t, discharge coefficient of the tertiary stream; C_Fx, axial thrust coefficient.