Supersonic flow behavior in jet engine nozzles from subsonic to supersonic regimes: Turbulence influence on shock structures and performance metrics

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Abstract
This study presents a numerical investigation of supersonic flows through a convergent conical rocket engine nozzle, focusing on the influence of turbulence models on shock structures and nozzle performance. Simulations were performed in ANSYS Fluent for nozzle pressure ratios (NPRs) from 1.4 to 7.0 under steady-state conditions. Four turbulence models [Realizable k–ε, Standard k–ω, Shear Stress Transport (SST) transition model, and Reynolds Stress Model (RSM)] were evaluated for their ability to predict Mach distributions, shock-cell structures, and pressure-based performance metrics. Results indicated that the SST k–ω model provided sharper, more accurate shock-cell structures and captured shock–boundary-layer interactions more effectively, especially at higher NPRs. At NPR = 5.0, the SST model predicteda maximum exit Mach number of 1.85, closely matching the experimental 1.88 ± 0.03, whereas the Realizable k–ε model underestimated it at 1.75. The k–ε model offered greater numerical stability and lower computational cost but tended to oversimplify flow features and underpredict shock intensity. RSM captured anisotropic turbulence effects but required more computational resources and exhibited higher sensitivity. Aerodynamic performance evaluation showed that the SST model predicted thrust and discharge coefficients (CV, CD) more accurately across all NPRs. At NPR = 4.0, it produced a CV of 0.92 and a CD within 3% of experimental values, compared to 0.87 and up to 7% deviation for the k–ε model. Therefore, the SST model was recommended for high-fidelity analyses requiring accurate prediction of shock behavior and nozzle performance, while the realizable k–ε model was suitable for preliminary analyses prioritizing faster, stable convergence with reduced detail.

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