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Abstract: The nozzle is a critical component responsible for generating most of the net thrust in a scramjet engine. The quality of its design directly affects the performance of the entire propulsion system. However, most turbulence models struggle to make accurate predictions for subsonic and supersonic flows in nozzles. In this study, we explored a novel model—the algebraic stress model k-kL-ARSM+J—to enhance the accuracy of turbulence numerical simulations. This new model was used to conduct numerical simulations of the design and off-design performance of a three-dimensional supersonic asymmetric truncated nozzle designed in our laboratory, with the aim of providing a realistic pattern of changes. The research indicate that, compared to linear eddy viscosity turbulence models such as k-kL and SST, the k-kL-ARSM+J algebraic stress model shows better accuracy in predicting the performance of supersonic nozzles. Its predictions were identical to the experimental values, enabling precise calculations of the nozzle. The performance trends of the nozzle are as follows: as the inlet Mach number increases, both thrust and pitching moment increase, but the rate of increase slows down. Lift peaks near the design Mach number and then rapidly decreases. With increasing inlet pressure, the nozzle thrust, lift, and pitching moment all show linear growth. As the flight altitude rises, the internal flow field within the nozzle remains relatively consistent due to the same supersonic nozzle inlet flow conditions. However, external to the nozzle, the change in external flow pressure results in the nozzle exit transitioning from over-expanded to under-expanded, leading to a shear layer behind the nozzle that initially converges towards the nozzle center and then diverges.