Separation of supersonic flow in a convergent–divergent nozzle can be widely found in aerospace applications. When a supersonic nozzle is operating in an overexpanded condition, in which the theoretical wall exit pressure is well below the ambient pressure, a shock occurs inside the nozzle and the shock separates from the nozzle walls in downstream. Even though this flow is very basic, it remains poorly understood. In this paper, the numerical simulations of shock-induced flow separation in the J-2S nozzle were conducted by solving unsteady Reynolds Averaged Navier Stokes (RANS) equations. The results computed for a range of pressure ratios (PRs) have shown the appearance of oscillating (free shock separation) FSS↔RSS (restricted shock separation) transition at PR = 43, which is in close agreement with the reported experimental FSS↔RSS transition value.

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