The difficulties associated with thrust-optimized contour nozzles have led to significant advances in our knowledge of the physical phenomena associated with flow separation. In this study, a fully implicit scheme is implemented using a combined weight function for splitting the flux to analyze the shock patterns in the optimized contour (TOC) that occur during the process of separation, leading to free (FSS) or restricted (RSS) shock separation. The switching FSS/RSS hysteresis at startup and shutdown is also investigated. To better understand and validate the findings and study the properties of the oscillating flow during the start-up procedure, an axisymmetric two-dimensional numerical simulation was performed for the TOC nozzle. A code was developed to solve the unsteady Navier-Stokes equations for compressible nozzle flow with boundary layer/shock wave interactions with the implementation of a full RSM-Omega turbulence model. These findings were used to analyze the separation structures, shock wave interactions, and hysteresis phenomena.
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