Numerical simulation of shock-induced separated flows in overexpanded rocket nozzles

Flow separation in rocket nozzles is undesirable because of its unsteady and nonsymmetric nature, which leads to dangerous side-loads. At the initial stages of start-up, when a thrust optimized contour (TOC) nozzle operates under overexpanded conditions, free shock separation (FSS) takes place. Under certain conditions, this free separated flow reattaches back to the nozzle wall and forms restricted shock separation (RSS). The appearance of restricted shock separated flow depends upon the nozzle contour in a well-defined range of nozzle pressure ratios (NPR) and is characterized by a cap-shock pattern. The flow transition process from FSS to RSS flow configurations is a complex phenomenon and has been an area of interest for a few decades now. In the present study, an attempt has been made to understand the formation of the cap-shock pattern and the RSS flow configuration in a thrust optimized contour (TOC) nozzle. The presented research work consists of two parts. In the first part of the paper, numerical investigation of flow transition (FSS→RSS) has been performed to understand the formation of the cap-shock pattern, which is believed to be the main cause for this flow transition from FSS to RSS. Axisymmetric numerical calculations on a wide range of NPRs (15 25) are performed to reproduce the forward transition process and are found to be in good agreement with the experiments. In the second part, some light has been shed on various aspects of RSS flow regime. Three-dimensional (3D) numerical simulations have been performed on a wide range of NPRs, i. e., 25.0, 30.0, 38.0, 41.0, and 46.0. Detailed analysis of these numerical results allows examining the evolution of the separation point and the cap-shock pattern with respect to the NPR. Furthermore, some insights based on the axial momentum along the nozzle axis and radial momentum distributions across the quadruple point are given