Scale analysis and experimental observations of shock-induced turbulent boundary layer separation in nozzles

Time average shock-induced boundary layer separation is investigated using scale analyses, analytical modeling, and experiments. While the study focuses on turbulent boundary layer separation in overexpanded rocket nozzles, many of the analyses presented apply to the broad family of free interaction, shock-separated flows in which the structure of the boundary layer–shock interaction zone is self-similar and independent of the shock generator. The scale analyses lead to two approximate expressions for the wall pressure ratio at separation; over a range of separation Mach numbers, both models provide reasonable predictions of observed separation pressure ratios. The second model, representing a refinement of the first, appears to provide a fairly general description of free interaction separation: the model approximately captures separation pressure ratios observed in supersonic flow over backward facing steps and in the case of overexpanded nozzle flow, provides predictions that are consistent with the free interaction model. Experiments are carried out in a sub-scale nozzle under overexpanded, cold-flow conditions. The principal observations are as follows: (i) For the range of separation Mach numbers investigated (5.0⩽Mi⩽5.4), nominal separation line locations can be predicted with reasonable accuracy using the classical generalized quasi-one-dimensional compressible flow model and an appropriate separation criterion. (ii) Over the same range of overexpanded flow conditions, the time-average pressure rise over the shock interaction zone can be accurately fit by the free interaction model.