Incipient separation in shock wave/boundary layer interactions as induced by sharp fin

The incipient separation induced by the shock wave/turbulent boundary layer interaction at the sharp fin is the subject of the present study. Existing theories for the prediction of incipient separation, such as those put forward by McCabe (1966) and Dou and Deng (1992), can thus far only predic the direction of surface streamline and tend to overpredict the incipient separation condition based on the Stanbrook's criterion. In this paper, the incipient separation is first predicted with Dou and Deng (1992)'s theory and then compared with Lu and Settles' (1990) experimental data. The physical mechanism of the incipient separation as induced by the shock wave/turbulent boundary layer interactions at sharp fin is explained via surface flow pattern analysis. Furthermore, the reason for the observed discrepancy between the predicted and experimental incipient separation conditions is clarified. It is found that when the wall-limiting streamlines behind the shock wave becomes aligned with one ray from the virtual origin as the strength of the shock wave increases, the incipient separation line is formed at which the wall-limiting streamline becomes perpendicular to the local pressure gradient. The formation of this incipient separation line is the beginning of the separation process. The effects of Reynolds number and Mach number on incipient separation are also discussed. Finally, a correlation for the correction of the incipient separation angle as predicted by the theory is also given.