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

Abstract

The incipient separation induced by the shock wave/ turbulent boundary layer interaction at the sharp fin is the subject of present study. Existing theories for the prediction of incipient separation, such as those put forward by McCabe (1966) and Dou and Deng (1992), can have thus far only predicting the direction of surface streamline and tend to over-predict the incipient separation condition based on the Stanbrook's criterion. In this paper, the incipient separation is firstly predicted with Dou and Deng (1992)'s theory and then compared with ' 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 the 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 aligning with one ray from the virtual origin as the strength of shock wave increases, the incipient separation line is formed at which the wall limiting streamline becomes perpen- Knight et al., 2003). However, the cost of a full Navier-Stokes calculation is still fairly exorbitant, especially for 3D flows. In addition, issues relating to the accuracy from a physical point of view (besides the numerical accuracy) for purpose of quantitative comparison to experiments and the elucidation of the complex physical flow are not always satisfactory. Therefore, some analytical work like the simple predictive methods is still imperative for an initial estimate of the main flow physics based on preliminary design and then for progress to the subsequent stages leading eventually to the final prototype. To try to do a thorough simulation at the preliminary design stage is just too costly and most probably ineffective.In the past over 30 years or so, there are limited works carried out on the separation behaviour in SW/TBLI induced by a sharp fin on a flat plate as typified by Fig. 1 (Bogdonoff, 1987;Delery and Marvin, 1986;Green, 1970;Panaras, 1996;Settles and Dolling, 1992;Neumann and Hayes, 2002). As the onset or occurrence of flow separation invariably changes the topology of the flow field, one important and critical problem to resolve is how to judge or predict the incipient separation and its underlying flow physics. A typical topology of the surface flow pattern is shown schematically in outside the boundary layer. This analysis appears to have more fundamental physical basis than those by McCabe (1966), Korkegi (1973), or Lu (1989. Their results also show the trend of α i decreasing with increasing Re θ which had been previously discussed in Lu (1993) and Leung and Squire (1995). It may be noted that Leung and Squire's (1995) experimental data confirmed the same trend for α i versus Re θ as in Dou and Deng's theory. Furthermore, McCabe (1966) and Dou and Deng (1992c) found that the incipient separation angle α i via skin-friction line (also called ...