On the scaling of three dimensional shock induced separated flow due to protuberances

Supersonic flow over 3-dimensional bodies protruding out of the turbulent boundary layer was investigated by means of experiments and numerical computations. A parametric study was performed by varying the shape and dimensions of the protuberance, as well as the freestream Mach number (1.5, 2, 2.5, 2.89, 3.5). The rise in surface pressure at mid-span due to separation (plateau pressure) was dependent only on the incoming flow parameters, and independent of protuberance geometry. The 2-dimensional free interaction theory closely predicts the mid-span plateau pressure. Although protuberances are of varying shapes and dimensions, the inviscid bow shock provided generalized scales. The radius of curvature of the inviscid shock on the wall plane at the nose, which is theoretically related to the local second derivative (along the shock) of pressure jump, was found to be a determining parameter of mid-span separation length (Lsep). Since the spanwise distance of the sonic point on the inviscid shock was found to be strongly correlated to its nose radius of curvature, it follows that the 'strong' portion of the inviscid bow shock fixes the mid-span separation location. These observations concerning mid-span plateau pressure, and the role of strong shock portion in fixing mid-span separation, suggest that the Lsep shall be predicted from a modification of the scaling laws for the length of plateau pressure region in 2-dimensional shock boundary layer interaction, with the inclusion of spanwise relieving effect. A correlation is obtained relating the Lsep with various incoming flow parameters and inviscid shock nose radius.