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

Abstract

Supersonic flow over three-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 numbers (1.5, 2, 2.5, 2.89, and 3.5). Surface streak line visualization, surface pressure measurements, and time-resolved Schlieren visualization were employed along with Reynolds-averaged Navier–Stokes computations to elicit the complex flow features such as the separation line, shock pattern, and the horseshoe vortex, which greatly influence the flow dynamics in the separated region. 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 two-dimensional free interaction theory, applied for normal shock-induced separation, closely predicts the mid-span plateau pressure. Although protuberances are of varying shapes and dimensions, the inviscid bow shock (obtained from Euler computations) provided generalized scales, whose effects on shock boundary layer interactions are analyzed. 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 ([Formula: see text]). Since the spanwise distance of the sonic point on the inviscid shock was found to be strongly correlated with 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 [Formula: see text] shall be predicted from a modification of the scaling laws for the length of plateau pressure region in two-dimensional shock boundary layer interaction, with the inclusion of a spanwise relieving effect. A correlation is obtained relating the [Formula: see text] with various incoming flow parameters and inviscid shock nose radius. The mid-span vortex core position was found to be linearly related to the [Formula: see text]. The radius of curvature of the separation shock is, however, found to be influenced by the entire inviscid shock, including the “weak” portion.