Upstream Influence of Conical Shock Wave—Turbulent Boundary Layer Interactions

Conical shock wave interacting with the boundary layer on a flat plate (Conical SBLI) is a complex three-dimensional phenomenon distinguished by a hyperbolic shock trace and spanwise variation in interaction intensity. This study investigates upstream-influence behavior in a conical shock wave and turbulent boundary layer interaction using numerical simulations at a Mach number of 2 and a unit Reynolds number of [Formula: see text]. The simulations were performed for cone-half angles ranging from 14–30 deg, and results were validated against existing experimental data. The analysis reveals that the upstream influence length on the symmetry plane scales with the pressure rise, following a power law similar to that observed in two-dimensional (2D) shock wave and boundary layer interactions. Spanwise measurements show that the normal upstream influence length increases along the span, transitioning from cylindrical similarity near the symmetry plane to a conical similarity further outboard. These findings provide new insights into conical shock wave and turbulent boundary layer interaction, and offer a framework for predicting upstream influence length in practical supersonic flows over conical geometries.