On 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 conical shock wave and turbulent boundary layer interaction using numerical simulations at a Mach number of 2 and a unit Reynolds number of 30 × 10^6 /��. The simulations were performed for cone-half angle ranging from 14◦ to 30◦, 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 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 in practical supersonic flows over conical geometries.