Direct numerical simulation of conical shock wave/turbulent boundary layer interaction

Abstract

Direct numerical simulation of the Navier-Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_\infty = 2.05$ and Reynolds number $Re_\theta \approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\theta _c = 25^\circ$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behavior is strongly affected by the imposed pressure gradient, with streaks which are locally suppressed in adverse pressure gradient (APG) zones, and which suddenly reform in the downstream region with favourable pressure gradient (FPG). Three-dimensional mean flow separation is only observed in the first APG region associated with formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical two-dimensional wedge-generated shock/boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to isotropic state in APG regions, and to a two-component anisotropic state in FPG.