Recovery of a supersonic turbulent boundary layer after an expansion corner

Abstract

Supersonic turbulent flows at Mach 2.7 over expansion corners with deflection angles of 0° (flat plate), 2°, and 4° have been studied using direct numerical simulation. Distributions of skin friction, pressure, velocity, and boundary layer growth show that the turbulent boundary layer experiences a recovery from a non-equilibrium to an equilibrium state downstream of the expansion corner. Analysis of velocity profiles indicates that the streamwise velocity undergoes a reduction in the near-wall region even though the velocity in the core part of the boundary layer is accelerated after the expansion corner. Growth of the boundary layer was evaluated and a higher shape factor was found in the expansion cases. Turbulence was found to be mostly suppressed downstream of the corner, and throughout the recovery region, even though turbulence is regenerated in the near-wall region. The expansion ramp increases the near-wall streak spacing compared to a flat plate, and turbulent kinetic energy profiles and budgets exhibit a characteristic two-layer structure. Near-wall turbulence recovers to a balance between the local production and dissipation equilibrium more quickly in the inner layer than in the outer layer. The two-layer structure is due to a history effect of turbulence decay in the outer part of the boundary layer downstream of the expansion corner, with limited momentum and energy exchange between the inner layer and the main stream.