Mach number effects on shock-boundary layer interactions over curved surfaces of supersonic turbine cascades

The effects of inlet Mach number on the unsteadiness of shock-boundary layer interactions (SBLIs) over curved surfaces are investigated for a supersonic turbine cascade using wall-resolved large eddy simulations. Three inlet Mach numbers, 1.85, 2.00, and 2.15 are considered at a chord-based Reynolds number 395,000. The curved walls of the airfoils impact the SBLIs due to the state of the incoming boundary layers and local pressure gradients. On the suction side, due to the convex wall, the boundary layer entering the SBLI evolves under a favorable pressure gradient and bulk dilatation. On the other hand, the concave wall on the pressure side imposes an adverse pressure gradient and bulk compression. Variations in the inlet Mach number induce different shock impingement locations, enhancing these effects. A detailed characterization of the suction side boundary layers indicates that a higher Mach number leads to larger shape factors, favoring separation and larger bubbles, while the reverse holds for the pressure side. A time-frequency analysis reveals the presence of intermittent events in the separated flow occurring predominantly at low-frequencies on the suction side and at mid-frequencies on the pressure side. Increasing the inlet Mach number leads to an increase in the time scales of the intermittent events on the suction side, which are associated with instants when high-speed streaks penetrate the bubble, causing local flow reattachment and bubble contractions. Instantaneous flow visualizations show the presence of streamwise vortices developing on the turbulent boundary layers on both airfoil sides and along the bubbles. These vortices influence the formation of the large-scale longitudinal structures in the boundary layers, affecting the mass imbalance inside the separation bubbles.