Viscosity, shock-induced separation, and shock reversal -- Oscillating wing section in transonic flow

We numerically examine the mechanisms that describe the shock-boundary layer interactions in transonic flow past an oscillating wing section. At moderate and high angles of incidence but low amplitudes of oscillation, shock induced flow separation or shock-stall is observed accompanied by shock reversal. Even though the power input to the airfoil by the viscous forces is three orders of magnitude lower than that due to the pressure forces on the airfoil, the boundary layer manipulates the shock location and shock motion and redistributes the power input to the airfoil by the pressure forces. The shock motion is reversed relative to that in an inviscid flow as the boundary layer cannot sustain an adverse pressure gradient posed by the shock, causing the shock to move upstream leading to an early separation. The shock motion shows a phase difference with reference to the airfoil motion and is a function of the frequency of the oscillation. At low angles of incidence, and low amplitudes of oscillation, the boundary layer changes the profile presented to the external flow, leads to a slower expansion of the flow resulting in an early shock, and a diffused shock-foot caused by the boundary layer.