Physics of a Flexible Panel Subject to Shock Wave/Boundary Layer Interactions

Supersonic flows involve shock waves across which pressure steeply rises. The adverse pressure gradient across a shock wave can lead to significant distortion of boundary layer profile, eventually causing flow separation. Further, the phenomenon is unsteady, especially in turbulent boundary layers. This is owing to the turbulent fluctuations within the boundary layer, which induce low frequency shock foot oscillations and separation region pulsations. The shock oscillation frequencies are typically in resonance with the fundamental vibration modes of the aircraft structure. The coupled mechanism eventually results in shock induced limit cycle oscillations (LCOs) and flutter. This work investigates into this phenomenon by analytically deriving an equation for the low frequency shock foot oscillations over any elastic panel. Suitable approximations are used, with supporting evidence from CFD results using RANS. The derived equation shows the panel flexibility to be a forcing as well as a damping term for the shock foot motions.