Synchronized shock wave and compliant wall interactions: Experimental characterization and aeroelastic modeling

The static and dynamic interaction of a normal shock wave (upstream Mach number 1.35) with a compliant wall is characterized experimentally by schlieren visualizations and an optical displacement sensor. Depending on the location of the shock wave along the compliant wall, three different regimes of interaction are found: large-amplitude synchronized regime, small-amplitude synchronized regime and unsynchronized regime. The regime of large-amplitude synchronized oscillations is found for shock locations close to the mid-point of the compliant wall along the streamwise direction; at this location, the coupled system locks to the second vibration frequency of the structure. Three regimes of small-amplitude synchronized oscillations are found depending on the shock position. When the shock is located upstream the center of the compliant wall, the shock may oscillate either periodically at the frequency of the first vibration mode or quasi-periodically with highest amplitudes at the three frequencies of the vibration modes. When the shock is located downstream the center of the compliant wall, the shock oscillates periodically at the frequency of the third vibration mode. Finally, close to the trailing edge of the compliant wall, the shock oscillation is not synchronized with the compliant wall which oscillates with a very small amplitude. An empirical model is proposed to investigate the energy exchange between the flow and the compliant wall during the limit cycle oscillations. A negative aerodynamic damping – and, hence, the possibility of a limit cycle – is observed when a sufficiently extended separation is considered in the model for the pressure distribution at the wall.