Low order analysis of panel vibration under ramp-induced shock / boundary layer interaction

Abstract

A thin compliant panel was tested in a Mach 2 wind tunnel. The panel was mounted flush with the tunnel floor and was of dimensions L=121.9 mm (chord), W=63.5 mm (span) and h=0.254 mm (thickness). A 22° compression ramp was placed 5 mm downstream of the model, which induced a shock/boundary layer interaction with fully separated flow over parts of the panel. Full-field deformation was measured using Digital Image Correlation and the surface pressure field was obtained from fast-response pressure-sensitive paint. Analysis of the shock foot motion was performed using a curve-fitting method. Comparison of the shock motion between a rigid and compliant panel case showed no difference in the size of the intermittent region but found that the shock motion over the compliant panel is affected by the panel vibration. Proper Orthogonal Decomposition revealed that the surface pressure is dominated by low-frequency unsteady shock motion, in both cases (rigid and compliant panel). The sixth POD mode clearly shows the streamwise shock foot motion oscillates at the first panel vibration frequency. The surface pressure field upstream of the shock foot is dominated by piston-theory aerodynamics and thus correlated to the slope of the compliant panel. The Sparse Identification of Nonlinear Dynamic Systems algorithm was employed to find low-order representations of the system dynamics. Linear stiffness matrices could be consistently recovered. The measurement noise however prevented extraction of additional relations, such as linear damping matrices or forcing terms from the surface pressure.