Numerical simulation of the interaction of a transitional boundary layer with a 2-D flexible panel in the subsonic regime

Abstract

The self-sustained oscillations arising in subsonic transitional flow over a flexible finite panel are investigated numerically. The flowfields are obtained by solving the full compressible Navier–Stokes equations employing a recently developed sixth-order implicit code which is capable of retaining its superior accuracy on deforming meshes. The panel mechanics is described by means of the nonlinear von Karman plate equations which are solved with a previously validated structural module. An iterative implicit coupling of the fluid and structural solvers is provided in order to eliminate lagging errors at the fluid/solid interface. Computations are performed for two freestream Mach numbers ( M ∞=0.2,0.8), and for a range of Reynolds number and dynamic pressure. At both flow speeds, self-excited oscillations develop in the absence of an applied external forcing. At M ∞=0.2, the origin of the instability appears to be of an aeroelastic nature (i.e., flutter) and is found to persist even at very low Reynolds numbers. The fluctuating surface also generates boundary-layer instability modes downstream of the panel trailing edge. At the higher Mach number, static divergence occurs followed by the onset of travelling wave flutter (TWF), with frequency and wavelength compatible with those of Tollmien–Schlichting (T–S) waves. The observed limit-cycle oscillations appear to originate from the coupling of T–S waves with the higher-mode flexural waves on the elastic panel, and therefore subside below a critical value of Reynolds number. The TWF also generates significant acoustic radiation above the fluttering panel. The previous instabilities are observed for panels with either pinned or fully clamped edge conditions. Sensitivity of the solutions to the prescribed cavity pressure underneath the panel is noted. This dependence arises due to the different response of the boundary layer to the favorable or adverse pressure gradient induced by the upward or downward panel deflections, respectively.