Experimental and Numerical Investigation of Nonlinear Effects in Transonic Flutter

Abstract

In order to study each of the typical transonic phenomena in as pure a form as possible, we used a model having a simple geometry (2D wing) for both our experimental and numerical investigations. From the results of measurements in the Transonic Wind-Tunnel Göttingen (TWG), we found that various manifestations of small-amplitude limit-cycle oscillations occurred in which either one or two degrees of freedom were involved. In addition, we observed an alternating excitation and coexisting limit cycles. We have also demonstrated how very small control forces were sufficient to influence the state of the system, as is generally possible the case in nonlinear systems, and thereby suppress flutter oscillations. Limit cycles occur under free and forced transition in both a perforated and an adaptive test section, so we can exclude the possibility that they are artifacts. The results of corresponding experiments with a conventional NACA 0012 airfoil showed no comparable small-amplitude limit-cycle oscillations. Flutter calculations based on measured aerodynamic forces yield stability limits whose values show good agreement with directly measured ones. The results of a numerical simulation of the unsteady force coefficients for forced harmonic pitch oscillations qualitatively reproduced the measured curve as a function of Mach number. In the buffeting region, the numerical simulation leads to a frequency for the self-excited shock oscillation that is confirmed by experiment. The insight gained from these investigations leads to the conclusion that, for limiting the amplitude of transonic flutter, we have to take account of the three possible mechanisms responsible for it, viz., the flow separation at the trailing edge, 3D effects, and the interactions between the shock and the marginal region of separated flow beneath it.