Nonlinear damping model for supersonic air-intake buzz

Abstract

Air-intake buzz was initiated at Mach number of 3.0 on a two-dimensional isolated air-intake model in a wind tunnel by throttling the exit area. Schlieren images of shock oscillation around the intake entry during buzz were recorded using a high-speed camera. The recordings show a strong coupling between the bow-shock at the cowl lip and the oblique shock from the ramp. Image analyses were carried out, considering each image as a matrix of pixels and the change of intensity of light analyzed. A dominant frequency of 103.8 Hz (Strouhal no = 0.008 based on throat height) associated with the shock oscillations and harmonics of the shock oscillations are indicated. Phase-plots of the intensity and the rate of change of intensity show nearly perfect ellipse after filtering at the dominant frequency. Thus, the buzz phenomenon is associated with a limit-cycle oscillation as in a nonlinear Van-Der Pol oscillator. The computed damping factor synchronizes with the amplitude at all times, establishing that buzz is a stable and self-sustained oscillation with equilibrium between inertial and damping forces. It is proposed that a control scheme based on feed-forward control system using a suitable forcing function could be mathematically developed to suppress supersonic air-intake buzz.