Study of tonal noise behavior of an airfoil by using parabolized stability equations

Abstract

Tonal noise or whistle noise is an aerodynamic noise known to be generated due to boundary layer instability. The relation between the instability of Tollmien-Schlichting wave and the tonal noise was dealt with, in previous studies, for rather limited cases that employed linear stability analysis or results for idealized flow configuration. To investigate the relation between the instability wave and tonal noise in a more thorough and systematic way, we employ the parabolized stability equation approach to compute details of the stability characteristics of boundary layer developed over pressure side surface of an airfoil at various angles of attack and various free-stream velocities. Discussions on the relation between the instability and the tonal noise have been given based on the comparison of the present computational results with the experimental data. We confirm that the overall U (1.5) dependency of the noise frequency with velocity is caused by the most amplified Tollmien-Schlichting wave. Application of a simple feedback model to the stability data of the present work provides us with the results that explain well the ladder-like structure and local U (0.8) dependency of the tonal noise. Effects of angle of attack and chord length on the tonal noise including the frequency, velocity range, and frequency difference between peaks of the noise are also examined.