Generation of sound and instability waves due to unsteady suction and injection

Abstract

This paper analyses the generation of sound and Tollmien–Schlichting (T–S) waves in a compressible boundary layer that is subject to unsteady suction and injection. An asymptotic approach based on the triple-deck formulation has been developed to calculate the sound field. It is shown that in addition to the three familiar asymptotic regions that govern the near-field hydrodynamic motion, an extra outer region controlling the sound radiation must be introduced. The near-field solution is sought via an asymptotic expansion in ascending powers of ε = R^−1/8, where R is the global Reynolds number. The first three terms in the asymptotic series are found to act as quadrupole, dipole and monopole sources respectively, and make equal order-of-magnitude contributions to the acoustic far field. The analysis also allows the amplitude of the excited T–S waves to be determined to O(ε) accuracy. It is believed that the flow structure and solution procedure may be used to solve a range of aeroacoustic problems.