Generalization of Amiet’s theory for small reduced-frequency and nearly-critical gusts

Abstract

Amiet’s theory is an airfoil noise prediction technique based on the resolution of a convected Helmholtz equation for small velocity potential and pressure disturbances. In this approach, the partial differential equation can be classified as hyperbolic or elliptic depending on the sign of the Helmholtz equation parameter. Existing solutions present non-physical results at the transition between these two regimes. In this study, a new approximation aiming at accurately predict back-scattering effects of small reduced-frequency and nearly-critical gusts is proposed. Our approach reduces the necessity of regularization and ad-hoc corrections adopted in previous literature. Moreover, our solution matches published results for gusts of large reduced-frequency. We present analytical derivations of the pressure trace that are applicable to the leading- and the trailing-edge airfoil noise prediction. The proposed formulation is particularly applicable to acoustically compact airfoils. In practical applications, this condition is verified for the low-frequency aerodynamic noise produced by ventilation systems and automotive fans.