A quasi-potential flow formulation for the prediction of the effect of the circulation on the acoustic shielding from a lifting body by means of a finite element method

Abstract

This paper presents a new simplified approach for the prediction of the acoustic shielding from lifting
bodies by means of a finite element method. It extends a method already validated for aerodynamic
applications to Aeroacoustics on the basis of the small perturbation expansion. A numerical model
to represent the effect of the circulation developed by a slender body on the noise radiation in
an unbounded domain is provided. A quasi-potential flow formulation is adopted by introducing a
simplified shear layer model: a frozen wake with finite thickness and extent. The effect of the sound
diffraction in the wake region is accounted for by applying the continuity of pressure across the
wake line in the aeroacoustic field. An incompressible steady mean flow is considered and the Kutta
condition is applied to overcome the singularity at the trailing edge. The circulation in the mean
flow is predicted by reducing the potential solution to a single-valued problem. The non- uniform
base flow is superimposed on the wave propagation and the linear aeroacoustic problem is solved
by means of the full acoustic potential equation. The finite element method is applied both to the
solution of the base flow and to the acoustic radiation. The acoustic field scattered by a 2D airfoil
from a line source in presence of a non-uniform base flow is predicted as a numerical example of the
proposed model. The circulation modifies the extent of the acoustic shielding by altering the wave
propagation around the slender body, the wave diffraction at the trailing edge and the refraction in
the shear layer.

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