Re-expansion method for generalized radiation impedance of a circular aperture in an infinite flange

Abstract

The paper applies the re-expansion method to analyze the sound radiation from a flanged circular pipe. The axial velocity in the aperture is expressed by means of some orthogonal polynomials combining the properties of Jacobi's polynomials and hypergeometric functions, and also accounting for the velocity singularities at the edge points of the aperture. This makes it possible to reveal the physical parameters of the problem with a very limited number of terms. Besides the classical case when the flange covers the whole plane outside the pipe, the method also permits one to study also the case of the flange extending with zero thickness over a part of the circular pipe. Finally, the paper includes the extension of the results beyond the plane wave region achieving good accuracy and convergence.