Calculation of the radiated sound field using an open Kirchhoff surface

TLDR: In this paper, the authors used an asymptotic analysis for large temporal wave number to analyze time harmonic integral forms and provided correction terms to partially account for the missing portion of the integral surface.

Abstract: Means of improving the accuracy of Kirchhoff integral solutions for sound fields in cases where the surface may not be completely closed are investigated. Asymptotic analysis for large temporal wave number is used to analyze time harmonic integral forms. Extension to time dependent equations is discussed briefly. Applicability to the "moderate" temporal wave numbers of real problems is discussed. Stationary phase arguments are used to show geometrically where good results are expected from a Kirchhoff integral . on an open surface. A similar asymptotic analysis is used to provide correction terms to partially account for the missing portion of the integral surface. The present study is restricted to the case where the mean flow is parallel to the open surface, but results are applicable to arbitrary flow situations in any number of dimensions. Two dimensional numerical examples are given to demonstrate and evaluate the method. It is found that the correction terms can dramatically reduce the error in an open surface calculation of the radiated sound field.