Calculation of the radiated sound field using an open Kirchhoff surface

Means of improving the accuracy of Kirchhoff surface-integral evaluations 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. 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 account partially for the missing portion of the integral surface. The present study is restricted to the case where the mean flow is parallel to the available portion of the surface. The analysis is extended to time-domain formulation of transient problems. Two- and three-dimensional numerical examples are given to demonstrate and evaluate the method. It is found that the derived correction terms can reduce the error in an open-surface calculation of the radiated sound field by more than an order of magnitude.