Some benchmark problems for computational aeroacoustics

This paper presents analytical results for high-speed leading-edge noise which may be useful for benchmark testing of computational aeroacoustics codes. The source of the noise is a convected gust striking the leading edge of a wing or fan blade at arbitrary subsonic Mach number; the streamwise shape of the gust is top-hat, Gaussian, or sinusoidal, and the cross-stream shape is top-hat, Gaussian, or uniform. Detailed results are given for all nine combinations of shapes; six combinations give three-dimensional sound fields, and three give two-dimensional fields. The gust shapes depend on numerical parameters, such as frequency, rise time, and width, which may be varied arbitrarily in relation to aeroacoustic code parameters, such as time-step, grid size, and artificial viscosity. Hence it is possible to determine values of code parameters suitable for accurate calculation of a given acoustic feature, e.g., the impulsive sound field produced by a gust with sharp edges, or a full three-dimensional acoustic directivity pattern, or a complicated multi-lobed directivity. Another possibility is to check how accurately a code can determine the far acoustic field from nearfield data; a parameter here would be the distance from the leading edge at which the data are taken.