To assess the aeroacoustic noise, Lighthill's equation remains the most widely used acoustic analogy, especially because of its tractable numerical implementation and physically appealing interpretations. The use of its integral form is particularly justified for low Mach number flows. In the presence of a solid obstacle, the mere knowledge of the incompressible-flow surface pressure fluctuations is sufficient to provide a good estimation of the radiated sound as long as the wavelength is large compared to the dimension of the problem. In practice, obstacles can be non-compact or become so for sufficiently high frequencies and the previous observation has to be reassessed. In order to deal with non-compact surfaces, an alternative form of Lighthill's integral equation is presented. These simplified and approximate formulations are interesting from a numerical point of view as they do not necessitate the calculation of Lighthill's stress tensor. Numerical predictions compare favorably with experimental data for the specific cases of a diaphragm and a flap inserted in a rectangular duct.
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