Edge-source acoustic Green's function for an airfoil of arbitrary chord, with application to trailing-edge noise

Approximations are derived for the three-dimensional, time-harmonic acousti c Green's function whose normal derivative vanishes on the surface of an ai rfoil of finite thickness and chord l for source locations in the neighbour hood of either the leading or trailing edge. The acoustic wavelength is ass umed to be large relative to the airfoil thickness, but no restriction is p laced on its magnitude relative to l. A multiple scattering calculation is performed for high frequencies that involves an expansion in terms of the s uccessive scattering of waves from the leading and trailing edges of the ai rfoil. The 'principal subseries' of the expansion is summed and shown to pr ovide an excellent approximation for the Green's function when K(o)l greate r than or equal to 1, where K-o is the acoustic wavenumber. The solution is extended down to k(o)l = 0 by interpolation with the corresponding Green's function for an airfoil of acoustically compact chord. The results extend the single scattering approximation introduced by R. K. Amiet (AIAAJ. 12 19 70), and are illustrated by application to the problem of trailing-edge noi se generated by nominally steady, low Mach number flow past the airfoil. Ex periments and numerical simulations of such flows often include acoustic fr equencies that are sufficiently small that the usual assumption of trailing -edge noise theory, that the airfoil is semi-infinite, is not valid.