On compact Green's functions and asymptotic expansions for flow-induced sound predictions

Both compact Green's functions and asymptotic expansions are widely used to analytically predict sound generated by low Mach number ( 1 << M ) fluid-dynamic sources, where the acoustic compactness of the source region is satisfied. By mathematically investigating the detailed assumptions involved in each of the two methods and by using two classical examples of flow noise problems, it is shown that the applicability of compact Green's function is restricted to a receiver location, r, at the acoustic far-field with / o r c ω →∞ where ω is the frequency and is the speed of sound, and that the solution from matched asymptotic expansions can be applied less restrictively starting at o c / ~ 1 o r c ω . Significant differences between the two solutions are shown when / ~ 1 o r c ω . In the acoustic far-field, the solutions from the two methods are analytically proved identical.