The Robustness of Acoustic Analogies

Acoustic analogies for the prediction of flow noise are exact rearrangements of the flow equations N(right arrow q) = 0 into a nominal sound source S(right arrow q) and sound propagation operator L such that L(right arrow q) = S(right arrow q). In practice, the sound source is typically modeled and the propagation operator inverted to make predictions. Since the rearrangement is exact, any sufficiently accurate model of the source will yield the correct sound, so other factors must determine the merits of any particular formulation. Using data from a two-dimensional mixing layer direct numerical simulation (DNS), we evaluate the robustness of two analogy formulations to different errors intentionally introduced into the source. The motivation is that since S can not be perfectly modeled, analogies that are less sensitive to errors in S are preferable. Our assessment is made within the framework of Goldstein's generalized acoustic analogy, in which different choices of a base flow used in constructing L give different sources S and thus different analogies. A uniform base flow yields a Lighthill-like analogy, which we evaluate against a formulation in which the base flow is the actual mean flow of the DNS. The more complex mean flow formulation is found to be significantly more robust to errors in the energetic turbulent fluctuations, but its advantage is less pronounced when errors are made in the smaller scales.