Robustness of Acoustic Analogies for Predicting Mixing-Layer Noise

Abstract

Acoustic analogies for the prediction of flow noise are exact rearrangements of the flow equations N(q) = 0 into a nominal sound source S(q) and sound propagation operator C such that L q = S(q). In practice, the sound source is typically modeled and the propagation operator inverted to make predictions. Because the rearrangement is exact, any sufficiently accurate model of the source will yield the correct sound, and so other factors must determine the merits of any particular formulation. Using data from a two-dimensional mixing-layer direct numerical simulation, we evaluate the robustness of several formulations to different errors intentionally introduced into the source. The motivation is that because S cannot 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. 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 direct numerical simulation and also against a globally parallel base flow that gives a Lilley-like analogy. The more complex mean-flow formulations are found to be significantly more robust to errors in the energetic turbulent fluctuations, but the advantage is less clear when errors are introduced at smaller scales.