Improved jet noise predictions in subsonic flows using an approximate composite asymptotic expansion of the adjoint Green's function in Goldstein's analogy

摘要

Our recent work on jet noise modeling (Afsar et al. 2019, PhilTrans. A., vol. 377) has confirmed that non-parallel flow effects are needed to determine the wave propagation aspect of the jet noise problem. The acoustic spectrum calculated using an asymptotic representation of non-parallel flow effects produces the correct spectral shape of the small angle radiation beyond that which can be predicted using a parallel (i.e. non-spreading) mean flow approximation to determine the wave propagation tensor in Goldstein's generalized acoustic analogy formulation. While the peak noise predicted using this approach works remarkably well at low frequencies (up to and slightly beyond the peak Strouhal number), the high frequency prediction in Afsar et al. (2019) relied upon an ad-hoc composite asymptotic formula for the propagator that was also restricted to the small angle spectra. In this paper we therefore attempt to remedy this defect by using the O(1) frequency locally parallel flow Green's function as a kind-of outer solution to the propagator tensor in which the non-parallel flow theory used in the latter reference acts as the 'inner' solution that is valid at low frequencies and is transcendentally small beyond the peak frequency. The hope is that this approach will allow more robust high frequency predictions with a single set of turbulence parameters for the acoustic spectrum at any given acoustic Mach number. In other words, both non-parallel and locally parallel regions of the propagator tensor solution are multiplied by the same turbulence source structure in the acoustic spectrum integral. The paper highlights the basic formalism of the low frequency jet noise theory and summarises the technical problems and strategy we use to extend this approach to higher frequencies.