Azimuthal mode analysis of broadband shock-associated noise in an under-expanded axisymmetric jet

Abstract

Broadband shock-associated noise (BBSAN) is a high frequency noise generated in imperfectly expanded jets from the interaction of turbulent structures and shock-cells. This paper presents an azimuthal mode analysis of BBSAN in the jet, near-field and far-field from an unstructured large-eddy simulation of a non-screeching supersonic under-expanded jet. The studied supersonic jet is issued from a round convergent nozzle with a perfectly expanded Mach number of 1.15 and Reynolds number based on the nozzle diameter of 1.25 × 106. Aerodynamic and far-field acoustic numerical results are validated against experiments. Pressure fluctuations represented in the frequency-wavenumber domain follow the neutral waves from a vortex-sheet model of an ideally expanded jet. The far-field pressure field is decomposed in azimuthal modes based on Fourier coefficients, showing three different regions: broadband behaviour of the mixing noise for downstream angles below 50° with the first modes containing most of the energy, BBSAN with similar amplitudes for the first 4 azimuthal modes at central angles between 50° and 130°, and distinct modes at upstream angles above 130°. A decomposition in negative/positive phase-velocity waves of the jet and near-field pressure field allows the identification of these characteristic modes. The complexity of the flow is illustrated with the analysis of the root-mean-square and spectral contents of the first 4 azimuthal modes. The modes exhibit peaks at different shock-cells and radial positions as well as depicting particular radiation patterns that depend on both the mode and frequency.