Wavepacket modelling of broadband shock-associated noise in supersonic jets

We present a two-point model to investigate the underlying source mechanisms for broadband shock-associated noise (BBSAN) in shock-containing supersonic jets. In the model presented, the generation of BBSAN is assumed to arise from the nonlinear interaction between downstream-propagating coherent structures with the quasi-periodic shock cells in the jet plume. The turbulent perturbations are represented as axially extended wavepackets and the shock cells are modelled as a set of stationary waveguide modes. Unlike previous BBSAN models, the physical parameters describing the hydrodynamic components are not scaled using the acoustic field. Instead, the source characteristics of both the turbulent and shock components are extracted from the hydrodynamic region of large-eddy simulation and particle image velocimetry datasets. Apart from using extracted data, a reduced-order description of the wavepacket structure is obtained using parabolised stability equations. The validity of the model is tested by comparing far-field sound pressure level predictions to azimuthally decomposed experimental acoustic data from a cold Mach 1.5 underexpanded jet. At polar angles and frequencies where BBSAN dominates, encouraging comparisons of the radiated noise spectra for the first three azimuthal modes, in both frequency and amplitude (at peak frequency), reinforce the suitability of using reduced-order wavepacket sources for predicting BBSAN peaks. On the other hand, wavepacket jitter is found to have a critical role in recovering sound amplitude at interpeak frequencies. The paper presents a quantitative demonstration that the wavepacket-shock interaction, carefully reconstructed by extracting components from data or linearised models, contains the correct essential flow physics that accounts for most features of the far-field BBSAN spectra.