Wave-Packet Representation of Shock-Cell Noise for a Single Round Jet

Abstract

From a viewpoint analogous to the wave-packet model, the shock-cell-noise model developed by Harper-Bourne and Fisher (“The Noise from Shock Waves in Supersonic Jets,” AGARD Rept. CP-131, 1974) is directly evaluated using unsteady pressure fields computed with a large-eddy simulation. Continuum two-point correlation functions of near-field pressure fluctuations in a single round jet are projected to acoustic fields as a boundary-value problem, and the expression is transformed into a discrete representation equivalent to the Harper-Bourne and Fisher model. In this process, the two-point correlation is reconstructed using the snapshot proper orthogonal decomposition technique in the frequency domain (namely, the cross-spectral correlation). Accordingly, hydrodynamic and acoustic fields associated with shock-cell noise are visualized for each azimuthal mode. From explicit correspondence between the Harper-Bourne and Fisher model and the cross-spectral correlation function, the validity of the model is analyzed in terms of the active shock-cell sites, the correlation length, the phase velocity, and the contributions from azimuthal modes as a function of the Strouhal number. Many aspects of the Harper-Bourne and Fisher model, such as the discrete nature and the correlation length scale, are justified; on the other hand, the importance of some missing aspects, especially the azimuthal content and the harmonic wave-number components, is found at a Strouhal number of approximately two or higher.