Resolvent-based jet noise models: a projection approach

Abstract

Linear resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-deduced counterparts from high-fidelity large-eddy simulations (LES). However, leveraging resolvent modes for reconstructing statistics of the far acoustic field remains elusive. In this study, we use a LES database to produce an ensemble of realizations for the acoustic field that we project on to a limited set of n resolvent modes. The projections are done on a restricted acoustic output domain, r/D= [5,6], and allow for the LES realizations to be recast in the resolvent basis via a data-deduced, low-rank, n x n cross-spectral density matrix. We find substantial improvements to the acoustic field reconstructions with the addition of a RANS-derived eddy-viscosity model to the resolvent operator. The reconstructions quantitatively match the most energetic regions of the acoustic field across Strouhal numbers, St= [0−1], and azimuthal wavenumbers, m= [0,2], using only three resolvent modes. Finally, the characteristics of the resulting n x n covariance matrices are examined and suggest off-diagonal terms may be neglected for n ≤ 3. Results are presented for round, isothermal, Mach 1.5 and 0.9 jets.