Adjoint Linearised Euler solver and Source Modelling for Goldstein acoustic analogy equations for 3D jet flow problems: verification and capability study

The Adjoint Linearised Euler Solver of Karabasov and Hynes (2006), which includes an efficient iterative solution of linearised Euler equations in the frequency domain, has been extended to a 3D framework. Numerical tests performed for the problem of sound scattering from an axi-symmetric Gaussian jet flow show a very good performance of the method for a range of frequencies and observer angles as compared with the reference semianalytical solution. A new approach has been introduced for evaluating the source terms of the Goldstein acoustic analogy equations based on the second-order statistics provided directly from Large Eddy Simulation (LES). In comparison with the previous works, the new procedure is completely free from modelling assumptions, such as the functional behavior of the auto-covariance stress tensor or the dependence of the correlation scales of frequency. This makes the Goldstein acoustic analogy modelling based on LES practically applicable to general 3D flows and allows not only computing the far-field pressure spectra but also the reconstruction of effective volume noise sources. In comparison with the standard integral surface methods such as the Ffowcs Williams – Hawkings (FW-H) penetrable surface formulation, the new approach is potentially more robust since it has no sensitivity to the acoustic surface location. For the proof-of-concept study, acoustic predictions are made for two static single-stream co-axial jets at acoustic Mach number V /c = 0.875 that correspond to the temperature ratios T /T = 1 and T /T = 2.5. Comparisons with the reference penetrable FW-H solutions and the scaled QinetiQ experiment data are performed. The budgets of acoustic power spectral density for the individual source terms of the acoustic analogy model are also provided.