Non-linear propagation of plane wave in a 2D duct

The non-linear implementation is validated against the analytical solution, exact for the first and second order terms given by C. Campos-Pozuelo & J. A. Gallego-Juarez [2]. The test case is a plane wave with high amplitude propa­gating in a 2D duct. According to the theory, the second harmonic will grow proportionally to the distance of the source location. The frequency of the plane wave is 100 Hz, the duct length is 10 m, the mesh size is 201×11 and it is a zero few case. Only two harmonics are considered in the computation. The real part of the pressure for the 1st and the 2nd harmonics versus distance from the source plane are plotted in Figure 16. The comparison between analytical and computational amplitude of the 2nd harmonic along the duct is shown in Figure 17. Excellent agreement is achieved, although some refection at the outflow boundary is present. The present method is therefore suitable for the propagation of N-wave. An example of such computation with 4 harmonics is shown in Figure 18 and Fig ure 19. The N-wave characteristics are conserved during the propagation, showing that the current modeling might be suitable for the modeling of the spinning mode with high sound pressure level or N – wave type.

Radiation of duct mode with acoustic liner

In [15], the present solver is validated with experimental data with wall case. The same type of computation is reported here with the filght inlet from the experimental set-up reported by Silcox [17]. Figure 6 illustrates the resultant acoustic wave patterns for the mode (2,2) ka=11.67 corresponding the Figure 12 of [17]. The corresponding far-field SPL is displayed in Figure 7. The three lobes pattern in SPL are particular to the 2nd radial mode. The computed far – field SPL reproduces well the directivity as well as the magnitude. The second lobe is underestimated by about 2-4 dB.

Now, the ability of the code is demonstrated with acoustic liner. The case from [15] is repeated with the acoustic liner set-up with the following param­eters: Z=(2.21,-1.54),2 different frequencies (853 Hz and 1853 Hz) and mode (4,0). Figure 7 and 9 illustrates the acoustic pressure contours (real part). It is clear from the acoustic pressure contours that the liner caused absorption of sound, and that the scattering of higher radial modes is present for higher cut – on mode (1853Hz). At the fan face, only the first radial mode was imposed, but the SPL in far-field will exhibits a strong three lobes pattern from the 2nd radial mode. The first radial mode is also present but not clear due to its lower amplitude.