Non-linear propagation of plane-wave mode in an axisymteric lined duct

We now consider the non-linear propagation of a plane-wave (ka=7.39, R=1) with 2 harmonics. The impedances for the first and second harmonic are (3,­0.1) and (2,-0.1). The mesh size is 201×11. At the fan face, only the first harmonic is imposed with a high amplitude of 4000 Pa corresponding to 172 dB SPL. The liner is positionned between x=2.5 and x=7.5. The real part of the acoustic pressure is displayed in Figure 12. It is clear that the second harmonic grows fairly rapidly due to the non-linear effect and reachs more than 160 dB at the liner leading edge. Next both amplitudes decreased due to the presence of the liner. It is noted that the amplitude of the second harmonic grows again in the hard wall section. The SPL at the tip section is shown in Figure 13 for both harmonic. It is noted that the mesh size is sufficient for the highest harmonic with about 8.5 PPW.

2. Summary

A numerical method for studying the linear and non-linear, 2D and axisy – metric propagation of acoustic waves has been presented. The numerical re­sults confirm its accuracy and efficiency. Excellent results were obtained for the NASA Flow impedance tube. The propagation and radiation of spinning mode in a lined duct are presented. Good agreements are obtained for non­linear propagation in a 2D duct. The propagation of high SPL fan tone noise is presented with the lined duct. Further work will be focused on the non­linear propagation and radiation of spinning mode with acoustic liner as well as validations.

Figure 1. NASA Flow Impedance Tube: SPL for M = 0.3 and f = 500 Hz

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f igure 2. NASA Flow Impedance Tube: Phase tor M = 0.3 and t = 500 Н/

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-і 1П 1 ‘ ‘ ■ ■ 1 ■ ■ ■ 1.. ………………… ……….. _____ I_____ I L

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Figure 6. Acoustic field with the fight inlet

Figure 7. Far-field sound pressure level for the (2,2) mode with ka = 11.67

Figure 10. Pressure distribution of the first and second harmonics

Figure 11.

Amplitude of the second harmonics

Figure 12. Acoustic field of the first and second harmonics for a plane wave propagation in a axisymetric lined duct. Top: 1st harmonic – Bottom: 2nd harmonic

Figure 13. SPL (tip) of the first and second harmonics for a plane wave propagation in a axisymetric lined duct Z1 = (3,-0.1),Z2 = (2,-0.1)