A numerical comparison between the multiple-scale and finite-element solution for sound propagation in lined flow ducts.

*(English)*Zbl 0982.76077Summary: An explicit analytical multiple-scale solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining is tested against a numerical finite element solution, solving the same potential flow equations. The test geometry is representative of a high-bypass turbofan aircraft engine, with typical Mach number of 0.5-0.7, circumferential mode numbers \(m\) of 10-40, dimensionless wave-numbers of 10-50, and both hard and acoustically treated inlet walls of impedance \(Z= 2-i\). Of special interest is the presence of the spinner, which incorporates a geometrical complexity which could previously only be handled by fully numerical solutions. The results for predicted power attenuation loss show in general a very good agreement. The result for iso-pressure contour plots compare quite well in the cases where scattering into many higher radial modes can easily occur (high frequency, low angular mode), and again a very good agreement is found in other cases.

##### MSC:

76Q05 | Hydro- and aero-acoustics |

76M10 | Finite element methods applied to problems in fluid mechanics |