A numerical comparison between multiple-scales and eem solution for sound propagation s lined flow ducts

An explicit, analytical, multiple-scales solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining, is tested against a numerically "exact" finite element solution. The test geometry taken is representative of a high-bypass turbo fan aircraft engine, with typical Mach numbers 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 in predicted power attenuation loss show in general a very good agreement. The results in iso-pressure contour plots show good comparison in the cases where scattering into many higher radial modes can occur easily (high frequency, low angular mode), and again a very good agreement in the other cases.