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

Abstract

An explicit, analytical, multiple-scales 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 taken is representative of a high-bypass turbofan aircraft engine, with typical Mach numbers of 0.5-0.7, circumferential mode numbers m of 10-40, dimensionless wavenumbers 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 results for iso-pressure contour plots compare quite well 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.

On the Azimuthal Mode Propagation in Axisymmetric Duct FLows

“…8 The main pattern of the CAA results agree rather well with the FEM and MS solutions. However, the CAA solutions are much more close to the FEM solutions.…”

“…For furtherly showing the capability of the 2.5D CAA procedure, an axisymmetric inlet with aero-engine like geometry from the paper of Rienstra & Eversman 8 is selected for benchmarking. The outer and inner wall radius r 2 and r 1 are described by…”

“…This is different from the quasi one-dimensional potential mean flow used in the FEM and MS computations. 8 Since the analytical sound source requires a uniform mean flow, this difference results in the inconsistence at the source boundary region in the CAA computations. For this reason, unsmoothed numerical solutions should be expected to be observed in the current numerical results.…”

“…Furthermore some numerical results are given for an aeroengine inlet duct geometry with flow and compared with the results of the FEM and MS methods. 8 Finally a turning plane case is simulated and analyzed.…”

Cut-on Cut-off Transition in Flow Ducts: Comparing Multiple-scales and Finite-element Solutions

“…Indeed, a recent comparison of multiple-scales solutions of sound propagation with those obtained from a numerical finite-element method shows good agreement across a range of realistic engine frequencies. 5 The multiple-scales approach allows sound transmission to be represented by a summation of slowly varying modes, which depend on a slow axial variable based on the the slope of the duct walls as a small parameter. Crucially, the amplitudes of these modes vary on the slow scale and are determined via a solvability condition.…”