On the calculation of the complex wavenumber of plane waves in rigid-walled low-Mach-number turbulent pipe flows

A numerical method for calculating the wavenumbers of axisymmetric plane waves in rigid walled low-Mach-number turbulent flows is proposed, which is based on solving the linearized Navier-Stokes equations with an eddy viscosity model. In addition, theoretical models for the wavenurnbers are reviewed, and the main effects (the viscothermal effects, the mean flow convection and refraction effects, the turbulent absorption, and the moderate compressibility effects) which may influence the sound propagation are discussed. Compared to the theoretical models, the proposed numerical method has the advantage of potentially including more effects in the computed wavenurnbers. The numerical results of the vvavenumbers are compared with the reviewed theoretical models, as well as experimental data from the literature. It shows that the proposed numerical method can give satisfactory prediction of both the real part (phase shift) and the imaginary part (attenuation) of the measured wavenumbers, especially when the refraction effects or the turbulent absorption effects become important. (C) 2015 Elsevier Ltd. All rights reserved.