Reflection Of Plane Acoustic Waves Research Articles

Identification of aero-acoustic scattering matrices from large eddy simulation. Application to a sudden area expansion of a duct

A methodology is presented which allows to determine the coefficients of transmission and reflection of plane acoustic waves at flow discontinuities in piping systems by combining large eddy simulation (LES) of turbulent compressible flows with system identification. The method works as follows. At first, an LES with external, broadband excitation of acoustic waves is carried out. Time series of acoustic data are extracted from the computed flow field and analyzed with system identification techniques in order to determine the acoustic scattering coefficients for a range of frequencies. The combination of broadband excitation with highly parallelized LES makes the overall approach quite efficient, despite the difficulties associated with simulation of low-Mach number compressible flows. The method is very general, here it is applied to study the scattering behavior of acoustic waves at a sudden change in cross-section in a duct system. The complex aero-acoustic interactions between acoustic waves and free shear layers are captured in detail by high resolution compressible LES, such that the scattering coefficients can be determined accurately from first principles. In order to demonstrate the reliability and accuracy of the method, the results for the scattering behavior and the acoustic impedance are presented and physically interpreted in combination with several analytical models and experimental data.

Reflection of plane acoustic waves from a layer of varying density

Analytical solutions of the Helmholtz equation are derived for the reflection of plane acoustic waves from a layer of varying density between two homogeneous media. The solutions show that the reflection coefficient is dependent on dimensionless vertical wavenumber and on the shape of the density profile in the intermediate layer. The most general case considered is one in which a step change in density is followed by a continuously varying density profile in a transition layer of finite thickness. Results are presented illustrating the dependence of reflection coefficient on wavenumber and on the structure of the transition layer. It is demonstrated that, in the limit of very low wavenumber or grazing incidence, the reflection coefficient tends to the Rayleigh coefficient appropriate to the overall density change between upper and lower media, while, in the high wavenumber limit, the reflection is given by the Rayleigh coefficient for the step change only.

Wave reflection from a sediment layer with depth-dependent properties

The reflection of plane acoustic waves at the water–sediment interface is analyzed. The sediments are modeled using Biot’s equations with depth-dependent coefficients. Computations are made of the reflection coefficient as a function of the incident wave frequency and angle for representative sediment properties. The results are compared to those obtained by modeling the sediments as a homogeneous viscoelastic material and as a viscoelastic material with depth-dependent properties. It is shown that both of these models yield predictions of the reflection coefficient that can differ substantially from the Biot model.