Sound radiation in turbulent channel flows

Lighthill’s acoustic analogy is formulated for turbulent channel flow with pressure as the acoustic variable, and integrated over the channel width to produce a two-dimensional inhomogeneous wave equation. The equivalent sources consist of a dipole distribution related to the sum of the viscous shear stresses on the two walls, together with monopole and quadrupole distributions related to the unsteady turbulent dissipation and Reynolds stresses respectively. Using a rigid-boundary Green function, an expression is found for the power spectrum of the far-field pressure radiated per unit channel area. Direct numerical simulations (DNS) of turbulent plane Poiseuille and Couette flow have been performed in large computational domains in order to obtain good resolution of the low-wavenumber source behaviour. Analysis of the DNS databases for all sound radiation sources shows that their wavenumber–frequency spectra have non-zero limits at low wavenumber. The sound power per unit channel area radiated by the dipole distribution is proportional to Mach number squared, while the monopole and quadrupole contributions are proportional to the fourth power of Mach number. Below a particular Mach number determined by the frequency and radiation direction, the dipole radiation due to the wall shear stress dominates the far field. The quadrupole takes over at Mach numbers above about 0.1, while the monopole is always the smallest term. The resultant acoustic field at any point in the channel consists of a statistically diffuse assembly of plane waves, with spectrum limited by damping to a value that is independent of Mach number in the low-M limit

Sound radiation from a turbulent boundary layer

Sound radiation due to fluctuating viscous wall shear stresses in a plane turbulent boundary layer is investigated by a two-stage procedure using direct numerical simulation (DNS) databases for incompressible turbulent Poiseuille flow in a plane channel, at Reynolds numbers up to Re?=1440. The power spectral density of radiated pressure and spectra of sound power per unit wall area are calculated in the low Mach number limit by substituting source terms obtained from DNS into a Ffowcs Williams–Hawkings wave equation and using a half-space Green function. The same DNS data are used to predict the spectrum of turbulent boundary layer noise measured in a diffuser downstream of a fully developed channel flow [Greshilov and Mironov, Sov. Phys. Acoust. 29, 275 (1983)]. The measured spectrum is ~15 dB higher at low frequencies, but converges with the prediction at high frequencies

Linear and nonlinear mechanisms of sound radiation by instability waves in subsonic jets

Linear and nonlinear mechanisms of sound generation in subsonic jets are investigated by numerical simulations of the compressible Navier–Stokes equations. The main goal is to demonstrate that low-frequency waves resulting from nonlinear interaction between primary, highly amplified, instability waves can be efficient sound radiators in subsonic jets. The current approach allows linear, weakly nonlinear and highly nonlinear mechanisms to be distinguished. It is demonstrated that low-frequency waves resulting from nonlinear interaction are more efficient in radiating sound when compared to linear instability waves radiating directly at the same frequencies. The results show that low-frequency sound radiated predominantly in the downstream direction and characterized by a broadband spectral peak near St = 0.2 can be observed in the simulations and described in terms of the nonlinear interaction model. It is also shown that coherent low-frequency sound radiated at higher angles to the jet axis (? = 60°–707°) is likely to come from the interaction between two helical modes with azimuthal wavenumbers n = ±1. High-frequency noise in both downstream and side-line directions seems to originate from the breakdown of the jet into smaller structure

Validating the ffowcs williams and hawkings acoustic analogy implementation in antares

Progress is presented in the development of a Ffowcs Williams and Hawkings (FW-H) acoustic analogy post-processor for time-resolved Computational Fluid Dynamics (CFD) simulations. The tool is coded in Python and embedded in Antares, a post-treatment package (developed by Cerfacs, France) of wide access and usability for the scientific community. Tests on monopoles, dipoles, and quadrupoles show good predictions of pressure fluctuation and directivity against reference analytical results, validating the software for applications to stationary elementary sources. The proximity of these sources to a corner of the FW-H integration surface is shown to adversely affect the predictions and good agreement with the benchmark sound field is restored by an appropriate sizing and placement of the FW-H surface. Guidelines for obtaining predictions that are substantially independent of the size and placement of the FW-H surface are provided in terms of the spatial resolution of the discretised FW-H surface