Sound generation by turbulence and surfaces in arbitrary motion

Abstract

The Lighthill-Curle theory of aerodynamic sound is extended to include arbitrary convective motion. The Kirchhoff description of a homogeneous wave field in terms of surface boundary conditions is also generalized to surfaces in arbitrary motion. The extension is at variance with the two previously published accounts of this problem which are erroneous. When both the bounding surfaces and the turbulence are compact relative to the radiated length scales, the turbulence is acoustically equivalent to a volume distribution of moving quadrupoles and the surfaces to dipole and monopole distributions. At low convective speed, their field increases as powers of the Doppler factor [1 - M ,[ -1 Convective acceleration generally gives rise to new source terms at this condition. At the Mach wave condition when the Doppler factor is singular, both the turbulence and surfaces are non-compact and are acoustically equivalent to monopole distributions. Convective acceleration then tends to limit the radiation. At this condition the surface sources are quite unrelated to the low-speed sources, being second order in the field variable contrasting with the linear low-speed terms. At high supersonic convective speeds, the field is dominated by an intensive beaming along the directions of Mach wave emission that lie normal to the surface. The magnitude of the field then varies inversely as the Gaussian surface curvature. If the surface has only single curvature the field is proportional to r 12 and if it is locally plane at this condition, the field no longer decays with distance travelled. There are indications that the surfaceinduced intensity increases as the square of surface speed at high supersonic speeds.

Numerical Investigation of Hydrodynamic Instabilities in Singing Risers

“…The main idea is to locate the acoustic point sources in an incompressible model and assess their energy level by means of the Lighthill tensor and in a next step, compute Green's functions of their far field radiation. Ffowcs Williams and Hawkings [14], Powell [41] and Howe [19] adopt similar approaches using the Lighthill tensor.…”

“…First of all, we recall the incompressible steady Navier-Stokes equations: (13) We consider the following velocity and pressure profiles: (14) The perturbed equations are deduced by introducing this velocity profile in the NS equations:…”

Impact of chevron spacing and asymmetric distribution on supersonic jet acoustics and flow

“…The unilateral reductions in comparison to the standard configuration were not achieved by the beveled configuration, with the spacing in the overexpanded regime exceeding the standard configuration. Back calculation of the BSAN peak frequency assuming the convective velocity is 70 percent of the fully expanded jet velocity [63] (Eq. (2)) indicated that the relation between the configuration and the peak frequency increase was captured using this analysis method.…”

Broadband noise prediction when turbulence simulation is available—Derivation of Formulation 2B and its statistical analysis

“…Let r' be the density perturbation and define p' = c 2 r £ , with c being the speed of sound in the undisturbed medium. The FW-H equation is [12]:…”

“…To improve broadband noise prediction, a physics based methodology based on FW-H or FW -H pds equations is proposed here assuming that the detailed pressure and velocity fluctuations are known on or near the blade (FW-H eq. [12]) or on the data surface (FW -H pds eq. [13]).…”