Effects of jet flow on jet noise via an extension to the Lighthill model

Abstract

The Lighthill formalism for jet noise prediction is extended to accommodate wave transport by the mean jet flow. The extended theory combines the simplicity of the Lighthill approach with the generality of the more complex Lilley approach. There is full allowance for ‘flow-acoustic’ effects: shielding, as well as the refractive ‘cone of (relative) silence’. A source term expansion yielda a convected wave equation that retains the basic Lighthill source term. This leads to a general formula for power spectral density emitted from unit volume as the Lighthill-based value multiplied by a squared ‘normalized’ Green's function. The Green's function, referred to a stationary point source, delineates the refraction dominated ‘cone of silence’. The convective motion of the sources, with its powerful amplifying effect, also directional, is accounted for in the Lighthill factor. Source convection and wave convection are thereby decoupled, in contrast with the Lilley approach: this makes the physics more transparent. Moreover, the normalized Green's function appears to be near unity outside the ‘cone of silence’. This greatly reduces the labour of calculation: the relatively simple Lighthill-based prediction may be used beyond the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected ‘point’ source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are coaxial or shrouding jets: in that case the difference from unity will quantify the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g. hot jets).

On compressibility assumptions in aeroacoustic integrals: A numerical study with subsonic mixing layers

“…These simulations provide both the reference acoustic field and the input data for the Kirchhoff solution (5) and the computation of the Lighthill source quantities (7), (10), (15) and (16).…”

Aero-acoustic computations of wind turbines

“…To solve the Lighthill's acoustic equation, one needs to find a compact region containing source terms and then evaluating integrals around the domain. However, Lighthill's equation is the representation of the source terms where the effect of mean flow to acoustic field is considered [40,38]. This makes it difficult to take into account all the effects where the source region is not only the compact turbulence region [38] but also containing all acoustic-flow interactions.…”

Contribución al estudio y caracterización de la generación de ruido de flujo en el sistema de escape.

“…Para ello, se propone considerar el principio de reciprocidad en la función de Green, que se explicará posteriormente en el apartado 4.3.2. En relación al efecto de la refracción, Ribner [149] señala que la equivalencia entre las aproximaciones realizadas en diversas teorías se produce siempre fuera del cono de silencio, lo que permite considerar que el tratamiento de los efectos acústicos del flujo en el cono refractivo es lo que diferencia unas teorías de otras. Así Ribner sigue considerando el fluido como no viscoso, al igual que clásicamente, y también sigue interpretando el miembro de la derecha de la ecuación (4.1) como una distribución espacial de fuentes de sonido, incorporando todos los efectos del flujo (la turbulencia y flujo medio) en el término fuente, a fin de considerar los efectos de refracción.…”

“…En la misma línea, Ribner [149] comenta que la función de Green referida a un punto fuente estacionario delimita la refracción denominada 'cono de silencio'.…”

“…En todas las teorías descritas anteriormente es posible introducir los efectos de la convección turbulenta a velocidad U c , a través de la teoría de convección de Lighthill-Ffowcs Williams [149].…”