Extensions of Lighthill's acoustic analogy with application to computational aeroacoustics

Abstract

Lighthill's aeroacoustic analogy is formulated for bounded domains in a general way that allows pressure-based alternatives to the fluid density as wave variable. The advantage relative to the standard version (Ffowcs Williams & Hawkings 1969 Phil. Trans. R. Soc. A 264 , 321–342) is that the equivalent surface source terms needed for boundary value problems do not involve the local density. Difficulties encountered in computational aeroacoustics with standard wave extrapolation procedures, due to advection of density inhomogeneities across the control surface, are thereby avoided. Likewise, in initial-value problems, the equivalent volume source terms that represent initial conditions do not involve the density either. The paper ends with an extension to parallel shear flows, in which a modified aeroacoustic analogy due to Goldstein (Goldstein 2001 J. Fluid Mech . 443 , 231–236) is formulated for bounded domains using a similar windowed-variable approach. The results provide a basis for acoustic wave extrapolation from jets and boundary layers, where the control surface cuts through a sheared mean flow.