Convected Wave Equation for a Moving Body in an Inhomogeneous Flow 2018-01-1517

Sound field around a moving body in a mean flow of fluid is commonly estimated with Ffowcs Williams and Hawkings equation. Similarly as Lighthill’s aeroacoustic analogy, Ffowcs Williams and Hawkings equation includes sound propagation phenomena in moving and inhomogeneous media, such as convection and refraction, implicitly within the source terms on the right-hand side of the equation. Consequently, the equation is primarily applicable when the surrounding fluid is quiescent everywhere outside the source region. In this work, we follow the approach of Phillips and derive an exact aeroacoustic equation for a moving body in an inviscid and isentropic flow, which separates source and propagation terms on the two sides of the equation. As such, the equation can be used even when the sound propagation effects have a significant influence on the sound field. In order to acquire a formulation with pressure perturbation as the unknown variable, linearized form of the equation is derived, which assumes small perturbations of the mean flow and constant static pressure. Although the linearized formulation is not suitable for essentially non-linear aeroacoustic sources, it remains valid for linear flow-acoustic interaction, for example at sharp trailing edges. This is demonstrated on an example of sound radiation from an open pipe with a hot mean flow. Supplied with an appropriate model for vortex-sound interaction terms, the equation can be used for estimation of sound field in low Mach number flows, for example, at the outlets of HVAC systems.