Unifying the stationary and convective Ffowcs Williams and Hawkings solutions for aeroacoustic predictions via a Lorentz transformation

Abstract

The convective Ffowcs Williams and Hawkings (FW-H) equation and its integral solutions are often used for noise predictions of aeroacoustic phenomena in moving mediums. In this study, a set of unified integral solutions for stationary and convective FW-H equations are proposed by making use of the extended Lorentz transformation for arbitrary mean flow orientations. The new solutions in Euclidean coordinates have compact forms that resemble the well-known F1 and F1A solutions of Farassat, with the main differences from existing ones in the definitions of the equivalent monopole and dipole sources, and also their associated equivalent thickness noise and loading noise. Validations have been performed for two benchmark problems in moving mediums, one is a stationery monopole source and the other is a rotating dipole source. Apart from the well-recognized distorted acoustic fields due to the convective amplification, the results also show that the convective effects induce dipole-like acoustic components for a pure monopole source and monopole-like acoustic components for a pure dipole source. These are explained well by the newly-derived unified integral solutions and provide more insights on the noise source mechanisms.