A Mode-Matching Model for Sound Radiation From Jet Exhausts With Liners

A semi-analytical model is formulated to predict the radiation of noise out of a jet exhaust with acoustic liners. The exhaust nozzle is described as a semi-infinite straight duct with an infinite centre-body. An acoustic liner can be defined on the duct wall and centre-body surface. This liner is locally reacting and can be segmented in the axial direction. The duct carries a uniform flow that is surrounded by a uniform ambient flow. The two flows are separated by a vortex sheet shed from the duct. The radiation to the far field is modelled using a perfectly matched layer on the outer boundary. The sound field in each segment is expanded in terms of the eigenmodes of the duct that are calculated numerically using a spectral method. A mode-matching procedure is then applied to match the sound fields across the interfaces between the segments. While this model is relatively simple, it is easier to implement than analytical models based on the Wiener-Hopf technique. It is significantly faster than more detailed numerical models using CAA techniques (finite elements, finite differences, etc). The model is described and validated against a number of reference solutions obtained with the Wiener-Hopf method. The effects of the ambient flow and the jet temperature on the radiation are investigated.