Mechanisms of Sound Absorption in Nanofibrous Materials

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In this project, in collaboration with our industrial partner, we will investigate how acoustic waves propagate in ducts of various shapes and forms. We will in particular study two specific aspects:- the influence of a background flow on the acoustic propagation- the influence of surface lining on the acoustic propagationThe aim being to reduce the sound propagation to one simple equation with some boundary conditions (of impedance type) on the surface of the duct while retaining the important physical aspects of the problem.Over the past 20 years, a lot of work has been carried out in this area including- considering boundary conditions that take the boundary layer of the flow into consideration and ensure that the obtained equations are numerically stable- considering different types of background flows- considering the effect of viscosity- ducts with different cross-sections and/or with slowly varying geometryThe project will start by reviewing and reproducing these results. The ultimate aim being to consider acoustic propagation within an annulus duct whose outer radius increases slowly in the downstream direction. The flow within the duct will be of swirling type, and we will assume that the walls of the duct are lined. The objective is to obtain a simple equation and associated impedance type boundary condition that will effectively model the acoustic propagation within such ducts that our industrial partner could use as a predictive modelling tool.The student will use a mix of analytical and numerical techniques. In particular, a complex eigenvalue tracking algorithm will play a crucial role in the project.