Microstructure based modelling of the thermal and viscous dissipation of a transversely isotropic porous fibrous insulation material

This paper focusses on the modelling and prediction of two of the main mechanisms of acoustic attenuation, the dynamic drag and thermal heat transfer, of a bundle of fibres typical of lightweight fibrous porous materials. The methodology uses geometrical properties derived from microscopy, and is based on the assumption that the interaction between the shear stress fields as well as the thermal fields of neighbouring fibres, may be neglected in the predicted dynamic impedances of an individual fibre. Analytical procedures are discussed which provide an estimation of the impedances acting on infinite longitudinal and transversely orientated cylinders. The frequency-dependent viscous and thermal contributions may be scaled in terms of statistical fibre diameter distributions and orientation angles. Using these analytical models, a three-dimensional poroelastic model of coupled acoustic and structural wave propagation through a transversely isotropic, fibrous, highly porous thermal insulation material is presented.QC 20181213