A Isoparametric Hermitian Finite Element for Duct Acoustics with Flow

A new cubic isoparametric Hermitian hexahedral finite element is developed to efficiently model the propagation of sound through rigid walled duct bends and junctions. With the goal of improved technology transfer, the computer programs developed are implemented on a desk top computer. The element is first tested for the acoustic enclosure eigenvalue problem and the incompressible potential fluid flow problem. It is demonstrated that the new element generally gives more accurate results, on a degree of freedom basis, than the conventional cubic isoparametric element, but under certain distortions is less accurate. A finite element model using this element is then developed to study the propagation of sound through duct bends and junctions including the convective effect of low Mach number steady fluid flow, modeled using incompressible potential flow theory. The finite element solution for the flow field is obtained first and then used in the acoustic finite element model. Higher order mode boundary conditions are considered in linking the junction or bend finite element models to anechoically terminated straight ducts containing uniform flow. The method is then tested by considering up to and including third cross mode propagation in a two -dimensional straight duct with a uniform flow at Mach 0.1. Models with three elements across the duct width gave accurate predictions up to a duct width to wavelength ratio of two. The procedure is then used to study several duct bends and junctions. It is found that due to the complexity of the geometry and sound fields, with the largest numerical models that could be handled by the desk top computer, accurate results could only be obtained for propagation of the plane wave and first cross mode up to a duct width to wavelength ratio approaching one. A 90^ circ and a 45^circ side branch are considered. The effect of varying the side branch width and flow is demonstrated. It is found that, for inlet Mach numbers of 0.1 or less, the effect of flow on the bend and junction transmission losses is small.