A high-order finite element model for acoustic propagation

Abstract

Sound propagation in complex non-uniform mean flows is an important research area for transport, building and power generation industries. Unsteady flows are responsible for noise generation in rotating and pulsating machines. Sound propagates in ducts and radiates through their openings. Duct discontinuities and complex flow effects on acoustic propagation need to be investigated. Although it provides accurate results, the most commonly used Computational AeroAcoustics propagation method, the full potential theory, does not describe the whole physics. Turbofan exhaust noise radiation involves strong refraction of the sound field occurring through jet shear layer, as well as interaction between the acoustic field and the vorticity/entropy waves. The Linearised Euler Equations are able to represent these effects. Solving these equations with time-domain solvers presents shortcomings such as linear instabilities and impedance modelling, which can be avoided by solving in the frequency domain. Nevertheless the classical Finite Element Method in frequency domain suffers from dispersion error and high memory requirements. These drawbacks are particularly critical at high frequencies and with the Linearised Euler Equations, which involve up to five unknowns. To circumvent these obstacles a novel approach is developed in this thesis, using a high-order Finite Element Method to solve the Linearised Euler Equations in the frequency domain. The model involves high-order polynomial shape functions with unstructured triangular meshes, numerical stabilisation and Perfectly Matched Layers. The computational effort is further optimised by coupling the Linearised Euler Equations in the regions of complex sheared mean flow with the Linearised Potential Equation in the regions of irrotational mean flow. The numerical model is applied to aeroengine acoustic propagation either by an intake or by an exhaust. Comparisons with analytic solutions demonstrate the method accuracy which properly represents the acoustic and vorticity waves, as well as the refraction of the sound field across the jet shear layer. The benefits in terms of memory requirements and computation time are significant in comparison to the standard low-order Finite Element Method, even more so with the coupling technique.

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