SummarySound propagation in complex non-uniform mean flows is an important feature of turbofan exhaust noise radiation. The Linearised Euler Equations are able to represent the strong shear layer refraction effects on the sound field, as well as multiple length scales. Frequency domain solvers are suitable for tonal noise and considered a way to avoid linear instabilities, which may occur with time domain solvers. However, the classical Finite Element Method suffers from dispersion error and high memory requirements. These shortcomings are particularly critical for high frequencies and for the Linearised Euler Equations, which involve up to five unknowns. In this paper, a high-order Finite Element Method is used to solve the Linearised Euler Equations in the frequency domain in order to overcome those issues. The model involves high-order polynomial shape functions, unstructured triangular meshes, numerical stabilisation and Perfectly Matched Layers. The acoustic radiation from a straight circular semi-infinite hard-wall duct with several mean flow configurations is computed. Comparisons with analytic solutions demonstrate the method accuracy. The acoustic and vorticity waves are well represented, as well as the refraction of the sound field across the jet shear layer. The high-order approach allows to use coarse meshes, while maintaining a sufficient accuracy. The benefits in terms of memory requirements are significant when compared to standard low-order Finite Element Method.

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The propagation of sound in complex flows is a critical issue for many industries. When modeling turbomachinery noise radiating from engine exhausts, the jet shear layer induces a strong refraction of the sound waves. This can be described by the Linearised Euler Equations (LEE). Most of the difficulties associated with time-domain solutions of the LEE can be avoided by working in the frequency domain. Standard finite elements suffer from large dispersion errors and to improve the computational efficiency we resort here to highorder FEM. The FEM is also known to encounter stability issues for advection-diffusion problems that can be corrected by adding artificial diffusion terms in the formulation. In this paper, we aim at investigating dedicated high-order stabilisation schemes for the time-harmonic LEE. A dispersion analysis of the one-dimensional time-harmonic transport equation is provided. The optimal stabilisation parameter is derived so as to cancel the dispersion error, for each polynomial order of the shape functions. The performance of the resulting stabilised formulation is investigated on a two-dimensional test case with unstructured meshes. The steady parameter used in the literature for the LEE performs well in the high-resolution regime, as attested by the results of the sound propagation from a semi-infinite circular duct with non-uniform mean flow. The sound propagation and radiation are accurately described, as well as the interactions between the acoustic waves and the hydrodynamic field resulting in the vorticity shedding from the duct lip.

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As in many industries, NVH reduction in the automotive market requires car manufacturers to adapt their designs and development methods. In particular duct system design necessitates accurate methods to capture the resonance frequencies and address noise phenomena. To do so, engineers evaluate the quality of the components through numerical simulations and validate against real-life measurements. Two main challenges arise: the simulations are often ran by non-numerical experts, who might have difficulties with setting up the models. Secondly, the computation techniques, together with the model preparation, need to be efficient to improve productivity. In this paper, an automated workflow is presented to democratize numerical techniques in duct design and sound transmission loss computation. It gives the possibility for non-experts to easily set up and solve their models with few input parameters. Furthermore, effective numerical techniques based on high-order shape functions with a-priori error estimator are used to optimize performance and accuracy: FEMAO and BEMAO (Finite/Boundary Element Methods with Adaptive Order). Two models are exposed: a simple duct line with three Helmholtz resonators, and a more complex intake system. The numerical results of the different methods are compared, as well as measurements.