| Περίληψη: | The prediction of the acoustic field produced by a known sound source around a complex geometry is investigated. On the triangulated surface of a solid object sound is reflected from the planar surfaces of the triangles and is diffracted by edges of two adjacent triangles that are not co-planar. The present thesis involves the use of existing frequency-domain solutions to describe the contribution of each part of the geometry and an algorithm, suited for complex geometries with large number of triangles, which replaces each part of the geometry with its corresponding virtual source. Specifically, planar surfaces are replaced with virtual sources according to the image source method (to account for reflections), while the edges of adjacent non-planar surfaces by virtual sources according to the Directive Line Source Model (to account for edge diffraction). This method has been proven by Menounou, Klagkos to be quite accurate even though multiple-diffraction propagation paths could not be calculated and were ignored by the algorithm.
In this thesis, the method is extended to include multiple and higher-order diffraction by wedges using the enhanced Directive Line Source Model . The algorithm we propose here proves to be able to identify every propagation path regardless the geometry of the problem. Complex propagation paths that include multiple reflections between diffractions can now be handled, making sure that no physical path is ignored.
The virtual source method, being an image source method, does not suffer from numerical or undersampling errors which occur in ray and beam tracing methods and computational aeroacoustics methods. Moreover, the computational cost remains the same irrespective of the sound source frequency or the propagation distance. Thus, it is applicable to any geometry and for any frequency, unlike the finite element and boundary element methods which encounter problems when the frequency is high or when the geometry is complex.
The geometries considered span from noise barriers on the ground and desks configurations inside an office, to airfoil geometries. In the cases examined the surrounding fluid was considered quiescent and homogenous, the sound source an omni-directional spherical source, while the surfaces of the objects rigid or partially absorbing. The results obtained with our model show good agreement with experimental data and/or results from other numerical methods, especially in the cases where parallel edges are present like double or triple knife-edge barriers, single wide barriers and the doubly inclined barrier. The discrepancies that appear in the case of the desk geometry can be eliminated by increasing the order of diffraction and the order of reflection in order to achieve convergence and by employing more realistic absorption coefficients. In the case of the airfoil, despite not having experimental data for comparison, the predicted acoustic pressure field seems to be realistic as we increase the order of diffraction. The predicted diffraction paths illuminate areas that were previously in the shadow regions.
The results produced by the algorithm validate the analytical approach that we use. Even in the case where there is not an absolute agreement with the experimental data, the algorithm proves to be able to produce the correct pattern and the discrepancies that appear are due to false values of the absorption coefficients that we use.
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