Low-cost airlines have significantly increased air transport, thus an increase in aviation noise. Therefore, predicting aircraft noise is an important component for designing an aircraft to reduce its impact on environmental noise along with the cost of testing and certification. The aim of this work is to develop a three-dimensional Boundary Element Method (BEM), which can predict the sound propagation and scattering over metamaterials and metasurfaces in mean flow. A methodology for the implementation of metamaterials and metasurfaces in BEM as an impedance patch is presented here. A three-dimensional BEM named as BEM3D has been developed to solve the aero-acoustics problems, which incorporates the Fast Multipole Method to solve large scale acoustics problems, Taylor’s transformation to account for uniform and non-uniform mean flow, impedance and non-local boundary conditions for the implementation of metamaterials. To validate BEM3D, the predictions have been benchmarked against the Finite Element Method (FEM) simulations and experimental data. It has been concluded that for no flow case BEM3D gives identical acoustics potential values against benchmarked FEM (COMSOL) predictions. For Mach number of 0.1, the BEM3D and FEM (COMSOL) predictions show small differences. The difference between BEM3D and FEM (COMSOL) predictions increases further for higher Mach number of 0.2 and 0.3. The increase in difference with Mach number is because Taylor’s Transformation gives an approximate solution for the boundary integral equation. Nevertheless, it has been concluded that Taylor’s transformation gives reasonable predictions for low Mach number of up to 0.3. BEM3D predictions have been validated against experimental data on a flat plate and a duct. Very good agreement has been found between the measured data and BEM3D predictions for sound propagation without and with the mean flow at low Mach number.

中文翻译：

---

开发 3D 边界元方法，用于在航空航天应用中模拟平均流中的声学超材料/超表面

低成本航空公司显着增加了航空运输，从而增加了航空噪音。因此，预测飞机噪声是设计飞机以减少其对环境噪声的影响以及测试和认证成本的重要组成部分。这项工作的目的是开发一种三维边界元方法 (BEM)，它可以预测平均流中超材料和超表面上的声音传播和散射。这里介绍了一种在 BEM 中实现超材料和超表面作为阻抗贴片的方法。已经开发了名为 BEM3D 的三维边界元法来解决气动声学问题，它结合了快速多极方法来解决大规模声学问题，泰勒变换来解释均匀和非均匀平均流动，用于实现超材料的阻抗和非局部边界条件。为了验证 BEM3D，预测已针对有限元方法 (FEM) 模拟和实验数据进行了基准测试。得出的结论是，对于无流动情况，BEM3D 给出了与基准 FEM (COMSOL) 预测相比相同的声学潜在值。对于 0.1 马赫数，BEM3D 和 FEM (COMSOL) 预测显示出很小的差异。对于更高的马赫数 0.2 和 0.3，BEM3D 和 FEM (COMSOL) 预测之间的差异进一步增加。与马赫数的差异增加是因为泰勒变换给出了边界积分方程的近似解。尽管如此，已经得出结论，泰勒变换对低至 0.3 的马赫数给出了合理的预测。BEM3D 预测已根据平板和管道的实验数据进行了验证。在低马赫数下没有和有平均流的声音传播的测量数据和 BEM3D 预测之间已经发现非常好的一致性。