Abstract This work is a contribution to the ongoing debate about the role of quadrupoles in low Mach number flows, studied through the use of solid and permeable surface Ffowcs-Williams & Hawkings (FW-H) integrals for landing gear numerical noise predictions. It rests upon the key idea that the dominance of surface sources over volume sources can only be guaranteed when the compact-source condition is met. We propose here to express this property as a condition on the smallness of the product between the Mach and Strouhal numbers, or formally as MSt 1. Overall, determining the real significance of quadrupoles was challenging as numerical errors or misleading effects such as near-field terms, surface discretization, or source domain truncation biased the initial permeable surface results. Even when these sources of bias are removed, non-negligible differences are found between the solid and permeable noise spectra at non-compact St values, while both formulations are equivalent at lower Strouhal numbers. The analysis of these differences is extended to the determination of their impact on frequency-domain noise maps obtained with the DAMAS algorithm fed with far-field signals computed with both FW-H approaches. A tentative interpretation of the wheel noise sources is finally proposed, highlighting the dominant role of the scattering of aerodynamic sources by the cavity downstream edge at low Strouhal numbers, while wake sources dominate at higher Strouhal numbers.

中文翻译：

---

FW-H 方程的离体和体上控制面的比较：在非紧凑型起落架上的应用

摘要 这项工作是对四极杆在低马赫数流动中的作用的持续辩论的贡献，通过使用固体和可渗透表面 Ffowcs-Williams & Hawkings (FW-H) 积分对起落架数值噪声预测进行研究。它依赖于一个关键思想，即只有在满足紧凑源条件时才能保证面源优于体源。我们在此建议将此属性表示为马赫数和斯特劳哈尔数之间的乘积很小的条件，或正式表示为 MSt 1。总的来说，确定四极杆的真正意义是具有挑战性的，因为数值错误或误导效应，如近场项、表面离散化或源域截断会使初始渗透表面结果产生偏差。即使消除了这些偏见的来源，在非紧凑 St 值下，固体和可渗透噪声光谱之间存在不可忽略的差异，而两种公式在较低 Strouhal 数下等效。对这些差异的分析扩展到确定它们对使用 DAMAS 算法获得的频域噪声图的影响，该算法采用两种 FW-H 方法计算的远场信号。最后提出了对车轮噪声源的初步解释，强调了在低 Strouhal 数下腔下游边缘的空气动力源散射的主要作用，而尾流源在较高 Strouhal 数下占主导地位。对这些差异的分析扩展到确定它们对使用 DAMAS 算法获得的频域噪声图的影响，该算法采用两种 FW-H 方法计算的远场信号。最后提出了对车轮噪声源的初步解释，强调了在低 Strouhal 数下腔下游边缘的空气动力源散射的主要作用，而尾流源在较高 Strouhal 数下占主导地位。对这些差异的分析扩展到确定它们对使用 DAMAS 算法获得的频域噪声图的影响，该算法采用两种 FW-H 方法计算的远场信号。最后提出了对车轮噪声源的初步解释，强调了在低 Strouhal 数下腔下游边缘的空气动力源散射的主要作用，而尾流源在较高 Strouhal 数下占主导地位。