In this study, asymptotic analysis of the frequency-domain formulation to compute the tonal noise of the small rotors in the now ubiquitously multi-rotor powered drones is conducted. Simple scaling laws are proposed to evaluate the impacts of the influential parameters such as blade number, flow speed, rotation speed, unsteady motion, thrust and observer angle on the tonal noise. The rate of noise increment with thrust (or rotational speed) is determined by orders of blade passing frequency harmonics and the unsteady motion. The axial mean flow influence can be approximated by quadratic functions. At given thrust, the sound decreases rapidly with the radius and blade number as the surface pressure becomes less intensive. The higher tonal harmonics are significantly increased if unsteady motions, although of small-amplitude, are existed, as indicated by the defined sensitivity function, emphasizing that the unsteady motions should be avoided for quiet rotor designs. The scaling laws are examined by comparing with the full computations of the rotor noise using the frequency-domain method, the implementation of which has been validated by comparing with experiments. Good data collapse is obtained when the proposed scaling laws, which highlights the dominant influence of the design parameters, are incorporated.

中文翻译：

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重新审视小转子的音调噪声

在这项研究中，进行了频域公式的渐近分析，以计算现在无处不在的多旋翼动力无人机中小旋翼的音调噪声。提出了简单的标度律来评估叶片数、流速、转速、非定常运动、推力和观察角等影响参数对音调噪声的影响。噪声随推力（或转速）增加的速率由叶片通过频率谐波和非定常运动的阶数决定。轴向平均流影响可以用二次函数近似。在给定的推力下，随着表面压力变得不那么强烈，声音会随着半径和叶片数量的增加而迅速降低。如果存在不稳定的运动，尽管幅度很小，则较高的谐波会显着增加，如定义的灵敏度函数所示，强调对于安静的转子设计应避免不稳定运动。通过与使用频域方法对转子噪声的完整计算进行比较来检验标度律，并通过与实验比较来验证其实现。当提出的标度法则突出设计参数的主要影响时，可以获得良好的数据崩溃。