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.

In this study, we investigated the performance of flexible trailing edge serrations of various shapes for airfoil self-noise reduction through anechoic wind tunnel experiments. A flat plate model was tested at zero angle of attack. The chord-based Reynolds number was between 1.6 × 105 and 4 × 105. The boundary layers were fully tripped near the leading edge. Add-on type trailing edge serrations were cut from flexible polyethylene terephthalate sheets. It is observed that compared with rigid serrations, flexible serrations can achieve an additional broadband noise reduction up to 2 dB–3 dB at high frequencies, and the effect also depends on the geometry of the serrations. Complementary deformation measurement and aerodynamic force measurement show that flexible serrations can align better with the flow and are expected to reduce the crossflow intensity near the serration roots, which has been related to the extraneous high-frequency noise generated by serrations in previous studies. An inviscid model is proposed to predict the wake structure and the loadings for serrations of various shapes. Although the model over-predicts the crossflow speed due to the omission of the viscous effect, the relative intensity corresponding to different serration geometry is consistent with experimental observations. Last, we show that the recent analytical noise prediction model [B. Lyu and L. J. Ayton, “Rapid noise prediction models for serrated leading and trailing edges,” J. Sound Vib. 469, 115136 (2020)] for a serrated trailing edge still significantly overpredicts the noise reduction capacity by serrations and does not reveal the role of serration shape properly. This indicates the necessity to include the non-frozen turbulent properties near serrations in the future prediction models.

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