1. Introduction
The proliferation of unmanned aerial vehicles (UAVs), particularly multi-rotor configurations, has accelerated in recent years. The unique capabilities of rotorcraft UAVs—vertical take-off and landing (VTOL), precise hovering, and simplified control mechanisms—have enabled their adoption across diverse sectors, including aerial photography, precision agriculture, infrastructure inspection, logistics, and military reconnaissance. However, the operational benefits of these rotorcraft are accompanied by a significant acoustic drawback. The high-speed rotation of rotors generates both discrete tonal noise and broadband noise, which contributes to environmental noise pollution and severely restricts UAV deployment in noise-sensitive areas such as urban environments, ecological reserves, and tactical military operations.
The challenge of mitigating aerodynamic noise from rotors has been approached from two primary directions: active noise control (ANC) and passive noise control (PNC). Active control methods, while effective in certain scenarios, typically require complex actuation systems that are impractical for small-scale UAVs due to weight and power constraints. Passive methods, which involve geometric modifications to the rotor blade, have emerged as a practical solution. A particularly promising source of inspiration for passive noise reduction is found in nature. Owls, known for their silent flight, possess a unique combination of feather adaptations—leading-edge combs, trailing-edge fringes, and a velvet-like surface texture—that suppress aerodynamic noise without compromising flight performance. This remarkable biological feature has inspired a class of bionic noise reduction techniques.
The present research is motivated by the need to develop a practical, high-efficiency noise reduction technology for small multi-rotor UAVs. The primary objective of my study is to design and evaluate a novel bionic serrated structure, derived from the trailing-edge serrations of owl primary feathers, and to assess its effectiveness in reducing rotor aerodynamic noise while carefully analyzing its impact on rotor aerodynamic performance. This work establishes a comprehensive evaluation framework by integrating computational fluid dynamics (CFD) simulations, acoustic analogy methods, and experimental validation.
2. Fundamental Theory and Numerical Methods
To accurately simulate and analyze the aerodynamic and acoustic performance of UAV rotors, a solid theoretical foundation is essential. The following sections outline the core theories and numerical techniques applied in this research.
2.1 Rotor Aerodynamic Theory
Three primary theoretical pillars support rotor aerodynamics:
Momentum Theory treats the rotor as an infinitesimally thin, permeable disc that imparts a uniform velocity change to the air passing through it. This theory, based on mass, momentum, and energy conservation, allows for a preliminary estimation of rotor thrust. For an annular element at radius \(r\) with radial width \(dr\), the incremental thrust \( \Delta T \) and torque \( \Delta M \) are given by equations (2.1) and (2.2):
$$ \Delta T = 2 \rho v (2\pi r) dr \quad (2.1) $$
$$ \Delta M = 2 \rho uv r (2\pi r) dr \quad (2.2) $$
where \( \rho \) is the air density, \( v \) is the axial induced velocity, and \( u \) is the tangential induced velocity.
Blade Element Theory (BET) takes a different approach by dividing the blade into small, two-dimensional airfoil sections. By calculating the lift and drag of each section and integrating along the blade span, the total rotor performance can be determined. The lift \( \Delta L \) and drag \( \Delta D \) on a blade element are:
$$ \Delta L = q C_L c dr $$
$$ \Delta D = q C_D c dr $$
where \(q\) is the local dynamic pressure, \(C_L\) and \(C_D\) are the lift and drag coefficients, and \(c\) is the chord length.
Vortex Theory provides a more refined model by representing the blade as a lifting line with bound vortices. It accounts for the generation of trailing vortices and tip vortices, which play a dominant role in the rotor wake and induced velocity field. This theory is crucial for understanding the complex vortical flow structures that are primary sources of noise.
2.2 Governing Equations of Fluid Flow
The flow field around a rotor is governed by the Navier-Stokes equations. We solve them numerically using a structured approach, initially in a steady state and subsequently in a transient form. The relevant equations are:
Conservation of Mass:
$$ \frac{\partial \rho}{\partial t} +
abla \cdot (\rho \mathbf{U}) = 0 \quad (2.8) $$
Conservation of Momentum:
$$ \frac{\partial (\rho u)}{\partial t} +
abla \cdot (\rho u \mathbf{U}) = -\frac{\partial p}{\partial x} +
abla \cdot (\mu
abla u) + S_u \quad (2.10) $$
In these equations, \( \rho \) is density, \(t\) is time, \( \mathbf{U} \) is the velocity vector, \(p\) is pressure, \(\mu\) is dynamic viscosity, and \(S_u\) represents the momentum source term.
In my simulations, the Mach number of the rotor tip remains below the compressibility threshold, allowing me to adopt an incompressible flow assumption. This decouples the energy equation from the momentum equation, enabling a more computationally efficient solution.
2.3 Turbulence Models
The choice of turbulence model is critical to simulation accuracy.
– For the steady-state aerodynamic performance analysis, I employed the Shear Stress Transport (SST) \(k-\omega\) model. This two-equation model excels at predicting flow separation under adverse pressure gradients by blending the standard \(k-\omega\) model in the near-wall region with the \(k-\epsilon\) model in the far field. The turbulent eddy viscosity \(\mu_t\) is calculated using a specific formulation to account for shear stress transport.
– For the transient acoustic analysis, I deployed the Large Eddy Simulation (LES) approach. LES directly resolves the large-scale turbulent eddies that dominate the noise generation process while modeling the smaller, more isotropic scales using a subgrid-scale model. Specifically, I used the Wall-Adapting Local Eddy-Viscosity (WALE) model. The subgrid-scale eddy viscosity \(\mu_t\) in the WALE model is given by:
$$ \mu_t = \rho L_s^2 \frac{(S_{ij}^d S_{ij}^d)^{3/2}}{(S_{ij} S_{ij})^{5/2} + (S_{ij}^d S_{ij}^d)^{5/4}} $$
where \(L_s\) is the subgrid-scale mixing length, \(S_{ij}\) is the resolved strain-rate tensor, and \(S_{ij}^d\) is the traceless symmetric part of the square of the velocity gradient tensor.
2.4 Aeroacoustic Theory and Methods
The noise generated by a rotor is categorized into discrete tonal noise and broadband noise. Tonal noise components include thickness noise and loading noise, while broadband noise arises from the unsteady pressure fluctuations in the turbulent boundary layer and wake. The ratio of these components depends on the observer’s location relative to the rotor.
The acoustic field was predicted using the Ffowcs Williams-Hawkings (FW-H) equation, an acoustic analogy method. This approach allows for the propagation of sound generated by the computed near-field flow data to a far-field observer. The acoustic pressure \(p'(\mathbf{x}, t)\) at an observer point is composed of the thickness and loading components:
$$ p'(\mathbf{x}, t) = p’_T(\mathbf{x}, t) + p’_L(\mathbf{x}, t) $$
The thickness noise \(p’_T(\mathbf{x}, t)\) is calculated from the blade geometry and kinematics, while the loading noise \(p’_L(\mathbf{x}, t)\) is derived from the aerodynamic forces on the blade surface.
3. Design and Aerodynamic Analysis of the Bionic Serrated Structure
This chapter details the methodology for creating a bionic rotor model and the subsequent analysis of its aerodynamic performance.
3.1 Rotor Model and Numerical Setup
I selected the 9450 rotor, commonly used on the F450 quadcopter, as the baseline model. This rotor has a diameter of 9.4 inches (23.87 cm) and a pitch of 5.0 inches (12.7 cm). Given its complex 3D curved surface, I used reverse engineering for precise modeling. The process involved three-dimensional scanning to obtain point cloud data, processing this data in Geomagic to generate a surface profile, and then creating the final 3D CAD model in SolidWorks. The resulting model displayed the characteristic under-cambered airfoil shape.
For steady-state simulation, I used the Multiple Reference Frame (MRF) method. The computational domain was configured as a large stationary cylinder (dimension: diameter of 1500 mm, height of 2000 mm) containing a smaller rotating cylindrical sub-domain (dimension: diameter of 250 mm, height of 48 mm) where the rotor blades are housed. This setup allows the flow field to develop around the rotating domain without backflow contamination.
Meshing was performed using a poly-hexcore approach. To accurately resolve the boundary layer, I generated 12 inflation layers with an initial thickness of 0.005 mm and a growth rate of 1.2 on the rotor surface. A mesh independence study was conducted with five mesh densities. The calculated lift force at 5400 r/min was used as the key metric for validation. I found that as the mesh size increased, the change in lift force became increasingly negligible. The final mesh configuration consisted of approximately 4.4 million elements, satisfying both accuracy and computational budget.
The boundary conditions were set to simulate a hovering condition, with the inlet and outlet of the stationary domain defined as pressure-inlet and pressure-outlet, respectively. The rotor walls were modeled as moving walls to account for rotation. I used the SST \(k-\omega\) turbulence model for this steady-state analysis, and a reference pressure of 1 atm was applied.
3.2 Analysis of Baseline Rotor Performance
The baseline rotor’s aerodynamic performance was evaluated across six different rotational speeds, and the results are summarized in Table 3.1.
Table 3.1 Aerodynamic Performance Data of the Original Rotor
| Rotational Speed (r/min) | Lift (N) | Torque (N·m) |
|—————————|———-|————–|
| 4200 | 1.64 | 0.025 |
| 4600 | 2.00 | 0.030 |
| 5000 | 2.42 | 0.037 |
| 5400 | 2.88 | 0.043 |
| 5800 | 3.24 | 0.048 |
| 6200 | 3.63 | 0.054 |
The analysis shows a non-linear increase in lift and torque with increasing rotational speed. The pressure distribution on the rotor surface revealed that the maximum pressure difference is concentrated near the tip region, confirming that this is the primary area of lift generation and a critical source region for loading noise.
3.3 Bionic Serrated Structure Design
In my study, I abstracted the trailing-edge serrations from the owl’s primary feathers into an asymmetric, curved sawtooth profile. This design was not just a simple triangular cut but aimed to mimic the complex geometry observed in nature. The key geometric parameters defining the structure are the serration angle (θ), serration length (L), and serration spacing (T). To ensure these parameters are investigated independently, I used a single-factor experimental design, with values normalized to the free-stream flow characteristics. The parameters for the bionic structures are listed in Table 3.2.
Table 3.2 Design Parameters for the Bionic Serrated Structures
| Rotor ID | Serration Angle θ (degrees) | Serration Length L (mm) | Serration Spacing T (mm) |
|————-|——————————|—————————|—————————|
| O (Baseline)| 0 | 0 | 0 |
| A1 | 40 | 2.3 | 0 |
| A2 | 50 | 2.3 | 0 |
| A3 | 60 | 2.3 | 0 |
| B1 | 50 | 2.3 | 0 |
| B2 | 50 | 2.8 | 0 |
| B3 | 50 | 3.3 | 0 |
| C1 | 50 | 2.8 | 0 |
| C2 | 50 | 2.8 | 0.5 |
| C3 | 50 | 2.8 | 1.0 |
The serrations were strategically placed on the rotor at a spanwise location between 55% and 90% of the rotor radius. This placement was chosen to avoid a significant loss of lift, as the tip region is critical for lift generation. The implementation involved directly removing material from the rotor blade, ensuring that the shape of the serrations is the only variable being investigated.
3.4 Aerodynamic Performance Results and Comparison
The aerodynamic performance of the baseline and bionic rotors was evaluated at the same six rotational speeds. The results, compared in Figures 3.7 and 3.8, showed a consistent trend. The addition of the bionic serrations resulted in a reduction of both the lift and torque generated by the rotor at all rotational speeds. The percentage reduction for different parameter groups at 5400 r/min is detailed in Table 3.3.
Table 3.3 Aerodynamic Performance Change Relative to Baseline Rotor at 5400 r/min
| Rotor ID | Lift Reduction (%) | Torque Reduction (%) |
|————-|——————–|———————-|
| A2 | 7.3 | 8.7 |
| B1 | 7.2 | 8.7 |
| B2 | 8.7 | 10.4 |
| B3 | 7.6 | 9.6 |
| C1 | 8.7 | 10.3 |
| C2 | 10.2 | 11.8 |
| C3 | 10.6 | 13.0 |
The key observations from the aerodynamic analysis were that the change in serration angle (Group A) had little influence on both lift and torque. In contrast, the serration length (Group B) showed an optimal value, with the rotor B2 demonstrating a greater reduction in torque compared to other lengths. The serration spacing (Group C) had a linear effect: as the spacing increased, the losses in both lift and torque also increased, which is expected as a larger portion of the blade surface is modified.
3.5 Flow Field Analysis for Mechanism Insight
To explain the observed aerodynamic changes, I conducted a detailed analysis of the flow fields, focusing on the pressure and velocity distributions.
The pressure coefficient (\(C_p\)) analysis along the chord for rotor A2 showed that the serrations do not disturb the flow at the leading edge. However, at the tooth root section, the pressure recovery process is abruptly truncated at approximately 85% of the chord length. This prevents the formation of the pressure difference at the trailing edge, leading to a reduction in the overall lift force. The velocity streamlines showed that the high-speed core region on the suction surface of the bionic rotor shrinks compared to the baseline, which directly reduces the pressure difference and, consequently, the generated lift. The analysis of the downwash flow in the rotor wake showed a decrease in the peak velocity and a broadening of the shear layer of the bionic rotor, indicating a more rapid dissipation of kinetic energy downstream of the rotor.
4. Acoustic Performance Analysis of the Bionic Serrated Structure
This chapter assesses the acoustic impact of the bionic structures. I used a hybrid approach: Large Eddy Simulation (LES) to resolve the near-field turbulent noise sources and the FW-H acoustic analogy to propagate these fluctuations to the far-field observer locations.
4.1 Computational Setup
The converged steady-state flow field was used as the initial condition for the transient LES simulation. The mesh motion was switched to the sliding mesh approach to allow the rotor to rotate through the stationary domain. The WALE subgrid-scale model was chosen for LES. A transient simulation was run with an initial time-step of \(2.5 \times 10^{-5}\) seconds to capture frequencies up to 20 kHz. The total simulation time was 0.055 seconds, and solution stability was monitored using the rotor’s lift and residual curves.
4.2 Sound Pressure Level and Directivity
I strategically placed acoustic monitors to map the sound field. A total of 24 monitors were arranged in a circle of 1-meter radius within the rotor rotation plane and the vertical plane at 15° intervals. Additionally, four monitors were placed along the axis below the rotor at intervals of 0.5 meters.
The analysis of the baseline rotor showed that the overall sound pressure level (OASPL) distribution on the rotation plane is almost uniform, characteristic of the omnidirectional radiation of thickness noise. In contrast, the OASPL distribution on the vertical plane shows a “figure-8” pattern, which is a hallmark of a dipole sound source, dominated by the loading noise component. The maximum noise radiation occurs along the rotor axis.
4.3 Effect of Serration Parameters on OASPL
The acoustic performance of all bionic rotors was compared to the baseline. Key results for the axial monitor at 1 meter are summarized in Table 4.1.
Table 4.1 OASPL (dB) at Axial Distance of 1 Meter for All Rotor Configurations
| Rotor ID | OASPL (dB) at 1m | Noise Reduction (dB) |
|————-|——————|———————-|
| O | 69.89 | – |
| A1 | 66.19 | 3.70 |
| A2 | 66.08 | 3.81 |
| A3 | 67.08 | 2.81 |
| B1 | 66.08 | 3.81 |
| B2 | 64.07 | 5.82 |
| B3 | 64.49 | 5.40 |
| C1 | 64.07 | 5.82 |
| C2 | 64.83 | 5.06 |
| C3 | 65.89 | 4.00 |
The findings confirm that all bionic serrations contribute to noise reduction, irrespective of their specific parameters. Within the tested parameter range, rotor B2 achieved the highest noise reduction of 5.82 dB, representing an 8.3% decrease in OASPL. The directivity analysis revealed that the serration structures do not alter the fundamental spatial distribution pattern of the noise; instead, they primarily attenuate the source strength. The effects of the geometric parameters were evident:
– The serration angle and length each have an optimal value, with the best performance observed at 50° and 2.8 mm, respectively.
– The noise reduction effectiveness of the serration spacing decreased monotonically as the spacing increased.
4.4 Spectral Analysis
Frequency spectrum analysis of the axial monitor provides deeper insight into the noise reduction capabilities. The analysis of the 1/3-octave band spectrum is detailed in Table 4.2 for some representative configurations.
Table 4.2 Sound Pressure Level (dB) in Different Frequency Bands for Selected Rotors
| Rotor ID | Frequency Band (Hz) | SPL (dB) |
|————-|———————-|———–|
| O | 2000-6300 (Peak) | 65.8 |
| B2 | 2000-6300 (Peak) | ~59.95 |
| B3 | 2000-6300 (Peak) | ~61.5 |
| O | 6300-20000 | ~50 |
| B2 | 6300-20000 | ~44 |
The serrated structures were effective across the entire frequency spectrum, but the most pronounced noise reduction occurred in the mid-to-high frequency bands. These bands are primarily associated with broadband noise from turbulence-wake interactions, confirming that the serrations effectively disrupt coherent flow structures that generate this type of noise. The near-identical spectral performance of B2 and B3 (which differ in length) suggests that beyond a certain length, additional increases yield diminishing returns in noise reduction.
4.5 Flow Mechanism: Vortex Structure Identification
To visually confirm the noise reduction mechanism, I used the Q-criterion to identify and compare the vortex structures in the rotor wake. A comparison of the baseline rotor O and the optimized rotor B2 revealed stark differences in their wake characteristics.
The baseline rotor O exhibited large, continuous, sheet-like vortices shedding directly from the entire trailing edge. These large, coherent structures are highly efficient at generating sound. In contrast, the wake of the bionic rotor B2 was characterized by numerous smaller, more discrete vortices. The serrations effectively break the spanwise coherence of the trailing-edge vortices, forcing them to break down into smaller, less energetic structures. This process accelerates energy dissipation before the vortices can strongly interact with the solid surface, thereby suppressing the generation of the pressure fluctuations that lead to aerodynamic noise. The evolution of these vortex structures over time confirmed that while the bionic rotor does not change the mean flow topology, it fundamentally alters the unsteady wake dynamics to reduce acoustic radiation.
5. Experimental Validation
To validate the findings from the numerical simulations, I conducted a series of experiments to measure the aerodynamic and acoustic performances of the physical rotors.
5.1 Experimental Setup
The experiments were conducted in two main phases: single-rotor testing and full-UAV testing. Physical models of the baseline rotor O and the series of Group B rotors (B1, B2, B3) were manufactured using high-precision 3D printing with a photosensitive resin. The single-rotor tests were performed using a G10 propulsion system test stand, which is designed for measuring thrust, torque, rotational speed, and power.
For the full-UAV testing, an F450 frame was used and equipped with an APM 2.8 flight controller to ensure stable hovering. A total of two rotor sets were prepared for the full-UAV test: one with the original rotors and one with the optimized B2 bionic rotors. The acoustic measurements were taken with an SM8768 noise sensor connected to a data acquisition system. Tests were conducted in an indoor environment with temporary soundproofing to minimize reflections, and background noise levels were confirmed to be within acceptable limits.
5.2 Aerodynamic Performance Validation
The experimental results for the aerodynamic performance of the baseline and Group B rotors across the investigated speed range are shown in Figures 5.2 and 5.3. The primary observations are as follows.
– The general trend of lift and power as a function of rotational speed in the experimental data closely matches the numerical predictions.
– The experimental values for lift are slightly lower (within 7% relative error), and power is slightly higher than the simulation values. This discrepancy can be attributed to the non-ideal surface finish of the 3D-printed rotors, the mechanical friction losses in the test stand, and potential minor aerodynamic interference, all of which are common in experimental setups.
– Critically, the relative performance between the rotors was consistent with the simulations. At the same rotational speed, all bionic rotors produced less lift and consumed less power than the baseline rotor, with rotor B2 consistently showing the lowest power consumption.
5.3 Acoustic Performance Validation
The acoustic experiments were performed at the same rotor speeds and monitoring points used in the simulations. A comparison between the simulated and experimental OASPL at a distance of 1 meter from the rotor is shown in Table 5.1.
Table 5.1 Comparison of Simulated and Experimental OASPL for Various Rotors
| Rotor ID | Simulated OASPL (dB) | Experimental OASPL (dB) |
|————-|———————-|—————————|
| O | 69.89 | 72.3 |
| B1 | 66.08 | 68.6 |
| B2 | 64.07 | 65.8 |
| B3 | 64.49 | 66.1 |
The absolute values of OASPL are higher in the experiments due to the less-than-ideal anechoic environment and background noise. However, the relative trend shows that the bionic rotors consistently produce less noise than the baseline rotor across all monitor locations. The measured noise reduction trend aligns well with the simulation predictions, thereby validating the accuracy of the numerical methods employed.
Further tests evaluated the noise level when the rotors generated the same amount of lift. The results for a lift force of 3 N are presented in Table 5.2.
Table 5.2 Noise Reduction of Bionic Rotors at the Same Lift Condition (3 N)
| Rotor Configuration | Lift (N) | OASPL (dB) | Noise Reduction (dB) |
|———————|———-|————|———————-|
| Baseline (O) | 3.0 | 80.2 | – |
| Rotor B1 | 3.0 | 78.3 | 1.9 |
| Rotor B2 | 3.0 | 77.3 | 2.9 |
| Rotor B3 | 3.0 | 77.9 | 2.3 |
The data clearly show that at the same thrust, all bionic rotors are quieter than the baseline rotor, with rotor B2 achieving a significant noise reduction of 2.9 dB. This is a crucial advantage, as it demonstrates that the noise reduction is not achieved at the expense of hover performance.
In the final phase, the full-UAV tests were conducted in an outdoor environment. The noise levels of a UAV equipped with the baseline rotors and the optimized B2 bionic rotors were compared during a hover at a distance of 5 meters. The resulting noise reduction was measured at 4.3 dB, confirming the practical effectiveness of the bionic technology at the complete aircraft level.
6. Conclusion
This dissertation carried out a systematic investigation into the design, simulation, and experimental validation of a bionic serrated structure for the application of aerodynamic noise reduction on the rotors of unmanned aerial vehicles. The key findings and contributions are summarized below.
(1) A bionic serrated structure was designed and implemented on a 9450 rotor. The design successfully mimics the trailing-edge features found on the feathers of owls. To ensure the studied parameters are independent, the serration lengths, angles, and spacings were systematically varied.
(2) The aerodynamic performance, as assessed via steady-state simulations, showed that the bionic serrations reduce both the lift and torque of the rotor. The reduction in torque was generally greater than the reduction in lift, which is beneficial for the aerodynamic efficiency of the rotor. This is because the serrations diminish the effective pressure difference on the blade surface and break up the high-drag region at the trailing edge.
(3) The acoustic performance, assessed via unsteady simulations, demonstrated that all bionic rotor configurations effectively lower the overall sound pressure level when compared to the baseline rotor under the same rotational speed. The noise directivity pattern remains unchanged, indicating that the serrations act on the source and not on the propagation path. The primary noise reduction mechanism is the disruption of spanwise-coherent trailing-edge vortices, which are broken down into smaller, less efficient acoustic sources. Among the tested configurations, the rotor with serration angle \(50^\circ\), length 2.8 mm, and no spacing (rotor B2) provided the best performance, achieving a 5.82 dB reduction in OASPL.
(4) The experimental results confirmed the simulations in terms of both relative trends and general magnitude. The experimental data at the same lift force show a maximum noise reduction of 2.9 dB for a single bionic rotor. When installed on a full quadrotor unmanned aerial vehicle platform, the bionic rotor demonstrated a 4.3 dB reduction in noise during a 5-meter hover, thereby proving the practical applicability of the bionic design.
Future Work
While this research provides a solid foundation, there are several directions for further development:
(1) This study focused on the individual effects of the serration parameters. Future work would benefit from a multi-objective optimization study, such as a response surface methodology or genetic algorithm, to discover the optimal combination of these parameters that minimizes noise while maximizing aerodynamic efficiency.
(2) The scope of this study was limited to the hovering condition of the unmanned aerial vehicle. Since UAVs operate in a variety of flight modes, including forward flight, there is a need to study the performance of the bionic serrations under different flight conditions, which may involve understanding their interaction with the freestream flow and different rotor inflow conditions.
(3) This experimental validation was conducted in a semi-anechoic environment. To obtain more precise absolute measurements of the noise directivity, future experiments should be performed in a fully anechoic chamber using a microphone array. This would allow for a more precise mapping of the sound field and provide further insight into the noise source distribution across the blade span.