Experimental and Numerical Study of a UAV Propeller Printed in Clear Resin

Abstract

This paper presents an experimental and numerical investigation of a 254 mm resin-printed propeller operating at rotational speeds between 3000 and 9000 RPM. Propeller thrust and torque were measured using a six-degree-of-freedom load cell, while acoustic data were captured with a microphone positioned three times the propeller diameter from the center. To complement the experimental analysis, computational simulations were conducted using ANSYS Fluent with the detached eddy simulation (DES) model, the Ffowcs-Williams and Hawkings (FW-H) model, and a transient flow solver. The figure of merit (FM) results show that the resin propeller slightly outperforms two commercial counterparts with a marginal difference between the wood and resin propellers. Additionally, the resin propeller demonstrates better noise performance, exhibiting the lowest primary tonal noise, broadband noise, and overall sound pressure level (OASPL), with minimal differences between the two commercial counterparts. ANSYS Fluent simulations predict thrust and torque within a 10% error margin, showing particularly accurate results for primary tonal noise. A new trade-off index is proposed to assess the balance between propeller performance and aeroacoustics, revealing distinct trends compared to traditional metrics. Furthermore, aerodynamic phenomena such as flow separation on the leading edge near the tip, flow separation behind the middle trailing edge, and vortex interactions at the root are identified as key contributors to tonal and broadband noise. These findings provide valuable insights into propeller design and aeroacoustic optimization.

1. Introduction

Unmanned aerial vehicles (UAVs), or drones, are now capable of performing increasingly complex missions, ranging from surveillance and remote inspection to product delivery [1], especially with the emergence of the urban air mobility (UAM) concept. As illustrated in Figure 1 [2], drones are categorized by size and function, ranging from larger UAVs to miniature devices such as smart dust (SD). These classifications vary in terms of weight, vehicle size, operational range, and endurance. With smaller drones, thrust is typically generated by electric motor-driven propellers, and vehicle performance is ultimately constrained by the onboard battery capacity. Thus, optimizing propeller performance is essential for efficiency, not only in maximizing thrust but also in managing propeller torque, which directly affects battery consumption. Excess torque can overburden electric motors, leading to potential burnout [3]. In addition, it requires an electronic speed controller (ESC) with higher current capacity, which can increase the overall cost of building a UAV.

To achieve a highly efficient propeller, various characteristics such as Reynolds number [4], twist rate [5], number of blades [6], blade shape [7], and airfoil selection [8] are investigated by careful modifications. For example, selecting the appropriate Reynolds number range is essential to minimize viscous losses and enhance aerodynamic performance. Similarly, adjusting the twist rate can help maintain an optimal angle of attack along the blade span, thus improving lift-to-drag ratios. The choice of the number of blades and their spacing affects not only the thrust but also noise levels, making it an important consideration for UAM applications. Additionally, the blade shape and the airfoil profile are crucial for maximizing lift while minimizing drag, directly impacting the efficiency and energy consumption of UAVs.

Recent studies, on topics such as slotted propellers [9] and shrouded propellers [10], have shown promising potential in enhancing net thrust. The addition of slots along the blade surface can delay flow separation and improve pressure distribution, leading to increased aerodynamic efficiency. On the other hand, shrouded propellers, which utilize a protective duct around the blades, can reduce tip vortices and improve thrust by creating a more favorable flow environment. However, slotted propellers have not yet been widely commercialized, likely due to concerns over structural strength. For shrouded propellers, the added ducts can significantly increase the vehicle’s empty weight. Therefore, for most drones, conventional propellers with carefully selected blade shapes remain the primary solution for achieving optimal performance.

The inclusion of propellers in drones raises significant concerns, particularly regarding noise pollution in UAM operation [11]. As these drones will primarily operate over urban and suburban areas, reducing propeller noise has become a critical focus. Strategies such as serrated trailing edges and toroidal propellers have been explored to address this issue. Gu et al. [12] examined the effects of serrated trailing edges on propeller noise, but their findings showed that serrated propellers consumed more power, as indicated by the propeller power curve in their study. Recently, researchers at the Massachusetts Institute of Technology (MIT) patented a toroidal propeller design, which they claim can reduce noise while maintaining performance comparable to conventional propellers [13]. However, the first author’s preliminary investigation [14] on a 254 mm-diameter toroidal propeller revealed inherent performance drawbacks, attributed to the interaction between the leading and trailing blades. Thus, commercializing a viable propeller design requires balancing noise reduction and performance. A significant reduction in noise, if accompanied by substantial performance losses, would render the propeller impractical for widespread use.

Based on the aforementioned discussion, the literature has not adequately addressed the balance between propeller performance and aeroacoustics. Focusing solely on performance or aeroacoustics is insufficient, especially with the advent of the UAM concept. This paper begins with experiments on different propellers, including a resin-printed propeller developed by the first author and two commercial counterparts of the same diameter, examining both propeller performance and aeroacoustics. These experimental cases are then replicated in the commercial software ANSYS Fluent to gain further insights. After comparing the propeller performance and aeroacoustics, a new trade-off index is proposed for propeller evaluation. This is followed by an analytical prediction of propeller thrust using a momentum theory-based approach. Finally, vorticity iso-surfaces, quantified using the normalized Q-criterion, and the root mean square (RMS) of the time rate of static pressure on the propeller surface reveal key aerodynamic phenomena contributing to noise generation.

2. Experimental Approach

2.1. Propeller Geometry

The designed propeller features a central hub supporting two blades, as illustrated in Figure 2a. The chord length profile and pitch angle distribution are presented in Figure 2b and Figure 2c, respectively. The propeller was fabricated using additive manufacturing with clear resin on a Formlabs 3B printer (Formlabs Inc., Somerville, MA, USA), followed by curing and surface sanding for post-processing.

Table 1. Details of the propeller printed in clear resin.

Radius (R):	127 mm
Chord (c):	variable
${\displaystyle \frac{A_{cutout}}{A_{disk}}}$:	0.01
Thickness:	variable
Solidity ($\sigma$):	0.07
Pitch:	twisted
Material:	epoxy
Tensile strength (MPa):	65
Elastic modulus (GPa):	2.80
Density (kg/m3):	1110
Resin usage (mL):	26.97 with support
Cost (dollar):	4.02
Printing time (hour):	7.25

provides an overview of the propeller’s specifications, material properties, and printing details. It is worth noting that the costs of the printer and curing machine are not included.

2.2. Test Apparatus

To investigate the aerodynamic performance and aeroacoustics of the propeller, a test setup was constructed (Figure 3). Experiments were conducted in the anechoic chamber at North Carolina State University (NCSU), characterized by dimensions of 5.2 m × 5.2 m × 5.3 m (depth × width × height). This chamber adheres to ISO 3745 standards [15], with a low-frequency cutoff of around 80 Hz, and flow recirculation in the chamber was checked at 3000 and 3600 RPM [16]. The chamber’s floor is grated, with wedge-shaped absorbers strategically placed beneath.

Propeller thrust and torque data were collected using an ATI mini 40 load cell (ATI Industrial Automation, Apex, NC, USA) equipped with six degrees of freedom. For far-field acoustics measurements, a Bruel & Kjaer Type 4188-A-021 microphone (Brüel & Kjær, Nærum, Denmark) was employed. The microphone was positioned at a distance of $6R$ from the propeller center horizontally at the propeller plane, following the recommendation of Barry et al. [17] for far-field noise.

2.3. Data Acquisition System

Propeller thrust (T) and torque (Q) were measured using an ATI Mini 40 load cell, which has a resolution of 0.01 N and 1/8000 N·m for force and torque, with respective ranges of 60 N and 1 N·m. Data collection for the load cell was performed through two National Instruments (NIs) NI-9237 analog input models. For acoustic data, a Bruel & Kjaer Type 4188-A-021 microphone with a sensitivity of 33.08 mV/Pa was employed. Acoustic collection was facilitated by an NI-9234 sound and vibration module, and all three modules were housed in an NI cDAQ-9174 chasis, connected to a PC via USB.

The propeller was driven by a Turnigy Aerodrive 3536–1400 kv motor, connected to a Phoenix Edge Lite 75 A electronic speed controller powered by a 14.8 V lithium battery. To measure the propeller rotational speed, a powered Hall effect sensor (A3144) was utilized, tracking a small neodymium magnet placed on the motor shaft. The signal was acquired using an NI USB-6008 DAQ recorder (National Instruments, Austin, TX, USA). For adjusting the rotation speed, a potentiometer was used to set the pulse width modulation output from an Arduino Uno controller (Arduino LLC, Monza, Italy) to the electronic speed controller. Ambient pressure and temperature were measured using a Mensor CPG-2400 digital barometer (Mensor, San Marcos, TX, USA) and an Extech Insturments 421502 thermometer (Extech Instruments, Nashua, NH, USA), respectively.

2.4. Test Procedure

To ensure unbiased initial readings for force testing, the load cell was zeroed before actual data acquisition. Ambient pressure and temperature were recorded for each run to determine air density. Propeller rotational speed adjustments were made through the potentiometer/Arduino unit, monitored by a Hall effect sensor to maintain constancy throughout each test. Force and torque data were captured when the preset propeller rotational speed was attained. The load cell was sampled at 10,000 Hz for 10 s. For each test point, force and torque data tests were repeated three times, and the results were averaged. Acoustic data were collected when the set RPM was achieved as well. The microphone was sampled at 25.6 kHz for a duration of 10 s. Acoustic data tests were performed once for each given condition. The analysis of force data and uncertainty is detailed in Chen and Hubner [18], while the aeroacoustic data processing is presented in Chen et al. [19]. The following points summarize the aeroacoustic data-processing methods.

1.

The electric motor noise is not excluded from the aeroacoustic signature, similar to the approach in Gojon et al. [20].

2.

For broadband noise, noise peaks are removed using a built-in function in MATLAB (Version 2021).

3.

To identify tonal noises, the frequencies obtained after performing a fast Fourier transform are normalized by the blade passing frequency (BPF) (Equation (1)). The tonal noises are then represented by the peaks at integer values of $f^{+}$.

$$f^{+}={\displaystyle \frac{f}{\mathrm{BPF}}}$$

(1)

BPF is defined in Equation (2).

$$\mathrm{BPF}={\displaystyle \frac{N·\mathrm{\Omega }}{60}}$$

(2)

where N is the number of the blades, and $\mathrm{\Omega }$ is the rotational speed in revolutions per minute.

3. Numerical Approach

3.1. Flow Solver

The detached eddy simulation (DES) equations, instead of the Reynolds-averaged Navier–Stokes (RANS) equations, were selected to simulate the flow, with the Spalart–Allmaras (SA) model used for turbulence modeling. In Chen et al. [14], the RANS equations were shown to accurately predict only the main tonal noise at $f^{+}$ = 1 when compared to experimental noise results, while the prediction of broadband noise was much less accurate. As a result, the DES approach, as demonstrated by Si et al. [21], was explored to determine whether it could improve the prediction of propeller aeroacoustics. Computational fluid dynamics (CFD) simulations were conducted using ANSYS Fluent (Version 21.2), a commercial software package.

A velocity inlet boundary condition with a magnitude of 0.1 m/s was applied at the inlet, and a pressure outlet was used to define the end of the computational domain, as illustrated in Figure 4. To model the rotation of the propeller, a small rotating domain with a diameter of 1.1 D and a depth of 0.2 D (where D represents the rotor diameter) was included within the stationary domain. The stationary domain is cylindrical with dimensions of 10 D by 10 D (diameter by length). The pressure-based coupled algorithm was utilized for solving pressure–velocity coupling. Momentum equations were discretized using a second-order upwind scheme, while turbulence properties were handled with a second-order upwind scheme. The convergence criteria were set to ${10}^{-6}$ for residuals. In the transient solver, the time step ($dt$) was calculated using Equation (3).

$$dt\le {\displaystyle \frac{1}{2\ast freq}}$$

(3)

where $freq$ denotes the maximum frequency of interest. To facilitate comparison of aeroacoustic results across different rotational speeds, this frequency accounts for the BPF defined in Equation (2) and increases with higher rotational speed. For each rotational speed, the total simulation duration was set to two seconds.

Finally, the Ffowcs-Williams and Hawkings (FW–H) acoustic analogy, expressed in Equation (4) and adapted in Zhi et al. [22] to match the original formulation in Williams and Hawkings [23], was employed in conjunction with the transient flow solver to predict the far-field noise generated by the propeller at the same microphone location shown in Figure 3.

$${\displaystyle \frac{1}{c_0^2}}{\displaystyle \frac{{\mathrm{\partial }}^2{p}^{\prime }}{{\mathrm{\partial }}^{2}t}}-{\nabla }^2{p}^{\prime }={\displaystyle \frac{{\mathrm{\partial }}^2}{\mathrm{\partial }x\mathrm{\partial }y}}{T}_{ij}H\left(f\right)-{\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }{x}_i}}[P_{ij}{n}_j+\rho u_i(u_n-v_n)]\delta \left(f\right)+{\displaystyle \frac{\mathrm{\partial }}{\mathrm{\partial }t}}[{\rho }_0{v}_n+\rho (u_n-v_n)]\delta \left(f\right)$$

(4)

Here, $p^{\prime }$ represents the acoustic pressure; $c_0$ is the ambient speed of sound; $\rho$ is the density, with the subscript “0” denoting ambient conditions; u is the flow velocity; and v is the moving velocity of the data surface. The subscript n denotes the local normal tern of the data surface. $T_{ij}$ and $P_{ij}$ correspond to the Lighthill stress tensor and the compressive stress tensor, respectively, while $H\left(f\right)$ and $\delta \left(f\right)$ are the Heaviside and Dirac delta functions. The default FW-H model in ANSYS Fluent was used without implementing any user-defined functions (UDFs). Based on previous experience, propeller noise signatures at the propeller plane exhibit minimal directivity and are nearly identical in all directions. Therefore, only one receiver location was selected.

3.2. Grid

The computational domain was discretized utilizing an unstructured, polyhydra-dominated mesh, as illustrated in Figure 5a at 3000 RPM. Last-ratio boundary layers were added to improve boundary layer resolution along the propeller surfaces, a critical factor for capturing precise near-wall characteristics, alongside face sizing. This setup consisted of five layers with a transition ratio of 0.2, with the initial layer height set at 0.01 mm, resulting in a $y^{+}$ value of less than 1 for the first layer above the propeller surfaces. A grid independence study, concentrating on the refinement of the rotating domain and the propeller surfaces, was carried out to optimize the trade-off between computational time and numerical accuracy for the same RPM using the transient solver, as presented in Figure 5b. It was found that the variation in thrust was within 1.5% after 3.9 million cells. Further mesh refinement did not significantly enhance the results. Consequently, a mesh of approximately 3.9 million cells was selected for subsequent analysis across all test scenarios.

4. Results and Discussion

This section begins with an analysis of propeller performance, aeroacoustics, and the proposed performance–noise trade-off index across all tested rotational speeds. Next, CFD simulation results at 9000 RPM are presented to provide further insight into the resin propeller’s characteristics.

4.1. Propeller Performance

To evaluate propeller performance in hover, the figure of merit ($FM$)—a widely used metric for assessing propeller or rotor efficiency in the absence of forward flight—is calculated using Equation (5) [24].

$$FM={\displaystyle \frac{C_T^{3/2}}{\sqrt{2}{C}_P}}={\displaystyle \frac{C_T^{3/2}}{\sqrt{2}{C}_Q}}<1$$

(5)

where $C_T$, $C_P$, and $C_Q$ represent the propeller thrust, power, and torque coefficients, respectively. For clarification, using the nondimensionalization method in the textbook [24], $C_P$ and $C_Q$ are numerically equivalent.

To further evaluate the performance of the propeller, two commercial counterparts with the same diameter were tested: an advanced precision composite (APC) (254 mm × 177.8 mm) and a JZ Zinger (254 mm × 152.4 mm, wood) propeller. As shown in Figure 6a,b, the resin propeller maintains relatively constant values of $C_T$ and $C_Q$, with ANSYS Fluent predicting them within a 10% error. In contrast, both the APC and wooden propellers exhibit a slight increase in $C_T$ as rotational speed increases. For $C_Q$, the APC propeller shows a decreasing trend, whereas the wooden propeller remains nearly constant.

However, the $FM$, presented in Figure 6c, reveals different trends. The experimental results show significant deviations, primarily due to measurement uncertainty in the load cell and the sensitivity of $FM$ to small changes in $C_T$ and $C_Q$. For the resin and wooden propellers, it is difficult to determine a clear performance advantage due to significant variations in $FM$. ANSYS Fluent predicts $FM$ with an average error of 10% but the largest error, with the highest deviation (≈13%) occurring at 3000 RPM. The APC propeller, on the other hand, shows an increasing $FM$ as rotational speed rises.

To facilitate comparison, the averaged values are summarized in

Table 2. Comparison of averaged performance and weight between different propellers.

Propeller	${\mathit{C}}_{\mathit{T}}$	${\mathit{C}}_{\mathit{Q}}$	FM	Weight [Gram]
Experiment and APC	0.0160	0.0024	0.61	30.7
Experiment and Wood	0.0172	0.0025	0.63	14.2
Experiment and Resin	0.0102	0.0012	0.64	17.0
ANSYS Fluent and Resin	0.0100	0.0012	0.58	-
Constant pitch [25]	0.0125	0.0032	0.31	21.0

, along with the propeller weights. A constant-pitch aluminum propeller is also included for reference. The data indicate that the resin propeller achieves a slightly higher $FM$ than the others. For the APC and wooden propellers, $C_Q$ is approximately doubled, and for the constant-pitch aluminum propeller, it is nearly tripled. In terms of weight, the resin propeller is the second lightest among those tested.

4.2. Propeller Aeroacoustics

For propeller aeroacoustics, the primary tonal noise ($f^{+}$ = 1), broadband noise, and overal sound pressure level (OASPL) were analyzed following the application of a Fast Fourier Transform (FFT) on the pressure data, as described by Welch [26]. The results are presented in Figure 7a, Figure 7b and Figure 7c, respectively. The OASPL values obtained from ANSYS Fluent were cross-validated using a custom MATLAB script developed by the authors. In general, the primary tonal noise increases with disk loading (propeller thrust divided by propeller disk area, in units of N/m²), with ANSYS Fluent capturing this trend more accurately. The largest discrepancy occurred at 6600 RPM.

To extract broadband noise, the built-in findpeaks function in MATLAB 2021 was used to automatically detect and remove tonal peaks, leaving only the broadband noise component by summing the remaining sound pressure level (SPL) values [16]. However, the default settings of this function may fail to remove certain peaks due to limitations in its peak detection algorithm. As a result, deviations in broadband noise between ANSYS Fluent and the experiment, as seen in Figure 7b, can be attributed to missed peak detection, further supported by the SPL plot in Figure 7d, which shows that ANSYS Fluent exhibits a higher density of peaks. The FW-H equation primarily predicts tonal noise from propellers but can also capture some low-frequency broadband noise if the surface pressure fluctuations are well resolved; however, accurately predicting broadband noise requires alternative approaches, such as Lighthill’s analogy. This limitation represents a second contributing factor to the discrepancies in broadband noise. Figure 8 illustrates the turbulence level, quantified by the normalized Q-criterion (Q = 0.05), around the resin propeller. The flow field includes flow separation on the top (toward the leading edge) and bottom surfaces, flow separation after the trailing edge, and the development of tip vortices. These flow separation effects impact broadband noise predictions, further influencing the observed discrepancies. Additionally, flow separation influences propeller torque, making it essential to maintain consistent disk loading and torque at the same RPMs when assessing the propeller’s impact on noise reduction [14].

Another contributing factor is the noise from the electric motor, which is included in the experimental broadband noise and OASPL. This is evident in Figure 7d, where peaks appear at half of the $f^{+}$ integer frequencies. Additionally, isolating propeller noise from electric motor noise in experiments is challenging, as motor noise cannot easily be separated from propeller noise due to the nonlinear nature of noise sources. Yangzhou et al. [27] attempted to remove electric motor noise from the propeller noise spectrum, but discrepancies between experimental and numerical results persisted, particularly because the motor noise differed between loaded and unloaded conditions. This issue complicates the analysis of propeller acoustics. Consequently, as in Gojon et al. [20], motor noise is included here.

For OASPL, ANSYS Fluent provides more accurate predictions at higher rotational speeds. Below 6600 RPM, the electric motor appears to have a more significant influence on OASPL, as all three propellers exhibit identical trends. Additionally, both the second and third factors contribute to the underestimation of OASPL by ANSYS Fluent. Among the three propellers, the resin propeller consistently produces the lowest noise levels. However, distinguishing between the APC and wood propellers is challenging, as their noise levels are very similar.

4.3. Propeller Trade-Off Index

From the FM and aeroacoustics results presented in the previous two subsections, neither analysis alone provides a clear ranking of the three tested propellers as they are not directly linked. To bridge the gap between propeller performance and aeroacoustics, the thrust-noise ratio (TNR), defined as thrust divided by OASPL (in units of N/dB), is introduced and presented in Figure 9a. It is important to note that TNR is not a direct performance metric, as it does not account for propeller torque. Additionally, a meaningful comparison of TNR should be conducted at matched thrust and torque levels. Therefore, while Figure 9a shows that the resin propeller has the lowest TNR values, this may be misleading. A higher TNR generally indicates more efficient propulsion with lower noise; however, the resin propeller exhibits the lowest noise levels, as seen in Figure 7a–c.

To provide a more comprehensive evaluation, we propose a new index, the propeller trade-off index ($\chi$), which accounts for both propeller performance (quantified by $FM$) and aeroacoustic characteristics. This index, defined in Equation (6), serves as a criterion for propeller selection. Since primary tonal noise is the most perceptible to human hearing, and prolonged exposure to levels exceeding 85 dBA (A-weighted) for eight hours can cause hearing damage, both primary tonal noise and the 85 dBA threshold are considered in the aeroacoustic evaluation. The results are shown in Figure 9b. As depicted in Figure 9b, $\chi$ exhibits a linear decreasing trend with increasing rotational speed for all three propellers. Among them, the resin propeller consistently has the highest $\chi$ values across all rotational speeds, followed by the wood propeller and then the APC propeller. This trend is clearly identifiable in Figure 9b, providing a more balanced assessment of the trade-off between aerodynamic performance and noise emissions.

$$\chi =[w_1\ast FM+w_2\ast \{1-{\displaystyle \frac{Primarytonalnoise\left(\mathrm{dB}\right)}{85\mathrm{dBA}}}\}]<1$$

(6)

Here, $w_1$ and $w_2$ are weights both set to 0.5, and their sum equals 1, indicating that propeller performance and noise levels are of equal importance. Potential users can adjust these values based on their priorities. For example, $w_2$ could be increased if greater emphasis is placed on minimizing noise signatures. Additionally, OASPL could be used in place of primary tonal noise for the evaluation.

4.4. Propeller Velocity Profile

Momentum theory can be used to estimate propeller thrust by modeling the flow with a uniform velocity profile and the actuator disk concept [24], where A (in m²) represents the disk area. In theory, the velocity just above the propeller is assumed to be stationary, while the velocity in the far-field wake is used for analytical calculations. To validate the theory, Figure 10 presents the axial velocity profiles, nondimensionalized by the tip speed, for three cylindrical control volume sizes, all matching the propeller disk size, at 9000 RPM. The plots indicate that at one propeller diameter above the propeller center, the air remains nearly stationary. To quickly estimate propeller thrust at this rotational speed, the axial velocity profile within the wake, below one propeller diameter from the propeller center, is considered. At both top and bottom locations, static pressure is assumed to be equal to atmospheric pressure, since the air at the top is stationary and the wake is treated as a free jet at the bottom. Consequently, propeller thrust can be approximated using $\dot{m}\overline{V}z$ = $\rho A{\left(\overline{V}z\right)}^2$, where $\overline{V}z$ is the average axial velocity at the bottom location in Figure 10c. This approach predicts a propeller thrust of 8.30 N, closely matching the 8.87 N obtained from ANSYS Fluent via integration over the entire blade surface. These results establish a link between the velocity profile and propeller thrust estimation.

4.5. Propeller Surface Pressure

To understand the phenomenon in Figure 7d from ANSYS Fluent, Figure 11 presents the RMS values of the time derivative of static pressure on the propeller surface, which represent sound sources when applying the FW-H acoustics model. Additionally, tangential velocity vectors at three blade locations (25% R, 50% R, and 75% R) are shown for 9000 RPM. Tangential velocity influences surface static pressure, which in turn determines local lift and induced drag, ultimately affecting thrust, torque, and noise generation.

As shown in Figure 11, high fluctuations in surface static pressure are concentrated in three key regions: (1) between the propeller hub and the trailing edge within 25% R (referred to as the root region), (2) along the trailing edge between 25% R and 50% R (referred to as the middle region), and (3) on the leading edge between 75% R and the propeller tip (referred to as the tip region). When analyzed alongside Figure 8, these fluctuations can be attributed to different aerodynamic interactions. The root region experiences disturbances due to blade interactions with vortices shed from upstream elements. The middle region is affected by flow separation behind the trailing edge, while the tip region is influenced by the formation of tip vortices and the associated unsteady pressure variations. The root and middle regions primarily contribute to broadband noise, whereas the tip region is associated with tonal noise, particularly loading noise, and potentially broadband noise as well.

To further assess the aerodynamic behavior on the propeller surfaces and its impact on noise generation, Figure 12 presents the static pressure coefficient ($c_p$) and the RMS of $dp/dt$ at three blade locations. The pressure coefficient distributions indicate that sectional lift increases toward the propeller tip, contributing to the overall thrust generation. The steep pressure gradients at the leading edge, particularly near 75% R and beyond, correlate with high RMS $dp/dt$ values, reinforcing their role in tonal noise generation. Meanwhile, the RMS $dp/dt$ plots suggest that the flow separation observed beneath the propeller blade in Figure 8 has a minimal direct impact on surface pressure fluctuations, implying that its contribution to broadband noise is secondary to the pressure disturbances in the root and middle regions. These observations provide a more detailed impression of the connection between pressure fluctuations and the acoustic characteristics captured in the simulations.

5. Conclusions

This paper experimentally and numerically investigates a 254 mm resin-printed propeller, examined at rotational speeds ranging from 3000 to 9000 RPM. Propeller thrust and torque measurements were obtained using a six-degree-of-freedom load cell, while acoustic measurements were gathered using a single microphone positioned radially at a distance of three times the propeller diameter from the propeller center, serving as reference data. To further understand the propeller’s performance and aeroacoustics, the experimental scenarios were replicated in the commercial CFD software ANSYS Fluent. The simulations employed the DES model in conjunction with the FW-H model and a transient flow solver. The comparison between the experimental and numerical results led to several conclusions:

• The resin propeller exhibits slightly better performance than two commercial counterparts, with an average FM of 0.64. However, the difference between the wood and resin propeller is marginal. The resin propeller is slightly heavier than the lightest wooden propeller and has higher printing costs and production time. ANSYS Fluent predicts propeller thrust and torque coefficients within a 10% error margin.
• Regarding aeroacoustics, the resin propeller generally exhibits the lowest noise levels in terms of primary tonal noise, broadband noise, and overall sound pressure level (OASPL). However, distinguishing the superior propeller between the APC and wooden propeller remains challenging. ANSYS Fluent accurately predicts primary tonal noise, but several factors affect the accuracy of broadband noise and OASPL predictions. Noticeably, the motor noise is not excluded from the experimental results.
• To balance propeller performance and aeroacoustics, a new trade-off index is proposed and evaluated for the three propellers. This index reveals distinct trends in identifying the best-performing propeller compared to the traditional TNR metric, standalone FM, and aeroacoustics alone.
• Using axial velocity profiles obtained from ANSYS Fluent, an analytical thrust estimation was performed following a momentum-theory-based approach.
• Vorticity iso-surfaces, quantified using the normalized Q-criterion, and the RMS of the time rate of static pressure on the propeller surface reveal key aerodynamic phenomena. Flow separation on the leading edge near the tip contributes to the formation of tip vortices, which in turn generate tonal noise. Flow separation behind the trailing edge between 25% R and 50% R contributes to broadband noise. At the root region around the trailing edge, pressure fluctuations result from blade interactions with vortices, further contributing to broadband noise. However, the flow separation formed underneath the propeller blade has a secondary effect on broadband noise, as it does not significantly alter pressure fluctuations.