This experimental study investigates the effect of blade phase angle on noise attenuation in two adjacent, electronically synchronized propellers. Acoustic measurements were performed in an aeroacoustic wind tunnel with a distributed electric propulsion system that involved the adjustment of relative phase angles of 2-bladed propellers between Δψ = 0° and 90°. Ranges of advance ratios (J = 0–0.73) were investigated at a fixed propeller rotation speed of 5000 rpm. The investigation explored the impact on noise directivity and frequency characteristics. The findings reveal significant reductions in noise directivity and tonal noise at the blade pass frequency (BPF). A relative phase angle of Δψ = 90° demonstrated the maximum noise reduction, with an 8 dB decrease at the first BPF and a 2 dB reduction in overall sound pressure level at J = 0. For in-flow conditions (J > 0), a relative phase angle of Δψ = 90° resulted in significant noise reductions of about 24 dB in the first BPF and 6 dB in overall sound pressure level, compared to Δψ = 0°. These observations offer critical insights into the use of the propeller's relative phase angle as an effective noise control method in the distributed electric propulsion system.

Urban air mobility has gained significant momentum as a prospective sustainable transportation solution within urban areas. Its goal is to promote efficient alternatives to ground transportation to reduce pollution and greenhouse gas emissions (Baledón and Kosoy, 2018; Rizzi , 2020). The rapidly growing interest in urban air mobility has, in turn, triggered notable advances in rotor technology that are vital to the development of novel aircraft architectures (Silva , 2018). However, rotor noise is considered one of the main challenges for the successful integration of urban air mobility into the conventional transportation framework. Therefore, the exploration of effective control methodologies for mitigating rotor noise is of paramount scientific and practical significance (Christiansen , 2016; Uragun and Tansel, 2014).

In the distributed electric propulsion (DEP) configuration, a series of electric motor-driven propellers is employed along the wing's span. The interaction effects between these propellers and the wing, as well as among the propellers themselves, are identified as critical aspects in the design of DEP systems (Kim , 2018). Additionally, the noise generated from these interactions is regarded as one of the main complexities inherent in such configurations (Turhan , 2023b; Zhou , 2017). The wing's potential field may also influence the propeller blade loading and alter propeller noise source (Huang , 2023; Turhan , 2023a).

Due to the strong interest in the development of novel adjacent propeller architectures, several researchers have investigated rotor–rotor aerodynamic and acoustic interactions (Intaratep , 2016; Lee and Lee, 2020; Schram and Bennett, 2024; Shukla and Komerath, 2019; Pascioni and Rizzi, 2018), and they have demonstrated that the aerodynamics and acoustics of multiple adjacent rotors can markedly alter the noise directivity pattern in hover conditions. Yet, the specific interaction mechanism responsible for the increased noise observed is still not well understood. The lack of interaction studies conducted in forward flight also makes it difficult to determine which physical mechanism is responsible for an increase in noise in DEP configurations.

In recent years, noise control methods have been categorized into active and passive methods. Passive methods reduce noise by altering the structure of the propeller and do not require energy to operate. Trailing- and leading-edge serrations of propeller blades are examples of passive control methods (Hersh , 1974; Lee , 2019; Zang , 2023). Such methods may negatively affect the rotor aerodynamic performance, limiting its noise reduction effect and potential benefits (Gur and Rosen, 2009). To reduce noise more effectively, researchers have explored a few active control methods, such as electronic sound absorbers (Lueg, 1936) and synchronization of the rotational speed and phase of a two-propeller setup (Schiller , 2019; Shao , 2022). Phase control, also known as phase synchronization, implies that the propellers' azimuthal blade positions are controlled relative to each other by a certain phase angle. This method aims at reducing the blade pass frequency (BPF) noise radiated in specific directions. Blades can be tuned to interfere with each other, thereby affecting the noise directivity, which can then be controlled to reduce the noise levels at the desired position.

Other related studies have explored the possibility of utilizing the propeller phase control method to modify acoustic characteristics, particularly at low frequencies. Pascioni (2019) achieved 6 dB reduction in the BPF for 3-bladed propellers; the standard deviation of a Gaussian phase error should not exceed approximately 0.5%. Similarly, a numerical study focusing on far-field noise prediction revealed the possibility of achieving a substantial 20 dB reduction in BPF noise at 5000 rpm and J = 0.6 using 2-bladed propellers (Pascioni and Rizzi, 2018). Guan (2021) focused on rotor interference, proposing a more systematic method for two-rotor noise reduction based on different relative phase angles. Their simulation-based analysis indicated the possibility of achieving, for single observation points, a remarkable noise reduction of up to 11–30 dB using phase synchronization. Zhou and Fattah (2017) studied experimental measurements and numerical prediction of 2-bladed propellers. They found that the phase angle between two propellers can impact their sound emissions by up to 10 dB at static thrust conditions. On the other hand, Schiller (2019) applied the phase control method both experimentally and theoretically at static thrust conditions, demonstrating that the use of relative phase angle can yield a reduction of the sound pressure level (SPL) at the first BPF of approximately 4–5 dB. Hertzman (2022) demonstrated experimentally that the operation of propellers with a relative phase angle of Δψ = 90, in static condition (i.e., no inflow), at rotational speed of 3000 rpm, could result in the reduction of up to 8 dB at the BPF.

Although previous numerical studies and limited experimental research under static thrust and inflow conditions have demonstrated the noise reduction benefits of phase synchronization (Patterson , 2019; Shao , 2022), as summarized in Table I, certain aspects are yet to be fully understood. The impact of phase synchronization on noise amplitude and directivity, particularly in DEP configurations under in-flow conditions, remains unclear. It is hypothesized that the relative phase angle may lead to acoustic interference effects, thus offering the possibility of far-field noise reduction. With the implementation of phase control, leveraging destructive interference of the acoustic source is anticipated to significantly modify the overall sound directivity (Guan , 2021; Pascioni , 2019). In the realm of electrically driven propellers, the use of motor-driven systems presents an opportunity to achieve precise control over the relative phase angles between propeller blades, thereby offering the potential to adjust noise-directivity patterns in a controlled manner. Despite this potential, the effectiveness of active phase control in achieving noise reduction is critically dependent on the ability to maintain precise control of both the rotational speeds and the blade phase angles. Achieving such a level of precision presents a formidable challenge, as it necessitates intricate synchronization of the propellers using an electronic control system. The primary challenge in electronic synchronization lies in the requirement for both high-bandwidth current control and high-bandwidth position feedback, alongside highly precise control components, including electronic speed controllers, motors, and sensors, each of which must be selected and calibrated with great care to ensure precise phase matching. The difficulty in achieving such precision has led to a predominant focus on mechanical synchronization methods in experimental studies to date. These mechanical approaches, while they might contaminate the aeroacoustic and aerodynamics measurements, they can offer simpler implementation and more dependable operation, making them a pragmatic choice for some studies (Pascioni , 2019; Patterson , 2020). However, this reliance on mechanical synchronization underscores a significant gap in the field, namely, the need for advanced electronic control systems capable of achieving the high level of precision required for effective phase control. This research will fill this gap by developing a specialized electronic speed controller system designed to facilitate precise electronic phase matching.

TABLE I.

Comparative analysis of previous studies on propeller phase synchronization.

Blade number Rotational speed (rpm) Propeller diameter (D) (in.) Propeller pitch (P) (in.) Advance ratio (J) Methodology BPF noise reduction (dB) Researchers
3-bladed  5100  16  Numerical and experimental  Pascioni (2019)  
2-bladed  5000  —  —  0.6  Numerical  20  Pascioni and Rizzi (2018)  
2-bladed  6000  12.5  —  0–0.1  Numerical  11–30  Guan (2021)  
2-bladed  5400  9.5  —  Numerical and experimental  10  Zhou and Fattah (2017)  
2-bladed  5100  12.5  4.5  Numerical and experimental  4–5  Schiller (2019)  
2-bladed  3000  17  5.8  Experimental  Hertzman (2022)  
2-bladed  4000  12  Experimental  1–11  Shao (2022)  
Blade number Rotational speed (rpm) Propeller diameter (D) (in.) Propeller pitch (P) (in.) Advance ratio (J) Methodology BPF noise reduction (dB) Researchers
3-bladed  5100  16  Numerical and experimental  Pascioni (2019)  
2-bladed  5000  —  —  0.6  Numerical  20  Pascioni and Rizzi (2018)  
2-bladed  6000  12.5  —  0–0.1  Numerical  11–30  Guan (2021)  
2-bladed  5400  9.5  —  Numerical and experimental  10  Zhou and Fattah (2017)  
2-bladed  5100  12.5  4.5  Numerical and experimental  4–5  Schiller (2019)  
2-bladed  3000  17  5.8  Experimental  Hertzman (2022)  
2-bladed  4000  12  Experimental  1–11  Shao (2022)  

The primary aim of this research is to explore the noise suppression capabilities of DEP systems under both static thrust and in-flow conditions through the implementation of electronic synchronization of the propellers. This approach is novel in the context of DEP systems and represents a significant advancement in the study of noise reduction techniques. Furthermore, the research uniquely investigates the impact of phase locking in conditions of non-zero inflow speed (i.e., advance ratio > 0), cases that have not been investigated in any previous experimental study, as shown in Table I. This analysis allows to explore noise suppression in DEP systems by identifying the optimum relative phase angle to obtain the lower noise level for an operating forward flight condition. Furthermore, to the authors' knowledge, this study will be the first to conduct phase-lock experimental campaigns with electronically phase-controlled propellers. This paper is organized as follows. Section II provides an overview of the experimental setup, propeller phase control, and analysis techniques. Section III discusses the acoustic results obtained from the experiments. Finally, Sec. IV summarizes the key findings of this research in the domain of noise reduction for DEP configurations.

The experiments were carried out in the aeroacoustic wind tunnel at the University of Bristol. The wind tunnel is a temperature-controlled, closed-circuit open-jet configured for a free-stream range from 15 m/s to 40 m/s, with a turbulent intensity as low as ∼0.2% in an anechoic environment (Mayer , 2019). The wind tunnel's exit nozzle has a width of 0.5 m and a height of 0.775 m, with a contraction ratio of 8.4. The test chamber is acoustically treated with an approximate cut-off frequency of 160 Hz, according to the ISO 3745 standardized testing procedure. Additionally, all exposed surfaces, including the model support struts, anechoic chamber, and contraction nozzle, are covered with foam wedges to ensure reduced acoustic reflection.

As shown in Fig. 1, the experimental setup consists of two propulsion units with propellers mounted on a wing, representative of a DEP configuration. The experiments were performed with 2-bladed propellers with a diameter of D = 9 in. (228.6 mm) and a pitch-to-diameter ratio of P/D = 1. The propellers, manufactured by Mejzlik (https://www.mejzlik.eu/), were made from carbon fiber/epoxy-based materials and had a Clark-Y aerofoil section. The 2-bladed propellers are of a constant-pitch type with both pitch and diameter chosen as 9 in. The blade chord and pitch angle distribution along the blade span are provided in Fig. 2. The wing, with a chord of c = 0.3 m and a span of L= 0.94 m, had a NACA0018 profile and was made of 6000 series aluminum. The propellers were mounted at a distance of 150 mm from the trailing edge of the propeller to the leading edge of the wing and approximately 0.5 m away from the nozzle exit, as is normal in relation to the tunnel free-stream flow. Because previous results by Shao (2022) revealed that phase synchronization is more advantageous for co-rotating propellers compared to counter-rotating propellers, it was decided in the current setup that both propellers to be configured to rotate in the same direction, specifically in a counterclockwise direction when looking from the front.

FIG. 1.

(Color online) Schematic representation of the experimental setup, illustrating the arrangement of phase-synced propellers and the far-field microphones.

FIG. 1.

(Color online) Schematic representation of the experimental setup, illustrating the arrangement of phase-synced propellers and the far-field microphones.

Close modal
FIG. 2.

(Color online) Distribution of the blade chord length (c/R) and the pitch angle for the 2-bladed 9 × 9 in.2 propeller used in this study.

FIG. 2.

(Color online) Distribution of the blade chord length (c/R) and the pitch angle for the 2-bladed 9 × 9 in.2 propeller used in this study.

Close modal

The propulsion unit driving each propeller was a 540 kV AT4125 T-motor with a maximum continuous power rating of 2.2 kW. The phase angle of the propeller blades was precisely tracked using a 12-bit RLS RE36IC incremental output encoder with an accuracy of ±0.3°. The relative phase angle of the propellers was controlled through a specialized setup, transmitting two distinct signals, each serving a unique function. The primary signal was designated for the motor control software to manage the relative phase angles, which is elaborated upon in Sec. II A. The secondary signal was relayed to an oscilloscope (Tektronix TBS1102C model) to monitor phase angle variations throughout the testing. Tektronix electric voltage probes were connected to the position signal, which was obtained by the controller after processing the position encoder pulses.

The definition of the relative phase angle (Δψ) of the two propeller systems and the other geometric parameters of the setup is illustrated in Fig. 3. Turhan (2023b) elucidated that variations in propeller separation distance have no significant impact on the aerodynamic performance of the propellers, while causing noise level variation of less than 2 dB. This is further supported by Zarri (2023) and Schiller (2019), who both concluded that the relative phase angle's effect on aerodynamic performance is negligible. In the experimental setup, the distance between the propellers, denoted as center-to-center separation distance, was adjusted at s/D = 1.05, chosen based on this understanding, to minimize any potential aerodynamic interactions and thus isolate the effects of acoustic interference. The relative phase angle is defined as the angle difference between propeller blades. Initially, the propellers were aligned along the wing span, i.e., horizontally, to set a reference angle, establishing an initial relative phase difference between the propellers of Δψ = 0°. Propeller 1 was designated as the master propeller, and Propeller 2 was termed the slave propeller. The adjustment of the blade position on Propeller 2 was performed to attain various relative phase angles, while Propeller 1 remained in its original position. The study encompassed seven distinct relative phase angles (Δψ) ranging from 0° to 90° in increments of 15°.

FIG. 3.

(Color online) Definition of the reference system for phase synchronization for the two-propeller configuration.

FIG. 3.

(Color online) Definition of the reference system for phase synchronization for the two-propeller configuration.

Close modal

The design of the phase angle control system required a bespoke approach to ensure precise synchronization and control of the propeller phase angle. Each propeller was equipped with its own dedicated motor and controller to allow independent revolutions per minute and phase control. Each propeller was capable of not only following a specified propeller position reference but also adjusting for user-defined offsets (Δψ), providing a high level of flexibility in a variety of operational settings. Importantly, the dynamic nature of the propeller position reference, which responds to changes in propeller speed, provides optimal performance even during high-speed rotations. Furthermore, a mechanism was implemented to synchronize the propeller position reference across all motor controllers to maintain a consistent angular relationship between the two propellers.

Integrating position and speed loops into a control system is crucial for achieving precise position synchronization and efficient load disturbance mitigation. High-bandwidth current control and high-bandwidth position feedback are fundamental contributors to the effectiveness of these loops, enabling rapid responses and precise rejection of load disturbances.

The system block diagram, depicted in Fig. 4, employs a field-oriented control strategy for the regulation of a motor via a three-phase voltage source inverter (Manias, 2017). The controller algorithm is implemented in the Texas Instruments LAUNCHXL-F280049C development board, which features the TMS320F280049C microcontroller. The 3-phase converter employed in this setup is the BOOSTXL-3PhGaNInv, also made by Texas Instruments. The controller sends control instructions containing the rotation speed and initial phase to the servo motor to drive the propeller to rotate with a specific initial phase and constant rotation speed, thus generating a stable noise sound field. The converter operates at a switching frequency of 100 kHz, while the controller functions at 25 kHz. A DC voltage of 20 V is applied to the converter.

FIG. 4.

(Color online) Block diagram of the control system for propeller phase synchronization.

FIG. 4.

(Color online) Block diagram of the control system for propeller phase synchronization.

Close modal

The blade angular position (θ) feedback is obtained from the motor-mounted 2000-count quadrature encoder. A simple mechanism is developed to synchronize the position controller. The reference position generates a square wave, where each edge is at the same time as the zero of the position. This pulse is also read by the other controller, for which the edge triggers the interrupt subroutine, which then resets its position reference to zero. In this manner, small deviations are corrected, ensuring the controllers remain synchronized. At an operational speed of 5000 rpm, the positional error consistently remains below 1°.

The speed controller receives its input from the user-defined speed reference (ω), which is passed through a low-pass filter to obtain the speed reference for the controller. Any deviation from the reference speed (ω) is rectified by the position controller as a minor correction (ωc) to align with the reference speed. The speed feedback is obtained from the quadrature encoder pulse at a rate of 25 samples per motor revolution. Furthermore, even under the same 5000 rpm condition, the peak-to-peak speed error consistently remains below 0.05% (2.5 rpm).

Figure 5 presents a comparison of the position signal voltage for the two propellers over time. The measurements were made using a Tektronix TBS1102C oscilloscope, chosen for its high precision in tracking dynamic signal fluctuations. Tektronix voltage probes were connected with the position signal, generated by the controller in response to processed pulses from the position encoder. The oscillation of the voltage from the oscilloscope shows the synchronized operation of the two propellers. Figure 5(a) shows the signal when both the propellers are in phase having a relative phase difference of Δψ = 0°, and Fig. 5(b) shows the operating conditions where the relative phase difference is set to Δψ = 90°.

FIG. 5.

(Color online) Position signal of the processed pulses from the position encoder for the two 2-bladed propellers (a) Δψ = 0° and (b) Δψ = 90°.

FIG. 5.

(Color online) Position signal of the processed pulses from the position encoder for the two 2-bladed propellers (a) Δψ = 0° and (b) Δψ = 90°.

Close modal
To analyze the far-field noise characteristics, measurements were carried out using an overhead array of 18 microphones encompassing the angles θ = 55° to θ = 130°, as shown in Fig. 1. The array was centered with the θ = 90° microphone position at 1.75 m above the center of the wing and equidistant between the two propellers. The far-field noise was measured using 1/4-in.-diameter G.R.A.S 40PL free-field microphones, with a frequency range of f = 10 Hz to 20 kHz, and dynamic range of 142 dB, with an accuracy of ±1 dB. The microphones were calibrated using a G.R.A.S 42AA pistonphone calibrator before and after the experiments. The data were acquired at a sampling frequency of 216 Hz and recorded for t = 40 s using a National Instruments PXIe-4499 Sound and Vibration module. The power spectra are constructed using the matlab Pwelch method (Welch, 1967), and the results are presented with a frequency resolution of 1 Hz. The SPL was calculated using the following equation:
SPL = 10 · log 10 ( ϕ p p p ref 2 ) ,
(1)
where ϕpp represents the power spectral density of the measured acoustic pressure, and pref is the reference acoustic pressure (equal to 20 μPa).
The tests were carried out at a constant propeller rotational speed of 5000 rpm. The first BPF was calculated using the following equation:
BPF = ω N b 60 ,
(2)
where ω is the rotation speed in revolutions per minute and Nb is the number of blades. For a constant rpm of 5000, this results in a BPF of 166.6 Hz for the 2-bladed propeller. The experiments were conducted at four different inflow velocities: 0, 9, 10, and 14 m/s, which corresponded to an advance ratio (J) of 0, 0.47, 0.53, and 0.73. The chosen ratios span the range of typical operating conditions for the propellers being studied (Baskaran , 2024). The advance ratio is a non-dimensional term defined as follows:
J = V n D ,
(3)
where V is the free-stream inflow velocity in m/s, n the rotational speed in revolution per second, and D is the propeller diameter in meters.

The aeroacoustic properties of the two propeller configurations are studied by assessing the impact of the propellers' relative phase angle on the far-field noise under static thrust (J = 0) and inflow conditions (J > 0). The analysis begins with an examination of frequency characteristics of the two propeller setups related to the influence of the phase angle. Building on these findings, the directivity of the first BPF and overall sound pressure level (OASPL) behavior is presented to verify the effectiveness of the blade phase-locking method on the radiated noise from such two-rotor configurations. Results are presented for a range of advance ratios. Subsequently, a time-frequency analysis is conducted, by using a continuous wavelet transform (CWT) to investigate the nature of the first BPF.

Figures 6(a) and 6(b) present the far-field SPL spectra at θ = 90° for relative blade phase angles of Δψ = 0° and Δψ = 90°, respectively. Results are presented for four advance ratios, J = 0, 0.47, 0.53, and 0.73, alongside the static propeller scenario (J = 0). The results for two distinct blade relative phase angles, Δψ = 0° and Δψ = 90°, exhibit the characteristic propeller far-field noise spectra, which include both tonal and broadband noise components. The tonal noise is primarily due to the BPF, at f = 166.6 Hz, and its harmonics, which manifest periodically with each rotation of the propeller. As seen in Fig. 6, the harmonics of the BPF present much lower amplitude peaks compared to the primary BPF. The motor mechanical noise, represented by the dashed light gray line, is characterized by discrete tones superimposed on a broadband noise level. The comparison shows that the propeller aerodynamic noise exceeds the motor mechanical noise by more than 15 dB, indicating that the motor noise has a negligible effect on the overall noise spectrum and that the propeller's aerodynamic noise is the predominant contributor to the noise collected using the far-field microphone array.

FIG. 6.

(Color online) Far-field SPL for two propellers at various advance ratios for observer angle θ = 90° and phase angles (a) Δψ = 0° and (b) Δψ = 90°.

FIG. 6.

(Color online) Far-field SPL for two propellers at various advance ratios for observer angle θ = 90° and phase angles (a) Δψ = 0° and (b) Δψ = 90°.

Close modal

Under the static propeller condition (J = 0), see Fig. 6(a), an increase in the broadband noise levels within the ƒ = 300–1000 Hz range is observed for both relative phase angles. With an increase in the advance ratio, there is a notable reduction in broadband noise levels in comparison to the static thrust condition in line with observations from previous studies (Bowen , 2023; Turhan , 2023b). The broadband noise reaches its minimum level at an advance ratio of J = 0.53, beyond which the noise levels begin to ascend with further increases in the advance ratio. At a static thrust condition (J = 0), where increased levels of broadband noise are observed, the dominant noise source is presumed to be turbulence ingestion at the leading edge, attributed to the wake generated by the previous blade. With increasing advance ratios, the noise contributions are primarily attributed to trailing edge noise (Grande , 2022). These alterations in broadband noise levels result from the changing positions of flow separation on the propellers and effective tip velocity, which are influenced by the varying advance ratios (Grande , 2022). As can be seen from the results, while changing the blade relative phase angle (Δψ), the SPL exhibits minimal variations in the propeller broadband energy content. The result shows that changing the blade relative phase angle from Δψ = 0° to 90° can lead to substantial changes to the magnitude of the BPF and its harmonics. It is also noted that this can be a sensitive function of the advance ratio. In what follows, we will focus on the impact of the blade relative phase angle (Δψ) on the amplitude of the BPF and its harmonics at different operating conditions.

Figure 7 presents the far-field SPL at an observer angle of θ = 90°, for three relative phase angles Δψ = 0°, 45°, and 90°. The results are provided for four advance ratios, J = 0, 0.47, 0.53, and 0.73. As discussed earlier, the blades' relative phase angle does not affect the broadband noise for a given advance ratio and the acoustic spectra are dominated by tones at low frequencies. This is consistent with previous investigations on propellers phase synchronization (Pascioni , 2019; Schiller , 2019; Shao , 2022; Zarri , 2023). An initial inspection of the results shows that a non-zero phase difference between the blades, i.e., Δψ = 45° and 90°, can lead to a noticeable reduction in noise at the first BPF and its subsequent harmonics. One can also see that as the phase angle difference increases, the reduction in the BPF becomes more pronounced. In the case of the static operation, i.e., J = 0, see Fig. 7(a), a reduction of approximately 1.4 dB is noted at Δψ = 45°, and a more substantial decrease in 8.1 dB is evident at Δψ = 90° in comparison to the propellers' reference location of Δψ = 0°.

FIG. 7.

(Color online) Far-field SPL for two propellers with a relative phase angle of Δψ = 0°, 45°, and 90°, at an observer angle of θ = 90°, for advance ratios (a) J = 0, (b) J = 0.47, (c) J = 0.53, and (d) J = 0.73.

FIG. 7.

(Color online) Far-field SPL for two propellers with a relative phase angle of Δψ = 0°, 45°, and 90°, at an observer angle of θ = 90°, for advance ratios (a) J = 0, (b) J = 0.47, (c) J = 0.53, and (d) J = 0.73.

Close modal

As can be seen from the results in Fig. 7, when the relative phase is set at Δψ = 0°, the amplitude of the first BPF remains constant, both under the static condition and across all advance ratios. However, when the relative phase is increased to Δψ = 45°, a slight decrease in noise levels at the first BPF is observed. Further increasing the relative phase angle to Δψ = 90° results in a distinct change in the noise signature at the BPF and its harmonics across all advance ratios [see Figs. 7(b)–7(d)]. A comparison between Δψ = 0° and Δψ = 90° reveals noise reductions ranging from approximately 16–24 dB at the BPF. The effects of blade phase synchronization on the BPF harmonics, up to the 5th harmonics, at different advance ratios, can be studied from the results in Fig. 7. One can see from the far-field noise that the relative phase of Δψ = 45° exhibits 2× and 3× BPF amplitudes that are lower than those obtained at a relative phase angle of Δψ = 90°. This behavior contrasts with what is observed at the first BPF. The higher BPF harmonic levels, beyond 3× BPF, are all found to be unaffected by phase synchronization. It should be emphasized that the noise reduction observed at the first BPF is consistently greater than at the BPF sub-harmonics. Therefore, the remaining acoustic results shown in this paper will focus on the first BPF.

Figure 8 presents a detailed comparison of the far-field noise directivity at the primary BPF over the polar angle range of 55° ≤ θ ≤ 130°, for seven different blades' relative phase angles, ranging from Δψ = 0° to 90°, in increments of 15°. Results are provided for J = 0, 0.47, 0.53 and 0.73. These findings provide insight into the behavior of the first BPF under both static and inflow conditions and contribute to a deeper understanding of noise reduction using blade synchronization at different observer angles, facilitating the interpretation of the first BPF behavior, previously analyzed at a single observer location.

FIG. 8.

(Color online) Comparison of the SPL directivity pattern at the first BPF for four advance ratios (a) J = 0, (b) J = 0.47, (c) J = 0.53, and (d) J = 0.73.

FIG. 8.

(Color online) Comparison of the SPL directivity pattern at the first BPF for four advance ratios (a) J = 0, (b) J = 0.47, (c) J = 0.53, and (d) J = 0.73.

Close modal

The results in Fig. 8 reveal the significant effect of the blades' relative phase angle on the amplitude of the first BPF, as well as the effect of observer location (θ). Overall, a considerable reduction in the first BPF noise is observed as the relative phase angle increases, irrespective of the advance ratio. Interestingly, across all directivity angles and advance ratios, the lowest noise level is consistently observed when the relative phase is set to Δψ = 90°. The results also show that the introduction of inflow improves the efficacy of noise reduction using blade synchronization. Figure 8(a) illustrates the variation in the noise of the first BPF as a function of the directivity angle (θ) at J = 0, representing a static thrust condition. The comparison of the results for different Δψ reveals that no significant noise reduction can be achieved for the relative phase difference of Δψ < 30° compared to the reference propeller's set position of Δψ = 0°. Beyond Δψ > 45°, a stepwise decrease in the SPL is evident for each subsequent phase angle. Notably, significant noise reduction is seen at downstream angles (θ > 90°), whereas the upstream angles exhibit only a slight decrease. Moreover, the results also show that the reduction for Δψ = 75° occurs primarily at downstream angles, while Δψ = 90° demonstrates a significant reduction across all directivity angles.

The results for the propellers operated with an inflow, corresponding to advance ratios of J = 0.47, 0.53, and 0.73, are presented in Figs. 8(b)–8(d). While these results exhibit a trend similar to that of J = 0, the noise reductions achieved due to propellers' phase synchronization are considerably more pronounced. As can be seen, in the case of two propellers operated with an inflow, clear noise reduction due to blade phase synchronization can be observed for a relative phase angle of Δψ > 30°, while that for the static condition (J = 0) was observed to be Δψ = 45°. Increasing the relative phase of the propellers results in a substantial and continuous reduction in noise levels. Significant levels of noise reduction for the inflow condition are also achieved at Δψ = 75° and 90°. The most significant noise reduction is consistently observed at a relative phase of Δψ = 90° across all directivity angles. Interestingly, for Δψ = 90°, the SPL of the first BPF exhibits a significant noise reduction of up to 24 dB, with a notable dip in the overall trend observed at θ = 80° for the advance ratios J = 0.53 and 0.73. This sharp drop in SPL at θ = 80° is not observed for J = 0.47. The results show that the blades' phase difference at high advance ratios can change the directivity pattern of the two-propeller system at the first BPF [see Figs. 8(c) and 8(d)]. Overall, the extent of noise reduction under inflow conditions is considerably greater than that under static conditions for all observer angles.

The primary objective of this study is to summarize the influence of propellers' relative phase angle, specifically examining the noise reduction achieved at the first BPF by comparing the optimal phase angle of Δψ = 90° with the reference position at Δψ = 0°. The term “ΔSPL” refers to the change in SPL between Δψ = 90° and the propeller's reference configuration at Δψ = 0°, a key metric in evaluating noise reduction effectiveness. In Fig. 9, a comparison of the ΔSPL at the first BPF is presented for four different advance ratios, J = 0, 0.47, 0.53, and 0.73. The ΔSPL for the static thrust condition (J = 0) shows a noise reduction of about 8 dB at the observer location of θ = 80°. These observations are consistent with established prior research. Schiller (2019) performed a numerical analysis to evaluate the potential benefits of phase synchronization techniques for noise reduction. Their results demonstrated that, for 2-bladed propellers, an optimal phase angle of Δψ = 90° is most effective in achieving SPL reduction of approximately 4–5 dB at the first BPF under hover conditions. Complementary research by de Vries (2021) corroborates this, revealing that the relative phase synchronization of propellers substantially influences noise directivity. Notably, a 5-bladed propeller with an advance ratio of J = 0.8 led to considerable noise reductions of up to 10 dB.

FIG. 9.

(Color online) Comparison of ΔSPL variation between Δψ = 90° and the propeller reference configuration (Δψ = 0°) across directivity angles for four advance ratios J = 0, 0.47, 0.53, and 0.73.

FIG. 9.

(Color online) Comparison of ΔSPL variation between Δψ = 90° and the propeller reference configuration (Δψ = 0°) across directivity angles for four advance ratios J = 0, 0.47, 0.53, and 0.73.

Close modal

As seen in Fig. 9, the introduction of an inflow has a substantial impact on noise reduction levels. With an inflow, the noise reduction exhibits an enhanced range of between 8 and 24 dB over the complete range of tested advance ratio and directivity angles. The dominant trend reveals that noise reduction progressively increases from J = 0 to J = 0.53, where the maximum noise reduction is achieved. Subsequently, the reduction diminishes at J = 0.73. While the results have shown that setting the blade phase at Δψ = 90° results in the reduction of the far-field noise at the first BPF compared to the propellers' reference position (Δψ = 0°) for all advance ratios, the least noise reduction is observed in the upstream region, i.e., small θ, near the propeller axis. Moving away from the propeller axis, i.e., larger θ, a noticeable increase in noise reduction is observed, reaching its peak at around the observer angle of θ = 80°. Following this peak, a minor decline in noise reduction is noted at downstream observer angles (θ > 80°). These patterns are consistent across all advance ratios, though a slight variation is evident at the lower advance ratio of J = 0.47 beyond the θ = 110° observer positions.

These results indicate that phase synchronization is a viable method for achieving a net reduction in acoustic radiation at the first BPF from two-propeller configurations. As demonstrated above, the effectiveness of noise reduction at the first BPF depends on both the relative phase angle of the blades and the advance ratio. The relative phase angle was found to have a more pronounced impact on noise reduction under inflow conditions than static thrust conditions across all directivity angles.

Having established the effect of blades' phase synchronization on the BPF noise and its directivity pattern at different operating conditions, here we extend our studies to the OASPL. It was observed that while phase matching does influence the harmonics of the BPF, its contribution to noise reduction in the OASPL is considerably less significant compared to the noise reduction achieved directly through BPF. This finding underscores the importance of analyzing OASPL in the context of both BPF and its sub-harmonics for a more comprehensive understanding. The OASPL is defined as follows:
OASPL = 10 · log 10 [ ϕ p p ( f ) d f p ref 2 ] ,
(4)
where the integral is performed over the frequency range of 100 Hz < ƒ < 1000 Hz, covering the BPF and its main harmonics, as observed in Fig. 7.

Figure 10 presents the directivity of the OASPL over 55° ≤ θ ≤ 130° for seven relative phase angles. As before, results are provided at four operational modes, namely, J = 0, 0.47, 0.53, and 0.73. In general, a considerable reduction in OASPL is observed as the relative phase angle increases across all directivity angles and for all operation conditions. As with the first BPF (see Fig. 8), the noise level is consistently lowest when the relative phase is set to Δψ = 90°. Figure 10(a) corresponds to a static thrust condition, i.e., J = 0, and as can be seen the directivity pattern is found to be relatively uniform. Changing the relative phase between the two propellers by Δψ = 90° reduces the noise level but has no other visible effect on the directivity pattern of the OASPL. The OASPL noise results under inflow conditions, i.e., J = 0.47, 0.53, and 0.73, are presented in Figs. 10(b)–10(d). While these results exhibit a trend similar to that of J = 0, the noise reductions that are achieved are noticeably more pronounced, consistent with earlier observations in Figs. 7 and 8. As before, under the inflow condition, a noticeable noise reduction is observed only when the propeller's relative phase is larger than 30°, while that for the static condition (J = 0) was found to be about Δψ = 75°.

FIG. 10.

(Color online) OASPL directivity for four advance ratios (a) J = 0, (b) J = 47, (c) J = 0.53, and (d) J = 0.73.

FIG. 10.

(Color online) OASPL directivity for four advance ratios (a) J = 0, (b) J = 47, (c) J = 0.53, and (d) J = 0.73.

Close modal

To illustrate the effectiveness of propellers' relative phase on the overall SPL and the effect of incoming flow speed, the results from Fig. 10 are summarized in Fig. 11. Here, we only present the results for an observer located at θ = 90°. The results are presented relative to the reference propeller location, i.e., Δψ = 0°. As can be seen, for J = 0, the noise reduction begins to increase at the relative phase of Δψ = 75°, culminating in a maximal reduction at Δψ = 90°, approximating 2 dB. Similarly, the cases with inflow show increasing noise reduction as the relative phase angle increases. The noise reduction with inflow exhibits small variations at a relative phase angle of Δψ < 30°, which offers almost no noticeable noise reduction. After that point, the noise reduction increases for all advance ratio cases (J > 0), with each reaching its maximum noise reduction of up to 6 dB at the relative phase angle of Δψ = 90°.

FIG. 11.

(Color online) Comparison of ΔOASPL across the tested phase angles relative to the propeller reference location (Δψ = 0°) for advance ratios J = 0, 0.47, 0.53, and 0.73, at observer angle θ = 90°.

FIG. 11.

(Color online) Comparison of ΔOASPL across the tested phase angles relative to the propeller reference location (Δψ = 0°) for advance ratios J = 0, 0.47, 0.53, and 0.73, at observer angle θ = 90°.

Close modal

The acoustic characteristics of propellers, both with and without phase synchronization, are analyzed through a time-frequency perspective using the CWT. This advanced method facilitates a detailed investigation into the temporal localization of acoustic characteristics across various frequencies. Unlike Fourier transform methods, which only offer frequency information, CWT provides a comprehensive understanding of how these acoustic properties evolve over time, crucial for identifying transient or intermittent phenomena in propeller acoustics (Farge, 1992; Jawahar , 2021). This study employs the CWT to analyze localized time-frequency fluctuations in microphone signals, focusing on the first BPF. The CWT effectively projects these signals onto a basis formed by translated and dilated versions of a mother wavelet function, facilitating precise temporal analysis of sound pressure variations (Morlet, 1983). Understanding the BPF's response to various stimuli is crucial for a comprehensive analysis, ensuring that any significant transient or quasi-transient behaviors are not overlooked, which is essential for interpreting the BPF's performance accurately. The behavior of the BPF was observed to be inherently time-variant (as seen in Fig. 12), meaning its characteristics evolve with time. Utilizing wavelet transform enabled us to capture these temporal changes by offering an in-depth view of the signal's frequency content as it changed over time. This approach allowed us to identify transient phenomena and non-stationary behaviors that might not be evident through strictly frequency-based analysis.

FIG. 12.

(Color online) Wavelet scalogram of the pressure signals obtained at observer angle θ = 90° for four advance ratios and two relative phase angles: (a) J = 0, Δψ = 0°, (b) J = 0, Δψ = 90°, (c) J = 0.47, Δψ = 0°, (d) J = 0.47, Δψ = 90°, (e) J = 0.53, Δψ = 0°, (f) J = 0.53, Δψ = 90°,(g) J = 0.73, Δψ = 0°, and (h) J = 0.73, Δψ = 90°.

FIG. 12.

(Color online) Wavelet scalogram of the pressure signals obtained at observer angle θ = 90° for four advance ratios and two relative phase angles: (a) J = 0, Δψ = 0°, (b) J = 0, Δψ = 90°, (c) J = 0.47, Δψ = 0°, (d) J = 0.47, Δψ = 90°, (e) J = 0.53, Δψ = 0°, (f) J = 0.53, Δψ = 90°,(g) J = 0.73, Δψ = 0°, and (h) J = 0.73, Δψ = 90°.

Close modal

Figure 12 displays the contour plots of the wavelet coefficient modulus (Wx) for the far-field microphone at 90°. The analysis encompasses four advance ratios (J = 0, 0.47, 0.53, and 0.73), alongside two relative phase angles, Δψ = 0° and Δψ = 90°. To highlight the influence of relative phase angles on the wavelet coefficient behavior at the first BPF, results are presented for a focused time window of 0.1 s. The first column [Figs. 12(a), 12(c), 12(e), 12(g)] illustrates the wavelet transform results at Δψ = 0°, while the second column [Figs. 12(b), 12(d), 12(f), 12(h)] corresponds to Δψ = 90° for each advance ratio. Initial observations suggest that the wavelet coefficients at the first BPF exhibit distinct response patterns, varying with both the relative phase angles and advance ratios.

The highest wavelet coefficient is observed in the static condition (J = 0) at the relative phase of Δψ = 0°, shown in Fig. 12(a). Under inflow conditions at a relative phase of Δψ = 0° [Figs. 12(c) and 12(d)], the strength of the wavelet coefficients is substantially similar across all advance ratios, with values lower than those produced in the static condition except the highest advance ratio J = 0.73 [Fig. 12(g)], which exhibits slightly lower levels than the other advance ratios. Notably, a significant reduction in tonal noise at the first BPF is observed at Δψ = 90°, in contrast to Δψ = 0°, where the coefficients' intensity diminishes in the time-frequency analysis under both static and inflow conditions. The amplitude of the wavelet coefficients at the first BPF is substantially weaker at Δψ = 90° compared to Δψ = 0°, as indicated in Figs. 12(b), 12(d), 12(f), and 12(h). Furthermore, the harmonic effects associated with the BPF are notably absent in static conditions.

The impact of relative phase angle on the acoustic signature is in line with prior acoustic analyses. This influence is particularly pronounced when observing two closely spaced adjacent propellers operating at a relative phase angle of Δψ = 0°. In contrast, at Δψ = 90°, there is a significant reduction in the generation of the first BPF tones, evident under both the static thrust and inflow conditions. From these observations, it could be hypothesized that the interaction of tonal noise from two two-bladed propellers operating at a fixed relative phase angle leads to constructive and destructive interference resulting in noise reduction observed at specific observer angles.

In summary, this study provides a comprehensive experimental analysis of the aeroacoustic characteristics of a DEP configuration, with a particular focus on the impact of the relative phase angle between adjacent propellers. The findings reveal that phase synchronization is an effective noise reduction technique in DEP systems, leveraging the principle of destructive interference in the coherent acoustic source field between the propellers.

The experiments were conducted across a range of advance ratios from J = 0 to J = 0.73 with a constant propeller rotation rate of 5000 rpm. The acoustic results demonstrate a clear correlation between increased relative phase angle and noise reduction in the far-field. The most notable acoustic attenuation was observed at a relative phase angle of Δψ = 90°, where reductions in both the first BPF amplitudes and OASPL were significantly higher compared to Δψ = 0° across all directivity angles. This reduction was observed as an 8 dB decrease in the first BPF and a 2 dB decrease in OASPL under static thrust conditions (J = 0), further increasing to a 24 dB decrease in the first BPF and a 6 dB decrease in OASPL under inflow conditions (J > 0).

The hypothesized mechanism driving this noise reduction is attributed to destructive wave interference, a phenomenon stemming from the relative angular positioning of the propeller blades. These results highlight the potential of relative phase control as a propeller noise reduction strategy in DEP systems. Furthermore, the sensitivity of the noise reduction benefits to the advance ratio highlights the need for careful consideration of operational conditions in the implementation of phase control techniques in DEP configurations. Overall, this study establishes the relative phase angle as a key parameter in the aeroacoustic optimization of DEP systems, offering a path forward for quieter and more environmentally friendly aviation technologies.

This work was supported by the Horizon 2020 research and innovation programme (Grant Agreement No. 882842) for the SilentProp project.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data will be made available on request.

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