Experimental Investigation of Rotor Noise in Reverse Non-Axial Inflow

Abstract

This paper experimentally characterises the far-field noise emissions of a rotor operating in reverse non-axial inflow conditions. Specifically, experiments were undertaken at a range of rotor tilting angles and inflow velocities to investigate the effects of negative tilting on rotor acoustics and their correlation with aerodynamic performance. The results show that the forces and moments experienced by the rotor blades change significantly with increasing inflow velocity and increasing negative tilting angle. Correspondingly, distinct modifications to the far-field acoustic spectra are observed for the negatively tilted rotor when compared to the edgewise condition, with the broadband noise content notably increasing. Moreover, for a given tilting angle, the broadband noise component is accentuated with increasing inflow velocity, similar to when the negative tilting angle is increased. With reference to the flow-field surveys conducted in the literature and a preliminary in-house flow measurement, the increase in broadband content can possibly be attributed to the heightened level of ingestion of blade self-turbulence, i.e., the ingestion of turbulent wake generated by the upstream portion of the rotor by the downstream portion. At lower inflow velocities, the magnitude of the blade passing frequency at each of the observer angles is found to change minimally with negative tilt. In contrast, at higher inflow velocities, the directivity pattern and intensity of both the blade passing frequency and the overall sound pressure level are shown to change with increases in magnitude, particularly at downstream observer locations with negative tilt. These findings have important ramifications for the design and suitable operational profile of aerial vehicles for future urban air mobility applications.

1. Introduction

In the contemporary landscape of aviation, the advent of Urban Air Mobility (UAM) and Advanced Air Mobility (AAM) represents a paradigm shift. These emerging fields have generated substantial attention and investment due to the potential they hold to revolutionize urban transportation, generating multiple start-ups and interest from governments around the world [1,2,3,4,5]. The nucleus of this transformation resides in the development and deployment of innovative electric Vertical Take-Off and Landing (eVTOL) aircraft and related configurations aimed at alleviating urban road congestion, reducing travel times and promoting environmental sustainability [6,7]. As these aerial vehicles approach integration within our urban environments, an array of operational challenges and considerations arises. One of the main challenges UAM and AAM faces is the likelihood of significant community noise impact, where, in particular, takeoff and landing at vertiports situated in densely populated areas present a major noise concern [5]. The development of methods to attenuate the noise emissions of these aircraft in different flight modes is vital to increase the social acceptance of such vehicles [8,9].

The unique propulsion architectures utilised in eVTOL aircraft present significant challenges related to the tilting angles of the rotors in different flight modes. The intricate and dynamic flow fields in these settings further compound the challenge of understanding noise characteristics. Among these, negative tilting may manifest under various conditions, including in encounters with gusts, as well as during the delicate phases of landing and approach (see Figure 1) [10,11]. During deceleration, negative tilting adds another layer of complexity to aerodynamic interactions, requiring a comprehensive investigation of the underlying flow phenomena and their impacts on noise generation. These operating conditions and modes have not been sufficiently studied when it comes to their significance for both aircraft performance and noise emissions [12]. Thus, understanding the noise generation mechanisms and the aerodynamic performance of this portion of the flight envelope will provide a necessary reference when attempting to understand how future vehicle and vertiport design may proceed within urban environments.

Rotor noise is typically subdivided into tonal and broadband components with distinct acoustic characteristics, where the lower frequency range is dominated by tones at fundamental and harmonics of the Blade Passing Frequency (BPF), while the higher frequencies are characterized by broadband noise [13]. Analytical studies have characterised rotor tonal noise, with its main sources having been attributed to blade loading conditions and thickness noise [14,15,16]. On the other hand, broadband noise is the result of unsteadiness in the pressure field resulting from interactions between the blade surface and inflow turbulence and vortex shedding [17]. Considerable experimental efforts have been made to explore the different noise generation mechanisms that contribute to rotor noise, in addition to efforts in evaluating the distinct noise characteristics across each of the rotor operational modes.

Cerny and Breitsamter [18] investigated the influence of non-axial inflow on isolated and ducted rotors and concluded that axial orientation has a major influence on thrust and torque. Additionally, the lift and yawing moments showed a dependency on inflow angles for forward-oriented flight. Unfortunately, the study did not evaluate the noise characteristics of rotors. Lößle et al. [19] tested rotors at a fixed-tip Mach speed of $M_T=0.25$ within a wind tunnel at both positive and negative tilting angles with respect to the freestream, taking aerodynamic and noise measurements of rotors oriented between −10° and 10°. Utilising background-oriented schlieren, Lößle et al. found evidence of blade–vortex interactions (BVI) occurring in edgewise flight conditions that were exacerbated as the inflow velocity increased. Unfortunately, the noise data for some cases included contamination of the broadband contents from the background, since the measurements were not conducted in the acoustic far field. Li et al. [20] investigated the aerodynamics and aeroacoustics of a drone rotor operating in descent using both experimental and numerical methods. It was observed that the aerodynamic performance significantly decreased with an increase in descent rate, with multiple humps in the acoustic spectra occurring at the BPF and its harmonics. Numerical simulations also corroborated these findings and offered further insight into the generation of vortex rings and wake structures.

Jamaluddin et al. [21] reported far-field noise measurements with complimentary flow-field analysis of rotors tilted at edgewise and positive angles with respect to the inflow while operating at relatively low-tip Mach numbers ($M_T=0.26$). They attributed observed increases in both the tonal noise at harmonics of the BPF and broadband noise to the ingestion of rotor self-induced turbulence while the rotor operated in edgewise flight conditions. Goyal et al. [22] used numerical simulations to investigate the aeroacoustic performance of rotors in positive and negative thrust conditions at different angles of attack across a tip Mach number range of $0.27<M_T<0.47$. One of the core noise generation mechanisms that resulted in changes to the noise directivity across the different non-axial flight conditions was found to be unsteady loading across the rotor blades. More recently, the authors conducted a preliminary in-house flow-field investigation using Particle Image Velocimetry (PIV) to complement the aeroacoustic data outlined in this paper [23]. The results confirm the findings of Jamaluddin et al. [24], who reported that in edgewise flight conditions, turbulent flow shed from the upstream portion of the rotor is observed to be re-ingested in the downstream portion of the blade, depending on the inflow velocity conditions. Similar to the flow-field results outlined by Cerny and Breitsamter [18] for negatively tilted propellers, the in-house PIV results showed evidence of strong turbulence re-ingestion while the rotor was tilted negatively to the freestream, with upstream wake and tip vortices being drawn into the downstream portion of the rotor disk, indicating the existence of a partial turbulent wake state.

As seen from the literature mentioned above, although there have been number of studies examining the aerodynamic and flow-field characteristics of a negatively tilted rotor, there has been limited work on aeroacoustic performance in similar operating conditions, not to mention correlating the aeroacoustic signature with the aerodynamic characteristics. Therefore, in this work, the aerodynamic performance and far-field acoustics of a rotor in reverse non-axial inflow are comprehensively investigated for a small-scale rotor to shed more light on the effects of negative tilting on the noise of a rotor operating at conditions representative of UAM/AAM vehicles. The paper is organised as follows. First, the experimental methodology is outlined, including a description of the aeroacoustic wind tunnel facility, the rotor test rig and the instrumentation used to collect aerodynamic loads and far-field noise measurements. Secondly, the results are presented, and through analysis of the time-averaged aerodynamic data, a thorough discussion of the effects of rotor tilting angle and the noise generation mechanisms observed in reverse non-axial inflow conditions is presented. Lastly, concluding remarks are made, summarising the key findings and scope for future work.

2. Methodology

In this section, the experimental methodology is comprehensively outlined. Details of the rotor test rig and its constituent elements are first described, including the electric motor and rotor geometry. Next, the aeroacoustic wind tunnel facility and the instrumentation used to collect data in the test campaign are documented. Finally, the data processing procedures are delineated.

2.1. Rotor Test Rig and Rotor Geometry

A rotor test rig was developed to enable investigation of aeroacoustic and aerodynamic performance across different rotor operating conditions. The test rig has been used in prior investigations of rotors operating in a broad range of operating conditions, including edgewise and tilting flight conditions [23,25,26]. These prior experimental results agreed well with the theoretical trends of rotor aerodynamic performance and the acoustic results predicted in numerical simulations [27,28], attesting to the robustness of the set-up. The rotor test rig assembly can be seen with component-level details in Figure 2. The rig includes an adjustable bracket, permitting the adjustment of tilting angles ($\alpha$). In the present study, $\alpha =0°$ represents the edgewise condition, while $\alpha =-12°$ represents the propeller tilting negatively to the freestream. A 14-pole (${\mathrm{N}}_{\mathrm{Poles}}=14$) outrunner brushless DC (BLDC) electric motor is fitted in the test rig to drive the rotor. To measure and control the rotational speed of the rotor ($\Omega$), a Lasertech LT2-ICP tachometer was utilized to generate once-per-revolution voltage peaks that could then be fed as input to a PID controller implemented within National Instruments LabVIEW.

The support structure for the rotor–motor assembly is connected to a 6-component, 120N ATI Mini40 (ATI Industrial Automation, Apex, NC, USA) multi-axis load cell to measure the relevant forces and moments across the x, y and z axes (see Figure 2a). The assembly was enclosed in a non-load-bearing cylindrical nacelle, which helped shield noise generated by the mechanical components and shrouded the assembly from possible flow interactions. The load cell is known to be influenced by temperature changes when collecting data, so to control for this, k-type thermocouples were attached to the load cell and near the motor support structure to monitor any temperature fluctuations. Additionally, a compressed air cooling system that makes use of a Ranque–Hilsch vortex tube [29] was fitted such that cold air passed over the motor surface to keep the temperature in the test rig stable during testing.

Rotors that are expected to experience reverse non-axial inflow in the context of UAM are likely to be selected for their ability to facilitate vertical take-off and landing (VTOL) maneuvers. As such, the rotors should generate sufficiently high thrust in static hovering conditions to minimize the time taken in the inefficient VTOL phase of flight. Additionally, recent studies have demonstrated a greater sensitivity of rotors with fewer blades to asymmetric inflow conditions [30]. With these factors in mind, in the present study, a representative rotor geometry featuring a relatively low pitch-to-diameter ratio of $P/D=0.5$ was selected. A two-bladed, 12″-diameter (D) fixed-pitch rotor was investigated, featuring a constant geometric pitch of 6″. The rotor comprised a Clark-Y airfoil cross-sectional profile across its entire span, with a variable chord length across the radial sections of the blades. Figure 3 shows the full chord and pitch angle distribution across the span of the rotor.

2.2. Wind Tunnel Facility and Instrumentation

The Pressure-Neutral Aeroacoustic Wind Tunnel at the University of Bristol was used to conduct an experimental campaign investigating the effects of reverse non-axial inflow conditions on rotor noise emissions. The aeroacoustic wind tunnel is an open-section, closed-loop facility with a convergent nozzle with a width of 1 m and a height of 0.7 m. The facility can generate steady freestream velocities (${\mathrm{U}}_{\infty }$) ranging from 0 to 35 ${\mathrm{ms}}^{-1}$ with a low turbulence intensity level of approximately $0.2\%$. Foam wedges are used to acoustically treat the walls, ceiling and floor of the chamber to minimize acoustic reflections. Previous research on rotor noise characteristics has successfully utilized this wind tunnel [23,25,26,27,28,31]. The rotor test rig was placed in the wind tunnel facility such that the rotor hub was located 0.86 m downstream of the open jet nozzle and centered with respect to the nozzle cross-section, as shown in Figure 4. The rig was placed such that the load cell measures the rotor thrust (T) on the z axis, with the pitching and yawing forces (F) and moments (M) on the x and y axes, respectively (see Figure 2a).

Far-field noise data were collected using a total of 61 GRAS 40PL-10 (GRAS Sound & Vibration, Holte, Denmark) free-field microphones mounted on two arrays in different planes, as shown in Figure 4. Glegg and Devenport [13] outlined that in order to take measurements in the acoustic far field, microphones should be placed at least one wavelength from the source. During wind tunnel testing, other considerations such as keeping the microphones sufficiently far from any flow disturbance and the chamber walls should also be accounted for. In the present experiments, the critical low-frequency contents were determined by the blade-pass frequency at 300 Hz, which translates to a wavelength of approximately 1.14 m based on the speed of sound at $20°\mathrm{C}$. Following this criterion, both microphone arrays were positioned within the acoustic far field located 1.5 m and 2 m away from the propeller hub. respectively. Each microphone features a flat frequency response from 10 Hz to 20 kHz, with a dynamic range up to 147 dB. On the advancing side of the rotor, 39 microphones were arranged on a linear side array located 2 m away from the rotor hub, orthogonal to the freestream. When corrected to a distance of 1.5 m, the microphone array spans polar angles ranging from $\varphi =66°$ to $\varphi =125°$. The array was positioned so $\varphi =90°$ was located directly in line with the rotor hub, parallel to the axis of rotation in the edgewise condition, as seen in Figure 4b. A second array was fixed to the ceiling of the wind tunnel facility, spanning angles between $\theta =40°$ and $\theta =145°$, with each microphone placed at $5°$ increments. The $\theta =90°$ microphone was oriented directly above the rotor hub at a distance of 1.5 m, with the array capturing the emitted noise in the plane oriented centrally with respect to the wind tunnel nozzle (see Figure 4a). To ensure accurate data collection, each GRAS 40PL-10 microphone was calibrated using a GRAS 42AA pistonphone calibrator before the measurements were taken.

2.3. Test Matrix and Data Acquisition

The primary goal of the present study was to characterize the effects of reverse non-axial inflow on the aerodynamic and aeroacoustic performance of rotors. To do this, the tilting angle ($\alpha$) was varied from pure edgewise flight conditions ($\alpha =0°$) to a moderate negative tilting angle ($\alpha =-12°$), with tests conducted at $4^{\circ }$ increments. To comprehensively explore the effect of reverse non-axial inflow, the inflow velocity (${\mathrm{U}}_{\infty }$) was varied across $4.4{\mathrm{ms}}^{-1}\le {\mathrm{U}}_{\infty }\le 26.5{\mathrm{ms}}^{-1}$, while the rotor was operated at each tilting angle. In each test case, the rotor rotational rate was fixed at $\Omega =9000$ RPM, corresponding to a tip Mach number of $M_T=0.42$. The Reynolds number of the rotor ($Re$) can be defined by the rotational speed, inflow velocity and chord at the 75% blade station, providing a operational range of 91,000 ≤ $Re$ ≤ 150,000 in the present study. At this tip Mach number, the tests can be considered more industrially relevant than many recent efforts, which were confined to experiments on rotors in incompressible flow regimes. Indeed, $M_T=0.42$ is close to the expected operating conditions of a full-scale eVTOL aircraft in high-thrust operation [32] and matches the $M_T$ used in recent hovering experiments that were designed to be more representative of eVTOL-sized rotors [33]. In this study, the rotor operating conditions were non-dimensionalised by defining the ratio between the freestream velocity in the rotor plane (${\mathrm{U}}_{\infty }cos\alpha$) and the rotor tip speed ($\Omega R$) as the advance ratio ($\mu$) following the approach outlined in [34,35] as follows:

$$\mu ={\displaystyle \frac{{\mathrm{U}}_{\infty }cos\alpha }{\Omega R}},$$

(1)

where R is the rotor radius. The present test matrix covers an the advance ratio range of $0.0296<\mu <0.184$.

For every combination of tilting angle ($\alpha$) and inflow velocity (${\mathrm{U}}_{\infty }$), the noise from all 61 far-field microphones and the aerodynamic forces and moments from the load cell were collected simultaneously using National Instruments (Austin, TX, USA) PXIe-4499 sound and vibration modules and a PXIe-6341 Multifunction I/O module mounted within a National Instruments PXIe-1026Q chassis. The data were sampled synchronously at $f=2^{16}$ Hz for a sampling time of 16 s. Much like the operating conditions, the time-averaged aerodynamic forces and moments were non-dimensionalised following widely used conventions [21]. The force coefficient (${\mathrm{C}}_{\mathrm{F}}$) for the forces measured in each of the x, y and z directions (see Figure 2) is defined as follows:

$${\mathrm{C}}_{\mathrm{F}}={\displaystyle \frac{\mathrm{F}}{\rho A{(R\Omega )}^2}},$$

(2)

where $\rho$ is the density of air and A is the rotor disk area. Following conventional nomenclature used in rotorcraft studies, the force coefficient in the rotor axial direction (along the z axis) is referred to as the thrust coefficient (${\mathrm{C}}_{\mathrm{T}}$). In this paper, the corresponding yaw forces along the y axis are defined as the yawing force coefficient (${\mathrm{C}}_{\mathrm{Fy}}$). To non-dimensionalise the moments about each axis, the moment coefficient (${\mathrm{C}}_{\mathrm{M}}$) is used as follows:

$${\mathrm{C}}_{\mathrm{M}}={\displaystyle \frac{\mathrm{M}}{\rho A{\Omega }^2{R}^3}}.$$

(3)

In the case of the moments measured about the z axis (i.e., the rotor torque (Q)), it is typical to calculate the power coefficient (${\mathrm{C}}_{\mathrm{P}}$) instead. First, the power (P) must be calculated from the torque using the following expression:

$$\mathrm{P}=\Omega Q,$$

(4)

leading to the power coefficient being defined as follows:

$${\mathrm{C}}_{\mathrm{P}}={\displaystyle \frac{\mathrm{P}}{\rho A{(R\Omega )}^3}}.$$

(5)

The far-field noise data in this study are presented in terms of the frequency-dependent energy content of the pressure fluctuations as the sound pressure level (SPL).

$$\mathrm{SPL}=10{\log }_{10}\left({\displaystyle \frac{\mathrm{PSD}\left(f\right)\Delta f}{p_{\mathrm{ref}}^2}}\right),$$

(6)

where $\mathrm{PSD}\left(f\right)$ denotes the frequency-dependent power spectral density based on the unsteady pressure ($p^{\prime }\left(t\right)$, where $p^{\prime }\left(t\right)=p\left(t\right)-p_{\mathrm{mean}}$), and $p_{\mathrm{ref}}=20$ μPa is the reference pressure. Welch’s method was utilized to compute the PSD of the pressure signal from each microphone with a frequency resolution of $\Delta f=4$ Hz [36], with the time series data divided into segments of equal lengths with a 50% overlap between each segment and a Hamming window. To ascertain the overall noise directivity trends, the far-field acoustic power spectral density can be integrated to obtain the Overall Sound Pressure Level (OASPL) as follows:

$$\mathrm{OASPL}=10{\log }_{10}\left({\displaystyle \frac{\int \mathrm{PSD}\left(f\right)\mathrm{d}f}{p_{\mathrm{ref}}^2}}\right).$$

(7)

In this study, the OASPL was calculated by integrating the PSD over a frequency range of 160 Hz–10 kHz for each of the 61 microphones. Alongside the OASPL directivity, the BPF directivity was calculated by finding the peak magnitude of the BPF tone in each calculated SPL spectra for every microphone. The noise characteristics of the wind tunnel facility and test rig were evaluated to consider potential sources of noise contamination, with the background noise levels analysed for each inflow velocity and tilting condition. The reader should note that at the highest velocity of ${\mathrm{U}}_{\infty }=26.5{\mathrm{ms}}^{-1}$, the background noise becomes comparable to that of the rotor noise at frequencies below approximately 250 Hz. Care should be exercised when interpreting the far-field acoustic results at such low frequencies while the rotor operates at higher inflow velocities.

3. Results and Discussion

To better understand the effect of reverse non-axial inflow on rotor acoustics, it is useful to first examine the flow and aerodynamic characteristics of the rotor under various operating conditions. Therefore, this section begins by highlighting the critical rotor–flow interaction events that are expected to take place in edgewise and negatively tilted conditions, followed by a discussion of the time-averaged aerodynamic coefficients, including thrust, power, yaw force and moment. Subsequently, the far-field acoustic spectra are presented and discussed with a focus on the effects of inflow velocity (i.e., advance ratio) and the tilting angle. Lastly, the directivity of tonal noise at the fundamental BPF and the overall sound pressure level are discussed and related to both the observed flow and aerodynamic effects to shed more light on the modification of rotor acoustics when the rotor experiences reverse non-axial inflow.

3.1. Interpretation of Rotor–Flow Interaction

Rotors in edgewise and negative tilting orientations with respect to the freestream experience complex interactions with the flow, as reported in the literature. Cerny and Breitsamter [18] performed PIV measurements on a rotor in non-axial inflow conditions. Their findings suggested that when the rotor was operating in a negative tilting orientation, both the separated flow and tip vortex being shed by the upstream advancing blade were upwashed and convected along the upper side of the rotor blade. Subsequently, these turbulent structures were re-ingested by the blades. Although no acoustic measurements were conducted, they remarked that the rotor under negative tilting was considerably louder. Similar observations were also reported in a more recent study by Jamaluddin et al. [21]. For a rotor operating under the edgewise condition, i.e., $\alpha =0^{\circ }$, significant ingestion of self-induced turbulence from the advancing half of the rotor into the retreating half was found, leading to an increase in both the broadband and tonal noise. Indeed, tonal noise associated with higher-order harmonics of the BPF are likely to appear due to enhanced levels of the unsteady loading sources, such as BVI and wake ingestion [37].

Although the previous studies have examined the near-field flow characteristics of rotors in negative tilting conditions and the far-field acoustics in edgewise conditions, the far-field acoustics for rotors in the negative tilting orientation have not yet been comprehensively investigated. However, there has been sufficient knowledge learned to reasonably elucidate the rotor–flow interaction expected for negatively tilted rotors. Figure 5 depicts a flow-field interpretation of a rotor in the negative tilting orientation at two different inflow velocities based on previous studies [18,21] and preliminary in-house PIV measurements [23], showing that re-ingestion of rotor turbulence is likely to take place at this orientation and an increase in the inflow velocity leads to a larger portion of the rotor experiencing such re-ingestion. Therefore, for the present study, an increase in the broadband noise and the emergence of tones at higher-order harmonics of the BPF are likely to occur at the negative tilting orientation [24,38], which will be further analysed and discussed in the following section, including the impact of changing inflow velocity and tilting angle on the acoustics.

3.2. Time-Averaged Aerodynamic Performance

It is well established that rotor noise relevant in the context of eVTOL operation is likely to be dominated by steady and unsteady loading noise sources consisting of both deterministic and nondeterministic components [39]. As such, understanding the aerodynamic performance of rotors in reverse non-axial inflow is a crucial aspect of evaluating and contextualizing the noise emitted by the rotor. The rotor, when operating in both edgewise ($\alpha =0^{\circ }$) and negative tilting orientations ($\alpha <0^{\circ }$), experiences asymmetric inflow velocity conditions through each phase angle, leading to a complex, three-dimensional flow field with significant flow separation in the retreating half of the blade [18,40], as the local angle of attack periodically changes across the blade sections. This periodicity affects the thrust generated by the rotor, as well as its power consumption. Additionally, given the expected rotor–flow interactions outlined in Section 3.1, analysis of the load cell data may indicate changes in the operating state of the rotor or the presence of re-ingestion effects. Previous investigations by Cerny and Breitsamter [18] showed that substantial changes in the yawing moments can be expected when non-axial inflow conditions are experienced by rotors, so the yawing forces and moments are considered in the analysis outlined in this study.

Figure 6 presents the time-averaged thrust coefficient (${\mathrm{C}}_{\mathrm{T}}$), power coefficient (${\mathrm{C}}_{\mathrm{P}}$), yawing force coefficient (${\mathrm{C}}_{\mathrm{Fy}}$) and yawing moment coefficient (${\mathrm{C}}_{\mathrm{My}}$) as functions of the advance ratio ($\mu$) for different rotor tilting angles ($-{12}^{\circ }\le \alpha \le 0^{\circ }$). In general, at a given tilting angle, each of the coefficients is observed to increase in magnitude as the advance ratio increases. This is expected as the advance ratio increases solely with the inflow velocity (${\mathrm{U}}_{\infty }$), and the increase in the inflow velocity, by virtue of the rotor being negatively tilted (i.e., tilting in the freestream direction), induces a higher effective angle of attack along the sections of blades across a large part of the blade phase over a full revolution, which leads to increased time-averaged forces and moments [21].

Figure 6a presents the changes in the thrust coefficient (${\mathrm{C}}_{\mathrm{T}}$) as a function of the advance ratio ($\mu$) for different rotor tilting angles ($-{12}^{\circ }\le \alpha \le 0^{\circ }$). The relationship between $\mu$ and ${\mathrm{C}}_{\mathrm{T}}$ is closely aligned for each of the tilting angles considered in the present study. While the rotor operates in edgewise flight conditions ($\alpha =0^{\circ }$), the ${\mathrm{C}}_{\mathrm{T}}$ initially slightly reduces with an increasing advance ratio, while the rotor operates in a lower advance ratio regime ($\mu \le 0.075$). Subsequent increases in the advance ratio ($\mu >0.075$) lead to a rapid increase in ${\mathrm{C}}_{\mathrm{T}}$, consistent with trends reported by both Cai and Gunasekaran [40] and Simmons and Hatke [41]. As the rotor tilts backwards ($\alpha <0^{\circ }$) and begins to operate in reverse non-axial inflow conditions, the ${\mathrm{C}}_{\mathrm{T}}$ follows a similar trend with $\mu$ to that under edgewise conditions, with slight reductions in magnitude at low advance ratios ($\mu \le 0.075$). Notably, in this advance ratio range, the magnitude of the ${\mathrm{C}}_{\mathrm{T}}$ is greater, while the rotor is tilted negatively compared to that in edgewise conditions. At higher advance ratios, much like the edgewise flight case, the ${\mathrm{C}}_{\mathrm{T}}$ increases notably with increasing $\mu$. In this range ($\mu \ge 0.075$), the differences in ${\mathrm{C}}_{\mathrm{T}}$ magnitude between the negatively tilted rotor ($\alpha <0^{\circ }$) and the edgewise rotor ($\alpha =0^{\circ }$) are amplified. The increase in ${\mathrm{C}}_{\mathrm{T}}$ in these operating conditions is likely the result of an overall increase in the effective angle of attack of the blade sections induced by a higher inflow velocity, which leads to higher time-averaged lift and, thus, produced thrust force. Rotor steady loading is directly related to the tonal noise at the BPF [42]. Thus, observing the fact that for a given advance ratio, the ${\mathrm{C}}_{\mathrm{T}}$ is observed to generally increase as the rotor tilts backward with respect to the freestream ($\alpha <0^{\circ }$), the characteristics of the BPF tones are likely to change.

Figure 6b presents the variation in the power coefficient (${\mathrm{C}}_{\mathrm{P}}$) as a function of the advance ratio ($\mu$) for different rotor tilting angles ($-{12}^{\circ }\le \alpha \le 0^{\circ }$). Much like the thrust coefficient, the relationship between $\mu$ and ${\mathrm{C}}_{\mathrm{P}}$ is closely aligned for each of the tilting angles considered in the present study; as the advance ratio ($\mu$) increases, the power coefficient (${\mathrm{C}}_{\mathrm{P}}$) increases. When the rotor operates in edgewise flight conditions ($\alpha =0^{\circ }$) at lower advance ratios ($\mu \le 0.075$), the power consumption is higher than that observed in the negative tilting cases ($\alpha <0^{\circ }$). However, as the advance ratio increases ($\mu >0.075$), the edgewise case ceases to have the largest ${\mathrm{C}}_{\mathrm{P}}$, with the $\alpha =-{12}^{\circ }$ case having a consistently higher power coefficient under high-inflow velocity conditions. At smaller negative tilting angles ($-{12}^{\circ }<\alpha <0^{\circ }$), it has been observed that the ${\mathrm{C}}_{\mathrm{P}}$ is consistently lower than the power coefficient observed both for the $\alpha =0^{\circ }$ and $\alpha =-{12}^{\circ }$ cases across each of the considered advance ratios. As the rotor tilts negatively to the freestream, the ${\mathrm{C}}_{\mathrm{P}}$ at smaller tilting angles of $-{12}^{\circ }\le \alpha \le 0^{\circ }$ decreases compared to the edgewise condition ($\alpha =0^{\circ }$). This trend is consistent with the results reported by Cerny and Breitsamter [18], who observed that any increase in the negative tilting angle (as denoted by κ in their study) leads to decreases in the thrust and power coefficient. They attributed the reduction to the changes in the effective angle of attack of the blades induced by the axial velocity component. Indeed, the presence of an axial velocity component when the propeller is tilted can lead to a decrease in the effective angle of attack and, thus, the aerodynamic performance of the propeller. The scenario is further complicated by the blade’s interaction with the tip vortices and self-wake. As the propeller is negatively tilted, the regions where the advancing and retreating blades interact with the propeller wake and tip vortices grow and could potentially lead to flow separation and, thus, degradation of the thrust and power [18]. At even higher negative tilting angles, i.e., $\alpha =-{16}^{\circ }$, the operational modes of the propeller change, which could, again, lead to an increase in the power coefficients. However, further investigations are required to fully understand the negatively tilted cases.

The aerodynamic forces on the y axis are evaluated in Figure 6c, where the variation of the yaw force coefficient (${\mathrm{C}}_{\mathrm{Fy}}$) is presented as a function of the advance ratio ($\mu$) for different rotor tilting angles ($-{12}^{\circ }\le \alpha \le 0^{\circ }$). Despite generally possessing a lower magnitude than the thrust coefficient, the ${\mathrm{C}}_{\mathrm{Fy}}$ still shows noticeable levels of loading, which may indicate changes in the noise emissions of the rotor. In accordance with the other coefficients, ${\mathrm{C}}_{\mathrm{Fy}}$ is observed to increase at each given tilting angle ($\alpha$) as the advance ratio ($\mu$) increases. The largest yaw force is observed across all the advance ratios for the $\alpha =0^{\circ }$ case. As the rotor tilts negatively with respect to the freestream into reverse non-axial inflow conditions ($-8^{\circ }\le \alpha \le -4^{\circ }$), the ${\mathrm{C}}_{\mathrm{Fy}}$ reduces substantially, leading to sub-zero values at lower advance ratios ($\mu \le 0.108$), indicating an inversion of the yawing force direction. When the rotor operates in more severe negative tilting orientations ($\alpha =-{12}^{\circ }$), the ${\mathrm{C}}_{\mathrm{Fy}}$ increases compared to the other tested negative tilting angles whilst still maintaining a lower magnitude than the edgewise case ($\alpha =0^{\circ }$) across each of the advance ratios. When the rotor is negatively tilted at smaller tilting angles of $-{12}^{\circ }\le \alpha \le 0^{\circ }$, the side force produced by the rotor (${\mathrm{C}}_{\mathrm{Fy}}$) also decreases compared to the edgewise flight condition, similar to the trends observed for the thrust and power coefficients. This is in agreement with the results reported by Cerny and Breitsamter [18] for negatively tilted propellers, which they attributed to the complex flow interaction between the blades and the rotor self-wake. Nevertheless, to fully explain the behaviour would require blade-level information. Hence, further investigations using advanced experimental and numerical tools are needed to better understand the changes in the side force.

Figure 6d presents the variation of the yawing moment coefficient (${\mathrm{C}}_{\mathrm{My}}$) as a function of the advance ratio ($\mu$) for different rotor tilting angles ($-{12}^{\circ }\le \alpha \le 0^{\circ }$). Each of the tilting orientations show very similar behaviour at lower advance ratios ($\mu \le 0.09$), with a linear increase in ${\mathrm{C}}_{\mathrm{My}}$ observed as the advance ratio increases. Beyond this advance ratio ($\mu >0.09$), the influence of reverse non-axial inflow conditions on the relationship between the ${\mathrm{C}}_{\mathrm{My}}$ and $\mu$ becomes apparent at each of the tested tilting angles. For the edgewise condition ($\alpha =0^{\circ }$), the yawing moment coefficient continues to increase as the advance ratio (i.e., the inflow velocity, ${\mathrm{U}}_{\infty }$) increases, with the magnitude at the highest advance ratio ($\mu =0.184$) being substantially greater than that observed under near-static hover conditions ($\mu =0.0145$). Clearly, the yawing moment experienced by the rotor is significantly affected by non-axial inflow conditions—a trend consistent with prior findings by Cerny and Breitsamter [18]. As the rotor tilts negatively, the trend varies noticeably, with the ${\mathrm{C}}_{\mathrm{My}}$ increasing moderately at $\alpha =-4^{\circ }$, remaining largely constant in the case of $\alpha =-8^{\circ }$ and reducing at the most extreme negative tilting angle of $\alpha =-{12}^{\circ }$ as the advance ratio increases. The stark change in behaviour delimited by $\mu =0.09$ is notable and requires further examination to understand the root cause, with the behaviour at each tilting angle showing clear divergence at ${\mathrm{U}}_{\infty }=15.6{\mathrm{ms}}^{-1}$. There is clearly a strong interplay between the rotor tilting condition ($\alpha$); the advance ratio ($\mu$); the generated levels of force and moment; and, thus, the loading on the blades. Complex loading is instigated as the rotor enters reverse non-axial inflow operating conditions, possibly indicating the onset of a partial turbulent wake state (TWS), as noted by Cerny and Breitsamter [18]. The noise emissions are likely to change substantially as a result of this, as explored in greater depth in Section 3.3.

3.3. Far-Field Noise

For edgewise and negatively tilted rotors, BVI noise becomes a major contributor to the noise spectra, enriching the spectra with higher harmonics of the blade passing frequency [19]. Following the changes observed in the aerodynamic performance, in this section, the aeroacoustic performance of rotors is evaluated. First, the far-field noise results are presented in the form of Sound Pressure Level (SPL) spectra; then, the BPF directivities and Overall Sound Pressure Level (OASPL) directivities from both the top and side arrays are presented and analysed.

3.3.1. Sound Pressure Level Spectra

Rotor noise consists of two separate elements known as the tonal and broadband components [17], which can be clearly identified in the far-field noise spectra presented in this paper. As reviewed above, the PIV data [18,23] in the case of reverse non-axial inflow conditions suggested that the tip vortex being shed by the upstream portion of the blade is expected to be re-ingested in the downstream portion of the rotor disk, giving rise to the emergence of additional harmonics in the mid-frequencies. Similar observations were also reported in a recent study by Jamaluddin et al. [21] for a rotor operating under the edgewise condition, i.e., $\alpha =0^{\circ }$, where significant ingestion of rotor self-induced turbulence from the front half of the rotor into the rear half was found to lead to a significant increase in the broadband noise signature of the rotor, as well as the emergence of high-order BPF harmonics. As previously shown, higher-order harmonics are likely to appear due to increased levels of unsteady loading sources, such as BVI noise and wake ingestion [37]. For the current experimental campaign, we expect the rotor turbulence ingestion to increase as the rotor tilts negatively to the freestream and as the inflow velocity increases, leading to increased broadband noise and the emergence of more intense high-order harmonics [24,38]. Lastly, tilt angle has been found to affect the shaft tones, as reported by Jamaluddin et al. [21], who observed an increase in shaft noise due to turbulence ingestion and moment imbalances. Since significant changes were observed in multiple components of the aerodynamic forces and moments in Section 3.2, we can expect similar trends in the shaft tones for the study reported here. In what follows, a detailed far-field noise analysis of a rotor operating in edgewise and negatively tilted configurations at different inflow speeds is presented and discussed.

Figure 7 presents the noise spectra for three microphones placed at $\theta ={60}^{\circ }$, ${90}^{\circ }$ and ${120}^{\circ }$ on the top array at different inflow velocities of ${\mathrm{U}}_{\infty }=8.7,15.6,20$ and $26.5{\mathrm{ms}}^{-1}$ and different rotor tilt angles of $\alpha =0^{\circ },-4^{\circ },-8^{\circ }$ and $-{12}^{\circ }$. It is worthwhile to mention that the far-field sound pressure level spectra are presented without any weighting functions to allow for direct comparison of the spectral behaviour with respect to the effects of inflow velocity and tilting angle. To ease discussion of the spectral results, the frequency range of interest is categorised into three frequency bands (see Figure 7c), namely low-frequency (LF) ($160\mathrm{Hz}\le f<3\mathrm{kHz}$), mid-frequency (MF) ($3\mathrm{kHz}\le f<10\mathrm{kHz}$) and high-frequency (HF) ($f\ge 10\mathrm{kHz}$). As can be seen from the results, the fundamental BPF of the rotor ($m=f/\mathrm{BPF}=1$) operating at 9000 RPM is observed at 300 Hz. The subsequent peaks correspond to the harmonics of the BPF ($m=2,3,4,\dots$), which dominate the low frequencies ($160\mathrm{Hz}\le f<3\mathrm{kHz}$) and are related to both the steady and unsteady loading of the blades [43]. For instance, the amplitude of the harmonics of the BPF can significantly increase in the presence of unsteady aerodynamic loading caused by the interaction of the rotor with strong incoming turbulent flow, BVI or rotor self-induced turbulence [21].

At low inflow velocities (${\mathrm{U}}_{\infty }=8.7{\mathrm{ms}}^{-1}$; see Figure 7a–c), the acoustic spectra are found to be made of two distinct frequency regimes, with the LF band dominated by the BPF and its main harmonics (m = 1–5), as well as the rotor shaft tones at $m=0.5,1.5,2.5,\dots$ and the MF and HF bands dominated by rotor self-noise, which is broadband in nature and peaks at around $f=4$ kHz to 6 kHz. As can be seen from the results, the introduction of negative tilt at low inflow speeds can result in significant changes in the mid- and high-frequency broadband noise radiated from the rotor, particularly near the peak frequency. Furthermore, the rotor tilt does not seem to cause any major changes to the broadband energy content of the radiated noise in the LF regions. This effect is consistent at all three microphone locations. The effects of tilt angle and inflow velocity on the BPF amplitude and directivity of the radiated noise are discussed in Section 3.3.3.

As the inflow velocity is increased to ${\mathrm{U}}_{\infty }=15.6{\mathrm{ms}}^{-1}$ (see Figure 7d–f), a clear increase in broadband noise at LF can be observed when comparing the spectra to the case with lower inflow velocity. Increasing the negative tilt of the rotor has less of an effect on the MF and HF broadband self-noise components ($f>3$ kHz), instead showing more significant changes to the low-frequency broadband content surrounding the BPF harmonics (m = 2–5, or $0.6<f<3$ kHz), with a maximum increase of 4 dB. As can be seen, the more negatively tilted rotor orientation yields the highest SPL values at the downstream locations, i.e., $\theta ={60}^{\circ }$ and ${90}^{\circ }$ (see Figure 7d,e, respectively). On the other hand, the changes to the broadband energy content for locations upstream of the rotor Figure 7f are found to be less pronounced. This suggests that the additional noise generation mechanism causing this LF broadband noise increase is highly directional. This is further discussed in Section 3.3.2 and Section 3.3.3. Additionally, compared to the lower-velocity case, additional and stronger higher harmonics of the BPF are found in the region up to 3000 Hz, suggesting the presence of a stronger, unsteady aerodynamic load acting on the rotor [21]. Furthermore, the two distinct frequency regions observed in the case of ${\mathrm{U}}_{\infty }=8.7{\mathrm{ms}}^{-1}$ are merged into a continuous band of high noise frequencies. This is mainly due to the shift of the rotor self-noise to the lower frequencies as the inflow velocity increases and, more importantly, the emergence of a new source of noise in the LF band, i.e., rotor turbulence ingestion. Recalling the results presented in Figure 6, it is noteworthy that this shift in noise characteristics is observed where the onset of divergence in the yawing moment coefficient (${\mathrm{C}}_{\mathrm{My}}$) at different tilting angles was reported.

A further increase in inflow velocity (${\mathrm{U}}_{\infty }=20{\mathrm{ms}}^{-1}$; see Figure 7g–i) results in a significant increase in broadband noise in the LF band ($160\mathrm{Hz}\le f<3\mathrm{kHz}$), as well as the appearance of distinct haystacks around the first three harmonics (m = 2–4). As before, the HF broadband noise region ($f\ge 10\mathrm{kHz}$) exhibits minimal changes with an increased negative tilting angle. Notably, the haystacking phenomenon observed at this velocity is only prominent for the $\alpha =-{12}^{\circ }$ case, whilst the other noise spectra ($\alpha =0^{\circ },-4^{\circ }$ and $-8^{\circ }$) behave similarly to the ${\mathrm{U}}_{\infty }=15.6{\mathrm{ms}}^{-1}$ case and only exhibit increased levels of broadband noise. Furthermore, as can be seen from the acoustic spectra, at this velocity, the two distinct noise regions of LF tonal noise and HF self-noise can be seen to have fully merged into an LF and MF region of higher energy content due to the strong contribution from turbulence ingestion noise. The haystacks near the first and second harmonics are found to be highly directional and more dominant at downstream locations ($\theta <{90}^{\circ }$), as seen in Figure 7g,h. While the haystacks can also be seen at upstream observer locations (see Figure 7i), they appear lower in amplitude and with a reduced frequency width. Accompanying this change to haystacking behaviour at upstream locations is an increase in the number and magnitude of higher harmonics of the BPF, with dominant tonal peaks observed up to the $m=26$ harmonic for the $\alpha =-{12}^{\circ }$ case.

Finally, for the most extreme inflow velocity condition of ${\mathrm{U}}_{\infty }=26.5{\mathrm{ms}}^{-1}$, additional haystacking behaviour can be observed, even at shallower negative tilting angles ($\alpha =-4^{\circ }$ and $-8^{\circ }$), signifying the presence of large turbulence structures interacting with the blades, as schematically shown in Figure 5b. Similar to the ${\mathrm{U}}_{\infty }=20{\mathrm{ms}}^{-1}$ condition, in the case of ${\mathrm{U}}_{\infty }=26.5{\mathrm{ms}}^{-1}$, there are notable changes in the broadband noise levels in the LF and MF regions. However, here, the change in the tilt angle is observed to also affect the high-frequency broadband noise content, suggesting a change in rotor self-noise characteristics under such extreme inflow conditions. As previously discussed, the presence of unsteady loading due to turbulence interaction can result in the amplification of high-order BPF harmonics, making them protrude well above the broadband content of the rotor [21]. Indeed, recalling the results presented in Figure 6, the largest differences in the yawing moment coefficient (${\mathrm{C}}_{\mathrm{My}}$) at different tilting angles was reported under these inflow velocity conditions, indicating the presence of a complex loading cycle on the rotor. This can be readily observed in the tones represented in Figure 7j–l. However, the number of identifiable high-order BPF harmonics is found to change at different observer locations, with more tones observed at upstream locations ($\theta >{90}^{\circ }$), indicating that the BPF harmonics can be highly directional.

In addition to the BPF ($m=1$) and its harmonics ($m=2,3,\dots$), high-amplitude sub-harmonic tonal components are observed at $m=0.5,1.5,2.5,\dots$, often referred to as the shaft noise. Motor-induced aerodynamic loading and moment imbalance have been reported to affect the shaft tone amplitude. A recent study on forward-tilting rotors showed that the significance of the $m=0.5$ and $1.5$ shaft tones compared to the fundamental BPF ($m=1$) reduces with the rotor forward tilt angle, i.e., tilting in the flow direction, and the inflow velocity [21]. In the case of negatively tilted rotors, the SPL spectra show that at low inflow velocities (${\mathrm{U}}_{\infty }=8.7{\mathrm{ms}}^{-1}$), the rotor tilt angle has an influence on the shaft tone amplitude, with noise increases observed for the $\alpha =-8^{\circ }$ and $\alpha =-{12}^{\circ }$ cases when compared to the edgewise configuration ($\alpha =0^{\circ }$). At higher inflow velocities (${\mathrm{U}}_{\infty }\ge 15.6{\mathrm{ms}}^{-1}$), as the rotor tilts more negatively with respect to the freestream, a reduction in the magnitude of the $m=0.5$ tone is observed. In general, the $m=0.5$ tone is found to be stronger than the BPF at low inflow velocities, which is consistent with the findings of Jamaluddin et al. [21]. As the inflow increases, the significance of the $m=0.5$ tone relative to the BPF is observed to reduce.

The results at the $m=1.5$ shaft tone also show changes with rotor tilting angle and inflow velocity, which manifest in slightly different trends to that seen for the $m=0.5$ tone. The effect of a negative tilting angle is clearly interlinked with the rotor advance ratio; at lower inflow velocities (${\mathrm{U}}_{\infty }=8.7{\mathrm{ms}}^{-1}$), complex behaviour is observed, with the $m=1.5$ tone initially reducing at shallow negative tilting angles ($\alpha =-4^{\circ }$) when compared to the edgewise flight case ($\alpha =0^{\circ }$). As the rotor tilts further backwards, approaching $\alpha =-{12}^{\circ }$, the $m=1.5$ tone shows smaller reductions and, at the most extreme negative tilting angles ($\alpha =-{12}^{\circ }$), matches or slightly supersedes the levels observed at $\alpha =0^{\circ }$. Notably, as the inflow velocity increases, the shaft noise decreases as the tilting angle is reduced. This effect is corroborated by Figure 6d, which displays an initial common trend for the yawing moment that deviates as $\mu$ is increased beyond $\mu =0.09$ and the tilt angle is decreased, suggesting a change in aerodynamic loading and moment imbalance. The relevance of the shaft noise peak is also gradually diminished as the flow noise and broadband contribution shift towards the LF band of the spectra.

Figure 8 presents the noise spectra for the side array (see Figure 4b for the orientation of the array) at three observer locations of $\varphi ={74}^{\circ }$, ${90}^{\circ }$ and ${107}^{\circ }$ under the same inflow conditions and tilt angles presented in Figure 7. These observer locations are of particular interest, as they can provide us with information about the noise signature of the rotor below, at and above the rotor plane of rotation, which is relevant to noise at vertiports or in cities with high-rise buildings. The noise characteristics observed in Figure 8a, which corresponds to the lowest inflow velocity, behave similarly to the results for the top arc presented in Figure 7, with two distinct frequency regions, i.e., low frequencies ($160\mathrm{Hz}\le f<3\mathrm{kHz}$) dominated by the BPF and its harmonics and rotor self-noise at mid- and high frequencies ($3<f<20$ kHz). At lower inflow velocities, the rotor self-noise is found to be sensitive to the rotor tilt angle, particularly for the observers below the rotor plane ($\varphi <{90}^{\circ }$). Increasing the inflow velocity to ${\mathrm{U}}_{\infty }=15.6{\mathrm{ms}}^{-1}$ leads to a greater number of higher harmonic peaks in the SPL spectrum. Once again, the sensitivity of the MF and HF broadband self-noise decreases with increasing negative tilt, while the spectral broadband energy content at low frequencies around the BPF and its harmonics is found to increase due to the emergence of turbulence ingestion noise, as discussed above. As before, a distinct separation between the mid- to high-frequency broadband and low-frequency tonal content of the spectra can be observed. As the velocity is further increased to ${\mathrm{U}}_{\infty }=20.0{\mathrm{ms}}^{-1}$, the broadband energy content of the rotor due to the turbulence ingestion extends further to the lower frequencies, reaching the $m=2$ harmonic, leading to a haystacking effect at the $m=2,3$ and 4 harmonics, particularly in the case of $\alpha =-{12}^{\circ }$. This is also consistent with the prior observations presented in Figure 7. Finally, as for the top arc, rotor shaft noise can be clearly observed at $m=0.5,1.5,2.5,\dots$, although the amplitudes are generally lower than the neighboring BPF and harmonics, indicating that the rotor shaft noise is highly directional. The significance of the $m=0.5$ tone compared to the BPF amplitude is found to reduce with inflow velocity and tilt angle.

3.3.2. Blade Passing Frequency Directivity

The overall energy frequency content of the radiated noise due to the rotor self-noise and turbulence ingestion noise, particularly the broadband components, were studied in Section 3.3.1. In this section, we focus our attention on the directivity pattern of the radiated noise at the BPF (${\mathrm{SPL}}_{m=1}$) using the top and side arrays (see Figure 4). As before, the results are presented for different negative tilt angles and inflow speeds.

At the lowest inflow velocity of ${\mathrm{U}}_{\infty }=8.7{\mathrm{ms}}^{-1}$, as presented in Figure 9a, the results do not show a significant change as the tilt angle is varied from the edgewise condition ($\alpha =0^{\circ }$) to a negative tilting condition ($\alpha =-{12}^{\circ }$). As can be seen, at the BPF, the radiated noise has two main directivity lobes, with the major lobe pointing towards $\theta ={135}^{\circ }$ (upstream of the rotor) and the minor lobe towards $\theta ={65}^{\circ }$. As observed from Figure 9b,c, increases in inflow speed to ${\mathrm{U}}_{\infty }=15.6{\mathrm{ms}}^{-1}$ and ${\mathrm{U}}_{\infty }=20{\mathrm{ms}}^{-1}$ lead to significant changes to the directivity pattern at the BPF. The results for $\alpha =0^{\circ }$ show that the minor downstream lobe observed in Figure 9a at $\theta ={65}^{\circ }$ becomes stronger and shifts towards $\theta ={90}^{\circ }$ as the inflow velocity increases. Additionally, in this inflow velocity range (${\mathrm{U}}_{\infty }=15.6{\mathrm{ms}}^{-1}$ and ${\mathrm{U}}_{\infty }=20{\mathrm{ms}}^{-1}$), the effect of negative rotor tilting relative to the freestream is more influential on the BPF when compared to the $\alpha =0^{\circ }$ case. While the results of $\alpha =-4^{\circ }$, $-8^{\circ }$ and $-{12}^{\circ }$ are fairly similar across the top array, they show a significant increase compared to the $\alpha =0$ case in the rotor’s downstream region, i.e., $\theta <{110}^{\circ }$. On the other hand, rotor tilt does not significantly change the BPF noise level and directivity pattern in the upstream region ($\theta >{120}^{\circ }$). Finally, in the case of ${\mathrm{U}}_{\infty }=26.5{\mathrm{ms}}^{-1}$, as shown in Figure 9d, the BPF directivity patterns change drastically compared to lower inflow speeds—a notable trend when a significant level of turbulence ingestion is expected to occur in these conditions, as discussed in Section 3.3.1. In the rotor’s downstream region (${30}^{\circ }<\theta <{90}^{\circ }$), the ${\mathrm{SPL}}_{m=1}$ results exhibit a weak dependence on the rotor tilting angle, while in the upstream region ($\theta >{110}^{\circ }$), a decrease in the rotor tilt angle is shown to reduce the rotor BPF noise level substantially. As such, the main directivity lobe in the case of $\alpha =-{12}^{\circ }$ shifts towards $\theta ={80}^{\circ }$, indicating a significant change in the BPF noise generation mechanism under this extreme operating condition. As outlined in Section 3.3.1 and as discussed in prior studies [18,21], the steady and unsteady loading exerted on the rotor is expected to change significantly across the operational envelope (${\mathrm{U}}_{\infty },\alpha$) considered here. This is due to the combined effects of the freestream and tilting angle, resulting in the flow moving up through the rotor disk from the wake region and high levels of turbulence ingestion across the upstream and downstream blades, as shown in Figure 5. To comprehensively understand the BPF directivity patterns and uncover the underlying physics at play within this operational range requires in-depth blade-level analysis using high-fidelity CFD, which will be the subject of future work.

Lastly, the BPF directivity across the side array under different operating conditions is presented in Figure 10. The results at ${\mathrm{U}}_{\infty }=8.7{\mathrm{ms}}^{-1}$, as shown in Figure 10a, show that the BPF directivity has a large lobe, with a peak at $\varphi ={80}^{\circ }$, i.e., below the plane of rotation. The rotor tilt angle does not significantly change the BPF noise level or its directivity pattern. The BPF directivity results at moderate inflow velocities (${\mathrm{U}}_{\infty }=15.6{\mathrm{ms}}^{-1}$ and ${\mathrm{U}}_{\infty }=20{\mathrm{ms}}^{-1}$), as shown in Figure 10b,c, respectively, exhibit a double-lobe directivity pattern, with one lobe pointing towards $\varphi ={80}^{\circ }$ (below the rotor plane) and one pointing upwards, unlike the results at low velocities (Figure 10a). The peak angle of the lobe located above the rotor plane of rotation was not captured due to the microphone array range used in this study. As before, the BPF level is not found to vary significantly with rotor tilting. It is, however, interesting to note that at ${\mathrm{U}}_{\infty }=20{\mathrm{ms}}^{-1}$, the rotor operating at a tilting angle of $\alpha =-{12}^{\circ }$ is 2–5 dB quieter than the edgewise condition ($\alpha =0^{\circ }$). Similar observations can be noted at the extreme inflow condition of ${\mathrm{U}}_{\infty }=26.5{\mathrm{ms}}^{-1}$, as shown in Figure 10d. Overall, the BPF behaviour is shown to change in a directive manner across both of the utilised microphone arrays, with the rotor tilting angle and the inflow velocity conditions leading to changes in the tonal emissions.

3.3.3. Overall Sound Pressure Level Directivity

Due to the substantial variations observed in the noise spectra under different rotor operating conditions, specifically with different combinations of inflow velocity and tilting angle, it is crucial to analyse the overall sound pressure level and the corresponding directivity of the radiated noise. The overall sound pressure level (OASPL) is a key parameter in the evaluation of sound sources, particularly in the context of noise directivity and the impact on observers at different locations. The OASPL is obtained by integrating the respective noise spectrum over the frequency range of 160 Hz to 10 kHz, as defined in Equation (7).

Figure 11 displays the OASPL results for the rotor operating at inflow velocities of ${\mathrm{U}}_{\infty }=8.7,15.6,20.0$ and $26.5{\mathrm{ms}}^{-1}$ and tilting angles of $\alpha =0^{\circ },-4^{\circ },-8^{\circ }$ and $-{12}^{\circ }$. As can be seen from the results, the rotor tilt angle has a strong effect on the overall level and directivity of the radiated noise at each of the inflow velocities considered here. The OASPL directivity results show that tilting the rotor negatively to the freestream results in a significant noise increase in the downstream region of the rotor (${30}^{\circ }<\theta <{90}^{\circ }$) but does not significantly change the noise at the very upstream locations (i.e., $\theta >{120}^{\circ }$). At ${\mathrm{U}}_{\infty }=8.66{\mathrm{ms}}^{-1}$, changing the rotor tilt from $\alpha =0^{\circ }$ to $-{12}^{\circ }$ shifts the main directivity lobe peak from $\theta ={130}^{\circ }$ to approximately ${70}^{\circ }$, with an increase of up to 4 dB in downstream regions. While the rotor tilt itself can lead to a slight angular shift in directivity, the significant directivity changes observed here are related to the changes in the rotor self-noise at high frequencies, as discussed in Section 3.3.1 (see Figure 7a). Especially since the rotor tilt angle was not found to change the BPF amplitude and directivity under these inflow velocity conditions (see Figure 9a). The directivity results presented in Figure 11b,c, for higher inflow velocities (${\mathrm{U}}_{\infty }=15.6,20.0$ and $26.5{\mathrm{ms}}^{-1}$) show a slightly different directivity pattern at negative tilt angles, with the main directivity lobe pointing towards $\theta ={90}^{\circ }$, signifying the presence of an additional noise source compared to the results presented in Figure 11a. As previously described in Section 3.3.1, operating rotors at a negative tilting orientation with medium to high inflow velocities can result in the emergence of low- and mid-frequency turbulence ingestion noise (see Figure 5), which is believed to be the reason for the changes in the directivity patterns observed in Figure 11b,c. Again, it is important to note that varying the tilt angle between $\alpha =-4^{\circ }$ and $-{12}^{\circ }$ was not found to alter the directivity or amplitude of the BPF tone in the upstream region, i.e., ${30}^{\circ }<\theta <{90}^{\circ }$ (see Figure 9b–d). Therefore, the turbulence ingestion and the LF and MF broadband noise increases observed in Figure 7b–d are likely the root cause of the changes in the OASPL directivity at high inflow velocities.

Figure 12 presents the OASPL results collected using the side array at different inflow velocities ($8.7{\mathrm{ms}}^{-1}\le {\mathrm{U}}_{\infty }\le 26.5{\mathrm{ms}}^{-1}$) and rotor tilt angles ($-{12}^{\circ }\le \alpha \le 0^{\circ }$). An inspection of the results reveals several key observations and trends that can have significant implications for our understanding of the acoustic characteristics of rotors operating at negative tilt angles. Similar to the top microphone array, the OASPL is observed to increase as the inflow velocity is increased; however, the results exhibit a dipole-like radiation pattern characterised by a dip in the sound pressure levels at the rotor plane, i.e., at $\varphi ={90}^{\circ }$, as seen in Figure 12. The dipole-like directivity property becomes more dominant as the velocity is increased, with a sharper dip at $\varphi ={90}^{\circ }$. At low inflow velocities, i.e., ${\mathrm{U}}_{\infty }=8.7{\mathrm{ms}}^{-1}$, the change in the rotor tilting angle does not appear to change the noise characteristics of the rotor significantly. As the velocity increases between ${\mathrm{U}}_{\infty }=15.6{\mathrm{ms}}^{-1}$ and ${\mathrm{U}}_{\infty }=26.5{\mathrm{ms}}^{-1}$, there is a notable increase in the noise levels, particularly for observers below and above the rotor plane of rotation. Notably, this takes place as the loading conditions outlined in Figure 6 show the onset of diverging behaviour between the tilting angles for the yawing moment coefficient (${\mathrm{C}}_{\mathrm{My}}$). The results show that the effect of rotor tilt is more pronounced as the velocity is increased, with a strong increase for observers above the rotor plane. As discussed in Section 3.3.2, at high inflow speeds (Figure 10d), a negative rotor tilting angle reduces the magnitude of noise at the BPF. As such, the main reason for the strong increase in the OASPL and the directivity shapes above the rotor plane is believed to be the low- and mid-frequency turbulence ingestion noise, as well as the onset of haystacking behaviours, which are observed to spread energy about the BPF tones. These observations are of particular interest to UAM vehicle designers and to the regulatory bodies considering potential operational envelopes for UAM aircraft during take-off and landing at vertiports, which are likely to be psycho-acoustically critical phases of flight, as they are closest to ground observers. The demonstrated sensitivity of rotors to even slight levels of tilt and the resultant reverse non-axial inflow conditions experienced by the rotor are crucial considerations for industry when designing quiet eVTOL aircraft intended for UAM operations. The intensity and directivity of radiated noise of even a single rotor in these conditions clearly changes substantially under reverse non-axial inflow conditions.

4. Conclusions

A comprehensive study of rotor noise emissions and aerodynamic performance under reverse non-axial inflow conditions was conducted experimentally by testing a single, two-bladed rotor operating at a tip Mach number of $M_T=0.42$. The rotor was tested under different inflow velocity conditions ($4.4{\mathrm{ms}}^{-1}\le {\mathrm{U}}_{\infty }\le 26.5{\mathrm{ms}}^{-1}$) at a range of tilting angles ($-{12}^{\circ }\le \alpha \le 0^{\circ }$) to evaluate possible relationships between the rotor advance ratio and tilting angle with the generated noise. The time-averaged aerodynamic coefficients showed an increase in the loading and moments on the rotor blades as the inflow velocity increased. Notably, while operating at inflow velocities of ${\mathrm{U}}_{\infty }\ge 15.6{\mathrm{ms}}^{-1}$, the yawing moment was observed to diverge as the rotor tilted negatively, indicating complex aerodynamic behaviour as the rotor experiences reverse non-axial inflow conditions.

Far-field noise results indicate significant changes in the noise emissions of the rotor as the rotor is tilted negatively. At the lower tested inflow velocities, the rotor self-noise is observed to increase as the rotor tilts further backwards, leading to broadband noise increases at higher frequencies. The advance ratio is found to greatly influence the noise characteristics, with an increasing inflow velocity leading to noise increases from rotor self-noise shifting to a lower frequency band located about the BPF and its harmonics. Crucially, the emergence of additional noise in the low- and mid-frequency ranges is indicative of another noise generation mechanism in reverse non-axial inflow conditions, namely rotor turbulence ingestion. The unsteady loading conditions resulting from the rotor re-ingesting its own blade wake also leads to haystacking about the BPF and its harmonics, with additional harmonic peaks observed for the negatively tilted cases. The rotor tilting angle is observed to change the directivity pattern of the fundamental BPF tone, again showing a clear dependence on the rotor advance ratio ($\mu$), with both increases and decreases in the tonal noise observed at different observer angles as $\mu$ changes. Overall, the noise emissions are shown to increase notably in terms of the OASPL across both microphone arrays as the rotor tilts negatively to the freestream, with the added noise increases of the rotor self-noise and turbulence ingestion noise being the main contributing factors. Given the attention given to UAM concepts and the necessity of aircraft operating in UAM applications emitting minimal noise, the experimental results reported here provide an important benchmark to aid in the understanding of rotors operating under reverse non-axial inflow conditions. In future studies, it will be interesting to examine the perception of noise increases with a negatively tilted propeller using psycho-acoustic analysis and A-weighted spectra. Additionally, as the present study was carried out with the propeller operating at a relatively high RPM ($\Omega =9000\mathrm{RPM}$), it is potentially viable to utilise the acoustic spectra as a reference to larger-scale rotors found on UAM vehicles. In an earlier study, Boxwell et al. [44] examined blade–vortex interaction (BVI) on the main rotor of a 1/7 scale helicopter and compared the results to those of full-scale tests. They found that to ensure that small-scale tests could be directly used for full-scale aircraft, the time (hence, frequency) of the collected data needed to be scaled by the geometric ratio between the small-scale and full-scale rotor and that the tip Mach number had to be matched. For instance, with a geometric ratio of 10 between the full-scale and model-scale rotor, the frequency scale of acoustic spectra from the model-scale rotor should be divided by a factor of 10 when being compared to the full-scale rotor. Therefore, with reference to the study of Boxwell et al. [44], we suggest that the present measurements could be used in a future study to inform larger-scale rotors if the tip Mach number is matched. When interpreting the acoustic spectra, a geometric ratio would have to be applied to the frequency scale; moreover, such a comparison would be more accurate if the thrust coefficient of the larger-scale propeller is similar to that used in the present experiments under any given operating condition. To further reveal the origin of the noise and its associated generation mechanisms, detailed knowledge of the turbulence fields is necessary, which can be a potential avenue for future studies using computational fluid dynamics and experimental flow-field studies.