Prediction and Control of Broadband Noise Associated with Advanced Air Mobility—A Review

Abstract

This review presents an overview of advanced air mobility broadband noise (BBN) prediction and control techniques, highlighting significant advancements in various prediction models. Methods such as the semi-empirical Brooks–Pope–Marcolini (BPM) model, analytical Amiet model, and time-domain models based on the FW-H equation have been extensively studied. Machine learning (ML) shows promise in BBN prediction but requires extensive data training and application to noise source mechanisms. Passive control methods, such as leading and trailing edge serrations and blade tip designs, have been partially successful but often compromise the aerodynamic performance. Active control methods, like suction and blowing control, trim adjustments, and dielectric barrier discharge (DBD) plasma actuators, show great potential, with the latter two being particularly effective for reducing BBN in thin propeller structures. Overall, while progress has been made in understanding and predicting BBN, further research is needed to refine these methods and develop comprehensive noise control strategies. These advancements hold significant promise for effective and efficient noise mitigation in future AAM vehicles.

1. Introduction

Advanced air mobility (AAM) encompasses a range of innovative air transportation systems designed to move people and goods in urban and rural areas using new, highly automated, and electric aircraft. AAM includes several types, such as urban air mobility (UAM); small, unmanned aircraft systems (sUAS); and regional air mobility (RAM).

UAM operates within urban environments, with take-off and landing at a vertiport. UAM vehicles are powered by multiple electrical rotors or propellers, which we also call eVTOL. There are serval configurations that have been tested, including multirotor, compound-wing VTOL, tiltrotor/propeller, tiltwing, and ducted fan [1], as shown in Figure 1. The sUAS is a small version of UAM with missions for aerial work or cargo delivery. RAM extends the UAM operation range to 500 miles and normally adopts electric conventional take-off and landing (eCTOL) and electric short take-off and landing (eSTOL) aircraft [2].

AAM operates near populated communities, which will face two big obstacles: safety and noise. Noise pollution has significant implications for public acceptance, regulatory compliance, and environmental impact. Since AAM operates in populated areas, AAM noise needs to be addressed, particularly near vertiports, where the population is dense and close to the noise sources. The Federal Aviation Administration (FAA) has noise certification standards for AAM to avoid noise pollution [3]. AAM is propelled by distributed propellers, which are the dominant noise sources. The noise generated by propellers can be categorized into tonal noise and broadband noise (BBN). Tonal noise is characterized by discrete frequencies often associated with rotating components, while broadband noise encompasses a wide range of frequencies, resulting in a continuous noise spectrum. Tonal noise is typically divided into loading noise and thickness noise, characterized by tonal noise at the blade-passing frequency (BPF) and its harmonics. Broadband noise (BBN) is characterized by unsteady turbulence loading due to blade–wake interaction, turbulence in the boundary layer, and turbulence ingestion [4].

Figure 1. Rotor noise variation by tip Mach number [5].

Figure 1. Rotor noise variation by tip Mach number [5].

AAM propellers have more blades and are smaller, with diameters that can be 20 times less than those of traditional helicopter rotors, which causes their significantly lower tip speeds. The noise signatures of AAM propellers differ from those of full-scale helicopter rotors due to their lower tip speeds. Figure 1 shows that the BBN becomes more important with a decrease in the tip Mach number, dominating below 0.5 Ma. Furthermore, AAM has a complicated structure and multiple rotors or propellers; the propellers interact and ingest more structure wake. Additionally, in an urban atmosphere and an environment dominated by buildings exists non-uniform flow compromising wakes, vortex, gust, and turbulence, among other irregularities. For these reasons, broadband noise may have a comparable amplitude to that of the blade passage frequency (BPF) and associated harmonics.

This paper reviews broadband noise (BBN) resources, prediction methods, and passive and active control techniques for BBN reduction. To begin, we explore the available resources for understanding BBN, focusing on both theoretical foundations and empirical data. Following this, we examine various prediction methods, highlighting computational models and experimental approaches that have shown promise in accurately forecasting BBN levels. Then, we move to control strategies, focusing on passive control methods that are easy to apply. Throughout the paper, we emphasize the importance of these strategies in the context of AAM, particularly given the unique noise challenges posed by smaller, lower-tip-speed propellers. By leveraging recent advances in theory, computational methods, and experimental approaches, there are significant opportunities to further understand and reduce BBN in AAM, enhancing the sustainability and public acceptance of this emerging technology.

2. Sources/Types of BBN

Broadband noise arises from unsteady, nondeterministic blade loading, with sources attributed to turbulent disturbances from flow–surface interactions. As depicted in Figure 2, noise sources are classified into three main categories: inflow turbulence ingestion noise (TIN), blade self-noise, and blade–wake interaction noise (BWI). Among these, blade self-noise is the predominant source and is further subdivided into five distinct boundary layer turbulence mechanisms, detailed in subsequent sections. AAM has a complex configuration that leads to noise interactions, such as blade–airframe interaction, fuselage–wake interaction, and rotor–rotor interaction. However, it is unnecessary to define these interactions separately, as their mechanisms are fundamentally associated with the primary noise sources mentioned above. Thus, the dominant source of BBN in AAM remains blade self-noise, while TIN and BWI are becoming increasingly significant and cannot be overlooked, especially given the structured wake generation and the operation of AAM vehicles in urban environments.

2.1. Inflow Turbulence Noise

Ingestion noise is broadband noise caused by a propeller ingesting turbulence. This turbulence may originate from a variety of sources, such as atmospheric turbulence or wake turbulence shed by other propellers or airframe components, as shown in Figure 3. Anisotropic turbulence will be chopped several times as it passes through the rotor, which leads to narrow-band noise around the harmonics of the blade-passing frequency, also known as haystacking, which was first reported by Hanson [6]. Additionally, Amiet [7] assumes the inflow turbulence noise as leading-edge noise.

2.2. Blade–Wake Interaction Noise

Blade–wake interaction or BWI noise is a mid-frequency broadband noise source that is due to the blade interaction with turbulent (nondeterministic) portions of the wakes of preceding blades, as shown in Figure 4. BWI noise was first introduced as a prominent broadband noise source by Brooks et al. [8]; the presence of this noise source was only postulated for forward flight conditions. Since the disturbances associated with BWI originate at the leading edge, it can also be referred to as leading-edge noise [9].

2.3. Blade Self-Noise

Self-noise is caused by the interaction between an airfoil blade and the turbulence produced in its own boundary layer and wake space. If an airfoil encounters smooth inflow, self-noise is the only kind of noise generated. Figure 5 shows five self-noise mechanisms for subsonic flow: turbulent boundary layer trailing-edge noise (TBL-TE), trailing edge separation/stall noise (angle dependence for TBL-TE), bluntness vortex shedding noise (BVS), tip vortex formation noise, and laminar boundary layer vortex shedding noise (LBL-VS). Turbulent boundary layer trailing edge (TBL-TE) noise arises when the turbulent boundary layer convects past the trailing edge of the airfoil, generating a scattering of sound waves. Trailing edge separation/stall noise occurs when the boundary layer separates from the airfoil surface, often at high angles of attack, causing large-scale unsteady flows that produce significant noise. Bluntness vortex shedding (BVS) noise is generated by the formation and shedding of vortices from a blunt trailing edge, resulting in periodic sound waves. Tip vortex formation noise is caused by the tip vortices that form at the blade tips and interact with the surrounding flow, producing noise. Lastly, laminar boundary layer vortex shedding (LBL-VS) noise occurs when vortices shed from the laminar boundary layer interact with the trailing edge, generating discrete tonal noise.

3. Methods for Prediction of BBN

3.1. Experimental Observations

Inflow Turbulence Noise: Several experimental investigations of propeller noise under different non-uniform flows have been conducted. Yauwenas et al. [11] researched the noise of the third-party 1206 APC propeller (12-inch diameter) under the cylinder wake (see Figure 6a). They found the cylinder wake increased the BBN level at all ranges, especially at the mid-range of the frequency, as shown in Figure 6b. Similar research was conducted by Castelucci et al. [12], whose results demonstrated that both tonal and broadband noise levels increased under the influence of the cylinder wake. Specifically, the broadband noise increased by 12 dB, while the tonal noise experienced a 1 dB increase for a 2-blade propeller. These findings corroborate the hypothesis that inflow turbulence significantly contributes to BBN, highlighting the impact of non-uniform flow conditions on propeller noise characteristics.

In Figure 7b, we present the results by Bowen et al. [13], who studied the effect of distributed five-bladed propellers’ noise under the influence of three different grid turbulence ingestions (Figure 7a) at varying advance ratios. All the grid turbulence scenarios caused significant variations in the broadband noise (BBN), particularly within the mid-to-high frequency range. Notably, grid 3, which generated the highest turbulence intensity (twice as strong as grid 1), resulted in the greatest increase in BBN. They also observed the haystacking phenomena at the blade passing frequency at θ = 60° with the increased turbulent length scale. Jamaluddin et al. [14,15] conducted grid turbulence ingestion for a single two-bladed propeller at forward inflow and edgewise directions, respectively. Both resulted in a larger contribution of turbulence ingestion to the broadband noise radiation at the low-to-mid-frequency. However, the inflow condition still has a higher variation of BBN above 1 kHz, whereas the edgewise condition did not show a similar trend.

Another aspect of turbulence ingestion, specifically, boundary layer turbulence, was investigated by Zaman et al. [16]. They examined the effects of varying the turbulence ingestion by adjusting the tip gap between the plate and a 2-bladed propeller with a 12-inch diameter to study the haystacking phenomenon, as illustrated in Figure 8a. Their findings indicate that increasing thrust led to more pronounced haystacking, which was more evident at perpendicular angle observer points. Additionally, they discovered that a lower tip gap, which results in greater ingestion of boundary layer turbulence, caused a significant increase in broadband noise (BBN) and the prominence of haystacking peaks. However, once the tip gap was reduced to 10 mm, further decreases did not result in a substantial increase in BBN, as depicted in Figure 8b.

BWI noise: BWI dominates the spectra in the mid-frequencies for flight conditions. Jamaluddin et al. [17] conducted a single 2-bladed propeller noise test at an edgewise inflow condition, that is, forward flight. As seen in Figure 9a–d, a strong wake structure behind the propeller was generated by the flow, which resulted in localized acceleration zones, as indicated by the increased velocity. Moreover, with the increasing tilting angle, the flow velocity increased in the wake of the blade. Meanwhile, as shown in Figure 9e, the mid-frequency noise remained comparable, which suggested BWI noise. The phenomenon was also observed in multi-rotor forward flight condition noise tests conducted by Zawodny et al. [18], which further evidenced that noise behavior was strongly governed by rotor–wake interactions. Additionally, propellers operating in ground effect exhibit tip vortex interactions that contributed to BWI noise. This was also observed by Paruchuri et al. [19] and Chen et al. [20], further corroborating the significant impact of wake interactions on mid-frequency noise characteristics in various flight conditions and configurations.

Blade self-noise: Self-noise is inherent noise in a propeller. If an isolated propeller is tested at static or uniform inflow conditions, the only BBN is the blade self-noise. Several investigations have been conducted, such as that of Brooks et al. [8] and Intaratep et al. [21]. However, five self-noise mechanisms coexist, and they are hard to separate by experiment but could be identified by an analytical or a semi-empirical method.

3.2. BBN Prediction Models

Semi-empirical model: The widely used and most successful model is the semi-empirical one developed by Brooks et al. [8], commonly known as the BPM model. This approach provided some boundary layer corrections using the NACA 0012 experimental test. The self-noise spectrum is the sum of all five self-noise mechanisms’ spectra. Because the trailing-edge noise and separation/stall noise are generated from the trailing edge boundary layer, the equation names them as TBL-TE, $G_{TBL-TE}(f)=G_{TBL-TE,p}(f)+G_{TBL-TE,s}(f)+G_{TBL-TE,{\alpha }_{\ast }}(f)$, where $G_{TBL-TE,p}(f)$ is the pressure side of the blade segment, $G_{TBL-TE,s}(f)$ is from the suction side, and $G_{TBL-TE,{\alpha }_{\ast }}(f)$ is the TE separated flow noise. Each component is calculated as follows:

$$G_{TBL-TE,p}(f)={\displaystyle \frac{{\delta }_p^{\ast }{M}^{5}L{\overline{D}}_h}{r_e^2}}\cdot H_p\left({\displaystyle \frac{f{\delta }_p^{\ast }}{U}},M,{\mathrm{Re}}_c,{\mathrm{Re}}_{{\delta }_p^{\ast }}\right)$$

(1)

$$G_{TBL-TE,s}(f)={\displaystyle \frac{{\delta }_s^{\ast }{M}^{5}L{\overline{D}}_h}{r_e^2}}\cdot H_s\left({\displaystyle \frac{f{\delta }_s^{\ast }}{U}},M,{\mathrm{Re}}_c\right)$$

(2)

$$G_{TBL-TE,{\alpha }_{\ast }}(f)={\displaystyle \frac{{\delta }_s^{\ast }{M}^{5}L{\overline{D}}_h}{r_e^2}}\cdot H_{{\alpha }_{\ast }}\left({\displaystyle \frac{f{\delta }_s^{\ast }}{U}},{\alpha }_{\ast },M,{\mathrm{Re}}_c\right)$$

(3)

$$G_{LBL-VS}(f)={\displaystyle \frac{{\delta }_p{M}^{5}L{\overline{D}}_h}{r_e^2}}\cdot H_l\left({\displaystyle \frac{f{\delta }_p}{U}},{\alpha }_{\ast },M,{\mathrm{Re}}_c\right)$$

(4)

$$G_{BTE}(f)={\displaystyle \frac{h{M}^{5.5}L{\overline{D}}_h}{r_e^2}}\cdot H_b\left({\displaystyle \frac{h}{{\delta }_{avg}^{\ast }}},{\displaystyle \frac{f{\delta }_{avg}^{\ast }}{U}},{\displaystyle \frac{fh}{U}},\psi \right)$$

(5)

$$G_{Tip}(f)={\displaystyle \frac{M^2{M}_{\max }^{3}l{\overline{D}}_h}{r_e^2}}\cdot H_t\left({\displaystyle \frac{fl}{U}},{{\alpha }^{\prime }}_{Tip}\right)$$

(6)

where ${\delta }_p^{\ast }$, ${\delta }_s^{\ast }$, and ${\delta }_{avg}^{\ast }$ are boundary layer displacement thicknesses for the pressure, suction sides, and average, respectively. ${\delta }_p$ is boundary layer thickness. $h$ is the trailing edge thickness. $M$ is the Mach number. $L$ is the blade segment spanwise length. ${\overline{D}}_h$ is the half-plane-baffled-type directivity term. $r_e$ is the observer distance in retarded coordinates from the TE. $\psi$ is the solid angle. $M_{\max }$ is the maximum velocity in or about the vortex near the TE. ${{\alpha }^{\prime }}_{Tip}$ is the effective blade angle at the blade tip. $l$ is the spanwise extent. If $\left|{\alpha }_{\ast }\right|>12.5°$, the turbulent boundary trailing edge (TBL-TE) noise will be written as

$$G_{TBL-TE}(f)=G_{TBL-TE,{\alpha }_{\ast }}(f)={\displaystyle \frac{{\delta }_s^{\ast }{M}^{5}L{\overline{D}}_l}{r_e^2}}\cdot {H^{\prime }}_{{\alpha }_{\ast }}\left({\displaystyle \frac{f{\delta }_s^{\ast }}{U}},{\alpha }_{\ast },M,{\mathrm{Re}}_c\right)$$

(7)

The BPM model only considers self-noise, so to improve the accuracy of BBN, Burley and Brooks [10] introduced the BWI noise to the BPM model. The BWI noise spectral contribution from the mn^th blade segment was found to be the following:

$$G_{BWI}(f)={\left({\displaystyle \frac{\omega z_r}{4\pi c_0{\sigma }^2}}\right)}^2{G}_{LE\Delta p}(f)\cdot {\left[bC\right]}^2\left({\displaystyle \frac{2L(\zeta \omega /U)}{{(\zeta \omega /U)}^2+{(\omega y_r/c_0\sigma )}^2}}\right)$$

(8)

where $\omega =2\pi f$. $c_0$ is the speed of sound. $G_{LE\Delta p}(f)$ is the auto-spectrum of the unsteady pressure differential near the leading edge. L and C are the span and chord length of a segment, respectively. $b$ and $\zeta$ are constant factors. r indicates the retarded coordinates.

The BPM model is well-regarded for its accuracy and easy application in predicting BBN noise. However, as a semi-empirical model, BPM relies on empirical data and assumptions, which may limit its accuracy or applicability outside the range of the conditions for which it was originally developed. Additionally, it may not be valid in all practical applications, particularly in cases involving unsteady or turbulent flow.

Analytical model: The dominant noise component of broadband noise (BBN) is trailing-edge noise. Historically, there has been quite extensive work in the field of airfoils, with a few researchers applying them to rotating blades. The most prominent analytical theory was proposed by Amiet [22] and could be derived for rotor TE noise by Schlinker and Amiet [23]. They derived an airfoil in rectilinear motion:

$$S_{pp}(x,\omega )={\left({\displaystyle \frac{K_{x}Mzb}{2\pi {\sigma }^2}}\right)}^2{\displaystyle \frac{\pi s}{2U_c}}{\left|L\left(x,K_x,\lambda ,K_y\right)\right|}^2{\Phi }_{qq}(\lambda ,K_y)$$

(9)

$$\left|L\right|={\displaystyle {\int }_{-c}^{0}g\left(x_0,K_x,\lambda ,K_y\right)}{e}^{-i\mu x_0(M-x/\sigma )}{\displaystyle \frac{d{x}_0}{b}}$$

(10)

$$K_y={\displaystyle \frac{\omega y}{c_0\sigma }}$$

(11)

$${\sigma }^2=x^2+{\beta }^2(y^2+z^2)$$

(12)

where s is the airfoil span and ${\Phi }_{qq}$ is the wavenumber spectrum produced by the turbulence. The effective lift function is $L$. Transforming Equation (9) to rotating and introducing the Doppler-shifted frequency $\omega /{\omega }_0$, the azimuthally averaged spectrum is then as follows:

$$S_{pp}(\underset{\_}{x},\omega )={\displaystyle \frac{1}{2\pi }}{\displaystyle {\int }_0^{2\pi }\frac{\omega }{{\omega }_0}{S^{\prime }}_{pp}(\underset{\_}{x},{\omega }_0,\gamma )d\gamma }$$

(13)

Sinayoko et al. [24] proposed a new formulation of trailing-edge noise for rotating blades. They gave the instantaneous spectrum, as shown in Equation (14), and time-averaged PSD, as shown in Equation (15), and validated with Schlinker and Amiet [23].

$$S_{pp}(x_o,\omega ,t)={\displaystyle {\int }_{R_h}^{R_t}{\displaystyle \sum _{m=-\infty }^{+\infty }B(m\Omega )e^{-im({\gamma }_o-\pi /2)}}\times \left({\displaystyle \sum _{n=-\infty }^{+\infty }{\tilde{I}}_{n,n+m}(\omega ,m\Omega ,r)}\right)e^{in\Omega t}dr}$$

(14)

$${\overline{S}}_{pp}(x_o,\omega )={\displaystyle {\int }_{R_h}^{R_t}B(0){\displaystyle \sum _{m=-\infty }^{+\infty }{\tilde{I}}_n(\omega ,m\Omega ,r)dr}}$$

(15)

The analytical model is a physical-based frequency domain approach, which helps in understanding the mechanisms of noise generation and allows for detailed analysis across different frequencies. However, the mathematical rigor of the analytical model introduces a level of complexity that can be challenging to implement. Its applicability is primarily limited to trailing-edge noise, and the derivation of its mathematical equations necessitates several assumptions and simplifications, such as the adoption of linear acoustics and the assumption of steady flow conditions. These assumptions may constrain the model’s accuracy. Moreover, it lacks the accuracy necessary for low-frequency BBN.

Time domain model: BBN can be predicted in the time domain by solving the Ffowcs-Williams and Hawkings (FW-H) equation [25]. At a low Mach number, the quadrupole noise is negligible; the noise is dominated by the thickness noise and loading noise. The BBN is the unsteady loading noise and takes the form of a dipole, which can be solved by the loading part of Farassat’s 1A Formulation [26]:

$$4\pi {p^{\prime }}_L\left(x,t\right)={\displaystyle \frac{1}{c}}{\displaystyle {\int }_{f=0}{\left[\frac{{\dot{L}}_r}{r{(1-M_r)}^2}\right]}_{ret}dS+}{\displaystyle {\int }_{f=0}{\left[\frac{L_r-L_M}{r^2{(1-M_r)}^2}\right]}_{ret}dS}+{\displaystyle \frac{1}{c}}{\displaystyle {\int }_{f=0}{\left[\frac{L_r\left(r{\dot{M}}_r+c(M_r-M^2)\right)}{r^2{(1-M_r)}^3}\right]}_{ret}dS}$$

(16)

where $M$ is the surface motion Mach number, r is the distance between the source and observer, and $L$ is the loading term that is obtained from simulations. ${\dot{L}}_r$ and ${\dot{M}}_r$ represent the source time derivatives. The subscript $r$ denotes a dot product of the vector with the unit vector in the radiation direction. The term $L_M=L_i{M}_i$. The formulation above assumes a control surface defined by $f=0$.

More recently, Casper and Farassat [27,28] devised a new time domain Formulation 1B for broadband noise predictions, which is a solution of FW-H. Their method demonstrates that time domain approaches could be effectively employed for predicting broadband noise of a propeller/rotor. However, Formulation 1B has certain limitations that do not strictly meet the geometry, kinematics, validation, and observer requirements. Consequently, Farassat and Casper [29] proposed an improved version, Formulation 2B. Despite its enhancements, Formulation 2B was not recommended for discrete-frequency noise prediction of a propeller/rotor due to its reliance on numerical differentiations and the calculation of retarded times, which are computationally expensive and complex.

The time domain model is recognized as the most accurate approach for predicting broadband noise (BBN), which relies on high-fidelity simulations. This high level of accuracy, however, comes with a significant computational cost. A refined region is crucial to capturing detailed acoustic phenomena. This refinement, while essential for enhancing the accuracy of BBN predictions, further escalates the computational expense.

Empirical model: Analytical or semi-empirical methods are computationally expensive. Equation (17) provides a basis to represent three empirical broadband noise models with different values for k and C: Davidson and Harcest [30], Schlegel and Mull [31], and Stuckey and Goddard [32], which were derived from different helicopter rotor experimental tests.

$$OASPL=10{\log }_{10}\left[{\left(\Omega R\right)}^6{A}_b{\left(C_T/\sigma \right)}^k\right]-C+20{\log }_{10}\left({\displaystyle \frac{\sin {\theta }_0}{s_0/150}}\right)$$

(17)

where ${\theta }_0$ is an observer elevation angle, s₀ is the distance from the rotor hub to the observer, $C_T/\sigma$ is blade loading, and $\Omega R$ is blade tip speed. The distinct constants employed by the models are shown in

Table 1. k and C of different empirical models [33].

Models	k	C
DH	2	36.7
SKM	2	42.9
SG	1.66	39.9

.

Earlier empirical broadband noise prediction models have constraints when applied to AAM and were based on a limited number of noise experiments conducted with larger and high tip-speed helicopter rotors. Recently, a new empirical BBN prediction model for AAM was developed by Gill and Lee [33]. They expanded their noise data sets to cover all size propeller/rotors, including small drone rotors, medium-sized propellers, and larger helicopter rotors, such as the CH-53A and CH-3C. This broader data inclusion enhances the model’s accuracy and applicability across a wider range of rotorcraft types, as detailed in Equation (18). They also developed the one-third octave band spectral model by “Gene Expression Programming”, as presented in Equation (19).

$$OASPL=\left({\sin }^{0.01}\left|{\theta }_0\right|\right)\left[10{\log }_{10}\left(V_t^{6.77}{C}_T^2{\sigma }^{-1}\right)-32.73\right]-\left[9.25+0.73\left(1-\sin \left|{\theta }_0\right|\right)\right]\log {\displaystyle \frac{s_0}{D}}$$

(18)

$$SP{L}_{1/3}={\displaystyle \frac{10{\log }_{10}{V}_t^{7.84}{\Delta }^{0.6}}{{\left[\Delta -2M_t^2+2.06\right]}^{-C_T{M}_t\left(C_T-\sin \left|{\theta }_0\right|+2.06\right)+1}+{\left[C_T\Delta \right]}^{4.97C_T\sin \left|{\theta }_0\right|\left(1.5\left(s_0/R\right)M_t-\left(s_0/R\right)+15\right)}}}$$

(19)

where $\Delta =fc/V_t-\left(\sigma {\log }_{10}{C}_T+0.9M_t\sigma \left(M_t+3.82\right){\log }_{10}\sigma \right)$.

Some code: The popular NASA code, ANOPP [34], adopts the BPM model [4] to predict several types of broadband noise: turbulent boundary layer trailing-edge noise (TBL-TE), trailing-edge separation/stall noise (angle dependence of TBL-TE), bluntness vortex shedding noise (BTE), and laminar boundary layer vortex shedding noise (LBL-VS). For the tip vortex formation noise, the code applied the Brooks and Marcolini [35] model. ANOPP also provides alternative models, such as Grosveld’s [36] for the trailing-edge-bluntness vortex-shedding noise and Schlinker and Amiet’s [23] for TBL-TE and angle dependence of TBL-TE.

Similarly, the UCD-QuietFly code [37] is designed to predict broadband noise for urban air mobility (UAM) applications. This program utilizes Schlinker and Amiet’s [23] model for trailing-edge noise and incorporates the semi-empirical BPM model [4] to predict trailing-edge bluntness noise and stall noise.

Time-domain programs, such as PSU-WOPWOP [38,39] and ASSPIN [40], use Farassat’s Formulation 1A [26]. Recently, NASA released ANOPP2 [41], which employs the Ffowcs-Williams and Hawkings (FW-H) equation to enhance noise prediction capabilities.

Turbulence ingestion noise model: Turbulence ingestion noise presents significant challenges in prediction due to the need to account for both turbulence and unsteady loading models, or the development of new noise prediction models. Paterson and Amiet [42] and Amiet [7] approached this by assuming that turbulence ingestion noise could be treated as leading-edge noise resulting from vertical gusts. The spectrum of an airfoil in rectilinear motion, as described in their work, is given by the following:

$$S_{pp}(\omega )={\left({\displaystyle \frac{\omega bz{\rho }_0}{c_0{\sigma }^2}}\right)}^2\pi U_{c}d{\left|L\left({\overline{K}}_x,\overline{\lambda },K_y\right)\right|}^2{\Phi }_{ww}(\lambda ,K_y)$$

(20)

where L is the effective lift that can be derived from the Sears function [43] and ${\Phi }_{ww}$ is the wavenumber spectrum of the airfoil surface pressure replaced by the von Kármán spectrum, ${\Phi }_{ww}\left(k_x,k_y,k_z\right)={\displaystyle \frac{E\left(k\right)}{4\pi k^2}}\left(1-k_z^2/k^2\right)$. The rotating frame spectrum equation is the same as the Equation (13). Amiet [44] mentioned that if the ingested turbulence is chopped by more than one blade, the noise will tend to be narrowband at blade passage frequency, while if there is only one blade, there is no blade-to-blade correlation. Thus, for the no blade-to-blade correlation form, ${S^{\prime }}_{pp}(\underset{\_}{x},{\omega }_0,\gamma )=\omega /{\omega }_0{S}_{pp}(\underset{\_}{x},{\omega }_0,\gamma )$, which is the same as the no turbulence ingestion, while the blade-to-blade correlation form with the introduced Equation (20) can be written as follows:

$${S^{\prime }}_{pp}(\omega )={\left({\displaystyle \frac{\omega bz{\rho }_0}{c_0{\sigma }^2}}\right)}^2\pi U_{c}d\omega /{\omega }_0{\left|L\left(K_x,\lambda ,M\right)\right|}^2\overline{u^2}{b}^2{\displaystyle {\sum }_{n=-\infty }^{\infty }{\Phi }_{ww}(\lambda ,K_y,K_z^{(n)})}{\displaystyle \frac{2\pi }{\overline{u^2}{b}^{2}Z}}$$

(21)

Majumdar and Peake [45] derived frequency-domain models from the wave equation by rapid distortion theory and a potential mean flow. They utilized the von Kármán turbulence model coupled with the unsteady blade force solution developed by Smith [46] to solve the wave equation.

Glegg et al. [47] conducted similar frequency-domain model research, deriving their model from the loading noise predictions of the FW-H equation. Like Amiet [7], they employed the Sears function to model the unsteady force acting on the blade. For modeling turbulence, they assumed anisotropic turbulence and utilized the Kerschen and Gliebe [48] model, which accommodates the directional dependence of turbulence effects. This approach allowed them to capture the complex interactions between the turbulent flow and the blade, providing a more accurate prediction of the resulting noise.

Glegg et al. [49] reported that the frequency domain model was numerically slower due to the Bessel functions. Furthermore, characterizing turbulence through its wavenumber spectrum posed challenges, as it was often difficult to model the entire wavenumber range. To address these issues, they investigated a time-domain method derived from the loading noise predictions of the FW-H equation. This method was coupled with the Sears function to model unsteady forces, offering a more practical approach for capturing the intermediate turbulence ingestion noise while avoiding the limitations of frequency-domain analysis.

3.3. Low-Fidelity Methods

The low-fidelity models of no turbulence ingestion normally employ the blade element momentum theory (BEMT) and XFOIL or 2D RANS in conjunction with one of the above-established noise prediction models or codes. Casalino et al. [50] investigated a low-fidelity benchmark study by two-bladed APC-96 with 0.3 m diameter. They used XFOIL and BEMT to determine the aerodynamic performance, then applied the Roger and Moreau [51] model that is the corrected form of Amiet’s trailing-edge noise model to predict the BBN. Figure 10 shows that the low-fidelity approach demonstrated good agreement with the experiment and high-fidelity results at mid-to-high frequencies, despite some underpredictions, particularly at low frequencies. Similarly, Yunus et al. [52] performed a study using the same methodology to explore the noise characteristics of 5-blade and 7-blade propellers, further validating the effectiveness of low-fidelity models in predicting propeller noise.

Li and Lee [53] performed validations on a NASA ideally twisted rotor, an SUI Endurance rotor, and a DJI-CF propeller using noise code UCD-QuietFly, with BEMT and XFOIL as the aerodynamic inputs. Various rotational speeds and surface roughness conditions were considered in the hovering and forward flight conditions. The predictions from UCD-QuietFly agreed well with the experiments in various small-scale rotor conditions at mid-to-high frequencies, as shown in Figure 11.

Gill et al. [54] utilized the blade element momentum theory (BEMT) to evaluate three empirical broadband noise (BBN) equations specifically designed for helicopters, applying them to small propellers. The models were validated using data from APC and DJI propellers. As illustrated in

Table 2. BBN OASPL results of three empirical models.

	OASPL (dB)—3600 RPM	OASPL (dB)—4200 RPM	OASPL (dB)—4800 RPM
Experimental data—APC-SF	54.35	54.83	60.81
DH model	61.08	65.38	69.31
SKM model	54.88	59.15	63.11
SG model	61.18	65.41	69.29
	OASPL (dB)—4800 RPM	OASPL (dB)—5400 RPM	OASPL (dB)—6000 RPM
Experimental data—DJI-CF	62.86	63.53	62.89
DH model	61.28	63.93	67.29
SKM model	55.08	57.73	61.09
SG model	61.36	64.09	67.34

and Figure 12, the DH and SG models were overpredicted, while the SKM model provided the closest results to the experimental data. Additionally, the discrepancies vary significantly when applied to propellers of different diameters, indicating that the three models lack robustness. Therefore, a new empirical model specifically designed for AAM propeller/rotor needs to be developed.

Serval low-fidelity turbulence ingestion studies have been developed recently. Karve et al. [55] studied the turbulence boundary layer ingestion BBN of a fan with the Amiet [7] model. They employed Kerschen and Gliebe’s [56] model for the boundary layer turbulence, which was validated by the experiment. They validated the model against the experiment by three different advanced ratios, as shown in Figure 13. The results show that they overpredicted haystacking at the first BPF at J = 0.87, as well as at the second BPF at all the advance ratios. Conversely, they underpredicted the high-frequency noise, particularly at J = 1.44 and J = 1.05, likely due to the limitations of the turbulence model’s accuracy. Despite these discrepancies, the model showed good agreement with the experimental data.

Similar work was conducted by Raposo and Azarpeyvand [57]. They revised Amiet’s [7] model and compared the original model and experimental data by applying them to an open rotor. They reported that Amiet’s [7] model is the most effective model to predict the TIN of rotors, given its accuracy and lower computational cost.

3.4. Numerical Methods

A mid-fidelity method has recently been investigated for BBN prediction of a rotor. Su Jung et al. [9] compared different mid-fidelity methods to predict the noise from a DJI 9443 CF rotor. As mentioned before, the BPM BBN prediction model needs a boundary layer parameter and an effective angle of attack as inputs. To obtain these inputs, 2D and 3D RANS simulations were applied to obtain the boundary layer parameters, while the effective AOA was extracted from 3D RANS and FLIGHTLAB [58], which employed Peter–He’s [59] finite state wake model. Figure 14a,b shows the difference of BBN prediction based on the effect of the AOA computational sources. The 3D RANS approach demonstrated higher accuracy than FLIGHTLAB at high frequencies but showed worse underprediction at low-to-mid frequencies due to laminar boundary layer vortex shedding (LBL-VS) noise. They explained that the noise mechanism associated with LBL-VS needs further study, considering the limitation of the LBL-VS noise production for ideal flow. It was worth noticing that the BBN results used 2D boundary layer parameters have better agreement with experiment, as shown in Figure 14c,d. This could be due to the fact that the boundary layer correction in the BPM method used 2D experimental data.

Other mid-fidelity methods were tested for tone noise prediction that might be applied to predict BBN in the future, such as a non-linear unsteady vortex lattice method coupled with F1A [60] and a modern surface-vorticity panel solver coupled with F1A [61].

Higher fidelity requires resolving the fluctuation turbulence structure. Thus, conventional Reynolds-averaged Navier–Stokes solutions are not appropriate. An unsteady RANS (URANS) approach is the lowest computational cost, but it is unable to capture the transient flow physics and therefore less accurately predicts noise. Zawodny et al. [62] used the ANOPP suite to predict the blade self-noise of the DJI-CF by OVERFLOW2, which is an unsteady Reynolds-average Navier–Stokes (URANS) code. The individual source mechanisms that contribute to the total broadband noise are presented in Figure 15. The overall trends of the broadband predictions were seen to agree with the experimental data, and the result proved that the turbulence boundary layer source mechanisms were prominent BBN source for a rotor at a high frequency. However, it underpredicted at mid-frequency. The researchers explained that maybe the ineffective extraction technique caused retained mid-frequency tonal content that contaminated the extracted broadband signals from the experiment.

The hybrid LES–URANS (DES) model is a competitive method for rotor simulation. It is less time-consuming compared with LES but more accurate compared with URANS. Mankbadi et al. [63] utilized a hybrid LES–unsteady RANS (DES) approach to model the aerodynamics of a 2-bladed 9-inch DJI propeller in hovering condition. The approach utilizes large eddy simulation (LES) away from the wall and unsteady RANS with the Spalart–Allmaras turbulence model near the walls, effectively reducing computational costs while maintaining high resolution. For far-field noise prediction, Farassat’s 1A Formulation was employed. As shown in Figure 16, the broadband noise (BBN) calculated from a permeable control surface closely matched the experimental data, whereas the BBN predictions from an impermeable surface (blade surface) were underpredicted, highlighting the significant contribution of the propeller wake to the BBN. To delve deeper into the BBN analysis, the spectral proper orthogonal decomposition (SPOD) technique [64] was applied. They found that at low frequencies, blade self-noise and wake noise are comparable sources of broadband noise. However, at higher frequencies, blade self-noise became the dominant contributor to the noise spectrum.

The same approach was applied to the case of two counter-rotating propellers by Afari and Mankbadi [65]. In this scenario, the increased broadband noise was attributed to the close proximity of the rotors and the effects of wake mixing.

A large eddy simulation (LES) resolves large-scale eddies through the filtered Navier–Stokes equations and models small-scale eddies through subgrid-scale (SGS) models. LES is one of the higher accuracy numerical methods and is suitable for rotor noise source simulations but is expensive. The more efficient method is the implicit large eddy simulation (ILES), which does not use an explicit subgrid-scale (SGS) model replaced by numerical dissipation. Although it may not capture very small-scale turbulence with high accuracy, it offers advantages in terms of computational cost and implementation. Kunz et al. [66] utilized this solver to predict the propeller BBN at hover and forward flight conditions by Formulation 1A. Despite the discrepancies between the numerical and experimental curves that may be caused by ignoring the nonlinear quadrupole noise terms of the FW-H formulation, Figure 17 demonstrates a good agreement between the experimental and numerical results for both hovering and forward flight conditions. However, in the forward case, the numerical analysis exhibited greater variation at higher frequencies and underpredicted the sound pressure level (SPL) in the low-to-mid-frequency range below 1 kHz, as shown in Figure 17b. They attributed this discrepancy to higher frequency contamination from the motor and background noise, which was clearly observed in the experimental data. Additionally, the low-to-mid-frequency contamination from interactions with the fairing could not be simulated by the simplified isolated propeller model used in the numerical analysis.

The lattice Boltzmann method (LBM) is a computational fluid dynamics (CFD) technique used to simulate fluid flows. It is based on microscopic models and mesoscopic kinetic equations, rather than the macroscopic Navier–Stokes equations traditionally used in CFD. Thurman et al. [67] studied the lattice Boltzmann method–very-large-eddy simulation (LBM-VLES) using PowerFLOW software to predict the BBN of a DJI-9450 propeller. The far-felid noise was computed using F1A formulation. Figure 18 illustrates a good agreement between the experimental and numerical results in the BBN curve trends. However, it overpredicted below 1.5 kHz and over 10 kHz. They explained the discrepancy below 1.5 kHz as turbulence generated by the rotor itself in the simulation having the spatial difference from the real experiment. The error above 10 kHz was attributed to the mesh size, as demonstrated by the grid sensitivity analysis. Additionally, they investigated the broadband noise sources in more detail by calculating the SPL_1/3 values of the unsteady pressure perturbations on the rotor blade suction surface. Figure 19 illustrates higher SPL_1/3 values at the trailing edge and tip of the blade, indicating that trailing-edge noise and tip vortex formation noise dominated in hovering conditions. This suggests that blade self-noise is the primary contributor to BBN. The lower SPL_1/3 values around the leading edge indicated that blade–wake interaction (BWI) noise could be ignored in hovering conditions, which was corroborated by the experimental test [68].

They explored more details for the BBN of a rotor by LBM simulation, such as broadband noise source identification [69] and blade vortex shedding noise [70].

Recently, more high-fidelity research for wake/turbulence ingestion noise has been conducted. Trascinelli et al. [71] utilized the LBM coupled with the Ffowcs-Williams and Hawkings acoustic analogy to predict cylinder-induced turbulence ingestion noise of propeller. Their numerical method revealed that the interaction between the cylinder wake and rotor led to an increase in the broadband noise. Although the SPL spectrum indicated an underprediction of broadband noise, particularly at low frequencies, compared with the experiment, the method still demonstrated a strong capability in predicting TIN.

3.5. Machine Learning

Recent advances in machine learning have demonstrated significant potential for predicting rotor noise. Li and Lee [72] developed a data-driven model based on basic rotor parameters, such as tip Mach number, collective pitch angle, twist angle, rotor solidity, and rotor radius to predict the trailing edge broadband noise of a multirotor UAM. They collected the data set by BEMT and XFOIL for aerodynamic and UCD-QuietFly for BBN. All of them were fed into an artificial neural network (ANN) (see Figure 20) for rotorcraft broadband noise training and a linear regression approach, as shown in Equations (22) and (23). When comparing the new parameter inputs with UCD-QuietFly, the artificial neural network (ANN) model demonstrated strong alignment with the results, while the linear regression model captured the overall trends effectively, though less precisely.

$$OASPL={\alpha }_1+{\alpha }_2{M}_{tip}+{\alpha }_3{\theta }_0+{\alpha }_4\theta +{\alpha }_5\sigma +{\alpha }_{6}R+{\alpha }_7{M}_{tip}^2+{\alpha }_8{\theta }_0^2+{\alpha }_9{\theta }^2+{\alpha }_{10}{\sigma }^2+{\alpha }_{11}{R}^2$$

(22)

$$SPL(f)={\beta }_1+{\beta }_2{M}_{tip}+{\beta }_3{\theta }_0+{\beta }_4\theta +{\beta }_5\sigma +{\beta }_{6}R+{\beta }_{7}f+{\beta }_8{M}_{tip}^2+{\beta }_9{\theta }_0^2+{\beta }_{10}{\theta }^2+{\beta }_{11}{f}^2+{\beta }_{12}{\sigma }^2+{\beta }_{13}{R}^2$$

(23)

Similar work was conducted by Thurman and Zawodny [73], who used the same machine learning (ML) model and low-fidelity methods to optimize hovering rotors. They utilized the ANOPP and ANOPP2 codes to predict the tonal noise and broadband noise (BBN), respectively. They confirmed that the machine learning (ML) model could accurately predict noise levels. To optimize the broadband noise (BBN), they identified the thrust conditions and pitch as the key factors.

ML needs larger training data. High-fidelity data are expensive, and low-fidelity data are less accurate. To solve this problem, Zhou et al. [74] proposed a multi-fidelity ML model for propeller noise prediction. In their study, a deep neural network (DNN) machine learning (ML) model was employed, incorporating transfer learning (TL) to integrate data of varying fidelities. Initially, the model was trained on low-fidelity simulations that utilized blade element momentum theory (BEMT) coupled with Amiet’s theory. This was then further refined using a limited number of aeroacoustics wind tunnel measurements for 2-bladed propellers, applied through transfer learning (TL). The results confirmed that the TL-based multi-fidelity ML model could accurately predict noise levels when using new experimental parameter inputs. Moreover, comparisons with an ML model trained solely on low-fidelity or high-fidelity data demonstrated that the TL-enhanced model provided more accurate predictions.

4. Passive Reduction of BBN

4.1. Leading- and Trailing-Edge Serrations

Wei et al. [75] presented a comparative numerical and experimental study of LE serrations (see Figure 21) with different morphologies based on a P17 × 5.8 carbon fiber propeller, which has a diameter of 431.2 mm. Figure 22 shows the spectrum of different propellers at 2400 rpm and 3200 rpm, respectively. An obvious BBN reduction in the sawtooth propeller was achieved between 2 kHz to 12 kHz. To investigate the reduction mechanism, they conducted numerical simulations, which revealed that the LE serrations generated vortices that influenced the boundary layer turbulence. Additionally, the LE serrations were shown to reduce velocity fluctuations, contributing to the reduction of broadband noise (BBN). Finally, they performed a multi-rotor hovering test using three LE serration propellers, with better performance than the single propeller test. The results indicate that the sawtooth propeller outperformed the others, not only in noise reduction but also in thrust generation. Similar research was conducted by Butt and Talha [76], who examined the effects of leading-edge serrations on various propellers. Their findings indicate that propellers with LE serrations could achieve significant noise reduction across variable-pitch propellers and under different flight conditions.

Lee et al. [77] investigated the trailing-edge serration of a propeller by experimenting at four different RPMs. They designed three types of serrations: half flat tip, quarter flat tip, and rectangular for a 2-blade propeller with a 0.225 m radius, as shown in Figure 23. Figure 24 illustrates the SPL at 2000 RPM, where all the serrated propellers achieved a noticeable reduction in broadband noise (BBN). However, at 3000 RPM, only the half flat tip propeller maintained effective noise reduction, while the other two designs actually increased BBN at low–mid frequencies. Additionally, the serrations led to a decrease in thrust, with the half flat tip propeller experiencing the smallest loss, approximately 16.8%. Consequently, they concluded that the half flat tip design was the better choice. Cambray et al. [78] conducted similar experimental work, focusing on the impact of saw-tooth serrations of a 2-blade propeller with an 8-inch diameter. Their findings indicate that the depth of the serration plays a significant role in BBN reduction. Specifically, larger serration depths resulted in a reduction in BBN by 3 dB at 3 kHz, with the reduction increasing to 5 dB at 10 kHz. However, they also reported that serration wavelength or size may lead to tonal noise increase, and noise reduction benefits are most pronounced at lower tip speeds.

4.2. Airfoil or Blade Shape Design

Won and Lee [79] investigated the airfoil shape optimization of rotors focusing on blade trailing-edge noise reduction using a low-fidelity method. They used an ideally twisted small-scale rotor with the NACA 0012 airfoil and a modified XV-15 blade as their baseline parameters. To reconstruct the airfoil shape, they utilized three airfoil parameterization methods. For aerodynamic analysis, they employed XFOIL and blade element momentum theory (BEMT), while UCD-QuietFly was applied to predict the broadband noise. The optimization process involved the use of a genetic algorithm. To further accelerate the optimization, a Kriging surrogate model was employed as a predictive tool, allowing the process to bypass direct function evaluations. Their optimized airfoil shape, shown in Figure 25, resulted in a 4 dBA reduction in the overall sound pressure level (OASPL) of BBN during hovering conditions and a 3–4 dBA decrease during vertical climb conditions for the XV-15 blade.

Peixun et al. [80] conducted a blade shape optimization study to reduce noise generated by a 6-bladed propeller. They employed the free-form deformation (FFD) method to characterize changes in the geometric space of the propeller. To obtain aerodynamic data, they utilized the unsteady Reynolds-averaged Navier–Stokes (URANS) model with the multiple reference frame (MRF) method in CFX software. For noise prediction, they applied Hanson’s theory to predict tonal noise and Amiet’s theory for broadband noise (BBN). Their optimized blade shape, as illustrated in Figure 26, achieved a 5 dB reduction and kept the same aerodynamic performance. Although the exact reduction in broadband noise (BBN) was not quantified, it remains a promising approach for BBN reduction.

4.3. Other Ideals

Trip: Broadband noise (BBN) is influenced by the trailing edge boundary layer thickness, which is often caused by a laminar separation bubble on the suction side of the propeller. Leslie et al. [81] conducted a study to investigate the primary sources of BBN for small-scale propellers operating at low Reynolds numbers. They identified that the trailing edge boundary layer thickness, due to a laminar separation bubble, is a significant contributor to BBN. To address this, they experimented with leading-edge serrated and straight trips (as shown in Figure 27a,b) positioned before the laminar separation to reduce trailing edge thickness. This modification led to a reduction in turbulent boundary-layer trailing-edge noise, with an overall broadband noise reduction of up to 4 dB observed during static tests at a rotational rate of 5000 rpm. As depicted in Figure 27c, at 3500 rpm, the serrated trip achieved greater broadband noise reduction at higher frequencies by approximately 2 dB. This suggests that the trailing edge boundary layer interaction noise may be more critical than laminar separation bubble interaction noise in this context. However, it is important to note that the effectiveness of this noise reduction method is limited to conditions where a laminar separation bubble is present, which typically occurs during cruise conditions.

Notched Leading Edge: Demoret and Wisniewski [82] introduced an innovative approach by modifying a 9.4-inch DJI Phantom 2-bladed propeller to explore noise reduction techniques. They investigated the impact of adding a leading-edge notch by cutting a groove into the stock blade (as shown in Figure 28). Their findings indicate that placing the notch at an r/R of 0.90 resulted in the most significant reduction in broadband noise (BBN), though it came at the cost of a 9% increase in power required to maintain similar thrust conditions. As shown in Figure 28b, the sound pressure level (SPL) spectrum revealed a notable reduction in broadband noise (BBN) above 100 Hz compared to the stock blade, although there was a slight increase around 80 Hz. This demonstrates that the notched blade has a strong capability for BBN reduction. Their smoke flow visualization explained that the notch created a barrier between the high-pressure and low-pressure surfaces, causing the flow on the high-pressure surface to move in the opposite direction, thereby disrupting the tip vortices. While this method shows promise for noise control, it also introduces a penalty of power increase when maintaining the same thrust. Moreover, scaling this technique to larger rotors could present structural challenges.

Tip shape design: A special tip shape may reduce the tip vortex and BWI noise. Sebastian and Strem [83] proposed a toroidal propeller, as shown in Figure 29, with a significant reduction in the strength of the trailing tip that was a key source of tip vortex noise. They performed 3D printing for different geometry and evaluated them by experiment. They reported a good noise reduction in the toroidal propeller by comparing it with DJI propellers. Although this design is hard to manufacture, it still gives a good idea to replace traditional propellers in the future.

Another straightforward application idea is an applied wing tip design to rotor tip design. Afshari and Karimian [84] investigated the noise of nine different tip shape rotors by numerical method based on a Bell UH-1H helicopter rotor and found that not all tip geometries achieved significant noise reduction, although many demonstrated good aerodynamic performance. The Eagle tip design showed the best noise reduction, with a decrease of approximately 4.5%, and also improved the figure of merit ratio by up to 17%. It is understood that tip design can influence tip vortex formation noise and potentially affect BWI and other noise sources. However, since the study did not focus on broadband noise (BBN) and lacked a detailed SPL spectrum analysis, the extent of BBN reduction and the underlying mechanisms remain unclear, indicating a need for further investigation.

5. Active Noise Control Technologies of BBN

Reducing noise radiation through passive control can negatively impact aerodynamic performance. Therefore, an alternative approach is to integrate passive control into the propeller system design, optimizing it for regular flight operations. ANC should be engaged only in specific situations when noise levels temporarily exceed acceptable limits, such as near a vertiport or when the aircraft encounters turbulence.

As mentioned earlier, the dominant source of broadband noise (BBN) is boundary layer turbulence. Active noise control (ANC) techniques aim to manage the boundary layer, including methods such as suction and blowing control. Several studies have investigated these techniques for airfoil noise reduction. Wolf et al. [85] conducted experiments using suction at the upper front area of an airfoil to reduce boundary layer thickness. Their findings demonstrate a reduction in trailing-edge noise by 3.5 dB. Yang et al. [86] achieved even greater noise reduction by incorporating trailing-edge blowing into the airfoil section. Their numerical simulations indicated a maximum noise reduction of 20 dB.

Ingested turbulence impinging the leading edge generates leading-edge noise [22]. A more effective approach is to control the flow at the leading edge. Zhang et al. [87] investigated the leading-edge blowing effect of rod wake ingestion noise of an airfoil. They designed single and double-orifices airfoils mounted behind the rod (see Figure 30) and evaluated them in a wind tunnel for 15 and 25 m/s inflow conditions with 0 and 10 angles of attack. They found the blowing could slightly reduce the low frequency BBN, while increasing mid-to-high-frequency BBN at 25 m/s inflow condition, as shown in Figure 31. The increase in self-noise was attributed to leading-edge (LE) blowing, suggesting that LE blowing might not be an optimal solution due to the additional high-frequency broadband noise (BBN) it introduces. However, it is not definitive that LE blowing is inherently problematic, as the effectiveness is significantly influenced by the orifice design. Therefore, further investigation is needed to better understand its impact.

Few studies have been conducted for turbine rotors. A trailing edge rotor blowing blade is shown in Figure 32, which was evaluated by Sutliff [88] in the Aeroacoustics Propulsion Laboratory. They observed that trailing-edge blowing reduced the turbulence level downstream of the rotor by 25 to 50 percent and achieved an average decrease in broadband sound pressure level (SPL) over the stator vane of 2 to 3 dB.

While the aforementioned ANC technologies, such as suction and blowing control, have demonstrated effectiveness in reducing noise for airfoils and turbine fans, they are challenging to implement for propellers. However, these techniques can inspire ANC studies for advanced air mobility (AAM) applications.

Recently, Bernardini et al. [89] proposed a novel ideal to reduce the BBN for multi-rotor systems in hovering condition. The concept was to employ the trim control strategy commonly used in multi-rotor systems (see Figure 33). The trim procedure was to change the pitch angle and RPM of both front and rear rotors that guarantee the desired steady-state flight conditions while, at the same time, optimizing selected target functions, such as performance or OASPL, which are calculated by the compact F1A equation. By comparison with other trim strategy, it improved more than 5 dB reduction in BBN.

Dielectric barrier discharge (DBD) plasma actuators could produce electric wind by ionization of the air particles and provide another ideal to control the boundary layer flow. Polonsky et al. [90] conducted an experimental study by installing two copper electrodes along the leading edges of helicopter model blades with a 0.73 m diameter, as shown in Figure 34a. The blades were set at a constant pitch angle of 12°, which might induce some surface separation. The experiment aimed to suppress vortex shedding from the leading edge using downward electric winds generated by plasma, potentially altering the separation and reducing pressure perturbations on the blade. Figure 34b illustrates a significant decrease in broadband noise at low-to-mid frequencies, attributed to the actuation-induced separation control. The study also found that this actuation not only reduced the overall sound OASPL of BBN by 8 dB but also improved the figure of merit by 25%. Tonal noise was reduced by only 3 dB, further supporting the conclusion that dielectric barrier discharge (DBD) actuation effectively reduces broadband noise (BBN), particularly when separation is present, and BBN is the dominant noise source.

6. Discussion

This review presents an overview of advanced air mobility broadband noise (BBN) prediction and control techniques. Significant advancements have been highlighted in BBN prediction models, applicable across low- to high-fidelity methods. One of the widely used BBN prediction models is the semi-empirical BPM model [4], which considers blade self-noise and requires boundary layer and effective angle parameters. To enhance accuracy, Burley and Brooks [10] introduced the blade–wake interaction (BWI) noise to the BPM model; however, it cannot predict turbulence ingestion noise (TIN). The analytical model by Schlinker and Amiet [23] considers only the trailing-edge noise and requires force loading data. To address TIN, Amiet [7] proposed a model assuming TIN as the leading-edge noise, derived using a similar approach to the trailing-edge noise model. The time-domain model based on the Ffowcs Williams and Hawkings (FW-H) equation [25] can calculate all BBN categories, offering a comprehensive approach. Recently, there have been some advancements, such as Sinayoko et al. [24], F1B [27], F2B [28], Majumdar and Peake [50], Glegg et al. [47], and Glegg et al. [49], but we still need further validation and improvement. Empirical models are rarely used due to their limitations and reliance on experimental data rather than underlying mechanisms, such as the new empirical model by Gill and Lee [33]. However, empirical models can be beneficial for optimization of these design studies.

All the prediction models are related to the aerodynamic model. The primary limitation for predicting rotor noise is the fidelity of the aerodynamic modeling blade element theory, which has demonstrated superior capabilities for predicting blade loads and, with appropriate corrections, can accurately predict the steady thrust and torque of the blades. More recent methods, such as the surface-vorticity panel solver [61] and non-linear vortex lattice methods [60], have been shown to predict unsteady loading but cannot predict separated flows, although they are computationally efficient compared to the more expensive URANS, DES, and LES approaches. Additionally, the lattice Boltzmann method (LBM) has shown potential in propeller simulations. However, it exhibits lower accuracy and certain limitations compared to the Navier–Stokes solver. Among these methods, it is accepted that only the more costly approaches, such as DES or LES combined with the FW-H equation, can accurately predict broadband noise.

To improve the performance and accuracy of lower fidelity methods, studies such as those by Casalino et al. [50], Li and Lee [53], and Gill et al. [54] have integrated the blade element momentum theory (BEMT) with Amiet’s model, UCD-QuietFly, and empirical models, respectively. These approaches have demonstrated a good degree of accuracy in predicting blade self-noise, though they fall short in capturing lower frequency noise. Several low-fidelity turbulence ingestion studies have been conducted by Karve et al. [55] and Raposo and Azarpeyvand [57]. They utilized the Sears function for unsteady loading coupled with Amiet’s [7] model, reporting that Amiet’s theory can accurately predict turbulence ingestion noise from open rotors.

A review of various experimental and numerical studies reveals that broadband noise originates from both blade self-noise and wake effects, with blade self-noise being dominant at higher frequencies. While blade–wake interaction (BWI) noise may be negligible during hovering, it cannot be ignored during edgewise flight. The haystacking phenomenon at the blade-passing frequency becomes apparent when turbulence is ingested. In multi-rotor systems, studies on forward flight have suggested that the increase in broadband noise is primarily due to rotor–wake interaction effects.

Machine learning (ML) demonstrates significant potential for predicting broadband noise. However, current applications are equation-based and rely on extensive data training. Future work could extend ML applications to the mechanisms of broadband noise sources, which could be a key focus for further research.

Several passive control methods have been reviewed, including leading and trailing edge serrations, leading edge trips, leading edge notches, blade shape, and tip designs. These methods have shown some success in mitigating blade noise but often reduce the aerodynamic performance of the rotors. These still have some trade-offs that may work as intended but may result in difficulty in manufacturing or may present some structural difficulties. For example, serrations, trips, and tip designs involve 3D geometries with numerous unconstrained parameters, making it challenging to determine the optimal shape design. Additionally, they have thin and complex structures, which can pose manufacturing challenges and may be prone to damage during use.

Among these active control methods, suction and blowing techniques have demonstrated considerable success in reducing broadband noise for airfoils and turbine fans. These methods effectively manipulate the boundary layer to diminish noise generation, as seen in the studies by Wolf et al. [85] and Yang et al. [86]. However, applying these techniques to propellers presents significant design challenges. The thin structural profile of propeller blades complicates the integration of hollow channels necessary for suction or blowing, making these methods less feasible for propeller noise control. In response to these challenges, two novel approaches show great promise for broadband noise control. One such approach is the trim control strategy proposed by Bernardini et al. [89]. By adjusting the pitch angle and RPM of the front and rear rotors, this strategy optimizes the overall system performance while significantly reducing noise levels. This approach not only mitigates BBN but also maintains the aerodynamic efficiency of the rotors. Another approach involves the use of dielectric barrier discharge (DBD) plasma actuators, as explored by Polonsky et al. [90]. DBD plasma actuators generate electric wind by ionizing air particles, which can be used to control the boundary layer flow on blade surfaces. The experimental study conducted on helicopter model blades demonstrated that DBD actuation could significantly reduce broadband noise, particularly in the low-to-mid-frequency range, while also enhancing the overall aerodynamic performance.

7. Conclusions and Future Work

A comprehensive overview of BBN prediction and control techniques relevant to AAM has been conducted. Notable progress has been made in BBN prediction models, with approaches ranging from semi-empirical models, like the BPM model, to more sophisticated time-domain models based on the FW-H equation. The fidelity of aerodynamic models plays a crucial role in the accuracy of rotor noise predictions. Low- and mid-fidelity models can quickly predict mid- to high-frequency BBN, while high-fidelity methods like DES and LES offer greater accuracy, especially when combined with the FW-H equation. Despite these advancements, challenges persist, particularly the computational expense of high-fidelity simulations, the difficulty in accurately predicting TIN, and the limitations of low- and mid-fidelity models in capturing low-frequency noise.

Experimental studies have consistently shown that blade self-noise remains the dominant source of BBN, particularly at higher frequencies. However, interactions such as BWI become increasingly significant during edgewise flight and in multi-rotor systems. For TIN, the BBN noise increases substantially, and the haystacking phenomenon has been observed.

Both passive and active control methods have been reviewed for their effectiveness in mitigating BBN. While passive methods like serrations and blade shape modifications can reduce noise, they often involve trade-offs in aerodynamic performance. Active control methods, such as suction and blowing, have demonstrated considerable success in reducing noise for airfoils and turbine fans but face significant challenges when applied to propellers. To address these challenges, novel approaches like trim control and dielectric barrier discharge (DBD) plasma actuators have shown great promise.

In conclusion, while substantial progress has been made in BBN prediction and control, ongoing research and development are essential to overcome existing limitations and fully realize the potential of these techniques in real-world AAM applications. Future work should focus on refining low-fidelity methods to improve their ability to capture low-frequency BBN, balancing the trade-offs in high-fidelity simulations, and expanding the analytical model to include other self-noise mechanisms. Additionally, more accurate unsteady models and wavenumber spectra should be developed for analytical TIN models. Further development is needed for semi-empirical and empirical models to better predict TIN. New noise control methods, particularly for TIN, should be explored, and the applicability of machine learning should be extended to enhance noise prediction and reduction strategies. Moreover, more complex turbulence environments should be studied in noise experiments to better understand real-world scenarios.