A multivariate statistical analysis of the noise emitted by an installed propeller

Novel-aircraft concepts consider the possibility of placing the propulsor very close to the fuselage to ingest the incoming airframe boundary layer. In this configuration, the engine takes the inflow at a reduced velocity, consuming less fuel in the combustion process. However, this induces a series of noise consequences that alter tonal and broadband noise components. The present work reports an experimental investigation to analyse the sound emitted by a propeller ingesting a turbulent boundary layer. Experiments have been performed in the anechoic wind tunnel at the University of Bristol and the set-up consisted of a two-bladed propeller close to a tangential flat plate to simulate the installed effects. A tripping device was placed 1 m upstream of the propeller and was used to generate a turbulent boundary layer at the propeller location. The wind tunnel velocity was fixed at 33 m/s keeping the advance ratio at J = 0.65. Far-field noise has been acquired using a microphone array positioned parallel to the plate, directly overhead of the propeller. The data were analysed in the frequency domain, providing a characterisation of spectral quantities. Furthermore, wavelet analysis was performed to investigate the time evolution of the identified pressure features. Results show evident haystacking humps close to higher BPF harmonics, due to the ingestion of the boundary layer. Moreover, the wavelet analysis revealed the intermittent nature of the haystacking humps, clearly visible at higher BPF harmonics with low-frequency energy content.


Introduction
Boundary layer ingestion (BLI) is a concept that utilises the slower-moving air in the airframe boundary layer to reduce fuel consumption and drag losses by the propulsor.By taking in and accelerating the flow, the propulsor can use less fuel in the combustion process and decrease viscous drag losses compared to using pure freestream intake.The principle of BLI was first proposed by A. Smith and Roberts in 1947 [1] as a way to reduce drag and increase flight range by driving the boundary layer velocity profiles developed along the side of the fuselage into the jet engine.Subsequently, Douglass (1970) [2] published studies relating to the performance of BLI.They reported fuel consumption savings of up to 16% , but lacked the fidelity and empirical data of more modern approaches.Several years later, L. H. Smith (1993) [3] analysed the efficiency of a propeller ingesting a flow distorted by an asymmetric wake.This preliminary investigation has been based on an incompressible, inviscid actuator disk analysis and highlighted that a 7% power saving was possible if the entire wake was ingested.Recent studies, such as those by Ahuja and Mavris (2021) [4] and Yildirim et al. (2021) [5], have shown significant power savings from various BLI configurations.Implementing BLI requires close integration between the engine and airframe, which may necessitate more radical aircraft designs.The NOVA -NextGen ONERA Versatile Aircraft is an example of a BLI configuration that uses ducted fan propulsion systems to ingest a large amount of the aircraft's fuselage boundary layer air into propulsors placed close to the tail of the aircraft.One significant issue with BLI is the noise produced by the propulsion system.Indeed, ingesting turbulence generates a broadband noise signature that is a combination of turbulence ingestion noise and airfoil self-noise (Glegg et al, 2015) [6].Additionally, BLI can create haystacks of broadband noise in the far-field acoustic spectra, caused by the rotor blades cutting through the large eddies of the ingested turbulence.The haystacking phenomenon has been studied by several researchers such as Murray et al. (2018) [7], Hickling (2020) [8], and De Vries et al. (2021) [9], who observed a series of spectral humps centered slightly above the Blade Passage Frequency (BPF) and its harmonics in the far-field acoustic spectra.The reason for the slight shifting of the haystacking peaks is well described by Murray (2016) [10].
In this framework, the present paper provides an experimental investigation of the noise emitted by a two-bladed propeller ingesting a turbulent boundary layer.In particular, both a classic Fourier domain approach and a wavelet-based analysis have been applied to the far-field pressure fluctuations.Focusing on the haystacking effect, the wavelet technique has revealed the haystacking intermittent nature, which was not visible by applying a simple Fourier transform to the dataset.The paper is organised as follows: the experimental setup is reported in Sec. 2, and the results are illustrated in Sec. 3. Conclusions are presented in Sec. 4.

Experimental setup 2.1. Facility description
The presented measurements were carried out at the University of Bristol's Lawson aeroacoustic wind tunnel.This facility is a closed-circuit, temperature-controlled wind tunnel that is 16.6 m long, 6.8 m wide, and 4.6 m high.The wind tunnel uses a nozzle with a contraction ratio of 8.4 and exit dimensions of 775 mm in height and 500 mm in width, which can achieve freestream velocities of up to 40 m/s and has a high flow uniformity across its exit plane.The anechoic chamber is acoustically lined with acoustic foam wedges and it allows for anechoic measurements down to 160 Hz, according to the ISO 3745 standardised testing procedure (see for more details [11,12]).A general overview of the experimental setup inside the anechoic chamber of the aeroacoustic facility at the University of Bristol is described in figure 1.A two-bladed propeller with a radius of R = 0.152 m was mounted on a steel rig 1 m downstream of the wind tunnel contraction.A flat plate was positioned near the propeller to simulate the boundary layer ingestion and specifically t = 5 mm from the propeller tip.A semicircular array with a radius of 1.75 m made of 21 GRAS 40 PL microphones was positioned on the plate plane to measure the far-field noise.Its polar angle range covers angles from φ = 55 • to φ = 125 • .The operative conditions were selected to reach low advance ratios (high thrust) to observe the haystacking effect as described by Murray et al. (2018) [7].In particular, the wind tunnel speed was fixed at U ∞ = 33 m/s and the rotor speed at 10000 RPM.As a result, the advance ratio was equal to J = 0.65.A tripping device was placed after the contraction exit and 1 m upstream of the propeller location.Its purpose was to create a turbulent boundary layer ingested by the propeller itself.A coarse uncompressed Aluminium metal foam porous material 25 mm wide and 10 mm thick with a porosity of β = 90.92% was used.After a hot-wire preliminary test, the boundary layer thickness at the propeller position was equal to δ = 2/3 R.This result was evaluated without the propeller installed and it was an estimated value of the boundary layer ingested by the propeller.

Far-field acoustics measurements
An array consisting of 21 GRAS 40PL free field microphones was installed on the plate plane to capture far-field pressure fluctuations (see figure 1).These microphones are capable of measuring frequencies ranging from 10 Hz to 20 kHz, with a dynamic range of 142 dB.They have a flat frequency response, with a maximum variation of ±1 dB for frequencies from 10 Hz to 10 kHz.Acoustic data were acquired using a National Instrument PXle -4499.Far-field measurements were taken at a sampling frequency of 2 16 Hz over a measurement time of 32 seconds.The sensitivities for the GRAS microphones were obtained from the manufacturer.

Results
As the first outcome, figure 2 compares the tripped case and the isolated case (propeller positioned 1 m downstream of the contraction exit without the plate installed) in the Fourier domain.Results are reported in terms of Sound Pressure Level (SPL) evaluated as follows: where PSD is the Power Spectral Density, and P ref is the reference pressure equal to 20µP a. Specifically, the PSD was calculated using a Hanning window with 50% of overlap.Considering a sampling frequency of f s = 2 16 Hz and a windowing of win = 2 14 samples, the frequency bandwidth has been set at ∆f = 4 Hz.It is worth noting that in all the three polar angles reported in figure 2, the BPF and the first two harmonics are clearly visible at the lower frequencies resulting in slightly amplified with the ingestion of the boundary layer.On the other hand, the broadband hump observed in the tripped case, probably generated by the combination of turbulence ingestion noise and airfoil self-noise, dominates the higher frequencies.Specifically, this effect is more evident at higher polar angles and reduces moving upstream.A crucial observation concerns the presence of haystacking humps close to the second and third harmonics, which, according to Murray et al. (2018) [7], are skewed to the higher frequencies.This effect is more evident at φ = 90 • and φ = 125 • .According to the cited literature, this phenomenon should be generated by the blade cutting of the turbulent eddies passing through the propeller.As a result of the vortex cutting, the haystacking features should present intermittency in the time domain.To further investigate the haystacking behaviour, the second part of the analysis has been performed in the wavelet domain.Unlike the Fourier transform, the wavelet decomposition is a useful tool when it comes to analysing a temporal signal in terms of the time shift (t) and the resolution time scale (s) [13,14].The formal definition is reported as follows: where W (s, t) are the wavelet coefficients, s is the scale dilatation parameter corresponding to the width of the wavelet, τ is the translation parameter corresponding to the position of the wavelet, C −1/2 ψ is a constant that takes the mean value of ψ(t) into account, and ψ * t−τ s is the complex conjugate of the dilated and translated mother wavelet ψ(t), which was chosen as the Morlet kernel.For the sake of completeness, the real-valued Morlet mother-wavelet is a cosine wave localized by a Gaussian window, as following defined [15]: where σ is the standard deviation.
The coefficients represent changes in the signal at a specific scale and location.According to [16], the squared wavelet coefficient |W (s, t)| 2 quantifies the energy level or stimulation of a particular pressure field p(t) in terms of space, scale, and direction.Therefore, if the changes in a signal are smooth at a given time, the wavelet coefficients remain small, but they increase in value locally for large fluctuations, such as coherent structures.Figure 3 shows the energy level content for the isolated case (a) and for the tripped case (b) with respect to the frequency domain scaled on the blade passing frequency and a portion of the whole time length.The analysis has been performed at φ = 90 • , as at this polar location, the haystacking feature was clearly evinced.It should be highlighted that both studied cases present high energy-level content in the first and second BPF, which, as expected, produces signatures persistent in time.Nevertheless, a series of new intermittent bumps slightly skewed to higher frequencies than the BPF harmonics are observed in figure 3 (b).These signatures are neglectable for the isolated case (figure 3 (a)), and it is thought to belong to the haystacking phenomenon.To better understand the intermittency of this phenomenon, the Local Intermittency Measure (LIM) is plotted in figure 4 for the isolated and tripped cases.The LIM function is defined as follows [17]:  [7], and Hickling (2020) [8]).
Finally, the PSD of the wavelet coefficient moduli time series at frequencies of interest would further aid in understanding the haystacking signature behaviour.Figure 5 shows the PSD of the wavelet coefficients for the isolated case and tripped case at 3.2 BPF, which is one of the frequencies where the humps appear in figure 3 (b).It is worth noting that the frequency modulation of the humps is mostly enclosed at low frequencies, particularly between 10 Hz and 500 Hz.A possible explanation for this low-frequency intermittency can be outlined starting from the physics of the haystacking phenomenon.Indeed, the higher peak at the BPF for the tripped case is due to the cutting of coherent structures by the blades.This happens for every passage of the blade.As a result, higher energy content is visible at the BPF.Regarding the discrepancy for frequencies lower than the BPF, this could happen because the coherent structures are not as frequent as the blade passing, and they are ingested by the propeller fewer times.

Conclusions
An experimental investigation has been presented detailing the far-field noise emitted by a BLI configuration.A wavelet analysis of the experimental data has been carried out to investigate the haystacking phenomenon.The experimental set-up was placed at the anechoic wind tunnel of the University of Bristol.It consisted of a two-bladed propeller mounted close to a flat plate to allow the boundary layer ingestion by the propeller.An array of 21 GRAS 40 PL microphones was placed on the plate plane to study the far-field noise.Measurements were performed for the isolated propeller case without the plate and for the BLI case in which a tripping device was used to generate a turbulent boundary layer at the propeller location.An advance ratio of J = 0.65 was fixed, keeping the wind tunnel speed at 33 m/s with a rotor speed of 10000 RPM.This was chosen in order to perform a low advance ratio in which the haystacking phenomenon is generally more evident.A qualitative description of the far-field acoustics was performed using a classic Fourier analysis in the frequency domain and a more complex wavelet analysis in the time-frequency domain.The frequency-domain analysis, performed in terms of SPL, highlighted haystcking humps at frequencies slightly higher than the BPF harmonics.In particular, this phenomenon is visible when the propeller ingests a turbulent boundary layer.Furthermore, a wavelet time-frequency analysis revealed the intermittency of the haystacking phenomenon due to the cutting of the turbulent structures by the propeller.This phenomenon has been observed to have a low-frequency modulation.

Figure 1 .
Figure 1.(a) experimental setup overview and (b) schematic of the experiment.

Figure 3 .
Figure 3. Wavelet scalograms for the isolated case (a) and for the tripped case (b).

Figure 4 .
Figure 4. Local Intermittency Measure (LIM) for the isolated case (a) and for the tripped case (b).

Figure 5 .
Figure 5. PSD of the wavelet coefficients for 3.2 BPF.