Acoustic Stall Detection of Variable Pitch Propeller for Unmanned Aerial Vehicles

This paper presents an analysis of acoustic emission and performance data of a UAV rotor equipped with a variable pitch propeller. The proposed study aims to show propeller noise features that indicate stall flow regime on the blade. Analysis of the noise characteristics around the propeller in terms of power spectral density allow to detect the stall. The study shows that a microphone located at different angles around the propeller can provide data sufficient to determine if the blade angle of attack has forced the propeller into the stall regime. In this range, the propeller’s efficiency in hover decreases and leads to an increase in power consumption. The reresearch is a suggests a method of data treatment to obtain a single parameter indicating a blade stall.


Introduction
Unmanned Aerial Vehicles (UAVs) are increasingly commonly used in many fields like inspections, land measurements, agriculture, search and rescue, transport and military, to name a few [1,2].The ability to connect large numbers of UAVs into one system encourages the use of UAVs in even larger numbers [3].Swarms of drones are no longer a futuristic vision but a reality for modern generations [4,5], the more that flying vehicles are being introduced to cities [6].Companies interested in UAV parcel delivery systems are considering using significant amounts of flying vehicles to make the distribution system more efficient [7].The abovementioned development trends show that the number of drones will significantly increase in the next decade [8].
Most UAVs use propellers for thrust generation.However, a spinning rotor generates a significant amount of noise that can be substantially more annoying than road traffic or aircrafts due to its particular acoustic characteristics.Tonal and highfrequency broadband noise has a significant negative impact on the human perception of drone noise [9].While propeller noise has been widely studied over the years, this was primarily done for helicopter applications, characterized by higher Reynolds numbers and lower tonal emissions [10][11][12].Drone propeller noise generation has been studied very recently; several methods were proposed to reduce noise [13].Blade geometry significantly impacts propeller acoustic emission, which can be altered in the blade design process by applying, among other things, serrated trailing edges [14].Special cover layers can also be applied to the propeller's surface to reduce noise [15].Alternatively, shrouded propellers have a different noise spectrum, and ducts can be designed to minimize noise [16].In specific types of UAVs, where propulsion systems involve coaxial rotors, the optimization of propellers distance gives the ability to modify the acoustic spectrum of the propulsion system [17].
The UAV variable pitch propeller (VPP) is a system that can be used to increase thrust generation efficiency [18].The propeller pitch change can also influence the acoustic properties of the propulsion system.One of the main risks of using the VPP is associated with choosing value of the pitch angle.If the angle is too high, the stall can occur, initially at a part of the blade.This can lead to reduce of efficiency in flight [19] and produce oscillations [20] or even stall flutter [21].
The present study is focused on stall detection.The commonly used methods used for this purpose in case of airfoils involve pressure sensors mounted close to or embedded into the airfoil surface.However, regarding stall detection on propeller blades, this method becomes very difficult to be implemented [22].This complexity led to a shift towards other approaches, like Particle Image Velocimetry (PIV) [23], methods involving pressure-sensitive paint [24], or Differential Infrared Thermography (DIT) [25].Each of those methods can provide a substantial amount of data that allows for determining the character of the airflow in a particular section of the blade.However, this significant amount of data comes together with the need for sophisticated laboratory equipment and procedures for data collection that can not be easily implemented on flying aircraft.
The presented paper is the continuation of the previous study [26], where general acoustic parameters of the propeller were shown.The current paper explores the acoustics of a UAV propeller in combination with its performance to achieve additional information from collected signals.The potential correlations between acoustic data and propeller performance can lead to simple methods of detection of rotor state without expensive equipment and help with rotor diagnostics.This paper shows the methodology and materials needed to perform acoustic analysis.Next, the experimental and numerical results are shown.Based on the correlation between some of the collected signals, the simple method of stall detection is presented with conclusions.

Test Bench
In this work, a custom UAV rotor is the subject of the test.The rotor is composed of a 5015 BLDC motor; a mechanism that allows changing the pitch angle of the blades; and blades taken from a KDE 16.5x5.3propeller (see Fig. 1).The propeller blades are made of carbon fiber composite and have no winglets.The twist angle of the blade and the chord displacement at the blade radius (where r/R is the dimensionless radius of the propeller) are shown in Fig. 2. The blade airfoil is NACA44XX type, with varying airfoil thickness along the span.For simplicity, a constant mean NACA4412 geometry was used in numerical calculations.
The experiment was conducted in the anechoic chamber of the Institute of Turbomachinery at Lodz University of Technology (IMP TUL).The chamber plenum dimensions are 12.51m x 6.51m x 4.59m (see [27]).The measurement systems for propeller performance and acoustic emissions were separated.The rotor was placed at the test stand approximately 1.3m above the ground (see Fig. 3).At the same elevation four microphones were placed downstream of the propeller at a 1m distance.The microphones were directed towards the center of the propeller and displaced at 0deg, 30deg, 60deg, and 90deg from the rotation plane, 0deg meaning the plane of rotation and 90deg: the axis of rotation.
During the experiment, the following parameters were collected from the performance measuring system: thrust, torque, current, battery voltage, and number of impulses corresponding to the motor rotation velocity.The Norsonic Nor850 acoustic data acquisition system collected measurement results from four GRAS 46AE free-field standard directional microphones equipped with windscreens (see full setup overview in Fig. 4).

Testing Method
The specific target thrust values were set during the experiment for every pitch angle (0deg, 3deg, 5deg, 11deg).For each thrust value (10N , 15N , 20N , 25N , 30N ), a sound wave series of 20s duration time was collected (see Table 1).The sound waves have a sample rate of 48k H z and 24Bit resolution.For all other signals, the measuring sample rate value was 2000 samples per second per channel.The static state of the airflow was achieved by introducing the 30s delay after each set-point of measurement.This approach was possible thanks to the relatively large plenum of the anechoic chamber, which ensures that the flow develops appropriately.
In addition to tests in the anechoic chamber, performance characteristics of the rotor were collected, for elevated amount of operating points (see Fig. 8).This test was performed using the same equipment as the acoustic measurements, only without sound data acquisition.

Data Processing
The performance data of the propeller was averaged at each of the rotor operating points.The collected acoustic samples were additionally transformed into power spectral density (PSD) data in the frequency domain.The transformation begins with the Fast Fourier Transform, as described by Algorithm 1, where data is a signal from a microphone and Fs is the sample rate.
As a result of this operation, one obtains power spectral density PSD in the frequency spectrum f.The moving average was used in the next step with a window of 0.001% of the data range.The basic performance data definitions are as follows: The performance data is primarily analyzed in the rotational speed domain.For better visualization, the results were also transformed into the pitch angle domain.This transformation was performed with linear interpolation, sufficient thanks to the high density of measuring points.In addition to the experiment, a simple Blade Element-Momentum (BEM) analysis was made in order to estimate the Reynolds numbers and angles of attack on the blade under the analyzed operating conditions.Using the standard XFoil software [28], blade airfoil characteristic was obtained for a range of Reynolds numbers.Those characteristics were, in the next step, used in the BEM propeller simulation based on [29].

Numerical Results
The propeller profile NACA4412 is an asymmetrical airfoil with maximum value of Cl/Cd = 50 for Re = 1e5.Figure 5 shows the lift coefficient for various Reynolds numbers.Most Fig. 5 Lift coefficient NACA4412 X-foil Fig. 6 Reynolds number along propeller radius notably, this airfoil has double-stall characteristics, with the first stall appearing at angle of attack α approximately 18 -20 degrees.The Reynolds numbers at which the propeller works (between 5e4 and 25e4) are shown in Fig. 6, while Fig. 7 presents α distribution along the blade span for different pitch angles.The horizontal dashed line at 20 degrees in the latter figure represents the angle above which the stall should occur.For pitch angle of 11 degrees the stall is expected to occur at most of the blade; in contrast, for 5 degrees only a small fraction of the blade will be affected by this phenomenon.The whole blade works below stall conditions for pitch equal to 0 and 3 degrees.

Experimental Results
The most critical performance and acoustic parameters of UAV propulsion are presented in this section.The propeller's thrust largely depends on the blade pitch and rotor speed.In a Fig. 7 Angle of attack along propeller radius Fig. 8 Thrust of propeller specific range, the thrust is directly proportional to the pitch.For higher pitch angles the thrust increase is less pronounced, and for even higher angles it starts to decrease (see Fig. 8).This behavior is not observed in terms of mechanical power, which is growing at the whole range of measured pitch angles (see Fig. 9).This effect is related to the stall phenomenon.
One of the crucial elements of the propulsion system is the BLDC motor.It has a varying efficiency depending on rotational speed and torque (see Fig. 10).The final analyzed parameter is total hover efficiency.It can be seen (Fig. 11) that for every rotational speed of the propeller there is a single value of blade pitch angle, where the hover efficiency is the highest.
The acoustic spectrum of sound emitted by the propeller is composed of several elements: background noise, harmonic peaks correlated with rotational frequency, and noise associated with aerodynamic phenomena and thrust generation [30].The background noise is generally the same for all microphones, and harmonic peaks frequency is exactly known.The main difference for individual pitch angles is thus the flow around propeller and in the wake.Results collected by the microphones in the wake flow show higher PSD for lower frequencies, compared with the microphone situated in rotor plane, which may be traced back to the fact that the propagating rotor wake breaks down from regular helical vortex to irregular eddies.At the same time, there is a significant difference between the PSD spectrum for various pitch angles at high frequencies (see Figs. 12, 13, 14, and 15).For low-pitch angles, the PSD at high frequencies is composed of relatively low broadband noise and harmonic peaks.The high-frequency broadband noise attains much higher PSD values for higher pitch angles, while the harmonic peaks remain at values similar to those for lower pitch cases.This phenomenon is visible for all microphones and thrust settings, but is least pronounced in the data from microphone at 0 deg position (plane of rotation, see Fig. 12).

Combined Analysis
An additional analysis of the obtained experimental results shows a correlation between the stall on the part of the propeller and higher PSD noise at high frequencies.There is thus a possibility of using acoustic signals for stall detection.It is possible to define a parameter (ξ ), which can act as a stall indicator.Firstly, a sound sample must be collected, and the rotor speed must be determined.Next, the sound sample has to be transformed as described in Algorithm 1. to obtain PSD For further processing, a frequency window is chosen and isolated from the full sound signal spectrum.The window should cover the range of high frequencies generated form the stall turbulencesof self noise [12].In this study, the window spans between 10 and 14 times the rotational frequencies.After that operation, the value of ξ can be determined.

−abs(mean(P S D)))/abs(mean(P S D))
( The results of the operation are shown in Fig. 16.The ξ parameter is close to 0 during normal conditions and drops down when the stall occurs.For most cases, the drop-down bellow −5e − 3 can be used as a threshold that indicates stall at part of the propellers' blade.This approach is useful due to the low computing power need, however it may be laden with dependency on particular rotor geometry and operating conditions.In the future, possibility to track the ξ value and use the high gradient as an stall indicator may be preferred instead.

Discussion
The correlation between stall and higher noise at high frequencies of the spectrum has a simple explanation in the physics of stall phenomenon.In this regime, the flow separates from the upper part of the airfoil, producing eddies of wide range of sizes and frequencies.This chaotic airflow generates acoustic power, detected by microphones, similarly to the helicopter rotor generating self noise of the blade (see [12,31]).The additional acoustic power emitted from the propeller is one of the symptoms of lower efficiency of the rotor due to the loses of energy in the highly turbulent separated wake.This loss is visible in the power spectrum of acoustic signals.The mean and median of the PSD clearly show the change in emitting power.Those parameters are straightforward, fast to calculate, and suitable for onboard computing.
The well-known FFT algorithm consumes a majority of computational power in the process, so computation can be performed rapidly as the FFT is already a fast algorithm.
Other parameters and indicators were tested during the study, but none gave better results than the one presented in this paper with the same straightforward, low-cost computing.
The turbulences in every studied case appear when the pitch angle is above 5 degrees.In this case, the decrease of pitch angle is needed to improve hover efficiency.The proposed method's best results are obtained for microphones at 30 and 60 degrees.The ξ parameter has a lower correlation with the thrust for those angles.
Compared to other stall detection and analysis methods [22][23][24][25], the presented approach is much simpler.Although it can't provide a robust analysis of the flow around propeller blades, the ability to determine if a stall occurs or not in real time is a significant advantage of high applicability.The method can be used to create a low-cost, onboard stall indicator for aircraft and drones, while other methods require a much more complex apparatus that is not designed for a small and medium size UAV.The presented method has been tested on one propeller, and the threshold value of ξ can be different for other propellers due to the different geometry.To calibrate the threshold ξ , there is necessary to conduct two experimentsone experiment where we can ensure stall and another where stall does not occur.The window of frequencies also can be slightly changed to meet the best results of a particular rotor.The exact limitations of the method have yet to be found.It requires additional experimental campaigns, including testing setup in different environments and at different UAV platforms.Additionally, the range of microphones should be tested to specify minimal hardware requirements for the proposed method.
This study is focused on exploring the sound features of rotor noise.The ξ parameter was used as the simple indicator of the stall, but there is room for further explanation of this topic and the introduction of better indicators.In future studies topic of finding better indicators should be addressed.The problem of acoustic stall detection when multiple rotors are working in noisy surrounding conditions must also be solved to integrate a system with a multirotor UAV.

Conclusions
The presented study shows the general performance of the variable pitch propeller in combination with its acoustic char-acteristics.The discovered correlation between the stall on the propeller's blade and specific acoustic features in the PSD spectrum allows us to determine if a stall occurs from the sound sample.Presented data acquisition and data processing methods will enable us to successfully determine if a stall occurs at the part of the propeller's blade.The experiment shows the possibility of detecting stall from any angle, but the best results were achieved from 30 and 60 degree angles.There was introduced a single parameter that indicates stall.The proposed method of stall detection can provide information if the stall occurs.It involves low-cost and low-weight equipment, as it requires just one microphone, and the computational power required by the process is low.The presented method is valid for simple case scenarios, but further investigation has to be done to test the method in more complex environments.
Michał Lipian: Manuscript review edition, Supervision.All authors read and approved the final manuscript.

Fig. 13
Fig. 13 Power Spectral Density for microphone at 30 deg

Fig. 15
Fig. 15 Power Spectral Density for microphone at 90 deg

Table 1
Motor rotational frequency