Numerical study of the rotor thickness noise reduction based on the concept of sound field cancellation

Runze XIA, Yongjie SHI,*, Teng LI, Guohu XU

a National Key Laboratory of Rotorcraft Aeromechanics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

b China Helicopter Research and Development Institute, Jingdezhen 333001, China

KEYWORDS Active rotor;Helicopter;Noise reduction;Sound field cancellation;Thickness noise

Abstract Numerical studies were performed to investigate the mechanism and potential of several active rotors for reducing low-frequency in-plane thickness noise generated by rotating blades. A numerical method coupling the blade element theory, prescribed wake model and Fowcs Williams-Hawkings(FW-H)equation was established for rotor noise prediction.It is indicated that the excitation force on the blade tip can generate anti-noise that to partly cancel the in-plane thickness noise with an appropriate actuation law. Results from the phase, frequency and amplitude sweeps show that the excitation force direction and actuation law are the crucial factors affecting the noise reduction, which determine the noise reduction area in the elevation and azimuth directions, respectively. The active trailing-flap rotor can generate the in-plane excitation force, but because of large lift-drag ratio the anti-noise is mainly from the vertical lift,which is caused by flap deflection similar to a variable camber airfoil.For the harmonic control rotor and active twist rotor,the excitation force is also attributed to the vertical blade lift.The vertical force can reduce the noise near the rotor plane,it will also cause the noise increase in most other areas.Finally,two new active rotors were proposed to generate the in-plane chordwise and spanwise excitation force. With the modified actuation law, the noise in most areas around the rotor was reduced, which improved the acoustic characteristics of rotor significantly.

1. Introduction

Noise is a very important issue for both civilian and military helicopter.Rotor noise,which is the main source of noise produced by a helicopter, has many generation mechanisms. This includes thickness noise, loading noise, Blade-Vortex Interaction (BVI) noise, high speed impulsive noise and broadband noise.The rotor thickness noise features low frequency (typically less than 200 Hz)and slow attenuation. It can propagate large distance because the helicopter usually operates at low altitudes and the rotor has a slight downward tilt. It is the major composition of helicopter far-field noise and the principal subject of acoustic detection. Consequently, the reduction of in-plane rotor thickness noise is particularly important.

In past decades, a plenty of techniques including passive and active controls, have been used for rotor noise reduction.Lowering the blade tip speed is of great benefit to noise,but it also has significantly adverse impact on vibration and safety.So most of studies focus on noise reduction by altering the blade shape (sweep, taper or thin airfoil on blade tip).One of the representatives is the Blue edge blade.However,the rotor blade design requirements for reducing noise are not always consistent with performance, aerodynamic, and structural requirements,significant trade-offs are usually made during the process of the rotor design. The active control is a more attractive way to reduce rotor noise. It has been studied for several years, and most studies were for BVI noise reduction, for example, harmonic control,active flapsand active twist.The experimental and numerical results demonstrate that the active controls are effective for BVI noise and vibration reduction. Comparatively, the studies on thickness noise reduction are limited. Gopalan and Schmitz,Simseparately proposed the novel control method for reducing the in-plane rotor noise in the principle of sound field cancelation. They compared the noise reduction of single monopole and dipole sources, as well as multiple controllers.Sargent and Schmitzconducted theoretical and experimental investigations on noise reduction with a tip-blowing rotor.The results showed that about the 2 dB reduction of thickness noise was achieved for the observation locates near the rotor plane.Yang et al.studied the relation between the loading solution and resulting noise and proposed two active devices for inplane noise reduction. Sim et al.conducted the wind tunnel test of the full-scale active flap rotor, Boeing-SMART rotor.The blade in test has high aspect ratio and low torsional rigidity.The test results illustrated that the noise energy in the first six blade-passing harmonics was reduced by up to 6 dB at a moderate level flight with advance ratio of 0.30.They reported that the reduced noise was attributed to the in-plane component of unsteady lift caused by the aeroelastic deformation of blade, and little contribution from the flap drag. It can be inferred that more noise reduction should be achieved for the harmonic control rotors based on the torsion of whole blade, e.g., higher harmonic control rotor. Unfortunately,few relevant findings have been reported in previous studies.In 2018, Shi et al.carried out the test of a 2 m-dimater,trailing-flap rotor in an anechoic chamber and the noise reduction of 2–3 dB is observed in some microphones. The low aspect ratio blade is stiff in torsion and is hard to produce torsional deformation under the external torque, and it is uncertain whether the exciting force to reduce noise is attributed to the lift or drag of the blade. Therefore, the research effort is still required to study the effects of active rotors on thickness noise reduction.

The purpose of this paper focuses on the application of concept of acoustic field cancellation for rotor thickness noise reduction.First of all,a numerical method coupling blade element theory, wake model and Fowcs Williams-Hawkings(FW-H) equation is established for active rotor blade loading and noise predictions. Based on this method, the acoustic propagation characteristics generating from vertical and inplane unsteady force, i.e. lift and drag, and their reduction mechanism of thickness noise is investigated. Then, the feasibility and potential of three representative active rotors are studied through a serial of simulations of frequency, phase and amplitude sweeps in different flight states. Finally, the new active rotors configurations and modified actuation law are proposed to improve the noise reduction in terms of the principle of sound field cancelation.

2. Concept and methodology

2.1. Noise reduction concept

The noise generated from rotating rotor blade is governed by the FW-H equation. An integral form, formulation F1A,is employed in present research for noise prediction.The acoustic pressure pin F1A formulation can be expressed as a summation of thickness noise pand loading noise p:

where x is the observer coordinate; t is time; f=0 represents blade surface;ρand aare density and sound speed in undisturbed air; vis the local normal velocity of blade surface; r is the length of radiation vector r;M is the sectional Mach number; the subscript ‘‘r” denotes radiation direction (e.g.,M=M ∙r,where M is the local Mach number);F is the force on the blade surface;F=FM,the subscript‘‘i”denotes the direction of component;the superscript‘‘∙”denotes the rate of variation with respect to source time; the subscript ‘‘ret” indicates that the integrals are evaluated at the retarded time; S is the integral surface.

The terms with rare inversely proportional to the square of distance, and can be neglected when the observers are far away from rotor, then the Eqs. (2) and (3) can be rewritten as

The concept of sound field cancelation for thickness noise reduction is introduced briefly first. The rotor thickness noise is caused by the periodic displacement of air by rotating blades. The sound pressure comes from the contributions of oscillation of airflow velocity and its time derivative. From view of mathematics, Eqs. (4) and (5) has a consistent form.For example, if we replace the product of density and normal velocity in Eq. (4) with force, then we can obtain the loading noise formulation, Eq. (5). As shown in Fig. 1, the unsteady aerodynamic force is arranged at the outer portion of the blade. A controllable sound wave (anti-noise) that is opposite to the original noise (thickness noise) is generated through adjusting the amplitude and direction of unsteady force. The superposition of them could cancel the sound pressure in a certain area, thereby reducing noise.

2.2. Noise prediction method

The rotor noise is predicted with a hybrid method, that is, the blade airload is calculated by rotor aerodynamic method and then the noise is calculated by the integral FW-H equation.Because the Computational Fluid Dynamics (CFD) method has difficulty in simulating some active rotor configurations and performing excessive simulations including phase, frequency and amplitude sweeps, the rotor aerodynamic method based on the blade element theory and the prescribed wake model was developed for the blade airload calculation. The methods above were integrated into the code of Rotor AeroDynamics and Acoustics Solver (RADAS) in Nanjing University of Aeronautics and Astronautics, which has been widely used for conventional rotor simulations.For the active rotors work through blade overall or local deformations to improve the rotor performance and reduce vibration, the modeling of them can be treated by the way the same as conventional rotor.To be specific,the aerodynamic characteristics of airfoils at different blade segments are obtained, and then the airload distribution of blade is calculated by rotor aerodynamic method. The influence of active deformation on wake geometry is not modeled in present analysis.

In simulation, each blade is divided into 30 segments in spanwise and one revolution is divided into 73 stations with an interval of 5°. The blade airload can be considered as a chordwise compact and spanwise non-compact source, and the loading noise is simply obtained by integrating the noise generated from each sectional segment.However,the thickness noise is non-compact sound source in both directions, it is required to segment the blade both spanwise and chordwise.Each sectional segment was divided into two parts and the quadratic distribution and linear distribution are used for the leading edge and trailing edge part, respectively.

where qand qare the segment indexes of leading edge and trailing edge;Nand Nis the number of chordwise segments;kis separation point,k=0.25c,c is chord length.The calculation results(Fig.2)showed that 15 chordwise segments are adequate for thickness noise prediction, where N is chordwise segment number.

2.3. Validation for noise prediction method

The noise prediction method is validated against the hover cases of UH-1H rotor and forward flight cases of AH-1/Operational Load Survey (OLS) rotor.

Firstly, the capability of prediction for conditions that thickness noise dominates is validated by comparing with the 1/7 scale model of UH-1H hovering noise.The main parameters of full scale UH-1H rotor are listed in Table 1.Due to the lack of experiment data of moderate tip speed hovering noise,the present prediction method is validated by comparing with Baeder’s simulation result.Baeder’s method was verified by good agreement with various high tip Mach number experiments,thus the simulation result of Baeder’s for moderate tip speed can be a reliable reference. Fig. 3 shows the calculated sound pressure time history of the in-plane observer at 3.09 rotor radii for tip Mach number Mto be 0.6 and 0.7,respectively. As is shown, the calculated data agrees well with Baeder’s data.

Fig. 1 Concept of sound field cancelation for thickness noise reduction.29

Fig. 2 Variation of predicted thickness noise with number of chordwise segments.

Table 1 UH-1H rotor parameters.

The method is further verified by comparing with AH-1/OLS forward flight experiment datafor overall noise prediction. The AH-1/OLS is a 1/7 scale model of AH-1 rotor, and the main parametersof AH-1/OLS rotor are listed in Table 2.The calculated flight conditionis the Run 10,014 case, with an advance ratio of 0.164, a tip-path plane of 1°, a hover tip Mach number of 0.664 and a thrust coefficient of 0.0054.Sound pressure time history for two microphones #3(-2.85 m, 0 m, -1.65 m) and #9 (-2.47 m, -1.43 m,-1.65 m)are shown in Fig.4,where T is period of rotor.There is a good correlation of sound pressure peaks shown by the comparation between experiment dataand the present calculation for both microphones.

3. Noise reduction potentials of active control rotors

There are several ways to generate excitation force,but few can be for rotor application. The potential of three representative active control rotors(Fig.5),i.e.,trailing-flap rotor,harmonic control rotor and active twist rotor,in reducing rotor thickness noise was analyzed first.These active rotors generate unsteady excitation force via changing the overall or local deformation of the blades. In Section 3.4, two configurations of active rotors are proposed to improve the noise reduction capability.

Fig. 3 Sound pressure history of in-plane observer at 3.09 rotor radii for 1/7 scaled UH-1H rotor.

Table 2 AH-1/OLS rotor parameters.

3.1. Trailing-flap rotor

As shown in Fig.5(a),the blade of Active Trailing-Flap(ATF)rotor has a high-frequency rotation flap on its trailing edge.The aerodynamic force and moment of the blade segment can be modified to achieve the required control target by designed flap actuation schedule. As stated in Section 1, the thickness noise reduction of ATF rotor has been demonstrated in several experiments, but the source of force remains to be determined. Therefore, the noise reduction mechanism of ATF rotor is analyzed by numerical method with a model rotor in Ref.. The model rotor has two blades. The radius R is 1.0 m, the chord length c is 0.13 m, and the linear twist is -8°. The OA212 airfoil is used throughout the blade in the experiment, but the NACA0012 airfoil was used instead in the numerical simulation for simplification. The trailingedge flap has a length of 0.118 m and the chord length is 0.02 m. The noise experiment was carried out in a rotor anechoic chamber in China Helicopter Research and Development Institute (Fig. 6). Only a few test results are presented,more details are found in Ref.

Fig. 4 Sound pressure history of in-plane observer for AH-1/OLS rotor.

Fig. 7 shows the variation of the Sound Pressure Level(SPL) with the initial phase and actuation frequency of flap.The microphone locates at 180°azimuth and 4R from hub center. As Fig. 7 shown, the optimal initial phase with which the maximum noise reduction is achieved varies with the actuation frequency of flap.Because the step of phase sweep in the test is large (about 30°), the optimal initial phase under the first and second order actuation is around 270°and 180°respectively.In the first order actuation, the maximum SPL is reduced by 2.5 dB. The time histories of sound pressure with and without control at three observation positions are compared in Fig. 8.

Firstly, the noise characteristics of blade lift and drag are analyzed. If only sectional segment at 0.8R of blade is considered, the blade is then simplified as an airfoil rotating around the hub center.In this way,the noise generated by unsteady lift and drag, and the effect on thickness noise reduction can be well compared. In the control state, the blade pitch angle θ consists of control input, (i.e., collective pitch θ, cyclic pitch θ, θ), and actuation input θ, as

Fig. 5 Three active control rotors.

Fig. 6 Rotor noise test in anechoic chamber.

where Ω is the rotating speed of rotor;n is the harmonic order number of the actuation input;ψis the initial actuation phase.ψ is the azimuth of the blade, ψ=Ωt.

To eliminate the influence of rotor loading noise introduced by the azimuthal variation of blade loading caused by pitch,the rotor control input is set to 0,and only the actuation input is retained. In the first order actuation, the optimal initial phase derived from theoretical analysisis 0°, hence the variation of pitch is θ=-1cos(ψ+0) with θ=-1°. Fig. 9 shows the variation of sectional lift and drag of blade with azimuth, where L and D is the lift and drag. The lift is linearly dependent on the Angle of Attack (AOA) and exhibits a variation in harmonic form.Although the drag also increases with the angle of attack,it changes little in the range of small angles of attack, which makes the time change rate of drag small,thereby affecting the noise generation.

Fig. 7 Noise reduction varies with deflection frequency measured in experiment.

Fig. 8 Time history of sound pressure at three observations measured in experiment.

Fig. 9 Variation of sectional lift and drag at 0.8 rotor radius.

Fig. 10 shows the thickness noise, anti-noise and overall noise at three observation positions in front of the rotor.Fig.10(a),(c),(e)and Fig.10(b),(d),(f)correspond to the vertical excitation force (lift) and the in-plane excitation force(drag). In terms of the radiation directivity of various noises,the thickness noise mainly propagates along the rotor plane and decreases as the elevation angle increases; in contrary,the noise generated by lift is the lowest near the rotor plane and gradually increases with the elevation angle. As shown in Fig. 10(a), (c), (e), the noise waveform generated by unsteady lift is opposite to the thickness noise, and the total noise is reduced in small elevation angles.However,as the continuous increase of anti-noise and decrease of thickness noise,the anti-noise exceeds the thickness noise and increases the total noise at large elevation angles, for example the observer at 45° elevation. This is one of the main disadvantages of vertical excitation force used for sound field cancellation, that is,it reduces the noise near the rotor plane but also causes the noise increase in most other areas. Anti-noise generated by the in-plane drag propagates along the rotor plane that is similar to thickness noise.But in this simulation case,the sectional drag has little effect on thickness noise reduction because the drag and its time-derivative are small.

The static airfoil aerodynamic data in C81 format is used in the above calculation, then the CFD method is employed to simulate the dynamic aerodynamic characteristics of the conventional airfoil (NACA0012) and trailing-flap airfoil. As shown in Fig. 11, the variation of AOA of the conventional airfoil is α=1°sin(ωt),where ω is oscillation frequency of airfoil and trailing-flap; the variation of deflection angle of the trailing-flap is β=3°sin(ωt),and the AOA of the main airfoil is held constant α=0°.

Fig. 10 Comparison of anti-noise generated by lift and drag.

Fig. 11 Schematic of oscillating motion of airfoil.

The oscillation frequency ω of airfoil and trailing-flap,equals to the rotor rotation speed Ω, thus the period exactly corresponds to one revolution of rotor.Fig.12 shows the variation of aerodynamic coefficients of two airfoils in one oscillation period. The lift and drag of the conventional airfoil exhibit the approximate first order and second order harmonic variations, respectively. The deflection of trailing-edge flap is equivalent to changing the airfoil camber,and the lift and drag of trailing-flap airfoil with 3° flap deflection are close to the conventional airfoil. The instantaneous flow field and surface pressure distribution in Fig. 13 clearly shows the influence of flap deflection on airfoil aerodynamic characteristics, where x is chordwise position. For a real rotor, there is a gap between the flap and main airfoil.Previous studieshave shown that the disturbance of the trailing-edge flap can affect the main airfoil in subsonic flow when the gap is small.Back to the rotor in Ref.,although the blade is rigid and not easy to produce elastic torsion, the deflection of flap can cause the variation of aerodynamic force by modifying the airfoil shape. Because of the large lift-drag ratio of the airfoil, the lift is much greater than the drag with the increase of flap deflection angle, so the vertical lift is the excitation force generating the anti-noise.

Fig.12 Variation of aerodynamic force and moment during one period.

3.2. Harmonic control rotor

The potential of harmonic control rotor for thickness noise reduction is estimated. The distinct feature of this technology is that the whole blade is actuated to experiences high-order pitch when the harmonic control works. It includes high harmonic control and individual blade control.Harmonic control rotor was first used for rotor vibration reduction. Later, the researchersfound that it also has ability to reduce the BVI noise by modifying the local induced velocity and the rotor tip vortex. However, there is few reports on thickness noise reduction by harmonic control rotor in previous studies.

3.2.1. Hover

First, the noise characteristics of hover condition is analyzed.The control input is set to 0 to minimize the influence of rotor loading noise introduced by the azimuthal variation of blade loading caused by pitch. Because the noise generated by drag is small, only the effect of unsteady lift on thickness noise is discussed.Fig.14(a)shows the variation of SPL with the initial phase in the first order actuation (n=1). It can be seen that when the initial phase is in the third and fourth quadrants,i.e.the azimuth is between(270°–360°–90°),the thickness noise is reduced, with a maximum reduction of about 6 dB. From theoretical analysis, the optimal initial phase is 0° for the far-field observation position at the 180° azimuth in the rotor plane. However, because the non-compact chordwise force is used in simulation, the initial phase appears between 0° and 20°. The further phase sweep with interval of 2° gives that the optimal initial phase is 11°.The time histories of thickness,anti-noise and total noise are plotted in Fig. 14(b).

The contours of SPL in a hemispherical surface 100R from the hub center is shown in Fig.15.The distribution pattern of thickness noise is axisymmetric in hover condition, but the noise level in front and rear of the rotor changes significantly when the blade actuation is applied. To compare directly the noise level variation before and after control, the difference contour is plotted in Fig. 15(c). The negative value indicates noise reduction.Observed from Fig.15(c),the noise is reduced in the area near the rotor plane where the thickness noise is dominant, and the maximum SPL is reduced up to 8 dB at the positions with the elevation angle of 25°. But in the rear of rotor, the noise is increased. The alternative reduction and increase of the noise are caused by the harmonic form of actuation.The excitation force is F=Fcos(ψ+11°),where Fis the amplitude of the excitation force, and its time derivative-Fsin(ψ+11°) reaches the negative peak near the 90° azimuth, which can effectively reduce the thickness noise, meanwhile the derivative reaches the positive peak at the 270°azimuth,which will generate the noise in phase with the thickness noise, thereby increasing the noise.

It should be pointed out that the rotor collective pitch is about 10° in real flight condition, and the blade loading noise is higher than the anti noise generated by excitation force. In addition, when the helicopter is in forward flight, the noise level in the rear area is lower than that in the front area due to the Doppler amplification effect.Both of them can alleviate the adverse effect arising by the vertical excitation force to a certain extent.

Then the effect of force amplitude on noise reduction is studied. The optimal initial phase changes little with the force amplitude when the actuation frequency is held constant,hence the variation of the blade pitch is θ=θcos(Ωt+11°), θ=1°, 2°, 3°. Fig. 16 compares sound pressure time history and difference contour of SPL under different actuation inputs. The excitation force and the generated anti-noise are linearly proportional to the actuation input. With the increase of the input, the anti-noise produced by the vertical excitation force increases, it will be higher than the thickness noise, which results in the increase of total noise and reducing the effective noise reduction area.

Fig. 13 Pressure contour and pressure coefficient.

The actuation frequency is another important factor affecting the anti-noise. The optimal initial phase changes with the actuation frequency. Table 3 lists the optimal initial phases at four actuation frequencies obtained from phase sweep. In each case, the optimal phase lags behind the theoretical value about 10°.

The noise is proportional to the load time-derivative, the amplitudes of high-order actuation inputs are reduced in the analysis to limit the excitation force not be excessive,as shown in Table 3.The time histories of sound pressure at four actuation frequencies are compared in Fig.17.The thickness noise is reduced in varying degrees at different frequencies, and the reduction is 6.65, 10.89, 1.82, 3.40 dB respectively. It is interesting to note that the noise waveform of low actuation frequency shows some differences with that of high actuation frequency. In low-order actuation the sound pressure before the positive peak increases slowly, while in high-order actuation, a distinct negative peak exists in sound pressure. As the actuation law is in terms of cosine function,the harmonic force generates equal number of positive and negative peaks of force time derivative in one rotor revolution. The noise waveforms generated from positive and negative peaks are exactly opposite. In the low order actuation, the phase shift between two peaks is large, and there is little interaction between the positive and negative sound pressure. With the increase of actuation frequency, the phase shift is reduced, so the superposition of two distinct noise changes the noise waveform.

Fig. 18 are the contour and difference contour of SPL at four actuation frequencies. As expected, the pattern of alternating increase and decrease of noise is shown in the contour.The frequency equals to the order of actuation. From the difference contour, the noise is reduced in the region near the plane, while it is increased in most other regions.

Fig. 14 Result of phase sweep with harmonic control in hover.

3.2.2. Forward flight

Then, the effect of harmonic control rotor on noise reduction in forward flight is investigated. The advance ratio is 0.2. To minimize the effect of blade airload caused by pitch input,the control input is set to 0, only the actuation input is kept.Fig. 19(a) shows the variation of SPL with initial actuation phase. The optimal initial phase is about 11°, and the maximum reduction is 4.2 dB.The optimal initial phase is the same as that in hover state.It means that the flight condition has little effect on the optimal initial phase.The time history of antinoise generated by the excitation force is similar to that in hover (Fig. 19(b)).

Fig.20 compares the contours of SPL with or without control. In forward flight, the thickness noise level in the rear of rotor is lower than that in the front due to Doppler amplification effect.When the first order actuation is applied,the noise distribution is changed significantly. From the difference contour, it is seen that only the noise in the range of small elevation angles in front of rotor is reduced, which is caused by vertical excitation load in the form of harmonic.

Fig.21 gives the variations of sound pressure and SPL with actuation inputs.Although increasing the amount of actuation input can lower the noise level in the narrow area near the rotor, the noise reduction area will also decrease. As can be seen from Figs. 16 and 21, the influence of actuation input on the noise reduction characteristics is general the same in hover and forward flight.

Fig. 15 Contours of SPL in a hemispherical surface with harmonic control.

3.3. Active twist rotor

The Active Twist (ATW) rotor uses advanced deformable materials and micro-actuator mechanism to drive the blade deforms in selective region, so as to achieve the required control with minimum energy and negative impact cost.The noise reduction potential of ATW rotors is estimated. For the convenience of modeling,the structure and geometric deformation of ATW are simplified, and assume that the blade segment of 0.8R–0.9R can twist freely.

Fig. 16 Variations of sound pressure and SPL with actuation inputs.

Table 3 Optimal initial phases at four frequencies.

In view of the similar results in hover and forward flight,only analyzes the noise reduction in hover. For ATW rotor,the deformation of active twist segment(i.e.,0.8R–0.9R)is the superposition of blade control input and local twist. Neglecting the control input, the deformation law of twist segment can be expressed as θ=θcos(nΩt+ψ). Fig. 22 shows the result of phase sweep under first order actuation. The optimal initial phase is 12°,which is consistent with the harmonic control rotor.

Fig. 17 Variation of sound pressure with force frequency.

Fig. 23 plots the variation of sound pressure and SPL with the twist angle of deformation segment. When the twist angle increases from 1° to 3°, the noise reduction increases from 1.4 dB to 5.0 dB. It is seen from the contours of SPL that the noise distribution pattern around the rotor, the variation of noise reduction with the twist angle are similar to the harmonic control. Therefore, the detailed analysis and discussion are not presented here.

3.4. Improvements of noise reduction

Although the three control rotors investigated in Sections 3.1–3.3 can reduce the in-plane thickness noise in varying degrees,it will increase the noise in a large area below the rotor plane because of the vertical excitation force. In addition, the harmonic excitation force will cause the noise around the rotor to increase and decrease alternately. In conclusion, the three control strategies for the cancellation of thickness noise studied in Sections 3.1 to 3.3 are not really practical in consideration of the overall noise variation. In order to improve the thickness noise reduction capability, and to minimize the area in which noise may increase,it is necessary to design new control devices on the blade to generate in-plane excitation force.Fig. 24 shows two hypothetical active rotors proposed. The first one is to deploy a movable flat on the blade tip, which can generate unsteady chordwise in-plane force by changing the windward area of the flat. The second one is to deploy a winglet on the blade tip to generate a spanwise in-plane excitation force by changing the AOA of the winglet.Although these configurations may be difficult to achieve in practice,our purpose is to investigate the influence of in-plane excitation force on thickness noise reduction by means of these control devices.We first analyze the active flat configuration.Let the length of flat is 0.1R, located at 0.8R–0.9R of blade, and the drag(chordwise force) of flat can be expressed as

where Dis the drag of winglet; ρ is air density; vis inflow velcoity at the flat; Cis drag coefficient; s is the area of flat.

The drag coefficient Cis taken from the empirical drag coefficient of the plate, and the resultant drag of flat varies with its area. Given the rotor operation condition and the motion law of flat, the chordwise excitation force of flat can be obtained from Eq. (8). From the result of phase sweep under first order actuation, the optimal initial phase is 6°.Fig. 25 shows the contour and difference contour of SPL around the rotor after applying the active flat.The noise distribution is quite different from that in the case of the vertical force, e.g. Fig. 15. Two distinct features are observed from the difference contour, one is that the noise is effectively reduced in a wide range of elevation angles in front of the rotor, not only in the narrow area near rotor plane; the other is that even in the area behind the rotor,the increase of sound pressure level is not significant, about 2 dB.

Fig. 18 Contours of SPL at different actuation frequencies.

Fig. 19 Variation of noise reduction with initial phase in forward flight.

Fig. 20 Contours of SPL with harmonic control in forward flight.

Then the active winglet configuration is analyzed.As shown in Fig.24(b),the chordwise and spanwise components of aerodynamic force of winglet can be expressed as

The loading noise generated by the spanwise propagates along the spanwise of blade, thus the corresponding optimal initial phase is different from the other force types. In order to reduce the thickness noise in front of the rotor (e.g., 180°azimuth), the anti-noise needs to propagate along the axis of 0°–180°, that is, the peak of the spanwise force should be achieved at the 90°azimuth.The theoretical analysis and phase sweep give the optimal initial phase are 90° and 98°, respectively. Fig. 26 shows the contour and difference contour of SPL around the rotor after applying the active winglet.Similar to the case of chordwise force, the noise is reduced in most areas in front of the rotor, and only increased in the rear of the rotor.

The in-plane excitation force effectively expands the noise reduction area in elevation direction around the rotor, but the noise on the side and rear of the rotor is still increased,which is caused by the harmonic excitation force. To improve the acoustic characteristics of the rotor in the azimuth direction, the actuation law of the excitation force should be modified. For the observation position in front of the rotor, the design principle of the actuation law is to make the force time derivative reach the maximum only in the optimal initial phase and approach 0 in other azimuth angles, in addition, the amplitude of the force itself should be as small as possible.Our research does not carry out the in-depth design of actuation law,the two control laws given below are just simple modifications of the original harmonic law.As shown in Fig.27,in Actuation law 1 the force reaches the maximum around the 90°azimuth,and set to 0 on the retreating side.In Actuation law 2 the deflection of winglet between 172° and 352° azimuth is reversed, so that the time derivative of force is positive on the retreating side.

Fig. 21 Variations of sound pressure and SPL with actuation inputs in forward flight.

Fig. 22 Result of phase sweep with active twist rotor.

Fig. 23 Variation of sound pressure and SPL with actuation input.

Fig. 28 shows the difference contours of SPL on the hemispherical surface under two modified actuation laws. The Actuation law 1 reduces the excitation force on the retreating side, which significantly expands the noise reduction area around the rotor,and more reduction is achieved in the thickness noise dominant area compared with the baseline condition. The Actuation law 2 further introduces appropriate anti-noise in the rear of the rotor,which effectively reduce the noise in most areas around the rotor. The noise still increases in the region with an elevation angle greater than 60°, but it has little influence on the far-field propagation. Although the above two laws are only simple modification of the original one, the noise reduction ability is significantly improved. It indicates that the concept of sound field cancellation can be effectively employed to the reduce rotor noise by selecting appropriate excitation force (in-plane force) and welldesigned actuation law.

Fig. 24 Two hypothetical active control rotors.

Fig. 25 Contours of SPL with active flat.

4. Conclusions

Fig. 26 Contours of SPL with active winglet.

(1) The excitation force on the blade tip can generate antinoise that to partly cancel the in-plane thickness noise with an appropriate actuation law. The force direction determines the radiation directionality of the anti-noise and affects the noise reduction range in elevation. The vertical force,e.g.lift,can reduce the noise of the observers near the rotor plane,but it will increase the noise in a wide range of elevation angles. In comparison, the radiation directionality of anti-noise generated by inplane force is consistent with thickness noise, it is an ideal excitation force.

(2) The other factor that affects the features of anti-noise is the actuation law of excitation force, which determines the noise reduction range in azimuth direction around the rotor. Because of the periodicity of the excitation force in harmonic form, it causes the noise around the rotor to increase and decrease alternately. The adverse effect of the harmonic force on some azimuth angles can be eliminated by designing the actuation law. It is also found that the optimal actuation law of excitation force changes little with flight conditions.

(3) From the results of phase, amplitude and frequency sweeps, it can be seen that the harmonic control rotor and active twist rotor can generate the anti-noise to reduce the thickness noise through the overall or local blade deformation, but the excitation force generating anti-noise only comes from the vertical lift due to the large lift-drag ration of airfoil. Therefore, these two active control rotors can not be effectively employed for thickness noise reduction.

Fig. 27 Modified actuation law for noise reduction at 0.8 rotor radius.

(4) From the simulation result of dynamic aerodynamic characteristics of trailing-flap airfoil, the flap deflection is equivalent to the change of airfoil camber which will lead to the change of aerodynamic force of main airfoil even if there is no aeroelastic coupling between flap and main. For the active trailing-flap rotor, both blade lift and in-plane drag caused by flap deflection can generate the anti-noise,but the drag is relatively small because of large lift-drag ratio of airfoil.

Fig. 28 Difference contours of SPL with modified actuation laws.

(5) In the end of the research,two active configurations are proposed to generate the in-plane chordwise and spanwise excitation force,and the actuation law of excitation forces is re-designed in terms of the generation mechanism of anti-noise.The numerical results show that compared with aforementioned active rotors, both chordwise and spanwise forces can significantly expand the noise reduction area in the elevation direction. In addition, the modified actuation law further increases the noise reduction area in the azimuth direction and greatly improves the acoustic characteristics around the rotor.

The feasibility and potential of the concept of sound field cancellation for rotor thickness noise reduction are demonstrated through the numerical study of a variety of active control rotors. The focus of the future research is to explore the practical devices or measures that can generate in-plane excitation force, to design the optimal actuation law of excitation force and to evaluate the net benefit by conducting CFD analysis.

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

This study was supported by the National Natural Science Foundation of China (No. 11972190) and the Aeronautical Science Foundation of China (No. 20185752).