Pressure feedback-based blade–vortex interaction noise controller for helicopter rotors

Abstract

With the aim of alleviating the noise annoyance emitted by blade–vortex interactions occurring on helicopter main rotors, the present work presents a methodology suitable for the identification of a multi-cyclic harmonic controller based on the actuation of rotor blades equipped with Miniature Trailing Edge Effectors. The objective of the control methodology is the direct suppression of the aerodynamic noise sources by generation of localized high-harmonic blade–vortex interaction counter-actions. The set-up of control devices is selected on the basis of the blade–vortex interaction scenario, taking into account a trade-off between effectiveness and power requirement. The control law is efficiently identified by means of an optimal controller synthesized through suitable two-dimensional multi-vortex, parallel blade–vortex interaction problems. The proposed methodology is validated by the application to realistic helicopter main rotors during low-speed descent flights, numerically simulated through high-fidelity aerodynamic and aeroacoustic solvers based, respectively, upon a three-dimensional free-wake boundary element method to solve the potential flow around rotors in blade–vortex interaction conditions and the Farassat 1A formulation. Results concerning the capability of the proposed controller to alleviate the blade–vortex interaction noise emitted by a realistic helicopter main rotor are presented and discussed.

Keywords

Blade–vortex interaction loads Blade–vortex interaction noise rotor aeroacoustics rotor aerodynamics multi-cyclic control

Introduction

Nowadays, the aerodynamic noise generated by helicopter rotors and irradiated to the far field and to the ground is one of the main topics related to the rotorcraft acoustic certification.¹ The extremely complex environment related to helicopter rotors contributes to noise generation through several mechanisms. Among them, the blade–vortex interaction (BVI) noise is one of the most annoying, as it occurs during hovering and low-speed descent flights, which are typical maneuvers in near-ground operations. As is well known, the BVI phenomenon occurs when strong rotor wake tip vortices impinge or pass in close proximity of rotor blades, producing impulsive changes in blade loading, along with high noise and vibrations. Therefore, the BVI noise is one of the critical issues for a wide helicopter public acceptance.

In the last decades, considerable efforts have been devoted to the definition of effective control strategies for the alleviation of BVI effects. Active controls like higher harmonic control (HHC),^2–4 individual blade control (IBC),^5–8 or active trailing-edge (TE) flap control^9–11 have been shown to possess the ability of considerable BVI noise reduction. Usually, these approaches are based on relatively low-frequency actuation inputs aimed at producing blade dynamic response increasing the miss distance (i.e. the relative distance between vortex and blade), thus alleviating BVI effects. However, their success often produces increased rotor vibration levels.

With the aim of overcoming this drawback, in previous publications the authors proposed a high-frequency BVI-noise control technique based on the generation of unsteady aerodynamic loads (as much as possible equal and opposite to those produced by BVI phenomena, called anti-BVI loads) aimed at canceling out those caused by the BVI events. The proposed procedure allows to reduce BVI noise without increasing structural vibrations. In Modini et al.^12–14 a control action consisting of a multi-harmonic pitch motion non-uniformly actuated along the blade span (a suited Gaussian distribution is used as weighting function of sectional pitch control) has been introduced. The actuation harmonics were those of BVI loads, with amplitudes given by a closed-loop control law determined through an optimal linear-quadratic multi-cyclic controller, efficiently synthesized by exploiting two-dimensional (2D) equivalent parallel BVI problems. A similar approach based upon an individual blade high-frequency controller, exploiting active twist actuation to reduce BVI rotor noise, has been also proposed and investigated in Anobile et al.^15,16. Numerical solutions presented in Modini et al.^12–14 and Anobile et al.^15,16 have shown promising results, suggesting the need of further developments and investigations aimed at assessing the feasibility of such kind of control approach.

Since the generation of anti-BVI loads requires the availability of actuation devices able to operate at frequencies higher than those provided by traditional IBCs, Miniature Trailing edge Effectors (MiTEs) seem to be suitable candidates for the realistic application of such BVI-noise control method. MiTEs (also referred to deployable Gurney flaps) reduced actuation power and easiness of implementation are key factors making them suitable for the integration in smart rotors.^17–19 Although nowadays there are not helicopters equipped with MiTEs able to operate at the frequency ranges required by the anti-BVI loads generation, in the AGF (Active Gurney Flap) project funded under the CleanSky demonstration program “GRC1-Innovative rotors blades”, prototype validation tests on a scaled model rotor blade demonstrated that a new concept of miniaturized active Gurney flap can operate at blade rotating speed of 1600 r/min, with actuation frequencies up to 150 Hz (see http://cordis.europa.eu/result/rcn/184746_en.html). In the literature,²⁰ the authors proposed a controller exploiting the high-frequency actuation of MiTEs, aimed at directly suppressing the BVI loads (anti-BVI loads generation), which was successfully applied to the BVI-noise reduction of the EC/ONERA 7A main rotor in descent flight conditions. However, all the BVI-noise control techniques proposed in the past by the authors^12–14,20 would require the availability of measuring devices on the rotor blades to detect the BVI loads needed to evaluate the controller actions in closed-loop applications.

Here, in order to overcome the manufacturing difficulties to insert pressure transducers in rotating blades, as well as the problem of the signal transmission from a rotating to a non-rotating system, a control approach exploiting measurements of noise on a set of microphones, suitably placed on the helicopter skids, is proposed. The control law is here synthesized through an optimal multi-cyclic control approach, taking into account the trade-off between control effectiveness and power requirement. The controller synthesis process is particularly efficient in that exploits low-fidelity 2D, parallel-BVI simulations to determine the transfer matrix appearing in the control algorithm, thus drastically reducing the computational effort required by its identification through a large number of three-dimensional (3D) aerodynamic solutions. Specifically, by using computational tools for rotor aerodynamics and aeroacoustics developed in the past by some of the authors,²¹ the identification of the equivalent 2D BVI problem is carried out by simulating, through a suitable sequence of traveling parallel vortices, the aerodynamic environment experienced by main rotor blades cross sections during realistic BVI conditions.¹² Once the aerodynamic loads during a blade revolution are known from the 2D aerodynamic analysis, the emitted noise is efficiently evaluated by exploiting a compact-source aeroacoustic formulation.²²

The controller performance is assessed by the application to a realistic rotor, numerically investigated through high-fidelity aerodynamic and aeroacoustic tools based, respectively, on a free-wake, boundary element method (BEM) approach for potential flows,²¹ and on the Farassat 1A formulation.^23,24 These aerodynamic and aeroacoustic formulations have been extensively validated in the past against available experimental and numerical data, including those concerning the European Project HELISHAPE and the HART II test database.^21,25,26 In the present aerodynamic simulations, MiTEs are properly replaced by TE plain flaps providing equivalent responses.^17,20,26

The following sections outline the multi-cyclic, optimal control approach applied for the identification of the control law aimed at BVI loads and noise alleviation as well as the methodologies used to make 2D equivalent problems able to mimic both the BVI aerodynamics and aeroacoustics. Finally, the numerical investigation on a realistic helicopter main rotor in descent flight is presented and discussed. The aims of the analysis are the validation of the proposed control strategy, the assessment of its efficiency and sensitivity to the devices position and number as well as the estimation of the required control power, so as to infer its feasibility for real-life applications.

The BVI noise controller

Differently from the methodologies proposed in the literature for active BVI noise control (i.e. traditional HHC and IBC), which are typically based on the modification of either the rotor wake environment and/or the local blade-to-vortex miss distance, the technique proposed here investigates a closed-loop optimal approach for identifying control laws aimed at generating high-frequency unsteady aerodynamic loads (anti-BVI loads) able to suppress/alleviate those caused by BVIs. This would allow for reducing, at the same time, the impulsive BVI noise and the associated structural vibrations. From the authors experience,^12–14 such a task can be efficiently performed by using a high-frequency control action, localized in both space (where BVIs occur) and time (when BVIs occur). The control limited-time actuation should minimize the blade structural response, avoiding significant effects on the rotor wake flow field and low-frequency blade dynamics.

From the above considerations, MiTEs could be selected as control devices, in that they allow high-frequency localized actuation with low-power requirement. However, in the following numerical investigations these are replaced by equivalent TE flaps which, accordingly with the literature results, may provide equivalent aerodynamic responses at lower computational costs.^17,20,27 A low-fidelity aeroacoustic–aerodynamic model is used in the control synthesis process, while a high-fidelity model is applied for the validation of its performance. Specifically, from the knowledge of the BVI scenario obtained through a BEM aerodynamic analysis of the helicopter flight condition under consideration, 2D parallel-BVI simulations are used to efficiently evaluate the transfer matrix relating the cyclic components of the flap deflection to the corresponding BVI-noise harmonics detected by a set of microphones located on the helicopter skids. Then, the controller effectiveness in reducing BVI noise is assessed by testing it on a realistic helicopter main rotor in steady-state flight conditions, simulated through high-fidelity aerodynamic–aeroacoustic tools.^21,23,24 In this application, the optimal control is updated up to convergence through a closed-loop algorithm based on the numerical outcomes.

Optimal control methodology

With the aim of alleviating BVI noise sources by generation of the so-called anti-BVI loads, a closed-loop control algorithm for multi-harmonic actuation of TE plain flaps is here defined following the optimal control approach introduced in Johnson.²⁸ Such an approach has been widely used in the past by some of the authors for the synthesis of control laws for the reduction of vibrations in rotorcraft applications^29–31 as well as for aircarft cabin noise alleviation.^32–34 Since an in-depth analysis of the BVI control technique has been presented in Modini et al.,¹² hereafter only the key steps of the procedure will be recalled.

Due to the inherently time-periodic nature of the problem, the optimal harmonic control procedure is identified by minimizing the following cost function

J = z^{T} W_{z} z + u^{T} W_{u} u

(1)

where u is the vector collecting the actuated harmonics of the control variables (input) to be determined, z is the vector of the harmonic quantities to be reduced (output), while W _z and W _u are the corresponding weighting matrices, defined by the designer so as to get the best compromise between control effectiveness and control effort. This control approach involves the harmonics of input and output variables only, without concerning the evolution of transients. Therefore, u contains the sine and cosine harmonic components of the TE-flap deflections which are effective for control purposes, while z consists in the sound pressure levels detected by the microphones located on the helicopter skids.

Akin to the standard optimal Linear Quadratic Regulator method (of which the present approach may be considered as the natural extension for applications to steady-periodic systems), the minimization of the cost function is obtained under the constraint of satisfying the governing equations describing the behavior of the controlled system. This constraint is not directly represented by the governing equations of the system, but rather by the following linear relationship between the control variables and the controlled ones, representing the linear response of the system to the control action

z_{n} = z_{n - 1} + T_{n - 1} (u_{n} - u_{n - 1})

(2)

where T _n _–1 is the (gradient) transfer matrix evaluated for

u = u_{n - 1}

, which provides the perturbed response of the system due to a perturbation of the control action. This transfer matrix is here numerically evaluated from the aeroacoustic/aerodynamic responses of the system to a suited set of control variable perturbations. Since the nonlinearity of the rotor aerodynamic response (mainly due to wake distortion effects) yields a u-dependent gradient matrix, the main drawback in using this matrix within a control algorithm lies in the significant computational cost for its evaluation at each step of the control process (note that the evaluation of the gradient matrix requires the determination of the sensitivities of the BVI noise with respect to each harmonic considered in the control actuation). Here, for the sake of computational efficiency, the transfer matrix, T, is derived from the least squares polynomial approximation of numerically evaluated open-loop data relating the BVI sound pressure levels to the variation of each harmonic component of the TE-flaps (control variables) about the zero value. Specifically, starting from clean (unflapped) rotor blades, given a suitable set of input vectors, u, with different TE-flap deflection amplitudes, the corresponding output vectors, z, are evaluated as open-loop responses; these form the database the least squares polynomial approximations of the functions relating output variables to input variables are based on, from which, in turn, each element of the gradient matrix,

T_{i j} = \partial z_{i} / \partial u_{j}

, can be evaluated analytically.

As stated above, in order to improve the performance of the control process synthesis, the numerical evaluation of the transfer matrix is based upon the responses of 2D parallel-BVI problems, based upon 2D aerodynamic/aeroacoustic analyses instead of realistic 3D rotor simulations.

Once the transfer matrix is evaluated by exploiting 2D problems, evaluating equation (1) for $z = z_{n}$ and $u = u_{n}$ , and minimizing the resulting cost function under the constraint given by equation (2), the following optimal control is obtained

u_{n} = G_{u} u_{n - 1} - G_{z} z_{n - 1}

(3)

where the gain matrices, G _u and G _z , are expressed as a combination of the transfer matrix and of the weighting matrices as

G_{u} = D T_{n - 1}^{T} W_{z} T_{n - 1}

(4)

G_{z} = D T_{n - 1}^{T} W_{z}

(5)

with

D = {(T_{n - 1}^{T} W_{z} T_{n - 1} + W_{u})}^{- 1}

(6)

Equation (3) has to be used in a recursive way: starting from a given control input and corresponding output, the law of the optimal controller is updated until convergence. First, this procedure may be applied to identify the weighting matrices that assure the best control performance, and then may be used as a closed-loop control process in which, at each nth control step, measured BVI noise is used as feedback to update the control law.

Note that, due to the time-periodic nature of the proposed control approach, the time interval between each control step should be long enough to allow for rotor aerodynamics reaching the steady-periodic condition corresponding to the updated control inputs.³⁵

To synthesize, the idea of the proposed BVI control methodology consists of: (i) computing the 3D free-wake aerodynamic solution of the uncontrolled rotor configuration under examination; (ii) identifying a multi-vortex parallel-BVI equivalent configuration that simulates (with a satisfactory level of accuracy) the BVI noise detected by representative microphones; (iii) performing the (low-cost) evaluation of a proper set of corresponding 2D aeroacoustic responses to TE-flap harmonic deflection in order to determine the database required for computing transfer matrix, T _n ; (iv) defining the weighting matrices, W _z and W _u , that yield those control gain matrices G _z and G _u that guarantee the optimal controller performance; (v) finally, applying the control algorithm of equation (3) to the examined rotor configuration, with the evaluation of the gain matrices based on the weighting and transfer matrices identified from the equivalent 2D, parallel-BVI problems.

Numerical results

The numerical investigation concerns preliminary results aimed at assessing the effectiveness of the proposed control approach to alleviate rotor BVI loads and radiated noise, as well as its sensitivity to the devices position and number. In this context an estimation of the control power required is performed, as well. For this purpose, the rotor considered is the four-bladed EC/ONERA 7A main rotor, which has been extensively tested at the Deutsch-Niederlandische Windkanale (DNW) wind tunnel within the European project HELISHAPE,³⁶ at several flight conditions characterized by BVI occurrences. The rotor blades have aspect ratio equal to 14 and rectangular planform. The examined flight condition is a 6° steady descent, with the angular speed Ω = 101 rad/s, advance ratio μ = 0.166, and rotational tip Mach number M = 0.615 (HELISHAPE Datapoint 70). From a convergence analysis, not shown here for the sake of conciseness, the discretization used to perform all the high-fidelity 3D aerodynamic/aeroacoustic analyses presented in this paper, applies 23 panels along the blade chord, 26 panels along blade radial direction, 180 time steps per blade revolution, and a 3-spiral-long wake, assuring practically converged numerical results. Note that, since the purpose of this numerical investigation is focused on the analysis of the effectiveness of the proposed BVI control, for the sake of simplicity and with no loss of generality on the results achieved,¹⁴ the blades are assumed to be rigid.

Controller synthesis

Following the procedure presented above, the 3D, free-wake aerodynamic solution of the uncontrolled rotor configuration under examination is computed in order to focus the BVI scenario. Then, on the basis of the BVI scenario, multi-vortex, parallel-BVI equivalent configurations are identified for each actuated TE-flap set-up. For the sake of controller efficacy, control devices are placed where the rotor blade is affected by the BVI impulsive loads causing the most annoying acoustic disturbances. Since BVIs are high-frequency phenomena typically localized in two regions of the rotor disk (one on the advancing side and one on the retreating side), the BVI aerodynamic effects on rotor blades are estimated by evaluating the so-called BVI perturbation lift coefficient, $c_{L}^{B V I}$ , obtained by windowing the lift coefficient (i.e. the section lift normalized with respect to the local hovering dynamic pressure, $0.5 ρ {(Ω r)}^{2}$ , where Ω is the rotor angular velocity and r is the radial position of the blade section) in these azimuth regions and filtering out the low-frequency blade loading (<8/ev). Therefore, the control device radial positions can be selected from the spectral analysis of the signal $c_{L}^{B V I} M^{2} / (1 - M^{2})$ , which takes into account the so-called Doppler factor too, $1 / (1 - M^{2})$ , that acts as modulator of the acoustic sources.²⁴ Here, the selection process is based upon the average power of the windowed BVI loads (APBVI) on a blade revolution. Accordingly to the APBVI- $c_{L}^{B V I} M^{2} / (1 - M^{2})$ radial behaviors depicted in Figure 1, two devices placed, respectively, at 75% and 85% of the blade radius (i.e. where the advancing and retreating APBVI- $c_{L}^{B V I} M^{2} / (1 - M^{2})$ distributions reach their maximum values) are considered. A dual-system consisting of the simultaneous actuation of the two devices is examined too (see Figure 1, where the selected control-device configurations are sketched). This placement of the control devices allows to locally modify the aerodynamic field in the blade region where high-frequency loads responsible for the BVI noise arise, with the aim of canceling out or at least alleviating them.

Figure 1.

Sketch of the control-device systems (bottom) selected on the basis of the advancing and retreating APBVI radial distributions (top).

Different transfer (T) and gain (G _u and G _z ) matrices are determined for each actuated control device exploiting the corresponding 2D equivalent BVI problem. Hereafter, for the sake of conciseness, only results from the procedure used to identify the equivalent BVI problem related to the 75%-radius control device will be presented.

Starting from the time history of the loads acting at the blade representative cross section (i.e. cross section in the middle of the flap) computed through the 3D high-fidelity BEM aerodynamic solver, the filtering procedure to define the BVI loads is applied: the signal is windowed and a Fourier analysis of the time-bounded signal is performed to extract the harmonic components of the filtered signal. Then the BVI loads are reconstructed in terms of the harmonics multiple of the window fundamental frequency, filtered out by the low-frequency content. For the blade cross section r = 0.75R (with R denoting the blade radius), Figures 2 and 3 depict the BVI loads in terms of time history (Figure 2) and harmonic components (Figure 3) of the BVI perturbation lift coefficient: the advancing and retreating BVIs are localized around the azimuth position $ψ = 60^{°}$ and $ψ = 280^{°}$ , respectively, both covering approximately one-sixth of the blade revolution period. Furthermore, Figure 3 shows that only harmonics $n^{B V I} = 12, 18, 24, 30, 36$ /rev are used to reconstruct the BVI perturbation lift coefficient, in that the window fundamental frequency (6/rev) is lower than the minimum frequency (8/rev) used in this study to define BVI loads.

Figure 2.

Time history of the high-frequency harmonic content (≥8∕rev) of lift coefficient, at r = 0.75R.

Figure 3.

Harmonic components of BVI loads.

Then, both relevant BVI events, clearly observable in Figure 2, are simulated by almost equivalent 2D, parallel-BVI problems, consisting of sequences of traveling counter-rotating vortices (as many as the load peaks), spatially separated by a distance related to the oscillation frequency of the BVI aerodynamic loads.

To exemplify, considering the loads at the representative blade section located at r = 0.75R, Figure 4 compares the results from the 3D high-fidelity BEM aerodynamic solver with those from the 2D, parallel-BVI analyses, performed with six and 10 vortices (respectively, for the retreating and the advancing side) impinging on the corresponding flapped airfoil. A good quality of the 2D computations can be observed in terms of detection of regions where BVI occurs, magnitude of load peaks, and harmonic content, confirming 2D computations accuracy for control synthesis purposes.

Figure 4.

Simulation of high-frequency lift coefficient content at r = 0.75R, by equivalent two-dimensional, multi-vortex, parallel-BVI configurations.

With the aim of reproducing the load field induced by BVIs on the overall rotor disk, the BVI sectional loads (depicted in Figure 4) must be suitably spread along the rotor blade radius to simulate the BVI effects really experienced by rotors during BVI. For this purpose, the spectral analysis of the signal $c_{L}^{B V I} M^{2}$ (supplied by uncontrolled realistic high-fidelity rotor solutions) allows to evaluate the distribution of the BVI loads along the blade span in terms of average power (APBVI): since the APBVI distribution highlights the blade region most severely affected by BVI aerodynamic effects, the sectional loads from 2D BVI problems are radially spread on the rotor blades accordingly with the APBVI trend of $c_{L}^{B V I} M^{2}$ .

Figure 5 compares the rotor distributions of the BVI perturbation lift coefficient as carried out by the 3D, free-wake rotor simulation (see Figure 5(a)) and by the above identified 2D equivalent parallel-BVI problems (see Figure 5(b)). It is worth noting that the $c_{L}^{B V I} M^{2}$ oscillations in the BVI regions are approximated with sufficient accuracy, although the radial behavior from 3D analysis is slightly different from that predicted by 2D simulations: this is essentially due to the presence of oblique blade–vortex interactions (BVIs) accurately modelled in 3D analysis and completely neglected in 2D simulations, where only entirely parallel interactions along the rotor blade radius (see Figure 5(b)) are allowed.

Figure 5.

Rotor disk distribution of the BVI impulsive loads: 3D free-wake BEM simulation (a) and 2D equivalent parallel BVI solution (b).

Then, in order to efficiently evaluate the BVI noise field too, the rotor loading distribution identified by exploiting 2D equivalent BVI problems (Figure 5(b)) is supplied to an aeroacoustic compact-source formulation derived from the Farassat 1A formulation²⁴ for the solution of the Ffowcs Williams and Hawkings (FWH) equation,²³ giving an integral representation for the acoustic pressure in the field in terms of the spanwise distribution of the section aerodynamic loads.^22,37 In addition, to further improve the computational efficiency of the noise radiation process, only the contributions from BVI events are considered in the evaluation of the acoustic pressure field. In other words, during a blade revolution, the noise radiation through the compact-source formulation is performed only in the time periods in which BVI effects are not negligible.

Figure 6 depicts the comparison between the acoustic fields in terms of BVI Sound Pressure Level (BVISPL) contour plots (the sound pressure levels related to the acoustic harmonics most affected by BVIs, i.e. 6–40 blade passage frequency, evaluated on a carpet of 187 microphones located 1.25R below the rotor disk) supplied by realistic rotor simulations based upon the 3D free-wake BEM solver²¹ for the aerodynamic analysis and the boundary-integral Farassat 1A formulation²⁴ for the evaluation of the noise field (Figure 6(a)), with those from the equivalent 2D parallel BVI simulations (Figure 6(b)). Also, in this case, the quality of the 2D results is quite good both in terms of pressure peaks and noise directivity, thus restating the suitability of the proposed 2D formulation for control synthesis purposes.

Figure 6.

BVISPL contour plots: 3D free-wake BEM simulation (a) and 2D equivalent parallel BVI solution (b).

In order to determine the BVI noise sensitivity with respect to the control action, once the 2D equivalent parallel-BVI problems suitable to mimic the BVI rotor problem in terms of aerodynamic and aeroacoustic effects are identified, the gradient matrix database computation is carried out by perturbing each control variable (the actuated TE-flap harmonics) and evaluating the corresponding outputs (the sound pressure levels detected by microphones on the helicopter skids). The TE-flaps are actuated only when BVIs occur by a suited windowing process (see Figure 2), with a frequency spectrum matching that of the sectional loads induced on the airfoil surface by the traveling vortex sequences (i.e. n = 12, 18, 24, 390, 36/rev, see Figure 3). Here, the database used in the least squares procedure aimed at deriving the transfer matrix, T, consists of nine gradient matrices sampled for nine incremental values of the TE-flap harmonics in the range $[- 10^{°}, 10^{°}]$ .

In the proposed BVI-noise control algorithm, the control vector, u, collects the sine and cosine components of the TE-flap actuated harmonics, whereas the entries of the controlled variables, z, are the sine and cosine components of the harmonics of BVI noise at a given set of microphones. In order to identify the locations of the microphones most suited to detect the BVI noise, a preliminary analysis considering independent propagations of the noise emitted by the blade impulsive loads due to the retreating- and advancing-BVI is performed: Figure 7(a) shows the BVISPLs related to the advancing-BVI, whereas Figure 7(b) depicts that related to the retreating-BVI.

Figure 7.

Sketch of the skid-microphones selected as noise-indicators on the basis of the BVISPL contour plots for the advancing (a) and retreating (b) blade.

The kinematics of the retreating blades gives a signal directivity that focuses the BVI noise on the carpet right area behind the rotor disk while advancing blades radiate the noise in the rotor disk left area (with respect to the motion direction). Consequently, three microphones on the helicopter left skid are selected for the advancing-BVI control while three others are placed on the right skid for the retreating one (see Figure 7, where the microphone locations are sketched).

Note that blades of rotors flying in BVI conditions usually experience strong wake impacts for short time intervals in the advancing and in the retreating sides, and hence two corresponding multi-vortex, parallel-BVI equivalent configurations are identified. Different transfer and gain matrices are determined for each event.

Controller validation

With the aim of assessing the effectiveness and robustness to model variation of the proposed methodology for BVI noise alleviation, the controller synthesized through the low-fidelity model is applied to a more realistic aerodynamic-aeroacoustic model of the EC/ONERA 7A main rotor in BVI conditions.

Once the transfer matrix T and gain matrices, G _u and G _z , are determined for each actuated control device, by perturbing the corresponding 2D equivalent BVI problem (under the constraint of absolute maximum TE-flap deflection lower than $15^{°}$ ), the BVI noise controller is applied within the rotor high-fidelity aerodynamic–aeroacoustic solution process, with the optimal control law (equation (3)) updated up to convergence of a closed-loop algorithm based on the numerical outcomes. The TE-plain flaps used here have a spanwise length equal to 6% of the rotor radius and a chordwise length equal to 10% of the chord.

The following results compare the performance obtained through the examined BVI noise controllers: the mono-flap placed at 75% of the rotor blade radius (see Figures 8); the mono-flap placed at 85% of the radius (see Figures 9); and (see Figures 10) the dual-flap system (see Figure 1, bottom). Due to the aerodynamic interference effects occurring during dual-flap system actuation, its effectiveness is assessed by applying a closed-loop algorithm based on the simultaneous actuation of the two TE-flaps. Note that each control-device system is actuated to control both separately and simultaneously the advancing- and retreating-BVIs.

Figure 8.

BVISPL variation contour plots obtained by the 75%-radius TE-flap: retreating (a); advancing (b), and simultaneous advancing–retreating controller (c).

Figure 9.

BVISPL variation contour plots obtained by the 85%-radius TE-flap: retreating (a); advancing (b); and simultaneous advancing–retreating controller (c).

Figure 10.

BVISPL variation contour plots obtained by the dual-flap: retreating (a); advancing (b); and simultaneous advancing–retreating controller (c).

The control assessment is performed in terms of BVI-noise reduction on a carpet of 187 microphones located 1.25R below the rotor disk. Specifically, Figures 8 to 10 compare the BVI noise alleviations, given in terms of variation contour plots of the BVISPLs (i.e. the sound pressure levels most affected by BVIs), obtained through each one of all the examined control strategies. These results show that the advancing- and retreating-BVI controllers produce noise reductions localised on well-defined distinct zones: the carpet right area behind the rotor disk for the retreating control strategy and the left area of the rotor disk for the advancing one. The simultaneous control of advancing- and retreating-BVIs seems to give a noise reduction more uniformly distributed on the whole carpet. Moreover, as expected, the dual-flap system produces the most satisfactory BVI noise control: BVISPLs are mitigated in the whole microphone carpet, and reductions up to 3 dB are detected in regions where the BVI noise is mainly radiated.

With the aim of introducing synthetic parameters suited to describe the performance of the single control strategy, both in terms of effectiveness and actuation power requirements, three merit indices are introduced and presented in Figure 11. Specifically, this figure shows the merit indices aimed at assessing the control effectiveness in alleviating maximum (x¹) and mean (x²) BVI noise and the index x³ defining the control effort in terms of requested actuation power. The mean BVI noise reduction x² is evaluated by summing the BVISPLs related to the overall microphone carpet, while the maximum BVI noise reduction x¹ is detected by considering only the four microphones placed below the rotor disk (i.e. the most affected by BVI noise). Note that the merit indices are normalized by the corresponding maximum values. Moreover, to give information about the performance of the control systems in terms of raw data, Table 1 compares the three control devices in terms of both maximum and mean BVISPL reductions.

Figure 11.

Performance of the control systems in terms of synthetic merit indices: maximum (a) and mean (b) BVI noise reduction, and requested actuation power (c).

Table 1.

Performance of the control systems: maximum and mean BVISPL (dB) reductions.

Controller		75%-flap	85%-flap	Dual-flap
Retreating	Maximum	+0.5	−0.2	−0.1
	Mean	−0.2	−0.4	−0.7
Advancing	Maximum	−1.4	−1.9	−3.0
	Mean	−0.6	−0.7	−1.3
Simultaneous	Maximum	−1.4	−1.9	−3.1
	Mean	−0.8	−1.1	−1.9

The above results show that the controller aimed at suppressing only advancing-BVI loads induces very large BVI noise alleviation in terms of both mean and maximum BVI noise, although involving limited power requirements. In all cases, the advancing-BVI controller outperforms the retreating-BVI one, in terms of all the merit indices. Such remark can be explained by analyzing the time-history BVI perturbation lift coefficient, $c_{L}^{B V I}$ , supplied by the uncontrolled rotor simulation (see Figure 2): the advancing-BVI sectional loads are lower than the retreating ones (so the power requested for generating advancing-BVI counter-action is lower) but the faster local velocities of the advancing blades amplify the related acoustic disturbances. Moreover, the retreating BVI control seems to be ineffective in alleviating the maximum BVI noise (see Figure 11(b)), according to the results presented in Figures 8(a) to 10(a) which show that the retreating control action does not produce important effects below the rotor disk (where BVI noise is maximum) but on the carpet right area behind it. Therefore, the retreating-BVI control is unfavorable in terms of both BVI noise alleviation and power requirements, with respect to the other two control strategies. The results obtained for the rotor equipped with a TE-flap placed around the APBVI- $c_{L}^{B V I} M^{2} / (1 - M^{2})$ maximum radial station (i.e. at the 85% of blade span) outperforms the one provided by the inner control-device actuation. Furthermore, it is confirmed that the dual-system produces the most satisfactory BVI noise control, but it is associated to the highest actuation power too.

Note that, although the suppression of the BVI impulsive loads is not directly included in the control law synthesis, it represents an indirect benefit of the present control methodology (i.e. aimed at generating BVI aerodynamic counter-actions) as shown in Figure 12, where the uncontrolled BVI loads on the blade cross section r = 0.85R are compared with the corresponding ones controlled by actuating the control device located there.

Figure 12.

Uncontrolled and controlled BVI perturbation lift coefficient at blade section r = 0.85R.

Now, with the aim of selecting the best controller depending on problem targets, the merit function, OF, suited for identifying an optimal compromise between control effectiveness and control effort is proposed

O F = α_{1} x^{1} + α_{2} x^{2} + α_{3} x^{3}

(7)

with the weighting coefficients α_i selected (under the constraint of unitary sum) according to the control priorities. As an example, focusing on maximum BVI noise reduction (α₂ = 0.6), taking care of power requirements (α₃ = 0.3), and considering only marginally the mean noise reduction (α¹ = 0.1), the merit functions of the investigated control strategies are evaluated and compared in Figure 13.

Figure 13.

Merit functions of investigated controllers as defined in equation (7).

The comparison of the results in Figure 13 highlights that, under the assumed weighting coefficients, the advancing-BVI control, obtained by actuating the dual-flap system, is the most effective controller among those here examined: it guarantees the largest maximum noise reduction (localized in the carpet region affected by high BVI noise levels, see Figure 10(c)) with limited power requirements (see Figure 11(c)).

For this controller, Figure 14 shows the BVISPLs radiated by the uncontrolled rotor (Figure 14(a)) and by the controlled one (Figure 14(b)), demonstrating a significant effectiveness without spillover effects.

Figure 14.

BVISPL contour plots from uncontrolled (a) and controlled rotor (b).

Conclusions

An optimal multi-cyclic control actuation methodology based on pressure feedback measured by microphones placed on helicopter skids has been developed and applied to alleviate BVI impulsive loads as well as the corresponding noise annoyance. The control-law synthesis derives from a local controller approach combined with computationally efficient 2D, parallel-BVI equivalent problem solutions for aerodynamic and aeroacoustic predictions. Effectiveness and robustness of the proposed control procedure have been examined and assessed considering realistic helicopter rotor flight conditions affected by significant BVI noise generation. Two different mono-flap controllers (located at 75% and 85% of the rotor blade radius, respectively) and a dual-flap one, aimed at controlling advancing- and retreating-BVIs, both separately and simultaneously, have been investigated. Moreover, a straightforward criterion for choosing the best controller, based upon a merit function taking into account both control effectiveness and power requirements, has been proposed and applied to choose the best control system. Numerical results have shown that: (i) the synthesized controllers are robust with respect to the model variation, when used in closed-loop control processes, (ii) the strategies devoted to the reduction of the advancing-BVI noise outperform those aimed at reducing the retreating-BVI, both in terms of effectiveness and power requirements, (iii) the advancing-BVI control through a dual-flap system is the most effective controller among those examined, ensuring the largest maximum BVI-noise reduction with limited power requirements. This numerical investigation, although preliminary, suggests that the proposed control approach seems to be really effective in reducing BVI noise, and hence appears to be promising for future implementation in real-life applications. However, more in-depth investigation aimed at further assessing control effectiveness and feasibility is deserved. For instance, the introduction of blade elasticity effects might increase the degree of accuracy of the high-fidelity aerodynamic–aeroacoustic simulations carried out for validation purposes, allowing to take into account the optimal control synthesis aspects related to vibratory loads, too.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: ENAC (Italian Civil Aviation Authority) provided funding for this study through a research grant.

References

Federal Aviation Administration. Stage 3 helicopter noise certification standards (77 FR 57524). USA: Federal Aviation Administration, 2012.

McHugh

and Shaw

Helicopter vibration reduction with higher harmonic blade pitch.

J Am Helicopter Soc 1978; 23, 26–35.

Hammond

CE.

Wind tunnel results showing rotor vibratory loads reduction using higher harmonic blade pitch.

J Am Helicopter Soc 1983; 28: 10–15.

Molusis

JA.

The importance of nonlinearity on the higher harmonic control of helicopter vibration. In: Proceedings of the 39th annual forum of the American helicopter society, 1983, pp. 624–647. Alexandria, VA: American Helicopter Society.

Morbitzer

Arnold

and Muller

Vibration and noise reduction through individual blade control experimental and theoretical results. In: Proceedings of 24th European rotorcraft forum, Marseille, France, 15-17 September, 1998.

Kessler

Active rotor control for helicopters: individual blade control and swashplateless rotor designs.

CEAS Aeronaut J 2011; 1: 23–54.

Chia

Padthe

and Friedmann

PP.

A parametric study of on-blade control device performance for helicopter vibration and noise reduction. In: Proceedings of 70th annual forum of the American helicopter society, Montreal, Quebec, Canada, 20-22 May, 2014.

Anobile

Bernardini

Gennaretti

et al . Synthesis of active twist controller for rotor BVI noise alleviation . J Aircr 2016; 21: 239–248.

Straub

Kennedy

Stemple

et al . Development and whirl tower test of the SMART active flap rotor. In: Proceedings of SPIE, Vol. 5388, 2004, pp. 202–212. USA: The International Society of Optical Engineering.

10.

Straub

and Hassan

AA.

Aeromechanical considerations in the design of a rotor with smart material actuated trailing edge flaps. In: American helicopter society 52nd annual forum, Washington, DC, USA, 4-6 June, 1996.

11.

Viswamurthy

SR and

Ganguli

Optimal placement of piezoelectric actuated trailing-edge flaps for helicopter vibration control.

J Aircr 2009; 46: 244–253.

12.

Modini

Graziani

Bernardini

et al . Parallel blade-vortex interaction modelling for helicopter rotor noise control synthesis. Int J Aeroacoust 2014; 13: 587–606.

13.

Modini

Graziani

Bernardini

et al . Parallel blade-vortex interaction analyses and rotor noise control synthesis. In: 19th AIAA/CEAS aeroacoustics conference (34th AIAA aeroacoustics conference ), Berlin, Germany, 26–29 May 2013.

14.

Modini

Graziani

Bernardini

et al . Synthesis of a rotor noise controller by parallel blade-vortex interaction aeroelastic modeling. In: ASME 2014 pressure vessels and piping conference proceedings, Vol. 4, PVP2014-28258, Anaheim, California, USA, 20–24 July 2014.

15.

Anobile

Bernardini

Gennaretti

Active twist rotor controller identification for blade–vortex interaction noise alleviation. 00 In: 19th AIAA/CEAS aeroacoustics conference (34th AIAA aeroacoustics conference), Berlin, Germany, 27–29 May 2013, AIAA paper 2013-2290.

16.

Anobile

Bernardini

and Gennaretti

Investigation on a high-frequency controller for rotor BVI noise alleviation.

Int J Acoust Vibr 2016; 21: 239–248.

17.

Palacios

Kinzel

and Overmeyer

Active gurney flaps: their application in a rotor blade centrifugal field.

J Aircr 2014; 51: 473–489.

18.

Kinzel

Maughmer

and Lesieutre

GA.

Miniature trailing-edge effectors for rotorcraft performance enhancement.

J Am Helicopter Soc 2007; 52: 146–158.

19.

Kentfield

JAC.

The potential of gurney flaps for improving the aerodynamic performance of helicopter rotors. In: AIAA international powered lift conference, AIAA-93-4883-CP, Santa Clara, CA, USA, 1-3 December, 1993.

20.

Modini

Graziani

Bernardini

et al . Analytical identification of blade-vortex interaction noise controller suited for miniature trailing edge effectors. In: AHS international’s 72nd annual forum, Palm Beach, Florida, 16–19 May 2016.

21.

Gennaretti

and Bernardini

Novel boundary integral formulation for blade-vortex interaction aerodynamics of helicopter rotors.

AIAA J. 2007; 45: 1169–1176.

22.

Bernardini

Gennaretti

and Testa

Spectral-boundary-integral compact-source formulation for aero-hydroacoustics of rotors.

AIAA J 2016; 54: 3349–3360. Vol.

23.

Ffowcs Williams

and Hawkings

DL.

Sound generated by turbulence and surfaces in arbitrary motion.

Philos Trans R Soc 1969; A264: 321–342.

24.

Farassat

Derivation of formulations 1 and 1A of Farassat. NASA TM-2007-214853, NASA 2007.

25.

Bernardini

Serafini

Gennaretti

et al . Assessment of computational models for the effect of aeroelasticity on BVI noise prediction. Int J Aeroacoust 2007; 6: 199–222.

26.

Gennaretti

Bernardini

Serafini

et al . Assessment of a comprehensive aero–acousto–elastic solver for rotors in BVI conditions. In: 43nd European rotorcraft forum, Milano, Italy, 12-15 September, 2017.

27.

Nakafuji

DTY

Van Dam

Smith

et al . Active load control for airfoils using microtabs. J Sol Energy Eng 2001; 123: 282–289.

28.

Johnson

Self-tuning regulators for multicyclic control of helicopter vibration. NASA/TP-1996, NASA 1982.

29.

Gennaretti

Molica Colella

Serafini

et al . Combined action of variable-stiffness devices and trailing-edge flap for helicopter hub loads reduction. In: 34th European rotorcraft forum, ERF34, The Royal Aeronautical Society, Vol. 3, 2008, pp. 2072–2092. Liverpool, UK.

30.

Molica Colella

Bernardini

G and

Gennaretti

Tiltrotor wing-root vibratory loads reduction through higher harmonic control actuation. J Aircr 2012; 49: 1813–1820.

31.

Gennaretti

Bernardini

Serafini

et al . Helicopter vibratory loads alleviation through combined action of trailing-edge flap and variable-stiffness devices. Int J Aerospace Eng 2015; 2015: 10.

32.

Testa

Bernardini

and Gennaretti

Aircraft cabin tonal noise alleviation through fuselage skin embedded piezoelectric actuators.

J Vib Acoust 2011; 133: 051009-1–051009-10.

33.

Bernardini

Testa

and Gennaretti

Optimal design of tonal noise control inside smart-stiffened cylindrical shells.

J Vibr Control 2012; 18: 1233–1246.

34.

Bernardini

Testa

and Gennaretti

Tiltrotor cabin noise control through smart actuators.

J Vibr Control 2016; 22: 3–17.

35.

Patt

Liu

and Friedmann

PP.

Rotorcraft vibration reduction and noise predictions using a unified aeroelastic response simulation.

J Am Helicopter Soc 2005; 50: 95–106.

36.

Splettstoesser

Niesl

Cenedese

et al . The HELINOISE aeroacustic rotor test in the DNW test documentation and representative results. DLR-Mitteiling, Cologne 1993.

37.

Brentner

Bres

Perez

et al . Maneuvering rotorcraft noise prediction: a new code for a new problem. In: AHS aerodynamics, aeroacoustics and test evaluation specialist meeting, San Francisco, CA, 23–25 January 2002.