Efficient prediction of ground noise from helicopters and parametric studies based on acoustic mapping

Accepted Manuscript Review Article Efficient prediction of ground noise from helicopters and parametric studies based on acoustic mapping Fei Wang, Guohua Xu, Yongjie Shi PII: DOI: Reference:

S1000-9361(17)30260-1 https://doi.org/10.1016/j.cja.2017.11.013 CJA 943

To appear in:

Chinese Journal of Aeronautics

Received Date: Revised Date: Accepted Date:

1 December 2016 23 June 2017 2 August 2017

Please cite this article as: F. Wang, G. Xu, Y. Shi, Efficient prediction of ground noise from helicopters and parametric studies based on acoustic mapping, Chinese Journal of Aeronautics (2017), doi: https://doi.org/10.1016/ j.cja.2017.11.013

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Final Accepted Version Chinese Journal of Aeronautics 28 (2015) xx-xx

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Chinese Journal of Aeronautics journal homepage: www.elsevier.com/locate/cja

Efficient prediction of ground noise from helicopters and parametric studies based on acoustic mapping Fei WANG, Guohua XU *, Yongjie SHI National Key Laboratory of Rotorcraft Aeromechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Received 1 December 2016; revised 23 June 2017; accepted 2 August 2017

Abstract

Based on the acoustic mapping, a prediction model for the ground noise radiated from an in-flight helicopter is established. For the enhancement of calculation efficiency, a high-efficiency second-level acoustic radiation model capable of taking the influence of atmosphere absorption on noise into account is first developed by the combination of the point-source idea and the rotor noise radiation characteristics. The comparison between the present model and the direct computation method of noise is done and the high efficiency of the model is validated. Rotor free-wake analysis method and Ffowcs Williams-Hawkings(FW-H) equation are applied to the aerodynamics and noise prediction in the present model. Secondly, a database of noise spheres with the characteristic parameters of advance ratio and tip-path-plane angle is established by the helicopter trim model together with a parametric modeling approach. Furthermore, based on acoustic mapping, a method of rapid simulation for the ground noise radiated from an in-flight helicopter is developed. The noise footprint for AH-1 rotor is then calculated and the influence of some parameters including advance ratio and flight path angle on ground noise is deeply analyzed using the developed model. The results suggest that with the increase of advance ratio and flight path angle, the peak noise levels on the ground first increase and then decrease, in the meantime, the maximum Sound Exposure Level (SEL) noise on the ground shifts toward the advancing side of rotor. Besides, through the analysis of the effects of longitudinal forces on miss-distance and rotor Blade-Vortex Interaction（BVI） noise in descent flight, some meaningful results for reducing the BVI noise on the ground are obtained. Keywords: Helicopter; Rotor noise; Second-level acoustic radiation model; Noise footprint; Acoustic mapping *Corresponding author. E-mail address: [email protected]

1. Introduction Although helicopters with the unique ability to take off and land vertically, hover as well as flexibly maneuver have been widely used, the high level of noise radiated by their rotors has drawn more and more attention. In particular, the unique Blade-Vortex Interaction (BVI) noise of helicopters in descent flight has a severe influence on ground objects. In the past, a lot of work on rotor noise analysis methods 1-3, noise-generating mechanism4 as well as acoustic properties5 have been done. However, researches on the rotor noise footprint prediction method and corresponding rotor noise radiation characteristics when the helicopter is in flight have barely been carried out. Commonly, the boundary integral method1-3 and Computational Aero Acoustics (CAA) method6 are used for the calculation of rotor noise. Given a unique spot of the helicopter, both methods are mainly used to calculate the rotor noise directly and generally cannot take the influence of atmosphere absorption into account. Whereas, for the

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prediction of ground noise radiated from a helicopter in flight, the calculation time will significantly increase and the demand of high computation efficiency ensues. This is because the flight path will contain lots of track points rather than one7, and for a better understanding of ground noise characteristics, an observer plane instead of one or several observers is used, which consists of numerous orderly distributed observers. Besides, impacts of atmosphere absorption8 on rotor noise have to be considered in the propagation of rotor noise. There will be excessive computations when applying the two aforementioned methods directly to the prediction of ground noise from an in-flight helicopter directly. Specifically, the CAA method itself not only has such problems as numerical dissipation but also need to compute the noise throughout the entire computation domain, which extends to ground observers, and the amount of calculation will increase dramatically with the increase of computation domain. Relative to the CAA method，the boundary integral method has a higher computation efficiency, where sound sources are computed using aerodynamic analysis models, and then near-field noise is propagated to far-field by the acoustic equation. However, the boundary integral method is not suitable for the calculation of dynamic ground noise from an in-flight helicopter due to the time-consuming computation of sound sources and radiation of noise radiated from rotating rotors in one period by solving the retarded time equation repeatedly9. Conner7 and Fleming10 et al conducted researches where an experiment based method was used to predict the noise footprint of a helicopter in flight. In the research, the measurement of ground noise of a helicopter in different flight conditions came first and then the database of radiation spheres was built, which projects inversely ground noise to the near field of rotors by the Acoustic Repropagation Technique (ART). Then in simulation of ground noise, the noise footprint was obtained by the projection of the corresponding radiation spheres extracted from the database when the helicopter “flied” along the flight trajectory rather than calculated from analysis models directly. This is what makes the method efficient. However, since the method is constrained by test conditions, the experiment based ground noise prediction technically and economically demands more, which is especially embodied in outfield noise tests where the ever-changing flight conditions and ambient atmosphere data need to be recorded continuously. In view of this, this paper attempts to develop a high-efficiency method for the simulation of noise footprint from an in-flight helicopter by employing the idea of radiation spheres. At first, a second-level acoustic radiation model capable of accounting for atmosphere absorption by the combination of the idea of point source and rotor noise radiation properties is built. The efficiency is improved by substituting a single stationary radiation point on the surface of the second-level radiation sphere in this model for surface radiation points rotating with blades. Secondly, the helicopter trim model is derived and the parametric modeling is performed. Furthermore, a database of radiation spheres taking advance ratio and Tip-Path-Plane (TPP) angle as characteristic parameters is generated. Then a notable improvement in computational efficiency is obtained by mapping the noise on the radiation sphere surface to ground observers in the ground noise simulation. In addition, the descent flight is taken as a numerical example, and the effects of different advance ratios and flight path angles on the ground noise are analyzed by using the method developed. On the basis of the analysis, meaningful results for descent trajectory with low ground noise are obtained. 2 Efficient prediction model of ground noise In order to predict the different time-variant characteristics and sound pressure level at various directions, a second-level acoustic radiation model that can account for spherical spreading and atmosphere absorption is built referring to the point-source theory11. On the basis of parametric expression of rotor noise derived from helicopter trim model, a high-efficient ground noise prediction model based on acoustic mapping is established. 2.1 Second-level acoustic radiation model In the prediction of ground noise from an in-flight helicopter, flight trajectory is discretized first. In this paper, the trajectory is discretized according to the distance traveled by helicopter over one rotor revolution, namely, 2πμR （ μ is advance ratio, and R is rotor radius）. The comparison between second-level acoustic radiation model and direct ground noise prediction method is sketched in Fig. 1. In general, the computation of ground noise is composed of the rotor aerodynamics prediction, rotor noise radiation as well as post-processing of ground noise. The efficient ground noise method is achieved by inserting the second-level acoustic radiation sphere between phase ① and phase ② in Fig. 1, from which the rotor noise is propagated. The Sound Exposure Level (SEL) in the figure is the weighted Sound Pressure Level （SPL）taking the effect of time exposure into account. In the figure, Γ MAX means the maximum bound circulation over a blade.

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Fig.1 Comparison of two ground noise prediction methods.

Corresponding to the discretization period of flight path, the mapping surface of acoustic radiation spheres representing acoustic energy radiated by a helicopter rotor over one rotor revolution is calculated. The zero degree in elevation angle direction is located in the tip-path-plane and the elevation angle will be negative blow the tip-path-plane. The zero degree in azimuth direction points toward the rear of helicopter. The radiation points on the radiation sphere surface are distributed with an interval of 5 ° in both the elevation angle and azimuth angle. The SPL is computed at every radiation point. The noise characteristics at different radiation points represent the noise radiation property in the corresponding direction. The mapping surface is located at 25R from the rotor hub. The distance insures that radiation sphere only captures far-field acoustic radiation (namely it insures that the attenuation of noise is linear with the increase of radiation distance without near-field noise). In the process of noise propagation, a line connecting the sphere center (namely rotor hub) to the ground observer represents the ray along which noise propagates from the helicopter rotor to the observer. The point of the intersection between sphere surface and the line represents the second-level sound source, whose noise will be mapped to the ground observer along the ray. The SPL at the ground observer can be expressed as:

L(r )  L(r0 )  Ageometry  Aatmosphere

(1)

where L(r ) is the SPL at the ground observer location r， L(r0 ) the SPL of the second-level radiation point r0， and Ageometry represents spherical spreading loss， Aatmosphere the atmospheric losses8。 As described in introduction, this paper focuses on the establishment of the efficient method and the research of rotor noise radiation characteristics of an in-flight helicopter. The observers are set to be on the ground. So, in the process of noise propagation, the effects of terrain conditions on noise are not considered. This is a conventional method that has been adopted by other researchers in Refs.12-14. The noise calculation of radiation points on mapping surface includes air-loading and noise radiation calculation. The free-wake method with rotor trimming is used to predict the aerodynamics. A schematic of rotor wake model15 is shown in Fig. 2. The rotor wake model is composed of near-wake and far-wake. The near-wake includes trailed vortices and shed vortices resulting from the differences of bound vortex strengths in spanwise and azimuthal direction respectively. The far-wake comprises only a single tip vortex filament which evolves from a roll-up of the near-wake detached from the trailing edge of blade after a revolve of 30 °. The motion equation of a vortex filament can be written as:

d r  , ζ   V  r  , ζ   dt where r  , ζ  defines the positions of control points,



age angle, t the time and V r  , ζ 





(2)

the azimuth at which the blade located,

ζ the wake

is the velocity of control points including free-stream and induced veloci-

ties from bound vortex as well as the other vortex filaments. The induced velocities are computed by Biot-Savart law with Scully vortex core model16 and an initial vortex core radius of 0.2c (c is blade chord).

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Fig.2 Schematic of rotor free-wake model.

To eliminate rotor pitching and rolling moments and match the calculated rotor thrust coefficient to the desired level, a rotor trimming model is presented, in which the difference correction of control angles is calculated using Newton-Rhapson iterative methods. The expression is as follows:

 CT  θ 0 Δθ0   Δθ    CMy  1c   θ Δθ1s   0  CMx   θ0 where,

C

cients.

 0 , 1c , 1s 

desire T

CT θ1c CMy θ1c CMx θ1c

1

CT  θ1s   CTdesire  CT  CMy       CMx  θ1s   CMy   CMx    θ1s 

(3)

, 0, 0  are the desired trim state.  CT , CMx , CMy  are the calculated thrust and moment coeffirepresents the adjustment of rotor collective and cyclic pitch angle. The subscript T,

Mx and My represents for the rotor thrust, x moment and y moment respectively. 1c and 1s represents for the first harmonic cosine and first harmonic sine. The rotor noise prediction comes after the calculation of rotor air-loading using the well-known Farassat 1A equation9 as follows:

p'  x, t   pT'  x, t   p'L  x, t  '

(4)

'

where pT and pL are the thickness and loading noise respectively, x the observation location vector, and t is the observation time. 2.2 High-efficiency prediction model for ground noise Previous studies17 reveal that under trimmed steady-state flights, the BVI noise is governed by four parameters: rotor thrust coefficient

CT , hover tip Mach number Maht , rotor tip-path-plane angle αTPP and advance ratio

μ . Fig. 3 shows the forces exerted on a helicopter under steady-state flight in the longitudinal plane.

Fig. 3 Schematic of forces exerted on helicopter.

Equilibrium equations of the helicopter in the longitudinal plane are given in Eq. (5).

 Fx: T sin(αTPP )  Df  H cos αTPP  W sin γ  0   Fy: T cos(αTPP )  H sin(αTPP )  W cos γ  0

(5)

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where T and H are rotor thrust and drag force respectively, Df and W the fuselage drag and helicopter

weight, and  denotes helicopter path angle. In descent, the H-force is negligible18. The rotor thrust is assumed to be equal to helicopter weight. Solving Eq.(5) yields the following expression for tip-path-plane angle:

D   =  f    TPP W  1  D  V 2 f f   2

(6)

where f represents equivalent flat plate area, ρ the air density, and V is helicopter velocity. It is observed that tip-path-plane angle is governed by helicopter fuselage drag, weight, velocity and flight path angle. From Eq. (6), the variation of tip-path-plane angle with advance ration for the AH-1 helicopter is shown in Fig. 4 for various flight angles. Descending flight tends to increase the tip-path-plane angle, while climbing flight tends to decrease the tip-path-plane angle.

Fig. 4 Tip-path-plane angle vs advance ratio for several flight path angles.

In descent, rotor thrust and hover tip Mach number are assumed to be constant in general and thus the governing parameters will be the advance ratio and tip-path-plane angle. A database of radiation spheres characterizing advance ratio and tip-path-plane angle is then prebuilt using the built aerodynamic method and noise equation. The database is shown in the right-hand side of Fig.5. In the computation of ground noise, the radiation sphere at every flight path spot will be selected from the database according to the flight state (advance ration and tip-path-plane angle). Then the ground noise is calculated by projecting the noise on the sphere to ground observers rather than calculated in real-time with analysis models. This is what makes the method efficient further. The flow chart of the ground noise calculation using the present method is depicted in Fig.5. The calculation procedure can be divided into three steps: First of all, the flight trajectory is discretized and the corresponding flight parameters

 μ, αTPP 

are calculated at each discretized point. Secondly, the radiation sphere is selected and ori-

ented by rotating an angle γ  αTPP . The radiation point is ascertained by connecting the discretized point to the ground observer and the corresponding noise is propagated to the ground. Finally, the post-processing of ground noise is conducted. In this figure, t1and t2 denotes different noise emission time, v denotes the helicopter velocity.

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Fig.5 Flow chart of high-efficiency ground noise computation.

3 Validation of calculation methods In order to validate the capability of the present wake models, Elliot et al’s experiment rotor 19 is first taken as a numerical example and induced velocities are compared. Then the BVI blade loads and noise are calculated on the well-known Operational Loads Survey (OLS) rotor and compared with available data17. By comparing the calculation time between the second-level acoustic radiation model and direct calculation method of noise, the high computation efficiency of the present model is verified. 3.1 Validation of free-wake model To verify the capacity of present free-wake in inflow prediction. The experiment data19 measured at the conditions with CT =0.008 , advance ratio μ=0.15 and μ=0.23 are used in this section. In the experiment, the inflow one chord above the rotor disk was measured and non-dimensioned with respect to the blade tip speed. The four-bladed rotor has a forward shaft tilt angle of 3 °. The blade has a linear twist of 8° from the root to tip, a radius of 0.86 m, and the aspect ratio is 13. Fig. 6 gives the comparisons of inflow ratio among the experimental data, the results by time-marching free-wake method in Ref.21 and the present calculation was given. In Fig. 6, the inflow ratio is calculated in rotor-fixed reference frame, where the x points to the rear of rotor.As is shown, the present results demonstrate better agreements with the experimental data when compared with the results by the time-marching method. The discrepancies of inflow in central regions may be caused by the presence of fuselage and rotor hub in experiment since the blockage effects of fuselage and rotor hub have not been simulated in the present method. Besides, the influence of “vortex-induced” upwash at the front of the rotor disk is also precisely predicted with the present method.

Fig. 6 Comparisons of inflow ratio across disk at different advance ratios.

The rotor used for BVI loads and noise validation is the two-bladed OLS rotor-- a 1/7 scale model of AH-1 helicopter main rotor. The blade has an aspect ratio of 9.22 and a linear twist of 8.2°. The simulation condition is

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as follows: an advance ratio of 0.164, thrust coefficient of 0.0054 and hover tip Mach number of 0.664. Table 1 gives control angles calculated by the present method, experiment17 and Ref.

 0 , 1s , 1c 

collective angle , longitudinal and lateral cyclic pitch angle.

20

.

0 ,1s ,1c 

represents for the

gives the coning angle, longitudinal

flapping and lateral flapping angle. Table 1. Control angles of OLS rotor

1c

0

1s

1c

0

1s

Experiment

6.14

1.39

0.9

0.5

0

1.0

Ref.20

6.07

2.37

1.2

0.5

0

1.0

Present

6.51

2.28

1.5

0.5

0

1.0

Blade motion

Fig. 7 shows the comparison of the predicted blade loads between the present method and other three methods （AFDD, DLR, ONERA） from Ref. 21 at 0.91R and 0.95R spanwise locations. L represents for magnitude of loads in the figure. It is shown that the predicted value by present method is intermediate compared with other results and has good agreements with them. In addition, the present method captures several BVI interactions on the advancing side, while the other methods only capture a single strong interaction.

Fig. 7 Comparisons of blade loadings at several spanwise locations.

3.2 Validation of noise prediction method The noise signal of OLS rotor at two observers are calculated in this paper under the same condition (as shown in Table 1). Both observers (as shown in Fig.8) are 3.44R away from the rotor hub, 30° below the rotor plane. Laterally, observers No.3 and No.9 are located at

  180

and

  210

respectively.

Fig. 8 Observation locations in radiation sphere.

The comparisons of sound pressure time histories at two different observations among predicted values, experimental data and results from Ref. 21 are presented in Fig.9. It can be seen that the present method has the capability of capturing two peaks of noise signals and a better agreement with the experiment data. But the method shows a little discrepancy with experimental results at non-dimensional observer time t *  0.2 , where the peak

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drop is not captured well.

Fig. 9 Comparisons of sound pressure time history at two observations.

3.3 Computational efficiency validation of second-level acoustic radiation model The comparison of calculation time between two methods when the helicopter is located at a specified spot is listed in Table 2. In this case, the number of the sound sources on blade surface is 18×28×201 (spanwise segments × chordwise segments × the number of points of pressure signature). It is necessary to calculate the noise radiated from all the sound sources with the direct calculation method of rotor noise. As a contrast, only one second-level sound source on the mapping surface of radiation sphere is needed to be calculated with the present second-level acoustic radiation method. Namely, noise of every observer was radiated from only one radiation point for the latter method, while noise of every observer was radiated from 101304 radiation points for the former method. As seen in Table 2, it takes only five minutes to calculate the ground noise with one hundred thousand observers compared to three hours by direct calculation method (operated on PC with Core i7、3.6GHz). It is concluded that the present method is high-efficiency when compared with direct computation method and the computation accuracy is almost the same. The conclusion remains unchanged even if the number of observers decrease dramatically (not shown). It should be pointed out that, although the efficiency can be greatly improved with second-level acoustic radiation method, the present method is not suitable for the computation of near-field observer. This is because that the radiation sphere will capture both near-field and far-field acoustic radiation, and the attenuation of noise will be nonlinear with the increase of radiation distance. The direct calculation method should be applied under the situation. Table 2 Comparison of computation time between two different methods. Methods

Present

Direct

Number of radiation points

1

101304

Number of observers

100000

100000

Computation time

5 min

3.2 h

4 Parametric studies and discussions

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In this section, the ground noise is simulated using the developed method and the effects of flight velocity and flight path angle on ground noise are analyzed on the AH-1 helicopter. The schematic of ground observer plane and flight trajectory is depicted in Fig. 10. The observer plane which has observers with an interval of 2.5 m in both directions extends to 60 m from the origin to either side of y axis and is 190 m in length along the x-direction. Flight trajectory is right above the centerline (y=0). To simulate the final stages of the approach, the helicopter will fly another 20 m. Three specified observers locating at the advancing/retreating side of rotor and below the flight trajectory are set to examine SPL time histories in different directions. In the subsequent parametric studies, both SEL contours on the ground and SPL time histories at three specified observers are calculated. In Fig. 11, the observer time is negative because the source emission time is stipulated to be zero when the helicopter arrives at the landing point (see Fig. 10).

Fig. 10 Schematic of helicopter trajectory and observer plane.

4.1 Effects of flight path angle The effect of flight path angle on ground noise is investigated and the results are plotted in Fig. 11. In Fig.11, the ground noise is calculated in ground-fixed reference frame, where the X points to the flight direction of helicopter, as shown in Fig.10. The SEL contours and SPL time histories are calculated for the approach flight with advance ratio of 0.164 as well as flight path angles of 0°, 6° and 9°. For all the cases shown in Fig. 11, it can be seen that: (1) The same noise variation trend at three observers is exhibited, where the SPL increases with the approach of helicopter and decreases with the departure of the helicopter. Observer B has the highest SPL value because of a closer proximity to the trajectory and thus a lower attenuation of atmospheric absorption as well as spherical spreading loss. Observer A has a higher SPL value than Observer C because the advancing side is the preferred propagated direction of BVI noise. (2) The SEL increases along the centerline (y=0) as the helicopter flies forward. The max SEL increases first and then decreases as the flight path angle increases, meanwhile the SEL gradually turns asymmetric about the ground centerline, namely, the max SEL contour shifts from the centerline to the advancing side (bottom-half of observer plane). For interpreting the above results, the noise radiation characteristics of helicopter rotor at one fixed location for three flight states are calculated and analyzed. In calculations, the required tip-path-plane angle can be obtained according to the relationship of tip-path-plane angle with flight path angle shown in Fig. 4. In the figure,  indicates the rotor rotation direction.

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Fig. 11 Ground noise for different flight path angles

In Fig. 12, the noise spheres with a radius of 25R radiated from a helicopter located at a fixed position are cal22 culated and projected by Lambert projection . The computational parameters are   0.164 and

TPP  1.5 ,4.5 ,7.5 . It is shown from Fig. 12 that the peak SPL exhibits a trend of increasing first and then decreasing with the increase of tip-path-plane angle, and the maximum SPL gradually shifts to the advancing side of the main rotor. This is why the SEL contours in Fig. 11 have a similar trend with that shown in Fig.12. The inflow as a function of the advance ratio for several flight path angles is depicted in Fig. 12(d). The inflow and advance ratio have been non-dimensioned by hover induced velocity of rotor. It can be seen that in level flight the inflow across the tip-path-plane is negative and thus rotor wake is blown downward. So, the miss-distance between blade and vortex is relatively large and the BVI noise is low. However, the inflow ratio (which is negative) is nearly zero with the steeper of flight path angle and the wake is not blown downward as strongly as level flight. At the same time, a steeper flight path tends to tilt the tip-path-plane in the nose-up direction. Both mentioned factors make the miss-distance decrease and thus the maximum BVI noise increase dramatically. Meanwhile, with the tilting back of the tip-path-plane, interactions on the rear side of the rotor disk are strengthened and the max SEL are radiated to the advancing side of the main rotor. But, the inflow across the tip-path-plane turns to outflow as the rotor disk tilts back further (flight path angle of 9°) and then the rotor wakes are blew toward the upper side of the tip-path-plane, leading to the increase of miss-distance and the reduction of BVI noise.

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Fig. 12 Radiation characteristics of rotor noise under different tip-path-plane angles and inflow ratio as a function of forward velocity.

4.2 Effects of advance ratio SEL contours on ground and SPL time histories at three specified observers for the approach flight with a flight path angle of 6° and several advance ratios are presented in Fig. 13. It shows the same trend, as mentioned in section 4.1, that the value of SEL increases along the centerline as the helicopter flies. The reasons are the same with section 4.1. The figures also indicate that the peak SPL exhibits a trend of increasing first and then decreasing with the increase of tip-path-plane angles. Meanwhile, the location of maximum SEL contours is changed with the increase of advance ratio from location Y=0 mm to location Y=5 mm then to location Y=10 mm. It means the maximum SEL shifts from ahead of rotor to the advancing side of the rotor. This is mainly because that the rotor wakes move to the rear of the rotor disk faster as the forward velocity is increased. Accordingly, the interactions at the rear of rotor disk are strengthened and thus, the BVI noise is radiated more toward the advancing side. However, with the further increase of forward velocity, the inflow turns positive gradually and the wake will move above the tip-path-plane, which is below the tip-path-plane initially. Therefore, the miss-distances will decrease first and then increase in an opposite direction, which makes the peak BVI noise exhibit a reverse trend.

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Fig. 13. Ground noise for different advance ratios.

4.3 Effects of longitudinal forces Based on the analysis above, it is noticed that BVI noise will increase as the rotor wake moves close to the tip-path-plane and decrease as the rotor wake moves away from the tip-path-plane. In this section, effects of x-forces and z-forces4 on miss-distances (thus BVI noise) are calculated and some conclusions are drawn. For the generation of x-forces and z-forces, the researchers in Ref. 4 had conducted some experiments on the longitudinal forces generation devices. It was found that Micro-Drag Generator (MDG) strip is an effective device to generate enough forces. The MDG strip is mounted around helicopter fuselage and the strip generate expected forces by controlling the jets. Previous studies23, 24 indicate that the region of strong BVI sources is located between 60°-70° and 0.8R-0.9R radius. In this paper, the miss-distance (vertical distance) between a free vortex element and the blade segment located at selected 0.8R from the rotor hub at 60° azimuth angle is computed for AH-1 helicopter where CT  0.0054 and   0.164 . As shown in Fig. 14, the vortex element, located initially on the edge of the front side of the rotor disk, moves along the path shown in the figure. The y coordinate of the particle holds because the speed in y-axis is negligible in approach flight when compared to the forward velocity and inflow velocity.

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Fig. 14 Schematic of vortex element convected path. The formula for the calculation of miss-distance is given in Eq.(7):

 z   λ     x  y μ

(7)

where λ represents rotor inflow; z coordinate is set to be perpendicular to the rotor disk and positive upward; x coordinate is positive toward zero azimuth angle. The rotor wake is above the rotor disk when the calculated z is positive and the rotor wake is below the rotor disk when the calculated z is negative. In the calculation of miss-distance, the rotor inflow is first calculated by the method built in Section 2; then, the miss-distance is obtained by integrating Eq. (7). The effects of x-forces on miss-distance for different flight path angles γ are shown in Fig. 15. The x-coordinate is the ratio of x-forces to helicopter’s weight and y-coordinate is the miss-distance non-dimensioned by rotor radius. It can be seen that the miss-distance will increase by adding the drag force (x-force is positive) when the flight angle is shallow. In this case, tip-path-plane will tilt forward to keep the balance of forces when extra drag force is added. Considering that the vortex particle is below the tip-path-plane initially (the negative displacement when x-force is zero as shown in the figure), the forward tilt leads to the increase of miss-distance. Conversely, the added thrust (x-force is negative) will tilt the tip-path-plane backward and thus decrease the miss-distance. For the steep descent ( γ =  9° ), the trend is the other way around. From these cases, it can be concluded that the miss-distance is changed owing to the tilt of the tip-path-plane for keeping the helicopter in trim after adding extra x-forces.

Fig. 15 Miss-Distance vs additional x-force.

On one hand, the miss-distance is related to tip-path-plane angle, while it is influenced by induced velocity across the tip-path-plane on the other hand. As a contrast, the effects of z-forces on miss-distances are also calculated for the flight angle of 8° in Fig. 16. The x-coordinate is the longitudinal forces as a fraction of helicopter weight and the y-coordinate is the same as in Fig. 15. The vortex is above the tip-path-plane before adding forces. It will move away from the tip-path-plane after adding z-forces (positive). This is because in order to keep the balance of forces in normal direction (as shown in Eq. (5)), the added z-force will reduce the rotor thrust and thus reduce the induced velocity18. By comparing the distance caused by the same magnitude of added x-force and z-force, adding x-force is a more effective way of changing miss-distance compared to adding z-force.

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Fig.16 Miss-distance vs longitudinal forces

The effects of longitudinal forces on miss-distance are analyzed above. Next, this paper analyzes the effects of longitudinal forces on BVI noise, taking the effects of z-forces on BVI noise as an example. The SPL contours of OLS rotor in different z-forces are presented in Fig. 17. The semidiameter of radiation sphere is 3.44R. The z-forces are 0.1W, 0.1W; and the corresponding coefficients are 0.00594 and 0.00486. By comparison, the difference value of the maximum SPL is 3 dB. It should be mentioned that adding z-forces is a less effective way to reduce rotor noise than adding x-forces. So, it can be concluded that modification of miss-distance by longitudinal forces is an effective means to reduce rotor noise.

Fig. 17 Effects of z-forces on BVI noise 5 Conclusion A high-efficiency method for the calculation of ground noise radiated from an in-flight helicopter is proposed. And the ground noise characteristics are analyzed for different advancing ratios and flight path angles by the method. Based on the analysis, effects of longitudinal forces (x-force and z-force) on miss-distances are studied. The effects of z-forces on BVI noise are calculated. The conclusions are as follows: (1) A significant enhancement in computational efficiency is obtained by two models. The first is second-level radiation sphere model, by which the noise from only one sound source is radiated. The second is the prebuilt database of radiation spheres. In the simulation of noise footprint, the radiation sphere is selected or interpolated from the database. The computational efficiency is improved further. (2) The peak SEL contours exhibit a trend of increasing first and then decreasing with the increase of both flight path angle and advancing ratio. Meanwhile, the peak SEL gradually shifts to the advancing side of the rotor disk because of the variation of miss-distance. (3) Adding helicopter drag or downward thrust leads to bigger miss-distances and thus lower BVI noise for a relatively shallow descent flight. For a relatively steep descent flight, the same result can be obtained by adding thrust either in X-direction or in z-direction. (4) The effects of z-forces on BVI noise are calculated. It is found that modification of miss-distance by longitudinal forces is an effective means to reduce rotor noise. (5) The method established in this paper can be used to study the rotor noise radiation characteristics of an in-flight helicopter. In the following study, the effects of terrain conditions on ground noise will be considered. Acknowledgements This study was supported by the Funding of Jiangsu Innovation Program for Graduate Education (No.

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