A review of rotating blade noise technology

Journal of Sound and Vibration (1971) 19 (3), 227-249

A REVIEW

OF ROTATING

BLADE NOISE TECHNOLOGYJ-

H. H. HUBBARD, D. L. LANSING AND H. L. RUNYAN N.A.S.A. Langley Research Center, Hampton, Virginia 23365, U.S.A. (Received 21 December 1970, and in revisedform 21 July 1971) Rotating blade noise is a topic of wide concern because it is the source of a variety of noise problems. These concerns range from safety, on the one hand, to community acceptability on the other. The purpose of this paper is to provide a general technical background for the problems of noise due to rotating blades. The topics to be covered are the following: the vehicles and components for which these problems are pertinent, the nature of the noise produced, the sources of the noise, concepts of noise generation, identification of the significant parameters in noise generation and reduction, and the methods of noise prediction. Both free rotors and ducted rotors are considered. In addition to the references cited in the text, this paper presents a bibliography of some of the more recent work (since 1968) in the areas of rotor and propeller noise, compressor and fan noise, and duct acoustics.

I. INTRODUCTION The nature of some of the problem in Table 1.

areas associated

with rotating

blade noise is indicated

TABLE 1 Blade noise problem areas Vibration of vehicle structures Damage to skin surfaces and frames Damage to attachments, brackets, tubing, etc. Malfunction of instrumentation and equipment Vibration of ground structures Noise transmission Induced vibrations Damage to brittle components Exposure of humans Annoyance Speech masking Hearing damage Vibration of vehicle structures is a well-known result of exposure of the skin surfaces of the vehicle to noise from the power plants [ 1,2]. The many loading cycles to which a structure is exposed due to the high-frequency noise can result in fatigue failure of the skin surface components and of the interior attachments such as hydraulic tubing, electrical wiring, and t Presented at the Aerodynamic Noise Symposium sponsored by the British Acoustical Society and the Royal Aeronautical Society at Loughborough University of Technology, Loughborough, England, 14-l 7 September 1970. 127 15

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H. H. HUBBARD, D. L. LANSING AND H. L. RUNYAN

so forth. It can also cause malfunction of electronic and sensitive mechanical equipment within the vehicle. Under certain conditions, building structures on the ground under the flight path can be caused to vibrate by aircraft flying overhead [3]. This may occur at low altitudes and low speeds in climbout from an airport and in landing approach to an airport. Such building vibrations are directly significant in subjective reaction, can result in transmission of noise to the building interior, may induce vibrations in various furnishings and hanging objects, and, in the extreme case, may damage some of the brittle components of the building, particularly those composed of plaster, tile, and glass.

@Iii@ Space

module

Saace

station

CTOL

General aviation

STOL

V/

High

speed

ground

transportation

STOL

Ground

effect

machine

Figure 1. Vehicles with rotating blade components.

Noise components from many rotating blade configurations are at frequencies which cause annoyance to people in the community or mask conversational speech or both [4]. In the extreme case hearing loss may be caused by short-term exposure to intense noises as, for instance, those experienced by aircraft ground crews, and by lower IeveIs over longer time periods as, for instance, those experienced by flight crews. Rotating blade noise is a main noise component for several different types of vehicles. Some of these are illustrated in Figure 2. Such vehicles as spacecraft and orbiting laboratories, jet aircraft of all types, helicopters, V/STOL aircraft, general aviation, and executive aircraft, ground-effect machines, and high-speed rail transport vehicles, all have onboard rotating blade systems. Such systems involve a variety of components such as rotors, propellers, fans, compressors, turbines, and impellers.

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REVIEW OF ROTATING BLADE NOISETECHNOLOGY

The above systems components vary markedly in their geometry and in their operating conditions from one application to another as indicated in Figure 2 and Table 2. Some of the components of interest are illustrated schematically in Figure 2. Both ducted rotors and free rotors are included. The ducted rotors include such components as multistage compressors and turbines of jet engines, the fan sections of turbofan engines, lift fans and Ducted

Fan-

Free

rotors

compressor-

turbine

iift

Ducted

fan

propeller

rotors

Main

Tail

rotor

Tilt

rotor

Propeller

rotor

Figure 2. Rotating blade components.

TABLE 2 Rotating blade dimensions and operating conditions Ranges of values <

Components Propellers Helicopter rotors Fans, compressors, turbines Space system impeders

Diameter Number Chord length Tip speed Power of blades (ft =0.3048 m) (ft = 0.3048m) (ft/s = O-3048m/s) (hp = 746 W) 2-6 2-6

0.3-l *o 0.3-2.0

15-80

0*05-0*5

2-10

0.02-0.05

5-12 5-70 0.5-g 0.05

500-1000 500-900

50-5000

500-1200

5&50000

200-400

0.1-l

50-10000

ducted propellers. The ducts are a significant factor in noise radiation and will be discussed in some detail later in the paper. The free rotors include such components as helicopter main rotors, helicopter tail rotors, wing-mounted tilt rotors, and propellers. The radiated noise is related in all cases to the geometry and the operating conditions of the rotors. The data of Table 2 indicate the ranges of dimensions and operating conditions for several types of propulsion system components. The ranges of blade number, chord length, diameter, tip speed, and power are listed for each. For instance, helicopter rotors and propellers have blade numbers from 2 to 6, blade diameters from about 5 to 70 ft (l-524 to 21.336 m), and

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H. H. HUBBARD, D. L. LANSING AND H. L. RUNYAN

blade chord lengths from a few inches to a few feet depending on their application. Fans, compressors, and turbines of jet engines, on the other hand, generally have a much larger number of blades and much smaller blade dimensions. Likewise, some high-speed impellers which are important noise sources in spacecraft life support systems can be as small as a fraction of an inch in diameter. The operating conditions for rotating blades also vary considerably. For instance, tip speeds can vary from low subsonic to supersonic and the associated power absorbed can vary from a fraction of a horsepower to several thousand horsepower. 2. ROTATING BLADE NOISE SOURCES Some of the characteristics of rotor noise can be illustrated by means of the example of a turbine-powered helicopter noise spectrum in Figure 3. Noise levels are plotted as a function of frequency and several different noise components are identified on the Figure. Main rotor harmonics begin at the low end of the frequency spectrum. Tail rotor harmonics show up at higher frequencies because of the higher shaft rotational speed. Although, for the sake of clarity, only a few of these harmonics are shown in Figure 2, measurements have been I

I

/Main

I

I

1

rotor harmonics II rotor harmonics

Frequency

(Hz)

Figure 3. Turbine powered helicopter spectrum.

Inflow

Figure 4. Rotating blade noise sources. Non-viscous blade loads: steady; fluctuating (periodic). Viscous blade loads: fluctuating (random and periodic), Aerodynamic flow.

made which show 50 to 100 such discrete harmonics. The turbo-shaft engine compressor noise occurs at still higher frequencies because of the combination of higher shaft speed and large number of blades. In addition, there is a broad spectrum of noise which extends from relatively low frequencies to the extreme frequency range of the measurements. Most of the various discrete frequencies are readily identifiable in this example spectrum, because of a knowledge of the geometries and rotational speeds of the components. Such identification, in most cases, may be difficult because of possible superposition of the frequencies. This is also true to some extent in the example spectrum since the random noise, for instance, may be a composite spectrum from several different sources. The sources of noise due to a blade moving through the air are categorized in Figure 4. These noise sources are related to the non-viscous loads on the blade, the viscous blade

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231

loads, and the aerodynamic flow, Noise arises from the non-viscous steady blade loads because of the fact that the blades are rotating and thus vary in distance periodically from the observer. This periodic distance variation results in characteristic noise frequencies. Non-viscous fluctuating blade loads may be due to several aerodynamic and mechanical phenomena which result in periodic load variations on the blade surfaces. The effects of viscosity in the airflow result in fluctuating blade loads which may be either random or periodic in nature. Although the aerodynamic wake may radiate noise directly into the surrounding medium, it is, in most cases, of secondary importance and will not be considered further in this paper. The relative importance of the steady loads and the fluctuating loads in noise generation depends on the geometry and the operating conditions of the blades.

Tim8

c

& -+ /

r

J’

/

t

0

-lx

--

-

/

Figure 5. Sources of steady loads. Torque, Q; thrust, T, coning,

C; thickness, t.

The sources of steady loads on a rotating blade, that is, loads which do not vary as a function of time or azimuthal position, are illustrated in Figure 5. These loads are related to the torque, which depends on the drag, to the thrust, the coning, and the thickness forces on the blade, and are represented by the vectors in the two sketches shown in the figure. The thrust vector is generally in the direction of the axis of rotation of the blade (z-axis), the torque vector is generally in the plane of rotation of the blade (xy-plane), and the coning vector, which is important only for helicopter rotors, is generally in the radial direction. All of these sources are dipole in nature and can be represented by force dipoles [5]. An additional steady force is that due to thickness which results in a displacement of the air as the blade moves through it (see lower right-hand sketch). This phenomenon can be represented by an array of monopole sources [6, 71. Fluctuating blade loads can be categorized broadly as periodic and non-periodic. The sources of fluctuating loads which vary periodically as a function of time are listed in Figure 6. Periodic loads may arise from such phenomena as variable in-flow direction and velocity to the rotor disk, potential field interactions, blade vibrations, mechanical unbalance of the rotor, cyclic blade controls and blade-vortex interactions as in helicopters, blade-vane interactions as in axial flow compressors, fans, and turbines, and localized critical Mach number effects. The non-periodic loads are those which vary in a random manner as a function of time or azimuthal position as indicated in Figure 7. These non-periodic loads are related to the viscosity effects of the air and arise from such phenomena as in-flow turbulence; blade

232

H. H. HUBBARD,

D. L. LANSING AND H. L. RUNYAN

boundary layers, including the effects of surface roughness; separated flows as in stall; and vortex shedding. The forces due to vortex shedding may be either random or nearly periodic, depending on the cross-sectional geometry of the blade, vane, or strut, and its operating conditions.

Time

Figure 6. Sources of periodic fluctuating loads. Variable inflow; potential field interactions; blade vibrations; mechanical unbalance; cyclic blade controls; blade-vortex interactions; blade-vane interactions; critical Mach number.

Ttme

Figure 7. Sources of non-periodic roughness); separated flows.

fluctuating loads. Inflow turbulence;

blade boundary layer (including

For some blunt-body configurations, it is possible to observe nearly periodic vortex shedding in certain Reynolds number ranges. On the other hand, for streamlined bodies such as thin airfoils, periodic vortex shedding is difficult to observe for any flow conditions. For rotating blades, the vortex shedding frequencies cover a broad spectrum.

3.

3.1.

ROTATIONAL

CONCEPTS OF FREE ROTOR NOISE GENERATION NOISE PREDICTION

The basic equation for the classical Gutin theory of propeller and rotor noise is shown in Figure 8. In this theory it is assumed that the blade load distribution does not vary with time, as indicated in Figure 5. An element of area in the rotor disk receives an impulse each time a blade passes. These impulses are represented by a distribution of pressure dipoles over the disk, properly phased to take into account the time interval between successive blade passages. The amplitudes of the dipoles are obtained from the rotor thrust and torque distributions. The sound field produced by the pulsating dipoles is periodic and can be analyzed into a series of discrete harmonics. The fundamental frequency is B!C2where B is the number of blades and J2 is the rate of rotation. The amplitude of the nth sound harmonic, P,(R,$), depends upon the rotor operating conditions and the observer position (R,a,h) as shown in the equation. The Bessel functionJ&BM, sin+) and the term cos$ are responsible for certain characteristic directivity patterns which will be discussed later in the paper. The Gutin theory was subsequently modified by Garrick and Watkins [8] to include forward speed. Noise radiation due to periodic variations of blade loading around the rotor disk was studied by Wright and Lowson [9, IO]. As indicated in Figure 9, a periodic, but not necessarily sinusoidal, variation in thrust or torque around the rotor disk can be represented as a Fourier

REVIEW OF ROTATING BLADE NOISE TECHNOLOGY

233

series of blade loading harmonics, TA in thrust and QA in torque, where A is the loading harmonic number. Each of these loading harmonics contributes to the sound field which can be expressed as a series of harmonics with fundamental frequency BL?. The formula at the bottom of Figure 9 is the expression for the amplitude of the nth sound harmonic.

Observer

Figure 8. Noise radiation due to steady blade loads.

where n - harmonic number, B - blade number, 9 = shaft speed, M, = tip Mach speed, T= thrust, Q = torque, & = effective radius and Jfis = Bessel number.

R

W

Observer

Figure 9. Noise radiation due to periodic blade loads.

The h = 0 terms in this series correspond to the Gutin theory. It is seen that the amplitude of a single sound harmonic depends upon all of the loading harmonics and upon the observer’s azimuth angle 0. Studies by Wright and Lowson indicate that the higher loading harmonics can be very efficient sound radiators which may completely overwhelm the noise due to the steady loads. This theory has received considerable attention in connection with helicopter noise radiation where it is applicable to such diverse phenomena as asymmetric loading due to forward flight, periodic vortex shedding, and periodic impulsive loadings such as could be due to blade slap. The dependence of the loading harmonics, Th and QA, on the operating conditions of a rotor is not well understood at the present time. From an analysis of limited experimental data, Lowson obtained an approximate trend for the amplitudes of TAand QAwhich seemed

234

H. H. HUBBARD, D. L. LANSING AND H. L. RUNYAN

to be valid for a wide range of operating conditions. However, this approximation is not universally accepted as the best compromise for all vehicles and flight regimes, and there are questions regarding the proper treatment of phase effects. Further experimental investigations involving simultaneous noise and blade loading measurements are clearly needed to resolve these questions. The blade loads associated with several types of operating conditions are shown in Figure 10. The solid curve represents an impulsive type of loading associated with blade slap. A non-impulsive but still rapid change in loading such as might result from sudden loss of lift during blade stall is indicated by the dashed curve. Also shown are a still more gradual lift variation suggestive of forward flight and a steady blade load which is independent of

Time

Figure 10. Sample fluctuating load time histories.

Blade

Forward

stall

speed

\ Frequency

Figure 11. Rotor noise radiation from fluctuating loads.

time. All of these various types of loading could occur at different times if the vehicle is operated in an unsteady flight condition. The blade loads shown here can be Fourier analyzed around the rotor disk to give the loading harmonic amplitudes Th and Q,+ An impulsive load will have many harmonics of nearly equal amplitude, whereas, at the other extreme, a steady load has only one harmonic, the constant term in the Fourier series. The loading harmonics can then be used to compute the radiated noise from the equation at the bottom of Figure 9. It appears from Lowson’s and Wright’s work that many Ioading harmonics may be necessary to accurately predict the higher sound harmonics. Calculated trends of the amplitudes of the radiated sound harmonics for the various blade loads of Figure 10 are shown in Figure 11 [l 11. An impulsive loading gives rise to a sound spectrum which increases at 6 dB per octave. The blade stall type of loading gives a flat spectrum and the forward tlight condition produces a spectrum which decreases at about 6 dB per octave. All three of the fluctuating loads are seen to predict sound harmonic amplitudes considerably higher than the steady load alone.

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BLADE NOISE TECHNOLOGY

235

Figure 12 contains schematic diagrams [l, 1l] of the rotational noise radiation patterns from several rotor noise sources. (Note that amplitudes are not necessarily to scale.) For all of the radiation pattern sketches, the rotor orientation illustrated in the upper left applies: that is, the axis of rotation is vertical and the plane of rotation is horizontal. The noise due to steady torque is a maximum in the plane of rotation and a minimum on the axis. Likewise, the noise component due to thickness is a maximum in the plane of rotation. The noise component due to steady thrust has a four-leaf-clover pattern, as illustrated in the lower left sketch. The sketch at the lower right indicates the changes in directivity that occur

_-_ _+_ _-_ +

_-*-

-+_

Steady torque

Thickness

Axes through

Unsteady thrust associated with motion

Figure 12. Rotor noise radiation patterns.

Harmonic number

Figure 13. Helicopter rotor rotational O----O, steady loads theory [5].

noise. E, Measured data; O-O,

fluctuating loads theory ill];

in the thrust noise pattern due to unsteady thrust forces on a rotor in sideways motion. These latter results suggest that the directivity patterns become distorted in the direction of motion, and the maximum amplitude is larger than for the steady thrust case. The example shown represents a mild asymmetry of the thrust loads. In many actual cases of rotors in forward motion, the loading asymmetries can be more pronounced and the resulting noise pattern is more distorted. An indication of the validity of the prediction methods of Figures 8 and 9 is given in Figure 13. Two sets of calculations of the noise levels for a helicopter in flight are compared with measured data. It can be seen that the calculated steady loads values are in best agreement at the lowest harmonic number but are markedly lower than the measurements at the higher harmonic numbers. On the other hand, the calculated unsteady loads values are in relatively

236

H. H. HUBBARD, D. L. LANSING AND H. L. RUNYAN

good agreement with the measurements over the range of harmonic numbers. It may be concluded that the steady loads theory is useful for predicting low-order harmonic noises that are most significant for structural problems but is not adequate for predicting the higher order harmonic noises that are most significant for subjective reaction. 3.2. BROAD-BANDNOISEPREDICTION The theories discussed in the preceding section have been concerned with both steady and periodic blade loads and with the associated periodic noises. As indicated in Figure 7, the viscosity of the medium can give rise to non-periodic blade load fluctuations which are random in nature. These force fluctuations are the principal sources of broad-band noise 112, 131. There are a number of methods for predicting broad-band noise levels for rotors based on a knowledge of gross geometric and operating parameters [14, 151. Predictions starting from a knowledge of the underlying physical phenomena will require use of methods from random process theory. Observer

Time

Figure 14. Noise radiation due to random blade loads. cm tj iX(t - R/c)

W,s4t)=~R

at

,

(1)

T

R,_(T)=,“;

-t

& j-L(t)L(t

+ T)dt,

(2)

-T

(3) P,m.s.(R,$4= UMW1’z.

(4)

The theoretical concepts appropriate to noise generation by random force fluctuations are indicated in Figure 14 for a simple two-dimensional airfoil [16]. If the wavelength of the radiated sound is large compared to the airfoil dimension so that retarded time effects can be ignored and if the fluctuating lift force is well correlated across the chord so that its integrated value L(t) may be considered to act at a single point, one obtains the simple relation in equation (1) between the instantaneous pressure P(R, 9, t) at the observer position (R, 4) and the total instantaneous lift L(t). Equation (2) of Figure 16 defines the autocorrelation of the lift RL(7) ; a similar expression defines the autocorrelation of the sound field &(T). Equation (3) shows the relationship between these two autocorrelation functions. If &(T) is known, the mean-square pressure at any point in the field can be obtained from equation (4). Additional complications arise if retarded time effects cannot be ignored or if correlation areas are small compared with blade areas. Broad-band noise from compressors, helicopters, and propellers involves random fluctuating force distributions on several rotating blades. The extension of these equations to account for rotation has been carried out by FfowcsWilliams [17]. Blade-to-blade correlation and modulation effects of rotation may then also become important. Application of these concepts to practical cases requires autocorrelation information which is difficult to measure.

REVIEW OF ROTATING

3.3.

BLADE NOISE TECHNOLOGY

237

ROTOR NOISE MEASUREMENTS

Noise from a free rotor is known to be a function of the geometry and operating conditions of the rotor. In order to illustrate the effects of some of the significant factors in rotor noise, the data of Figures 15-17 are included. These data were obtained from two-bladed helicopter rotors operating on a helicopter rotor test tower at various tip speeds and disk loadings. Noise measurements were made at stations on the ground at distances varying from 60 to 100 ft from the center of rotation. The noise data contain both discrete frequency and broadband components.

60 0

,

I

I

I

2

3

Disk

loading

(Ib/ft’=

479

4 N/m?

Figure 15. Tip speed and disk loading effects on rotor noise. Tip speed: H, 900 ft/s (274.32 m/s); W, 800 ft/s (243.84 m/s); A-A, 700 ft/s (213.36 m/s); O-O, 600 ft/s (182.88 m/s); B---U, 450 ft/s (137.16 m/s); o--o, 300 ft/s (9144 m/s).

50-

40

' ?O75

I 75150

I 150300

I 300600

1 6001200

/ I IZOO-2400-48002400 4800 1OooO

Octave

band

frequency

(Hz)

Figure 16. Effects of disk loading on rotor noisespectra. A ----A, Disk loading= 2.0 Ib/ft* (95.8 N/m*), blade angle = 14”; b-0, disk loading = 1.1 Ib/ft’ (52.7 N/m2), blade angle = 7’; 00, disk loading = 0.1 Ibift’ (4.79 N/m*), blade angle = 0.5”.

The data of Figure 15 are for a 52-ft (15.85 m) diameter two-blade rotor at a measuring point 60 ft (18.29 m) from the axis of rotation at ground level. It can be seen that both tip speed and disk loading affect the overall noise levels. For instance, at a given value of disk loading the noise levels decrease markedly as tip speed decreases, particularly at the lower disk loadings. Likewise, at any particular tip speed, the noise levels decrease as the disk loading decreases [ 181. The above disk-loading effect is further illustrated by the spectrum plots of Figure 16. These data were taken on a 37.5ft (1 l-43 m) diameter rotor for the same range of disk

238

H. H. HUBBARD, D. L. LANSING AND H. L. RUNYAN

loadings as for Figure 15. It can be seen that as the blade angles are increased to increase the disk loading, there are marked changes in the spectra. For instance, as the blade angle varies from 0.5” to 7”, the low-frequency noise components decrease and the high-frequency components increase in level. As the blade angle is further increased, spectrum levels of all frequencies increase. There is thus an indication that the different noise generating mechanisms discussed in Figures 4-7 may be important in the various frequency ranges.

Disk ioadlng Ub/ft2= 47.9 N/m2)

Frequency (Hz)

Figure 17. Effects of blade roughness on rotor noise.

The data of Figure 17 illustrate the effects on the noise generated, of the addition of roughness (sand particles) to the surfaces of the blades. The corresponding noise levels for both the roughened and the smooth blades as a function of disk loading are shown in the Figure. It can be seen that the addition of roughness results in about a 5-dB increase in overall noise levels over the range of disk loadings. The right-hand sketch of the Figure contains spectra obtained at points A and B, respectively, to indicate the effects of roughness on the radiated noise spectra. It can be seen that the spectrum levels are increased due to roughness over a wide range of frequencies and particularly at the lower frequencies. The addition of roughness seems to have eliminated some high-frequency flow-induced noise which was evident for the smooth blade. As in Figure 16, there is some evidence of the existence of more than one significant noise generation phenomenon.

4. INFLUENCES

4.1.

OF THE DUCT

IN THE ROTOR

NOISE PROBLEM

CONCEPTS OF DUCT PROPAGATION

If a rotor operates within a duct, additional phenomena are significant and must be taken into account. These phenomena result from the fact that the sound field is confined laterally. Under these conditions, the wave equation has solutions in the form of a discrete spectrum of eigenfunctions or modes [19-221. These modes are standing wave patterns of pressure across the duct which, once excited, propagate along the duct without change of form, but possibly with change in amplitude due to attenuation. The importance of the mode concept arises from the fact that the acoustic field generated in the duct by any source distribution can be represented as a linear combination of the modes. Hence, anything which influences the shapes of the modes or their attenuation also influences the transmission of sound along the duct and ultimately the sound radiated out through an inlet or exhaust. The primary factors which affect the shapes and attenuation of the modes in a duct due

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a sound source in the duct are listed in Figure 18. These are acoustic impedance of the walls, sound frequency, airflow in the duct, and cross-sectional area development. The principal effect of wall impedance is to increase the axial attenuation of the modes and hence to reduce sound transmission and radiation. In the presence of absorptive walls, the mode shapes are dependent upon the sound frequency. Cross-sectional area development affects the cutoff frequencies in the duct as well as mode shapes. An increasing cross-sectional area will enhance radiation by improving the impedance match between the interior and exterior of the duct. Airflow has several effects. Convection of the sound, which is present even in a uniform flow, produces the well-known Doppler shift in sound frequency and tends to decrease the attenuation due to a given wall impedance [23]. Refraction of the sound, such as takes place in a boundary-layer shear flow, can either bend the sound field toward or away from the walls, depending on whether the sound travels with or against the flow [24,25]. This behavior has a significant effect on the usefulness of acoustic liners. Some factors which determine how the acoustic energy of a source is proportioned among the various modes are listed at the bottom of Figure 18. Different types of sources such as monopoles, dipoles, and quadrupoles will excite a given mode with different amplitudes.

to

Figure 18. Duct mode considerations. Mode shapes and attenuation depend on: wall impedance: source frequency; air flow; cross-sectional area. Source-mode coupling depends on: source type; source distribution ; flow and wall impedance.

Modal amplitudes also depend upon the area or volume distribution of the source within the duct. In general, a mode couples strongly to the source when the pressure distributions in the mode and in the source are similar. When both airflow and acoustically absorptive walls are present, the modes are not orthogonal, and hence classical analytical methods for determining modal amplitudes are no longer applicable. An analytical model for the radiation of compressor and fan rotational noise from a circular duct with hard walls is shown in Figure 19. This model has been developed by Lansing [26] and is a generalization of Lowson’s work [27] on sound generation by rotorstator interactions in a free field. The duct has one open end which is unbaffled so as to resemble a type of jet engine inlet. The model gives an exact treatment of reflections at the open end and diffraction around the inlet lip. The increased complexity which comes about by taking the duct into account is apparent by comparing these equations with those for an unducted rotor as shown in Figure 9. in Figure 19, B and V are the number of rotor blades and stator vanes, respectively, M, is the tip Mach number; R, is the effective blade radius, Tk and Qk are the harmonics of the thrust and torque on the rotor, and the functions KY) (4 and K$!” (kcost,b) account for diffraction and reflection at the inlet. In the far field the pressure P,,(R, 0, #) in the nth sound harmonic involves a summation over all the loading harmonics. It can be seen that each loading harmonic excites an infinite series of duct modes although not all of these modes are efficient radiators. It has been found that the duct can have a significant influence on the radiated sound power and directivity of a source.

240

H. H. HUBBARD, D. L. LANSING AND H. L. RUNYAN

A number of other models which are under development for the radiation of sound from ducts are illustrated in Table 3. The motivation behind this work is an improved understanding of noise transmission in and radiation from the inlets and fan discharge ducts of turbofan engines. P. E. Doak developed an extensive theory based on a hard-walled rectangular duct of finite length with two open ends. The theory of Doak is being adapted to an annular

Observer

Figure 19. Noise radiation due to periodic blade loads in a duct.

v=nB-kV,

k = nBM,,

J:bm) = 0, 0, = 2/k_. TABLE 3

Duct configurations for compressor noise radiation

Investigator

Doak

Description

Finite rectangular duct

Finite annular duct

Martenson

Variable cross-section duct

Lansing

Circular-annular duct

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241

duct by H. E. Plumblee and his coworkers at Lockheed. This latter configuration represents an experimental facility being developed at the Lockheed-Georgia Company for detailed duct technology studies which will include shear flow and acoustic liners. A. 5. Martenson, of the General Electric Company, has developed a finite element representation of an axisymmetric duct of arbitrary cross section [23]. The boundary conditions, for either hard or soft walls, are satisfied at a set of discrete points over the duct surface. This approach avoids the constraints of simple cross-sectional and axial area developments. D. L. Lansing is developing a soft-walled annular-circular duct model which is representative of an acoustically lined long engine inlet duct with a large truncated center body. 4.2.

AERODYNAMIC CONSIDERATIONS

All of the models of Table 3 require, as input information, either a knowledge of the characteristics of the noise source or, equivalently, a knowledge of the pressure distribution across some section within the duct. Either of the above inputs is difficult to obtain in detail. As a first approximation, one can use the force predictions obtained from aerodynamic theories for unducted airfoils and cascades. As indicated in Figure 20, the rotating blades in a fan engine are clearly not in free space. Hence, it is possible that the complex environment

Figure 20. Compressor blade aerodynamics. Impedance presented to a blade depends on: presence of duct walls; presence of blade and vane rows, struts, splitters; acoustic liners and cavities; end reflections; air flow effects.

in which the blades operate may have significant interactions on the development of aerodynamic blade forces. Such effects are well known in acoustics and depend on the impedance presented to the blades. An analogous situation to the above is a sound source in a room for which the power output of the source is a function of the characteristic impedance of the medium, size and shape of the room, and the absorptivity properties of the walls. Similarly, the impedance presented to a pressure doublet used to represent aerodynamic forces on rotating blades will influence the manner in which the blade loads are produced. Some factors which determine the impedance presented to the doublet are the following: the presence of the duct walls, the presence of blade and vane rows, struts, and splitters, acoustic liners and cavities, end reflections, and airflow effects such as velocity, direction, and characteristic impedance of the air.

242

H. H. HUBBARD,

D. L. LANSING AND H. L. RUNYAN

An example of the effects of the duct walls on the development of oscillating aerodynamic forces is known as the “wind-tunnel wall effect”. This is an interference effect which arises from the fact that the pressure field produced by a dipole between reflecting walls consists of two parts: (i) the direct field of the source itself and (ii) the field of a series of images which represent the walls. The nature of wind-tunnel wall effects is shown in Figure 21 [28]. An

Air

flow

Cut-off

I,2

-‘y1 00

oooo

9

:

00

0.8

I

0

00

5

o-4

0

0.4

08

Ii

Frequency

ratio

Figure 21. Duct effects on oscillating airfoil aerodynamics.

-,

theory;

o, experiment.

airfoil spanning a hard-walled rectangular duct was oscillated in pitch through an angle of 1.2”. The ratio of the integrated lift and moment on the airfoil to that on the same airfoil in free-field conditions is plotted as a function of the ratio of the frequency of oscillation to the lowest cutoff frequency of the tunnel. It can be seen that as the frequency ratio approaches unity, the lift and moment on the airfoil section fall off markedly and then tend to increase again as frequency is further increased. Although it is not possible to generalize these results to the situation within a fan-jet engine, they do bear out the fact that at least in certain situations the development of blade forces depends significantly upon the impedance presented to the blade by the environment in which it operates. 4.3.

EFFECTS OF ACOUSTIC TREATMENT

Acoustic nacelle treatment has been found to be useful for alleviating fan engine noise. It has the advantage that it may be applied either in the development of new engines or in the modification of existing engines. This approach is illustrated in Figure 22 [4] which indicates the areas to which treatment might be applied to an engine. These areas include the inlet center body, concentric splitter rings, inlet wall, and all internal surfaces of the fan discharge ducts. Figure 23 shows some examples of the effects of wall impedance on mode shapes in a rectangular duct with one treated wall and no flow. The impedance was varied by varying the wall configuration as indicated in the sketches. The properties of the liner facing material and the characteristics of the air spring in the cavities behind the facing are significant in determining the impedance. The plots at the bottom of the figure show the amplitudes of the pressure across the duct from the untreated wall to the treated wall. All of these plots relate to the mode which would be a plane wave if all walls were untreated as in the left-hand plot. The plots show the substantial distortions produced on this one mode by different wall impedances. These changes in mode shape are important because they affect the ability of this mode to transmit sound from a given source.

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REVIEW OF ROTATING BLADE NOISE TECHNOLOGY

The mode shapes in a lined duct are also influqxed by the presence of flow. Figure 23 shows the effect of a uniform flow Mach number on the amplitude of the pressure in the “plane wave” mode in a rectangular duct with one treated wall. The wall impedance is held constant. The mode is propagating upstream, that is, from right to left in the sketch at the top of the figure. These calculations were made using the continuity of particle velocity form of the boundary condition at the absorptive wall. The flow has two effects on the mode

Concentric

rin

Nose

cowl

inlet

Figure 22. Duct acoustic treatment of fan-jet engine.

Untreated walls

Acoustic treotment+~]

L/i! s

0

0

d

Figure 23. Effect of wall impedance on duct

mode shapes.

shape, as can be seen in the sketches. As the Mach number increases, the pressure at the treated wall steadily decreases and the number of oscillations in the pressure distribution across the duct increases. At higher Mach numbers this “plane wave” mode resembles a high-order mode in an unlined duct and would tend to couple very weakly with a nearly uniform pressure distribution across the duct. On the other hand, as the Mach number increases, the mode axial attenuation decreases so that its sound transmitting efficiency increases. In this case, mode shape and mode attenuation play conflicting roles in sound transmission. 16

244

H. H. HUBBARD, D. L. LANSING AND H. L. RUNYAN

Air flow

d

Figure. 24. Effect of flow on mode shapes in a treated duct.

4.4. EFFECTS OF CROSS-SECTIONAL AREA DEVELOPMENT With the exception of the work done by Martenson and his associates on discrete point representations of ducts of variable cross section, most theoretical studies of sound radiation from ducts consider only simple cross-sectional shapes such as circles or rectangles, which do not vary along the length of the duct. This idealization is hardly representative of the actual cross-sectional area development of many turbofan engines.

0

I

Frequency

Figure 25. Comparison

2

ratio

of transmission efficiency of a conical (-)

and cylindrical (----)

duct.

Some calculations of the effect of increasing cross-section area on sound transmission in a duct are shown in Figure 25. The curves compare the transmission efficiency of several radial modes in a diverging conical duct with the efficiencies of the corresponding modes in a cylindrical duct with the same base area. The abscissa is the ratio of the frequency of excitation of a mode to the cutoff frequency of that mode in the cylindrical duct. As frequency increases, there is a steady rise in transmission efficiency until the cutoff frequency of the cylindrical duct is reached after which the efficiency decreases and eventually asymptotes the values for a cylindrical duct. A conical duct does not have an abrupt cutoff frequency, as does a circular duct. The duct acts as an impedance matching device which facilitates sound transmission at low frequencies. The cross-sectional area development at the inlet end of a particular research compressor is shown in Figure 26. Sound is generated by the rotating and stationary blades in an annular region bounded by the outer wall and a large center body. The cross-sectional area increases

REVIEW OF ROTATING

BLADE NOISE TECHNOLOGY

245

rather abruptly near the end of the center body. Sound then propagates down a long inlet section with steadily increasing area and is radiated from the end of the inlet whose radius is about twice that of the annular section. The sound transmission path from the point of generation to the point of radiation cannot be modeled by a simple circular or annular duct. Bell

inlet

Rotor-

stator

Figure 26. Inlet area of a research compressor.

Figure 27 shows a comparison of an experimental radiation pattern in front of the research compressor in Figure 26 with three theoretically determined patterns. The predominant rotor-stator interaction pattern consists of a single lobe rotating around the duct axis at a frequency of 10 000 Hz. The pattern based upon free-field rotor-stator interaction shows a very large number of individual lobes. The pattern based upon radiation from an annular duct with the same dimensions as at the rotor and stator vane location contains fewer lobes but still is not representative of the experiment. By far the best agreement is produced by considering the sound to radiate from the end of a circular duct with radius equal to that near the end of the bell mouth. These results show that the duct geometry has a strong influence on the directivity patterns of radiated noise and should be properly accounted for in any noise prediction method.

Free field

theory

Annular

duct theory

Circular

duct theory

Experiment

Figure 27. Radiation patterns for a research compressor.

5. CONCLUDING

REMARKS

A general discussion of rotating blade noise problems has been given. The vehicles and components for which these problems are pertinent, the nature of the noise produced, the sources of the noise, concepts of noise generation, identification of the significant parameters involved, and methods of prediction have been briefly discussed. Aspects which require more research have been identified.

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REFERENCES

1. E. J. RICHARDS~~~D. J. M~~~(Editors) 1968 NoiseandAcousticFutiguein Aeronautics. London: John Wiley and Sons Ltd. 2. W. J. TRAPP and D. M. FORNEY,JR (Editors) 1965 Proceedings of the Second International Conference, Dayton, Ohio, 29 April-Z May 1964, Syracuse University Press. Acoustical fatigue in aerospace structures. 3. H. D. CARDENand W. H. MAYER1970 (April) NASA TN D-5776. Measured vibration response characteristics of four residential structures excited by mechanical and acoustical loadings. 4. Conference held at Langley Research Center, Hampton, Virginia, 8-10 October 1968, NASA SP-189. Progress of NASA Research relating to noise alleviation of large subsonic jet aircraft. 5. L. GUTIN 1948 (October) NACA TM 1195. On the sound field of a rotating propeller. 6. A. F. DEMING1938 (December) NACA TN 679. Noise from propellers with symmetrical sections at zero blade angle, II. 7. K. N. DODD and G. M. ROPER 1958 (January) Royal Aircraft Establishment Technical Note No. M.S.45 (U. D.C. No. 533.662 (DEUCE)). A Deuce programme for propeller noise calculations. 8. I. E. GARRICK and C. E. WATKINS 1954 NACA Report 1198. A theoretical study of the effect of forward speed on the free-space sound-pressure field around propellers. 9. S. E. WRIGHT 1969 Journal of Sound and Vibration 9, 223-240. Sound radiation from a lifting rotor generated by asymmetric disk loading. 10. M. V. LoWsON 1966 Journal of Sound and Vibration 3, 454466. Basic mechanisms of noise generation by helicopters, V/STOL aircraft and ground effect machines. 11. M. V. LOW~~N and J. B. OLLERHEAD1969 Journal of Sound and Vibration 9, 197-222. A theoretical study of helicopter rotor noise. 12. E. Z. STOWELLand A. F. DEMING 1935 NACA Technical Note No. 519. Vortex noise from rotating cylindrical rods. 13. I. J. SHARLAND1964 Journal of Sound and Vibration 1, 302-322. Sources of noise in axial flow fans. 14. T. J. STUCKEYand J. 0. GODDARD1967 Journal of Sound and Vibration $50-80. Investigation and prediction of helicopter rotor noise. 15. R. G. SCHLEGELand W. E. BAUSCH1969 Journal of American Helicopter Society 14, 38-47. Helicopter rotor noise prediction and control. 16. P. J. F. CLARK and H. S. RIBNER 1969 Journal of the Acoustical Society of America (Part 2) 46, 802-805. Direct correlation of fluctuating lift with radiated sound for an airfoil in turbulent flow. 17. J. E. FFOWCS-WILLIAMS and D. L. HAWKINGS1969 Journal of Sound and Vibration 10, 10-21. Theory relating to the noise of rotating machinery. 18. H. H. HUBBARDand D. J. MAGLIER~1960 Journal of the Acoustical Society of America 32, 1105-l 107. Noise characteristics of helicopter rotors at tip speeds up to 900 feet per second. 19. P. M. MORSEand K. U. INGARD 1968 Theoretical Acoustics. New York: McGraw-Hill Book Company. 20. J. M. TYLERand T. G. S~FRIN 1962 Society of Automotive Engineers Transactions 70, 309-332. Axial flow compressor noise studies. 21. H. S. RIBNER (Editor) 1969 Aerodynamic Noise, Proceedings of AFOSR-UTZAS Symposium, Toronto, Canada, 2&21 May 1968. University of Toronto Press. 22. C. L. MORFEY1964 Journalof Soundand Vibration 1,60-87. Rotating pressure patterns in ducts: their generation and transmission. 23. P. MUNGUR and H. E. PLUMBLEE1969 NASA SP-207. Propagation and attenuation of sound in a softwalled annular duct containing a sheared flow. 24. P. MUNGUR and G. M. L. GLADWELL1969 Journal of Sound and Vibration 9, 28-48. Acoustic wave propagation in a sheared fluid. 25. D. C. PRIDMORE-BROWN 1958 Journal of Fluid Mechanics 4, 393-406. Sound propagation in a fluid flowing through an attenuating duct. 26. D. L. LANSING1969 Symposium held at Ames Research Center, Moffett Field, California, 28-30 October 1969, NASA SP-228,323-334. Exact solution for radiation of sound from a semi-infinite circular duct with application to fan and compressor noise. Analytic methods in aircraft aerodynamics. 27. M. V. LOWSON1969 (March) NASA CR-1287. Theoretical studies of compressor noise.

REVIEW OF ROTATING

BLADE NOISE TBCHNOLOGY

241

28. H. L. RUNYAN, D. S. WOOLSTON and A. G. RAINEY 1956 NACA Report 1262. Theoretical and experimental investigation of the effect of tunnel walls on the forces on an oscillating airfoil in two-dimensional subsonic compressible flow.

BIBLIOGRAPHY PROPELLER AND ROTORNOISE

1. F. B. MJZTZGER,B. MAGLIOZZI, G. B. TOWLE and L. GRAY 1969 Aerodynamic Noise, Proceedings of AFOSR-UTIAS Symposium, Toronto, Canada, 20-21 May 1968. University of Toronto Press. A study of propeller noise research. 2. J. W. LEVERTON1968 (October) NASA CR-1221. Helicopter noise-blade slap. Part 1: Review and theoretical study. 3. M. V. LOWSON and J. B. OLLERHEAD1969 (January) USAAVLABS Technical Report 68-60. Studies of helicopter rotor noise. 4. J. B. OLLERI-IEADand M. V. LOWSON 1969 Proceedings of AZAAIAHS VTOL Research, Design and Operations Meeting, Georgia Institute of Technology, Atlanta, Georgia, 17-19 February 1969, AZAA Paper No. 69-195. Problems of helicopter noise estimation and reduction. 5. S. G. SADLER and R. G. LOEWY 1969 (May) NASA CR-1333. A theory for predicting the rotational and vortex noise of lifting rotors in hover and forward flight. 6. S. E. WIDNALL 1969 Journal of Aircraft 6, 279-281. A correlation of vortex noise data from helicopter main rotors. 7. S. E. WRIGHT and J. W. LEVERTON1969 Proceedings Third Cornell Aeronautical Laboratories/ A VLABS Symposium on Aerodynamics of Rotary Wing and V/STOL Aircraft. Volume IRotor/Propeller Aerodynamics and Rotor Noise, Buffalo, New York, 18-20 June 1969. Helicopter rotor noise generation. 8. S. G. SADLER and R. G. LOEWY 1969 Proceedings Third Cornell Aeronautical Laboratories/ A VLABS Symposium on Aerodynamics of Rotary Wing and V/STOL Aircraft, Volume IRotor/Propeller Aerodynamics and Rotor Noise, Buffalo, New York, 18-20 June 1969. The importance of vortex shedding effects on helicopter rotor noise with and without blade slap. 9. R. J. KING and R. G. SCHLEGEL1969 Proceedings Third Cornell Aeronautical Laboratories/ A VLABS Symposium on Aerodynamics of Rotary Wing and VISTOL Aircraft. Volume IRotor/Propeller Aerodynamics and Rotor Noise, Buffalo, New York, 18-20 June 1969. Prediction methods and trends for helicopter rotor noise. 10. C. R. COX 1969 Proceedings Third Cornell Aeronautical Laboratories/A VLABS Symposium on Aerodynamics of Rotary Wing and V/STOL Aircraft. Volume I-Rotor/Propeller Aerodynamics and Rotor Noise, Buffalo, New York, 18-20 June 1969. Rotor noise measurements in wind tunnels. 11. J. E. MARTE and D. W. KURTZ 1970 (January) Jet Propulsion Laboratory Report No. 32-1462. A review of aerodynamic noise from propellers, rotors, and lift fans. 12. R. E. A. ARNDT and D. C. BORGMAN 1970 (June) 26th Annual National Forum Proceedings, American Helicopter Society Incorporated. Noise radiation from helicopter rotors operating at high tip math number. 13. R. H. SPENCER1970 (June) 26th Annual National Forum Proceedings, American Helicopter Society Incorporated. Application of vortex visualization test techniques to rotor noise research. 14. M. V. LOWSON 1970 Proceedings of Aerodynamic Noise Symposium, Loughborough University of Technology, Loughborough, England, 14-17 September 1970, Paper No. 0.2. Rotor noise radiation in non-uniform flow. 15. November 1970. Proceedings of the Joint Symposium on Environmental Effects on VTOL Design, Session II-External Noise and Downwash, Session V-Vibration and Internal Noise, University of Texas, Arlington, Texas, November 1970. 16. F. B. METZGER and T. G. GANGER 1970 (December) NASA CR-111842. Results of initial propfan model acoustic testing-Volume I. 17. R. H. LYON 1971 Journal of the Acoustical Society of America (Part 2) 49, 894-904. Radiation of sound by airfoils that accelerate near the speed of sound. COMPRESSOR AND FAN NOISE

1. C. L. MORFEY 1969 Aerodynamic Noise, Proceedings of AFOSR-UTIAS Symposium, Toronto, Canada, 20-21 May 1968, University of Toronto Press. A review of the sound-generating mechanisms in aircraft-engine fans and compressors.

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2. D. CHESTNUTT1968 (July) NASA Technical Note D-4682. Noise reduction by means of inletguide-van choking in an axial-flow compressor. 3. J. L. CRIGLER,W. L. COPELANDand G. J. MORRIS1968 (August) NASA TN D-4690. Turbojetengine noise studies to evaluate effects of inlet-guide-vane-rotor spacing. 4. M. V. LOWSON1969 (March) NASA CR-1287. Theoretical studies of compressor noise. 5. R. MANI 1969 Proceedings of Basic Aerodynamic Noise Research Conference, NASA Headquarters, Washington, D.C. 14-15 July 1969. NASA SP-207, 191-222. Some aspects of discrete frequency noise generation in axial-flow fans. 6. M. J. BENZAKEIN1969 Proceedings of Basic Aerodynamic Noise Research Conference, NASA Headquarters, Washington, D.C., 14-15 July 1969, NASA SP-207, 257-274. A study of fancompressor noise generation. 7. C. L. MORFEY1969 Proceedings of American Society of Mechanical Engineers Winter Annual Meeting, Los Angeles, California, 16-20 November 1969, Paper 69-WA/FE-4. Sound generation in subsonic turbomachinery. 8. N. J. LIPSTEIN and R. MANI 1970 Journal of Basic Engineering 92, 155-164. Experimental investigation of discrete frequency noise generated by unsteady blade forces. 9. J. B. OLLERHEADand C. L. MUNCH 1970 (April) NASA CR-1519. An application of theory to axial compressor noise. 10. S. KAJI and T. OKAZAKJ1970 Journal of Sound and Vibration 13,281-307. Generation of sound by rotor-stator interaction. 11. International Symposium on the Fluid Mechanics and Design of Turbomachinery, Pennsylvania State University, University Park, Pennsylvania, 3 September 1970. Session 7-Unsteady Flow and Noise. 12. B. BARRYand C. J. MOORE 1971 Journal of Sound and Vibration 17, 207-220. Subsonic fan noise. 13. N. CHANDRASHEKHARA 1970 Proceedings of the Aerodynamic Noise Symposium, Loughborough University of Technology, Loughborough, England, 14-17 September 1970, Paper No. E6. Sound radiation from random quadrupole source distributions in axial flow fans. This Paper has been published, in revised form, in Journalof Soundand Vibration 19,133-145, under the title “Sound radiation from inflow turbulence in axial flow fans”. 14. M. J. BENZAKEINand R. M. HOCHHEISER1970 Proceedings of American Society of Mechanical Engineers Winter Annual Meeting, New York, N. Y., 29 November-3 December 1970. Paper 70-WA/GT-12. Some results of fan/compressor noise research. 15. R. A. ARNOLDI 1971 (March) NASA CR-1743. Aerodynamic broadband noise mechanisms applicable to axial compressors. 16. U. BOLLETERand R. C. CHANAUD1971 Journal of the Acoustical Society of America (Part 1) 49, 627-638. Propagation of fan noise in cylindrical ducts. 17. B. D. MUGRIDGEand C. L. MORFEY1971 Proceedings of 81st Meeting of the Acoustical Society of America, Washington, D.C., 23 April 1971. Sources of noise in axial flow fans. DUCT ACOUSTICS 1. L. B. FELSENand H. Y. YEE 1968 Journal of the Acoustical Society of America 44, 1028-1039. Ray method for sound-wave reflection in an open-ended circular pipe. 2. E. J. RICE 1969 Proceedings of Basic Aerodynamic Noise Research Conference, NASA Headquarters, Washington, D.C., 14-15 July 1969, NASA SP-207, 345-355. Propagation of waves in an acoustically lined duct with a mean flow. 3. H. K. LIU and A. J. MARTENSON1969 Proceedings of Basic Aerodynamic Noise Research Conference, NASA Headquarters,

4. 5. 6. 7. 8.

Washington, D.C., 14-15 July 1969, NASA SP-207,425-434.

Optimum lining configurations. C. L. MORFEY1969 Journalof Soundand Vibration 9,367-372. A note on the radiation efficiency of acoustic duct modes. B. D. MUGRIDGE1969 Journal of Sound and Vibration 10,227-246. The measurement of spinning acoustic modes generated in an axial flow fan. V. MASON1969 Journalof Soundand Vibration 10,208-226. Someexperiments on the propagation of sound along a cylindrical duct containing flowing air. 1969 NASA Acoustically Treated Nacelle Program. A conference held at Langley Research Center, Hampton, Virginia, 15 October 1969. NASA SP-220. M. J. BENZAKEIN,R. E. KRAFT and E. B. SMITH 1969 Proceedings of American Society of Mechanical Engineers Winter Annual Meeting, Los Angeles, California, 16-20 November 1969.

Paper 69-WA/GT-11.

Sound attenuation

in acoustically treated turbomachinery

ducts.

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9. D. L. LANSING, J. A. DRISCHLER and C. G. PUSEY 1970 Proceedings of 79th Meeting of the Acoustical Society of America, Atlantic City, New Jersey, 21-24 April 1970. Radiation of sound from an unflanged circular duct with flow. 10. S. KAJI and T. OKAZAKI1970 Journal of Sound and Vibration 11,355-375.Propagation of sound waves through a blade row. II. Analysis based on the acceleration potential method. 11. 1970 Journal of the Acoustical Society of America (Part 3) 48, 780-842. Proceedings of a Symposium on Acoustical Duct Treatment for Aircraft. 12. W. EVERSMAN 1970 Journal of the Acoustical Society of America (Part 1) 48, 425-428. Effect of math number on the tuning of an acoustic lining in a flow duct. 13. P. E. DOAK and P. G. VAIDYA 1970 Journal of Sound and Vibration 12, 201-224. Attenuation of plane wave and higher order mode sound propagation in lined ducts. 14. R. AMIET 1971 Proceedings American Institute of Aeronautics and Astronautics 9th Aerospace Sciences Meeting, New York, New York, 25-27 January 1971, AZAA Paper No. 71-181. Transmission and reflection of sound by a blade row. 15. C. L. MORFEY1971 Journal of Soundand Vibration 14,37-55. Sound transmission and generation in ducts with flow. 16. L. S. WIRT 1971 Proceedings 8lst Meeting of Acoustical Society of America, Washington, D.C., 23 April 1971. Analysis testing and design of lined ducts. 17. P. HAREL and M. PERULLI1971 Journal of Sound and Vibration 15,455-474.The intluence of a stationary uniform axial flow on the propagation of acoustic modes of vibration in a cylindrical duct. 18. W. EVERSMAN1971 Journal of the Acoustical Society of America (Part 1) 49, 1372-1380. Effect of boundary layer on the transmission and attenuation of sound in an acoustically treated circular duct.