NASA Contractor Report 181789 

Noise Produced by Turbulent Flow 

Into a Rotor: 

Theory Manual for Atmospheric Turbulence 

Prediction and Mean Flow and Turbulence 

Contraction Prediction 

(liASA-CX-78ll89) YOISB PRODUCED BT uag-2iu6a 

4URBUL&1ST PLOU IilTO A ROTOR: TEIBORY BAlOAL 

FOR ATEOSPRERIC PUBBULEIOCE PRBbXCTIOP AND 

EEAI PLOW UD TURBULBNCB COITBaCTIOO flnclas 

PBBDICTIOTI Final Report IUeited G3/71 0224022 

J. C. Simonich 

United Technologies Research Center 

East Hartford, CT 

Contract NAS1-17763 

June 1989 

NASA 

National Aeronautics and 

Space Ad mi nist rat ion 

Langley Research Center 

Hampton, Virginia 23665-5225 

-. 
CONTENTS 

INTRODUCTION 1 

LIST OF SYMBOLS AND NOMENCLATURE 2 

ATMOSPHERIC TURBULENCE PROPERTIES 5 

Input .......................................... 5 

output ......................................... 5 

Method ......................................... 5 

DISTORTION TENSOR CALCULATION 11 

Input .......................................... 11 

output 12 

Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

Mean Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . 14 

Turbulence Contraction Model . . . . . . . . . . . . . . . . . . . . . . . . . 17 

. . . . . . . . . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . 

REFERENCES 19 

i 
INTRODUCTION 

Turbulence ingestion noise is a significant part of the broadband noise produced by helicopters. This sound generation mechanism involves the interaction of the rotating blades 

and the unsteady upwash velocity vectors associated with the atmospheric turbulent eddies ingested by the rotor. The resulting noise exists in the presence of loading noise and 

thickness noise mechanisms. It is also additive to the rotor trailing edge noise and vortex 

interactions noise generation mechanisms which represent additional broadband acoustic 

sources. 

This module incorporates three separate models: an atmospheric turbulence model, a 

rapid distortion turbulence contraction model, and a non-isotropic turbulent inflow acoustic source model. Together they determine the atmospheric turbulence ingestion noise 

produced by a helicopter in flight. 

Inputs to the combined mean inflow and turbulence models are controlled by atmospheric wind characteristics and helicopter operating conditions. 

1 
LIST OF SYMBOLS AND NOMENCLATURE 

A 

B 

CT 

d 

- e 

fc 

g 

G 

H 

k 

k 

- k 

kE 

L 

LWX 

n 

P 

r2 

Constant in geostrophic drag law 

Constant in geostrophic drag law 

Rotor thrust coefficient = T/plrR'(fZR)' 

Zero plane displacement height, m, (ft) 

Unit vector along one of the three upstream or downstream axes 

Wavenumber energy spectrum = 

Coriolis parameter, 2w sin 8 

Gravitational acceleration, m/s2, (fi/s2) 

Geostrophic wind speed, m/s, (ft/s) 

General rooftop level, m, (ft) 

Wave number, radians/m, (radians/ft) 

von Karman constant 

Wavevec t or of turbulence 

Wave number defined by Equation 21 

Monin-Obukhov length = -"' sk& 3, m, (ft) 

Integral length scale = Jr Rww(r2)dr2, m, (ft) 

Direction of the principle normal to the streamline 

Exponent in mean velocity power law 

Displacement in x direction, m, (ft) 

a;; (k)da 

2 
R Rotor radius, m, (ft) 

w z w z+r,) RWW Cross correlation coefficient = ( J 

3(aO/atr Ri Richardson number = e(au/az) 

T Temperature, K, (R) 

T Thrust, N, (lbf) 

U Turbulence velocity fluctuation, m/s, (ft/s) 

U Local time mean velocity, m/s, (ft/s) 

Val Horizontal freestream velocity, m/s, (ft/s) 

u* Friction velocity = m, m/s, (ft/s) 

KO Vertical freestream velocity, m/s, (ft/s) 

VO Rotor induced velocity = .r&, C QR m/s, (ft/s) 

W Vertical velocity fluctuations, m/s, (ft/s) 

@/Urn RMS turbulence intensity 

xi Upstream Cartesian coordinate system 

Z Height above ground, m, (ft) 

20 Roughness length, m, (ft) 

ZT Tropopause height, m, (ft) 

a! 

r( ) Gamma function 

Rotor tip path plane angle of attack, degrees 

6 Boundary layer thickness, m, (ft) 

3 
Alternating tensor 

Geographic latitude, degrees 

Potential temperature, K, (R) 

Wavelength of Fourier component of turbulence, m, (ft) 

Rotor inflow ratio, = Umsina-VQ 

Rotor advance ratio = 

Density, kg/ms, (16rn/ft3) 

Downstream Cartesian coordinate system 

Temperature fluctuations, K, (R) 

Wall shear stress, N/m2, (16f/ft2) 

Nondimensional wind speed gradient = 

Spectrum tensor = 1 J-", exp(-ik - r)R,i(r)dr 

Wake skew angle = arctan [ U, -U, sina-Kl cos a 1, degrees 

Rotation rate, radians/s 

Vorticity field and magnitude of a Fourier component of turbulence. 

See Equations 24 and 25. 

RR 

kZ dU 

(2xl3 

Superscripts 

U and D Specify the upstream or downstream location 

Subscripts 

ij,k Specify either a vector (such as one of the vectors - el, -93 e2 e ) or a component 

of a vector (such as the first Cartesian component of the vector - 

e2) 

4 
ATMOSPHERIC TURBULENCE PROPERTIES 

Input 

Name Description 

G Geostrophic wind speed (m/s) 

L Monin-Obukhov stability length (m) 

e Geographic latitude (degrees) 

20 Roughness height (m) 

z Height above ground (m) 

(note: for neutral conditions, input 0.0) 

output 

Name Description 

G Geostrophic wind speed (m/s) 

LWX Correlation length scale (m) 

@/Urn Vertical component of the rms turbulence normalized by the free stream velocity 

Method 

The atmospheric boundary layer is a fully three dimensional flow with boundary conditions which change in both space and time. Heat transfer is important as are the Coriolis 

forces due to the earth’s rotation. The complexity of the flow renders a complete analytic description of the flow impossible. For these reasons, the description of atmospheric 

turbulence is still basically empirical. 

The model presented below was chosen after a review of the current literature on 

the topic and is viewed as representative of the present state-of-the-art in atmospheric 

turbulence prediction. Most of the correlations are from Snyder [l]. These were chosen 

since they were the only ones found which included non-adiabatic effects (i.e. a non-neutral 

atmosphere where heat transfer is important). 

In order to render the problem tractable, the following simplifying assumptions are 

made: 

1) The flow is stationary. 

2) The flow is homogeneous in any horizontal plane. 

5 
3) The flow is isotropic. 

For neutral conditions, the boundary layer thickness is assumed to be constant at 600 

m. For unstable conditions the boundary layer varies from 1 to 2 km during the course of 

a day. It is assumed here to be constant at 1500 m. For stable conditions, the boundary 

layer thickness is given by the following two equations: 

-1 6= [-+-+-I 1 fc 1 

30L .25U, 2, 

Equation (1) must be solved iteratively in conjunction with Equation (2) below to 

determine 6. 

The friction velocity, U*, is described by the “geostrophic drag law”: 

G, the geostrophic wind speed, is a horizontal equilibrium wind which blows parallel 

to atmospheric isobars. It represents an exact balance between the horizontal pressure 

gradient force and the horizontal component of the Coriolis force. Geostrophic wind scales 

give a good approximation to the actual wind in the free atmosphere. The magnitude of 

G is given by: 

where fc is the Coriolis parameter = 2 usin0 and vHp is the horizontal pressure gradient. 

A and B are described by “constants” which are a function of the stability condition 

of the atmosphere: 

1) Neutral Conditions 

A = 1.7 

B = 4.7 

6 

(3) 
2) Stable Conditions 

A = ln(b/L) - .96(6/L) + 2.5 

B = 1.15(6/L) + 1.1 

3) Unstable Conditions 

A = ln(-6/L) + (fc6/U,) + 1.5 

k 

B=- + 1.8(fc6/U,) exp(.26/L) few* 

(4) 

(5) 

Within the atmospheric boundary layer, there exists a sublayer, called the surface layer, 

where stresses and fluxes are nearly constant. This layer can be as thick as 150 m in neutral 

and unstable conditions, but can be as thin as 10 - 20 m under stable conditions. 

In the surface layer, the log law is valid and a description of the mean velocity profile is 

given by the following equations for neutral, stable, and unstable conditions respectively: 

1) Ne ut tal Conditions 

U 1 2-d 

u* k 

- = - In (7) 

where d = 0 for Zo < .2 m 

and d = H - Zo/k for 20 > .2 m 

2) Stable Conditions 

- u1 = - [In (i) + 71 52 

u* k 

3) Unstable Conditions 

(7) 

7 
Equations (6), (7), and (8) are undefined if 20 is zero. For an actual atmospheric 

boundary layer, the surface roughness is never zero. Typical values of surface roughness 

length vary from .01 cm for sand to 100 cm for a pine forest [l]. 

For neutral conditions, the integral length scale is a function of height only and is given 

by: 

L," = .42 (9) 

For stable atmospheric conditions, the following equation from Kaimal (21 is used: 

2 

R, 

Lwz = .015- for .05 < < .2 

where = Richardson number 

- ZIL 1+5Z/L for Z/L > O (11) - 

ZIL for Z/L < O (12) - 

For unstable conditions, no correlation is available which takes into account stability 

parameters. Therefore, Equation 9 for neutral conditions is suggested. Strictly, the models 

for the integral length scale are valid only for the surface layer, typically the lower 10 to 

20 percent of the boundary layer. 

Under the assumption of isotropic turbulence, all longitudinal integral scales are equal 

to each other, as are the lateral integral scales, i.e. 

LUX = LVY = LWZ = LU 

and 

Teunissen [3] has shown since all longitudinal correlations are equal and all lateral 

correlations are equal, and by the use of the continuity equation that: 

8 
Lu = 2Lv 

so that 

The vertical component of the rms turbulence intensity is given for neutral, stable and 

unstable conditions respectively by the following equations: 

1) Neutral Conditions 

where p = .24 + .096 log,, ZO + .016(logl0 20)~ 

2) Stable Conditions (and Neutral) 

= 1.25U, for ZJL > -.3 

3) Unstable Conditions 

for Z/L < -1 

(17) 

Since these correlations are strictly valid only for the surface layer, following Counihan’s (41 suggestion a linear interpolation is used between the value at the top of the surface 

layer (assumed to be 15% of the boundary layer thickness) to a value of .01 at the top of 

the boundary layer. 

For neutral conditions, the longitudinal and lateral turbulence intensities are approximately: 

9 
and 

For nonadiabatic atmospheric boundary layers, the horizontal velocity components do 

not obey Monin-Obukhov similarity (as the vertical velocity fluctuations do) and no simple 

formula to describe them exists at the present. 

The von Karman model is used to describe the energy 

1k4 E(k) = 

where 

spectrum for isotropic turbulence: 

(19) 

and 

10 
DISTORTION TENSOR CALCULATION 

NISO 

ISTR 

ITIME 

XMIN 

XMAX 

YMIN 

YMAX 

ZMIN 

ZMAX 

c1 

OR 

VO 

R 

v, 

RERROR 

AERROR 

dS 

a 

Input 

Note that either meters or feet can be used for input as long as the user is consistent 

throughout. 

NAME FUNCTION 

NSS Relative time step resolution (s) 

Number of streamlines to compute 

Flag for outputing a streamline for plotting 

0 for no output file 

1 for streamline file 

Flag for outputing a deformation file 

0 for no output file 

1 for deformation tensor file 

(Note: either ISTR or ITIME can be 1 but not both at the same time) 

Minimum streamline domain limit in X direction (program will stop 

if it attempts to compute outside of this domain) 

Maximum streamline domain limit in X direction, radii 

Minimum streamline domain limit in Y direction, radii 

Maximum streamline domain limit in Y direction, radii 

Minimum streamline domain limit in Z direction, radii 

Maximum streamline domain limit in 2 direction, radii 

Rotor advance ratio 

Rotor tip speed (rotational frequency time radius) 

Rotor tip path plane angle of attack, degrees 

Induced velocity at the rotor, m/s, (ft/s) 

Rotor radius, m, (ft) 

V component velocity to be added to the hover case to simulate 

vertical ascent or descent, m/s, (ft/s) 

Relative error allowed in ODE solver 

(recommended value = 1 .OE- 10) 

Absolute error allowed in ODE solver 

(recommended value = 1.OE-10) 

Delta distance between streamlines used to compute the deformation 

tensor, radii 

(recommended value = 1.OE-4) 

11 
RECPOL 

NX 

NY 

NZ 

x1 

x2 

Y1 

Y2 

z1 

22 

NR 

NT 

R2 

01 

02 

Coordinate specification trigger 

'P' for polar specification of streamline starting coordinates 

'C' for Cartesian specification of streamline starting coordinates 

Number of X coordinate specification points 

Number of Y coordinate specification points 

Number of Z coordinate specification points 

Minimum X for Cartesian specification, radii 

Maximum X for Cartesian specification, radii 

Minimum Y for Cartesian specification, radii 

Maximum Y for Cartesian specification, radii 

Minimum Z for Cartesian specification, radii 

Maximum Z for Cartesian specification, radii 

Number of radial specification points 

Number of angular specification points 

Maximum radius for polar specification 

Mimimum angle for polar specification, degrees 

Maximum angle for polar specification, degrees 

output 

NAME FUNCTION 

TITLE 60 character alphanumeric title 

NR 

NT 

IH 

TSAV 

U 

V 

w 

XTSAV 

YTSAV 

ZTSAV 

XSLl 

r 

YSLl 

Number of radial specification points 

Number of angular specification points 

Code for selection of nonhomogeneous case 

Vortex circulation strength, m2/s, (ft2/s) 

Streamline drift time, s 

(time for fluid particle to travel from upstream to rotor) 

Velocity component in x direction, radii/sec 

Velocity component in y direction, radii/sec 

Velocity component in z direction, radii/sec 

Downstream X coordinate of streamline in rotor plane, radii 

Downstream Y coordinate of streamline in rotor plane, radii 

Downstream Z coordinate of streamline in rotor plane, radii 

Downstream X coordinate of streamline in standard Cartesian 

coordinate system, radii 

(standard coordinate system has x,y plane parallel to horizon with x axis in flight direct 

Downstream Y coordinate of streamline in standard Cartesian 

coordinate system, radii 

12 
ZL1 

XSL2 

YSL2 

ZSL2 

USAV 

VSAV 

WSAV 

XlA1, ETC Deformation tensor 

Downstream Z coordinate of streamline in standard Cartesian 

coordinate system, radii 

Upstream X coordinate of streamline in standard Cartesian 

coordinate system, radii 

Upstream Y coordinate of streamline in standard Cartesian 

coordinate system, radii 

Upstream Z coordinate of streamline in standard Cartesian 

coordinate system, radii 

Upstream U velocity component, radii/sec 

Upstream V velocity component, radii/sec 

Upstream W velocity component, radii/sec 

If ISTR = 1, a file is created named SFILE which contains the coordinate specifications 

of the streamlines 

The output parameters are described below. 

TITLE 

NISO 

NSS 

XMIN 

XMAX 

YMIN 

YMAX 

ZMIN 

XPLOT 

YPLOT 

ZPLOT 

60 character alphanumeric title 

Number of streamlines computed 

Relative time step resolution 

Minimum X streamline domain limit, radii 

Maximum X streamline domain limit, radii 

Minimum Y streamline domain limit, radii 

Maximum Y streamline domain limit, radii 

Minimum Z streamline domain limit, radii 

X streamline coordinate, radii 

Y streamline coordinate, radii 

Z streamline coordinate, radii 

13 
Method 

Mean Flow Model 

To calculate the distortion of the atmospheric turbulence field as it convects towards 

the helicopter rotor, it is first necessary to describe the flow into the rotor. The mean 

flow field is needed to define the streamlines (particle paths), and these in turn are used 

in computing the change in vorticity and wavenumber between far upstream and the rotor 

disk. A necessary part of the mean flow model is thus a procedure for computing these 

particle paths. 

The method chosen to calculate the mean flow into the helicopter rotor is to model 

the helicopter wake by a series of ring vortices. A graphical representation of the model is 

shown in Figure 1. The overall flow is made up of the velocity field due to the superposition 

of twenty ring vortices plus an ambient velocity. The spacing is varied so that the vortices 

are placed closer together near the rotor disk (see Figure l), with the circulation per 

unit length (along the wake) constant. The vortices extend to approximately ten rotor 

diameters along the line of the wake. 

The wake skew angle, X, (the angle between the normal to the rotor disk and the wake 

boundary) is defined by : 

1 -v cos a 

V sin a - Vo 

X = arctan 

The strength of the vortices is found by matching the predicted induced velocity at the 

rotor face with the input value. 

From momentum theory for helicopter aerodynamics, the rotor induced velocity is: 

R RCT 

vo = 2@TF 

where 

u, cos a 

flR 1.1 = Rotor advance ratio = 

and 

U, sin a - V, 

RR 

X = Rotor in flow ratio = 

14 
As stated, the rotor wake is described by a series of twenty ring vortices, along the 

skewed centerline of the wake. The velocity field at any point is found from the summation 

of the velocity field due to the individual vortices. The potential velocity for a ring vortex 

is given by Kuchemann and Weber [5] and by Castles and De Leeuw [6]. The axial and 

radial velocity at any point may be expressed by: 

v, = - (AB+CDF) 27rxR 

v, = - (Ah + CDk) -r 

27rxR 

where 

A = K(7) - E(7) 

x-1 x+l 

B=- +- 

dl d2 

1 p,4(1_ 1 + x2 + z2 

X dl d2 

15 
dl = dz2 + (x - 

d2 = dz2 + (x + 

d2 - dl 

d2 + dl 

r= 

x = radial distance from the axis of the vortex ring nondimensionalized by the ring 

radius 

1; = axial distance from the plane of the vortex ring nondimensionalized by the ring 

radius 

K(r) = complete eliptic integral of the first kind 

1 da 

E(r) = complete eliptic integral of the second kind 

= Lrl2 dmsin2a da 

Given the helicopter operating parameters, the procedure described above can ,e used 

to compute the velocity at any station in the flow field. A streamline can then be computed 

by integrating the streamline equations: 

dx = Udt 

dy = Vdt 

dz = Wdt 

16 
where U, V, and W are the local time mean velocities in the x, y, and z directions. 

These are three, coupled, ordinary differential equations. Starting at a given station, 

these expressions can be integrated forward or backward in the time domain to predict the 

next streamline position. A computer subroutine, written by Shampine and Gordon [7] 

was used for numerical integration. This method uses a modified divided difference form 

of the Adams - Pece formulas and local extrapolation. It adjusts the order and step size 

to control the local error per unit step in a generalized sense. 

Turbulence Contraction Model 

A “Rapid Distortion Theory” approach has been adopted for calculating the evolution 

of the turbulent flow. Basically the analysis models the flow field in terms of a primary 

flow, induced by the rotor, which convects (and distorts) the vortex filaments which are 

used to represent the turbulence. The rapid distortion approach thus accounts for the 

inherently three-dimensional processes of vortex stretching and tilting, which can change 

both the frequency distribution and the intensity of the turbulence. 

The assumptions inherent in this approach are: 1) the turbulence intensity is small, 2) 

the overturning time for a turbulent eddy is much larger than the time for the distortion 

of the mean flow, and 3) the Reynolds’ number associated with the turbulence is large. 

The basic concept of the Rapid Distortion Theory is to relate the components of the 

vorticity at given locations along a streamline. In a linearized rapid distortion analysis, 

these streamlines (along which the fluid particles are tracked) are streamlines associated 

with the mean flow. Thus the vortex filaments are regarded as being convected by the 

mean flow. The velocities induced by the perturbation vorticity are therefore neglected in 

considering the deformation of the vortex filaments. 

A general turbulent velocity field for incompressible flow can be expressed as a distribution of vorticity superimposed on a potential flow field. For an inviscid constant density 

flow, vortex lines move with the fluid in which they are embedded. Thus any deformation 

of the fluid will distort the vortex lines and in a contracting stream, the vortex filaments 

will be stretched and tilted, affecting the velocities induced by the vorticity. 

The distortion of the vortex lines from one point on a streamline to another can be 

described by a deformation tensor. This deformation can be decomposed into a fluid 

rotation (3 quantities), the directions of the principal axes (3 quantities), and the amount of 

contraction or extension along each axis (3 quantities). Denoting the upstream coordinates 

by xi and the downstream coordinates by (j, the deformation tensor is denoted by ax,/a[,. 

The basic equation for the vorticity at any location in terms of the initial vorticity 

17 
contained by a given fluid particle is: 

or 

The deformation tensor is calculated using the streamline tracing procedure described 

above. Starting at a given point on the rotor face the equations describing the streamIine 

coordinates are numerically integrated to trace a streamline from the rotor face to a far 

upstream location, usually taken as three radii from the rotor hub. A second streamline 

starting a distance d& from the first is then also traced for the same length of time as the 

first. At the upstream end of these streamlines a vector is drawn from the end of the first 

streamline to the end of the second. This vector determines three of the nine components 

of the deformation tensor: dxl/d&, dxz/dc~, &3/8&. The process is repeated for two 

other streamlines displaced a distance d& and d& respectively from the initial one, to 

yield the other six components of the distortion tensor. 

18 
REFERENCES 

[ 11 Snyder, W.H., Guideline for Fluid Modeling of Atmospheric Dijfusion, Environmental 

Protection Agency, Fluid Modeling Report No.10, April 1981. 

[2] Kaimal, J. C., Turbulence Spectra, Length Scales and Structure Parameters in the 

Stable Surface Layer, Boundary Layer Meteorol., Vol. 4, pp. 289-309, 1973. 

[3] Teunissen, H.W., Characteristics of the Mean Wind and Turbulence in the Planetary 

Boundary Layer, UTIAS Review 32, University of Toronto Institute for Aerospace 

Studies, October, 1970. 

[4] Counihan, J., Adiatmtic Atmospheric Boundary Layer: A Review and Analysis of Data 

from the Period 1880-1972, Atmos. Envir., Vol. 9, No. 10, pp. 871-905, 1975. 

[5] Kuchemann, D. and J. Weber, Aerodynamics of Propulsion, McGraw-Hill, 1953. 

[6] Castles, W., Jr., and J.H. De Leeuw, The Normal Component of the Induced Velocity 

in the Vicinity of a Lifting Rotor and Some Examples of Its Application, NACA TR 

1184, 1953. 

[7] Shampine, L.F. and M.F. Gordon, Computer Solution of Ordinary Differential 

Equations: The Initial Value Problem, Freeman Pub., 1975. 

19 
REGION OF INTEREST 

VORTEX RINGS 

Figure 1: Schematic Diagram of Wake Model 

20 
Report Documentation Page a 

1. Report No. 

NASA CR-181789 

2. Government Accession No. 

J. C. Simonich 

19. Security Classif. (of this report) 20. Security Classif. (of this pagel 21. No. of pages 

Unclassified Unclassified 22 

9. Performing Organization Name and Address 

United Technologies Research Center 

East Hartford, CT 06108 

22. Price 

A0 3 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Langely Research Center 

Hampton, VA 23665-5225 

15. Supplementary Notes 

Langley Technical Monitor: Thomas F. Brooks 

Final Report 

3. Recipient's Catalog No. 

5. Report Date 

June 1989 

6. Performing Organization Code 

8. Performing Organization Report No. 

10. Work Unit No. 

505-6 3-5 1 

11. Contract or Grant No. 

NAS1-17763 

13. Type of Report and Period Covered 

Contractor Report 

14. Sponsoring Agency Code 

16. Abstract 

,n analytic study has been carried out to predict helicopter main rotor noise due to 

ngestion of atmospheric turbulence. The analysis combines several different mod- 

!Is that describe the fluid mechanics of the turbulence and the ingestion process. 

'his report covers two models, atmospheric turbulence, and mean flow and turbulence 

ontraction. The third model, covered in a separate report, describes the rotor acous- 

,ic model. 

,ortion turbulence contraction description to determine the statistics of the anisotropi 

,urbulence at the rotor plane. 

de which has been incorporated in NASA's ROTONET helicopter noise prediction pro- 

;ram. 

'he mean flow and turbulence statistics associated with the atmospheric boundary layer 

Lave been modeled including effects of atmospheric stability length, wind speed. and 

Jtitude. 

'ilaments (which represent the turbulence field) by a mean flow field due to the ro- 

,or inflow. 

7. Kev Words (Suggested bv Author(s1) 

The method incorporates the atmospheric turbulence model and a rapid disThis study provides the analytical basis for a modThe turbulence distortion process is modeled as a deformation of vortex 

-- I 18. Distribution Statement 

noise prediction, Unclassified - Unlimited helicopter noise, turbulence ingestion 

noise, rotor noise 

Subject Category 71 

.