NASA Technical Memorandum 83199Part 2

Aircraft Noise Prediction Program

Theoretical Manual

William E. Zorumski

Langley Research Center

Hampton, Virginia

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CONTENTS

Part I*

I. INTRODUCTION ......................... I-I

2. AIRCRAFT FLIGHT DYNAMICS ........

2.1 ATMOSPHERIC MODULE .................... 2.1-I

2.2 GEOMETRY MODULE ...................... 2.2-1

2.3 FLIGHT DYNAMICS MODULE .................. 2.3-1

3. PROPAGATION EFFECTS

3.1 ATMOSPHERIC ABSORPTION MODUL2 ............... 3.1-1

3.2 GROUND REFLECTION AND ATTENUATION MODULE ......... 3.2-1

4. SOURCE NOISE PARAMETERS

4.1 FAN NOISE PARAMETERS MODULE ................ 4.1-1

4.2 CORE NOISE PARAMETERS MODULE ............... 4.2-1

4.3 TURBINE NOISE PAFJLMETERS MODULE .............. 4.3-1

4.4 JET NOISE PARAMETERS MODULE ................ 4.4-1

4.5 AIRFRAME NOISE PARAMETERS MODULE ............. 4.5-1

5. PROPAGATION

5.1 PROPAGATION MODULE .................... 5.1-1

5.2 GENERAL SUPPRESSION MODULE ............... . 5.2-1

6. RECEIVED NOISE

6.1 NOISE LEVELS MODULE .................... 6.1-1

6.2 EFFECTIVE NOISE .MODULE .................. 6.2-1

7. UTILITIES

7.1 ._"HEP_MODYNAMIC UTILITIES .................. 7.1-1

t

*Chapters I to 7 are published under separate cover.

iii

+

Part 2

8. NOISE SOURCES

8.1 FAN NOISE MODULE ..................... 8.1-I

8.2 COMBUSTION NOISE MODULE .................. 8.2-1

8.3 TURBINE NOISE .MODULE ................... 8.3-1

8.4 SINGLE STREAM CIRCULAR JET NOISE MODULE .......... 8.4-1

8.5 CIRCULAR JET SHOCK CELL NOISE MODULE ........... 8.5-1

8.6 STONE JET NOISE MODULE .................. 8.6-1

8.7 DUAL STREAM CCANNULAR JET NOISE MODULE .......... 8.7-1

8.8 AIRFRAME NOISE .MODULE ................... 8.8-1

8.9 SMITH AND BUSHELL TURBINE NOISE MODULE .......... 8.9-1

9. PP_DICTION PROCEDURES

9.1 ICAO REFERENCE NOISE-PP/EDICTIO:_ PROCEDURE (!978) ..... 9.1-1

iv

8. NOISE SOURCES

8.1 FAN NOISE MODULE

INTRODUCTION

l_ne Fan Noise Module predicts the broadband noise and pure tones for

an axial flow compressor or fan. The method is based on the method devel-

oped by M. F. Heidman (ref. 1). The method emploTs empirical functions to

predict the sound spectra as a function of frequent/ and polar direcrivity

angle.

The total fan noise is predicted by summing the noise from six sepa-

rate components. The six component sources selected are inlen broadband

noise, inlet rotor-stator interaction tones, inlet flow distortion tones,

combination tone noise, discharge broadband noise, and discharge rotor-

stator interaction tones. All noise sources are combined into a single

i/3-octave-band spectrum for each directivity angle.

The method requires input of several parameters. The fan entrance

and exit flow parameters can be provided by the Fan Noise Parameters

Module or directly by the user. Additional user-provided parameters are

required. The module is executed once for each set of values of the input

parameters. The output is a table of the mean-square acoustic pressure as

a function of frequency, polar directivity angle, and azimuthal direc-

tivity angle. Although fan noise is assumed not to vary with azimuthal

directivity angle, it is introduced so that the output table is compatible

widn other noise tables.

A

A e

a,b

B

C

Zoo

D

d

F

f

SYMBOLS

fan inlet cross-sectional Area, m 2

engine reference area, m 2 (ft 2)

exponents

number of rotor blades

mean rotor blade chord, m (ft)

ambient speed of sound, m/s (ft/s)

directivity function

fan rotor diameter, m (ft)

pc_er function

frequency, Hz

(ft 2 )

8.1-1

fb

G

i

K

k,£

Md

M r

M t

M

m

N

N e

n

<p2>"

Pref

r s

r*L

S

S

T

V

blade passing frequency, Hz

constant matrix

inlet guide vane index

constant

inlet flow distortion indices (eqs. (lO) and (ll))

fan rotor relative tip Mach number at design point

design point Mach number index, max (l,Md)

fan rotor relative tip Mach number

fan rotor tip Mach number

flow Mach n,m_ber

aircraft Mach number

mass flow rate, kg/s (slugs/s)

rotational speed, Hz

number of engines

tone harmonic number

mean-square acoustic pressure, re o2c 4

reference pressure, 2 × 10 ..5 Pa (4.177 _ 10 -7 Ib/ft 2)

distance from source to observer, m (ft)

source to observer, re _edimens icnless distance from

tone _pectr_m function

roter-stator spacing, m (ft)

total temperature rise across fan, K (oK)

ambient temperature, K (°R)

n_n%oer of stator vanes

cut-off factor

frequency parameter

polar /irect_vlt'_" angle, deg

_.I-2

.-

J

, J,

_ref

O_

acoustic power, re p c_A

reference power, 1 x 10 -12 W (7.376 x 10 -13 ft-lb/s)

ambient density, kg/m 3 (ib/ft 3)

azimuthal directivity angle, deg

Superscript:

* dimensionless quantity

INPUT

The fan parameters are required from either the output of the Fan

Noise Parameters Module or the user. Ambient conditions are required for

computation of sound pressure levels. The frequency, polar directivity

angle, and azimuthal directivity arrays establish the independent variable

values for the output table. The fan inlet cross-sectional area, number

of rotor blades, number of stator vanes, inlet guide vane index, inlet

flow distortion index, fan rotor diameter, fan rotor tip relative Mach

number at design point, and rotor-stator spacing are required for the geo-

metric description of the fan. Finally, the engine reference area, number

of engines, and distance to the observer are required. The range and

default values of the input parameters are given in table I.

A e engine reference area, m 2 (ft 2)

H e number of engines

Sdistance from source to observer, m (ft)

t

A

3

d *

I

Md

tS

V

Fan Geometry

fan inlet cross-sectional area, re A e

number of rotor blades

rotor diameter, re _efan

inlet guide vane index

fan rotor relative tip Mach number at design point

inlet flow distortion index

rotor-stator spacing, re C

n_._nber of stator vanes

8.1-3

e

N*

AT*

C

P_

Fan Noise Parameters

mass flow rate, re O_c_A e

rotational speed, re c /d

total temperature rise across fan, re T

Ambient Conditions

ambient speed of sound, m/s (ft/s)

aircraft Mach number

ambient density, kg/m 3 (slugs/ft 3)

Independent Variable Arrays

frequency, Hz

polar directivity angle, deg

azimuthal directivity angle, deg

OUTPUT

The output of this _nodule is a table of the mean-square acoustic

pressure as a function of frequency, polar directivity angle, and azi-

muthal directivity angle. In addition, the pseudo-observer distance r s

is provided for the Propagation Module.

r s distance from nozzle exit to pseudo-observer, m {ft)

Fan Noise Table

f frequency, Hz

9 polar directivity angle, deg

O azimuthal directivity angle, deg

<p2(f,9,,)>"2 4

mean-square acoustic pressure, re D c

METHOD

The prediction methodology presented in reference 1 is used to com-

pute the far-field noise. A schematic of a typical fan is shown in

figure i. The coordinate system and directivity angles are also shown.

The general approach for the prediction method is presented. Then, the

detailed prediction for each fan noise component is discussed.

8.1-4

J

The equation for the far-field mean-square acoustic pressure for a

fan is

<p2>* = A'Hi D(@) S(_)

4_I(rs )2 (i - M cos @)4

(1)

In equation (i), H* is the overall power, D is the directivity func-

tion, and S is the spectr,-- function. The source to observer dis-

tance r s is expressed in dimensionless form as

(2)

The forward velocity effect is accounted for by the Doppler factor,

(i - M cos 0)4. The frequency parameter _ is defined as

f

= (I - M cos @)f--b(3)

where the blade passing frequency fb is

N*Bc

fb = diA_e

The acoustic power _*_ for _he fan is expressed as

(4)

.L = K G(i,j) (si)-a(k' [)Mb(m*/A*) (.ST*) 2 F (Mr,M m) (5)m

Equation (5) contains several empirical constants and the empirical Dower

function F. The constant K is different for each noise component. The

constant G depends on the noise component and the indices i and j

defined as

and

Ii (Fan with no inlet guide vanes)

i = (6)

(Fan with inlet guide vanes)

i (_ > 1.05)j : (7)

(5 <-1.05)

8.1-5

/jr

The fuandamental tone cut-off factor 6 is defined as

M t

11where the fan rotor tip Mach number M t is

(8)

M t = WN* t.9)

If M t > 1.05, then _ = M t. The fundamental tone cut-off occurs when the

value of 0 is less than 1.05. The cut-off factor determines the range

of the tip Mach number where the fundamental blade passing frequency

dominates.

The rotor-stator spacing exponent a(k,£) depends on the noise

component and _he indices k and £ defined as

and

i ('-* _ i)

k = (I0)

(s* > i)

Ii (No inlet flow distortion)

[ = (Ii)

(Inlet flow distortion)

Inlet flow distortion tends to reduce rotor-stator spacing effects.

Inlet fl_w distortion is assumed to occur during static and ground roll

o_eratlons.

The design point Mach n_unber index M m is defined as

:_ = max (I,._d) (12)

where M d is the design value of the relative tip Mach number. The

exponent b in equation (5) gives the effect of [_m on each fan noise

component.

The final empirical quantity in equation (5) is the power func-

t&on F. _'_.e power function depends on the fan noise source and is, in

_ ofgeneral, _ _unc__on the relative tip Mach number M r and the design

point Mach n_ber indux. .-h.e relative tip Mach number is defined as

Mr x(13)

8.1-6

wherethe tip Machn_mberMt is defined by equation {9) and the axial

flow Mach number M x is equal to m*/A* since the inlet static density

and speed of sound can be assumed equal to the ambient values.

As indicated by equation (I), each fan noise source has its own

directivity function D and spectrum function S. Using these functions

and the acoustic power, the mean-square acoustic pressure is computed as

a function of frequency and polar directivity angle for a given set of

input parameters. The broadband noise is expressed as I/3-octave-band

data. The pure tones are values at discrete frequencies. The pure tones

must be added to the appropriate I/3-octave band so that a total

i/3-octave-band fan noise spectrum is determined. For a given value of

the i/3-octave-band center frequency parameter _ the lowest harmonic

number that falls within that band is

n£ = [lO-1/2o n] + i (14)

and the highest harmonic number is

nu = [lOI/2° n] (15)

where [ ] indicates the integer part of the enclosed real nu_.ber, if

n% > _u' then there is no tone within the band. If n[ -< nu, then there

are n u - n Z + i tenes within the band. The pure tone mean-square pres-

sures for each harmonic Dumber n are then added to the appropriate band.

The tones are propagated to the observer as I/3-octave-band data.

The empirical constants and functions used to compute the acoustic

._ower for t_e six fan noise components are summarized in table II. The

directivit 7 and spectrum functions are summzarized in tables III and IV,

respectively. Each fan ncise component is discussed in detail as

follows.

inlet Broadband Noise

Inlet broadband noise is associated with random unsteadines_ or

turbulence in Lhe flow passing the blading. Some of _he sources of this

random unsteady flow are turbulence in boundary layers, blade w_<es and

vortices, and _ne inlet flow. Although predictions of the individual

sources of broadband noise are beyond _he scope of this module, the total

broadband noise radiated from the inlet is predicted.

The acoustic _ower due to broadband noise from the inlet is

-" (1.552 ( 10 -4 ) (s*) "'_(k'/) _ "= M'(m'/A') (_T*) 2 F(M r) (16)m

8.1-7

--'W

where the constant a(k,£) is

(17)

The exponent a defined by equation (17) accounts for the fact that the

acoustic power varies inversely with the rotor-stator spacing except where

inlet flow distortion effects dominate rotor-stator spacing effects at

s > i. The power function F is

i (Mr -< 0.9)F = (18)

O. SLMr2 (M r > 0.9)

l4

i

which is plotted in figure 2.

The mean-square acoustic pressure due to inlet broadband noise is

computed from equation (i). The directJvity function D is given in

table III and plotted in figure 3. The spectral function 3 is given by

S = 0.116 exu -0.5 (n/2.5)_ (19)" in

where _ is the geometr{c mean deviation and is equal to 2.2. Equa-

tion (19) is plotted in figure 4.

Inlet Rotor-Stator Interaction Tones

Discrete tone generation is associated with lift fluctuations on

rotor or stator blades. Interaction tones are generated by rotor blades

intersecting the wakes from preceding starer vanes or inlet guide vanes

or by rotating wakes from a rotor impinging on stator vanes. The tones

are propagated from the blades as spinning duct modes. No attempt is

made to determine the specific characteristics of each propagated mode,

only the average far-field c_racteristics are predicted.

The acoustic power due to inlet rotor-stator interaction tones i_=

-" = (2.683 x !0 -4 ) G(i,_) (s')-a(k'[)M4"31(m*/A*) (iT') 2 F(Mr,M m)m

{20)

9.i-8

w •

where the constants are

and

G(i, j} =

a(k,£) =

IO 1.625

O. 580 l

0.205j

(21)

(22)

The constants in the matrix G account for the effect of inlet guide

vanes and fundamental tone cut-off. The exlDonent on the rotor-stator

spacing accounts for the inverse variation of the acoustic power except

when inlet flow distortion effects dominate at s > 1. The power

function F is

F ---

-2.310. 397M

m

2053C31,S (0 2r

0 .315M 3 "69M-8m r

(M r < 0.72)

< M r < 0.866Mm 0"462)

(0.866Mm 0"462 < Mr)

(23)

which is plotted in figure 5.

The mean-square acoustic pressure due to inlet rotor-stator inter-

action tones is computed from equation (i). The directivity function D

is given in table III and plotted in figure 6. The spectral function S

is a discrete function given by

n u

s(n) = _ S(n,i, j) (24)

n=n Z

where n Z and n u are the lower and upper values of t_e harmonic number

associated with the I/3-octave band with a center frequency parameter

value of _. For n = I,

S(1,i,j) _0. 799 0. 387_

(25;

8.1-9

and for n > I,

I_i 250 0"432 lS(n,i,j) = x I0 -0-3(n-2) (26)

i01 0. 307_

where i and j are defined by equations (6) and (7), respectively. The

function S(t]) is plotted in figures 7 to I0 prior to being converted to

i/3-octave-band data.

Inlet Flow Distortion Tones

Inlet flow distortion has an effect on broadband noise and rotor-

stator interaction tones. In addition, inlet fl,,w distortion can generate

unsteady lift on the blades which produces additioi_al pure tone noise.

The average properties of the far-field noise are predicted.

The acoustic :_wer due to inlet flow distortion tones is

I

• 9

•q* = (1.488 x 10 -4 ) (s*)-a(k,_)M4-31(m*/A*) (AT*)" F(Mr,.Xt m)m

(27)

-her,: a(k, 5) and F(>Ir,M m) arc defined by equations (22) and 23),

re_}_ectlvely, and the !xawer function F" is plotted in figure 5.

The mean-_,_uare acoustic _ressure due to inlet flow distortion toner;

: _ computed from equation (i). The directivity function D is the same

a:: for the inlet rotor-starer interaction tones as g'_ven in taDle ITI and

•_lotted in figure 6. The sVectral function S is given by

_U

/

n=n 2

i0-" (28%

w!_Ich is "..'lotted _n figure ii prior to beina converted to l,'3-octave-band

iata.

Combination Tone Noise

When tht, relat_v,: _eed of the rotor blade tiFs exceeds a Mach number

value of I, shock waves are formed at the leading edge of each rotor blade.

_Icse ._hock waves _rouagate through Lhe engine inlet as a series of Mach

waves• The resultlng sFectrum contains harmonics of the shaft speed

:n_tead ._f the blade passlng frequency. The resultant no_se is not purely

tonal but e×tends in a frequency: • interval on either side of the harmonic

frequenc[.'. This combination tone ._olse is often referred to as "buzz-saw"

_.i-i0

!

The acoustic power due to combination tone noise is

H* " K G(i,j)(m*IA*)(AT*) 2 F(M r) (29)

The acoustic power for three harmonics of the shaft rotational speed are

computed. They are expressed as fractions of the fundamental tone of the

blade passing frequency. The constants K for each harmoi_ic are

6.225 x 10 -4 for the I/8 fundamental combination tone, 2.030 x 10 -3 for

the 1/4 fundamental combination tone, and 2.525 x 10-3 for the I/2 funda-

mental combination tone. The constant G(i,j) is given b 7

.316 0.31

(._0)

This accounts for the fact that inlet guide vanes inhibit the propagation

of combir_tion tones through the inlet. The power function F is given

by

O (:% < I)

F(N r) = I0 -6"751!'61-Mr) (I -< H r -< 1.61)

-1.21 (Mr-l.61)i0 (1.61 < M r)

(31)

for the I.'S fundamental combination tone,

F (M r) O= i0-14" 75 (i" 322-Mr )

-1.33 (Mr-l. 322)

(M r - I)

(i "Mr < 1.3..)

(1.322 < M r)

t32)

for the [/4 fundameatal combination tone, and

OF(M r) = i0"31-85(i-146-M:}

I I0-1"41 (Mr-l. 146)

(_r < i )

(I -" M r -_ 1.146)

(I. 146 < M z )

(33)

8.1-11

for the 1/2 fundamental combination tone. The power function is plotted

in figure 12.

The mean-square acoustic pressure is computed separately for each

combination tone b 7 equation (i). Then, the three harmonics are summed to

yield the I/3-octave-band spectrum due to combination tone noise. The

directivity function D is the same for all three harmonics and is given

in table III and plotted in figure 13. The spectrum function S is given

by

-405(8D) 5 (D _ 0.125)

S (n) = (34)

405(8D) -3 (n > 0.125)

for the 1/8 fundamental combination tone,

s(n) = I_ "520(4n)5.520(4n) -5

for the 1/4 fundamental combination tone, and

S([_) = _ 0"33212_13

_,O. 332(2n "-3

(35)

(36)

for the 1/2 fundamental combination tone. The spectrum functions for

combination tone noise are /lotted in figure 14.

Discharge Broadband Noise

The discharge broadband noise is created by the same mechanisms as

the inlet broadband noise. The acoustic power of the discharge broadband

noise is

_L = (3.206 x 10 -4 ) _(i,j) (s*) -a(k'£) (m*/A*)(_T*) 2 F(M r) (37)

where a(k,[) is the same as for inlet broadband noise given by e_aa-

tion (17) and G(i j) is

(38)

8.1-12

The factor G shows that the presence of inlet guide vanes doubles t.he

acoustic power of the discharge broadband noise. The power function F

is given by

i (Mr -<i.0)F (M r) = 2

Mr (Mr > 1.0)

(39)

and is plotted in figure 15.

The mean-square acoustic pressure due to discharge broadband noise

is computed from equation (i). The directivity function D is give, in

table III and is plotted in figure 16. The spectrum function S is the

same as the inlet broadband noise spectrum as given in equation (19) and

plotted in figure 4.

Discharge Rotor-Stator Interaction Tones

The discharge rotor-stator interaction tones are created by the same

mechanisms as the inlet rotor-stator interacLion tones. The acoustic

power of the discharge rotor-stator interaction tones is

_* = (2 643 x 10 -4 ) G(i,j)(s_)-a(k'i)M2(m*/A*)(AT') 2 F(M r) (40)• m

qne matrix a(k,£) is Lhe same as for inlet rotor-stator tones given by

equation (21) and the matrix G(i,j) is

c,(_,j) =2 0.58O].59 0.820J

(41)

which gives the effect of inlet guide vanes and fundamental tone cut-off.

The power ftLnction F is the same as the discharge broadband noise as

given in equation (39) and plotted in figure 15.

The mean-square acoustic pressure due to discharge rotor-stator

interaction tones is _uted from equation (I). The directivity func-

tion D is given in table III and plotted in figure 17. The spect_ "_

functlon S is the same_ as the inlet r_tor-stator interaction tones as

given in equations (24) to (26) and plotted in figure_ 7 to i0.

8.1-13

OutputComputation

The I/3-octave-band mean-square acoustic pressure for a fan is the

sun of the mean-square pressures from the six fan noise components. The

user has the option of deleting one or more of the noise source compo-

nents if desired.

The mean-square acoustic pressure is computed for each desired value

of the frequency, polar directivity angle, and azimuthal directivity

angle. The total noise is the mean-square acoustic pressure multiplied

by the number of engines N e for the output table. In addition, printed

output is available of the sound pressure level SPL defined as

_®c_SPL = i0 lOgl0 /_kp22 * + 20 lOgl0 --

Pref

(42)

and d_e power level PWL defined as

0c_A*A e

(43)PWL = I0 lOgl0 _* + I0 logic _ref

I. Hei!mann, M. F.:

__ource Noise.

REFERENCE

Interim Prediction Method for Fan and Compressor

NASA TM X-71763, 1975.

8.1-14

m

TABLE I.- RANGE AND DEFAULT VALUES OF IN-PUT PAR/LMETERS

Input Minimum De fault Max imttmparameter

2Ae , m ......

N e ........ i

r S , m .......

0.01

1

0.01

_,14

1

A _ .... . . • o

d _ ........

1 .... . . . . °

Md ........

[ .........

S* . . . ° ° ° . o

".7 .........

._1" ....... °

"_,1o " ° ° " ° ° " °

"T* ........

C a, m/s ......

i , kg/m 3 .....

0.i

2

0.3

1

0.5

1

0.2

i0

0

0

0

0

200

0.2

1

20

I.!28

1

1.0

1

1

50

0.2

0

0.3

0.2

340.294

1.225

I0

4

i00

i0

i00

4

2

2.0

2

I0

200

i0

0.9

0.5

1.3

4OO

1.5

8.1-15

vIVl "J" vt Z X

c_A

_DV

VI _.

V!

A A

_ A

0

I O

'll

I",I

u_

Vl _.

v

°

t L.

i E

o _,

_ C

VI A

v

r2-'D

t

x

_n

, TO _

&_;

C "J

tc

,4

j -

0

8.1-13

0

I

6-

k_

v

r._

XVl A

I., leZ Z

V!

p-0

5"!

,-qw

IO

_t

Xv

t O

_PV _-_

le ,..4

XV!

1E

V!

I

v

a0

1O

I-4 ,,.4

Vl A

A _ l.JZ _r

X

_D

f-J

Ii.I

ol"_O ! t.

A A

w v

A _

v v

v

!O

O

O

'_ e 0

O O

2_.2

IO

x

,,,_ 8 _,

I

r_,:; o

o •

_0

x

r- O_U _., 0

0 0

,-4 _"

Vl A

,.,..I

0

_a2_

8.1-17

r

Z

Z<t,.

0

o3

I

m

0

e-U

,-4C

r. >,o

o.,-_ o o.i.J _ _ ,...4eJ o _J 0_1.4 _ ,.4 ot2 _

.,.4.,.¢ 01_

>,

0 _,_ 0

oc0

>_

e" Ol ,-4 0.,.4 14 _

0

0

0

_ _ > ,--40 0 0 0"_

>.

.,-Q -,'_ ¢) 0

0 0-_ 0

I I I I I I I I I I

O O_ 0 e 0 O_ O 0 0 0 0 0 O O O

i|il

oooooooooooooo_ooo

I I I I I i I I I I I I I I

g_ o o_ o_ e o o o • o • e_ o o_O0 _ 00000000 O0l I l I I I I I t I I I I I

I I I I I I I I I I I I

• ooo • • •

I I I l I I I I I I I I

g gggg ggg gg g ___0__ _

8.1-18

TABLE IV.- SPECTRUM FUNCTIONS FOR FAN NOISE

Source Spectrum function

Inlet

broadband

noise

inlet

rotor- stator

interaction

tones

Inlet flow

distortion

tones

1/8 funda-

mental

combination

tone noise

r_ ,hi2,,]qS(q) = 0.116 exp L 0.5 L In 2"_'.2 J J

n u

S(q) = I S(n,i,j)

n=n Z

whece

-0.499 0.136

S(l,i,j) =

0.799 0.387

%.2s0 0.43!S(n,i,9) =

2.1oi o.3o L

-0.3 (n-2)x i0

S (n) = 9

n u

In=n

&

i0 -n

s(n) = _ "°'4°5 (8n) 5

[.0.405 (sn) -3

(n > i)

(_ ! 0.125)

(D > 0.125)

8.1-19

i

TABLE IV.- Concluded

t

Source Spectrum function

1/4 funda-

mental

combination

tone noise

1/2 funda-

mental

combination

tone noise

Discharge

broadband

noise

Discharge

rotor-stator

interaction

tones

S(q) =

F

520 (4rl) -5

s(q) = 0.332(2n) 3

Lo 332(2q) -3

s(q) = 0.116 exp L°'5L in 2.2 j j

n u

s(n) =

n=n_

S(n,i,j)

where

S(l,i,j) = 0"1361

0.387J

S(n,i,j) = 0"4321

0. 307_

× i0-0.3 (n-2)

(rl -< 0.25)

(q > 0.25)

(n < 0.5)

(rl > 0.5)

(n> i)

8.1-20

N

r

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Figure i.- Schematic diagram of typical axial flow fan.

8.1-21

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8.1-37

i T _

8.2 COMBUSTION NOISE MODULE

INTRODUCTION

The Combustion Noise Module predicts the noise from conventional com-

bustors installed in gas turbine engines. The method is based on a pro-

posed appendix by R. K. Matta to SAE ARP 876. The method employs

empirical data of core noise from turboshaft, turbojet, and turbofan

engines to produce sound spectra as a function of frequency and polar

directivity angle.

The method requires input of several parameters. The combustor

entrance and exit flow parameters can be provided by the Core Noise

Parameters Module or directly by the user. Additional user-provided

parameters are required. The module is executed once for each set of

values of the input parameters. The output is a table of the mean-square

acoustic pressure as a function of frequency, polar directivity angle,

and azimuthal directivity angle. Although combustion noise is assumed

not to vary with azimuthal directivity angle, it is introduced so _at

the output table is compatible with other noise tables.

A

A e

ca

D

f

fp

H

&

N

<_2>*

Pre f

Pt

P=

SYMBOLS

combustor entrance area, m 2 (ft 2)

engine reference area, m- (ft 2)

ambient speed of sound, m/s (ft/s)

directivity function

frequency, Hz

spectrum peak frequency, Hz

aircraft Mach number

mass flow rate, kg/s (slugs/s)

number of engines

2 4mean-square acoustic pressure, re O_c_

reference pressure, 2 x 10 -5 Pa (4.177 × 10 -7 ib/ft 2)

total pressure, Pa (Ib/ft2)

ambient pressure, Pa (Ib/ft 2)

8.2-1

rs

tr

s

S

T

ATde s

8

II*

_ref

distance from source to observer, m (ft)

dimensionless distance from source to _bserver, re _e

spectral distribution function

total temperature, K (OR)

design turbine temperature extraction, K (OR)

ambient temperature, K (OR)

polar directivity angle, deg

acoustic power, re O C3Ae

reference power, 1 x 10 "12 W (7.376 x 10 -13 ft-lb/s)

ambient density, kg/m 3 (slugs/ft 3)

azimuthal directivity angle, deg

Subscripts:

i entrance

j exit

Superscript:

* dimensionless quantity

INPUT

The combustor entrance and exit parameters are required from either

the output of Lhe Core Noise Parameters .Module or from the user. Ambient

conditions are required for computation of the s_und pressure levels.

The frequency, polar directivity angle, and azi=_thal directivity angle

arrays establish the independent variable values for the output table.

Finally, the engine reference area, number of enqines, combustor entrance

area, and distance to observer are required. The range and default

values of _he input parameters are given in table I.

A

A e

N

r S

Input Constants

combustor entrance area, re A e

engine reference area, m 2 (ft 2)

number of engines

distance from source to observer, m (ft)

8.2-2

j_

L

Pt, i

T"J

T*A des

MoQ

Core Noise Parameters

combustor entrance mass flow rate, re D c A e

eombustor entrance total pressure, r_ Poe

combustor entrance total temperature, re T

combustor exit total temperature, re T_

design turbine temperature extraction, re Tm

Ambient Conditions

ambient sl_-ed of sound, m/s (ft,'s}

aircraft Math number

ambient density, kg/m ] (sluqs/ft ])

Ind,5_ndent Variable Arrays

t'requt,ncy, Hz

}k)L,lr dtrectivtty anqLe, deq

a;'.tmuthal dir,,ctivtty anqh,, deq

OUT PUT

The out_,ut of this module is a table of the mean-square, acoustic

|_ressure as a function of frequency, _olar direct_vi_y angle, and a:i-

mnthal directivity angle. _n addition, the observer distance r s is

[uovlded for the Proi_ation .Module.

r_

f

h

• O

distance from source to observer, m [ft)

Combustor Norse Table

frequ,,ncy, H:

polar dir_,ctivity anqleo ,|eq

azlmutha| dirt, ctivity anqle, deq

2 4

me.xll-_uare aCOUStiC Vressure, r_, ,_ Cp

.METHOD

The prediction methodology proposed by R. K..Matta is used to compute

_e combustor noise. Details of the development and validation of the

method are given in reference i. A schematic of a typical combustor is

shown in figure I. The coordinate system and directivity angles are also

shown.

The equation for the far-field mean-square acoustic pressure in a

I/3-octave band for a gas turbine combustor is

<p2> t = ntA * D(_) S(f) (I)

4_(r:) 2 (i - M cos @)4

Q

The dimensionless source to observer distance r s is defined as

The acoustic power ]* is related to the combustor entrance and exit

states as

&'/T" >2-* * ")2

T[ "'"

(3)

me aircraft Mach number term in equation (i) accounts for forward flight

effects.

Two empirical functions are required for equation (I). The direc-

t:vity f'_nction D is a function of the polaz directivity angle 0 and

is given in table II and plotted in figure 2. The spectrum function S

1& a function of logl0 (f/fp) and is given in table Ill and plotted in

figure 3. The _ak frequency fP is given by

f = 400 (4)

P 1 - M,_ cos 9

The mean-square pressure <?2>* i_ now computed from equation (I).

=_.e total noise _s the mean-square pressure multiplied by the number of

engines N. The output of this module is a table of the mean-square

acoustic pressure as a function of frequency, polar directivity angle,

and azimuthal d_rec_ivlty angle. In addition, printed outFut is available

of the sound ?ressure level SPL defined as

2,3 C

_P:.. 10 1ogi_ <p2>" :0 _ "= + l°gl0 Pref

(5)

8.2-4

f

and the power level PWL defined as

PWL = 10 lOgl0 H" + I0 logl0(6J

REFERENCE

I. Emmerlinq, d. J.; Kozin, S. B.; and Matta, R. K.: Core Engine Noise

Control Program. Volume Ill, Supplement 1 - Prediction Methods.

FAA-RD-74-125, III-I, Mar. 1976. (Available from DTIC as

AD A030 376.)

_.2-%

TABLEI.- RANGEANDDEFAULTVALUESOFINPUTPARAMETERS

Input Minimum Default Maximumparameter

A t . . o o o . . .

A e , m 2 ......

N ........

rSS m .......

m*. ° ° ° .... oi

'%_oo ........

P:,i .......

T. _ • . ° o ....1

T* ........

3

'_Tde s .......

Coo, m/S ......

_ , kg/m 3 ..... [

0.01

0.01

1

0.01

0

0

1

1

1

0

2OO

0.2

1

,_/4

1

0.2

0

i

1

2

0.5

340. 294

1.225

i0

I0

4

i00

i0

0.9

30.0

5.0

6.0

2.0

4OO

1.5

8.2-6

"----"I

>

[..,UM

ZQ

en

0U

!

Ul

e_

UI

0

0,...4

0

0

I | I I i I I i I I I I i i I I i I i I i I i I i I i i

o * • • • • * * * • o o * o . o_ • . o . . o . o . .__00000000000000 0000__I I I I i I I i I I I

Z©

i

)..,

o,-.4

0000 000 0 0 v O0 0

I I I I I i | i i I I i i I

OOOOOOOOOOOOO0_oOo00000000000000000000

8.2-7

J

Jj °

oooc_ o o ooc_ooo

X

Z

Figure I.- Schematic diagram of typical gas turbine combustor.

8.2-8

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G °tSOl

C,,I '¢ ¢0 aO

I I I I

X_,!^_0eJ!CI

00

I

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0

wO

0

uu3

0

m

I

0

I

l I I I l I•-- Cx; M') ,_- LD _ ;',."--I I I I I i I I

S °tSOl 'l_Aeq wn4o_d S

Q. '-_

0

o

0

o"°m 0

0 ...4

o

(j o

L. _jb_

I

8.2-10

-7

8.3 TURBINE NOISE .w_DULE

INTRODUCTIO_

The Turbine Noise Module predicts the broadband noise and pure tones

for an axial flow turbine. The method is based on a method developed by

the General Electric Compan 7 (ref. I). The method employs empirical

functions to produce sound spectra as a function of fxequency and polar

directivity angle. Each spectrum is the s,-- of a broadband noise compo-

nent and a pure tone component.

The met_hod requires input of several parameters. The turbine

entrance and exit flow parameters can be provided by the Turbine .Noise

Parameters Module or directly by the user. Additional user-provided

parameters are required. The module is executed once for each set of

values of the input parameters. The output is a table of the mean-square

acoustic pressure as a function of frequency, polar directivity angle,

and azimuthal directivity angle. Although turbine noise is assumed not

to vary with azimuthal directivity angle, it is introduced so that the

output table is compatible with other noise tables.

A

A e

a,b

B

c=0

D

d

f

fb

h"

h a

K

SYMBOl3

turbine inlet cross-sectional area, m 2 (ft 2)

engine reference area, m 2 (ft 2)

components

number of rotor blades

ambient speed of sound, m/s (ft/s)

directivity function

turbine rotor diameter, m (ft)

frequency, Hz

blade passing frequency, }:z

fuel-to-air ratio

specific enthalpy, re RT

absolute htunidity, percent mole fraction

constant

8.3-1

_m

H

e

n

<p2>

Pref

r s

r t

S

S

T

n

'ref

aircraft Mach number

rotational speed, Hz

number of engines

tone harmonic number

2 4mean-square acoustic pressure, re D_c

reference pressure, 2 x I0 -5 Pa (4.177 x i0 -7 ib/ft 2}

distance from source to observer, m (ft)

dimensionless distance from source to observer, re _e

gas constant, m2/(K-s 2) (ft2/(°R-s2))

sp_ctr,_ function

temperature, K (OR)

blade tip speed, m/s (ft/s)

frequenc/ parameter

polar directivity angle, deg

acoustic power, re D c3A

reference power, 1 × 10 -12 W (7.376 x 10 -13 ft-lb/s)

ambient densitq_, kg/m 3 (slugs/ft 3)

azimuthal directivity angle, deg

Su=scripts :

i entrance

3 exit

s static

t total

ambient

Su_Terscri.:t :

• dimensionless quantity

8.3-2

INPUT

The turbine parameters are required from either the output of the

Turbine Noise Parameters MJ_dule or from the user. Ambient conditions are

required for :omputation of sound pressure levels. The frequency, polar

directivity angle, and azimuthal directivity arrays establish the inde-

pendent variable values for the output table. The turbine inlet cross-

sectional area and number of rotor blades are requ/red for the geometric

description of the turbine. Finally, the engine reference area, number

of engines, and distance to the observer are required. The range and

default values of the input parameters are given in table I.

Ae

H e

r s

A •

B

d j

Input Constants

engine reference area, m 2 (ft 2)

number of engines

distance from source to observer, m (ft)

Turbine Geometry

turbine inlet cross-sectional area, re A e

number of rotor blades

rotor diameter, re _A_A_turbine

N*

°s,j

M

_z

Turbine _ise Parameters

fuel-to-alr ratio

rotational speed, re c /d

entrance total temperature, re T

exit static tem--_erature, re T

Ambient Conditions

ambient speed of sound, m/s (ft/s)

absolute humidi_/, percent mole fraction

aircraft Mach number

ambient density, kg/m 3 (slugs/ft 3)

8.3-3

IndependentVariable Arrays

frequency, Hz

polar directivity angle, deg

azimuthal directivity angle, deg

OUTPUT

The output to this module is a table of the mean-square acoustic

pressure as a function of frequency, polar directivity angle, and azi-

muthal directivity angle. In addition, the observer distance r s is

provided for the Propagation Module.

r s distance from source to observer, m (ft)

f

0

<p2_f,e,¢l>"

Turbine Noise Table

frequency, Hz

polar directivity angle, deg

azimuthal directivity angle, deg

2 4mean-square acoustic pressure, re pc

METHOD

The prediction method presented in reference i is used to compute

the far-field noise. A schematic of a typical turbine is shown in fig-

ure I. The coerdinate system and directlvity angles are also shown. The

general equations for the prediction method are presented. This presen-

tation is followed by a detailed discussion of the method for each

turbine noise component.

The equation for the far-field mean-square acoustic pressure for a

turb!x,c is

<p2>* = _*A* D(9) ._;(_)

4_(rs )2 (i - M cos @)4

(I}

In equation (i), _" is the overall power, D is the directivity func-

tion, and S is the spectrum function. The source to observer distance

r is expressed in dimensionless form ass

r::rs/ e (2)

8.3-4

Theforward velocity effect is accounted for by the Doppler factor

(i - _ cos 0) 4 . The frequency parameter q is defined as

rl = (1 - M cos _q]_--b

(3)

where the blade passing frequency fb is

(4]

The acoustic power for the turbine [[* is expressed as

_* = K t,i s,j (u_)b

\ ht,i

(S)

The constants K, a, and b are determined from empirical data of the

particular noise source being considered. The difference between the

entrance sI_-cific total enthalpy h;, i and the exit specific static*

e:,thal_y hs, %. is the idea[ _rk extraction of the turbine. Each spe-

cific enthalpy is computed fro.'.*the input temperatures, the fuel-to-air

ratio ,%, and the absohlte humidity h a with the appropriate Gas

?roi_:rties Utility. The rotor tip s|_eed U: is a functlon of the

rot.,tional speed and i:; given by

T •11 = _N _6)

A_ iudic:ited by equation (1), each turbine noise ,_ource has ._ts own

dir,,ctivity function D and spectrum function S. By using these func-

tions and the acoustic power, the mean-square acoustic pressure is com-

puted as a function of frequency and polar directivity angle for a given

:;et of in_,ut }_arameters. Th_ e broadband noise is expressed as I/I-octave-

band d.lta. The [_ure tones are values at discrete frequencies. T_e pure

tones must be added to the apFropriate I/3-octave band so that a to_al

h/3-octave-band turbine noise spectrum is determined. For a g_ven value

of the i/3-octave-band center frequency param_tez n, the lowest harmonic

number that falls within the band is

n. - [I0 "lz° n] + I (7}L

anJ th,, highest harmonic number is

n = [ 101/20 ".] (,g}U

S.3-5

whrre [ ] indicates the inteqe.r part of the enclosed real number. If

:I[ _ nu, then there are no tones within the band. If n& -< n u, then there

are n u - n£ + l tones within the band. The pure tone mean-square pres-

sures for each harmonic number n are then added to the appropriate band.

The tones are |:ropagated to the observer as i/3-octave-band data.

The empirical constants and functions used to compute the acoustic

_owor for turbine noise are given in table II. The directivity and s_ec-

trum functions are given in tables III and IV, respectively. Each turbine

noise com_x_nent is described in detail in the following two sections.

Turbine Broadband Noise

Turbine broadband noise is associated with random unsteadiness o_"

turbuh'ncc iu the flow |_assing the blading. Some o_ the sources of this

random, unsteady flow ,_re turbulence in boundlry layers, blade wakes and

vortices, and entrance flow. Although prediction of individual sources

of broadband noise is beyond the sconce of this module, the total broad-

band noise produced by the turbine is predicted.

The acoustic }_owor due to broadband noise from the turbine is

,,e

i-{S.SS'_ _ 10 -5 ) ' • " {UT )-1"27

hi, i

(9)

_,, dir,,ctivity function D is given in table Ill and plotted in fig-

ur,- 2. Th,, _l-,-ctr_rn function S is ,liw, u iI_ table IV and plotted in

'.'i,lure 3. Th,' moan-::qu.lr_, acou.qttc _re:;:_t:re i:_ thet_ computed by

,',lu.,t_ou (1).

T11rbine Pure Tone Noise

D_::crete tone gen,,ration is associated with lift fluctuations on

tutor" or starer bl.%des. These tones occur at frequencies that are

harmonic:_ of the turbine blade },ass_nq frequency. The average far-

fief,! c!l._r.lcterist_c:; are _,r,,d_cted.

The acou:_tic _.ow,,r due to turbin,, F:U:," tone no_sd is

<_ ,, )I .46

"t,_ -h:,%[_* = _I.162 _ lO'"_ (U_) -4"02

h:, i

_.3-6

_,e directivity function O is given in table ZlZ and plotted in fig-

ure 4. The spectrum function S is given by

S - 0.6838 _ lO "(n-I)/2 (ll)

which is plotted in figure 5. The mean-square acot,stic pressure is ".hen

computed b v equation (I).

Output Computation

The mean-square acoustic pressure for a turbine i:; the sum of t_.e

two components. It is computed for each des_r,,d value of the fL-eque._y,

_lar direct_v%ty angle, and a:imuthal directivity an_le. The t_ta] noise

is the mean-:_quare acoustic pressure multiplied by the numb_-r of er_::nes

N e for the output table. In addition, printed output is ava[|_Lb|e ;f

the _ound pressure level SPL defined as

SPL = I0 loqh_ <p22" ÷ 20 log|0-}_re f

(12)

and the _k_w,,t" l,,vel I'WL defined ,is

e

PWL - I0 lOqlo :: ÷ 10 lOql0 .?'ref

_WE_ENCE

i. Matt.%, R. K.; ._andusky, G. ?. ; al_d ."k_yle, V. L. : .:F, Cot,, .v.n_%t%_,_k-:_e

_:%v,'._tiqation - Low Emi:-sion _::%qit%es. FAA-KD-.'7-4, Feb. t._77.

(Avai|able from DTIC as AD A04S 5g0.)

S.3-7

TABLE I.- RANGE AND DEFAULT VALUES OF INPUT PARAMETERS

Input M inimum De fault Maximumpa tame te r

m 2Ace ° . . . . 0

Ne ........

i rs, ra .......

0.01

I

0.01

n14

I

t_ e ° o ° ° o ° ° °

• ° ° ° ° o o . ,

d4 o o • ° . ° . •

•%_ . ° ° o ° ° o .

o . . ° o ° . ,

_t ° . • • • • o •

T t ° • . . ° ° •t,i

T_, j .......

C , g%,' ._ ......

!I.%, % .......

_' , kq m 3 .....

0.I

2

0.01

0

0

0

0.5

0.5

I00

0

O. 2

i

20

I

0

0

O. 3

3

2

340.2')4

0

1.225

I0

4

I0O

I0

500

IoO

0.9

0.06767

0.5

6

4

400

4

1.5

TABL/_ If.- CONSTANTS FOR TURBINE ACOUSTIC POWER

Source K

Bro,hlb,_nd ,q, 5,q9 _ 10-5

Pure tone 1 162 _ 10-4

a b

1.27 -1.27

1.46 -4.02

_3.3-8

TABLE III.- TUP,_INE NOISE DIRECTIVITY LEVELS

deg

.

10.20.30.40.50.60.70.80.qO,

100.110.120.130.140.150.160,170.leO.

Broadband

directivity

level,

lOglo D

i

-0,789"0.689-0,59g-0.509-0,_09-0.319-0o219-0,1Z9-O*OZ9

0,0710.151O. ZZ10.Z310.Zll0.111

-0.029-0.229-0.549-0,869

Tone

directivity

level,

loglo D

-1.911-1.671-1.471-1.Z61-1.061-0.851-0.641-0.431-0,Z31-0.021

0.1890,38g0.5890.259

-0.191-0._91-0.931-1,271-I,611

TABLE ',V.- TURBINE BROADI_AND NOISE ._PECTRU._I

lOglo 'l logl0 S

-O.Q03

-0,796-O*bgg-0.602-O._OZ-O*3qB-0.301-O.Z01"0.097

0.0000.0970.2040.3010.60Z

-1,884-1.604-1.444-1.304-1.184-1,084-1.004

-o.gz4-0.844-0.784-1_004-1.204-1.384-l.gZ4

-----m

X

Y

Figure i.- Schematic diagram of typical axial flow turbine.

8.3-I0

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8.3-14

i

I/

8.4 SINGLE STREAM CIRCULAR JET NOISE MODULE

INTRODUCTION

The Single Stream Circular Jet Noise Module predicts the single

stream jet mixing noise from shock-free circular nozzles. The method is

based on SAEARP 876 (ref. 1). The method employs empirical data tabu-

lated in terms of relevant dimensionless groups to produce sound spectra

as a function of frequency and polar directivity angle.

The method requires input of several parameters. The nozzle exit

flow parameters can be provided by the Jet Noise Parameters Module or

directly by the user. Additional user-provided parameters are required.

The module is executed once for each set of values of the input param-

eters. The output is a table of the mean-square acoustic pressure as a

function of frequency, polar directivity angle, and azimuthal directivity

angle. Although jet exhaust noise is assumed not to vary with azimuthal

directivity angle, it is introduced so that the output table is compatible

with other noise tibles.

A e

_j

D

--4

F

f

t _

?

<p2> °

SYMBOLS

engine reference area, m 2 (ft 2)

fully expanded jet area, m 2 (ft 2)

ambient speed of sound, m/s (ft/s)

directivity function

fully expanded jet diameter, m (ft)

spectral distribution factor

frequency, Hz

Helmholtz number, f A_e/C _

aircraft Mach number

forward velocity index

number of engines

power deviation factor

mean-square acoustic pressure,

8.4-I

Pre f

r s

r s

SC

Tj

V_J

reference pressure, 2 x 10 -5 Pa (4.177 x 10 -7 Ib/ft 2)

distance from nozzle exit to observer, m (ft)

dimensionless distance from nozzle exit to observer, re _e

corrected Strouhal number, fdj/_Vj

jet total temperature, K (OR)

ambient temperature, K [°R)

exhaust jet veiocity, m/s (ft/s)

angle between flight vector and engine inlet axis, deg

polar directivity angle, deg

If*

_ref

O.3

0

Strouhal number correction factor

acoustic power, re 0 c_Aj

reference power, 1 × 10 -12 W (7.376 x 10 -13 ft-lb/s)

jet density, kg/m 3 (slugs/ft 3)

ambient density, kg/m 3 (slugs/ft 3)

azimuthal directivity angle, deg

density exponent

Superscript:

dimensionless quantity

INPUT

The 3et parameters are required from either the output of the Jet

.Noise Parameters .Module or the user. Ambient conditions are required for

computation of the Strouhal number and sound pressure levels. The fre-

quencf, polar directivity angle, _nd azimuthal directivity angle arrays

establish _ne independent variable values for the output table. Finally,

dne engine reference area, number of engines, engine axis offset, and

distance to the p:eudo-observer are required. The range and default

val_es of _ne input parameters are given in table I.

A e

N

Input Constants

engine reference area, m 2 (ft 2)

number of engines

8.4-2

!r

sdistance from nozzle exit to pseudo-observer, m (it)

angle between flight vector and engine inlet axis, deg

A:J

J

v:]

t

_j

Jet Noise Parameters

area of jet, re Ae

jet total temperature, re T

jet velocity, re c

jet density, re O_

Ambient Conditions

_cp

M

speed of sound, m/s (it/s)

aircraft M_ch number

denslty, kg/m 3 (slugs/it 3)

Independent Vari-=b!e Arrays

frequency, Hz

polar directivity angle, deg

azimuthal directivity angle, deg

OUT;L_

_ne output of this module is a table of the mean-square pressure as

a func=ion of frequency, polar directivity angle, and azimuthal direc-

tivlty angle. In addition, pseudo-obse.--ver distance r s is provided for

the Propagation Module.

r sdistance frcm nozzle exit to pseudo-observer, m (it)

f

Single Stream Circular Jet Noise Table

frequency, Hz

polar direc:_vlty angle, deg

azimuthal directlvity angle, deg

02c 4mean-square acoustic pressure, re _

_.4-3

METHOD

The prediction methodology presented in reference 1 is used to com-

pute the far-field noise. A schematic of a typical exhaust jet nozzle is

shown in figure I. The coordinate system and directivity angles are also

shown. Whenever empirical functions require extrapolation, the last value

is used, except for spectra which are linearly extrapolated.

The equation for the far-field mean-square acoustic pressure in a

i/3-octave band for a stationary jet is

<p2>* = _q*A; D(e,v;) F(Sc,e

4n(rs2 ) ,V;,T;)

(I)

In equation (i), _* is the overall power, D is the directivity func-

tion, and F is the spectral distribution function. Each of these

functions is discussed separately. The observer distance r s is

expressed in dimensionless form as

r: = rs/_e

The acoustic power Jq_ is civen by

(2)

t -*'_''(vj)*'8P'V*"_* = (6.67 x 10-5)_jj j) (3)

which is a variation of the classic V 8 law. Two empirical functions are

required for equation 13). The density exponent _ is a function of

logl0 V*3 and is given in table II and plotted in figure 2. The power

deviation factor P is the deviation of the acoustic power from the V 8

law. It is expressed as a function of lOgl0 V; in table III and

plotted in figure 3.

The normalized directivity function D of equation (I) is an

empirical function of the polar directivity angle @ and velocity

ratio lOgl0 Vj. It expresses the variation of the mean-square pressure

with 9 and is normalized such that

T

D(9,Vj) sin @ d6 = 1 (4)

The directivity function for a single stream circular jet is given in

table IV and plotted in figure 4.

The normalized spectral distribution factor F is an empirical func-

t_zon of corrected Strouhal number lOgl0 S c, polar directivity angle @,

velocity ratio log.^ V*, and temperature ratio T_. The correctediu 3

Strouhal number S c is defined as

8.4-4

wherethe jet diameter d_ is

(5)

(6)

and _ is the Strouhal ntLmber correction factor. The Strouhal number

correction factor is an empirical function of the velocity ratio

V* and the polar directivity angle 8 as shown in table V andl°gl0 3

figure 5. The normalized spectral distribution factor F is defined

s,lch that the sun,nation over i/3-octave-band Strouhal numbers is

_ V* -*" 1F(Sc,_, j,TjJ =

S c

(7)

and is given in table VI and plotted in figure 6.

Equation (i) is valid for a stationary 3:t (M = 0). To incorporate

fcrward flight effects, equation (i) should be rewritten as

<F > = 47(rs)2 x - _= cos (_ - 5) \/v*j (8)

The exponent m(@) is the forward velocity index given in table VII and

figure 7 as taken from reference 2, and _ is _he angle between the

flight vector and the engine inlet axis. In addition, the relative jet

veiocity must be taken into account by computing the corrected Strouhal

n-_--ube r as

Sc = [(v_ - :_)

(9)

The mean-square acoustic pressure can be computed for each desired

value of _e frequency, polar directivity angle, and azimuthal directivity

_ngle. The total noise is the mean-square acoustic pressure multiplie_ by

_ne number of engines N for _ne output table. In addition, printed

output is available of the mean-square pressure <p2>', sound pressure

level SPL defined as

8.4-5

SPL = lO iO91o<p_>* + zo I_io

and the power level PWL defined as

2 4

0_c=o

2

Pref

{I0)

_ref

P_V_ = i0 lOgl0 N" - I0 lOgl0 3A*A

_c j e

(II)

REFERENCES

i. Gas Turbine Jet Exhaust Noise Prediction. ARP 876, Soc. _tomot.

Eng., Mar. 1978.

2. Hoch, R. G.; Duponchel, J. P.; Cocking, B. J.; and B_-ce, W. D.:

Studies of the Influence of Density on Jet Noise. SNECMA and

_TE paper presented at the First International Symposium on Air

Breathing Engines (Marseille, France), "June 19-23, 1972.

8.4-6

TABLE I.- RANGE AND DEFAULT VALUES OF INPUT PARAMETERS

Input

parameter

Ae, m 2 ......

N ........

r S t m ........

5, deg ......

A*3 ° ° .... ° "

T"J ........

V _ ........

C_, _/5 ......

_, kg/m 3 .....

Minimum Default Maximum

0.01

1

0.01

0

0. 0001

0.7

0

0

0.2

2OO

0.2

"r/4

1

0

i

1

1.0

0

1.9

340. 294

1.225

i0

4

I00

3O

i0

4

2.5

0.9

1.2

400

!.5

8.4-7

TABLE II.- DENSITY EXPONENT u}

lOgl0 Vj/c

-,450-.400-.350-, 300-.ZSO-.200-,150-.I00-,0500.000

.050.i00.150.200.250

-1.000-.qO0-.760-.580-.410-.2200.000

,220.500.77C

1.0701.3901.7401.950

2.000

TASLE llI.- POWER DEVIATION LEVEL lOgl0 P

lOgl 0 Vj/c lOglo P

-.400-.350

-.300

-.250-.200

-.150-.100-.050

0.000.050,I00.150

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.300

.350

.400

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.I00

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.410

.430

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50Q

_

_-8 1 I 1 t ! 1 I--2.0 -- 1.5 -- 1.0 --.5 0 .5 1.0 1.5

J2.0

Corrected Strouhol Number. Iog_ e S=

or- --1

Q

"6

'_ 1 I I I. 1 I J--2.0 - 1.5 -- 1.0 --.5 0 " .5 1.0 1.5

Corrected Strouhol Nurnbmr. IOglo S¢

(g) Tj/T = 2.5; lOgl0 Vj/c = 0.125.

Figwe 6.- Continued.

12.0

8.4-52

0

--,L,'_-C,-_f _ - "_ _ 110

120130

..g_

.ba

.b

--50

-60

-70,

-2.0

D

1 1 J I I I I I-1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Corrected S_ouhoi Number, Iog_o S,

=,

J=

-60"--

--70

-80-2.0

I l I 1 I L I l- 1.5 -- ; .0 --.5 0 .5 1.0 1.5 2.0

Corrected Strouhol Number. Iog,o S=

(h) T]/T_ = 2.5: lOql 0 V3/c_ = 0.150.

Figure 6.- Continued.

8.4-53

0

=,

._ - 100

--60

-7o -

-80 I I i I I I I-_..o -_.s -1.o -.s o .s ,.o _.5

Corrected S_ouho! Number. |oglo $.

I2.0

--2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Corrected Strounol Number. Iog_o S.

(i) Tj/T_ = 2.5; lOgl0 Vj/c = 0.175.

Figure 6.- Continued.

8.4-54

0

-- 120= 130

,Q4=m

"6j:J¢,30

--5C

--6C

--7C

--8C--2.0

J I I I I ; I I--1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Corrected Strouhol Number. Iog,o S.

orL_

0 --1

--601---"5 14= I

¥ -7o,_--a- -8 I I ! 1 1 I I-2.0 --1.5 -1.0 --.5 0 .5 1.0 1.5

I2.0

Corrected Sb'ouhal Number. Ioglo S.

(j) Tj/Too = 2.5; iOgl0 Vj/Coo = 0.200.

Figure 6.- Continued.

8.4-55

0

o: - 10o

--2.0 --1.5 --1.0

Corrected 5_rouhol Number, IOg_o $6

I2.0

0

i -10

-20

-.30

-4o_/ _-'170

_ --50

o -60

0

-8ol I l L L I l I-2.o -_.s -,.o -.5 o .5 _.o _.5

Correc:ecl Strounol NumDer. IOg,o S.

(k) Tj/T = 2.5; lOgl0 V],'c : 0.225.

Figure 6.- Continued.

2.0

8.4-56

oF

_- I I I I I I I I--2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Corrected Strouhol Number, logic S=

--2C;

->>* -3C

-50

-60

-70

oF

-8o I I 1 I I I I J--2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Correct6cl Strou_al Number, =¢Kj,o S=

(i) Tj/T = 3.0; lOgl0 Vj/c = 0.I00.

Figure 6.- Continued.

8.4-57

T0 --2

-5 "" 120•1:, 130mo

--6C

--7C

--8C--2.0

I I I I L I I I--1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Correctea Sllrouhol Number. Ioglo S¢

°T

--20 _6a£_

25 --6C --

-so 1 I I 1 I 1 [-_.o -_ s -_.o -5 o .s 1.o _.5

l2.0

Correcte_ St_'ouho_ Number. 10910 S.

(m) Tj/T= = 3.0; lOgl0 Vj/c = 0.125.

Fiqure 6.- Continued.

8.4-58

r

or

o

e

- 120

1 I I I I l I I--2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

--60

--70

-80

Corrected Slrouhol Number. Iogto S,

oF-10

o -20

--30

_ -7o F-80 I I I 1 I l 1--2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5

I2.0

CorrectiKI Strouhal Number. log,o S=

(n) Tj/T= = 3.0; lOgl0 Vj/c= = 0.150.

Figure 6.- Continued.

8.4-59

0

-10

N _

.IDI_ -

-8oi I I I I I I I Jo .s 1.o 1.s 2.0--2.0 --1.5 --1.0 --.5

Corrected StTouhol Number. Iog,o S,

0Eo -10

o --20

--30

!:_ --60_-70

'_" -8OL _ l I I I 1 1-2.o - 1.5 -_.o -.s o .5 1.o _.s

12.0

Corrected Strouhol Number. lOglo S,

(o) T3/T _ = 3.0; loglO Vj/c = 0.175.

Figure 6.- Continued.

8.4-60

or

i --10

--20

--30

_ 110._ 4o_ -50 --

.m

"B-60-

-70-

-80

-2.0

, I L I I [ I I--1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Corrected 5trouha= Number. Io_lto S=

o_ --10

0 --20

--30

_ -40

lb.m

-50--

--60--

--70--

-eo I-2.0 -1.5

I I l i I I I-1.0 -.5 0 .5 1.0 1.5 2.0

Correcte_l Stro¢_ol Number. IOglo S,

(p) Tj/T = 3.0; lo_! 0 Vj/c= = 0.200.

Figure 6.- Continued.

9.4-61

_-.

e,_gJIE_

gO

10

I I I I I I I--1.0 --.5 0 .5 1.0 1.5 2.0

Corrected StTouhol Number. Iogto S,

0

_,=

- p- _---i 7o5 180

_5 6

i5 t4=

' -::T I l I l 1 I 1--2-0 -- 1.5 -- 1.0 --.5 0 .5 1.0 1.5

12.0

Correct=KI Strouhol Number. log_e S=

(q) TilT = 3.0; lOgl0 Vj/c= = 0.225.

Figure 6.- Continued.

i.

8.4-62

0

);o

1 1 I • I I I-2-0 -- 1.5 - 1.0 --.5 0 .5 1.0 1.5

Corrected Slrouho| Number. IOgso S s

i2.0

--10

"

'_ -8oi i I I ., I I 1 I-2.o -_.s -_.o -.s o .s _.o _.5

I2.0

Corrected C:_ouhol Number. log.> S,=

(r) rj/'r®= 3.5; lOglg Vj/c = O.lOC.

Figure 6.- Continued.

8.4-63

/

,. oF

!!ol I I I I I I

--2.0 -- 1.5 -- 1.0 --.5 0 .5 1.0 1.5

Corrected Strouhol Number. Iog_o S.

I2.0

oF

o

-_ l I i I I I 1-2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5

Correct4KI Sl_ouhcd Number. Io_i o S,

(s) Tj/T = 3.5; lOgl0 Vj/c = 0.125.

Figure 6.- Continued.

I2.0

.-t!

8.4-64

r ---

_ -=mms.-:-_w -'_

oF-10

-20

-30

--50 _I_

-70

- I I I I I 1 I--2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5

Corrected Strouhal Numbw', Iog_o S,

I2.0

oF

i --10

--20

--30

--40

15 -5°-80

_ 1 1 1 I i1 I-2.0 --1.5 -1.0 --.5 0 .5 1.0 1.5

Corrected Strouhal Number. Iog,o S,

I2.0

(t) Tj/T = 3.5; logl0 Vj/c = 0.150.

Figure 6.- Continued.

8.4-65

............ _ --c _- _ ...............................

oro --10

o

-50-- 130

.m-60 --

--70 --

--80.-2.0

i I l I [ I I J--1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Corrected SVouhol Number. iOglo S.

o_ --

o

o

-30

. --50

._m

(J0

-60

-70

--80- :.0

1 1 I J I I 1 I-- 1.5 - 1.0 --.5 C .5 1.0 1.5 2.0

Co4rrect:ed S_Ouhol Number. Io9,o S,

(u) Tj/T = 3.5; logl0 Vj/c = 0.175.

Figure 6.- Continued.

8.4-66

• -'J-:-. -

0

_ -10

C 0

50 1_

--60

_ --70-eol I I I I I I I J

-2.o -1.s -1.o -.s o .s 1.o 1.s 2.0

Corrected S_ouhal Number. loglo S=

or--10

-20

_ _

f--60

--70

or -8o I i I i I I I I--2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5 2.0

Corrected Sti-ouh_ Number, log_o S=

(v) Tj/T = 3.5; lOgl0 Vj/c = 0.200.

Figure 6.- Continued.

8.4-67

w. •

,/_k

0

--10

o --20

--30

--50_--60

-8ok_____-2.0 --I .5 I -L____L____L

- I.o -.s o .5 I.o 1.5--------

Correcte<l Strouhol Number. Iogto S¢

I2.0

0

--10

o -20

_ -50_ '_

_ -6C_u_ -70

-80 l i I I I -! I--2.0 --1.5 --1.0 --.5 0 .5 1.0 1.5

Corrected Sll]'ouhcd Number. Io@_o S,

(w) T_/T = 3.5; lo<910 Vj/c = 0.225.

Figure 6.- Concluded.

I2.0

8.4-68

I

I I I 1 I }¢_ oO r-. r,D la,')

IbIIm

no t-

o ="n ...

0

0

0

(e)ua 'xapul _'!oolaA pJDMJOA

8.4-69

k_

8.5 CIRCULAR JET SHOCK CELL NOISE MODULE

INTRODUCTION

The Circular Jet Shock Cell Noise Module predicts the broadband

shock-associated noise from a single convergent nozzle operating at super-

critical pressure ratios. The method is based on the proposed Appe._dix C

by H. K. Tanna to SAE ARP 876. The method employs master spectra func-

tions and a shock cell interference function to produce sound spectra as

a function of frequency and polar directivity angle.

The method requires input of several parameters. The jet noise

parameters can be provided by the Jet Noise Parameters Module or directly

by the user. Additional user-provided parameters are required. The

module is executed once for each set of values of the input parameters.

The output is a table of the mean-square acoustic pressure as a function

of frequency, polar directivity angle, and azimuthal directivity angle.

Although jet shock cell noise is assumed not to vary with azimuthal

directivity angle, it is introduced so that the output table is com-

patible with other noise tables.

A e

Aj

b

C

C a

f

H

_j

M=

N e

N s

<p2>"

Pref

SYMBOLS

engine reference area, m 2 (ft 2)

jet nozzle reference area, m 2 (ft 2)

proportional bandwidth constant

correlation coefficient spectrum

ambient speed of sound, m/s (ft/s]

frequency, Hz

Helmholtz number, f _e/C

group source strengt/n spectrum

jet Mach number

aircraft Mach number

number of engines

number of shocks

2 4

mean-square acoustic pressure, re D c

reference pressure, 2 x 10 -5 Pa (4.177 × 10 -7 Ib/ft 2)

8.5-1

r s

tr

s

T.

3

V.

3

distance from nozzle exit to observer, _ (ft)

dimensionless distance from nozzle exit to observer, re _e

jet total temperature, _ (oR)

ambient temperature, K (OR)

fully expanded jet velocity, m/s (ft/s)

shock cell interference function

pressure ratio parameter, _M_- 1) 1/2

angle between flight vector and engine inlet axis, deg

exponent

polar directivity angle, deg

ambient density, kg/m 3 (slugs/ft 3)

frequency parameter, 7.80S(I - M

azimuthal directivity angle, deg

Superscript:

* dimensionless quantity

cos 8)_jf*

INPUT

The jet noise parameters are required from either the Jet Noise

Parameters Module or the user. Ambient conditions are required for

computation of the frequency parameter and sound pressure levels. The

frequency, polar directivity angle, and azimuthal directivity angle

arrays establish the independent variable values for the output table.

Fin._lly, _ne englne reference area, number of engines, engine offset

angle, and distance to observer are required. The range and default

values of _ne input parameters are given in table I.

A e

N e

N s

r s

Input Constants

engine reference area, m 2 (ft 2)

number of engines

number of shocks

distance from nozzle exit to observer, m (ft)

At3

M]

Je_ Noise Parameters

area of ]et, re A

fully expanded 3et Mach number

8.5-2

/

J

T:3

v:]

Cam

M

jet total temperature, re T®

fully expanded jet velocity, re c

Ambient Conditions

ambient speed of sound, m/s (ft/s)

aircraft Mach number

ambient density, kg/m 3 (slugs/ft 3)

Independent Variable Arrays

frequency., Hz

polar directivity angle, deg

azimuthal directivity angle, deg

OUTPUT

The output of this module is a table of the mean-square acoustic

pressure as a function of frequency, polar directivity angle, and azi-

muthal directivity angle. In addition, the obse_2er distance r s is

provided for _he Propagation Module.

r sdistance from nozzle to observer, m (ft)

f

<p: {f, :,:)>"

Circular Jet Shock Cell .Noise Table

frequenc?, Hz

polar directivity angle, deg

aza=uthal directivity angle, deg

mean-square acoustic pressure, re _c_

METHOD

The _rediction methodology proposed by H. K. Tanna is used to com-

pute _e shock cell noise. Details of the development and validation of

_ne method are given in references 1 and 2. A schematic of a typical

exhaust 2et .nozzle _s shown in figure i. _'_..ecoordinate system and

directivit? angles are also shown. The total jet noise will be the sum

of the shock cell and jet mixing Pmise.

8.5-3

E

!

i=

L

I

I8

ii

i

PI

The normalized i/3-octave-band mean-square pressure for shock

associated noise is given by

<p2>* = (1.92o × lO-])

4_(r:) 2 _ - M cos (@- 6)] 4

n8 H(O) (i)

The dimensionless source to observer distance r*s

is defined as

r: = rsi_e

and the frequency parameter _ is

= 7.80_(i - M cos 8) _*. f*

The pressure ratio parameter is defined as

and is a measure of the relative shock strength. The pressure ratio

parameter _ must be greater than 0 for shock cell noise to occur.

exponent of the pressure ratio parameter D depends on the jet Mach

number Mj and the 3et total temperature T: asJ

i

= 2

4

(Unheated jet (T; < i.I) with _ > i)

(Heated jet (T; > I.i} with _ > i)

(All jets with 8 < i)

(2)

(3)

(4)

The

(5)

The shock cell interference function W is a function of the fre-

parameter _, polar directivity angle 9, and velocity ratio V_quenc/

and is expressed as

Ns-i N s-(k+l)

sin (bOqkm/2)

4 _ [c(_) ]k2W = Nsb bGqk m

k=l m=0

cos (Oqkm) (6)

where

qkm = l'7--Okrl-v$L 0"06<m + _'_>I (I + 0"TV; c°s 9)

3

(7)

8.5-4

and b • 0.23077. The two master spectrm, the correlation coefficient

spectrum C of equation (6) and the group source stronqO_ spectrum H of

t.xluation (i), are qiven in tables II and Ill and plotted in flquros 2

and 3, respectively. Per an unheated Jet, the value of I! should be

2 dB le:_s than the tabulated value. The shock cell interference func-

tion W is plotted in figure 4 for a value of N s • R. Once the mean-

square pressure has been computed by equation (I), it is multiplied by

the number of t,nqines N to produce the total shock cell noise.e

The output of thi:; module is a table of th,._ mean-square acoustic

pressure _p2_* as a function of frequency, |x_lar _lirectivity angle, and

.l=imuthal directivity angle. In addition, printed output is available of

the gound pro._._ure level SPL defined a._

2

SPL = i0 loglO <p2>' + 20 loqlo-

P r,! f

(n]

REYE KE.N_'E:;

I. H,irp,,r-_ut'no, M.; ,lad l'i:_her, M. ,I. : Tht_ Noise From ._:hock W,lvo_ in

.*:ul_r..;onLc ,h,t:_. No_.._o Mech,mi:;m,:, A_K_-CP-[31, H4v. [,174,

i,_,. ll-I - II-I _.

2. T,Inrla, 14. K. : Dean, P. D. ; .In_| l_tlrrin, R. ]!. : The Ct,n,,t._ttotl and

R.tdt.ltiot_ of ._u|',,r:;_nic ,let Not::,,. Vol_lm.o I%' - _hock-A._._oct.ltt'd

N,:l'.m D.tt.t. AF'APL-'PR-7_,-t_S, Voltm_, IV, LI.G. Air l'orco, ._t,|_t. l'_7_,.

• °s

j-

TABLE. I .- RANGE AND DEFAULT VALUES OF INPUT PAKAMETERS

InputMax imum De f,_u I t Max imum

parameter

9

Ae, m" . .....

Mr, ........

N . . . . ° . . .s

rs, m .......

_j ........

T_ . .......

v"_ ..... o ° .

_, ,leq ......

C ,_, m/' S ......

D , k,;/m ] .....

0.01

1

2

0.01

0.0001

0

0

0.7

0

0

200

0.2

",/4

1

S

1

0

1.414

1

1

,3

340. 294

1.225

]0

4

1O

I00

i0

0.9

2.0

6

3.5

30

400

1.5

S. 5-6

°

X

[-

u_

[-.

Z

E-.

0

I

2

<

0

0

f

I I I l l l I l I l l I I I I I I I I I I I I I I I

• • oooooQo •

[-(,

:A

[.-,

I

<

0

0

8.5-7

Figure I.- Schematic diaaram of single stream circular nozzle.

8.5-8

l

_f

l 1 I I J I I

0

t00

0

• ID

Eo1,..

0a.

ot-

3O"¢)1,,,.

la_

0

I/)

4.le.

0

0

0

0U

l

,0 'u-ln40'_dS 1ue!alJ,._aoo UOi]l:)lSJJO0

i 8.5-9

0

i0

0

q

I io

i ,- ,- _ _I I I I I

H °L6Ol 'uJru_aads q),6ua.n,S aoJno S dno.J 0

b

o

0

E0I,.-

0I:L

0c-

_r

I,,-

!,

L,4.1

U

P.,

r"

I,a4.;

(/1

UL,

0

0

I

,3

8.5-10

b

0

o

CQ_

Q;Eo

n

Q_

(TQ;

i,

0

.,J

Uf.

U

¢;

,-6

_JU

_J

0

I

l l ! I I _Q

"- '-- I ,---I

M "uo!'_oun.:t aoua_j._Ul lla 0 _looqs

8.5-11

- i

J

0

|$

o

e-.,-d

0

!

,_ 'uo!l.aun4 a:::}uaJa:l.Jal.Ul Ila9 )lo0qs

0

I

0

8.5-12

0

c

4J

0

(J

!

CJ

I I I0 _f3 0

M 'uo!),oun:l eoueJepe),Ul lleO >10oqs

00

I

i

8.5-13

_r

0

aO

N_ 'uo!_.aun-I aouaJa#a_.Ul ila 9 _aoqs

8.5-14

0

0000

./_ 'UO!_OUn_-] aouajaj.j9_,u I ii_0 >1oo4s

00

O0

I

b

0

o_0

..._, ,_

E e.

o _t,,,- t-

O on u

!

>_ ,,_

¢- o

o-t,.,.

i,

8.5-15

ilJ

'e

L

\

M 'u0!:[0un__ @::)u_)J;aJJa),ul IleO >looqs

8.5-16

0

r--

-- u0

-- 04

00

I

o

o

Q;

EoL.

o(3_

0c-

b_

U

_..0

(J

I

b_

8.6 STONE JET NOISE MODULE

INTRODUCTION

The Stone Jet _oise .Module predicts the far-field mean-square

acoustic pressure for single stream and coaxial circular jets. Included

in the prediction are both jet mixing noise and shock-turbulence inter-

action noise. The method used is that developed by J. R. Stone as pre-

sented in references 1 and 2. For coaxial nozzles, the method is limited

to jets whose core jet velocity is greater than the secondary jet velocity.

Further, only t_he core jet velocity may be supersonic.

The method requires input of several parameters. The nozzle exit

flow parame + _rs can be provided by the Jet Noise Parameters Module or

directly b? the user. Additional user-provided parameters are required.

The module _s executed once for each set of values of the input param-

eters. The output is a table of the mean-square acoustic pressure as a

function of frequency, polar directivity angle, and azimuthal directivity

angle. Jet exhaust noise is assumed independent of the azimuthal direc-

tivity angle; however, the prediction is tabulated as a (constant) func-

tion o_ azimuthal angle so that the output table is compatible with other

noise tables.

A_

"%.

3

_S

d_

d..q

d_J

P

Fm

F3

SYMBOLS

engine reference area, m 2 (ft 2)

fully expanded jet area, m 2 (ft 2)

ambient speed of sound, m/s (ft/s)

directivity function for 3et mixing noise

directivity function for shock noise

equivalent diameter, m (ft)

hydraulic diameter, m (ft)

jet diameter, m (ft)

plug diameter, m (ft)

spectral distribution factor for jet mixing noise

spectral distribution factor for shock noise

frequency, Hz

3.6-1

t

L

.<

S-

I

fs

%

Gp

gc

gp

M

m

N

<_2>"

frequency shift parameter

configuration factor for mean-square pressure for coaxial nozzle

configuration factor for mean-square pressure for plug nozzle

configuration factor for Strouhal number for coaxial nozzle

configuration factor for Strouhal number for plug nozzle

forward flight effects factor

Mach number

aircraft Mach number

exponent

number of engines

2 4

mean-square acoustic pressure, re p c

<p2(

Pref

R d

r S

S m

S 5

T

T

V

_5

&

2,'

&

mean-square acoustic pressure at the reference

distance _e at @ = 90 ° , re 0_c_

reference pressure, 2 x 10-5 Fa (4.177 x 10 -7 ib/ft 2)

ratio of hydraulic diameter to equivalent diameter

distance from source to observer, m (ft)

Strouhal number for jet mixing noise

Strouhal number for jet shock cell noise

fully expanded jet temperature, K (oR)

ambient temperature, K (OR)

fully expanded jet velocity, m/s (ft/s)

pressure ratio parameter, (N_ - 1) 1/2

angle between flight vector and engine inlet axis, deg

polar directivity angle, deg

modified directivity angle, (V_)0"Ig, deg

Mach angle, deg

fully expanded jet density, kg/m 3 (slugs/ft 3)

ambient density, kg/m 3 (slugs/ft 3)

L --

8.6-2

Jt

w

Wo

azimuthal directivity angle, deg

density exponent

stationary jet density exponent

Subscripts:

iL

i

i primary stream

2 secondary stream

Superscript:

dimensionless value

INPUT

The jet parameters are required from either the output of the Jet

Noise Parameters Module or the user. Ambient conditions are required.

The frequency, polar directivity angle, and azimuthal directivity angle

arrays establish the independent variable values for the output table.

Finally, the engine reference area, number of engines, engine axis offset,

and distance to the pseudo-observer are required. The range and default

values of the input parameters are given in table I.

A e

N

r S

3

Input Constants

engine reference area, m 2 (ft 2)

number of engines

distance from nozzle exit to pseudo-observer, m (ft)

angle between flight vector and engine inlet axis, deg

Jet Noise Parameters

Primary Stream

d;, 1

41

primary fully expanded jet area, re A e

actual primary stream equivalent diameter, re _e

actual primary stream hydraulic diameter, re

primary stream Mach number

primary stream total temperature, re T

°8.6-3

----4 ............

I

V 1 primary stream jet velocity, re c

_ primary stream jet density, re O=

_eco Ildd t_ . Stream

,CJ

Mr

T:

¢.._econdary fulty e-q_anded jet area, re A

e

_econdary ._troam Math numb_,r

.qecondary .,;trpam total teml_er,lture, re T

:_econdar\." :;tream _et velocity, re c+

secondary stream jot density, re.,

Ambient Condit ions

ambient sound st_ed, m/s (ft./._)

aircraft ._ach number

arab.lent density, kq/m 3 (.qiu_ls/ft 3)

Th,' outVut of thi:; _dule i_ a tabh, of _he t,%_an-squ.lre acoustic

|'r,'_',_;ur,,.,.q a function of fr,.qucncy, !x_l._r ,:irectivity an,_le, and ._:i-

muthAl d_rect_vity an_l_e. In addition the }-seudo-observer distance r:

l:; [,rovtd,,d rot t.h_, Pro[,._q.lt_on Module.

r. ,IX:_tanc,, from no::l,, ,'xZt to },.qeu,k_-obser':er, m (ft)

Stone's Method Jet l_k_se TAble

f frequency, H:

'_ },olAf ,i_r,,ctlv_,_,:' ,%nq[e, deg

._ Az_muth._l d_r,,ctlvtty angle, deq

<_,-'tf,_,:)>° me,_n-_quare acou:;tic _-res._ure. re o'c 4"

8.6-4

i

METHOD

The prediction method developed in references 1 and 2 is used to

compute the mean-square acoustic pressure in the far field. The method

uses empirically determined functions to provide the directivity and

spectral content of the field with the computed overall mean-square

= 90 )> , used to fix the amplitudeacousticpressure.t e 90o. o •throughout the field.

This module can be used to predict the noise for several exhaust

nozzle types including both subsonic and supersonic single s_ circular

nozzles, both with and without plugs, and coaxial jets.

The prediction schemes for all nozzle types are developed from two

basic equations, one each for jet mixing noise and shock-turbulence inter-

action noise, each of which is empirically determined. Furthermore, con-

figuration factors are used to adjust the levels predicted for single

stream circular nozzles to those for single stream plug nozzles or

coaxial nozzles. Illustrations of these various configurations, also

showing the coordinate axis and directivity angles, are provided in

figure i.

Jet Mixing Noise

The equation used to calculate the jet mixing noise at a distance

from the nozzle exit is

< I(r:) 2 1

x Dm(e' ) Fro(Sin,8' )

l_+[0:12 v[[2_]+ 0.62v_ cos 0) 2 + (0.124v[)

3/2

Hm(M_,@,VI,01,T I) GcG p

r s

(!:

In this equation <p2( A_e,90°)/ is the mean-square acoustic pressure for

a stationary jet calculated at the reference distance _ f._om the

nozzle exit at @ = 90 °, r: is the dimensionless distance from the

nozzle exit r s referred to _e' Fm(Sm'@') is a spectral distribution

function, Hm(M_,@,V_,O_,T _) is the forward flight effects factor, G c

and G are configuration factors, and Dm(@'} provides directivityP

information. Each of these factors is now considered in detail.

The mean-square acoustic pressure at the reference dista.n_e and

= 90 O, < p2(_e,90° ) >*, is cal<:ulated through use of the following

equation:

D

8.6-5

<p2(_e.gO°)>"=2.5O2x10-6A_,IC_Cv;_75

[i+(2)

Here, A_, 1 is the fully expanded jet area, P_ and V[ are the fully

expanded jet density and velocity, respectively, with all three quanti-

ties evaluated for the primary stream, and nondimensionalized by A e,

p_, and c , respectively. The density exponent w o is an empirically

determined function of V 1 given by

2(V_) 3"5 - 0.6

= (3)Loo(V,*) 3"5 + 0.6

&

The factor Fro(Sin,8') is a function of the modified directivity angle

9' = @(v_) 0"I and the jet mixing noise Strouhal number S m calculated by

S m =

0,v[Cl- .,,=Iv[,

.,_i/2

(I + 0.62V 1 cos _)2 + (0.124VI)2 / gcgP

_)

In this equation f* is the Helmholtz number given as

f_eC

(5)

M is the aircraft Mach number, and dj, 1is the jet diameter given as

(6)

Further ,5 is the angle between the flight vector and the engine inlet

axis, in degrees, and T_ is the fully expanded primary jet temperature

nondlmenslonalized by T . The function Fm(Sm,9') is normalized such

_nat the summation over i/3-octave Strouhal number is unity:

8.6-6

Fm(Sm, e ) = 1Sm

(7)

and is tabulated in table II and plotted in figure 2.

The function Dm(e') contains directivity information and is given

in table III and plotted in figure 3.

The factors gc and gp are configuration factors which are dis-

cussed when the configuration factors Gc and Gp of equation (i) are

considered.Thefo_ardflighte_fectsfactor_(.®,e,V_,_.T_isgiven by

+0.62(v"l-.®)cose]

(1 - _/v1)s(p;)_-_°

1 - M cos.(8 - $)(8)

where

0 1(9)

The function Hm is normalized such that it is unity if M,_ = 0 for all

values of the remaining parameters:

(I0)

The configuration factors Gp and G c take the mean-square acoustic

pressure predicted for a single stream circular nozzle and adjust it to

predict the mean-square acoustic pressure for plug and single nozzles,

respectively. The factor <;P is given by

10 * -- {Nozzle with plug)

(Nozzle without plug)

[Ii}

8.6-7

In this equation,

= d*Rd d:,ll e, 1

With _,i" the plug nozzle hydraulic diameter, given by

< = _

(12)

(13)

i"

and d:, I, the nozzle equivalent diameter, given by

where A_, 1 is the primary nozzle area and d: is the plug diameter:

these quantities are nondimensionalized by A e and _e' respectively.

The factor G c is given by

_C =

_'_l l- ,,_/,,_).,+ (l+ ,._,_/,,_,1)_(Coaxial nozzle)

1 (Single nozzle)

(14)

The exponent m is given by

,1

(15)

The factor gp or gc adjusts the Strouhal number S m for a

single stream circular jet to that for a plug nozzle or a single nozzle,

respectively. These factors are given by

gp = I (rod)

I1

0.4(Nozzle with plug)

(,Nozzle without plug)

(16)

8.6-8

I

_J

I

and

_- T_fs/,i)-1 (_o-xialno.-le_gc = (17)

(Single nozzle)

where fs is an empirically determined function of the area ratio param-

; /_; " ""eter 1 + A ,2 ,I and the velocity ratio V2_ I. This function is

tabulated in table IV and plotted in figure 4.

Shock Noise

The ll3-octave-band mean-square acoustic pressure due to shock-

turbulence interaction noise is calculated through use of the following

equation:

<p2>* =

(3.15 _ 10-4)A_),I

, 2

(r s )

.q4 Fs(S s) Ds(0,M I) G c

.4 i -M,,_ cos (_- <_)I - b

In this equation _ is the pressure ratio parameter as follows:

_: (.,,__ _)1"2

(18)

(19)

which must be qreater than zero for shock cell noise to occur.

The function Ds(0,M I) provides the dependence of the shock ceil

noise, for a stationa_- jet, on the directivity angle "_ and the fully

exFanded primary stream Mach number M I. This function is given by

P

_i (9 & 9 m)Ds (_,M 1 }

L1.189 (O > @m )

where 0m is the Mach anoie defined by

'?m = Arcsin (IIM I) (20)

i8.6-9

The spectral content of the shock noise is provided through the

function Fs(S s) which depends on the Strouhal number Ss:

ss = _ - _ cos - + +0.70V 1 (21)

The function Fs(S s) is tabulated in table V and plotted in

figure 5.

The total far-field jet noise will be the sum of the shock noise and

the jet mixing .,oise.

The mean-square acoustic pressure for one engine, which is _e stun of

the jet mixing noise, as computed by equation (i), and the shock noise, as

computed by equation (18), can be computed for each desired value of the

frequency, polar directivity angle, and azimuthal directivity angle. The

total noise is the mean-square acoustic pressure multiplied by the number

of engines N for the output table. In addition, printed output is

available of the mean-square pressure <p2>" and sound pressure level

SPL defined as

SPL = 10 lOql 0 <p2>*

01o:+ i0 logl0 2 (22)

Pref

Power level calculations are not performed by this module.

REFERENCES

I. Stone, J.Imes R.: Interim Prediction Method for Jet Noise. NASA

TM X-71618, 1974.

2. Stone, James R.; and Montegani, Francis J.: An Improved Prediction

Method for the .Noise Generated in Flight by Circular Jets. ,NASA

TM-81470, 1980.

8.6-I0

TABLE I .- RANGE AND DEFAULT VALUES OF INPUT PARAMETERS

InputMinimum Default Maximum

parameter

2Ae, m ......

S o . o ° . . . °

r S s m .......

6, deg ......

Aj, 1 .......

d:, 1 .......

,1 .......

M1 ........

T_ ........

V_ ........

0_ ........

A; ,-_ .......

M 2 ........

T_ ........

V 2 ° ° • • . . ° .

92 ........

•%_ . ° . . • o . °

D , kg/m 3 .....

0.01

1

0.01

0

0. 0001

2 × 10-2/_'_

2 x I0-2/_'_

0

0.7

0

0.2

0

0

0.7

0

0.2

30O

0

1.0

./4

1

0

1

1°0

1.0

1.0

1°0

0

0

1

0

1.0

340.194

0

! .225

i0.0

4

i00

30

!0

1.25

4.0

2-5

1.2

10

i

4

2.5

1.2

400

0.9

1.5

8.6-11

E

b.i

0

0.-.4

b.1

Z

0

[.-,

m

e,m

M

Z

Z

X

Ul

I

2

!

0

0," 0

C0 _"

0

00

22

:NI

0 !

cl

0

E

eooooo oooO oooooooo Ioo

IJl|JI Jill OII|||II|II|IIII|II

,,,,,,, ,,,,,°T_'''''* o,TT "°,,

I I I

oooo moo oooo oooooo

IIIlI IllOllIllllIlilllIlIII

Olle

IO

I I

II_.O0 • • •

"" I I I

ooomooomooooo_oomooomolooooooooo

__ I I I I __i___#_e# _

I I I I I I I I I I J I I I I I I I I I I I O I I t * I

II

Ir*l_I I

0 _

Ill Illilll llllillllllI|liillili

00"

I i

,4r _ 41%

"-* I I !

_l____O_m___O_oooeoooooooooooooo_ooeeoeooooooo

IIIIIlll Illllllllllllllllll

1151 __lr_r! I

_4M• o m

_ e,,,e ID

•d" ,.it _I I I

Ol__O__O____m_iIIIIIOIIIOtI|iIOltIIIIlIIIIOII!

IlJlllIIll IOllllllJllllllllJ

I_eel

_e,e

I I

.._0_[,

dr.4r_

! i !

m_m_Om_OO_OO__m_O__

Iii1111111111 illllillllilllllll

_.o

I I

perI_• m •

??T TTTT?TTTTTTT?TTTT,TTT,,,,,,,,_ ??

.._._._lllllllllO ___

llllllll

8.6-12

D

.f/

I

TABLE III.- JET MIXING NOISE DIRECTIVITY LEVEL

8, deg

110•0

120•0

130.0140•0

150.0

160.0170.0

180.0190.0

200.0

i0 lOgl0 Dm

0.00

-,51

-1 •07-1,56

-1 •98

-2•55-3•00

-3.50-4 •01

-4•52

i0 lOgl0 Dm

TABLE IV.- FREQUENCY SHIFT PARAMETER fs

0.00,05•10.15.20.75,30

,40.45._0

,60

,70.?S.80

.90

.951.001.051•101.151.ZO1•251.301.351.401.451.501.551.60

0.20

0•00•04•07.11,14•16

fs for V_/V_ of-

0.60

.19.21°24.25.27,28• 28•Z9,29,30.30,30,30•30•30,30•$0.30,10,$0•30,30.30.30,30.30.30

0.40

0.00.05•Oq•13,17.21,Z5,28.31•35,38• 41_,43.46,4P.51,53.55,57• 59,61•63•65,bb•68• 69•71•72.73,74,76•77,78

O. O0.06•lZ•18.z3•28•33•3?,41.45

,_1.93•56,_9.61,6**•65.67,69,71.73• 74.79.77,78• 7,9.81.8z.tL3.84.85.86

0.80

0,00,05,10.1S,ZO,Z9.Z9.33.37.40.43,46•48,SZ.54,96._S9,61,b:l.64.65.68.69• 7'0,?Z.73.?4.?'J.76.7,7.78,80.81

1.00

0.00,04,08.lZ.16,ZO.Z3.Z6.30.3Z.35.38,41.43,45.48,50,92,94.56

.60

.61

.63

.65

.66

.67,

.69

.7,0

.71

.7,3

.74

.?_

_L

8.6-13

TABLE V.- SEOCK NOISE SPECTRAL DISTRI_3TION

LEVEL I0 lOgl0 F s

l°gl0 S s

-1,8-1 o7-1,6-1,5-1,4-1,3-1.2-1 ol-1,0

--e9

--e8

--e7

--°6

--,5

--,3

--,Z

--°1

0,0,1,2,3,4,5,6°7,8,,9

1.01.11.Z1.31°41,51,61,71o8

i0 lOgl0 F s

-9t,60-89,69-84,60-79,60-74,60-69,60-6_,60-59°60-54,60-_9,60-_4,60-39,60-34,60-29,60-Z4,60-Z9,60-14,60

-9,60-7,60-8,60-9.60

-10,60-11,60-12,60-13,60-1_,60-19,60-16,60-17°60-18.60-19,60-20,60-21.60-22,60-Z3,60-24.60-Z5,60

8.6-14

T1 Vl _i X

(a) Single streamcircular nozzle.

:y

(b) Dual stream coaxial nozzle.

Figure i.- Schematic diagrams of nozzles.

B.6-15

I0

II

I0

I

I I I I I I ] 1 1! i

_.I ' ' i I I IS_BOI OL '10_1 uo._n_,l_l!(] Io4°lds

o

m

r.o

.M

o

o_°_ _

_,' _ -g

o. ,

!

! I

8.6-16

I

o

N.6-17

J

w

i I I L 1,,- ¢'4 P_J) _'

! I IQ

"0 °t6o! 0L "_!A.qooJ!Q

I

oo('1

oa0

o

v

E

,qrv-

U

0

Ill .,,,4

• _

X

l,J

0 _ID

I

C3

0C,4

o

8.6-18

.

iJ

q

m

!

°; "Je_,ewo.Jod 1,1!qS ,_ouenbe._,

,f

8.6-19

0

Ijjjjjjjjto=_ p'_ qf' _ lID I_. _ _ 0 I

0 I I ! I I I I I I --I

"le^Ol uo!;nqlJlS!Q IO'lOldS"3 °_5°t OL

Q

o

0

0 I

_4!

I

8.6-20

_"L

8.7 DUAL STREAM COANNULAR JET ._OISE MODULE

INTRODUCTION

The Dual Stream Coannular Jet Noise Module predicts the noise charac-

teristics of a coannular jet exhaust nozzle with an inverted velocity pro-

file. The dual stream jet has a se=ondary, or outer, flow which has a

higher jet velocity than the primary flow. The method converts the

coannular jet to an equivalent single stream jet with the same thrust,

mass flow, and energy. The prediction is based on the method developed by

Pao and Russell as presented in references 1 and 2.

The method requires input of several parameters. The two-nozzle exit

flow states can be provided by the Jet Noise Parameters Modul_ or directly

by the user. Additional user-provided parameters are required. The

module is executed once tot each set of values of the input parameters.

The output is a table of the mean-square acoustic pressure as a function

of frequency, polar directivity angle, and azimuthal directivity angle.

Although the jet noise is assumed not to vary with azimuthal directivity

angle, it is introduced so that the output table is compatible with other

noise tables.

A

A e

D

deq

d h

f

.t[

G

m

SYMBOLS

fully expanded jet area, m 2 (ft 2)

m 2engine reference area, (ft 2)

ambient speed of sound, m/s (ft/s)

directzvity function

equivalent jet diameter, m (ft)

jet hydraulic diameter, m (ft)

frequency, H:

Helmholt: number, f A_e#_

s_ectral distribution function

aircraft Mach number

forward velocity index

mass flow rate, kg/s (slugs/s)

8.7-I

m .

N

P

<p2>"

Pre f

rs

r:

S

S 1

S 2

T

V

j. i

d

_O

ref

J

J

d 1

number of engines

power deviation factor

2 4

mean-square acoustic pressure, re pc

reference pressure, I x 10-5 Pa (4.177 × 10 -7 Ib/ft 2)

distance from nozzle exit to observer, m (ft)

dimensionless distance from nozzle exit to observer, re _e

Strouhal number

first peak Strouhal number

second peak Strouhal number

total temperature, K (OR)

ambient temperature, K (OR)

jet velocity, m/s (ft/s)

relative spectral peak magnitude factor

= ._%2/A 1

ratio of specific heats

anqle between flight vector and engine inlet axis, deg

polar directivity angle, deg

power, re DaC3Aeqacoustic

reference power, 1 x 10 -12 W (7.376 x 10 -13 ft-lb/s)

jet density, kg/m 3 (slugs/ft 3)

ambient density, kg/m 3 (slugs/ft 3)

r_rmalized Strouhal number

first peak normalized 5trouhal number

second peak normalized Strouhal number

azimuthal directivity angle, deg

dens i ty exponent

8.7-2

Subscripts :

eq equivalent jet

1 primary jet

2 secondary jet

Superscript:

* dimensionless quantity

INPUT

The primary and secondary jet parameters are required from the output

of the Jet Noise Parameters Module or from the user. Ambient conditions

are required for computation of the Strouhal number and sound pressure

levels. The frequency, polar directivity angle, and azimuthal directivity

angle arrays establish the independent variable values for the output

table. Finally, the engine reference area, number of engines, engine

inlet axis offset, and distance to observer are required. The range and

default values of the input parameters are given in table I.

A e

N

rs

V*1

Y1

Input Constants

engine reference area, m 2 (ft 2)

number of engines

distance from nozzle exit to observer, m (ft)

angle between flight vector and engine inlet axis, deg

Primary Jet Parameters

primaz- l jet area, re Ae

primary jet total temperature, re T

primary jet velocity, re c

primary jet density, re Pm

ratio of specific heats for primary jet

Secondary Jet Parameters

secondary jet area, re A e

jet hydraulic diameter, re _esecondary

8.3-3

t

0 2

Y2

Co0

Mco

secondary jet total temperature, re T

secondary jet velocity, re c

secondary jet density, re D_

ratio of specific heats for secondary jet

Ambient Conditions

ambient speed of sound, m/s (ft/s)

aircraft Mach number

ambient density, kg/m 3 (slugs/ft 3)

Independent Variable Arrays

frequency, HZ

polar directivity angle, deg

azimuthal directivity angle, deg

OUTPUT

The output of this module is a table of the mean-square acoustic

pressure a: a function of frequency, polar directivity angle, and azi-

muthal directivity angle. In addition, the observer distance r s is

provided for the Propagation Module.

r s distance from nozzle exit to observer, m (ft)

Double Stream Coannular Jet Noise Table

f frequency, Hz

polar directivity angle, deg

azimuthal directivity angle, deg

4<p2(f,_,_)>" mean-square acoustic pressure, re _c

METHOO

The noise prediction method determ/nes the noise characteristics of a

slngle equivalent jet which has the saume total thrust, mass flow rate, and

energy as _he coannular jet. The i/3-octave-band mean-square acoustic

pressure is computed as a function of frequency, polar directivity angle,

8.7-4

.J

and azimuthal directivity angle for the input conditions. The method

used has been extracted from references £ and 2. A sc;,ematic of a typical

coannular jet nozzle is shown in figure 1.

The mass flow rate of the equivalent jet is given by

where m* + p*A*V*. The equivalent jet velocity is computed by equating

the equivalent jet thrust to the sum of the thrusts of the individual jets

as

eq .tmeq

By assuming that the products of combustion do not affect the value of the

gas constant, the equivalent jet temperature can be computed from the

energy equation as

T" = (3)

eq • • 71 • "{_2

ml Yl " 1 + m2 72 1

The equivalent specific heat ratio is determined by the mass average

Y1 * 72

Yeq m_ Y1 - 1 + m2 Y2 - i= (41

-- -t

Yeq 1 _ + m2

The equivalent jet density is found from the condition that the jet static

pressure is equal to the ambient static pressure. Rearranging the perfect

gas law yields

"= - (V } (5]eq eq 2

and _he equivalent jet area is

A, = eq

eq D" V"eq eq

(6)

8.7-5

a_ .....

irJ

_he equivalent jet diameter is

=.d_q (7)

The acoustic power _* is calculated for the equivalent jet using

the single stream circular jet method. A coannular benefit factor 0 is

added to this relation to account for double stream effects. The result-

ing expression for the acoustic power is

_* = (6.67 x 10 -5) (^*Weq_'"_'V*teq1"8p(Veq)Q(Veq,V2/VI)* * * * (8)

_%e power deviation factor P is a function of the velocity ratio

V:q_ and is give_ in table IT and plotted in figure 2. The densityioglO

exponent _ is a function of the velocity ratio lOgl0 V:q and is given

in table III and plotted in figure 3. The coannular benefit factor Q

is a function of velocity ratio V_/V_ and velocity ratio lOgl0 V:q_

and is given in table IV and plotted in figure 4.

The mean-square pressure is computed from the acoustic power using

a normalized directivity function and a normalized spectrum function.

For a directivity angle less than ii0 O, the I/3-octave-band mean-square

pr.essure is

<p2>* : eq . (9)4_(r.)2 -(@ - 6) G(@'CI) e

\ eq

and for directivity angles greater than ii0 °,

<p2>" = [°(°'°,' ..... '-I_=(r:)__ - _, cos(e- 6)[_ ;_; " 1÷_' j\ <_(I0)

%-_ere r*s = rs/A_--".,e The directivity function D in equations (g)

and (I0) is a function of polar directivity angle @ and velocity ratio

V_ and is given in table V and plotted in figure 5. The termsloglO

•_hich include the aircraft Mach number M account for forward flight

effects. The forward flight index m(@) is a function of "- Jar direc-

t_vity angle 9 and is given in _able VI and plotted in fibre 6. The

ar.gle _ allows for an offset between the engine inlet axas and the

d_rection of flight. T_._ ,maining terms in equations (9) and (I0) give

_ spectral distribution.

8.7-6

.. coannular jet has a spectrum characterized by two peaks. The

first peak corresponds to the characteristics of the outer stream and

exists for all values of the polar directivity angle. The second peak

corresponds to the characteristics of the mixed stream ar_ exists for

values of the polar directivity angle greater than 110 °. The spectra are

expressed in terms of the Strouhal number defined as

(Ii)

The peak Strouhal numbers are a function of polar directivity angle e

and velocity ratio log V* The first peak Strouhal number S I isI0 2 °

given in table VII and plotted in figure 7. The secor_ peak Strouhal

number S 2 is given in table VIII and plotted in figure 8. The Strouhal

nmmbers used to define the spectrum shape are normalized with respect to

the corresponding peak Strouhal number. The normalized Strou.hal num-

bers O are defined as

f*d_ (T_)0"4

Cl = "_i V;q - M®

(12)

and

i f*d_'2 (T;q)0"4

02 = S 2 V;q - M_

(13)

The two spectral peaks differ in magnitude by a factor e'. This

relative magnitude factor is dc=ined as

A •

e, = U(Veq,V2/Vl,B)--&--

Aeq

(14)

The spectral peak magnitude factor u is a function of the equivalent

velocity lOgl0 V_,__ the velocity ratio V_/V_, and the polar directivity

angle _. The values of the spectral peak magnitude factor a are given

in table IX and plotted in figure 9. The spectral shape is defined by the

spectral distribution G as a function of polar directivity angle @ and

normalized StroP,el number O. The values of the spectral distribution G

are given in table X and plotted in figure i0.

All of the terms in equations (9) and (I0) have been defined. The

mean-square acoustic pressure can be computed for each desired value of

frequency, polar directivity angle, and azimuthal directivity angle. The

total noise is the mean-square acoustic pressure multiplied by the number

of engines N for the output table. In addition, printed output is

available of the d/mensionless mean-square pressure <p2>*, the sound

pressure level SPL defined as

8.7-7

Pref

SPL = 10 lOglo <p2>" _ 20 lOglo---_

pc

and the power level PWL defined as

(15)

H

ref (16)

PWL = I0 lOglo H* - i0 lOglo O°°c3A_ Ae

REFERENCES

i. Pao, S. Paul: A Correlation of Mixing Noise From Coannular Jets With

Inverted Flow Profiles. NASA TP-1301, 1979.

2. Russell, James W.: A Methcd for Predicting the .Noise Levels of

Coannular Jets With Inverted Velocity Profiles. NASA CR-3176, 1979.

8.7-8

TABLEI .- RANGE AND DEFAULT VALUES OF INPUT PARAMETERS

Input .Minimum Default Maximumparameter

Ae, m 2 .....

. o . . . o .

rs, m ......

O, deg .....

A_ .......

T[ .......

V _ .... . . o

_4 ........

71 .......

A_ .......

_,2 ......

V_ .......

_w

_2 .... " " "

72 .......

c, m/s .....

D, kg/m 3 ....

0.01

1

0.01

0

0.0001

0.7

0

0

0.2

1.3

0

0.01

0.7

0

0.2

1.3

2OO

0.2

_/4

I

0

1

1

1.O

0

1.0

1.4

0

1

i

0

1.0

1.4

34(). 294

1.225

i0

4

i00

3o

i0

6

2.5

0.9

1.2

1.5

lO

io

6

2.5

1.2

1.5

4OO

1.5

B.7-9

TABLE II.- POWER DEVIATION FACTOR lOglo P

l°gl0 Veq/C_ l°gl0 P

-.400-.350-.300-.ZSO-,ZOO-.1_0-.I00-.0_00.000.050

.100

.150

.ZOO

.250,300.350

.400

-.130-.130-.130-.130-.130-.lZO-.100-.0500.000

.100,210.320.410.430,410,310.140

TABLE III.- DENSITY EXPONENT,

-- f

l°gl0 Veq/C_

-.450-.400-.350-.300-.2_0-.200-.150

-.100-,0500.000

.0_0

.100

.150

.ZOO

.2SO

_o

-!.000-.900-,760-.580-.410-.ZZO0.000

.Z20

.500

.770L.0701.3901.7401.950Z.O00

8.7-10

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• • • e • • • • • • • • • • • • • • •0 O00¢3000 0 ¢D¢)000 000 O0

a.7-12

TABLE VI.- FORWARD VELOCITY INDEX m(0)

1

re(e)deg

0.00010.00020.00030,00040*00050.00060.00070.00080.0009O.000

100.000110.000120.000130.000140,000150,000160.000170.000180.000

3,0001.6501.100

._00,ZOO

0.0000,000

.100,400

1.0001.9003.0004.7007,0008,5008.5008.5008,5008,500

8.7-13

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X

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8.8 AIRFRAME NOISE MODULE

I HTRODUCT I ON

The Airframe Noise Module predicts the broadband noise for the dcmi-

nant components of the airframe. The method is based on a method devel-

oped by Fink of the United Technologies Research Center for the Federal

Aviation Administration (ref. i). The method employs empirical and

ass_ned functions to produce sound spectra as a function of frequency,

polar directivity angle, and azimuthal directivity angle. Each spectrum

is the sum of all the airframe component spectra produced by the wing,

tail, landing gear, flaps, and leading-edge slats.

The method requires input of several parameters. The aircraft Mach

number and control settings can be provided by the Airframe Noise Param-

eters Module or directly by the user. Additional user-provided parameters

describe the airframe geometry. The module is executed once for each set

of values of the input parameters. The output is a table of the mean-

square acoustic pressure as a function of frequency, polar directivity

angle, and azimuthal directivity angle.

SYMBOLS

A area, m 2 (ft 2)

a exponent

b span, m (ft}

c ambient speed of sound, m/s (ft/s)

D directivity function

d tire diameter, m (ft)

F spectrum function

f frequency, Hz

G geometry function

I4Lg landing-gear position

K constant

£ landing-gear strut length, m (ft)

.M aircraft Mach number

8.8-i

N

n

<p2>"

Pre f

r s

e

r s

$

s

_f

0

_t

..

7'.ref

2

number of landing gear

number of wheels per landing gear

24

mean-square acoustic pressure, re p c

reference pressure, 2 × lO -5 Pa (4.177 × 10 -7 ib/ft 2)

distance from source to observer, m (ft)

dimensionless distance from source to observer, re b w

Strouhal number

number of slats for trailing-edge flaps

boundary-layer thickness, m (ft)

flap deflection angle, deg

polar directivity angle, deg

ambient dynamic viscosity, kg/m-s (slugs/ft-s)

, D c3b 2acoustic power re _ _ w

reference pc.wer, 1 × 10 -12 W (7.376 x 10 -13 ft-lb/s)

ambient den3ity, kg/m 3 (slugs/ft 3)

azimuthal directivity angle, deg

Subscripts:

f flap

h horizontal tail

m_ main landing gear

n_ nose landing gear

v vertical tail

w wing

Superscript:

• dimenslonless quantity

8.8-2

INPUT

Theaircraft Mach number, control settings, and ambient conditions

are required from either the output of the Aircraft Noise Parameters

Module or the user. The frequency, polar directivity angle, and azi-

muthal directivity angle arrays establish the independent variable values

for the output table. Several parameters are required for the geometric

description of the airframe. Finally, the distance to the pseudo-

observer is required. The range and default values of the input param-

eters are given in t_Ible I.

r s

Input Constant

distance from source to observer, m (ft)

Af

A h

%

%

bc

bV

d_c/

dng

ng

nng

N_

N..,N

S

Airframe Geometry

flap area, m 2 (ft 2)

horizontal tail _rea, m 2 (ft 2)

vertical tail area, m 2 (ft 2)

wing area, m 2 (ft 2)

flap span, m (ft)

horizontal tail span, m (ft)

vertical tail span, m (ft)

wing span, m (ft)

tire diameter of main landing gear, m

tire diameter of nose landing gear, m

main landing-gear strut length, m (ft)

nose landing-gear strut length, m (ft)

number of wheels per main landing gear

number of wheels per nose landing gear

number of main landing gear

number of nose landing gear

number of slots for tralling-edge flaps

(ft)

(ft)

8.8-3

Cop

M=

O=

Airframe Noise Parameters

landing-gear position

flap setting, deg

A_bient Conditions

ambient speed of sound, m/s (ft/s)

aircraft Mach number

ambient density, kg/m 3 (slugs/ft 3)

ambient dynamic viscosity, kg/m-s (slugs/ft-s)

Independent Variable Array

frequen_I, Hz

polar directivity angle, deg

azimuthal directivity angle, deg

OUTPUT

The output of this module is a table of the mean-square acoustic

pressure as a function of frequency, polar directivity angle, and azi-

muthal directivzty angle. In addition, the observer distance r s is

provided for Lhe Propagation .Module.

r Sdistance from source to observer, m (ft)

f

<p2 (f,_._)>°

Airframe Noise Table

frequency, Hz

polar directivity angle, deg

azimuthal directivity angle, deg

2 4

mean-square acoustic pressure, re D=c_

METHOD

Th.e prediction me_d presented in reference 1 is used to compute

_ne Car field noise. The az ;tame. - r_ r_ise components considered _n the

method are shown in figure i. The definitions of _he directivity angles

8.8-4

are shown in figure 2. In the following discussion, the general approach

for the prediction method is presented first and then the detailed method

is given for each airframe component.

The equation for the far-field mean-square acoustic pressure for

the airframe is

<p2>* = _** D(e,@) F(s) (I)4_(rs )2 (I - M cos @)4

In equation (i), _* is the overall power, D is the directivity func-

tion, and F is the spectrum function. The source to observer distance

* =

r s is expressed in dimensionless form as r s rs/b w. The forward

velocity effect is accounted for by the Doppler factor (i - M cos 9) 4

The Strouhal number S is defined as

S = fL (i - M cos e)M c

(2)

where L is some length scale characteristic of the particular airframe

noise source being computed.

The acoustic power for the airframe _* can be expressed as

* K (M) a_q = G (3)

where K and a are constants determined from empirical da_a. The

geometry function G is different for each airframe component and

incorporates all geometry effects on the acoustic power.

As indicated by equation (I), each airframe noise source has its own

directivity function D and spectrum function F. Using these :unctions

and the acoustic power, the mean-square acoustic pressure can be computed

as a function of frequency, polar directivity angle, and azlmuthal direc-

tivity angle for a given set of input parameters. The empirical constants

and functions used to compute the acoustic power are summarized in

table II. The directivity and spectrum functions are given in table III.

Each airframe noise component is described in detail below.

Trailing-Edge Noise

The primarf mechanism for noise generation for clean wing and tail

surfaces is the convection of the turbulent boundary layer past the

trailing edge. T_e turbulence intensity is assumed to be independent of

Reynolds number and the turbulent length scale is assumed to be the

boundary-layer thickness. The directivity function is assumed to be

aligned with the lift dipole, and the spectrum function is determined

empirically.

8.8-5

The acoustic power due to trailing-edge noise of a conventionally

constructed wing is

n* ,. (4.464 x 10"5)M56: (4)

The dimensionless turbulent boundary-layer thickness 6:

the standard flat-plate turbulent boundarT-layer model

Aw (P_M.C_Aw_ -0"2

<- 0.3, ./ ,5,

Similarly, the acoustic power for the horizontal tail is

ii • = 14.464 × IO-5)M _5 161

is computed from

and for the vertical tail is

17)

• •

The boundary-layer thicknesses 6h and 6 v are computed from equa-

tion (5) using the appropriate values of A and b. If the airplane

ks aerodynamically clean, such as a sailplane or jet aircraft with simple

trailing-edge flap mechanisms, the constants in equations (4), (6),

and (7) should be reduced to 7.075 x 10 -6 , an 8-dB decrease.

The directivity function D for the clean wing and horizontal tail

_s given by

D(8,¢) = 4 cos 2 _ cos 2 812 (8)

and for the vertical tail

D(@,¢) = 4 sin 2 ¢ cos" 9/2 (9)

These directivity functions are plotted in figures 2 and 3, respectively.

The sp_ctr_ function F is given by

5]-4F(S] = 0.613(I0S) 4 10S) 1"5 + O. (I0]

8.8-6

for rectangular wings and

= o.48s(1os)4 lOS) 1"3s + -4 (11)

for delta wings. These spectrum functions are plotted in figure 4. The

Strouhal number S is defined for this component as

f6*b (I

S = M-'_ - M cos 8)

(12)

where the appropriate value of the span b and the boundary-layer thick-

6"hess for the wing, vertical tail, or horizontal tail is used depend-

ing on the noise source being predicted. The mean-square acoustic pres-

sure is t.her computed from equation (I).

Leading-Edge-Slat Noise

The deployment of the leading-edge slats produces increased noise by

two different mechanisms. First, the slat produces an increment of wing

trailing-edge noise due to its impact on the boundary layer of the wing.

Second, the leading-edge slat itself produces trailing-edge noise. Both

mechanisms are accounted for in this method.

The added acoustic power due to the increase in wing trailing-edge

noise or thu slat trailing-edge noise is assumed to be equal to the clean

wing noise. Therefore, equation (4) can be used to predict the overall

acoustic power for either slat noise source. The directivity function

for either slat noise sourc_ is given by equation (8) and plotted in fig-

ure 2. The spectrum function for the added wing noise is given by equa-

tion (i0). The spectrum function for the slat noise is

s]-4F(S) = 0.613(2.19S) 4 2.19S] 1"5 + O. (13)

which assumes that the slat chord is 15 percent of the total wing chord.

The Strouhal number S is given by equation (12). The t_ spectrum

functions are plotted in figure 5, along with their sum, to show the

combined effect of slat noise. The mean-square acoustic pressure is

then computed from equation (I).

Flap Trailing-Edge Noise

Extension of the wing flaps increases the level of airframe noiz&.

This noise is assumed to be produced by the lift fluctuations due to the

incident turbulence on the flap. This noise Increases as the flap exten-

sion is increased. The noise is assumed to be aligned with the lift

dipole of the deflected flap.

8.8-7

The acoustic power due to flap noise for single or double

slotted flaps is

Af.q* = (2.787 x I0-4)M6--_ sin 2 6f

b_(14)

where 6f is the flap deflection angle. For triple slotted flaps, theoverall acoustic power is

Af

n" = (3.sogx io-4)_ sin2 _W

which increases the power by I dB to account for the added flap

complexity.

The directivity function D for the flap noise is

(15)

2D(8,¢) = 3(sin 6f cos 8 + cos 6f sin % cos ¢)

(16)

which is plotted in figure 6 for 6f = 30° • The spectruD functio_ Fare

0. 04805 fF(Sf) = O. 1406Sf 0"55

L216.49S; 3

(S < 2)

(2 -< S <- 20)

(20 < S]

(17)

for single and double slotted flaps and

FO.O257Sf

F(sf)= /o.o5365_-°'°625

LlTO_SS_a

(S < 2)

(2 <- S < 75)

(75 < S)

(18}

for triple slotted flaps. Using the flap chord as the reference length,

the Strouhal number is defined as

fAr

Sf = M bfc (1 M cos e)(19]

8.8-8

I

The spectrum functions given by equations (17) and (18) are plotted in

figures 7 and 8, respectively. The mean-square acoustic pressure is then

computed from equation (1).

Landing-Gear Noise

The mechan/sm for noise generation due to landing-gear extension is

complex and dependent on the particular landing-gear design being con-

sidered. The process has been simplified with the assumption, based on

the experimental comparisons made in reference i, that there are only two

predominant noise sources. Noise generated by the strut and wheel appears

to dominate other potential sources. Separate predictions are made for

the strut and wheel noise which are added together to yield the total

landing-gear noise.

For a one- or two-wheel landing gear, the acoustic power due to the

wheel noise is

(2O)

and due to the strut noise is

_* = (2.753 x I0-4)M6<_)2_(21)

Similarly, for a four-wheel landing gear, the acoustic power due to the

wheel noise is

_* = (3.414 x 10 -4)M6n<b_) 2(22)

and due to the strut noise is the same as equation (2_).

tions (20), (21), and (22), d is the tire diameter, £

length, and n is the number of wheels per landing gear.

In equa-

ls the strut

The directivity function for the landing-gear wheel noise is

3 2

D(9,¢) = _" sin @ (23)

and for the s_-ut noise

D(8,_) = 3 sin 2 @ sin 2 ¢ (24)

8.8-9

Thesedirectivity functions are plotted in figures 9 and 10, respectively.

For a one- or two-wheel landing gear, the spectrum function for the wheel

noise is

F(S5 = 13.59S 2(12.5 ÷ S 2)-2"25 {25)

and for the strut noise is

F(S} = 5.325S2(30 + S85 -I (265

Similarly, for the four-wheel landing gear, the spectrum function for the

wheel noise is

F(S) = 0.0577S2(i + 0.25S2) -1"5 (275

and for the strut noise is

F(S) = 1.280S3(i.06 + S25 -3 (285

If the tire diameter is used as the reference length, the Strouhal number

is defined as

fd

S = ooM_c-(l - M cos @) (29)

The four spectrum functions are plotted in figures Ii to 14. The wheel

and strut mean-square acoustic pressure are computed separltely by using

equation (I). They are then summed to yield the total landing-gear mean-

square acoustic pressure. The noise due to the main landing gear and nose

landing gear are computed separately.

Output Computation

The mean-square acoustic pressure for the airframe is the sum of all

_he components desired by the user. It is computed for each value of the

frequency, polar directivity angle, and azimuthal directivity angle for

the output table. In addition, printed output is available of the sound

pressure level SPL defined as

2

D c/ k*

SPL z i0 lOgl0 \p2/ + 20 lOgl0Pref

(30)

8.8-I0

_f

J,

and the power level PWL defined as

3 2_.clbw

PWL = I0 lOgl0 _" + I0 lOgl0 Href(31)

REFERENCE

I. Fink, Martin R.: Airframe Noise Prediction Method.

Mar. 1977. (Available from DTIC as AD A039 664.)

FAA-RD-77-29,

8.8-11

TABLEI.- RANGE AND DEFAULT VALUES OF IJPUT PARAMETERS

Input Minimum Default Maximumparame ter

b wrse m .......

2A f, m ......

Ah' m2 ......

Av, m 2 ......

2AWl m • o . • - o

b f, m .......

_ho m . . . . . . o

bV, m .......

# ra . o o . . . .

dmg, m ......

dng o m ......

£mg' m ......

£ng" m

...... • .

nng ........

Nng ........

S • . • o . • • •

IRg . . ......

"%_ao " " " ° ....

6f, deg ......

Crop # B_/ S . . . , . •

DaD, kg/m 3 .....

_, kg/m- s ....

0.01

0.01

0.02

0.02

0.i

0.01

0.02

_.02

0.I

0.001

0.001

0.003

0.003

1

1

1

1

1

0

0

0

200

0.2

1.5 x 10-5

I0

20

20

I00

5

I0

i0

20

1

1

3

3

4

2

2

1

3

1

0.3

O

340. 294

1.225

1.7894 x 16 -5

I00

I00

200

200

I000

20

20

40

i00

5

5

15

15

4

4

4

2

3

1

0.9

45

400

1.5

2.0 x I0 -5

8.8-12

TABLE II.- _PIRICAL COHSTANTS AND FUNCTIONS FOR

AIRFRAME ACCXJSTIC POWER

Source

Clean wing and

leading-edge slat

(conventional

construction} . .

Horizontal tail

(conventional

construction)

Vertical tail

(conventional

construction]

Clean wing

(aerodynamically

clean) .......

Horizontal tail

(aerodynamically

clean) .......

Vertical tail

(aerodynamically

clean) .......

Single ,,r double

slotte_ trailing-

edge flaps .....

Triple slotted

trailing-edge

flaps .......

One- or two-wheel

landing-gear wheel

noise .......

Four-wheel landing-

gear wheel noise .

Landing-gear strut

nolse .......

K a G

4.464 x I0 -5 5

4.464 x 10 -5 5

4.464 x 10 -5 5

7.075 x I0 -6 5

7. C 75 x 10 -6 5

7.075 x I0 -6 5

2.787 x 10 -4 6

3.509 x i0 -4 6

4.349 x i0 -4 6

3.414 x I0 -4 6

2.753 x I0 -4 6

6_c_w)2

_:Cb,/bw)2

6:

6h (bh/bw) 2

6: (bv/bw)2

2_sin 2 _f_f w/

(_/b_)sio2_f

n (d/b_) 2

n (d/b w) 2

(d/bw) 2 (t/d)

8.8-13

i

1

° .

El3(/1

0{ti

{/1Z0

E-UZ

r,.

M

e.,Z

r.

i 2,

T

8 _ I I 0

c; 6 c; ,.÷

÷ 4, ÷ o.4

• ° • °

Ul UI ;,_ _ t'lo o o o

U1 (/I U1 {I] ,,,e0 0 0 0 •

'/Vl V

vv

V!

v

CO 0 ql'

8 5.8 8 5.8 _.$ EIII

I I I I I

% % % '% %0 0 0 0 CU O U O rj

% % % _ %0 0 0 "_ 3U U U m

A

L)

C_

C

0U

4-

v

_a

91 el el "_

"T

O

8.8-14

I

lJ

@

0

I

b.q

s_

L.

A

vvl v

v!

C

O

,4!

v

T

-/

ffl

4.

v

O

n0

i

8

=:$

7

÷

A

0

OIj

_ A A A

X_ _8 Z8 X8

I I I !

I ',,Jr' ',Jr' X 8 _ X 8

%

c_

%

e,,i

mm:_11=

..4

t=,,q

"0

=11

:1

o

i q

4'0

m q,..4

e-

I:I 11

e-

O

I., O

0

e-

C

8° 8-15

TRAIL_EDGE FLAPS

CLEAN _G

VERTICAL TA.IL

0

NOSE _aUl_)nlG

Figure i.- Sources of airframe noise included in prediction model.

8.8-16

9O

(a) Variation with polar directivity angle.

2To 90

o

(b) Variation with azimuthal dizectivity =ngle.

Figure 2.- Dir_ctivity level for clean wing, horizontal _ail,

and leading-edge slat noise.

8.8-17

w

90

(a) Variation with polar directivity angle.

27O 9O

(b) Vaxiation with azimuthal directivity angle.

Figure 3.- Direc:ivity level for vertical-tail trailing-edge noise.

8.a-18

10

z

3

0

,.i

0

cq

or}

s,.--. tn

0

0

LJ

..(3

E

Z

0c-:30qL

(/3

-.4¢I

.,,ae"

0_-,,4

0 0_.. _-

t- '0-,.4

t_

U n_

0

E .,4

!

t_

t_

8.8-19

l(:3

CO

1u_

I

3 °_6ol 'l_^el uJn_oed_

0

0m

E:3

Zm

0c-

O

GO

0

4_

I_n

0

I/

U

I

u_

J,,,

°,,,4

8.8-20

i I I a

lk! I I/ i i I

f_ -- .

\%/ /%_t

- / J

I

//

(a) Variation with polar _irectivity angle.

100

270 I I I ! I i I I 90

\ I .-_° T _ /

#

(b) Variation with azimuthal directivity angle.

Figure 6.- Directivity level for flap trailing-edge noise

at a 30 ° flap _ngle.

8.8-21

[ 1 l 1 I ! o.CM

o _ o _ o _ ol.- ,- c,i _ _i

I I I I I I

.:1 °[601 'lava'] uJnjload S

8.8-22

i I

I

q

0

I

I

I

0I I i Io _. o. _. ol

! I I I I

-I°_fiOl'l_^el wn4o_d _

01

on.

0

¢I

0 Z

0 "_m

LJ

E 4J

:3 oZm ¢I

o _.3Z --_

0

:>

0w-4

E

'.30

!

OB

°°

8.8-23

f_

180

90

(a) Variation with polar directivity angle.

£&

180

270 90

0

(b) Variation with azimuthal directivity angle.

Figure 9.- Directivity level for landing-gear wheel noise.

8.8-24

r

L

90

(a) variation with polar directivity angle.

(b) Variation with azimuthal directivity angle.

Figure I0.- D1rectivity level for landing-gear strut noise.

8.8-25

90

I IO IZ)

I

I I I IO IZ') O

• ,e * i

I I I I

_-I °LSOI 'I_A'97 :'unJ",°_ds

jO

_O "

u') o

o

I

'v'--'

I

O

O Ir,')

i

IJ

I

,,,-4

8.8-26

i

q

0

I

8.8-27

I I0

I

0

0

u_

0

e

0

u_

I

0

I

I

0I I I Io _ o _ o I

I I I I I

_4 °L6Ol 'IB_B']Lun.qo_)ds

oi-,,4Ow.

e.

e-

ID

E =3

z "

o o

_I oIb-

¢.,1

I:1

I

,4

8.8-28

10

0

_Lr)

q

In,o

0

LC')

f

0m

,wP,-,-'

I

0c_

o IMI

J ! ! I J

I I I I

3 °L6ot "l_^_-i wn_ood S

OP

0m

r-'3Z

or-'30

in

m

0

w

L,

i

"0

!

o

L_

0W-;

>

,,-,i

L,

rJ

_.,

I

C'

8.8-29

8.9 SMITH AND BUSHELL 'I_I_INE NOISE MODULE

INTRODUCTION

The Smith and Bushell Turbine Noise Module predicts the broadband

noise for an axial flow turbine. The prediction is based on the method

developed by Smith and Bushel1 (re/. I). The method employs empirical

functions to produce sound spectra as a function of frequency and polar

directivity angle. The method assumes that the only significant noise

source is the "vortex" component, which is the broadband noise due to the

interaction of the rotating blades with random velocity patterns in the

flow.

The method requires input of several parameters. The turbine

entrance and exit flow parameters can be provided by the Turbine Noise

Parameters Module or directly by the user. Additional user-provided

parameters are required. The module is executed once for each set of

values of the input parameters. The output is a table of the mean-square

acoustic pressure as a function of frequency, polar directivity angle,

and azimuthal directivity angle. Although turbine noise is assumed not

to vary with azimuthal directivity angle, it is introduced so that the

output table is compatible with other noise tables.

A

A e

C

C

D

d

F

f

f"

fa

ha

Mt

SYMBOLS

turbine inlet cross-sectional area, m 2 (ft 2)

engine reference area, m 2 (ft 2)

ro_'oc blade mean axial chord, m (ft)

ambient speed of sound, m/s (ft/s)

directivity function

turbine rotor diameter, m (ft)

spectrum function

frequency, Hz

Helmholtz number, fC/c

fuel-to-air ratio

absolute humidity, percent mole fraction

rotor blade tip Mach number

8.9-1

T_

M

&

N

N e

N s

<p2>"

Pref

R

R

rs

rs

T

8

r/°

_ref

aircraft Mach number

mass flow rate, kg/s (slugs/s)

rotational speed, Hz

number of engines

number of turbine stages

2 4

mean-square acoustic pressure, re pc

reference pressure, 2 x 10 -5 Pa (4.177 × 10 -7 lb/ft 2)

dry air gas constant, re m2/K-s 2 (ft2/°R-s 2)

gas constant, m2/K-s 2 (ft2/°R-s 2)

distance from source to observer, m (ft)

dimensionless distance from source to observer, re _e

temperature, K (OR)

ratio of specific heats

polar directivity angle, deg

acoustic power, re p c3A

reference power, 1 x 10 -12 W (7.376 x 10 -13 ft-lb/s)

ambient density, kg/m 3 (slugs/ft 3)

azimuthal directivity angle, deg

Subscripts :

i en trance

j exit

s static

ambient

Superscript:

* dimensionless quantity

8.9-2

INPUT

Theturbine parameters are required from either the output of the

Turbine Noise Pa_-ameters Module or the user. Ambient conditions are

required for com_utation of sound pressure levels. The frequency, polar

directivity angle, and azimuthal directivity angle arrays establish the

independent variable values for the output table. The turbine inlet

cross-secr/onal area, rotor blade mean axial chord, and number of turbine

stages are required for the geometric descziption of the turbine.

Finally, the engine reference area, number of englnes, and distance to

the observer are required. The range and default values of the input

parameters are given in table I.

Ae

N e

r s

Input Constants

engine reference area, m 2 (ft 2)

number of engines

distance from source to observer, m (ft)

A e

C

NS

Turbine Geometry

turbine inlet cross-sectional area, re A e

rotor blade mean axial chord of the last stage, re

nummer of turbine stages

fa

N*

T*_,j

Turbine Noise Parameters

fuel-to-air ratio

core mass flow rate, re P camA e

rotational speed, re c=/d

exit static temperature, re T

Cam

h a

%

Ambient Conditions

ambient speed of sound, m/s (ft/s)

absolute humidity, percent mole fra:tion

aircraft Mach number

ambient density, kg/m 3 (slugs/ft 3)

8.9-3

f

e

IndependentVariable Arrays

Erequency, Hz

polar directivity angle, deg

azimuthal directivity angle, deg

OUTPUT

The output to this module is a table of the mean-square acoustic

pressure as a function of frequency, polar directivity angle• and azi-

muthal directivity angle. In addition, the observer distance r s is

provided for the Propagation Module.

r s distance from source to observer, m (ft)

f

9

<p2(f,@,_)>*

Turbine Noise Table

frequency, Hz

polar directivity angle• deg

azimuthal directivity angle• deg

• 02C 4mean-square acoustic pressure re _

METHOD

The prediction method presented in reference 1 is used to compute

the far-field noise. A schematic of a typical turbine is shown in fig-

ure i. The Smith and Bushell method uses the coordinate system and

directivity angles shown in this figure. The following prediction method

gives the prediction for broadband vortex noise.

The equation for the far-field mean-square pressure for a turbine is

<p2>* = _*A* D(@) F(f*) (i)4

4_(r:) 2 (i - M cos @)

In equation (i), _* is the overall power, D is the directivity func-

tion, and Y is the spectrtun function. The source to observer distance

r s is expressed in dimensionless form as

r S = r s(2)

8.9-4

The forward velocity effect is accounted for by the Doppler factor

(I - M cos @)4. The Helmhcltz ntmber f* is defined as

f* = fC*_e--(I - s= cos 0) (3)

C

whe:e C is the mean axial chord of the last stage turbine rotor blades.

The acoustic power H* for the turbine is

_* = (4.552 x IO-5)M3_*N _4)t s

oe

where N s is the number of stages and m is the core mass flow rate.

The blade tip Mach number M t is defined as

(5)

where N* is the rotational speed and T_,j is _he exit static tempera-

ture. The values of the local ratio of specific heats 7s and the local

constant R* = R/R are found from the input values of T_,j,gas

absolute humidity ha, and fuel-to-air ratio fa" The value of the

ambient ratio of specific heats y is 1.4.

The directivity function D is a function of polar directivity angle

and is given in table II and plotted in figure 2. The spectrum func-

tion F is a function of Helmholtz number and is given in table III and

plotted in figure 3. The mean-square acoustic pressure is then computed

from equation (i). The total noise _s the mean-square acoustic pressure

multiplied by the number of engines N e for the output table. In addi-

tion, printed output is available of the sound pressure level SPL

defined as

2

SPL = i0 loq!0 <p2>* + 20 lOgl0 Pref(6)

and the Dower level PWL defined as

PWL = i0 lOglo It + i0 lOql 0

"Lre f

(7)

8.9-5

R.I_E

1. Smith, M. J. T. ; and Bushell, K. W. : Turbine Noise - Its Significance

in the Civil Aircraft Noise Problem. Paper 69-WA/GT-12, American

Soc. Mech. Eng., ,Nov. 1969.

8.9-6

.m ........................!

TABLE I .- RANGE AND DEFAULT VALUES OF INPUT PARAM_

Input Minim, m De fault Maximumparameter

Ae, m 2 ......

A i ooo.o°oo

C Q . ° . . o ° . .

fa ........

ha , % .......

_t . • • .... .

N _ . o o . • . . o

Ne ........

T* . . . . . . .s,]

c, _/s ......

_ oo-oo--o

P_, kg/m 3 .....

[S # _ • • • ....

N S ........

0.01

0.i

0.01

0

0

0

0

I

0.i

200

0

0.2

0.01

I

_/4

1

1

0

0

0.2

0.3

1

2

340. 294

0

1.225

l

I0

i0

100

0. _6767

4

I0

0.5

4

4

400

0.9

1.5

I00

i0

8.9-7

...... _'7 -r_'_ . _

zQ

f..

A,

|

).4i*.¢

r..

0.-¢

0

o

0,,-4

0,,.¢

0000000000000000000000000000000000000000 0000 O0

•......................¢t,l_¢r_iOiDl_m_r_l,.cOe¢l_¢l_¢l .O_,lr I_*-*_'bID

I I I I I I I I I I I I I I I I I I I

oooooooooooooooooooooooooooooooooooooooooooooo

.., w_me we _-* m,__ 0 0 0 0 0 0 0 0 0 0 0 0 0 O0I ! I | t | I I ! I I I I ! I I I

z

[-.

).,

!

0

oooooooooooooooooooooooooooooooooooooo

,-*_._¢_,.* I I I I I I I I ii i i I

oooooooooooooooooooo ooooooooooooooooooo.o.ooooo, oooo.o.ooooooo00000000000000000 O0

e41ql_4, ti_Ol_._DO_O_l_ 4rt_4Dr,,,.m

8.9.-8

X

Figure i.- Schematic diagram of typical axial-flow turbine.

8.9-9

{0

Iu_

{0 t_ 0

I "-I

I

I

(] °{5°l 0}. 'l_ae-I K)!A_:_oj{O

0

,it---

m

0O0

0

0

0

0 o

I

0(0

0

0

00

_)

K_

"0

o_c-

<

o_

o

lb._m

r_

o13_

0-,-4

(J

0

,'m

"0e-

U]

L,

0

>

U

0

Z

!

8.9-10

.J .

J

[0

I 1 I I II I i I

1

0

I

_-I °L6ol 01. 'le^e7 wnAoeds

4J:)

0F..,

13

0N

0Z

!

8.9-11

9. PREDICTION PROCEDURES

_o

9.1 ICAO REFERENCE NOISE-PREDICTION PROCEDURE (1978)

INTRODUCTION

In June of 1977, Lhe International Civil Aviation Organization (ICAO)

formed a prediction subcommittee to determine a reference noise-prediction

procedure applicable to supersonic transports (SST's). The goals of the

subcommittee were to:

I. Establish an agreed upon reference noise-prediction procedure

2. Assess the accuracy of the reference procedure against available

measured flight-test nc,ise levels

3. Determine, Oy use of the "trial engine," the differences in pre-

dicted noise level between the reference procedure and those

procedures already used in parametric studies

4. Identify new noise problems associated wi_h SST's, and to make the

necessary recommendations so as to define an internationally

recommended prediction procedure

Participating in _he subcommittee work were NASA, British Aerospace

Corporation, SNECMA, the U.S.S.R., The Boeing Company, McDonnell Douglas

Corporation, LocKheed Corporation, Rolls-Royce Limited, General Electric

Company, and Pratt & Whitney Aircraft Group. Each provided their predic-

tions for a trial SST engine provided by SNECMA and for currently avail-

able measured data. Based on the results of these studies, a reference

noise-prediction procedure was agreed upon. The results of the subcom-

mittee study were presented to ICAO.

A s_mnary of the prediction procedure used by each participant and

Lhe reference noise-prediction procedure are presented in table I. The

results of the trial SST engine predictions for each method are presented

in table II. It is interesting to note some of Lhe wide variation in the

component maxim_un perceived noise level (P._L) computations. The accuracy

of _he application of the reference noise-prediction procedure to various

measured effective perceived noise level (EPNL) data is shown in

figure I.

All of the component methods in the ICAO reference noise-prediction

procedure are included in _NOPP as separate functional modules or variants

of the standard ANOPP functional modules. A discussion of each component

noise-prediction me_hod is presented subsequ, ently.

%.

9.1-1

c r

c

D

d

F

f

fp

h a

h r

L

role)

_2>"

p*

P,,.

5

S c

T"

T.]

T

_T

T

3

X

Y

1

SYMBOLS

standard sea level speed of sound, m/s (ft/s)

ambient speed of sound, m/s (ft/s}

directivity function

fan diameter, m (ft)

spectral distribution function

frequenc 7, Hz

peak frequency, Hz

absolute humidity, percent mole fraction

relative htmlidity, percent

acoustic liner length, m (ft)

forward-velocity index

2 4mean-square acoustic pressure, re pc

ambient pressure, re Pr

standard sea level pressure, Pa (ib/ft 2)

suppression factor

corrected 5trouhal number

ambient temperature, re T r

jet temperature, K (OR)

standard sea level temperature, K (oR)

thrust loss, percent

ambient temperature, K (OR)

jet velocity, re c

h_nidi ty ratio

vibrational absorption function

absorption coefficient, nepers/m (nepers/ft)

9.1-2

J

i

8 polar directivity angle, deg

p® ambient densit 7, kg/m 3 (sluqs/ft 3)

Subscripts :

cl classical

h high frequency

£ ic_ frequency

max maximum

n nitrogen

o oxygen

ref reference procedure

rot rotational

sup suppressed

vib vibrational

JET MIXING NOISE

The method for predicting jet mixing noise is based on the me_hod in

appendix A of Society of Automotive Engineers (SAE) Aerospace Recommended

Practice (ARP) 876 (ref. I). This is presented in ANOPP as the Single

Stream Zircular Jet Noise Module. The method employs empirical data

tabulated in terms of relevant dimensionless groups to produce so_-_

spectra as functions of frequency and polar directivity angle.

The ICAO reference method differs from the Single Stream Circular

Jet !_ise Module in two ways. First, a different forward-velocity

index m(@), defined 1n table III and figure 2, is used. Second, addi-

tional data for the spectral distribution factor F at a value of the

velocity ratio (lOgl0 V:) of 0.3 is included. The additional spect=al

data are given in table IV and plotted in figure 3.

SHOCK NOISE

The method for predicting jet shock cell noise is based on proposed

appendix C of SAE ARP 876 (ref. I). This is presented in ANOPP as the

Circular Jet Shock Cell Noise .Module. The method uses master spectra

functlons and a shock-cell interference function to produce sound spectra

as functions of frequeDcy and polar directivity angle.

9.1-3

The IC__O reference method has an additional function r_t found in

the Circular Jet Shock Cell Noise Module. The computed i/3-octave-band

mean-square pressure <p2>* is multiplied by an additional directivity

function D as follows :

<p2>* = _(el <p2>"ref

The additional directivity function is a function of polar directivity

angle 0 and is given in table V and plotted in figure 4.

(i)

COMBUSTION NOISE

The method for predicting combustion noise is based on the proposed

appendix C to reference i. This is presented in ANOPP as the Combustion

Noise Module. The method uses empirical data of core noise from turbo-

shaft, turbojet, and turbofan engines to produce sound spectra as func-

tions of frequency and polar directivity angle.

The ICAO reference method utilizes a different spectral distribution

function F than the Combustion Noise Module. This spectrum function,

called the "envelope spectrum," is given in table VI and plotted in

figure 5.

COMPRESSOR/FAN INTAKE NOISE

The method for predicting compressor/fan intake noise is based on

reference 2 by Heidman. This is presented in ANOPP as the F_n Noise

Module. The method uses empirical functions to predict the sound spectra

as functions of frequency and polar directivity angle.

The ICAO reference method uses the inlet broadband noise, inlet

rotor-stator interaction tone, and inlet flow-distortion tone components

from the Fan Noise Module. It is executed once for each of dne first two

3rages. If performance data for the second stage are not known, then the

second stage is taken to be similar to the first stage with _e tone

spectra shifted one i/3-octave band higher than the first stage.

COMPRESSOR/FAN DISCHARGE-DUCT NOISE

The ICAO reference method uses the discharge broadband n_ise and the

discharge rotor-stctor interaction tone components of Heidman's me_hod

(ref. 2) as presented in the Fan Noise Module. The discharge-duct noise

is only computed for bypass/fan engines. The noise is computed for a

maximu_ of _nree stages, and the bypass mass flow is assumed to be the

total flow. The last three stages are used if possible. If performance

data are not available for a given stage, it can be assu_ed to be similar

to the preceding stage with _he tone spectra shifted one I/3-octave band

higher. Tone levels should be reduced by 5 d6 if a core/bypass mixer or

multielement silencer is used.

9.1-4

TURBINENOISE

Themethodfor predicting turbine noise is the vortex component of

the Smith and Bushell method (ref. 3}. This is presented in _OPP as

the Smith and Bushell Turbine Noise Module. The method uses empirical

functions to predict sound spectra as functions of frequency and polar

directivity angle. The ICAO reference method requires no changes of the

Sm/th and Bushell Turbine .Noise Module.

AIRFRAME NOISE

The me,uhod for predicting airframe noise is based on the FAA report

by Fink (ref. 4). This is presented in ANOPP as _e Airframe Noise

.Module. The metnod uses empirical and assumed functions to predict sound

spectra as functions of frequency, polar directivity angle, and azimuthal

directivity angle. The ICAO reference method requires no chaunges in the

Airframe Noise Module.

ATMOSPHERIC ABSORPTION

The atmospheric-absorption method selected for the ICAO reference

procedure is that of SAE ARP 866A (zuf. 5). This method has been incor-

porated into the Atmospheric Absorption Module in ANOPP. The SAE absorp-

tion met.hod is similar in procedure to the American National Standards

Institute (ANSI) method contained in the module. The equations that fol-

low directly replace the corresponding equations for the ANSI method,

using the same nomenclature as the Atmospheric Absorption Module.

The sum of the absorption coefficients due to classical and molecular

rotational effects is given by

* 2/2.... i. 365 (T)

acl + _rot = 6.30 × 10 -9 [r/Cr)_*. + 0.3713 p*(2)

where a is the absorption coefficient in nepers per unit length as

defined in the Atmospheric Absorption Module. The sum of the vibrational

relaxation absorption coefficients for nitrogen and oxygen is given by

+ = 9.20 × 10 -4 (f/Cr) (T*) I/2 102"43(T*-I)y(x)_vib,n ]vib,o

where t-he parameter X is given by

-in rr*-l [41.9 cT*-ll-n. 5]+7.62}X = 4.05hrf 19

(3)

(4)

9.1-5

and Y(X) is the vibrational absorpt/on function given in table VII.

In equation (4), the relative humidity h r can be expressed in terms

of the absolute humidity h a as

h r = h_-10a

(8.4256-I0.1995/T*-4.922 lOgl0 T*) (5)

The total absorption coefficient is the sum of equations (2) and (3).

Then, the average dimensionless absorption coefficient is determined fol-

lowing the same procedure as the ANSI standard method.

PROPAGATION

Propagation of the sound spectra to the observer is accomplished by

the Propagation Module. The tasks performed include spherical spreading,

atmospheric absorption, and ground reflection and attenuation. The

standard SAE atmospheric-absorption model as presented in SAE ARP 8&6A

(ref. 5) is used. Ground reflection and attenuation is modeled by adding

2 dB to the free-field levels for a 1.2-m microphone height. _"ne desired

noise levels, including perceived noise level (PNL) and tone-corrected

perceived noise level, are computed by the Noise Levels Module. Finally,

the effective perceived noise level (EPNL) is computed by the Effective

.Noise Module.

SUPPRESSION

A variety of techniques have been developed for the suppression of

aircraft englne noise, including acoustic lining, flow mixers, and

silencing nozzles. The effects of noise suppression are accounted for in

_OPP by _he General Suppression Module. This module takes a table of the

suppression factor for a particular suppressor type as a function of fre-

quency, polar directivity angle, and azimuthal directivity angle and

multiplies each element of the appropriate noise-module output table.

The ICAO prediction subcommittee provided recommended techniques for

quantifying the effects of suppression on each noise-source component.

These me_hods are presented below for implementation by the user. Alter-

hate techniques for estzmating suppressor effects may also be used.

Jet-Noise Suppression

The ICAO Jet Suppressor Subgroup has produced a recommended technique

for quantifying all types of jet-noise suppression. The suppression

factor S is defined as follows:

,,p2>" ; (6)sup

9.1-6

where <p2>* is the unsuppressed mean-square acoustic pressure. The

expression for the jet-noise suppression factor is

0.1 (1+AS) SmaxD (8)S = I0 (7)

The maximum suppression Sma x for any kind of jet-noise suppressor has

been correlated with gross performance loss. The data of Sma x as a

function of gross thrust loss AT through use of the suppression tech-

nique are given in table VIII and plotted in figure 5. The following

three curves are presented: Pre-1972 technology, latest projected

technology, and a reccmDendation for parametric studies. A jet-velocity-

suppression correction factor AS must be multiplied with ¢ to"max

incorporate the effects of the magnitude of the jet velocity. The value

of AS as a function of the jet re'.-city V_. is given in table IX and

plotted in figure 7. Finally, a directivity function D(@), as given in

table X, must be applied.

Shock-Noise Suppression

The jet-noise suppression factor is applied to the shock noise with

no modifications.

Core-Noise Suppression

The core noise is assumed to be attenuated 3.3 dB/m (i.0 dB/ftl of

acoustic liner (S = 0.469 L£, where L£ is the length of the liner in

meters). The liner should be designed for low-frequency attenuation.

Turbine-Noise Suppression

Any liner designed to produce core-noise suppression will suppress

turbine noise by the same amount. In addition, an acoustic lining

designed to reduce high-frequency turbine noise will attenuate turbine

noise by 9.8 dB/m (3.0 dB/ft). Therefore, the total suppression factor S

is (0.469) L£ (0.i03) Lh, where LZ and _ are the lengths of each type

of liner in meters. The total turbine-noise suppression should be limited

to 20.0 dB.

Inlet-Noise Suppression

The compressor/fan intake noise is reduced i0 dB for each fan diam-

eter of equivalent length of effective wall lining (S = 0.100L/d). It is

suggested that the overall reduction be limited to I0.0 dB.

9.1-7

Bypass-Duct-NoiseSuppression

Thecompressor/fandischargeduct noise is reduced by 9.8 dB/m

(3.0 dB/ft) of acoustic treatment on both inner and outer walls

(S = 0.103L). If only the outer wall is treated, reduce the noise

6.6 dB/m (2.0 dB/ft) (S = 0.221 L) and if only the inner wall is treated,

reduce the noise 4.9 dB/m (1.5 dB/ft) (S = 0.322L). The bypass-duct

attenuation should be limited to 15 dB. For bypass ratios greater than 2,

a maximum attenuation of I0.0 dB is suggested.

INSTALLATION EFFECTS

The interaction of the engines and airframe and the engine location

affect the noise radiated from the aircraft. 'fhese de-"_tions from the

point source model are often referred to as installat: effects. The

ICAO prediction subcommittee recommended a 2.0-dB increase in the total

engine noise levels to account for installation effects likely on a new

SST.

REFERENCES

I. _:as Turbine Jet Exhaust Noise Prediction. ARP S76, Soc. Automot.

Eng., Mar. 1978.

2. Heidman, M. F.: Interim Prediction Method for Fan and Compressor

Source Noise. NASA TM X-71763, 1975.

3. Smith, M. J. T.; and Bushell, K. W.: Turbine Noise - Its Significance

in Lhe Civil Aircraft Noise Problem. Paper 69-WA/GT-12, American

Soc. Mech. Eng., Nov. 1969.

4. Fink, Martin R.: Airframe Noise Prediction Method. FAA-RD-77-29,

Mar. 1977. (Available from DTIC as AD A039 664.)

5. Standard Values of Atmosphere Absorption as a Function of Temperature

and H_midity for Use in Evaluating Aircraft Flyover Noise.

AF_ 866A, Soc. Automot. Eng., Aug. 1964.

9.1-8

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TABLE VII.- MO_ VIBRATIONAL ABSORPTION FUNL'TION

FOR SAE ATMOSPHERIC ABSORPTION METHOD

x Y(x)

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9.1-19

TABLE VIII.- MAXIMUM JET-NOISE SUPPRESSION FACTOR

\

_T,

percent

1.0002.0004.0O06.0008.000

I0.00012.00014.00016.0001_.000ZO,O00

Sma x, dB, for -

Demonstrated

pre-1972

technology

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Latest

technology

0.0005.100

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TABLE IX.- JET-NOISE SUPPRESSION FACTOR

VELOCITY CORRECTION

v* As3

0.0001.070

1.250

I..30l.bl0

1.790

1.970

3.000

-1,000-1.000

-.800-.bOO-.400-.ZOO

0.000

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9.1-20

?

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TABLE X.- DIRECTIVITY FUNCTrON FOR

JET-NOISE SUPPRESSION

_B

deg D (@ )

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I2.0

9.1-24

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I2.0

9.1-25

m

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Corrected Strouhal Number. Iog_o S_

Tj/T® = 2.5; lOgl0 v_ = 0.3.

Figure 3.- Continued.

9.1-26

DEGREES

90

10

130

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Correctsd Strouhol Nurr_m'. log m S=

I

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180JD

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(d) Tj/T = 3.0; lOqlo v_ = 0.3.

Figure 3.- Continued.

9.1-27

la,.

--4_ _'120

"130

--5

_-_ 1 1 I 1 I I 1-2.0 -,.s -_.o -.5 o .s _.o _s

I2.0

Correctecl Strounol Numoer. IOg_o S,

._L#e _ "170-4:_ "180

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I2.0

Corrected Strouhal Plumber. Iogso S,

(_) Tj/T = 3.5; ic_l 0 V_ = 0.3.

Figure 3-- Concluded.

9.1-28

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