NASA
Part 2
Technical
Memorandum
Aircraft Noise Prediction
Theoretical Manual
William
E. Zorumski
Langley
Research
Hampton,
Center
Virginia
NILq
Nateonal Aeronaul_cs
anO Space/_Om_ nJs_raT_on
_mNI
II_mltkm
Tge2
Tedmicd
arm_
83199
Program
t
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pP.GE
NOT Ftt..eiW
CONTENTS
Part
I.
INTRODUCTION
2.
AIRCRAFT
3.
4.
5.
6.
7.
.........................
FLIGHT
2.1
ATMOSPHERIC
2.2
GEOMETRY
2.3
FLIGHT
DYNAMICS
I-I
........
MODULE
....................
MODULE
2.1-I
......................
DYNAMICS
PROPAGATION
MODULE
2.2-1
..................
2.3-1
EFFECTS
3.1
ATMOSPHERIC
3.2
GROUND
SOURCE
I*
ABSORPTION
REFLECTION
NOISE
4.1
FAN
4.2
CORE
4.3
TURBINE
4.4
JET
4.5
AIRFRAME
MODUL2
AND
...............
ATTENUATION
MODULE
3.1-1
.........
3.2-1
PARAMETERS
NOISE
PARAMETERS
NOISE
PARAMETERS
NOISE
NOISE
MODULE
MODULE
PAFJLMETERS
PARAMETERS
NOISE
................
...............
MODULE
MODULE
PARAMETERS
4.1-1
4.2-1
..............
4.3-1
................
MODULE
4.4-1
.............
4.5-1
PROPAGATION
5.1
PROPAGATION
5.2
GENERAL
RECEIVED
MODULE
SUPPRESSION
....................
MODULE
5.1-1
...............
.
5.2-1
NOISE
6.1
NOISE
LEVELS
6.2
EFFECTIVE
MODULE
NOISE
....................
.MODULE
6.1-1
..................
6.2-1
..................
7.1-1
UTILITIES
7.1
._"HEP_MODYNAMIC
*Chapters
I
to
UTILITIES
7
are
published
iii
under
separate
cover.
+
Part
8.
9.
NOISE
SOURCES
8.1
FAN
8.2
COMBUSTION
8.3
TURBINE
8.4
SINGLE
8.5
CIRCULAR
8.6
STONE
8.7
DUAL
8.8
AIRFRAME
8.9
SMITH
PP_DICTION
9.1
2
ICAO
NOISE
MODULE
.....................
NOISE
NOISE
.MODULE
STREAM
SHOCK
NOISE
STREAM
BUSHELL
8.2-1
...................
JET
CELL
.MODULE
NOISE
NOISE
MODULE
CCANNULAR
NOISE
AND
..................
CIRCULAR
JET
JET
MODULE
8.1-I
MODULE
MODULE
8.3-1
..........
8.4-1
...........
8.5-1
..................
JET
NOISE
MODULE
8.6-1
..........
8.7-1
...................
TURBINE
NOISE
MODULE
8.8-1
..........
8.9-1
PROCEDURES
REFERENCE
NOISE-PP/EDICTIO:_
PROCEDURE
iv
(!978)
.....
9.1-1
8. NOISE
SOURCES
8.1
FAN
NOISE
MODULE
INTRODUCTION
l_ne
an
Fan
axial
oped
Noise
flow
by
M.
predict
F.
the
Module
predicts
compressor
or
Heidman
sound
(ref.
spectra
the
fan.
The
1).
The
a
function
as
broadband
method
noise
is
method
emploTs
of
and
based
on
pure
the
empirical
frequent/
and
tones
method
for
devel-
functions
polar
to
direcrivity
angle.
The
rate
total
fan
noise,
inlet
stator
The
tone
interaction
The
Module
flow
or
required.
tones.
function
tivity
other
by
The
of
the
user.
is
executed
output
is
frequency,
fan
it
noise
is
are
several
table
by
the
the
each
noise
is
Ae
engine
a,b
exponents
B
number
C
mean
Zoo
inlet
cross-sectional
not
that
reference
of
rotor
ambient
rotor
the
directivity
d
fan
F
pc_er
f
frequency,
rotor
m2
m2
(ft 2)
blades
blade
speed
D
area,
Area,
of
chord,
m
sound,
m/s
function
diameter,
m
function
Hz
8.1-1
(ft)
a
single
(ft)
(ft/s)
entrance
values
of
acoustic
to
output
(ft 2 )
fan
Parameters
parameters
of
and
SYMBOLS
fan
Noise
set
tables.
A
rotor-
into
The
Fan
angle,
assumed
so
sepa-
tones,
discharge
combined
mean-square
directivity
introduced
six
broadband
distortion
and
user-provided
for
of
flow
parameters.
provided
from
inlen
angle.
Additional
polar
Although
angle,
a
inlet
sources
once
noise
are
noise,
directivity
of
be
the
selected
tones,
noise
input
summing
broadband
each
can
module
angle.
directivity
widn
requires
The
parameters.
a
All
for
parameters
directly
by
sources
discharge
spectrum
method
predicted
component
interaction
noise,
i/3-octave-band
exit
is
six
rotor-stator
combination
and
noise
components.
with
table
input
pressure
azimuthal
vary
are
the
direcazimuthal
is
compatible
as
fb
blade
passing
G
constant
i
inlet
K
constant
k,£
inlet
Md
fan
frequency,
Hz
matrix
guide
vane
flow
index
distortion
rotor
indices
design
relative
point
tip
Mach
Mach
number
fan
rotor
relative
tip
M t
fan
rotor
tip
number
flow
Mach
M
aircraft
m
mass
N
rotational
N e
number
n
tone
flow
r s
distance
r*
L
dimens
S
tone
S
roter-stator
V
n_n%oer
polar
number
(slugs/s)
Hz
acoustic
pressure,
pressure,
2
source
×
to
Pa
o2c
4
observer,
(4.177
m
source
_
temperature
m
rise
to
observer,
temperature,
stator
(ft)
across
K
fan,
(°R)
vanes
factor
parameter
/irect_vlt'_"
angle,
deg
_.I-2
10 -7
Ib/ft
2)
(ft)
function
spacing,
of
re
10 ..5
from
distance
_pectr_m
frequency
(l,Md)
number
icnless
cut-off
point
engines
from
total
ambient
kg/s
harmonic
reference
T
rate,
of
Pref
Mach
max
design
(ll))
number
speed,
mean-square
at
and
n,m_ber
Mach
<p2>"
(lO)
number
index,
M r
Mach
(eqs.
K
(oK)
re
_e
.J
,
acoustic
power,
_ref
reference
O_
ambient
re
p
c_A
1
x
10 -12
power,
density,
azimuthal
kg/m
3
directivity
W
(7.376
(ib/ft
x
10 -13
J,
ft-lb/s)
3)
angle,
deg
Superscript:
*
dimensionless
quantity
INPUT
The
Noise
fan
parameters
Parameters
computation
of
sound
angle,
and
azimuthal
values
for
the
of
rotor
flow
blades,
metric
description
design
engines,
default
table.
of
The
the
reference
H e
number
of
distance
establish
the
area,
guide
fan
rotor
are
the
engine
are
required.
are
m2
polar
the
spacing
observer
of
are
given
vane
index,
tip
relative
required
The
table
source
to
m
(ft)
S
Fan
Geometry
t
A
fan
3
number
d *
fan
I
inlet
Md
fan
inlet
of
rotor
guide
rotor
inlet
flow
cross-sectional
rotor
re
rotor-stator
V
n_._nber
of
index
relative
tip
distortion
Mach
index
spacing,
stator
Ae
_e
t
S
re
blades
diameter,
vane
area,
vanes
8.1-3
re
C
number
at
design
point
number
inlet
for
Mach
the
area,
range
I.
(ft 2)
observer,
for
variable
area,
engines
from
Fan
independent
reference
in
the
required
directivity
cross-sectional
inlet
Finally,
output
frequency,
diameter,
parameters
the
conditions
inlet
vanes,
fan.
to
engine
fan
rotor-stator
input
A e
arrays
rotor
the
distance
of
levels.
The
and
either
Ambient
stator
fan
point,
and
values
of
from
user.
directivity
index,
at
the
pressure
number
distortion
required
or
output
number
of
are
Module
geo-
number
and
Fan
e
mass
flow
N*
rotational
AT*
total
rate,
Noise
re
Parameters
O_c_A
speed,
re
temperature
c
e
/d
rise
across
Ambient
ambient
C
speed
aircraft
Mach
ambient
P_
of
T
Conditions
sound,
m/s
kg/m
3
(ft/s)
(slugs/ft
Independent
polar
re
number
density,
frequency,
fan,
3)
Variable
Arrays
Hz
directivity
azimuthal
angle,
directivity
deg
angle,
deg
OUTPUT
The
output
pressure
muthal
is
as
a
of
directivity
provided
_nodule
of
for
the
is
In
frequency,
9
polar
O
azimuthal
of
polar
the
mean-square
directivity
the
nozzle
pseudo-observer
and
azi-
distance
rs
exit
to
Noise
pseudo-observer,
m
{ft)
Table
Hz
directivity
angle,
directivity
deg
angle,
deg
2
<p2(f,9,,)>"
acoustic
angle,
Module.
Fan
f
table
addition,
Propagation
from
a
frequency,
angle.
distance
r s
this
function
mean-square
acoustic
pressure,
re
D
4
c
METHOD
pute
The
prediction
the
far-field
figure
The
i.
general
detailed
The
methodology
noise.
coordinate
approach
prediction
for
for
A
presented
schematic
system
the
each
and
prediction
fan
noise
in
of
a
reference
typical
directivity
method
component
8.1-4
1
fan
angles
is
is
is
are
presented.
is
discussed.
used
to
shown
in
also
com-
shown.
Then,
the
J
The
fan
equation
for
the
<p2>*
=
A'Hi
4_I(rs
In
far-field
mean-square
acoustic
pressure
for
a
is
equation
tion,
(i),
and
tance
rs
H*
S
is
the
is
expressed
)2
is
(i
the
D(@)
S(_)
-
cos
overall
spectr,-in
M
(1)
@)4
power,
function.
D
The
dimensionless
is
the
source
form
to
directivity
observer
funcdis-
as
(2)
The
(i
forward
-
M
velocity
cos
0)4.
effect
The
is
accounted
frequency
for
parameter
by
_
the
is
Doppler
defined
factor,
as
f
(3)
=
where
the
(I -
blade
M
cos
passing
@)f--b
frequency
fb
is
N*Bc
(4)
fb
The
=
acoustic
.L
Equation
(5)
function
F.
constant
G
defined
diA_e
=
power
K
_*_
G(i,j)
contains
The
_he
(si)-a(k'
several
constant
depends
for
on
the
is
[)Mb(m*/A*)
m
empirical
K
fan
is
noise
expressed
(.ST*) 2
constants
as
F (Mr,M m)
and
the
noise
(5)
empirical
different
for
each
component
and
the
indices
i
inlet
inlet
guide
guide
vanes)
vanes)
Dower
component.
and
The
j
as
i
=
(6)
Ii
(Fan (Fan
with with
no
and
j
:
(7)
i
(_ <> 1.05)
1.05)
(5
8.1-5
/
jr
The
fuandamental
tone
cut-off
factor
6
is
defined
as
M t
(8)
11
where
the
fan
rotor
M t
If
M t >
value
of
of
the
=
tip
number
Mt
is
WN*
t.9)
1.05,
then
0
is less
tip
Mach
Mach
_ =
than
number
M t.
The
fundamental
1.05.
The
cut-off
where
the
fundamental
tone
factor
cut-off
occurs
when
the
determines
the
range
blade
passing
frequency
dominates.
The
rotor-stator
component
and
k
_he
spacing
indices
exponent
k
and
a(k,£)
£
depends
defined
on
the
noise
as
=
(I0)
i
('-* _>
(s*
i)
i)
and
[
=
(Ii)
Ii
(No (Inlet
inlet
Inlet
flow
distortion
tends
Inlet
fl_w
distortion
is
to
reduce
assumed
flow
flow
rotor-stator
to
occur
distortion)
distortion)
spacing
during
static
effects.
and
ground
roll
o_eratlons.
The
design
point
:_ = max
where
Md
is
exponent
b
the
in
Mach
n_unber
index
Mm
is
defined
as
(12)
(I,._
d)
design
value
equation
(5)
of
gives
the
relative
the
tip
effect
of
Mach
[_m
number.
on
each
The
fan
noise
component.
The
t&on
general,
point
final
F.
_
Mach
empirical
_'_.e power
_
_unc__on
n_ber
Mr
quantity
function
of
the
indux.
in
depends
relative
.-h.e relative
equation
on
tip
(5)
the
fan
Mach
tip
is
noise
number
Mach
number
the
power
source
Mr
and
is
funcand
is,
the
design
defined
in
as
(13)
x
8.1-6
wherethe tip Machn_mber Mt
is defined by equation {9)
and
flow
to
static
Mach
and
number
speed
of
As
a
the
of
The
be
The
added
to
fan
mean-square
and
polar
falls
ambient
fan
noise
at
is
that
pressure
so
determined.
parameter
band
_
its
is
for
a
as
band
axial
density
own
these
functions
computed
given
as
set
of
I/3-octave-band
frequencies.
I/3-octave
is
has
Using
expressed
the
values.
source
angle
discrete
frequency
inlet
S.
acoustic
noise
spectrum
within
the
directivity
values
center
the
function
the
noise
since
to
each
spectrum
appropriate
i/3-octave-band
that
(I),
and
are
the
equal
broadband
tones
m*/A*
assumed
equation
power,
i/3-octave-band
number
be
frequency
pure
equal
D
parameters.
must
the
can
by
acoustic
data.
is
function
function
input
sound
indicated
directivity
and
Mx
The
that
a
For
a
the
lowest
pure
tones
total
given
value
of
harmonic
is
n£ = [lO-1/2o n] + i
and
the
highest
harmonic
(14)
number
is
(15)
nu = [lOI/2° n]
where
n%
[
>
are
-
+
is
tenes
t_e
directivit
7
the
n
to
fan
the
Each
observer
functions
pure
is
nu_.ber,
-< nu,
tone
to
to
presband.
data.
the
in
in
acoustic
table
tables
discussed
there
appropriate
compute
in
if
then
mean-square
the
summarized
summzarized
component
n[
I/3-octave-band
used
are
real
If
added
as
are
enclosed
The
then
components
ncise
the
band.
band.
functions
fan
of
the
are
and
noise
spectrum
respectively.
part
within
Dumber
constants
six
and
tone
within
propagated
empirical
for
integer
no
harmonic
are
The
i
each
tones
the
there
n Z
for
._ower
indicates
then
nu
sures
The
]
_u'
II.
III
detail
The
and
IV,
as
follows.
inlet
Inlet
broadband
turbulence
random
in
Lhe
unsteady
vortices,
sources
The
flow
and
of
broadband
noise
flow
_ne
acoustic
-"
=
are
inlet
broadband
noise
is
passing
(1.552
are
due
(
in
beyond
the
to
_he
inlet
10 -4 ) (s*) "'_(k'/)
scope
is
unsteadines_
of
_he
layers,
predictions
broadband
8.1-7
random
Some
boundary
Although
from
_ower
with
blading.
turbulence
noise
Noise
associated
the
flow.
radiated
Broadband
blade
of
of
the
this
or
sources
of
w_<es
this
and
individual
module,
the
total
predicted.
noise
_ "
M'(m'/A')
m
from
the
(_T*)
inlet
2
F(M r)
is
(16)
--'W
l
where
the
constant
a(k,£)
4
is
i
(17)
The
exponent
acoustic
a
inlet
flow
s
>
defined
power
i.
by
varies
distortion
The
equation
inversely
effects
power
(17)
with
F
for
the
rotor-stator
dominate
function
accounts
the
fact
spacing
rotor-stator
that
the
except
spacing
where
effects
at
is
F =
(18)
i
(Mr -< 0.9)
O.
which
is
The
plotted
in
(M r
figure
mean-square
computed
table
SLMr2
from
III
and
S
=
pressure
(i).
plotted
in
0.116
The
figure
exu
tion
_
is
the
(19)
is
plotted
3.
-0.5
geometr{c
Discrete
rotor
or
tone
stator
intersecting
or
by
are
the
rotating
from
made
to
only
the
average
The
acoustic
-"
=
determine
(2.683
x
is
from
from
the
the
!0 -4
)
G(i,_)
is
given
3
is
in
given
by
equal
to
2.2.
Equa-
Tones
with
are
starer
spinning
to
inlet
lift
vanes
or
stator
duct
rotor-stator
(s')-a(k'[)M4"31(m*/A*)
m
rotor
blades
guide
vanes
inlet
vanes.
No
each
The
attempt
propagated
tones
is
mode,
predicted.
interaction
(iT')
9.i-8
on
by
modes.
of
are
fluctuations
generated
on
characteristics
c_racteristics
due
is
impinging
as
specific
power
is
function
and
tones
rotor
blades
far-field
noise
D
(19)
associated
preceding
a
spectral
Interaction
Interaction
wakes
broadband
4.
generation
wakes
propagated
The
Rotor-Stator
blades.
inlet
function
deviation
figure
Inlet
to
(n/2.5)_
in
mean
in
due
directJvity
"
where
0.9)
2.
acoustic
equation
>
2
F(Mr,M
tones
m)
i_=
{20)
where
the
constants
are
w •
G(i,
j}
(21)
O. 580 l
=
IO .625
1
0.205j
and
a(k,£)
The
constants
vanes
and
spacing
when
in
the
matrix
fundamental
accounts
inlet
function
(22)
=
for
flow
F
G
tone
the
account
cut-off.
inverse
distortion
for
The
variation
effects
the
effect
exlDonent
of
dominate
of
on
the
at
the
inlet
acoustic
s
>
1.
guide
rotor-stator
power
The
except
power
is
-2.31
0. 397M
(M r
<
0.72)
m
F
2053C31,
S
---
(0 2
<
r
0 .315M
3 "69M-8
m
which
is
The
action
plotted
given
is
a
is
in
discrete
III
0"462
(23)
0"462)
<
Mr)
5.
pressure
from
and
function
0.866Mm
(0.866Mm
acoustic
computed
table
<
r
figure
mean-square
tones
is
in
Mr
plotted
given
due
equation
(i).
in
figure
to
inlet
The
6.
rotor-stator
directivity
The
spectral
interfunction
D
function
S
by
n u
s(n)
=
_
S(n,i,
n=n
where
n Z
associated
value
of
and
nu
are
with
the
I/3-octave
_.
For
j)
(24)
Z
n
=
the
lower
and
band
upper
with
a
values
center
of
t_e
frequency
harmonic
number
parameter
I,
(25;
S(1,i,j)
_0.
799
0. 387_
8.1-9
and
for
n
>
I,
S(n,i,j)
=
x
I_i
where
i
and
function
j
are
S(t])
is
i/3-octave-band
250
i01
defined
by
plotted
in
Inlet
The
flow
distortion
interaction
unsteady
lift
average
The
(26)
equations
figures
(6)
7
to
I0
and
(7),
prior
to
respectively.
being
The
converted
to
data.
Inlet
stator
I0 -0-3(n-2)
0"432 l
0. 307_
Flow
has
tones.
on
the
properties
acoustic
an
In
blades
effect
the
due
broadband
inlet
produces
far-field
to
Tones
on
addition,
which
of
:_wer
Distortion
flow
are
(1.488
x
rotorcan
pure
tone
generate
noise.
predicted.
distortion
tones
•
•q* =
and
distortion
additioi_al
noise
inlet
noise
fl,,w
is
9
10 -4 ) (s*)-a(k,_)M4-31(m*/A*)
(AT*)"
(27)
F(Mr,.Xt m)
m
-her,:
a(k,
5)
re_}_ectlvely,
The
and
F(>Ir,M m)
and
the
!xawer
mean-_,_uare
: _ computed
from
a:: for
the
•_lotted
in
acoustic
equation
inlet
arc
6.
The
by
F"
is
due
The
directivity
to
interaction
sVectral
equations
plotted
_ressure
(i).
rotor-starer
figure
defined
function
(22)
in
inlet
and
figure
flow
distortion
function
D
tones
as
g'_ven
in
S
is
given
by
function
23),
5.
is
toner;
the
taDle
same
ITI
and
_U
i0-"
(28%
/
n=n
w!_Ich
iata.
is
"..'lotted
_n
2
figure
ii
prior
to
Combination
When
tht,
relat_v,:
_eed
value
of
I,
shock
waves
_Icse
._hock
waves
_rouagate
waves•
The
:n_tead
._f
tonal
but
frequenc[.'.
resultlng
the
e×tends
This
blade
in
are
of
a
combination
Noise
rotor
blade
the
Lhe
contains
frequency.
frequency:
engine
._olse
inlet
of
as
either
often
_.i-i0
a
the
resultant
on
is
of
l,'3-octave-band
exceeds
edge
harmonics
The
to
tiFs
leading
• interval
tone
converted
Tone
at
through
sFectrum
passlng
the
formed
beina
side
referred
a
each
rotor
series
shaft
of
number
blade.
Mach
speed
no_se
is
of
the
to
Mach
as
not
purely
harmonic
"buzz-saw"
I
!
The
acoustic
H*
The
acoustic
the
They
passing
x 10 -4
1/4
mental
K
due
to
combination
G(i,j)(m*IA*)(AT*)
power
computed.
blade
6.225
"
power
for
are
three
fundamental
as
noise
of
(29)
the
fractions
tone.
tone,
The
is
r)
shaft
of
the
The
constants
K
for
fundamental
combination
combination
combination
F(M
harmonics
expressed
frequency.
for
the
I/8
2
tone
and
constant
2.525
G(i,j)
rotational
speed
fundamental
tone
each
harmoi_ic
tone,
2.030
are
x 10 -3
x
10-3
is
for
given
the
I/2
are
of
the
for
funda-
b7
(._0)
.316
This
of
accounts
for
combir_tion
the
0.31
fact
tones
through
that
inlet
the
guide
inlet.
vanes
The
inhibit
power
the
function
propagation
F
is
given
by
F(N r)
=
I0 -6"751!'61-Mr)
(I -< H r
-< 1.61)
O
(:%
-1.21
the
I.'S
fundamental
(1.61
combination
<
=
i0-14"
O
-1.33
for
the
[/4
fundameatal
75 (i" 322-Mr
(Mr-l.
)
(i
322)
combination
"Mr <
=
O
i0"31-85(i-146-M:}
I I0-1"41
(Mr-l.
<
8.1-11
t32)
M r)
and
(I -" M r
146)
I)
1.3..)
(1.322
tone,
-
(_r
F(M r)
M r)
tone,
(M r
F (M r)
I)
(Mr-l.61)
i0
for
<
(31)
<
i )
-_ 1.146)
(I. 146
<
Mz)
(33)
for the 1/2
in
figure
The
tone
the
acoustic
b 7
tone.
III
and
(i).
The
D
plotted
is
Then,
spectrum
function
table
pressure
equation
I/3-octave-band
directivity
in
combination
mean-square
combination
yield
fundamental
power
function
is
plotted
12.
due
is
the
in
figure
same
computed
the
to
for
13.
three
separately
combination
all
The
three
for
harmonics
tone
summed
noise.
The
harmonics
spectrum
each
are
and
function
is
S
to
given
is
given
by
S (n)
=
(34)
-405(8D)
405(8D)
for
the
1/8
fundamental
5
-3
(D
(n
combination
_> 0.125)
tone,
(35)
s(n)
for
the
1/4
=
I_
"520(4n)5
.520(4n)
fundamental
S([_)
=
_
combination
the
1/2
fundamental
combination
tone
tone,
(36)
noise
"-3
combination
are
/lotted
Discharge
the
noise
The
inlet
tion
discharge
broadband
broadband
noise.
tone.
in
The
figure
Broadband
spectrum
functions
for
14.
Noise
noise
is created
The
acoustic
power
by the
same
mechanisms
as
of the
discharge
broadband
is
_L
where
and
0"33212_13
_,O. 332(2n
for
-5
=
(3.206
a(k,[)
(17)
and
x
is
G(i
10 -4 )
the
j)
same
_(i,j)
as
(s*) -a(k'£)
for
inlet
(m*/A*)(_T*)
broadband
noise
2
F(M r)
given
by
(37)
e_aa-
is
(38)
8.1-12
The
factor
G
acoustic
power
is
by
given
shows
of
that
the
the
presence
discharge
of
inlet
broadband
guide
noise.
The
vanes
doubles
power
function
t.he
F
(39)
F (M r)
and
is
plotted
The
is
as
and
the
plotted
in
(Mr -< i. 0)
(Mr > 1.0)
15.
acoustic
equation
is
in
The
discharge
power
of
_*
qne
as
=
matrix
equation
•
discharge
broadband
function
spectrum
spectrum
as
D
noise
is
function
given
in
643
x
interaction
rotor-stator
10 -4 )
is
and
Interaction
give,
in
is
the
S
equation
(19)
and
the
Tones
tones
are
interacLion
rotor-stator
a(k,£)
(21)
to
The
Rotor-Stator
inlet
discharge
(2
16.
noise
rotor-stator
the
the
directivity
4.
Discharge
mechanisms
due
The
figure
broadband
figure
pressure
(i).
plotted
inlet
in
2
figure
from
III
same
i
Mr
mean-square
computed
table
=
created
tones.
interaction
tones
The
Lhe
same
as
for
G(i,j)
inlet
the
same
is
G(i,j)(s_)-a(k'i)M2(m*/A*)(AT')
m
matrix
by
acoustic
2
rotor-stator
F(M
r)
tones
(40)
given
by
is
(41)
c,(_,j) =
2
which
The
gives
power
given
in
The
the
equation
D
functlon
given
is
S
in
F
(39)
mean-square
interaction
tion
effect
ftLnction
0.58O]
0.820J
.59
of
inlet
is
the
and
guide
same
plotted
in
figure
acoustic
pressure
is
_uted
from
given
in
table
is
equations
the
same_
(24)
as
to
the
(26)
and
8.1-13
due
equation
plotted
inlet
and
and
the
tones
III
vanes
as
fundamental
discharge
cut-off.
noise
as
15.
to
discharge
(I).
in
in
The
figure
r_tor-stator
plotted
tone
broadband
rotor-stator
directivity
17.
The
funcspect_
interaction
figure_
7
to
tones
i0.
"_
as
Output Computation
The
sun
of
user
has
nents
the
option
of
mean-square
The
by
the
output
pressures
acoustic
from
deleting
one
the
or
pressure
six
more
fan
of
for
noise
the
noise
a
fan
is
the
components.
source
The
compo-
desired.
frequency,
angle.
mean-square
mean-square
the
if
The
of
I/3-octave-band
the
total
acoustic
pressure
polar
directivity
noise
is
number
of engines
is available
of
the
is
angle,
computed
and
mean-square
for
azimuthal
acoustic
Ne
for
the
output
table.
the
sound
pressure
level
SPL
each
desired
value
directivity
pressure
multiplied
In addition,
defined
as
printed
_®c_
SPL
and
d_e
power
=
i0
level
lOgl0
PWL
/_kp22 *
+
20
defined
lOgl0
(42)
-Pref
as
0c_A*A
e
(43)
PWL
=
I0
lOgl0
_*
+
I0
logic
_ref
REFERENCE
I.
Hei!mann,
__ource
M.
F.:
Noise.
Interim
NASA
TM
Prediction
X-71763,
Method
1975.
8.1-14
for
Fan
and
Compressor
m
TABLE
I.-
RANGE
AND
Input
parameter
Minimum
2
Ae , m
N e
m
A _
d
[
•
o
.
.
.
.
1
°
°
°
.
i00
i0
20
i00
I.!28
1
"
°
°
"
°
°
"
1
1.0
......
i , kg/m 3 .....
2
2.0
1
2
1
I0
i0
50
200
°
0
0.2
i0
°
0
........
m/s
4
0.2
o
.........
.......
4
2
0.5
.
Max imttm
I0
_,14
1
.
"T*
De fault
1
°
........
"_,1o
IN-PUT PAR/LMETERS
0.i
.........
._1"
C a,
.
0.3
.
S*
".7
.
........
Md
OF
0.01
.......
....
VALUES
1
i
....
_
1
0.01
......
........
r S ,
DEFAULT
0
0.9
0
0.3
0.5
0
0.2
1.3
200
340.294
4OO
0.2
1.225
1.5
8.1-15
_D
c_
vI
V
A
Vl
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vt
Z
X
VI
A
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v
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r2-'D
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tc
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x
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j
8.1-13
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8.1-17
rU
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_
TABLE
IV.-
SPECTRUM
FUNCTIONS
Source
FOR
Spectrum
broadband
S(q)
noise
=
0.116
inlet
exp
L
0.5
NOISE
function
r_
Inlet
FAN
,hi2
,,]q
L
In
2"_'.2
J
J
n u
rotor-
stator
interaction
S(q)
=
tones
I
S(n,i,j)
n=n Z
whece
S(l,i,j)
-0.499
0.136
0.799
0.387
=
%.2s0
S(n,i,9)
x
2.1oi
Inlet
flow
i0
-0.3
(n-2)
(n
>
i)
o.3o L
n u
distortion
S (n)
tones
0.43!
=
=
9
I
i0 -n
n=n
&
1/8
funda-
mental
combination
tone
s(n) = _ "°'4°5
(8n) 5
[.0.405
(sn) -3
noise
8.1-19
(_
!
0.125)
(D
>
0.125)
i
TABLE
IV.-
Concluded
t
Source
Spectrum
function
F
1/4
fundaS(q)
mental
520
combination
tone
1/2
-< 0.25)
(4rl)
-5
(q
>
0.25)
noise
fundas(q)
mental
=
0.332(2n)
Lo
332(2q)
(n
<
0.5)
(rl
>
0.5)
3
combination
tone
(rl
=
-3
noise
Discharge
broadband
noise
s(q)
=
Discharge
0.116
exp
L°'5L
in
2.2
j
j
n u
rotor-stator
interaction
s(n)
S(n,i,j)
=
tones
n=n_
where
S(l,i,j)
=
0"1361
0.387J
S(n,i,j)
=
0"4321
0. 307_
8.1-20
×
i0-0.3
(n-2)
(n>
i)
N
/
r
/
Figure
i.-
Schematic
diagram
8.1-21
of
typical
axial
flow
fan.
1
_7
t
/
7
/
/
/
/
--
-Q
o
£
=
C)
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c
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8.2
COMBUSTION
NOISE
MODULE
INTRODUCTION
The
Combustion
bustors
Noise
Module
predicts
in
gas
turbine
engines.
by
R.
K.
of
core
installed
posed
appendix
empirical
data
engines
to
produce
directivity
The
and
Parameters
sound
are
of
acoustic
SAE
ARP
as
a
from
method
876.
The
turboshaft,
spectra
requires
exit
the
or
azimuthal
not
to
the
output
vary
directly
conventional
is
based
method
of
on
and
as
with
by
The
a
the
provided
user.
is
of
angle.
parameters.
be
The
function
azimuthal
is
several
module
and
executed
output
polar
other
a
for
table
polar
it
noise
is
combustor
Core
Noise
user-provided
of
each
set
the
noise
combustor
Ae
engine
ca
ambient
D
directivity
f
frequency,
fp
spectrum
peak
frequency,
H
aircraft
Mach
number
&
mass
N
number
<_2>*
mean-square
total
P=
ambient
area,
reference
speed
angle,
is
introduced
area,
of
m2
m-
sound,
(ft 2)
(ft 2)
m/s
(ft/s)
Hz
of
rate,
kg/s
Hz
(slugs/s)
engines
acoustic
pressure,
pressure,
pressure,
pressure,
Pa
2
x
re
10 -5
(Ib/ft2)
Pa
8.2-1
(Ib/ft
2)
Pa
2 4
O_c_
(4.177
×
10 -7
ib/ft
assumed
so
tables.
function
flow
reference
Pt
entrance
of
mean-square
directivity
combustion
angle,
with
the
once
is
frequency,
directivity
compatible
The
by
Additional
Although
A
f
pro-
turbofan
frequency
SYMBOLS
Pre
coma
employs
turbojet,
function
can
parameters.
directivity
table
of
parameters
required.
input
pressure
and
input
flow
Module
parameters
values
to
from
noise
The
angle.
method
entrance
Matta
noise
the
2)
_at
_
distance
r
from
source
to
observer,
m
(ft)
s
t
dimensionless
r
distance
from
source
to
_bserver,
re
_e
s
S
spectral
T
total
ATde
distribution
temperature,
design
s
function
K
turbine
ambient
(OR)
temperature
temperature,
8
polar
II*
acoustic
_ref
reference
K
directivity
O
C3Ae
1
x
10 "12
density,
azimuthal
kg/m
3
directivity
(OR)
deg
re
power,
K
(OR)
angle,
power,
ambient
extraction,
W
(7.376
(slugs/ft
angle,
x
10 -13
ft-lb/s)
3)
deg
Subscripts:
i
entrance
j
exit
Superscript:
*
dimensionless
quantity
INPUT
The
the
combustor
output
of
conditions
The
are
frequency,
arrays
values
A
Ae
N
the
and
of
exit
parameters
Noise
Parameters
required
for
computation
polar
the
engine
distance
_he
and
Core
establish
Finally,
area,
entrance
Lhe
directivity
angle,
independent
variable
reference
to
input
combustor
parameters
entrance
engine
reference
number
of
distance
area,
observer
or
of
s_und
the
and
number
of
required.
are
given
in
Input
Constants
area,
re
m2
for
source
to
the
The
table
Ae
(ft 2)
observer,
r S
8.2-2
m
(ft)
either
Ambient
levels.
directivity
the
range
I.
from
user.
pressure
enqines,
engines
from
required
from
azi=_thal
values
are
area,
are
.Module
output
angle
table.
combustor
and
default
entrance
j_
Core
L
Pt,
i
T"
J
A
T*
des
Noise
combustor
entrance
mass
eombustor
entrance
total
pressure,
combustor
entrance
total
temperature,
combustor
exit
design
total
turbine
flow
ambient
temperature
sl_-ed
aircraft
of
Math
ambient
mnthal
[uovlded
out_,ut
as
a
sound,
kg/m
dtrectivtty
m/s
]
for
module
of
angle.
the
from
frequ,,ncy,
polar
anqh,,
is
_n
•
T_
re
Tm
])
Arrays
deq
PUT
a
table
of
_olar
addition,
the
mean-square,
direct_vi_y
the
observer
angle,
distance
.Module.
source
to
observer,
Norse
m
[ft)
Table
H:
dir_,ctivity
azlmutha|
h
T
deq
Combustor
f
re
(ft,'s}
Variable
frequency,
Proi_ation
distance
r_
this
function
directivity
Poe
re
(sluqs/ft
anqLe,
dir,,ctivtty
of
r_
Ae
Conditions
OUT
The
c
Hz
a;'.tmuthal
|_ressure
D
extraction,
Ind,5_ndent
}k)L,lr
re
number
density,
t'requt,ncy,
rate,
temperature,
Ambient
MoQ
Parameters
anqleo
dirt, ctivity
,|eq
anqle,
deq
O
me.xll-_uare
aCOUStiC
Vressure,
2 4
r_, ,_ Cp
acoustic
and
rs
a:iis
.METHOD
The
_e
prediction
combustor
method
are
shown
in
methodology
noise.
given
in
figure
proposed
Details
reference
I.
The
of
the
i.
A
coordinate
by
R.
K..Matta
development
and
schematic
system
of
and
a
is
used
validation
typical
to
compute
of
the
combustor
directivity
angles
is
are
also
shown.
The
equation
I/3-octave
for
band
for
<p2>
t
a
=
the
far-field
gas
turbine
ntA *
mean-square
D(_)
4_(r:)
2
(i -
acoustic
combustor
pressure
in
a
is
S(f)
M
(I)
cos
@)4
Q
The
dimensionless
The
acoustic
states
source
power
to
]*
observer
is
distance
related
to
the
is
combustor
defined
as
entrance
and
exit
as
-*
*
&'/T"T[
me
rs
aircraft
Mach
number
term
in
")2
(3)
>2
"'"
equation
(i)
accounts
for
forward
for
equation
(I).
flight
effects.
Two
t:vity
empirical
functions
f'_nction
is
given
1&
a
in
table
function
figure
3.
D
f
The
engines
N.
acoustic
pressure
and
of
azimuthal
the
sound
The
the
as
of
a
?ressure
2.
given
The
in
given
The
spectrum
table
direc-
angle
0
function
Ill
and
plotted
and
S
in
by
(4)
<?2>*
i_
now
pressure
this
module
of
angle.
level
is
is
directivity
9
function
d_rec_ivlty
polaz
figure
and
mean-square
output
the
in
fP
pressure
_s
of
(f/fp)
400
M,_ cos
1 -
required
plotted
frequency
=
noise
are
function
and
mean-square
total
a
logl0
_ak
P
=_.e
II
of
The
is
a
from
by
table
frequency,
In
SPL
is
computed
multiplied
polar
addition,
defined
of
printed
the
equation
the
(I).
number
of
mean-square
directivity
outFut
angle,
is
available
as
2
,3
_P:.. 10 1ogi_ <p2>"
=
+
:0
l°gl0
C
_ "
Pref
8.2-4
(5)
f
and
the
power
PWL
level
=
10
PWL
defined
lOgl0
H"
+
as
I0
(6J
logl0
REFERENCE
I.
Emmerlinq,
Control
d.
FAA-RD-74-125,
AD
A030
J.;
Program.
Kozin,
S.
Volume
III-I,
B.;
Ill,
Mar.
376.)
_.2-%
and
Matta,
Supplement
1976.
R.
1
(Available
K.:
-
Core
Prediction
from
DTIC
Engine
Noise
Methods.
as
TABLE
I.- RANGE
ANDDEFAULT
VALUES
OFINPUTPARAMETERS
Input
parameter
A t
.
.
Ae , m 2
N
o
o
o
.
Minimum
.
.
......
Default
0.01
1
i0
0.01
,_/4
I0
1
4
1
........
0.01
rSS
m
i00
.......
m*.
i
°
'%_oo
........
P:,i
°
°
....
•
T*
........
.
°
o
0.2
0
o
i0
0
0
0.9
1
i
30.0
1
1
5.0
1
2
6.0
.......
T. _
1
Maximum
....
3
'_Tde s
Coo,
0
.......
m/S
340.
2OO
......
0.2
_
, kg/m
3
.....
[
8.2-6
0.5
2.0
294
4OO
1.225
1.5
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Figure
I.-
Schematic
diagram
of
typical
8.2-8
gas
turbine
combustor.
I
¢D
1
'¢
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e_l
I
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8.2-10
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-7
8.3
TURBINE
NOISE
.w_DULE
INTRODUCTIO_
The
Turbine
for
an
axial
the
General
functions
to
a
pure
The
met_hod
and
Parameters
to
vary
output
or
pressure
azimuthal
with
table
I).
based
The
as
a
is
input
of
noise
on
a
method
function
the
s,--
directly
can
by
The
a
a
the
of
angle.
fxequency
is
with
executed
output
engine
a,b
components
B
number
c=0
ambient
D
directivity
d
turbine
f
frequency,
fb
blade
inlet
other
a
polar
it
is
for
table
turbine
noise
cross-sectional
reference
of
area,
rotor
speed
polar
compo-
area,
m2
m 2
(ft 2)
sound,
m/s
(ft/s)
function
diameter,
m
(ft)
Hz
passing
frequency,
}:z
ratio
h"
specific
enthalpy,
re
ha
absolute
htunidity,
percent
K
constant
8.3-1
RT
mole
fraction
turbine
Turbine
of
each
the
directivity
noise
introduced
tables.
blades
of
rotor
fuel-to-air
by
.Noise
user-provided
once
is
frequency,
angle,
the
SYMBOl3
A e
and
noise
The
by
Additional
Although
directivity
compatible
turbine
tones
empirical
broadband
provided
user.
The
function
azimuthal
A
pure
developed
employs
of
of
and
method
parameters.
be
module
parameters.
as
several
parameters
directivity
is
broadband
is
component.
flow
input
(ref.
spectra
required.
the
the
method
spectrum
requires
are
of
acoustic
tone
exit
7
sound
Each
Module
parameters
values
and
produce
and
predicts
The
Compan
angle.
entrance
Module
turbine.
Electric
directivity
nent
Noise
flow
(ft 2)
is
set
of
mean-square
angle,
assumed
so
that
not
the
aircraft
Mach
number
_m
H
rotational
number
speed,
of
Hz
engines
e
n
tone
<p2>
mean-square
Pref
r s
r t
S
harmonic
acoustic
reference
pressure,
pressure,
distance
from
2
source
dimensionless
distance
gas
m2/(K-s
constant,
S
sp_ctr,_
T
temperature,
blade
n
number
I0 -5
to
Pa
(4.177
observer,
from
2)
m
source
K
tip
speed,
ambient
power,
power,
densitq_,
azimuthal
exit
s
static
t
total
m/s
•
re
_e
(ft/s)
angle,
re
1
deg
D
c3A
×
10 -12
W
(7.376
kg/m
directivity
3
(slugs/ft
angle,
3)
deg
ambient
Su_Terscri.:t
observer,
(ft2/(°R-s2))
:
3
2}
parameter
reference
entrance
ib/ft
(ft)
to
'ref
i
i0 -7
(OR)
directivity
acoustic
Su=scripts
x
function
frequenc/
polar
x
2 4
D_c
re
:
dimensionless
quantity
8.3-2
x
10 -13
ft-lb/s)
INPUT
The
Turbine
turbine
Parameters
for
:omputation
required
directivity
pendent
angle,
variable
sectional
area
description
of
of
and
engines,
default
parameters
Noise
values
are
of
and
or
for
and
number
the
turbine.
pressure
the
output
to
input
rotor
the
engine
reference
number
of
The
are
area,
given
in
(ft 2)
e
H e
r s
distance
engines
from
source
to
observer,
Turbine
A •
turbine
B
number
dj
turbine
inlet
of
rotor
rotor
fuel-to-alr
N*
°s,j
exit
diameter,
re
Turbine
_ise
total
re
c
_z
_A_A_
Parameters
temperature,
re
tem--_erature,
speed
of
absolute
humidi_/,
aircraft
Mach
ambient
re
/d
re
Ambient
M
area,
blades
speed,
static
ambient
(ft)
ratio
rotational
entrance
m
Geometry
cross-sectional
density,
T
T
Conditions
sound,
m/s
percent
(ft/s)
mole
fraction
number
kg/m
3
8.3-3
(slugs/ft
for
required.
3)
Ae
the
inlet
reference
Constants
m2
frequency,
turbine
requ/red
engine
of
the
inde-
geometric
range
I.
are
polar
cross-
area,
The
table
the
conditions
establish
The
are
parameters
output
levels.
are
the
observer
the
Ambient
arrays
blades
Input
A
either
user.
table.
Finally,
distance
the
directivity
the
of
from
from
sound
azimuthal
values
of
required
MJ_dule
number
and
IndependentVariable
frequency,
polar
Arrays
Hz
directivity
azimuthal
angle,
directivity
deg
angle,
deg
OUTPUT
The
output
pressure
as
muthal
provided
to
a
this
directivity
for
the
of
from
is
a
In
frequency,
0
polar
source
to
the
mean-square
directivity
the
observer,
observer
m
Noise
acoustic
angle,
and
distance
azi-
rs
is
(ft)
Table
Hz
directivity
azimuthal
<p2_f,e,¢l>"
of
polar
addition,
Module.
Turbine
f
table
frequency,
angle.
Propagation
distance
r s
module
function
angle,
directivity
mean-square
deg
angle,
deg
acoustic
pressure,
re
2
pc
4
METHOD
The
prediction
the
far-field
ure
I.
The
general
tation
method
noise.
coerdinate
equations
is
turbine
A
system
for
followed
noise
the
by
a
<p2>*
for
equation
r
and
is
and
a
reference
typical
method
discussion
i
is
used
turbine
directlvity
prediction
detailed
=
the
(i),
S
expressed
is
far-field
_*A*
4_(rs
tion,
in
of
is
angles
are
of
are
presented.
the
to
compute
shown
also
in
This
method
fig-
shown.
for
The
presen-
each
component.
The
equation
turb!x,c
is
In
presented
schematic
_"
the
in
)2
is
(i
the
spectrum
dimensionless
mean-square
D(9)
._;(_)
-
cos
M
overall
pressure
for
a
(I}
@)4
power,
function.
form
acoustic
The
D
is
the
source
to
directivity
observer
funcdistance
as
s
r::rs/ e
(2)
8.3-4
Theforward
velocity
(i
0) 4 .
-
_
cos
rl =
where
the
effect
The
(1 -
blade
is
accounted
frequency
M
cos
passing
for
parameter
by
q
the
is
Doppler
defined
factor
as
(3)
_q]_-b
frequency
fb
is
(4]
The
acoustic
power
_* = K
t,i
\
The
constants
particular
the
s,j
turbine
[[*
is
expressed
as
(S)
(u_)b
ht,i
K,
noise
entrance
for
a,
and
source
sI_-cific
b
are
being
total
determined
from
considered.
enthalpy
h;,
The
i
and
empirical
difference
the
exit
of
the
data
of
between
specific
the
the
static
*
e:,thal_y
cific
hs,
%.
enthalpy
is
the
idea[
is
computed
ratio
,%, and
the
?roi_:rties
Utility.
absohlte
The
rot.,tional
speed
11T
A_
=
_N
tions
and
puted
as
the
d.lta.
tones
must
by
added
the
number
to
turbine
falls
the
with
U:
spe-
fuel-to-air
the
appropriate
is a functlon
turbine
polar
Th_ e broadband
are
the
values
apFropriate
noise
spectrum
within
frequency
the
band
noise
function
mean-square
and
center
n. - [I0 "lz°
each
spectrum
frequency
tones
i/3-octave-band
that
(1),
and
power,
of
[_ure
h/3-octave-band
of
D
}_arameters.
be
ha
s|_eed
Each
the
of
Gas
the
by
equation
acoustic
The
turbine.
temperatures,
_6)
function
in_,ut
band
input
humidity
rotor
tip
i:; given
function
a
extraction
•
iudic:ited
dir,,ctivity
:;et of
and
_rk
fro.'.* the
S.
acoustic
directivity
noise
at
is
I/3-octave
._ts
these
pressure
angle
as
band
so
For
n,
the
a
comgiven
I/I-octaveT_e
that
a
own
func-
is
for
frequencies.
determined.
param_tez
has
using
expressed
discrete
is
,_ource
By
a
g_ven
lowest
pure
to_al
value
harmonic
is
n] + I
(7}
L
anJ
th,, highest
harmonic
=
n
[ 101/20
number
is
".]
(,g}
U
S.3-5
whrre
[
:I[ _
nu,
are
nu
sures
The
]
indicates
then
-
n£
for
The
l
are
|:ropagated
empirical
noise
the
number
n
the
are
com_x_nent
given
is
tables
described
Turbine
broadband
random,
iu
in
and
noise
noise
The
flow
,_re
III
acoustic
the
the
due
}_owor
to
to
II.
The
there
pres-
appropriate
band.
data.
compute
the
acoustic
directivity
following
with
and
s_ec-
Each
two
random
Some
boundlry
of
is
If
then
mean-square
the
respectively.
o_
turbine
sections.
unsteadiness
the
of
this
blade
of
this
wakes
and
individual
module,
o_"
sources
layers,
prediction
sconce
number.
-< n u,
Noise
in
turbine
tone
to
used
blading.
Although
n&
i/3-octave-band
the
associated
the
pure
IV,
in
turbulence
beyond
by
and
detail
is
flow.
is
produced
table
real
If
added
as
Broadband
|_assing
entrance
broadband
band
noise
flow
unsteady
vortices,
of
the
The
functions
in
enclosed
band.
then
observer
Turbine
turbuh'ncc
band.
given
in
the
the
are
and
are
of
within
within
to
noise
part
tones
constants
turbine
functions
inteqe.r
no
tones
harmonic
for
trum
+
are
each
tones
_owor
the
there
the
sources
total
broad-
predicted.
broadband
noise
from
the
turbine
is
,,e
{S.SS'_
_,,
dir,,ctivity
ur,-
2.
Th,,
'.'i,lure 3.
,',lu.,t_ou
_
10 -5 )
function
_l-,-ctr_rn
Th,'
D
'
is
function
moan-::qu.lr_,
given
S
harmonic:_
fief,!
tone
starer
of
gen,,ration
bl.%des.
the
turbine
c!l._r.lcterist_c:;
The
(9)
{UT )-1"27
table
,liw, u
Ill
and
iI_ table
_re:;:_t:re
plotted
IV
i:_ thet_
and
in
plotted
computed
figin
by
(1).
D_::crete
or
"
in
is
acou.qttc
T11rbine
tutor"
•
i
hi, i
acou:_tic
Pure
is
tones
blade
},ass_nq
_.ow,,r due
_I.162
_
with
occur
at
lift
fluctuations
frequencies
frequency.
The
that
average
_,r,,d_cted.
to
turbin,,
"t,_
[_* =
Noise
associated
These
are
Tone
F:U:," tone
no_sd
-h:,%
lO'"_
(U_) -4"02
<_ ,,
)I .46
h:,
i
_.3-6
is
on
are
far-
_,e directivity
ure
4.
The
S
which
is
computed
function
function
-
_
0.6838
plotted
bv
O
spectrum
in
given
S
The
_lar
is
5.
acoustic
It
direct_v%ty
the
for
the
_ound
the
The
mean-square
output
=
and
plotted
in
fig-
acot,stic
pressure
is
".hen
and
for
for
each
a:imuthal
In
level
SPL
loqh_
<p22"
20
value
of
an_le.
by
printed
defined
i:; the
turbine
multiplied
addition,
÷
a
des_r,,d
directivity
pressure
table.
I0
Computation
pressure
computed
acoustic
pressure
SPL
is
angle,
mean-:_quare
Ne
ZlZ
by
(I).
mean-square
components.
table
given
(ll)
Output
two
in
is
lO "(n-I)/2
figure
equation
is
the
output
sum
the
The
numb_-r
is
of
t_.e
fL-eque._y,
t_ta]
of
noise
er_::nes
ava[|_Lb|e
;f
as
(12)
log|0}_re f
and
the
_k_w,,t" l,,vel
I'WL
defined
,is
e
PWL
-
lOqlo
I0
::
÷
10
lOql0
.?
'ref
_WE_ENCE
i.
Matt.%,
R.
K.;
_:%v,'._tiqation
(Avai|able
._andusky,
from
Low
DTIC
G.
?. ; al_d
Emi:-sion
as
AD
S.3-7
."k_yle,
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A04S
5g0.)
V.
L. :
FAA-KD-.'7-4,
.:F, Cot,,
Feb.
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t._77.
TABLE
I.-
RANGE
AND
Input
pa tame te r
°
Ne
.
.
.
.
I0O
0
0
0.9
,
0
0
o
•
0
O. 3
°
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3
6
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2
4
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o
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°
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°
•
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°
T_, j
.......
0.I
2
,
0.01
I00
......
If.-
CONSTANTS
Source
FOR
0.5
400
0
4
1.225
O. 2
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0.06767
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0
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4
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500
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C
De fault
i
o
t,i
PARAMETERS
0.01
°
_t
INPUT
I
ra .......
t_ e
OF
0.01
0
........
i rs,
VALUES
M inimum
m2
Ace
DEFAULT
TURBINE
ACOUSTIC
a
K
1.5
POWER
b
Bro,hlb,_nd
,q, 5,q9 _ 10-5
1.27
-1.27
Pure
1 162
1.46
-4.02
tone
_ 10-4
_3.3-8
TABLE
III.-
TUP,_INE
NOISE
DIRECTIVITY
Tone
Broadband
directivity
deg
directivity
level,
level,
lOglo
LEVELS
loglo
D
D
i
-0,789
"0.689
-0,59g
-0.509
-0,_09
-0.319
-0o219
-0,1Z9
-O*OZ9
0,071
0.151
O. ZZ1
0.Z31
0.Zll
0.111
-0.029
-0.229
-0.549
-0,869
.
10.
20.
30.
40.
50.
60.
70.
80.
qO,
100.
110.
120.
130.
140.
150.
160,
170.
leO.
TABLE
',V.-
TURBINE
lOglo
-O.Q03
-0,796
-O*bgg
-0.602
-O._OZ
-O*3qB
-0.301
-O.Z01
"0.097
0.000
0.097
0.204
0.301
0.60Z
'l
BROADI_AND
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-1.671
-1.471
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-1.061
-0.851
-0.641
-0.431
-0,Z31
-0.021
0.189
0,38g
0.589
0.259
-0.191
-0._91
-0.931
-1,271
-I,611
NOISE
logl0
-1,884
-1.604
-1.444
-1.304
-1.184
-1,084
-1.004
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-0.844
-0.784
-1_004
-1.204
-1.384
-l.gZ4
._PECTRU._I
S
-----m
X
Y
Figure
i.-
Schematic
diagram
of
typical
8.3-I0
axial
flow
turbine.
.J
J
O
O
O
0
W
O
L
z_
•_
o
O
O
0
0
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a
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8.3-11
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8.3-12
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o
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00
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8.3-14
i
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/
8.4
SINGLE
STREAM
CIRCULAR
JET
NOISE
MODULE
INTRODUCTION
The
stream
based
lated
as
a
Single
jet
on
SAEARP
in
terms
function
The
flow
876
of
of
method
by
module
eters.
function
angle.
and
once
a
frequency,
of
employs
the
each
set
the
Noise
of
noise
so
assumed
that
engine
fully
_j
reference
area,
expanded
ambient
jet
speed
D
directivity
--4
fully
F
spectral
f
frequency,
of
m 2
area,
sound,
(ft 2)
m2
m/s
jet
diameter,
distribution
m
factor
Hz
t _
Helmholtz
number,
aircraft
number
?
<p2>
power
°
Mach
of
f A_e/C
_
number
velocity
index
engines
deviation
mean-square
(ft/s)
function
expanded
forward
(ft 2)
factor
acoustic
pressure,
8.4-I
(ft)
is
tabu-
sound
The
spectra
nozzle
values
of
the
acoustic
and
not
the
to
required.
input
param-
pressure
vary
or
are
azimuthal
output
exit
Module
parameters
angle,
is
introduced
produce
Parameters
mean-square
directivity
method
data
angle.
parameters.
Jet
SYMBOLS
A e
to
single
The
empirical
groups
several
the
nozzles.
user-provided
of
exhaust
angle,
it
is
noise
tibles.
predicts
directivity
by
for
table
polar
jet
method
polar
Additional
is
Module
circular
dimensionless
provided
executed
Noise
The
input
be
user.
Although
directivity
with
other
relevant
requires
the
Jet
shock-free
1).
frequency
output
of
from
(ref.
can
is
The
Circular
noise
parameters
directly
The
Stream
mixing
with
table
as
a
directivity
azimuthal
is
compatible
reference
pressure,
2
x
10 -5
Pa
(4.177
x
10 -7
m
(ft)
Ib/ft
2)
Pre f
distance
rs
from
nozzle
exit
rs
dimensionless
S
corrected
Strouhal
jet
temperature,
C
Tj
V_
distance
total
to
observer,
from
nozzle
number,
ambient
temperature,
exhaust
jet
to
observer,
re
_e
fdj/_Vj
K
K
exit
(OR)
[°R)
veiocity,
m/s
(ft/s)
J
If*
angle
between
polar
directivity
acoustic
power,
re
power,
density,
1
kg/m
density,
azimuthal
c_Aj
×
10 -12
3
directivity
density
W
(slugs/ft
kg/m
engine
inlet
axis,
deg
factor
0
3
and
deg
correction
ambient
0
angle,
number
jet
O.
3
vector
Strouhal
reference
_ref
flight
(7.376
x
10 -13
ft-lb/s)
3)
(slugs/ft
angle,
3)
deg
exponent
Superscript:
dimensionless
quantity
INPUT
The
.Noise
3et
parameters
Parameters
computation
quencf,
of
polar
establish
dne
distance
val_es
the
of
number
angle,
variable
area,
_nd
N
engine
reference
are
number
of
area,
azimuthal
of
for
engines,
required.
given
Input
A e
sound
values
are
parameters
either
Ambient
and
number
p:eudo-observer
input
from
user.
independent
the
_ne
the
Strouhal
reference
to
required
or
directivity
_ne
engine
are
.Module
in
Constants
m2
(ft 2)
engines
8.4-2
the
output
conditions
pressure
output
engine
The
table
axis
range
I.
the
Jet
required
levels.
directivity
the
of
are
The
angle
table.
arrays
Finally,
offset,
and
for
fre-
default
and
!
distance
r
from
nozzle
exit
to
flight
vector
pseudo-observer,
m
(it)
s
angle
between
Jet
A:
area
of
jet,
re
and
Noise
engine
inlet
axis,
deg
Parameters
A
e
J
J
v:
]
jet
total
temperature,
jet
velocity,
jet
density,
re
re
T
c
t
_j
re
O_
Ambient
speed
_cp
M
of
sound,
aircraft
M_ch
denslty,
kg/m
m/s
Conditions
(it/s)
number
3
(slugs/it
3)
Independent
frequency,
polar
Arrays
Hz
directivity
azimuthal
Vari-=b!e
angle,
directivity
deg
angle,
deg
OUT;L_
_ne
a
func=ion
output
of
tivlty
angle.
the
Propagation
r s
of
this
In addition,
Module.
distance
frcm
frequency,
polar
a
table
directivity
of
nozzle
exit
Stream
to
the
mean-square
angle,
pseudo-obse.--ver
and
distance
pseudo-observer,
Circular
Jet
Noise
angle,
directlvity
mean-square
angle,
acoustic
pressure,
re
_.4-3
is
m
Table
deg
deg
02c 4
_
pressure
azimuthal
rs
Hz
direc:_vlty
azimuthal
is
polar
Single
f
module
frequency,
as
direcprovided
(it)
for
METHOD
pute
The
prediction
the
far-field
shown
in
shown.
is
figure
methodology
The
The
coordinate
empirical
except
for
equation
i/3-octave
A
I.
Whenever
used,
for
<p2>*
=
In
equation
tion,
(i),
and
F
functions
expressed
The
which
r:
=
is
D(e,v;)
V*3
The
ratio
(6.67
and
nozzle
com-
angles
are
the
last
extrapolation,
is
also
value
extrapolated.
acoustic
pressure
in
a
is
overall
(I)
power,
D
distribution
is
is
the
directivity
function.
The
observer
Each
distance
func-
of
these
rs
is
as
is
the
classic
13).
P
civen
in
is
The
II
It
(3)
of
the
the
such
in
D
is
V;
of
of
function
2.
in
equation
@
the
III
(I)
and
power
from
table
are
of
The
power
angle
variation
functions
a
figure
acoustic
lOgl0
directivity
expresses
empirical
_
plotted
function
polar
Two
exponent
of
function
directivity
normalized
law.
and
deviation
a
the
V8
density
table
the
as
of
by
10-5)_jjt -*'_''(vj)*'8P'V*"j)
given
Vj.
is
Jq_
of
is expressed
in figure
3.
lOgl0
to
jet
F(Sc,e
separately.
form
x
equation
function
9
directivity
used
(2)
normalized
empirical
is
,V;,T;)
the
power
factor
It
with
=
and
1
exhaust
rs/_e
variation
for
deviation
law.
plotted
a
and
mean-square
jet
spectral
discussed
dimensionless
reference
typical
linearly
)
is
the
acoustic
required
logl0
_*
is
is
in
_*
far-field
_q*A;
a
require
are
stationary
4n(rs2
in
of
system
which
the
a
schematic
functions
spectra
for
band
presented
noise.
the
V8
and
is
an
velocity
mean-square
pressure
that
T
D(9,Vj)
The
directivity
table
IV
The
t_zon
of
and
sin
function
plotted
normalized
corrected
velocity
ratio
Strouhal
number
in
@
for
figure
spectral
Strouhal
d6
a
=
(4)
1
single
stream
distribution
number
log.^
V*,
and
iu
3
S c
is defined
circular
jet
is
given
in
4.
lOgl0
temperature
factor
S c,
polar
ratio
as
8.4-4
F
is
an
empirical
directivity
T_.
The
angle
corrected
func@,
(5)
wherethe jet diameter d_ is
(6)
and
_
is
the
correction
V*
3
5.
l°gl0
figure
s,lch
Strouhal
factor
and
the
The
that
the
ntLmber
is
an
correction
empirical
polar
directivity
normalized
angle
spectral
sun,nation
over
factor.
function
The
of
the
8
as
distribution
i/3-octave-band
Strouhal
velocity
shown
in
factor
F
Strouhal
number
ratio
table
V
is
defined
numbers
and
is
(7)
F(Sc,_, _
V*j,TjJ
-*"
1
=
S c
and
is
given
in
Equation
fcrward
table
(i)
flight
exponent
7
as
flight
vector
taken
must
n-_--ub
e r
and
valid
is
from
and
the
be
taken
plotted
for
a
equation
= 47(rs)2
m(@)
figure
veiocity
is
effects,
<F >
The
VI
in
figure
stationary
(i)
6.
3:t
should
(M
be
x - _= cos (_ - 5)
the
forward
reference
velocity
2,
engine
inlet
into
account
and
axis.
by
is
In
0).
To
incorporate
as
\/v*j
index
_
=
rewritten
(8)
given
_he
angle
addition,
computing
in
the
the
table
VII
between
relative
corrected
and
the
jet
Strouhal
as
(9)
Sc = [(v_ - :_)
The
value
_ngle.
_ne
mean-square
of
_e
The
number
output
is
level
SPL
acoustic
frequency,
total
of
noise
engines
available
defined
pressure
polar
is
N
of
the
directivity
the
for
mean-square
_ne
output
mean-square
as
8.4-5
can
be
computed
angle,
acoustic
table.
pressure
for
and
each
azimuthal
pressure
In
addition,
<p2>',
sound
desired
directivity
multiplie_
printed
pressure
by
2 4
0_c=o
SPL = lO iO91o<p_>* + zo I_io
and
the
power
level
PWL
defined
{I0)
2
Pref
as
_ref
(II)
P_V_
=
i0
lOgl0
N"
-
I0
lOgl0
3A*A
_c
j e
REFERENCES
i.
Gas
Turbine
Eng.,
2.
Hoch,
R.
Studies
_TE
Jet
Mar.
G.;
of
paper
Breathing
Exhaust
Noise
Prediction.
ARP
876,
J.;
and
Soc.
_tomot.
1978.
Duponchel,
the
presented
Engines
J.
Influence
at
P.;
of
the
(Marseille,
Cocking,
B.
Density
First
on
Jet
International
France),
8.4-6
"June
B_-ce,
Noise.
SNECMA
Symposium
19-23,
1972.
W.
D.:
and
on
Air
TABLE
I.-
RANGE
AND
DEFAULT
VALUES
OF
INPUT
PARAMETERS
Input
Minimum
parameter
Ae,
m 2
N
......
0.01
........
r S
5,
t
m
°
°
....
V
........
_
........
1
°
"
4
I00
0
0
3O
0. 0001
i
i0
0.7
1
4
T"
J
i0
0.01
......
A*
3
Maximum
"r/4
1
........
deg
Default
0
1.0
0
0.2
C_,
_/5
......
2OO
_,
kg/m
3
0.2
.....
8.4-7
2.5
0
340.
0.9
1.9
1.2
294
400
1.225
!.5
TABLE II.- DENSITY
EXPONENT
u}
lOgl0 Vj/c
-,450
-.400
-.350
-, 300
-.ZSO
-.200
-,150
-.I00
-,050
0.000
.050
.i00
.150
.200
.250
TASLE
-1.000
-.qO0
-.760
-.580
-.410
-.220
0.000
,220
.500
.77C
1.070
1.390
1.740
1.950
2.000
llI.- POWER DEVIATION
lOgl 0 Vj/c
-.400
-.350
-.300
-.250
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-.100
-.050
0.000
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,I00
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LEVEL
lOglo P
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-.130
-.130
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0.000
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0
.i
o
0
!
u_
_J
>
._'ao_,._O-I
uot_ogJJo::)
jaquJnN
8.4-45
IoqnoJ_,S
°
-10
_#
o
-20
-30
_40_------_
_
110
-50
--70
or -8
-2.0
1
-,.5
I
-,.o
I
-.s
Corre¢*,oO
I
o
_Vouh<]l
I
.5
1
,.o
Number.
I
,._
I
._.o
lO_h o S,
-10
i
-20
o_
:_ -7o
"._,
-60
f
_" -so
-2.o
I
-_.5
I
-_.o
Corre,;teo
(a)
F_ure
6.-
I
-.5
SVOUInol
Tj,"T,_ = 1.0;
Normalized
I
._
'
o
N=r_ber.
lOqlo
spectral
Vj/c,_
I
_.o
lo_jt o S.
: O. IO0.
distribution
8.4-46
level.
I
_.s
I
2.0
r
t
.......
•
r
_....-_.
rt, i
0
e. IEglEES
90
IO0
110
129
130
-2.0
I
I
-1.5
-1.0
l
I
--.5
0
Correcte_
0
Strouhol
L
I
.5
Numbor.
1.0
IOglo
1
1.5
l
2.0
$,
m
-10
o
-20
-30
-50
-4.0
-60
-70
-80
--2.0
I
L
L
-1.5
--1.0
--.5
Corr_tad
(b)
Tj/T=
L
0
SWo4J_ol Nutria'.
= 2.0;
lOqlo V;/c,
Figure 6.- Continued.
8.4-47
l
i
L
J
.5
1.0
1.5
2.0
_og,o S=
= 0. I00.
I
0
--10
...."
_
-20
-30
_
-5O
--
_
-6C
--
o
--7C --
i
-8c
--2.0
I
--1.5
I
I
--1.0
--.5
Corrected
I
I
0
.5
Strouhal
Number.
IOglo
I
I
1.0
1.5
1
2_.O
S=
oF
-20
--10
-30
_
-60
_
--2.0
I
1
I
--1.5
--1.0
--.5
Corrected
(c)
Tj/T=
J
Strouh_ll
= 2.0;
Figure
[
0
6.-
iCglO
1
.5
Number.
V]/c
Continued.
8.4-48
1.0
Iog,o
S=
= 0.]25.
I
I
1.5
2-O
07
o
-20
_--
120
-5C
"130
--6C--
-7a--ec
-2.o
I
-1.s
1
-_.o
I
-.5
Corrected
o
o
1
o
Strouhol
I
.s
Numbs.
I
_.o
iog_o
I
1.s
1
2.0
:_,
-10
-20
-50
I
-2.0
1
-1.5
I
-1.0
-.5
Corrected
(d]
Tj/T
L
9.4-49
i
.5
Stl'oUhcll
= 2.0;
Figure
[
0
6.-
iog10
Number.
V 3,,'c
Continued.
Ioglo
I
I
1.0
1.5
S,
= 0.150.
I
2.0
0
9O
100
110
120
130
.
Corrected
Strouhal
Number.
I
I
Iog_o
S_
oV
--10
o
--20
--30
-40
-60
_
--
1
--2.0
l
--1.5
--1.0
--.5
Corrected
(e)
T./T
0
Slbrouhol
= 2.0;
Figure
I
6.-
.5
Number.
lOglo
I
V3/c
Continued.
8.4-50
1.0
Iogto
S,
= 0.175.
l
I
1.5
2.0
i
1
-1.5
I
--1.0
1
--.S
Corrected
I
0
5¢ouhoJ
1
.5
Number,
1.0
Iog_o
I
1.5
I
2.0
$,
oF
i,
o
=
--1C
-2o
--30
o=
-40
--50
;='
-60
o
-70
-Sq
1
-- 1.5
1
I
-- 1.0
--.5
Correctea
(f)
Tj/T
Strounoi
= 2.5;
Figure
8.4-51
_jp
I¸
1
0
lOgl0
6.-
1
.5
Number.
Vj/c
Continued.
1.0
loglo
S=
= 0.i00.
1
1.5
I
2.0
0
50
Q
_
_-8
1
--2.0
I
-- 1.5
-- 1.0
1
t
!
--.5
0
.5
Corrected
Strouhol
1
1.0
Number.
I
1.5
J
2.0
Iog_ e S=
or
-
--1
Q
"6
'_
1
--2.0
I
- 1.5
I
-- 1.0
Corrected
(g)
Tj/T
I.
--.5
Strouhol
= 2.5;
Figwe
1
0
6.-
"
Nurnbmr.
lOgl0
I
.5
Vj/c
Continued.
8.4-52
1.0
IOglo
S¢
= 0.125.
J
1.5
1
2.0
0
--,L,'_-C,-_f
..g_ --50
.b
a
-60
_
- "_
_ 110
120
130
D
.b
-70,
1
-2.0
1
-1.5
--1.0
J
I
I
I
I
I
--.5
0
.5
1.0
1.5
2.0
Corrected
S_ouhoi
Number,
Iog_o
S,
=,
J=
-60"---70
-80
-2.0
I
l
- 1.5
I
-- ; .0
Corrected
(h)
T]/T_
1
--.5
0
Strouhol
= 2.5:
Figure
8.4-53
6.-
Number.
lOql 0 V3/c_
Continued.
I
L
I
l
.5
1.0
1.5
2.0
Iog,o
S=
= 0.150.
0
=,
._
-
100
--60
-7o -80
-_..o
I
-_.s
I
-1.o
i
-.s
Corrected
--2.0
--1.5
S_ouho!
--1.0
Tj/T_
0
Strounol
= 2.5;
Figure
I
.s
Number.
--.5
Corrected
(i)
I
o
6.-
|oglo
.5
Number.
lOgl0
Vj/c
Continued.
8.4-54
I
,.o
I
I
_.5
2.0
1.5
2.0
$.
1.0
Iog_o S.
= 0.175.
0
-=
,Q
4=
m
120
130
--5C
--6C
"6
j:J
¢,3
0
--7C
--8C
--2.0
J
I
I
--1.5
--1.0
--.5
Corrected
I
I
0
Strouhol
.5
Number.
Iog,o
;
I
1.0
1.5
I
2.0
S.
or
L_
0
--1
"5
4=
--601--1
I
¥
a-
-7o,_--8
-2.0
I
I
--1.5
!
-1.0
Corrected
(j)
1
--.5
Tj/Too =
Sb'ouhal
2.5;
Figure
8.4-55
1
0
6.-
iOgl0
.5
Number.
Vj/Coo
Continued.
Ioglo
=
I
I
I
1.0
1.5
2.0
S.
0.200.
0
o: -
10o
I
--2.0
--1.5
2.0
--1.0
Corrected
5_rouhol
Number,
L
-.5
L
o
IOg_o $6
0
-20
i
-10
-.30
_-'170
-4o_/
_
--50
o
-60
0
-8ol
-2.o
I
-_.s
l
-,.o
Correc:ecl
(k)
Tj/T
Strounol
= 2.5;
Figure
6.-
I
.5
NumDer.
lOgl0
V],'c
Continued.
8.4-56
l
_.o
IOg,o
:
S.
0.225.
I
_.5
2.0
oF
_--2.0
I
I
I
I
--1.5
--1.0
--.5
0
Corrected
Strouhol
I
.5
Number,
logic
I
I
1.0
1.5
I
2.0
S=
oF
--2C;
->>* -3C
-50
-60
-70
-8o
--2.0
I
I
--1.5
--1.0
1
--.5
Correct6cl
(i)
Tj/T
=
I
I
I
I
0
.5
1.0
1.5
Strou_al
3.0;
Figure
8.4-57
6.-
lOgl0
Number,
Vj/c
Continued.
=¢Kj,o S=
= 0.I00.
J
2.0
T
0
--2
-5
•1:,
m
o
"" 120
130
--6C
--7C
--8C
--2.0
I
I
I
I
--1.5
--1.0
--.5
0
Correctea
Sllrouhol
L
.5
Number.
Ioglo
I
I
I
1.0
1.5
2.0
S¢
°T
--20
_6a£_
25 --6C --
-so
-_.o
I
-_.o
1
-_ s
I
-5
Correcte_
(m)
Tj/T=
1
o
St_'ouho_
= 3.0;
Fiqure
6.-
I
.s
Number.
lOgl0
Vj/c
Continued.
8.4-58
1
1.o
10910
S.
= 0.125.
[
_.5
l
2.0
r
or
o
e
-
120
--60
--70
-80
--2.0
1
I
--1.5
--1.0
I
I
I
l
--.5
0
.5
1.0
Corrected
Slrouhol
Number.
I
I
1.5
2.0
Iogto S,
oF
-10
o
-20
--30
_
-7o
-80 F
--2.0
I
I
--1.5
I
--1.0
CorrectiKI
(n)
1
--.5
0
Strouhal
Tj/T= = 3.0;
Figure
8.4-59
I
l
1
I
.5
1.0
1.5
2.0
Number.
lOgl0 Vj/c=
6.- Continued.
log,o S=
= 0.150.
0
-10
N
_
.ID
I_ -8oi
--2.0
I
I
--1.5
I
--1.0
Corrected
o
o
-10
I
o
--.5
StTouhol
I
.s
Number.
I
1.o
Iog,o
I
1.s
J
2.0
1
_.s
2.0
S,
0E
--20
--30
!:
_
-70
--60_
'_" -8OL
-2.o
l
-_.o
_
- 1.5
I
-.s
Corrected
(o)
I
o
Strouhol
T3/T _ = 3.0;
Figure
6.-
I
.5
Number.
loglO
Vj/c
Continued.
8.4-60
1
1.o
lOglo
S,
= 0.175.
1
or
--20
i
--10
--30
_
._
_
110
4o
-50
--
.m
-60"B
-70-80
-2.0
,
I
--1.5
L
--1.0
Corrected
o_
--10
0
--20
I
--.5
I
0
5trouha=
[
.5
1.0
Number.
Io_lto
I
I
1.5
2.0
I
1.5
I
2.0
S=
--30
_
-40
-50--
lb
.m
--60---70--
-eo
-2.0
I
-1.5
I
-1.0
I
-.5
Correcte_l
(p)
Tj/T
Stro¢_ol
= 3.0;
Figure
9.4-61
_-.
l
0
i
.5
Number.
lo_! 0 Vj/c=
6.-
Continued.
I
1.0
IOglo
= 0.200.
S,
e,_gJIE_
gO
10
I
I
I
--1.0
--.5
0
Corrected
I
.5
StTouhol
Number.
Iogto
I
I
I
1.0
1.5
2.0
S,
0
_,=
_5
i5
4=
5
p-
_---i
7o
180
6
t
' -::T
--2-0
I
l
-- 1.5
-- 1.0
I
l
--.5
0
Correct=KI
(q)
TilT
Strouhol
= 3.0;
Figure
6.-
1
Number.
lOgl0
Vj/c=
Continued.
8.4-62
i.
I
.5
1.0
log_e
S=
= 0.225.
1
1.5
1
2.0
0
);
o
1
-2-0
1
-- 1.5
- 1.0
I
--.5
Corrected
•
0
Slrouho|
I
.5
Number.
I
I
i
1.0
1.5
2.0
IOgso S s
--10
"
'_
-8oi
-2.o
i
-_.s
I
-_.o
I .,
-.s
Corrected
(r)
rj/'r®=
I
o
C:_ouhol
3.5;
Figure
8.4-63
6.-
lOglg
I
.s
Number.
Vj/c
Continued.
1
_.o
log.>
S,=
= O.lOC.
I
_.5
I
2.0
/
,.
oF
!!o
l
--2.0
I
-- 1.5
-- 1.0
I
I
--.5
0
Corrected
I
.5
Strouhol
Number.
Iog_o
I
I
I
1.0
1.5
2.0
S.
oF
o
-_
-2.0
l
I
i
--1.5
--1.0
--.5
Correct4KI
(s)
Tj/T
I
Sl_ouhcd
= 3.5;
Figure
I
0
6.-
.5
Number.
lOgl0
Vj/c
Continued.
8.4-64
.-t!
I
1.0
Io_i o S,
= 0.125.
1
1.5
I
2.0
r
_
-=mms.-:-_w
---
-'_
oF
-10
-20
-30
--50
_I_
-70
--2.0
I
I
I
--1.5
--1.0
--.5
Corrected
I
I
0
1
Strouhal
.5
Numbw',
1.0
Iog_o
I
I
1.5
2.0
S,
oF
--20
i
--10
--30
15
-5°
-80
--40
_
1
-2.0
1
I
--1.5
-1.0
--.5
Corrected
(t)
Tj/T
1
0
Strouhal
= 3.5;
Figure
8.4-65
1
6.-
.5
Number.
logl0
Vj/c
Continued.
Iog,o
I
i
1.0
1.5
S,
= 0.150.
I
2.0
............
_
--c
_-
_
...............................
or
o
--10
o
-50--
130
.m
-60
--
--70
--
--80.
-2.0
i
I
l
I
--1.5
--1.0
--.5
0
Corrected
SVouhol
[
.5
Number.
iOglo
I
I
1.0
1.5
J
2.0
S.
o_ -o
o
-30
.
--50
._m
-60
(J
0
-70
--80
- :.0
1
-- 1.5
1
I
J
I
I
- 1.0
--.5
C
.5
1.0
Co4rrect:ed
(u)
Tj/T
S_Ouhol
= 3.5;
Figure
6.-
Number.
logl0
Vj/c
Continued.
8.4-66
Io9,o
S,
= 0.175.
1
1.5
I
2.0
•
-'J-:-.
-
0
_
-10
C
0
50
1_
--60
_
--70
-eol
-2.o
I
-1.s
I
-1.o
I
-.s
Corrected
I
o
S_ouhal
I
.s
Number.
I
1.o
loglo
I
1.s
J
2.0
S=
or
--10
-20
_
_
--60
--70
or
-8o
f
--2.0
I
i
--1.5
--1.0
I
i
I
I
I
I
--.5
0
.5
1.0
1.5
2.0
Corrected
(v)
Tj/T
Sti-ouh_
=
3.5;
Figure
8.4-67
Number,
lOgl0
6.-
Vj/c
Continued.
log_o
=
S=
0.200.
,/
_k
w.
•
0
--10
o
--20
--30
--50_
--60
-8ok_____
-2.0
--I .5
- I .o
-.s
Correcte<l
I
-L____L____L
o
.5
Strouhol
Number.
I .o
Iogto
I
1.5-------2.0
S¢
0
--10
o
-20
_
-50_
u_
_
-6C_
-70
-80
--2.0
'_
l
i
--1.5
--1.0
I
Corrected
(w)
T_/T
I
--.5
0
Sll]'ouhcd
= 3.5;
Figure
6.-
Number.
lo<910 Vj/c
Concluded.
8.4-68
I
I
.5
-!
1.0
Io@_ o S,
= 0.225.
I
1.5
I
2.0
Ib
Im
o
n
o
n
0
0
I
¢_
I
I
oO
r-.
(e)ua
1
r,D
'xapul
I
}
la,')
_'!oolaA pJDMJOA
8.4-69
0
I
t="
...
k_
8.5
CIRCULAR
JET
SHOCK
CELL
NOISE
MODULE
INTRODUCTION
The
Circular
Jet
shock-associated
critical
by
H.
tions
a
pressure
K.
and
a
The
method
can
The
of
SAE
shock
parameters
by the
module
to
of
ARP
cell
and
a
frequency,
Although
jet
directivity
patible
table
polar
it
other
of
the
is
on
to
is
introduced
of
acoustic
and
sound
The
Aj
engine
are
the
pressure
that
to
as
a
jet
nozzle
area,
reference
area,
b
proportional
bandwidth
C
correlation
coefficient
C a
f
ambient
speed
frequency,
of
with
output
angle.
azimuthal
table
is
(ft 2)
m 2
(ft 2)
constant
spectrum
sound,
m/s
(ft/s]
Hz
Helmholtz
number,
H
group
_j
jet
M=
aircraft
Ne
number
of
engines
Ns
number
of
shocks
<p2>"
m2
source
Mach
f _e/C
strengt/n
spectrum
number
Mach
number
2
mean-square
reference
acoustic
pressure,
pressure,
2
Pref
8.5-1
x
10 -5
re
Pa
D
4
c
(4.177
function
directivity
vary
the
directly
required.
The
input
parameters.
tables.
reference
as
noise
or
SYMBOLS
A e
C
func-
spectra
jet
Module
azimuthal
not
so
super-
Appe._dix
spectra
produce
Parameters
parameters
of
values
assumed
at
proposed
master
parameters.
Noise
angle,
broadband
operating
angle.
several
Jet
the
employs
mean-square
noise
noise
based
method
the
nozzle
directivity
by
the
cell
angle,
is
user-provided
for
each
set
of
predicts
function
polar
directivity
shock
with
The
input
provided
Module
convergent
method
876.
requires
be
Noise
single
interference
frequency
is
a
The
user.
Additional
is executed
once
output
Cell
from
ratios.
Tanna
function
Shock
noise
×
10 -7
Ib/ft
2)
com-
distance
r s
from
nozzle
exit
to
observer,
_
(ft)
t
dimensionless
r
distance
from
nozzle
exit
to
observer,
re
_e
s
jet
T.
total
temperature,
_
(oR)
3
ambient
V.
3
temperature,
fully
expanded
shock
cell
pressure
angle
K
jet
(OR)
velocity,
interference
ratio
m/s
function
parameter,
between
(ft/s)
flight
_M_-
vector
1) 1/2
and
engine
inlet
axis,
deg
exponent
polar
directivity
ambient
angle,
density,
kg/m
deg
3
(slugs/ft
frequency
parameter,
7.80S(I
azimuthal
directivity
angle,
3)
-
cos 8)_jf*
M
deg
Superscript:
*
dimensionless
quantity
INPUT
The
jet
noise
Parameters
Module
computation
of
frequency,
polar
arrays
parameters
or
the
_ne
angle,
and
values
of
frequency
the
englne
angle,
independent
to
input
required
Ambient
parameter
reference
distance
_ne
are
user.
directivity
establish
Fin._lly,
the
are
Input
reference
Ne
number
of
engines
N s
number
of
shocks
r s
distance
from
area,
nozzle
Je_
At
area
of
]et,
re
in
The
table
fully
expanded
m2
exit
Noise
Mach
range
I.
(ft 2)
to
observer,
Parameters
A
3et
the
Constants
3
M
for
number
]
8.5-2
/
J
m
Noise
for
levels.
directivity
engines,
required.
given
Jet
required
pressure
values
of
the
are
sound
number
are
either
azimuthal
variable
observer
engine
and
and
area,
parameters
A e
from
conditions
(ft)
The
angle
output
table.
engine
offset
and
default
T:
jet
3
v:
total
fully
]
temperature,
expanded
jet
T®
re
velocity,
re
Ambient
Cam
ambient
speed
M
aircraft
of
Mach
ambient
Conditions
sound,
m/s
kg/m
3
(slugs/ft
Independent
polar
(ft/s)
number
density,
frequency.,
c
3)
Variable
Arrays
Hz
directivity
azimuthal
angle,
directivity
deg
angle,
deg
OUTPUT
The
output
pressure
muthal
as
of
a
this
directivity
provided
for
of
angle.
_he
In
from
frequenc?,
polar
table
of
polar
addition,
nozzle
to
Jet
the
mean-square
directivity
the
obse_2er
acoustic
angle,
and
distance
azi-
rs
is
observer,
Shock
m
Cell
(ft)
.Noise
Table
Hz
directivity
aza=uthal
<p: {f, :,:)>"
a
Module.
Circular
f
is
frequency,
Propagation
distance
r s
module
function
angle,
directivity
mean-square
deg
angle,
acoustic
deg
pressure,
re
_c_
K.
Tanna
METHOD
The
_rediction
methodology
pute
_e
shock
cell
noise.
_ne
method
given
in
exhaust
are
2et
directivit?
of
the
shock
.nozzle
_s
angles
are
cell
and
proposed
Details
references
shown
also
jet
in
1
mixing
8.5-3
the
and
figure
shown.
by
of
i.
The
Pmise.
H.
development
2.
A
schematic
_'_..ecoordinate
total
jet
noise
is
and
used
to
validation
of
a
of
typical
system
will
com-
be
and
the
sum
E
!
The
normalized
associated
i/3-octave-band
noise
is
given
mean-square
pressure
for
shock
by
i=
n
<p2>* = (1.92o × lO-])
L
8
4_(r:)
The
dimensionless
r:
and
the
source
=
to
2
observer
_
-
M
cos
distance
(@-
r*
s
is
H(O)
(i)
6)] 4
defined
as
(2)
rsi_e
frequency
parameter
_
is
I
I
=
7.80_(i
-
M
cos
8) _*.
f*
(3)
8
i
i
The
pressure
ratio
parameter
is
defined
as
(4)
i
P
I
and
is
a
measure
parameter
exponent
number
_
of
Mj
of
must
the
be
relative
greater
the
pressure
and
the
3et
shock
than
ratio
total
0
strength.
for
parameter
=
D
temperature
(Unheated
2
(Heated
The
shock
cell
pressure
noise
depends
T:J
on
ratio
to
the
occur.
jet
The
Mach
as
jet
(T;
<
i.I)
with
_
>
i)
jet
(T;
>
I.i}
with
_
>
i)
jets
with
8
<
i)
(5)
i
4
The
quenc/
and
is
shock
(All
cell
parameter
expressed
interference
_,
as
polar
function
directivity
Ns-i
W
angle
W
=
_
a
and
function
of
velocity
the
ratio
freV_
N s-(k+l)
sin
4
Nsb
is
9,
[c(_)
(bOqkm/2)
]k2
cos
(Oqkm)
(6)
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k=l
m=0
where
qkm
=
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L
3
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+
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(I
8.5-4
+
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c°s
9)
(7)
and
b
•
0.23077.
spectrum
C
t.xluation
and
2
3,
dB
W
are
in
has
the
tables
an
II
4
N
to
Ill
Jet,
for
a
by
value
produce
the
of
cell
of
equation
spectrum
plotted
value
shock
coefficient
stronqO_
and
the
The
computed
correlation
source
and
unheated
figure
the
group
value.
been
t,nqines
spectrm,
and
tabulated
plotted
of
in
Per
pressure
number
master
(6)
qiven
the
than
is
two
equation
respectively.
square
the
(i),
le:_s
tion
The
of
Ns
(I),
total
in
flquros
I!
should
interference
•
R.
it
shock
of
be
func-
Once
is
H
2
the
mean-
multiplied
by
cell
noise.
e
The
pressure
output
of
_p2_*
.l=imuthal
directivity
the
pro._._ure
gound
thi:;
as
a
module
function
angle.
level
is
a
of
frequency,
In
SPL
table
of
addition,
defined
th,._ mean-square
|x_lar
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acoustic
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8.6
STONE
JET
NOISE
MODULE
INTRODUCTION
The
Stone
acoustic
in
the
noise.
sented
in
jets
The
The
module
_s
of
Jet
angle;
noise
input
be
once
is
a
noise
angle
so
than
secondary
the
Noise
that
The
of
and
table
required.
input
param-
pressure
the
as
is
reference
fully
"%.
area,
expanded
jet
m2
area,
(ft 2)
3
ambient
_S
speed
m/s
(ft/s)
function
for
3et
directivity
function
for
shock
hydraulic
d.
sound,
directivity
equivalent
d_
of
diameter,
m
diameter,
m
mixing
noise
noise
(ft)
(ft)
.q
jet
d_
diameter,
m
(ft)
J
plug
diameter,
m
(ft)
P
F
spectral
distribution
factor
for
jet
spectral
distribution
factor
for
shock
mixing
m
F
3
frequency,
Hz
3.6-1
noise
noise
a
direc-
(constant)
compatible
as
directivity
azimuthal
a
(ft 2)
m2
or
are
azimuthal
of
tabulated
output
the
acoustic
exit
Module
tables.
engine
prelimited
velocity.
nozzle
SYMBOLS
A_
is
jet
Parameters
values
independent
the
as
method
parameters
of
is
inter-
Stone
the
angle,
assumed
R.
nozzles,
mean-square
prediction
J.
parameters.
set
the
Included
supersonic.
Jet
directivity
is
the
each
of
polar
however,
azimuthal
the
by
user-provided
for
table
be
several
by
Additional
executed
exhaust
of
provided
user.
may
jets.
shock-turbulence
developed
greater
velocity
mean-square
circular
and
coaxial
is
far-field
coaxial
noise
that
For
velocity
frequency,
tivity
o_
can
is
2.
jet
the
and
mixing
used
and
jet
output
angle.
tion
1
predicts
stream
jet
method
requires
the
The
function
both
t_he core
+ _rs
b?
eters.
are
core
method
parame
directly
single
references
only
.Module
for
The
whose
Further,
flow
_oise
prediction
action
to
Jet
pressure
with
funcother
t
L
fs
frequency
shift
%
configuration
factor
for
mean-square
pressure
for
coaxial
Gp
configuration
factor
for
mean-square
pressure
for
plug
gc
configuration
factor
for
Strouhal
number
for
coaxial
gp
configuration
factor
for
Strouhal
number
for
plug
forward
parameter
flight
effects
M
I
Mach
nozzle
factor
number
aircraft
m
exponent
N
number
<_2>"
Mach
of
number
engines
2
mean-square
<p2(
acoustic
pressure,
mean-square
distance
Pref
reference
Rd
ratio
r S
distance
from
Sm
Strouhal
S5
Strouhal
T
fully
T
ambient
V
fully
of
&
2,'
&
x
10-5
Fa
to
number
for
jet
shock
cell
temperature,
K
jet
ratio
directivity
m
m/s
(N_
vector
angle,
(ft)
noise
(oR)
(ft/s)
-
and
1) 1/2
engine
inlet
axis,
deg
angle,
density,
jet
density,
kg/m
3
2)
diameter
(V_)0"Ig,
deg
deg
expanded
ib/ft
noise
kg/m
(slugs/ft
3
3)
8.6-2
L --
10 -7
reference
(OR)
parameter,
directivity
angle,
observer,
velocity,
flight
x
equivalent
mixing
K
90 ° ,
(4.177
jet
polar
ambient
0_c_
for
between
fully
the
re
=
number
angle
Mach
at
@
to
expanded
modified
pressure
at
source
temperature,
4
c
acoustic
diameter
jet
p
_e
2
hydraulic
expanded
pressure
_5
pressure,
re
(slugs/ft
3)
nozzle
nozzle
.<
S-
nozzle
deg
J
t
azimuthal
directivity
w
density
Wo
stationary
angle,
deg
exponent
jet
exponent
density
Subscripts:
i
L
i
primary
stream
2
secondary
stream
i
Superscript:
dimensionless
value
INPUT
The
Noise
The
jet
the
distance
values
polar
establish
Finally,
of
are
Module
frequency,
arrays
and
parameters
Parameters
the
or
required
the
angle,
independent
variable
reference
to
pseudo-observer
the
input
area,
are
engine
reference
N
number
of
rS
distance
3
angle
area,
41
in
the
engines,
engine
The
table
range
from
between
nozzle
exit
table.
axis
and
I.
(ft 2)
flight
vector
Noise
to
pseudo-observer,
and
engine
m
inlet
Parameters
fully
expanded
actual
primary
stream
equivalent
actual
primary
stream
hydraulic
primary
stream
Mach
primary
stream
total
jet
area,
re
Ae
diameter,
diameter,
number
temperature,
re
T
(ft)
axis,
re
re
_e
Jet
angle
output
Constants
m2
8.6-3
°
of
required.
the
required.
directivity
for
Stream
primary
d;, 1
number
of
are
engines
Jet
Primary
output
azimuthal
values
given
Input
the
conditions
and
are
parameters
A e
either
Ambient
directivity
engine
the
from
user.
deg
offset,
default
----4
............
I
V 1
primary
stream
jet
velocity,
_
primary
stream
jet
density,
_eco
Ildd
t_
,C
.
re
re
O=
Stream
._econdary
fulty
Mr
_econdary
._troam
Math
T:
.qecondary
.,;trpam
total
:_econdar\."
:;tream
_et
velocity,
secondary
stream
jot
density,
J
c
e-q_anded
jet
area,
re
A
¢.
numb_,r
teml_er,lture,
Ambient
ambient
Th,'
sound
aircraft
._ach
arab.lent
density,
outVut
|'r,'_',_;ur,,
.,.q a
of
thi:;
function
muthAl
d_rect_vity
l:; [,rovtd,,d
rot
r.
st_ed,
frequency,
'_
},olAf
._
Az_muth._l
<_,-'tf,_,:)>°
c+
re.,
Condit
m/s
kq/m
_dule
ions
(ft./._)
3
(.qiu_ls/ft
i_
a
no::l,,
,'xZt
Method
3)
tabh,
fr,.qucncy,
Stone's
f
T
number
of
from
re
re
of
!x_l._r
an_l_e.
In addition
t.h_, Pro[,._q.lt_on
Module.
,IX:_tanc,,
e
the
to
Jet
_he
t,%_an-squ.lre
,:irectivity
}-seudo-observer
},.qeu,k_-obser':er,
l_k_se
TAble
H:
,i_r,,ctlv_,_,:' ,%nq[e,
d_r,,ctlvtty
me,_n-_quare
acou:;tic
deg
angle,
deq
_-res._ure.
8.6-4
re
o'c 4"
acoustic
an,_le,
and
distance
m
(ft)
._:ir:
i
METHOD
The
uses
method
prediction
compute
the
mean-square
empirically
spectral
developed
acoustic
determined
content
of
the
in
functions
field
references
pressure
in
to
with
the
=
the
This
nozzle
nozzles,
can
with
used
without
each
each
of
coaxial
nozzles.
showing
the
figure
for
directivity
, used
used
The
to
method
and
mean-square
to
nozzle
mixing
to adjust
those
for
of
axis
and
for
fix
the
amplitude
exhaust
s_
circular
jets.
types
noise
several
single
coaxial
empirically
Illustrations
coordinate
noise
supersonic
and
all
jet
is
used
to
the
and
plugs,
for
which
figuration
factors
are
stream
circular
nozzles
predict
subsonic
schemes
one
noise,
to
both
and
prediction
equations,
action
be
including
both
The
basic
the
overall
)>
is
field.
o •
90
2
far
field.
module
types
provide
computed
acoustic
pressure
.t e 90
o.
throughout
1 and
the
are
and
developed
from
determined.
inter-
Furthermore,
the
levels
predicted
for
single
stream
plug
nozzles
these
various
directivity
two
shock-turbulence
configurations,
angles,
are
con-
single
or
also
provided
in
i.
Jet
from
The
equation
the
nozzle
used
exit
to
Mixing
calculate
Noise
the
jet
mixing
noise
at
a
distance
r s
is
3/2
l_+[0:12 v[[2_
]
<
x Dm(e'
In
a
this
equation
stationary
nozzle
exit
nozzle
exit
function,
and
G
=
90 O,
at
)
@
rs
A_e,90°)/
=
90 °,
referred
Each
of
the
r:
is
to
_e'
_)
is
these
<
) >*,
is
the
is
now
at
a
flight
Dm(@'}
_
distance
is
forward
and
spectral
effects
through
use
of
the
from
the
Gc
detail.
dista.n_e
the
for
distribution
directivity
in
reference
pressure
f._om
factor,
provides
considered
the
(!:
GcG p
acoustic
distance
dimensionless
cal<:ulated
8.6-5
I)
mean-square
Fm(Sm'@')
pressure
equation:
D
the
the
factors
acoustic
Hm(M_,@,VI,01,T
reference
factors,
mean-square
p2(_e,90°
)
is
at
configuration
+ 0.62v_ cos 0) 2 + (0.124v[)
1
Fro(Sin,8'
calculated
Hm(M_,@,V_,O_,T
are
P
information.
The
<p2(
jet
I
(r:) 2
and
following
x 10-6
A_,IC_Cv;_75
<p2
(_e.gO
°)
>"= 2.5O2
(2)
[i+
Here,
A_,
expanded
ties
1
the
and
c
for
,
determined
fully
density
evaluated
p_,
expanded
and
the
primary
-
0.6
(V,*) 3"5
+
0.6
V 1
area,
P_
respectively,
stream,
The
of
3"5
jet
velocity,
respectively.
function
2(V_)
Loo
is
jet
and
density
given
and
V[
with
all
are
nondimensionalized
exponent
wo
the
three
by
is
an
fully
quantiA e,
empirically
by
=
(3)
&
The
factor
9'
=
S m
=
Fro(Sin,8')
@(v_)
0"I
and
is
the
a
jet
function
mixing
of
noise
the
modified
Strouhal
directivity
number
Sm
angle
calculated
by
0,
v[Cl- .,,=Iv[,
.,_i/2
_)
(I
In
this
equation
+
0.62V
1
is
the
f*
_)2
cos
+
(0.124VI)2
Helmholtz
/
number
given
gcgP
as
f_e
(5)
C
M
is
the
aircraft
Mach
number,
and
is
dj, 1
the
jet
diameter
given
as
(6)
,5
Further
axis,
in
is
the
degrees,
angle
and
nondlmenslonalized
by
_nat
over
the
summation
between
T_
T
is
.
the
the
The
i/3-octave
flight
fully
vector
expanded
function
and
primary
Fm(Sm,9')
Strouhal
8.6-6
number
the
jet
is
is
engine
temperature
normalized
unity:
inlet
such
(7)
Fm(Sm, e ) = 1
Sm
and
is
tabulated
The
in table
The
cussed
in
function
III and
Dm(e')
plotted
factors
when
table
gc
the
II and
in
and
plotted
in
figure
contains
figure
directivity
3.
gp
configuration
configuration
are
factors
Gc
2.
information
and
factors
Gp
of
and
which
is
given
are
equation
dis-
(i)
are
considered.
Thefo_ard
flight
e_fects
factor
_(.®,e,V_,_.T_
is
given
by
+ 0.62
(v"
l - .®)cose]
(1 - _/v1)s(p;)_-_°
1 - M
(8)
cos.(8 - $)
where
0
The function
values
of the
(9)
1
Hm
is normalized
such
remaining
parameters:
that
it
is unity
if
M,_ = 0
for
all
(I0)
The
pressure
predict
configuration
predicted
for
the mean-square
respectively.
10
The
factors
Gp
a single
acoustic
stream
circular
nozzle
pressure
for plug and
factor
<;P
and
is given
* --
Gc
take
the
mean-square
acoustic
and adjust
it to
single
nozzles,
by
{Nozzle
with
plug)
[Ii}
(Nozzle
8.6-7
without
plug)
In
equation,
this
i"
=
Rd
With
_,i"
d*
e, 1
d:,ll
the
plug
(12)
nozzle
hydraulic
< =
and
d:, I,
where
the
A_, 1
these
is
The
factor
the
is
_'_l
_C
equivalent
primary
are
G c
given
by
_
nozzle
quantities
diameter,
(13)
diameter,
nozzle
area
and
nondimensionalized
given
given
by
d:
Ae
by
is
and
the
plug
_e'
by
l- ,,_/,,_).,+
(l+ ,._,_/,,_,1)
_
(14)
=
(Coaxial
1
The
diameter:
respectively.
nozzle)
(Single
exponent
m
is
given
nozzle)
by
,1
(15)
The
single
factor
stream
respectively.
gp
or
circular
These
gc
jet
factors
adjusts
to
that
are
the
for
given
Strouhal
a
plug
number
nozzle
or
Sm
a
for
single
a
nozzle,
by
0.4
(Nozzle
gp
with
plug)
= I (rod)
(16)
I1
(,Nozzle
8.6-8
without
plug)
I
_J
I
and
gc
where
fs
eter
1
is
+ A
tabulated
_- T_fs/,i)
-1
=
an
empirically
; /_;
,2
in
,I
table
and
IV
(_o-xial
no.-le_
the
and
The
ll3-octave-band
noise
(3.15
<p2>*
_
is
this
is
This
ratio
param-
function
is
Noise
acoustic
pressure
through
.q4
),I
_
I.
area
due
use
to
of
the
shockfollowing
10-4)A_
=
equation
the
4.
calculated
the
Fs(S
s)
Ds(0,M
I)
Gc
(18)
, 2
(r s )
In
V2_
figure
mean-square
interaction
of
""
ratio
in
Shock
turbulence
equation:
function
"
velocity
plotted
nozzle)
(Single
determined
I
pressure
-
b.4
ratio
i
-M,,_
cos
parameter
<_)
(_-
as
follows:
_: (.,,_
_ _)1"2
which
must
be
The
noise,
qreater
function
for
exFanded
a
than
Ds(0,M
primary
stream
(19)
zero
I)
stationa_-
(17)
for
provides
jet,
on
the
Mach
number
shock
the
cell
dependence
directivity
M I.
noise
This
angle
function
to
of
occur.
the
"_
shock
and
is
the
given
ceil
fully
by
P
_i
Ds (_,M 1 }
L
1.189
where
0m
is
'?m =
the
Mach
Arcsin
anoie
defined
&
9 m)
(O
>
@m )
by
(20)
(IIM I)
8.6-9
i
(9
The
spectral
function
Fs(S
content
s)
ss = _
- _
0.70V
the
jet
total
-
Fs(S
s)
far-field
mixing
The
is
provided
Strouhal
through
number
the
Ss:
+
+
is
tabulated
in
table
be
the
for
one
V
and
plotted
in
mean-square
by
frequency,
polar
engines
noise
acoustic
noise,
equation
noise
available
jet
will
sum
of
the
shock
noise
and
.,oise.
mixing
computed
SPL
cos
noise
the
(21)
function
The
jet
of
shock
on
5.
the
total
the
depends
1
The
figure
of
which
computed
(18),
can
directivity
the
mean-square
N
for
the
defined
the
by
be
output
mean-square
engine,
equation
computed
angle,
is
of
pressure
as
and
for
each
In
is
of
angle.
by
printed
sound
stun
noise,
value
multiplied
and
_e
shock
desired
addition,
<p2>"
the
directivity
pressure
pressure
which
and
azimuthal
acoustic
table.
(i),
as
the
The
the
number
output
pressure
of
is
level
as
01o:
SPL
=
10
lOql
0 <p2>*
+
i0
logl0
2
(22)
Pref
Power
level
calculations
are
not
performed
by
this
module.
REFERENCES
I.
Stone,
TM
2.
J.Imes
X-71618,
Stone,
James
Method
TM-81470,
for
R.:
Interim
Prediction
Method
for
Jet
Noise.
NASA
1974.
R.;
and
the
.Noise
Montegani,
Generated
Francis
in
J.:
Flight
1980.
8.6-I0
An
by
Improved
Circular
Prediction
Jets.
,NASA
TABLE
I .- RANGE
AND
DEFAULT
Input
parameter
VALUES
Minimum
OF
INPUT
PARAMETERS
Default
Maximum
2
Ae,
m
S
o
r S s
6,
m
.
o
°
.
.
.
./4
1
°
......
Aj, 1
.......
d:, 1
.......
i0.0
1
0.01
.......
deg
,1
0.01
......
4
i00
0
0. 0001
0
30
1
!0
2 × 10-2/_'_
2
.......
x I0-2/_'_
M1
........
0
1°0
1.25
T_
........
0.7
1.0
4.0
V_
........
0
1.0
2-5
1°0
1.2
0_
A;
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........
,-_
.......
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°
2
92
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8.6-12
D
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I
TABLE
III.-
JET
MIXING
NOISE
DIRECTIVITY
8, deg
TABLE
i0
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,60
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1.00
1.05
1•10
1.15
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1.30
1.35
1.40
1.45
1.50
1.55
1.60
0.00
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130.0
140•0
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-1,56
150.0
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160.0
170.0
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180.0
190.0
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-4 •01
200.0
-4•52
IV.-
FREQUENCY
SHIFT
i0
lOgl0
Dm
Dm
120•0
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PARAMETER
for
V_/V_
fs
of-
0.20
0.40
0.60
0.80
1.00
0•00
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,14
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8.6-13
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TABLE
V.-
SEOCK
NOISE
LEVEL
l°gl0
S s
-1,8
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-1,6
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1,5
1,6
1,7
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Fs
lOgl0
-9t,60
-89,69
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-Z4,60
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-7,60
-8,60
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-16,60
-17°60
-18.60
-19,60
-20,60
-21.60
-22,60
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8.6-14
Fs
T1
Vl
X
_i
(a) Single streamcircular
nozzle.
:y
(b)
Figure
Dual
i.-
stream
Schematic
B.6-15
coaxial
diagrams
nozzle.
of
nozzles.
o
m
r.
o
.M
o
o_
°_
_,'
_
o.
I
I
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8.6-20
_"L
I_.
I
_
_
I
I
0
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I
_4
8.7
DUAL
STREAM
COANNULAR
JET
._OISE
MODULE
INTRODUCTION
The
Dual
teristics
file.
The
higher
jet
Pao
by
The
of
and
the
is
a
it is
tables.
in
input
provided
is
of
Jet
table
of
each
of
the
mean-square
directivity
angle,
noise
is
introduced
assumed
so
that
the
values
to
vary
output
fully
Ae
engine
expanded
reference
ambient
D
speed
directzvity
d
jet
area,
m2
area,
of
m2
sound,
(ft 2)
(ft 2)
m/s
(ft/s)
function
equivalent
jet
diameter,
m
(ft)
eq
dh
jet
hydraulic
f
frequency,
diameter,
m
(ft)
H:
.t
[
Helmholt:
G
s_ectral
distribution
aircraft
Mach
m
forward
mass
number,
velocity
flow
rate,
f A_e#_
function
number
index
kg/s
(slugs/s)
8.7-I
m
.
method
a
thrust,
developed
by
two-nozzle
Modul_
or
are
required.
the
input
pressure
azimuthal
is
compatible
exit
directly
The
parameters.
as
directivity
with
table
pro-
has
the
same
The
azimuthal
SYMBOLS
A
of
acoustic
and
not
the
charac-
2.
Parameters
parameters
set
the
parameters.
Noise
user-provided
on
which
converts
with
and
noise
velocity
flow
method
based
the
inverted
outer,
jet
1
several
the
an
The
stream
references
by
tot
or
flow.
prediction
predicts
with
se=ondary,
single
The
once
jet
a
Module
nozzle
primary
presented
polar
the
has
the
Additional
executed
output
angle,
noise
be
Noise
exhaust
equivalent
requires
can
frequency,
Although
than
an
as
user.
is
jet
energy.
method
states
module
to
Jet
jet
stream
Russell
The
flow
Coannular
coannular
velocity
jet
flow,
and
a
dual
coannular
mass
Stream
of
a
function
angle.
directivity
with
other
N
number
P
power
<p2>"
Pre f
r
s
of
deviation
mean-square
reference
from
dimensionless
S
Strouhal
S1
first
S2
second
T
total
d
_O
J
10-5
exit
Strouhal
peak
Pa
to
from
4
(4.177
observer,
nozzle
exit
×
10 -7
m
(ft)
to
Ib/ft
2)
observer,
re
number
Strouhal
number
temperature,
K
(OR)
temperature,
velocity,
K
m/s
(OR)
(ft/s)
spectral
peak
magnitude
specific
heats
factor
._%2/A 1
ratio
of
anqle
between
polar
directivity
acoustic
ref
nozzle
x
distance
peak
relative
=
I
2
pc
re
number
ambient
j. i
pressure,
pressure,
distance
jet
factor
acoustic
r:
V
engines
power,
reference
jet
flight
ambient
angle,
re
power,
density,
kg/m
density,
3
(slugs/ft
kg/m
Strouhal
d 1
first
normalized
second
azimuthal
dens
i ty
peak
normalized
directivity
engine
inlet
axis,
DaC3Aeq
x
r_rmalized
and
deg
1
J
peak
vector
10 -12
3
W
(7.376
3)
(slugs/ft
3)
number
5trouhal
number
Strouhal
angle,
number
deg
exponent
8.7-2
x
10 -13
ft-lb/s)
deg
_e
Subscripts
:
eq
equivalent
1
primary
2
secondary
jet
jet
jet
Superscript:
*
dimensionless
quantity
INPUT
of
the
are
The
primary
Jet
Noise
required
levels.
angle
table.
inlet
default
and
secondary
jet
Parameters
Module
for
The
computation
frequency,
arrays
establish
Finally,
axis
values
the
the
offset,
the
input
to
engine
reference
N
number
of
rs
distance
angle
parameters
area,
V*
1
Y1
are
m2
between
nozzle
exit
to
flight
vector
Jet
area,
re
primary
jet
total
temperature,
primary
jet
velocity,
primary
jet
density,
of
for
of
in
directivity
the
engines,
required.
given
pressure
table
specific
A
re
jet
area,
re
secondary
jet
hydraulic
8.3-3
engine
I.
Parameters
re
T
Pm
for
Jet
primary
jet
Parameters
Ae
diameter,
re
(ft)
inlet
c
Secondary
secondary
and
m
e
re
heats
observer,
_e
axis,
output
engine
The
(ft 2)
jet
ratio
values
number
are
sound
azimuthal
engines
from
l
and
and
Constants
Primary
primaz-
area,
observer
Input
Ae
number
angle,
variable
reference
distance
the
Strouhal
directivity
independent
engine
and
of
of
polar
parameters
are
required
from
the
output
or
from
the
user.
Ambient
conditions
deg
range
and
secondary
jet
total
temperature,
secondary
jet
velocity,
0 2
secondary
jet
density,
Y2
ratio
re
re
T
c
t
of
specific
re
heats
for
Ambient
Co0
ambient
speed
Mco
aircraft
of
Mach
ambient
m/s
jet
(ft/s)
number
kg/m
3
(slugs/ft
Independent
polar
secondary
Conditions
sound,
density,
frequency,
D_
3)
Variable
Arrays
HZ
directivity
azimuthal
angle,
directivity
deg
angle,
deg
OUTPUT
The
pressure
muthal
provided
output
a:
a
of
directivity
for
the
module
of
from
Double
f
frequency,
polar
In
a
table
of
polar
addition,
Module.
exit
to
Stream
Coannular
the
mean-square
directivity
the
nozzle
angle,
observer
observer,
Jet
m
Noise
acoustic
and
distance
rs
aziis
(ft)
Table
Hz
directivity
azimuthal
is
frequency,
angle.
Propagation
distance
r s
this
function
angle,
directivity
deg
angle,
deg
4
<p2(f,_,_)>"
mean-square
acoustic
pressure,
re
_c
METHOO
The
noise
slngle
equivalent
energy
as
pressure
_he
is
prediction
jet
method
which
coannular
computed
jet.
as
a
determ/nes
has
the
The
function
saume
the
total
i/3-octave-band
of
frequency,
8.7-4
noise
thrust,
characteristics
mass
mean-square
polar
flow
of
rate,
and
acoustic
directivity
angle,
a
.J
and
azimuthal
used
has
coannular
the
mass
m*
angle
extracted
jet
The
where
directivity
been
nozzle
is
flow
+
from
p*A*V*.
equivalent
shown
rate
of
The
jet
for
the
references
in
the
figure
to
conditions.
£
and
2.
jet
is
jet
the
sum
A
The
sc;,ematic
method
of
a
typical
1.
equivalent
equivalent
thrust
input
given
velocity
of
the
is
by
computed
thrusts
of
by
the
equating
individual
jets
as
eq
By
gas
assuming
that
constant,
energy
.t
meq
the
the
equation
T"
products
combustion
jet
71
Yl
specific
•
Yeq
"
1
+
heat
m2
72
ratio
m_
Yeq
equivalent
jet
is
equal
equivalent
A,
eq
-
1
+
is
the
determined
by
the
mass
average
72
m2
density
to
the
_
+
is
found
ambient
Y2
-
i
(41
m2
from
static
=
-
(V
eq
the
condition
pressure.
that
Rearranging
the
jet
the
static
perfect
jet
}
(5]
2
area
is
eq
D" V"
eq eq
(6)
8.7-5
.....
of
the
-t
=
a_
value
from
yields
"
_he
Y1
1
eq
and
the
computed
1
*
=
--
law
affect
be
"{_2
Y1
gas
not
(3)
••
equivalent
pressure
can
=
ml
The
do
temperature
as
eq
The
of
equivalent
ri
J
_he
equivalent
jet
is
(7)
=.
d_q
The
diameter
acoustic
power
_*
the
single
stream
circular
added
to this
relation
to
ing
expression
for
_*
_%e
power
ioglO
table
and
is
III
and
The
x
give_
is
table
in
a
jet
benefit
effects.
factor
The
and
3.
is
The
less
and
than
*
the
in
ratio
velocity
lOgl0
coannular
from
a
the
normalized
ii0 O,
the
(8)
ratio
2.
The
V:q
and
benefit
density
is
given
factor
Q
ratio
lOgl0
V:q_
acoustic
power
using
spectrum
function.
I/3-octave-band
mean-square
is
<p2>*
:
eq
4_(r.)2
.
-(@
-
6)
G(@'CI)
for
directivity
<p2>"
angles
greater
than
eq
ii0 °,
[°(°'°,'
=
(9)
e
\
and
0
is
result-
*
figure
and
velocity
figure
4.
computed
function
of
plotted
velocity
figure
using
is
function
IT
the
pressure
angle
equivalent
ratio
V_/V_
and
plotted
in
directivity
directivity
for
(^*Weq_'"_'V*t
eq1"8p(Veq)Q(Veq,V2/V
I)*
*
of
plotted
the
A coannular
double
stream
power
P
in
function
mean-square
pr.essure
10 -5)
of velocity
in
table
IV
a normalized
a
a
calculated
acoustic
factor
is
_
is a function
and
is given
For
(6.67
deviation
V:q_
exponent
in
=
the
is
jet
method.
account
for
.....
_=(r:)__ - _, cos(e- 6)[_ ;_; " 1 ÷_' j\
<_
'-I
(I0)
%-_ere
and
r*s =
(I0)
rs/A_--".,
e
is
loglO
V_
•_hich
include
a
and
effects.
t_vity
The
angle
ar.gle
_
d_rection
_
spectral
is
the
directivity
of
given
in
aircraft
forward
9
and
allows
of
The
function
for
polar
table
Mach
flight
is given
an
flight.
offset
T_._
function
directivity
V
and
plotted
number
M
index
m(@)
in _able
VI
between
,maining
D
the
terms
in
equations
@
and
angle
in
figure
account
for
is a function
and
plotted
engine
in
distribution.
8.7-6
inlet
equations
(g)
velocity
5.
The
forward
ratio
terms
flight
of
"- Jar
direcin fibre
6.
The
axas
(9)
and
and
the
(I0)
give
..
first
coannular
peak
exists
for
all
corresponds
values
jet
has
corresponds
values
to
of
the
expressed
in
a
to
the
of
spectrum
the
the
characterized
polar
of
directivity
terms
of
the
of
directivity
characteristics
polar
by
characteristics
the
angle
Strouhal
stream
greater
than
peaks.
outer
angle.
mixed
number
two
the
and
The
second
peak
ar_
exists
for
110 °.
defined
The
stream
The
spectra
are
as
(Ii)
The
peak
and
velocity
given
Strouhal
in
number
nmmbers
the
numbers
ratio
table
S2
used
log
VII
O
a
and
function
The
are
peak
polar
peak
directivity
Strouhal
angle
e
SI
is
number
°
in
Strouhal
defined
of
first
figure
is given
in table
VIII
to define
the
spectrum
corresponding
bers
are
V*
I0
2
plotted
7.
The
and
plotted
shape
are
number.
secor_
peak
in figure
normalized
The
Strouhal
8.
with
normalized
The
Strouhal
respect
to
Strou.hal
num-
as
(T_)0"4
(12)
Cl
=
"_i V;q
=
i
f*d_'2
(T;q)0"4
S 2 V;q
- M_
(13)
02
f*d_
-
M®
and
The
two
relative
spectral
peaks
magnitude
factor
differ
is
A
e,
=
in
dc=ined
magnitude
by
a
factor
e'.
This
as
•
(14)
U(Veq,V2/Vl,B)--&-Aeq
The
spectral
velocity
angle
in
peak
lOgl0
_.
table
spectral
The
IX
All
in
of
of
plotted
polar
noise
engines
the
in
and
terms
in
directivity
N
for
the
pressure
level
in
equations
mean-square
the
The
output
can
defined
i0.
and
and
table.
pressure
In
8.7-7
addition,
pressure
directivity
a
is
are
given
defined
by
the
directivity
angle
@
and
spectral
distribution
been
have
for
azimuthal
mean-square
as
the
(I0)
computed
acoustic
d/mensionless
SPL
of
equivalent
polar
factor
polar
figure
the
the
shape
of
(9)
of
and
spectral
values
be
angle,
function
magnitude
The
function
O.
the
of
a
a
V_/V_,
peak
9.
plotted
pressure
is
spectral
as
is
available
u
ratio
figure
number
X
acoustic
frequency,
factor
velocity
G
table
the
mean-square
of
values
StroP,el
given
total
the
distribution
normalized
are
and
magnitude
V_,__
each
value
directivity
multiplied
printed
<p2>*,
The
defined.
desired
of
angle.
by
output
the
G
the
The
number
is
sound
SPL
and
the
power
= 10
lOglo
level
PWL
<p2>"
Pref
20 lOglo---_
pc
_
defined
(15)
as
H
ref
PWL
= I0 lOglo
H*
- i0
lOglo
(16)
O°°c3A_ Ae
REFERENCES
i. Pao,
S.
Paul:
Inverted
2. Russell,
A Correlation
Flow
James
Coannular
Profiles.
W.:
Jets
of
A Methcd
With
Mixing
NASA
Inverted
Noise
TP-1301,
for
Predicting
Velocity
From
Coannular
Jets
.Noise Levels
of
With
1979.
the
Profiles.
8.7-8
NASA
CR-3176,
1979.
TABLE
I .-
RANGE
Input
parameter
Ae,
m2
.
.
DEFAULT
.Minimum
.
VALUES
OF
.
o
INPUT
Default
i0
I
1
.
0.01
rs,
m
.....
A_
.......
T[
.......
V _
....
_4
........
i00
0
0
3o
1
i0
1
6
0.0001
0.7
.
.
1.O
0
o
1.0
1.2
1.4
1.5
1.3
A_
.......
0
0
lO
0.01
1
io
0.7
i
6
0
0
.......
_w
0.9
0.2
.......
......
2.5
0
0
71
V_
4
......
O, deg
_,2
PARAMETERS
Maximum
_/4
0.01
.....
o
AND
2.5
0.2
1.0
1.2
.......
1.3
1.4
1.5
c,
m/s
2OO
294
4OO
D,
kg/m 3 ....
_2
....
72
"
.....
"
"
0.2
B.7-9
34().
1.225
1.5
TABLE
II.-
POWER
l°gl0
DEVIATION
Veq/C_
l°gl0
III.-
l°gl0
DENSITY
_o
-!.000
-.900
-,760
-.580
-.410
-.ZZO
0.000
.Z20
.500
.770
L.070
1.390
1.740
1.950
Z.O00
8.7-10
--
f
P
EXPONENT,
Veq/C_
-.450
-.400
-.350
-.300
-.2_0
-.200
-.150
-.100
-,050
0.000
.0_0
.100
.150
.ZOO
.2SO
lOglo
-.130
-.130
-.130
-.130
-.130
-.lZO
-.100
-.050
0.000
.100
,210
.320
.410
.430
,410
,310
.140
-.400
-.350
-.300
-.ZSO
-,ZOO
-.1_0
-.I00
-.0_0
0.000
.050
.100
.150
.ZOO
.250
,300
.350
.400
TABLE
FACTOR
P
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0
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1
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0.000
10.000
20.000
30,000
40*000
50.000
60.000
70.000
80.000
9O.000
100.000
110.000
120.000
130.000
140,000
150,000
160.000
170.000
180.000
8.7-13
VELOCITY
INDEX
re(e)
3,000
1.650
1.100
._00
,ZOO
0.000
0,000
.100
,400
1.000
1.900
3.000
4.700
7,000
8,500
8.500
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8.7-14
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8.8
AIRFRAME
NOISE
I HTRODUCT
The
Airframe
nant
components
oped
by
Aviation
the
functions
polar
sum
of
landing
The
number
eters
gear,
method
control
Module
or
describe
the
values
flaps,
square
acoustic
angle,
and
the
by
the
user.
The
as
a
area,
m 2
a
exponent
b
span,
by
c
ambient
is
output
of
D
directivity
d
tire
F
spectrum
f
frequency,
G
geometry
I4
Lg
landing-gear
K
constant
£
landing-gear
.M
aircraft
of
sound,
m/s
(ft/s)
function
diameter,
m
(ft)
function
Hz
function
position
strut
Mach
length,
number
8.8-i
m
the
of
angle.
the
dcmi-
develFederal
and
frequency,
Each
produced
by
(ft)
The
the
spectrum
the
wing,
aircraft
Airframe
Noise
user-provided
executed
is
frequency,
angle.
(ft}
speed
for
function
Additional
(ft 2)
m
method
empirical
parameters.
module
The
for
a
slats.
SYMBOLS
A
a
spectra
function
directivity
Center
directivity
provided
parameters.
pressure
as
several
be
geometry.
input
azimuthal
of
can
on
employs
leading-edge
input
directly
spectra
noise
based
Research
component
and
is
method
azimuthal
settings
airframe
of
and
broadband
method
The
sound
airframe
requires
and
i).
produce
the
the
The
Technologies
(ref.
angle,
all
I ON
predicts
airframe.
United
to
directivity
the
tail,
of
of
Module
the
Administration
ass_ned
is
Fink
Noise
of
MODULE
a
parameters
once
table
polar
Mach
Param-
of
for
each
the
mean-
directivity
set
N
number
of
landing
n
number
of
wheels
<p2>"
mean-square
Pre
f
per
landing
acoustic
reference
from
gear
pressure,
pressure,
distance
r s
gear
2
source
×
re
lO -5
to
Pa
p
24
c
(4.177
observer,
m
×
10 -7
ib/ft
2)
observer,
re
bw
(ft)
e
r s
dimensionless
$
Strouhal
s
number
distance
flap
0
polar
of
slats
for
reference
2
ambient
,
pc.wer,
den3ity,
azimuthal
re
1
D
×
kg/m
directivity
_
(ft)
deg
viscosity,
power
flaps
deg
angle,
dynamic
7'.
m
angle,
directivity
acoustic
ref
to
trailing-edge
thickness,
deflection
ambient
_t
..
source
number
boundary-layer
_f
from
c3b
_
kg/m-s
2
w
10 -12
3
(slugs/ft-s)
W
(7.376
(slugs/ft
angle,
3)
deg
Subscripts:
f
flap
h
horizontal
m_
main
landing
gear
n_
nose
landing
gear
v
vertical
w
wing
tail
tail
Superscript:
•
dimenslonless
quantity
8.8-2
x
10 -13
ft-lb/s)
INPUT
Theaircraft
are
required
Module
or
muthal
directivity
for
the
the
description
eters
are
the
The
output
t_Ible
polar
range
r s
distance
area,
Ah
horizontal
%
vertical
%
wing
area,
m 2
bc
flap
span,
m
source
m 2
to
observer,
b
tail
_rea,
area,
(ft)
Geometry
m2
m2
(ft 2)
(ft 2)
(ft 2)
(ft)
tail
vertical
m
(ft 2)
tail
horizontal
values
Constant
Airframe
flap
required
I.
from
Af
are
distance
tail
span,
span,
m
m
(ft)
(ft)
V
d_c/
d
ng
ng
n
ng
N_
N..,N
S
wing
span,
m
(ft)
tire
diameter
of
main
landing
gear,
m
(ft)
tire
diameter
of
nose
landing
gear,
m
(ft)
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
8.8-3
flaps
conditions
Parameters
angle,
independent
default
Input
ambient
Noise
the
the
and
and
Aircraft
directivity
establish
Finally,
The
the
parameters
airframe.
in
settings,
of
frequency,
arrays
Several
required.
given
control
the
angle
table.
of
is
number,
either
user.
output
observer
Mach
from
and
variable
for
the
to
the
pseudo-
of
the
input
azivalues
geometric
param-
Airframe
landing-gear
flap
Noise
position
setting,
deg
A_bient
ambient
Cop
speed
aircraft
M=
O=
of
Mach
Conditions
sound,
m/s
density,
ambient
dynamic
kg/m
3
(slugs/ft
viscosity,
3)
kg/m-s
Independent
frequen_I,
(ft/s)
number
ambient
polar
Parameters
(slugs/ft-s)
Variable
Array
Hz
directivity
azimuthal
angle,
directivity
deg
angle,
deg
OUTPUT
The
pressure
muthal
output
as
of
a
this
directivzty
provided
for
module
function
of
angle.
Lhe
is
a
In
addition,
.Module.
from
to
source
the
of
polar
Propagation
distance
table
frequency,
mean-square
directivity
the
observer,
observer
m
acoustic
angle,
distance
and
rs
aziis
(ft)
r S
Airframe
f
frequency,
polar
Table
Hz
directivity
azimuthal
<p2 (f,_._)>°
Noise
angle,
directivity
mean-square
deg
angle,
acoustic
deg
pressure,
re
2 4
D=c_
METHOD
_ne
method
Th.e prediction
.Car - field
noise.
are
shown
in
me_d
The
figure
presented
az r_;tame
i.
The
in
r_ise
reference
components
definitions
8.8-4
of
1
is used
to
considered
_he
directivity
compute
_n the
angles
are
shown
for
the
is
in
figure
given
for
In
each
=
equation
F
(I
is
the
discussion,
first
is
expressed
in
velocity
effect
is
The
Strouhal
number
S
=
-
the
M
where
L
noise
is
some
source
The
power,
D
The
where
K
a
As
as
the
a
is
the
source
to
for
and
functions
table
Each
the
The
factor
forward
(i
-
of
the
a
airframe
_*
determined
different
D
to
on
(I),
and
the
given
for
effects
can
from
each
the
each
be
the
polar
set
of
compute
empirical
acoustic
mechanism
for
is
trailing
edge.
T_e
turbulence
Reynolds
number
and
the
with
convection
acoustic
lift
the
pressure
angle,
power
can
and
The
are
The
dipole,
generation
turbulent
directivity
empirically.
8.8-5
the
its
own
:unctions
be
computed
azlmuthal
direc-
empirical
summarized
for
clean
boundary
is
length
and
has
these
constants
in
in
table
III.
Noise
intensity
turbulent
The
and
source
Using
parameters.
acoustic
da_a.
power.
F.
directivity
noise
of
thickness.
the
as
component
noise
function
input
the
surfaces
boundary-layer
9) 4
airframe
expressed
airframe
airframe
spectrum
mean-square
frequency,
used
primarf
cos
particular
II.
The
directivity
and
spectrum
functions
are
given
airframe
noise
component
is described
in detail
below.
The
M
(2)
Trailing-Edge
aligned
rs/b w.
Doppler
(3)
equation
power,
angle
tivity
is
by
of
the
as
funcdistance
=
rs
characteristic
constants
function
acoustic
by
as
directivity
observer
G
geometry
indicated
function
for
e)
scale
for
G
all
directivity
a
are
function
incorporates
and
power
K (M)
and
geometry
form
cos
pressure
computed.
acoustic
=
method
@)4
function.
for
defined
M
length
being
_q*
-
approach
detailed
(I)
cos
dimensionless
(i
general
the
F(s)
overall
spectrum
accounted
S
is
fL
c
M
then
acoustic
*
rs
the
and
mean-square
D(e,@)
)2
_*
is
far-field
_**
(i),
and
following
presented
component.
the
4_(rs
tion,
is
airframe
for
<p2>*
In
the
method
The
equation
airframe
is
the
2.
prediction
assumed
scale
is
function
spectrum
wing
layer
to
be
assumed
is
function
tail
the
independent
to
assumed
is
and
past
be
of
the
to
determined
be
The
acoustic
constructed
power
wing
n*
,.
The
dimensionless
the
standard
due
to
trailing-edge
(4.464
x
turbulent
boundary-layer
turbulent
and
for
the
conventionally
14.464
vertical
6:
is
computed
from
model
-0"2
./
acoustic
=
thickness
boundarT-layer
Aw (P_M.C_Aw_
ii •
a
(4)
<- 0.3,
the
of
10"5)M56:
flat-plate
Similarly,
noise
is
×
power
for
IO-5)M
_5
tail
,5,
the
horizontal
tail
is
161
is
17)
•
The
boundary-layer
tion
ks
(5)
using
the
aerodynamically
trailing-edge
and
(7) should
The
_s
thicknesses
for
The
clean,
as
such
the
7.075
function
D
a
6v
are
A
and
b.
or
jet
of
sailplane
computed
from
If
the
aircraft
constants
in equations
x 10 -6 , an 8-dB
decrease.
for
the
clean
equaairplane
wing
and
with
(4),
simple
(6),
horizontal
tail
by
the
= 4 cos 2 _ cos 2 812
vertical
directivity
sp_ctr_
sin 2 ¢
cos"
functions
function
F(S]
=
(8)
tail
= 4
D(@,¢)
These
values
flap
mechanisms,
be reduced
to
D(8,¢)
and
and
appropriate
directivity
given
•
6h
are
F
is
0.613(I0S)
4
9/2
(9)
plotted
given
10S)
in
figures
2
and
3,
respectively.
by
1"5
+
O.
5]-4
8.8-6
(I0]
for
rectangular
wings
and
= o.48s(1os)4 lOS) 1"3s +
for
delta
wings.
Strouhal
These
number
S
f6*b
M-'_
=
S
the
appropriate
6"
for
on
the
is
the
M
cos
value
wing,
noise
t.her
for
are
this
of
the
vertical
source
being
computed
The
from
deployment
different
span
b
tail,
or
and
Second,
noise
the
are
The
wing
thu
acoustic
The
either
ure
2.
tion
The
The
which
The
=
assumes
combined
then
are
plotted
of
4
slat
is
in
slat
from
Extension
noise
incident
sion
dipole
is
is
of
increased.
of
the
is
figure
the
on
The
deflected
dependpres-
of
layer
of
the
by
wing
wing.
noise.
increase
Both
be
to
predict
used
The
2.19S]
1"5
+
(8)
wing
noise
along
function
plotted
is
clean
given
in
by
fig-
equa-
is
of
(13)
the
(12).
with
the
overall
s]-4
percent
equation
to
the
and
noise
O.
equal
directivity
equation
slat
15
trailing-edge
be
the
is
wing
to
source.
by
in
assumed
for
The
noise
increment
The
their
mean-square
total
t_
sum,
to
acoustic
wing
chord.
spectrum
show
the
pressure
is
(I).
wing
to
thick-
used
increased
trailing-edge
added
by
an
boundary
the
5,
noise.
is
acoustic
produces
the
can
given
chord
given
equation
assumed
turbulence
the
function
S
effect
to
noise
for
Flap
This
The
method.
noise
is
0.613(2.19S)
the
on
(4)
slat
tail
produces
produces
this
due
sourc_
number
computed
in
function
that
Strouhal
functions
either
spectrum
F(S)
impact
power
noise
slat
itself
for
boundary-layer
mean-square
slats
the
equation
spectrum
(i0).
its
slat
trailing-edge
for
slat
4.
Noise
leading-edge
to
Therefore,
power
for
due
acoustic
slat
noise.
figure
(I).
First,
accounted
added
or
the
leading-edge
mechanisms
noise
of
the
horizontal
predicted.
equation
mechanisms.
trailing-edge
in
as
8)
Leading-Edge-Slat
two
plotted
component
(12)
-
hess
sure
functions
defined
(11)
(I
where
ing
spectrum
is
-4
Trailing-Edge
flaps
be
the
increases
produced
flap.
noise
is
flap.
8.8-7
Noise
by
This
assumed
the
the
noise
to
level
lift
Increases
be
of
airframe
fluctuations
aligned
as
with
noiz&.
due
the
to
flap
the
lift
the
exten-
The
slotted
acoustic
flaps
power
due
to
flap
noise
for
single
or
double
is
Af
.q*
=
x
(2.787
I0-4)M6--_
(14)
sin 2 6f
b_
where
overall
6f
is the flap
acoustic
power
deflection
is
angle.
For
triple
slotted
flaps,
the
Af
n" = (3.sogx io-4)_
(15)
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
% cos
¢)
2
D(8,¢)
which
are
= 3(sin
is plotted
in
6f
figure
cos
8 + cos
6 for
6f =
6f
sin
30° •
The
spectruD
(16)
functio_
F
(S < 2)
F(Sf)
=
L216.49S;
for
single
and
(2 -< S <- 20)
O. 1406Sf
0.
04805 f 0"55
double
(20
3
slotted
flaps
(17)
< S]
and
(S < 2)
FO.O257Sf
(2 <- S < 75)
(18}
F(sf)= /o.o5365_-°'°625
(75
LlTO_SS_a
for
the
triple
slotted
flaps.
Using
the
Strouhal
number
is defined
as
flap
chord
as
the
< S)
reference
length,
fAr
(19]
Sf
= M bfc
(1
M
cos
e)
8.8-8
I
The
spectrum
figures
functions
7
and
computed
8,
from
given
by
equations
respectively.
equation
The
(17)
The
mechan/sm
and
sidered.
the
for
dependent
The
predominant
to
dominate
the
strut
the
has
noise
sources.
other
potential
and
wheel
are
plotted
in
pressure
is
then
due
particular
landing-gear
simplified
made
in
Noise
noise
Noise
generation
been
comparisons
landing-gear
to
with
the
reference
i,
generated
sources.
which
landing-gear
by
the
Separate
are
added
extension
design
being
assumption,
that
to
are
and
predictions
together
based
there
strut
is
con-
wheel
are
yield
on
only
made
the
two
appears
for
total
noise.
For
a
noise
wheel
noise
on
process
experimental
(18)
acoustic
(1).
Landing-Gear
complex
and
mean-square
oneis
or
two-wheel
landing
gear,
the
acoustic
power
due
to
the
(2O)
and
due
to
the
_*
Similarly,
wheel
noise
strut
=
for
is
noise
(2.753
a
x
is
(21)
I0-4)M6<_)2_
four-wheel
landing
gear,
the
acoustic
power
due
to
the
(22)
_*
and
due
tions
to
the
(20),
length,
(3.414
strut
(21),
and
The
=
n
and
for
is
the
is
(22),
the
=
number
3
2
_" sin
2
the
d
same
is
of
function
s_-ut
D(8,_)
10 -4)M6n<b_)
noise
and
directivity
D(9,¢)
x
as
the
tire
wheels
per
the
for
equation
(2_).
diameter,
landing
landing-gear
£
In
equa-
ls
the
strut
gear.
wheel
noise
is
(23)
@
noise
=
3
sin 2
@
sin
2
8.8-9
¢
(24)
Thesedirectivity
For
a
one-
noise
or
for
the
=
13.59S
strut
noise
F(S}
Similarly,
wheel
=
for
noise
gear,
in
the
figures
9
spectrum
and
10,
respectively.
function
for
the
wheel
for
the
the
is
defined
÷
S 2)-2"25
{25)
is
5.325S2(30
the
=
+
S85 -I
four-wheel
(265
landing
0.0577S2(i
strut
F(S)
If
2(12.5
gear,
the
spectrum
function
for
the
is
F(S)
and
landing
is
F(S5
and
functions are plotted
two-wheel
tire
noise
=
+
0.25S2)
(275
is
1.280S3(i.06
diameter
-1"5
is
+
used
S25 -3
as
the
(285
reference
length,
the
Strouhal
number
as
fd
S
The
four
and
strut
ooM_c-(l
spectrum
(I).
gear
M
cos
functions
are
are
plotted
summed
The
computed
(29)
noise
The
frequency,
the
mean-square
components
output
pressure
polar
by
In
SPL
the
to
the
to
14.
The
separltely
total
main
by
landing-gear
landing
gear
wheel
using
meanand
nose
Computation
pressure
the
for
user.
directivity
table.
level
yield
due
Ii
computed
separately.
acoustic
desired
figures
are
to
Output
_he
in
pressure
then
pressure.
are
@)
acoustic
They
acoustic
landing
-
mean-square
equation
square
=
angle,
addition,
It
and
printed
defined
the
is
airframe
computed
azimuthal
output
for
is
each
the
directivity
is
available
sum
value
of
of
all
of
the
angle
for
the
sound
as
2
D
/
SPL
z
i0
lOgl0
\p2/
c
k*
+
20
(30)
lOgl0
Pref
8.8-I0
_f
J,
and
the
power
level
PWL
defined
as
3 2
_.clbw
(31)
PWL
= I0 lOgl0
_" + I0
lOgl0
Href
REFERENCE
I. Fink,
Martin
Mar. 1977.
R.:
Airframe
Noise
Prediction
Method.
(Available
from DTIC as AD A039 664.)
8.8-11
FAA-RD-77-29,
TABLE
I.-
RANGE
Input
parame t er
rse
m
AND
DEFAULT
VALUES
Minimum
OF
IJPUT
PARAMETERS
Default
Maximum
0.01
bw
I00
.......
2
A f, m
......
0.01
I0
I00
Ah'
m2
......
0.02
20
200
Av,
m2
......
0.02
20
200
0.i
I00
I000
2
AWl
m
•
o
b f, m
.......
_ho
m
.
b V,
m
.......
#
ra
.
dmg,
.
o
.
o
.
.
.
m
......
dng o m
......
£mg'
m
......
£ng"
m
•
.
.
......
nng
-
.
.
•
o
o
.
........
S
•
IRg
. . ......
"%_ao
"
6f,
deg
......
Crop #
B_/ S
.
.
"
•
"
o
°
.
.
•
•
•
....
.
,
.
•
DaD, kg/m 3 .....
_,
kg/m- s
....
5
20
0.02
I0
20
_.02
i0
40
0.I
20
i00
0.001
1
5
0.001
1
5
0.003
3
15
0.003
3
15
1
4
4
1
2
4
1
2
4
1
1
2
1
3
3
0
1
1
.
........
Nng
0.01
1.5
x
0
0.3
0.9
0
O
45
200
340. 294
400
0.2
1.225
1.5
10-5
1.7894
8.8-12
x 16 -5
2.0
x
I0 -5
TABLE
II.-
_PIRICAL
COHSTANTS
AIRFRAME
ACCXJSTIC
K
Source
Clean
wing
AND
FUNCTIONS
FOR
POWER
a
G
and
leading-edge
slat
(conventional
construction}
Horizontal
.
.
4.464
x
I0 -5
5
4.464
x
10 -5
5
6_c_w)2
4.464
x
10 -5
5
_:Cb,/bw)2
7.075
x
I0 -6
5
6:
7. C 75
x
10 -6
5
6h (bh/bw)
7.075
x
I0 -6
5
6: (bv/bw)2
2.787
x
10 -4
6
tail
(conventional
construction)
Vertical
tail
(conventional
construction]
Clean
wing
(aerodynamically
clean)
.......
Horizontal
tail
(aerodynamically
clean)
Vertical
.......
2
tail
(aerodynamically
clean)
Single
.......
,,r double
slotte_
edge
trailingflaps
Triple
.....
2_sin
_f
2
_f
w/
slotted
trailing-edge
flaps
One-
or
.......
i0 -4
6
4.349
x
i0 -4
6
n (d/b_) 2
3.414
x
I0 -4
6
n (d/b w) 2
2.753
x
I0 -4
6
wheel
.......
Four-wheel
gear
x
two-wheel
landing-gear
noise
(_/b_)
sio
2 _f
3.509
landingwheel
noise
Landing-gear
strut
nolse
.......
.
8.8-13
i
(d/bw)
2 (t/d)
1
°
T
'/
Vl
8
_
I
I
V
0
v
c;
6
c;
,.
o.4
v
V!
÷
4,
÷
•
÷
°
•
°
Ul
UI
;,_
_
t'l
U1
0
(/I
0
U1
0
{I]
0
,,,e
•
o
o
o
o
v
CO
0
ql'
El3
(/1
8
0
{ti
5.8
8
5.8
_.$
EII
I
I
{/1
Z
0
I
I
I
I
EU
Z
r,.
A
M
L)
e.,
Z
C_
C
r.
%
%
%
0
U
0
O
0
U
'%
%
0
O
C
rj
0
U
i
2,
%
%
%
0
U
0
U
0
U
_
%
"_
m
4-
3
v
_a
"T
O
91
el
el
"_
8.8-14
lJ
I
.
A
v
vl
v
v!
s_
-/
,4
7
!
ffl
T
L.
÷
4.
C
v
O
v
O
_
A
A
A
X_
_8
Z8
X8
I
I
I
!
n
0
i
@
8
I ',,Jr'
=:$
',Jr'
X 8
_
X 8
0
I
A
b.q
0
%
e,,i
c_
O
Ij
m
t
=,,
q
m
%
:_11=
..4
o
e-
"0
C
ei
q
O
=11
:1
4'0
m
e-
8°
8-15
q
,..4
I
I:
11
I.,
0
O
TRAIL_EDGE
FLAPS
CLEAN _G
VERTICAL
TA.IL
0
NOSE _aUl_)nlG
Figure
i.-
Sources
of
airframe
noise
included
8.8-16
in prediction
model.
9O
(a) Variation
with
polar
directivity
angle.
2To
90
o
(b) Variation
Figure
2.-
Dir_ctivity
and
with
azimuthal
level
8.8-17
w
for
leading-edge
dizectivity
clean
slat
wing,
noise.
=ngle.
horizontal
_ail,
90
(a) Variation
with
polar
directivity
angle.
27O
Figure
3.-
(b) Vaxiation
with
Direc:ivity
level
9O
azimuthal
for
directivity
vertical-tail
8.a-18
angle.
trailing-edge
noise.
0
,.i
0
cq
-.4
¢I
or}
s,.--.
tn
0
.,,a
e"
0_
0
LJ
..(3
E
-,,4
0 0
_.. _-
t- '0
-,.4
t_
Z
0
c:3
0
U
n_
0
qL
(/3
E
!
z
t_
t_
1
0
3
8.8-19
.,4
0
4_
0
0
m
I
_n
E
:3
Z
m
0
0
cCO
O
I/
GO
U
I
u_
J,,,
°,,,4
l
(:3
1
u_
I
3 °_6ol 'l_^el
uJn_oed_
8.8-20
-
i
I
lk!
I
a
I
I/
i
f_
--
\%/
(a)
Variation
with
/
polar
J
i
I
I
.
/
/%_t
_irectivity
/
angle.
100
\
270
I .-_°
I
I
I
T
_ /
!
I
i
I
#
(b)
Figure
Variation
6.-
with
Directivity
at
azimuthal
level
a
30 °
8.8-21
for
flap
directivity
flap
_ngle.
angle.
trailing-edge
noise
I
90
[
o
1
l
1
_
o
.-
_
,-
I
I
I
.:1 °[601
'lava']
I
!
o
c,i
I
uJnjload
S
8.8-22
o.
CM
_
_
ol
_i
I
I
01
o
n.
0
¢I
0
q
m
0
Z
"_
LJ
E
4J
:3
Z
o
m
¢I
o
0
3Z
_.
--_
0
I
:>
0
w-4
E
'.3
0
I
!
OB
I
i
I
°°
I
I
i
I
0
o
_.
o.
_.
ol
!
I
I
I
I
I
-I°_fiOl'l_^el wn4o_d
8.8-23
_
f_
180
90
(a)
Variation
with
polar
directivity
angle.
180
270
90
0
(b)
Figure
£
&
9.-
Variation
Directivity
with
azimuthal
level
for
directivity
landing-gear
8.8-24
angle.
wheel
noise.
r
L
90
(a) variation
with
polar
directivity
angle.
90
(b) Variation
Figure
I0.-
with
D1rectivity
azimuthal
level
8.8-25
for
directivity
landing-gear
angle.
strut
noise.
jO
_O
"
u')
o
o
I
IJ
I
'v'--'
I
I
O
I
I
I
I
I
IZ)
O•
IZ')
,e
O*
i
I
I
_-I °LSOI
I
'I_A'97
I
:'unJ",°_ds
8.8-26
I
O
O
r,')
i
I
,,,-4
i
q
I
0
8.8-27
0
0
oi
-,,4
O
w.
e.
u_
0
e-
ID
E
=
z
"
o
o
_I
o
e
0
3
Ib-
u_
I
¢.,1
0
I:1
I
I
I
I
0
I
o
I
_
I
o
0
I
_
o
I
I
I
I
_4 °L6Ol 'IB_B']Lun.qo_)ds
8.8-28
I
I
I
I
,4
0
m
0
_Lr)
w
L,
O
P
q
i
0
m
"0
In
,o
0
r'3
Z
o
r'3
0
!
o
L_
0
W-;
in
LC')
>
,,-,i
f
L,
0
rJ
_.,
m
I
,wP,-,-'
I
1
J
!
!
I
J
0
0
c_
o
M
I
I
I
3 °L6ot "l_^_-i wn_ood
8.8-29
I
S
I
I
C'
8.9
SMITH
AND
BUSHELL
'I_I_INE
NOISE
MODULE
INTRODUCTION
The
noise
Smith
for
and
Bushell
an
axial
flow
developed
by
Smith
and
functions
to
directivity
source
is
the
The
and
Parameters
and
to
are
of
output
or
input
pressure
with
table
The
a
of
frequency,
Although
directivity
angle,
with
other
noise
patterns
The
by
the
Additional
a
polar
it
noise
is
for
table
turbine
turbine
A e
engine
C
ro_'oc
inlet
reference
blade
ambient
C
cross-sectional
mean
speed
D
directivity
d
turbine
F
spectrum
f
frequency,
f"
Helmholtz
fa
fuel-to-air
h
absolute
of
area,
m2
axial
chord,
m
m/s
(ft/s)
sound,
rotor
rotor
diameter,
m
(ft)
(ft)
function
Hz
number,
fC/c
ratio
humidity,
percent
blade
tip
Mach
number
8.9-1
T_
(ft 2)
function
a
Mt
m2
mole
fraction
due
to
in
the
turbine
Turbine
each
the
directivity
introduced
tables.
area,
of
noise
SYMBOLS
A
polar
noise
Noise
user-provided
once
is
and
significant
velocity
executed
method
empirical
broadband
provided
output
the
frequency
parameters.
be
angle.
compatible
of
the
broadband
on
employs
only
random
is
The
function
is
the
based
method
the
user.
module
is
function
that
several
the
parameters.
as
a
can
by
predicts
The
with
of
directly
azimuthal
is
as
parameters
directivity
I).
which
input
flow
Module
prediction
assumes
blades
required.
the
azimuthal
vary
spectra
component,
requires
exit
(re/.
method
rotating
Module
parameters
acoustic
the
method
entrance
The
"vortex"
of
Noise
The
Bushel1
sound
angle.
interaction
flow.
values
produce
Turbine
turbine.
(ft 2)
is
set
of
mean-square
angle,
assumed
so
that
not
the
the
M
aircraft
&
mass
N
rotational
Ne
number
of
engines
Ns
number
of
turbine
<p2>"
mean-square
Pref
Mach
flow
number
rate,
kg/s
speed,
Hz
stages
acoustic
reference
pressure,
pressure,
2
R
dry
air
gas
constant,
R
gas
constant,
m2/K-s
distance
r
(slugs/s)
from
x
10 -5
re
2
source
Pa
m2/K-s
4
(4.177
2
(ft2/°R-s
to
2
pc
re
×
10 -7
(ft2/°R-s
lb/ft
2)
re
_e
2)
2)
observer,
m
(ft)
s
r
s
T
dimensionless
distance
temperature,
K
ratio
of
8
polar
directivity
r/°
acoustic
_ref
reference
ambient
power,
density,
azimuthal
Subscripts
:
i
en trance
j
exit
s
static
source
to
heats
angle,
re
1
deg
p
c3A
x
10 -12
kg/m
directivity
3
W
(7.376
(slugs/ft
angle,
3)
deg
ambient
Superscript:
*
dimensionless
observer,
(OR)
specific
power,
from
quantity
8.9-2
x
10 -13
ft-lb/s)
INPUT
Theturbine
Turbine
Noise
required
parameters
for
angle,
independent
variable
cross-secr/onal
Finally,
the
are
the
are
are
sound
values
reference
given
in
the
mean
table
number
range
and
engine
reference
Ne
number
of
r s
distance
chord,
of
turbine
and
of
area,
(ft 2)
e
engines
from
source
to
observer,
Turbine
A e
C
N
S
turbine
inlet
rotor
blade
nummer
of
axial
turbine
fuel-to-air
area,
chord
of
the
re
last
stages
Turbine
f
(ft)
Geometry
cross-sectional
mean
m
Noise
Parameters
ratio
a
core
N*
T*
_,j
mass
flow
rotational
exit
rate,
speed,
static
re
re
P
c=/d
temperature,
re
Ambient
Cam
ambient
ha
absolute
humidity,
%
aircraft
Mach
ambient
speed
density,
of
camA e
T
Conditions
sound,
m/s
percent
(ft/s)
mole
fra:tion
number
kg/m
3
8.9-3
(slugs/ft
3)
Ae
stage,
of
turbine
distance
of
Constants
m2
the
turbine.
and
values
polar
inlet
number
the
englnes,
the
are
establish
I.
Input
A
The
default
of
frequency,
arrays
table.
axial
output
conditions
The
angle
descziption
area,
The
the
Ambient
levels.
output
geometric
required.
either
user.
pressure
blade
the
from
the
directivity
for
rotor
for
engine
or
azimuthal
area,
observer
parameters
of
and
required
required
Module
com_utation
directivity
stages
are
Pa_-ameters
re
the
input
to
IndependentVariable
f
Erequency,
e
polar
Arrays
Hz
directivity
azimuthal
angle,
directivity
deg
angle,
deg
OUTPUT
The
output
pressure
as
muthal
provided
to
a
this
directivity
for
the
of
from
is
a
In
addition,
Module.
source
frequency,
9
polar
to
the
mean-square
directivity
the
observer
observer,
m
Noise
acoustic
angle•
and
distance
azi-
rs
is
(ft)
Table
Hz
directivity
azimuthal
<p2(f,@,_)>*
of
polar
Turbine
f
table
frequency,
angle.
Propagation
distance
r s
module
function
angle•
directivity
mean-square
deg
angle•
acoustic
deg
pressure
•
re
02C
_ 4
METHOD
The
prediction
the
far-field
ure
i.
The
Smith
directivity
gives
the
The
method
noise.
A
and
angles
Bushell
shown
prediction
equation
in
for
=
in
of
this
reference
typical
uses
figure.
vortex
far-field
_*A*
a
method
broadband
the
for
<p2>*
presented
schematic
D(@)
1
is
turbine
used
is
the
coordinate
The
following
to
shown
system
prediction
compute
in
fig-
and
method
noise.
mean-square
pressure
for
a
turbine
F(f*)
is
(i)
4
4_(r:)
In
equation
tion,
rs
and
is
(i),
Y
is
expressed
rS
=
_*
2
is
(i
the
the
spectrtun
in
dimensionless
-
M
cos
overall
@)
power,
function.
form
The
D
is
source
the
to
directivity
observer
funcdistance
as
(2)
rs
8.9-4
The forward
(I -
M
velocity
cos
@)4.
f*
=
effect
The
is
accounted
Helmhcltz
fC*_e
--(I
-
for
ntmber
s=
cos
by
f*
is
the
Doppler
defined
factor
as
0)
(3)
C
whe:e
C
is
The
the
mean
acoustic
_*
axial
chord
of
for
the
IO-5)M3_*N
t
s
power
=
(4.552
H*
x
the
last
stage
turbine
turbine
rotor
blades.
is
_4)
oe
where
The
N s
is
blade
tip
the
number
Mach
of
number
stages
Mt
and
is
m
is
defined
the
core
mass
flow
rate.
as
(5)
where
N*
is
ture.
The
values
gas
constant
absolute
ratio
The
is
tion
of
=
F
is
in
a
equation
local
are
II
function
(i).
The
The
the
number
output
is
the
is
a
total
figure
number
and
acoustic
noise
of engines
available
_s
of
exit
static
tempera-
7s
and
values
of
T_,j,
value
of
fa"
function
mean-square
_he
heats
The
the
local
the
1.4.
in
Helmholtz
input
ratio
is
plotted
is
specific
from
y
D
and
of
3.
T_,j
of
fuel-to-air
heats
function
table
and
ratio
found
and
specific
figure
multiplied
by
tion,
printed
defined
R/R
directivity
in
speed
the
ha,
of
given
plotted
from
R*
rotational
humidity
ambient
and
the
the
Ne
the
of
polar
2.
The
is
given
pressure
mean-square
for
the
output
sound
pressure
directivity
spectrum
in
table
is
then
acoustic
table.
level
angle
funcIII
and
computed
pressure
In
SPL
addi-
as
2
(6)
SPL
and
the
Dower
PWL
=
i0
level
=
i0
loq!0
PWL
lOglo
<p2>*
+
defined
It
+
i0
20
lOgl0
Pref
as
(7)
lOql 0
"Lre f
8.9-5
R.I_E
1.
Smith,
M. J. T. ; and Bushell,
in the Civil
Aircraft
Noise
Soc. Mech.
Eng., ,Nov. 1969.
K. W. :
Problem.
Turbine
Paper
8.9-6
Noise - Its
69-WA/GT-12,
Significance
American
.m
!
........................
TABLE
I .- RANGE
AND
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C Q
.
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........
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.
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.
•
•
....
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o
o
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o
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.
.
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100
0
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1
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200
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294
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NS
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4
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1.225
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8.9-9
of
typical
axial-flow
turbine.
0
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01.
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8.9-11
wnAoeds
I
9.
_o
PREDICTION
PROCEDURES
9.1
ICAO
REFERENCE
NOISE-PREDICTION
PROCEDURE
(1978)
INTRODUCTION
In
formed
June
a
of
1977,
prediction
procedure
Lhe
applicable
subcommittee
to
were
I.
Establish
2.
Assess
an
the
agreed
Oy
Identify
new
noise
in
SNECMA,
Corporation,
LocKheed
A
Lhe
in
s_mnary
of
table
II.
component
of
_he
application
measured
figure
the
effective
All
the
of
the
are
standard
noise-prediction
the
in
and
SST's,
an
pre-
those
and
to
make
the
internationally
British
Limited,
Each
of
for
these
upon.
The
Douglas
General
Electric
provided
and
Aerospace
McDonnell
their
predic-
currently
studies,
results
a
of
availreference
the
subcom-
ICAO.
procedure
used
procedure
engine
interesting
are
to
note
level
reference
by
each
presented
predictions
noise
perceived
NASA,
Company,
SNECMA
results
agreed
for
some
each
of
(P._L)
Lhe
level
(EPNL)
participant
in
table
method
are
variation
The
procedure
is
shown
The
presented
wide
data
and
I.
computations.
noise-prediction
noise
component
included
ANOPP
me_hod
methods
in
_NOPP
functional
is
in
as
the
ICAO
separate
modules.
presented
9.1-1
%.
were
by
to
the
differences
define
Boeing
Group.
prediction
of
work
The
provided
on
perceived
available
procedure
wi_h
to
Rolls-Royce
was
SST
is
as
Aircraft
engine
Based
procedure
in
the
accuracy
to
various
in
I.
procedure
of
It
the
procedure
Whitney
trial
maxim_un
of
studies
associated
so
noise-prediction
the
goals
against
the
reference
parametric
subcommittee
presented
of
in
U.S.S.R.,
procedure
were
reference
results
&
data.
study
used
procedure
engine,"
the
Corporation,
SST
noise-prediction
mittee
The
noise-prediction
"trial
problems
_he
the
Pratt
trial
measured
(ICAO)
noise-prediction
levels
between
prediction
Participating
able
Organization
reference
(SST's).
reference
recommendations
Corporation,
a
the
of
level
recommended
and
the
nc,ise
already
necessary
for
a
reference
of
use
noise
procedures
tions
Aviation
determine
transports
upon
flight-test
dicted
Company,
supersonic
accuracy
Determine,
4.
Civil
to
to:
measured
3.
International
subcommittee
subsequ,
reference
functional
A
discussion
ently.
noise-prediction
modules
of
each
or
variants
component
SYMBOLS
cr
standard
c
ambient
D
directivity
d
fan
F
spectral
f
frequenc
fp
peak
ha
absolute
humidity,
percent
hr
relative
htmlidity,
percent
L
acoustic
liner
role)
forward-velocity
_2>"
mean-square
p*
of
speed
of
sound,
sound,
m/s
m
m/s
(ft/s)
(ft/s}
(ft)
distribution
7,
function
Hz
frequency,
Hz
length,
5
suppression
Sc
corrected
acoustic
sea
m
fraction
(ft)
pressure,
re
level
2
pc
re
4
Pr
pressure,
Pa
(ib/ft
2)
factor
5trouhal
ambient
mole
index
pressure,
standard
jet
speed
diameter,
P,,.
T.
level
function
ambient
T"
sea
number
temperature,
temperature,
re
K
Tr
(OR)
]
T
standard
_T
thrust
T
ambient
3
jet
sea
level
loss,
temperature,
(oR)
percent
temperature,
velocity,
re
K
(OR)
c
X
h_nidi
Y
vibrational
absorption
1
absorption
coefficient,
ty
K
ratio
function
nepers/m
(nepers/ft)
9.1-2
J
i
8
polar
directivity
p®
ambient
Subscripts
:
cl
classical
h
high
£
ic_
max
maximum
n
nitrogen
o
oxygen
ref
reference
rot
rotational
sup
suppressed
vib
vibrational
densit
angle,
7,
kg/m
deg
3
(sluqs/ft
frequency
frequency
procedure
JET
The
method
appendix
A
Practice
Stream
in
as
The
876
of
of
functions
index
m(@),
tional
data
of
in
defined
for
ratio
(lOgl0
data
given
in
are
is
presented
method
dimensionless
and
differs
ways.
First,
1n
table
III
table
IV
0.3
and
is
The
method
C
Circular
Jet
functlons
as
functions
of
and
for
SAE
Shock
a
of
876
Cell
shock-cell
frequeDcy
(ref.
Noise
shock
.Module.
9.1-3
in
the
me_hod
Recommended
as
the
Single
empirical
data
produce
so_-_
angle.
Single
Stream
Circular
forward-velocity
2,
is
used.
F
The
figure
at
Second,
a
value
additional
addiof
the
spect=al
3.
NOISE
I).
polar
ANOPP
to
factor
included.
interference
and
the
figure
plotted
jet
predicting
ARP
in
employs
different
on
Aerospace
directivity
from
and
SHOCK
appendix
polar
a
based
groups
distribution
of
is
(SAE)
The
method
V:)
velocity
This
two
spectral
noise
Engineers
frequency
the
NOISE
mixing
Module.
relevant
reference
Module
jet
I).
Noise
terms
MIXING
Automotive
(ref.
Jet
ICAO
!_ise
predicting
Society
(ARP)
spectra
Jet
for
of
Zircular
tabulated
3)
cell
This
is
The
noise
method
function
directivity
is
presented
in
uses
to
based
master
produce
angle.
on
ANOPP
proposed
as
the
spectra
sound
spectra
in
The IC__O
the
reference
Circular
Jet
mean-square
D
as
0
additional
is
multiplied
The
is
method
C
function
given
Noise
for
to
in
table
is
V
The
turbojet,
tions
of
The
ICAO
method
called
the
figure
5.
and
than
This
uses
and
a
is
method
2
polar
Module.
as
The
is
The
of
ICAO
a
the
interaction
Fan
3rages.
Noise
If
second
stage
spectra
is
shifted
uses
Module.
taken
one
to
It
be
similar
i/3-octave
The
ICAO
discharge
(ref.
is
2)
only
maximu_
total
data
to
to
as
presented
in
for
of
stages,
_nree
flow.
not
The
preceding
higher.
multielement
Tone
last
available
stage
the
Fan
three
for
with
levels
should
silencer
is
the
stages
a
given
_he
be
are
as
for
stage
tone
spectra
reduced
by
9.1-4
spectra
inlet
components
dne
first
two
known,
then
the
with
first
of
The
_e
tone
stage.
flow
is
d6
is
be
if
and
assumed
one
a
noise
for
to
If
assu_ed
be
a
the
performance
to
be
similar
I/3-octave
core/bypass
the
me_hod
computed
possible.
can
n_ise
Heidman's
discharge-duct
noise
shifted
used.
of
not
broadband
if
5
sound
NOISE
The
it
on
Noise
tone
stage
the
Module.
used
based
noise,
each
components
stage,
in
F_n
the
are
first
than
mass
is
the
broadband
discharge
bypass
function,
plotted
predict
once
the
the
Noise
and
flow-distortion
engines.
and
func-
angle.
inlet
tone
bypass/fan
turboas
distribution
noise
ANOPP
to
higher
uses
from
spectra
spectrum
VI
DISCHARGE-DUCT
method
proposed
Combustion
spectral
intake
second
band
the
the
NOISE
executed
interaction
computed
are
the
reference
rotor-stctor
the
the
COMPRESSOR/FAN
noise
sound
table
in
inlet
is
for
core
directivity
and
data
of
This
functions
method
tone,
performance
in
presented
polar
as
different
INTAKE
and
on
ANOPP
Module.
given
empirical
frequency
reference
rotor-stator
from
uses
is
based
in
produce
compressor/fan
This
directivity
4.
angle.
Noise
predicting
Heidman.
method
functions
in
directivity
polar
figure
is
data
to
utilizes
Combustion
of
in
noise
directivity
spectrum,"
for
by
additional
function
presented
COMPRESSOR/FAN
The
found
i/3-octave-band
NOISE
engines
method
the
"envelope
reference
an
plotted
empirical
turbofan
reference
F
by
combustion
i.
and
frequency
function
predicting
reference
Module.
shaft,
r_t
computed
(i)
COMBUSTION
appendix
function
The
:
directivity
and
an
Module.
= _(el <p2>"
ref
additional
has
Noise
<p2>*
follows
<p2>*
angle
Cell
pressure
function
The
method
Shock
mixer
band
or
TURBINE
NOISE
Themethodfor predicting
the
Smith
and
the
Smith
and
functions
method
Bushell
to
directivity
Sm/th
Bushell
Turbine
predict
The
Bushell
Turbine
as
The
me,uhod
Fink
.Module.
spectra
4).
The
metnod
as
requires
uses
angle.
Noise
in
and
frequency,
The
ICAO
The
tion
is
Institute
low
that
into
is
reference
the
same
The
where
sum
a
of
+
is
the
the
relaxation
is
based
as
_e
empirical
and
polar
no
changes
of
on
the
report
FAA
Airframe
functions
directivity
the
Noise
to
predict
angle,
requires
and
no
sound
azimuthal
chaunges
in
the
the
procedure
_rot
+
the
6.30
the
in
the
ICAO
method
has
ANOPP.
American
Atmospheric
The
The
the
to
absorp-
Standards
ANSI
Absorption
incor-
SAE
equations
for
due
reference
been
National
module.
equations
×
10 -9
that
fol-
method,
Module.
classical
* 2/2
....
i. 365 (T)
[r/Cr)_*.
+ 0.3713
coefficient
in
Absorption
coefficients
×
the
coefficients
absorption
9.20
for
This
and
molecular
by
Atmospheric
=
to
in
as
given
=
5).
Module
corresponding
absorption
is
selected
(zuf.
contained
the
ABSORPTION
Absorption
in
absorption
_vib,n
866A
nomenclature
acl
in
ARP
method
effects
defined
where
similar
replace
rotational
noise
method
method
SAE
Atmospheric
(ANSI)
directly
using
of
the
met.hod
as
Module.
atmospheric-absorption
porated
uses
frequency
ANOPP
assumed
polar
ATMOSPHERIC
procedure
of
_OPP
NOISE
presented
empirical
of
component
in
method
method
airframe
is
The
vortex
Module.
predicting
This
functions
directivity
Airframe
for
(ref.
presented
of
AIRFRAME
by
the
is
functions
reference
.Noise
is
This
Module.
spectra
ICAO
noise
3}.
Noise
sound
angle.
and
turbine
(ref.
10 -4
for
(f/Cr)
nepers
Module.
nitrogen
(T*) I/2
per
The
and
sum
(2)
p*
unit
of
oxygen
length
the
is
as
vibrational
given
by
(3)
102"43(T*-I)y(x)
]vib,o
t-he
parameter
X
is
given
-in
X
=
4.05hrf
rr*-l
19
9.1-5
by
[41.9 cT*-ll-n.
5]+7.62}
(4)
and
Y(X)
is
In
equation
of
the
the
vibrational
(4),
the
absolute
absorpt/on
relative
humidity
function
humidity
h a
hr
can
The
Then,
absorption
average
the
table
VII.
expressed
in
terms
lOgl0
T*)
(5)
h_-10
a
total
the
lowing
=
be
in
as
(8.4256-I0.1995/T*-4.922
hr
given
coefficient
dimensionless
same
procedure
is
the
absorption
as
the
ANSI
sum
of
equations
coefficient
standard
is
(2)
and
(3).
determined
fol-
accomplished
by
method.
PROPAGATION
Propagation
the
atmospheric
standard
(ref.
to
noise
is
spectra
The
tasks
and
to
used.
Ground
free-field
ground
effective
model
levels
for
a
are
perceived
noise
noise
in
is
microphone
the
(EPNL)
is
The
SAE
ARP
modeled
height.
(PNL)
Noise
spreading,
attenuation.
presented
level
by
level
and
spherical
attenuation
1.2-m
computed
is
include
as
and
perceived
level,
observer
reflection
reflection
including
noise
the
performed
atmospheric-absorption
levels,
.Noise
sound
absorption,
the
perceived
the
Module.
SAE
5)
2 dB
the
of
Propagation
and
8&6A
by
_"ne
adding
desired
tone-corrected
Levels
Module.
computed
by
the
Finally,
Effective
Module.
SUPPRESSION
A
variety
aircraft
silencing
_OPP
of
englne
by
nozzles.
_he
suppression
quency,
polar
ICAO
These
me_hods
hate
techniques
effects
for
a
element
effects
are
of
angle,
of
the
below
estzmating
The
ICAO
Jet
Suppressor
all
defined
types
as
Subgroup
of
jet-noise
follows:
as
each
a
in
of
of
the
fre-
and
table.
techniques
noise-source
by
for
table
angle
output
recommended
may
a
function
directivity
effects
of
and
accounted
takes
implementation
suppressor
Jet-Noise
for
quantifying
factor
S
is
on
for
are
noise-module
provided
suppression
mixers,
module
type
azimuthal
appropriate
suppression
presented
for
This
the
flow
suppression
suppressor
and
for
lining,
noise
subcommittee
of
developed
Module.
particular
prediction
the
been
acoustic
Suppression
directivity
each
quantifying
have
including
The
General
factor
multiplies
The
techniques
noise,
for
component.
the
also
user.
be
Alter-
used.
Suppression
has
produced
suppression.
,,p2>" ;
a
recommended
The
technique
suppression
(6)
sup
9.1-6
where
<p2>*
is
expression
for
the
unsuppressed
the
0.1
S
The
=
maximum
been
(1+AS)
nique
are
three
curves
gross
given
in
are
incorporate
the
a
in
figure
of
must
7.
be
Finally,
of
suppression
noise
acoustic
liner
(S
meters).
The
liner
Any
liner
noise
is
factor
=
assumed
0.469
L£,
should
designed
noise
by
is
(0.469)
of
to
liner
20.0
designed
by
to
reduce
9.8
dB/m
L£
in
dB.
eter
of
suggested
the
to
is
be
where
be
to
same
meters.
L£
Lh,
The
produce
where
A
jet-velocity-
with
¢
"max
velocity.
given
in
function
total
overall
of
applied
to
The
table
D(@),
In
is
for
the
value
IX
as
shock
dB/m
length
and
given
noise
(i.0
of
in
with
the
dB/ftl
liner
of
in
attenuation.
suppression
addition,
an
turbine
noise
will
Therefore,
the
total
and
noise
_
are
the
will
acoustic
suppress
lining
attenuate
turbine
suppression
lengths
suppression
of
should
factor
S
each
type
be
limited
Suppression
is
effective
reduction
the
low-frequency
turbine-noise
9.1-7
to
3.3
core-noise
LZ
intake
length
the
following
projected
Suppression
amount.
dB/ft).
compressor/fan
that
is
attenuated
designed
high-frequency
(3.0
(0.i03)
equivalent
V_.
a
tech-
Suppression
Inlet-Noise
The
The
studies.
jet
as
Suppression
Turbine-Noise
turbine
5.
latest
the
has
Sma x
suppression
multiplied
directivity
Core-Noise
core
be
re'.-city
a
the
figure
parametric
magnitude
jet
of
of
applied.
The
jet-noise
modifications.
The
in
must
Shock-Noise
no
The
suppressor
data
technology,
for
the
jet-noise
The
use
plotted
AS
the
of
loss.
through
and
factor
of
kind
Pre-1972
reccmDendation
function
any
AT
VIII
effects
as
X,
loss
table
a
for
performance
presented:
correction
table
gross
thrust
and
plotted
pressure.
is
(8)
Sma x
with
suppression
AS
factor
(7)
technology,
of
SmaxD
suppression
of
acoustic
suppression
I0
correlated
function
mean-square
jet-noise
reduced
wall
be
i0
lining
limited
to
dB
(S
I0.0
for
=
each
0.100L/d).
dB.
fan
diamIt
is
Bypass-Duct-Noise
Suppression
Thecompressor/fandischargeduct noise is
(3.0
(S
dB/ft)
=
6.6
of
acoustic
0.103L).
dB/m
reduce
If
(2.0
the
only
(S
4.9
should
a maximum
the
dB/ft)
noise
attenuation
treatment
=
outer
0.221
dB/m
be
attenuation
on
is
treated,
reduce
and
if
only
inner
(S
=
dB/ft)
limited
to
15
dB.
dB
is
suggested.
I0.0
For
INSTALLATION
The
interaction
affect
the
point
source
ICAO
prediction
engine
SST.
noise
of
the
radiated
model
are
often
levels
to
and
the
airframe
to
noise
is
treated,
bypass-duct
ratios
for
and
'fhese
as
recommended
account
The
bypass
aircraft.
referred
subcommittee
noise
the
wall
greater
than
EFFECTS
engines
from
the
0.322L).
of
dB/m
reduced
by 9.8
and
outer
walls
inner
wall
L)
(1.5
both
the
engine
installat:
a
2.0-dB
installation
location
de-"_tions
from
the
effects.
increase
effects
The
in
the
likely
on
total
a
new
REFERENCES
I.
_:as
Turbine
Eng.,
2.
Heidman,
M.
Source
3.
Smith,
in
M.
Fink,
Mar.
5.
Standard
Exhaust
F.:
J.
T.;
Civil
Mech.
866A,
Prediction
X-71763,
and
TM
Bushell,
Aircraft
ARP
S76,
Soc.
for
Fan
and
Noise
-
Automot.
Nov.
of
Soc.
Automot.
W.:
Turbine
Problem.
Noise
from
Atmosphere
Use
Compressor
Paper
Its
Significance
69-WA/GT-12,
American
1969.
Airframe
for
Method
1975.
K.
Noise
(Available
Values
AF_
Interim
R.:
1977.
H_midity
Prediction.
NASA
Eng.,
Martin
and
Noise
1978.
Noise.
Lhe
Soc.
4.
Jet
Mar.
in
Prediction
DTIC
as
AD
Absorption
Method.
A039
as
Evaluating
Aircraft
Eng.,
1964.
Aug.
9.1-8
FAA-RD-77-29,
664.)
a
Function
Flyover
of
Temperature
Noise.
2,
¢r_ .x
t
t{
T
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r.
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TABLE
VII.FOR
MO_
VIBRATIONAL
SAE ATMOSPHERIC
ABSORPTION
ABSORPTION
METHOD
x
Y(x)
0.00
.25
0.000
.50
.315
.700
.60
.840
.70
.80
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1.00
.996
1.000
i.i0
1.20
.970
.900
1.30
1.50
.840
1.70
2. O0
.670
.570
2.30
.495
2.5O
2.8O
.450
.975
.750
.40O
.370
.330
3. O0
3.30
.300
3.60
4.15
4.45
.260
.245
4.80
.230
5.25
.220
5.7O
6.05
.210
6.50
.205
.200
7._
I0.00
.200
.200
9.1-19
FUNL'TION
TABLE
VIII.-
MAXIMUM
JET-NOISE
SUPPRESSION
Sma x,
dB,
for
FACTOR
-
_T,
Recommended
percent
Demonstrated
for
\
Latest
pre-1972
parametric
technology
technology
studies
1.000
2.000
4.0O0
6.000
8.000
I0.000
12.000
14.000
16.000
1_.000
ZO,O00
0.000
2.200
4.600
6.000
7.000
7.600
8._00
8.800
9.200
9.800
I0.000
TABLE
IX.-
JET-NOISE
VELOCITY
0.000
5.100
10.400
13.400
15.700
17.300
18.bOO
19.800
20.800
21.700
22.600
0,000
3.5O0
6.200
9.300
I0.800
II.900
12.800
13.700
14.400
15.000
15.400
SUPPRESSION
FACTOR
CORRECTION
v*
As
3
0.000
1.070
1.250
I..30
l.bl0
1.790
1.970
3.000
-1,000
-1.000
-.800
-.bOO
-.400
-.ZOO
0.000
O, OOO
9.1-20
?
\
I
TABLE
X.-
DIRECTIVITY
JET-NOISE
FUNCTrON
FOR
SUPPRESSION
_B
deg
D (@ )
_30
0
6O
8O
.3
.5
i00
120
1.0
.7
>120
1.2
9.1-21
._
q
-
L
...................
° ._
U
U
0
f-
E
l,
m
E
0
o
t_
L]
U
0
_
E
U
0
_,
e,.,,-4
-,,4
0,1
[]
0
x
S
r"
'-'
E
0
0
t_
0
>
0
I
0
0
t_
.,,,,i
I
t
I
1
!
J
i
i
9.1-22
..
_
_
_i
_
I
__
M
N
L
0
0
0
,,¢
o
I,,-
0
0
(:9
-g
<:
o
iI
Wl_
gm
0
•
o
£3
,,,
_0
O
13_ "0
0
('4
I
0
I
(8)w
I
0
0
0O
'xapul
_[o01aA-PJDMJo3
9ol-23
i
-J
--3
g
-
100
120
130
_"
-75[
-2.0
I
I
--1.5
]
--1.0
I
--.5
Corrected
I
0
I
.5
Strouhol
Number,
1.0
I
1.5
I
2.0
log m S.
a
=, 4
7
-2.0
l
--1.5
1
1
I
-1.0
--.5
0
Corrected
(a)
Figure
3.-
Tj/T
S_ouhal
= l.O:
.Normalized
Nurnber.
loglo
spectral
1
.5
V_
I
I
1.5
2.0
S,
= 0.3.
distrzbution
9.1-24
Ioglo
I
1.0
factor.
O, DEGREES
9O
100
110
120
130
1
-- 1.5
-- 1.0
1
--.5
Corrected
0
Strouhol
I
I
I
I
.5
1.0
1.5
2.0
Number.
log10 S o
--35
, -45
--2L --
_5
170
-55_
-65
(
-751
--2.0
I
1
I
--1.5
--1.0
--.5
Corrected
(b)
1
0
S_ouhol
Tj/T
=
Figure
9.1-25
2._;
3.-
I
1
I
I
.5
1.0
1.5
2.0
Number.
lOgl0
Continued.
log,o
V_
=
0.3.
S.
m
o
_U,_
__"
'_
II0
"130
-7
--2.0
I
I
--1.5
--I.0
Corrected
•
t
I
I
I
I
-.5
0
.5
1.0
1.5
2.0
Strouhol
Number.
lOg_o SQ
), DEGREES
SO
"160
70
180
I
I
-- 1.O
Corrected
(c}
Tj/T®
I
--.5
Strouhal
= 2.5;
Figure
I
O
Number.
lOgl0
i
.5
1.0
Iog_o S_
v_ = 0.3.
3.- Continued.
9.1-26
DEGREES
90
10
130
_l
L
-- 1.5
1
-- 1.0
1
--.5
Correctsd
0
Strouhol
I
I
I
I
.5
1.0
1.5
2.0
Nurr_m'.
log m S=
I
L_
o
oc
-45
_"/
\_
160
170
180
JD
i5
J-
:_ -s5 --75
--2.0
[
-- 1.5
[
-- 1.0
I
[
!
i
I
--.5
0
.5
1.0
1.5
Corrected
(d)
Tj/T
StrotJhol
= 3.0;
Figure
9.1-27
3.-
Nun"_e'.
logic
lOqlo v_ = 0.3.
Continued.
S,
J
2.0
la,.
"130
_'120
--4_
--5
_-_
-2.0
1
-,.s
1
-_.o
I
-.5
Correctecl
-4:_
._L#e
-_
--2.0
1
o
Strounol
I
.s
Numoer.
I
_.o
1
_s
I
2.0
IOg_o S,
_ "180
"170
1
1
I
I
--1.5
--1.0
--.5
0
Corrected
(_)
Tj/T
Figure
=
Strouhal
3.5;
3--
1
.5
Plumber.
ic_l
0
V_
Concluded.
9.1-28
=
Iogso
0.3.
I
I
I
1.0
1.5
2.0
S,
0
,--m
&,-
Cn
_,
t..i
_-
"o
,-
>',
=
>
o
<
o--
!
0
_.-
0
0
I
.,-4
0
[
_J
El °tB°l
I
L
0
0
O L 'le^e7 X_,!^.P,
ogJ!(]
9.1-29
Z_
.....
mo
ur)
o
0
c
o
0
__
m
O
=
d
8
t_
o
_
E
O
E
u
_
I_"
IlJ
e_
e
-
u_
I
"-4
0
I
m
m
I
--2
u'3
I
I
[
0
.,--
I
0
I
I
I
0
,-
0
04
0
F'_
I
I
I
._ °LfiOl 01, 'l_^e7
uJn_0eds
9.1-30
m,,..z_...
Io
I
J
o
0
.-i
I'--- -_
C
E
x
I,-
E
I
O
O
O
U3
_4
8P
_'"S
'uo!ssajddns
wnw!xol_l
9.1-31
___:_L._
0
t
______.__L___J
o
0
u')
SV
'J°_°°3
u')
I
uo.qoajJo3
CD
u')
,__
I
I
uo!ssajddns
9.1-32
0
c,i