BOOM MICROPHONE 4. IMAGE PROPELLER. W. 0::: 500. ::> en en w. 0::: 0... U. 0 ..... ~ en. =>. C) u a: -500. 0 a. 150 a... :::t 140. 0. C"l 130. (l,). L-. CD 120. "'0.
NASA
Technical
Memorandum
88993 NASA-TM-88993
19860021866
ADVANCEDTURBOPROPNOISE PREDICTION-DEVELOPMENT OF A CODE AT NASA LANGLEYBASED
ON RECENTTHEORETICAL RESULTS
F. FARASSAT, MARKH. DUNN, AND SHARONL. PADULA
JULY1986
FoR REF_,_ENCE l_CTTO_ TA_g/_FIIO._!71IIS I_00_
[I [IA[tV t}0Pg
• NationalAeronautics and Space Administration Langley Research Center Hampton, Virginia23665
L__N IGLEY RESEARCH CENTER LI_xARY,NASA _,*.,_,__[..0_L .VIRGINIA
INTRODUCTION
Advanced back ,_
are highly
and run at supersonic
shown
that
turbofan design
in cruise
of advanced
turboprops
and manufacture
of these
turboprops
prototype
I.
saving
compared
designs
employ
One major design propellers.
interior
noise
This
handling.
One of the most [2].
the blade
as input.
effects
Development
useful
pressure
procedure propeller
such as fuselage
with
based
prediction
both
has made
it
substantial
data
is the acoustic
major
and codes
codes
noise
the cabin
analogy
geometric
several
or boundary
of each of these
frequency
on the acoustic
acoustics
The
of blades,
involves
to propeller
scattering
be Substantial.
large memory
utilizes
the
airports.
which
of noise
in addition
aerodynamics,
and verification
tools
will
of discrete
around
with
and they get into airline
to reduce
modelling
procedures
data
Thus a typical
such as propeller
computers
realistic
Noise prediction
surface
physical
On the community
of •high speed
to use sophisticated
is required
have
associated
(contra-rotating)
is the prediction
prediction
possible
airliners
one or two rows
problem
and the impact
The availability
to today's
studies
than the current
problems
are overcome
that are swept
Many
is higher
if the technological
the fuel
with blades
condition.
In fact,
of these
data
propellers
[I].
current
analogy
loaded
tlp speed
the efficiency
designs
service,
Fig.
turboprops
require
and kinemati_
prediction
which
model
codes other
laye r propagation.
is time consuming
and
expensive. This .
paper
describes
a computer
developed
at NASA Langley
acoustics
of high
on recent
signature
is then Fourier
analyzed
of the noise.
The blades
to the overall formu]atlons
which
noise
are used
are divld_d
into panels
of the propeller in the code.
prediction
theoretical
is in time domain
spectrum
Two acoustic
and based
noise
The computation
pressure
panel
Center
propeller
speed sources.
acoustic
of each
Research
code for advanced
to obtain
work
resulting
The code selects
in
the acoustic
and the contribution
is evaluated
on
Individualiy. one of the
2
two formulations
depending
time of a blade
examples with
process
of this
paper which
data.
In the appendix,
frequency
module
several
which
in using a more gained
recent
codes
noise
from
in development
two formulations
Wllllams-Hawkings Because noise this
source
of other
of the thin blades
noise
the nonlinear
Following
effects
evaluation that,
the acoustic
with
compared
the inclusion
analogy,
ANOPP
(see
acoustic
discrete
formulation.
here
is a
frequency
It is built
noise
on the
at Langley.
and loading
to thickness However,
propeller
[6].
source
terms only.
designs,
quadrupole
noise
the authors
do not claim
for advanced
effects,
of the Ffowcs
and loading
of the present
of nonlinear
can be explored
incorporate
at NASA
ANOPP
The code reported
advanced
negligible
of the effectiveness
of the discrete
of NASA,
are the solutions
thickness
in prediction.
are entirely
derived.
FO_TIONS
of the current
to be small
is not included
codes
of the code.
been developed
codes
rotors),
in the coding
(FW-H) equation
is believed
careful
used
prediction
the present
speed
have
.
on comparison
are briefly
for prediction
by researchers.
high
Several
in a section
and propellers
(helicopter
differs
in the first
and implementation.
are given
T_IEORETICAL The
at the emission
is described
used in the code
rotors
ROTONET
prediction
theory
computer
they are verified
program
experience
factor
show some of the capabilities
The two comprehensive
after
stand-alone
examples
of helicopter
[4] for propellers)and formulas
cover
the two formulations
noise [3].
noise
of this program
These
In the last decade,
Langley
of propeller
of applications
measured
of the Doppler
panel.
The entire two sections
on the value
code
perhaps
propellers.
[5].
Hence that
Rather,
is recommended. without
the use of
a
• °
3
Experience
.
in development
no single
solution
propeller
noise
reason
factor
I-M r .
must
efficiently
coded
blade
shape
to handle
should
using
time domain care
advantage
of using
published
number
time domain
is described
calculated
These
A very
of this paper.
many
by f(_,t)=0
MrO.
F=[f(_,r)]re t and K=[k(_,T)]re the edge
M2 n )QE + MnMau] }ret dY
[(P +
equation
(FW-H)
written
One with
,
sources on the mean surface [10].
The resulting expression for an open surface
is
I Q'F 2_pi(x,t). = Ff=0 r m
rMnMt"_
r L [-A--]retdr" - F f=0 I m
K>0
_
7 ]retdY
(4a)
,
_
K=0 Q
ApQ_ 4_pi(x't)" =
-f=0 _r F m K>0
I
[-_--]retdl
I
+ Ff=0 r- [_ (b_A-_ b - --cA;)lretd£ m K>0
APb v
+ F=0 f ?i [_]retdY o
,
(4b)
m K=0
In
the next
section
the method
of coding
of these
formulas
on a computer
is
presented.
IMPLEMENTATION ON A O3NPUTER The
first step
the blades. Ref.
[3].
blade
The geometric A blade
as follows.
propeller taken
in coding
The origin
axis and the blade
is taken normal
is right-handed.
(2), (3) and (4) is geometric
modelling
is described
at the propeller
ql-axis
Eqs.
shaft
of the present
in a Cartesian
of the frame pitch change axis
(B3),
to q2q3-plane
The chordwise
frame
code is similar (q-frame)
fixed
is at the intersection axis.
pitch
The three
change
axis
in such a way that
direction
modelling
axes
of
to that of to the
of the of the frame
are
(q2) and the the q-frame
is thus parallel
to the .)
q l_3-plane. To
specify
as a function
the blade,
of radial
the leading
distance
section shape and geometric number of radial stations.
edge cur_e, of the blade
q2 along
pitch
angle of attack The blade shape
change
axis.
is first
defined
The airfoil
(pitch) is then specified is constructed by
at a
7 laying
the airfoil
leading
sections
at their
edges on the leading
edge
unit normal
and the principal
information.
Blade geometric
which
may require
_
discussing
summing
the pressures
passage
frequency).
panels.
calculated
are discarded.
only
and declsion
This
and some
helical taken
inner
be made
constant
The mesh
the distance
from
unity
the blade
Formulation portion,
location
from one panel
divided
is
the saved
geometric for panels
be used.
Formulation
cut where
The input variable of the cut below
to be used while 3 must
be used.
of the blade
of lines
edge
by a chordwise
the sonic
line.
from
is with
leading respect
edge.
on the
for some of the A coarse
(or on the mean
in chordwise
the
€ (usually
in this way is that for all the panels
I-A needs
distance
leading
(i.e.=l-_).
surfaces
consists
nondimenslonal
and
on the blade
is first
I-A or 3 must
one
by shifting
(3) and (4) are used
into two portions
the exact
out on the upper and lower required.
of
of the code will now be presented.
is near
determines
on the outer
Before
of blades
(based
and then
as to when Formulation
is first divided
only
Eqs. (2),
2.
of only
is calculated
is predicted
of the blade
then
signature
a period
the sound
or as a table
into Panels
for dividing
portion,
panels
must
number
as 0.05)
The reason
revolution
Essentially,
of the Blades
Mach
requirement,
this
in Fig.
times as the number
the noise
such as the
on the method
The pressure
time within
for which
memory
other details
The blade
observer
The blade
for one complete
data
Division
in time as many
is shown
blades
their
code.
a few remarks
for several
from
analytically
program
be made.
and with
parameters
are then calculated
in detail,
will
for each
To reduce
geometric
can be specified
The signature
for one blade
of attack
to read into the computer
on the computer
the signature
angle
Blade
flow chart of the computer
is calculated.
into
data
some parts of the code
implementation blade
curve.
curvatures
interpolation
A simplified
prescribed
direction
mesh
surface)
and curves
Nondimensionalization
to the local
is laid
chord.
as
of of
The general
8
shape
of a panel
remaining
at the same
inner
and outer
panel
(see below subdivided
smaller
the coarse
panels,
is made
however,
mesh
to the leading itself.
to use different If Formulation
to select
into smaller
in chordwise
as the panel
of the blade.
for criterion
two edges
parallel
position
Provision
portions
for generating
edges
radial
panel shape.
further
with
two edges are approximately
directions typical
is a parallelogram
panels
formulation),
by exactly
on the blade.
the line integrals
direction.
The
and trailing
edge
See figure
panel
sizes
for the
3 is required
for one
then that panel
the procedure
Before
3 for a
the blade
" -
is
described
above
is divided
into
(of Eq. (3) or Eq. (4)) over
the
are evaluated.
Emission
Time
Calculation
The emission and the decision finding
making
the emission
position. times
time calculations process
time
The equation
program
curve
turned
circumstances
which
Considerable
equation
were
the blade leading
helical
speed.
Indeed,
The equation
of observer
emission
and a
code for this part of the several
making
for
time and
of a parabola
exceptional
and additional
to ensure
all roots
technique
similar
of the present the emission
be considered
emission
calculation
lines
of
of the emission
time
to that of references
_]
this equation.
of finding
edge will
and multiple
supersonic
A numerical
case
function
of a reliable
decision
of the precision
difficult
selection.
of intersection
was spent
for solving
As an example
single
effort
in the acoustic
in such a way that the required
difficult.
require
calculated.
employed
particularly
Development
out to be very
coding.
and _]was
is transcendental
of the points
[3,4].
occur
for formulation
can be written
are the abscissas
sinusoidal
are needed both
times
condition
time routine,
times of a small
now. " This segment
at the selected
Its operating
emission
observer
segment
which has time,
is recorded
a
both
is moving
in Table
of
I.
at The
9
SR-3
blade
distance
planform
along
segmen t were that
the edge.
calculated
the inboard
the rest
is used.
Figure
The emission
portion
of the line has three
curve
that looks
like a straight
these
two pieces
of curves
of precision
Criterion
supersonic noise
I-A, i.e.,
integration
are first determined
emission
time,
is used
by replacing
the E-surface
care
is required
integration
Formulation
to extend
into smaller
the source
numerically
for each
for which
of is an
Formulation fine-sized
sphere
for
in Fig.
(G-L) 3b.
The
If a node on
for that panel.
Only
at its
3 is used as follows. panels. This kind
method.
Equation
of integration
Again
to capture
(3)
considerable
all the
can be more
than one
in integration. 3 is used at three
also shown
shown
in the
(I-A or 3) for
at each node
this surface
Fomulatlo_
signature
The panels
3 is used
time integration
be included
panel
as shown
from Eq. (AS).
In particular,
must
panels
only.
The smoothness
to 100(10xl0).
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