/. t
)
/
I _: _'_' L_ r _ !
, ' _ / _ ,
/'
NASA Contractor Revort 159379 (N_.SA-CR-1593'?. 91 _. STUD( Ol OP_iUm COWL SHAPES ARD IL(,: _ORT LOC._TZONS _OR BINI_U8 DR_G WITH ETFECTI.VE ENNINE COC_I._G, VOLUME ! (North Carolina State Univ.) 119 p HC _06/M_ A01 CSCL 01_ G3/02
_83-16288
Un¢las 025q7
!
ii, _ ,
ASTUDY PORTLOCATIONS OFOPTIMUM FOR MINIMUMDRAGWITH COWL SHAPES AND _LOW
!: i_i
EFFECTIVE ENGINECOOLNG- VOLUME I
!' ,: ,, I:
Stan R. Fox.and Frederick O. Smetana
?-. )
i _:F
NORTHCAROLINASTATEUNIVERSITY Raleigh,NorthCarolina 27650
f t: L
NASAGrantNSG-1584 November1980 RELEASE DATE:
PUBLICLY RELEASE-ON_JANUARY31.
NationalAeronauticsancl SpaceAdministration Llngley Relur©h Center Hampton,Virginia23665
g='-' ,,==
1983
7.
+.
p
'
/
....
flOSTRflCT
+
_._
_l
The successful
I:_
craft
?._
present
work represents
:_i
through
an analytical
t
shape
depends
prediction
of the
heavily
engine
of
the performance
on an accurate an effort study
of
estimation
to reduce the
cowl and the
the
contributions
forward
of a new or modified of its
lift
and drag.
cruise
drag
of light
to
fuselage
the
area
drag
arising
and also
that
airThe aircraft from the resulting
from the cooling air mass flow through intake and exhaust sites on the nacelle. ii:l
It contains descriptions of the methods employed for the calculation of the potential flow about an arbitrary three-dimensional body with modifications to
include the effects of boundary layer displacement thickness, a nonuniform
onset
flow
field
(such
as that
due to a rotating
propeller),
and the
'i
of air intakes and exhausts.
_:*
automated scheme to better define or chanse the shape of a body.
!..i
A technique
has been
presence
It also contains a simple, reliable, largely
developed
which
can yield
physically-acceptable
skin-
friction and pressure drag coefficients for isolated light aircraft bodies. For test cases on a blunt-nose Cessna 182 fuselage, the technique predicted drag reductions as much as 28o5Z by body recontourlng and proper placements and sizing of the cooling air intakes and exhausts.
! I
•
I
i:I_ _/ I_
if:
I
h
%
_.
o
TRBLEOFCONTENT$
i !i
i"
_
Page
TABLE oFCONTENTS ............................ LIST OF FIGURES
iii iv
_eooooooeoeeeeoeoeooooeoeeeoe
_;.
:_
J
INTRODUCTION
oeooeeoeoeoeoooeeeQeoeeeoeooee
i
?}
r ) /.
THEORETICAL APPROACH OF HESS AND SMITH FOR CALCULATION OF THE POTENTIAL FLOW ABOUT THREE-DIMENSIONAL NON-LIFTING BODIES BY A SURFACE SOURCEDENSITY DISTRIBUTION METHOD........................
3 ...... •
BOUNDARY LAYER SIMULATION FOR BODIES IN AN INVISCID POTENTIAL FLOW FIELD .................................
i0
PROPELLER WAKESIMULATION ........................
i8
FLOW PORT LOCATIONS FOR MINIMUM DRAG AND EFFECTIVE ENGINE COOLING ......
39
A GRID REFINEMENT SCHEME FOR THE MODIFICATION OF A BODY'S GEOMETRIC DATA
51
_.
COMPUTER IMPLEMENTATION OF METHODS
68
! i _
DISCUSSION OF RESULTS ..........................
...................
69
CONCLUSIONS REFERENCES ...................
ii0 , ...........
111
li
'
LIST OF FIOURE$ Page
•
1.
Body surface
2.
Notation used in describing potential ............................
3.
represented
The approximate quadrilaterals
by an equation the
Displacement
thickness
5.
Illustration
of
6.
Definition
7.
Velocity
8.
Formation
9.
Hellcal-sh_ped
surface
the
form
S(x,y,z)
= 0 .
.
4
source-distribution 7
representation .........................
4.
of
\
of
to
strips
of wake body
body
surface
by •
addition
separated
the
a body
of
.............
elements
9 13
............
14
......................
15
]
11
I0.
induction
by element
of three-dlmenslonal
by free vortices
of the wake surface
of vortlclty
vortex
Motion
of
13.
Mutual
influences
14.
Leapfrog
15.
Doublet
16.
Matching
17.
Denotation of first and last body axial station of point numbering .....................
action potential doublet
of of
......................
vortex
two
two
ring
fre_
to
...................
vortex
vortex
flow
circular body
.........
19.
Vortex-ring fuselage
distribution in the wake
and diameter • propeller
Schematic
of cowl
interior
21.
Typical behaviors of parameter variation
the
,
.....
27
..............
28
....................
Equivalent
20.
27 .........
rings
18.
of
25
vortices
definition flow
" 24
12.
31 ................
33 with
illustration •
• •
, ............ variation ...............
about
an
34 36
aircraft 38
......................
40
interior pressure ..........................
coefficients
i
23
with a constant
Application
ring
20 22
................
11.
a single
rings
. • .
...............
System of trailing vortices of a propeller clrculatlon ........................... of
rlns vortex
with
V
PRiJCEOINQ PAGEBLANKNOT FILMED
48
,!
LIST OF FIGURES (continued)
22.
Schematic of-indexing panels .describing
Page
scheme used the half-body
for,a, 3-I .............
ellipsoid.with
40 . ....
• 52
7, i
23.
Typical translation system ..............
and rotation
24.
Coordinate
_
25 .
Exampl eS
::
26.
Example of equal-line
::
27.
Example
28.
Example of a three-view
29.
Example of a oblique
30.
_-xample of a perspective
31.
Example of
32,
Results of Cessna 182 fuselage (power-off) ............................
33.
34.
Of
i spur-
for
data
averaging
modif£
c
ation
•
ausmnCsCion
of user-specified
techniques •
•
.
scheme
orthographic
stereoscopic
•
•
•
.
.
•
•
•
•
.
58
61
.........
.......
.......
............
63 64
................
6S
.................
model with
66
uniform
flow 82
Results of recontoured Cessna 182 fuselage flow (power-off) ......................... Results of blunt-nose Cessna 182 fuselage flow (power-off) ..........................
model with
uniform 83
model with
uniform 84
Results
of ATLIT fuselage
36.
Results
of ATLIT nacelle
model with uniform
fl_w
(power-off)
....
86
37.
Results
of a fat
model with
flow
(power-off)
....
87
38.
Results of Cessna (power-on)
39.
40.
41,
nacelle
model with
182 fuselage
of recontoured Cessna. (power-on) ................
Results flow
of blunt-nose Cessna (power-on) ................. of ATLIT fuselage
uniform
flow
(power-off)
model with nonuniform
, • ,
85
flow 88
Results flow
Results
uniform
182 fuselage
182, fuselage
model_with
model with .nonuniform . .............. model with-nonun__form . .......
nonuniform
I :
59
scheme
projection
projection
•
54 57
.............
projection
projection
•
.......... •
line-au_nentation orthographic
coordinate
35,
_,
! '_
information
scheme of reference ........ ..............
flow
(power-on)
89 ..... 90 , ,
91
:I
_!
LIST OF FIGURES _continued)
,_
Pase
42.
Results
of
&TLIT nacelle
model_w/th
nonuniform
flow
(power-on)
.
.
92
43.
Results
of
a fat
model
nonuniform
flow
(power-on)
• • •
93
44.
Results flow,
of blunt-nose Cessna 182 fuselage model (nonuniform 74.563 kW power, intake and exhaust ports) .........
94
Results flow,
of blunt-nose Cessna 182 fuselage model (nonuniform 100.66 kW power, intake and exhaust ports) .........
96
Results flow,
of blunt-nose Cessna 182 fuselage model (nonuniform 223.69 kW power, intake and exhaust ports) ..........
98
45.
46.
47.
48.
nacelle
with
Variation of total drag coefficient nose Cessna £uselage model with sites .............................. Comparison of wind-tunnel
drab tests
coefficients ........................
CD with power for bluntfixed intake and exhaust 100
between
prediction
and 100
49.
Behavior
of
pressure
50.
Behavior
of
drag
51.
Results of blunt-nose Cessna 182 fuselage flow, 74.563 kW power, 0.023 m 2 initial exhaust sites) ..........................
model (nonuniform EOA, intake and
Results of blunt-nose Cessna 182 fuselage flow, 74.563 kW power, 0.046 m2 initial exhaust sites) ..........................
model (nonuniform EOA, intake and
Results of blunt-nose Cessna 182 fuaelase flow, ?4.563 kW power, 0.093 m2 initial exhaust sites) ..........................
model (nonuniform EOA, intake and
Results of blunt-nose Cessna 182 fuselase flow, 74.563 kW power, 0.93 m2 initial exhaust sites) .......................
model (nonuniform EOA, intake and
52.
53.
54.
coefficients
coefficient
with with
vii
.
ef£ective
effective
orifice
orifice area
area
.
.
.
......
101 lO1
102
104
106
, .
.
108
_
_
The successful craft
depends
prediction
heavily
of
the
performance
on an accurate
of
estimation
of
a new or
its
lift
modified
and
air-
drag.
Althoush
i
the
importance
and most
of
o_ wind order
to
For
some
time
have
aircraft.
some the in
of
and
-
to
These
from due
the
ensine the
coolins
nacelle.
Since
8eneral
aviation
consumption advance
in
of
air
efficient operations, a variety
technolosy,
performance of
these core
the
i,I :
rules
of
Several
five
to
without
ten
shapes
flight
an effort study
of
reduce
forward
fuselase
flowing
throu|h
intake
is
aircraft
the
to
-
_.
._
reduce
sacrifices points
without
cruise
procedure
to
area and
an increasinsly
through
years
startinB
contributions
the
use
large
the
expen-
tests.
to the
light
•attempts
sis_ificant
aircraft
and
comof
consume
storage.
new or modified tunnel
disital
characteristics
techniques
last
estimates
any desisn of
personal
high-speed
suitable
fuel
manufacturers semi-empirical
with
provide
and
mass
the
within
represents
shape
alons
advances
an analytical cowl
on the
data
computer
these
wind
work
through
to
perfozm
aircraft
utilizing
most
and
made
"test"
test
predict
accurate,
been
lish_
essentially
flisht
technolosical,
to
The present
depend
techniques
time
have
many
estimates.
to
quite
time-consumin8
aircraft
and
available
designer
to
sophisticated
required
the
recosnized,
these
computational
accuracy.
sive
develop
been
successful time
for
tunnel
Although
amounts
is
continue
in
puters
data
universities
correlations thumb
these
drag the
and
dras
as well
exhaust
sites
important which
a dra8
can
clean-up
lower is
of
lisht
arising as
that
on the
factor
in
the
fuel
i
a welcomed i
ii r:-
latlon
of the
i:
appropriate over
flow
produced
_
exhaust flow
modifications
the body,
_i'
!i
potential
Thisrep_°rtc°nt_nBdescr_pt_°ns°f"the_eth°ds"_P_°yedf°rt_ecalcul
about
an a_b_trary
three-dlmenslonal
body with
i
1
solution
second
kind,
field,
and the
ditious
the effects
onset
propeller,
flow
and (c)
on the body for
engine
is
by a solution
accomplished
while _he effects air
intake
to the Fredholm As an aid this
report
geometry
scheme
techniques.
digital
computer define
(a)
about
the presence purposes.
the boundary
!
of air
'_
of a Fredholm
sites
are
intake
and
potential
equation
.'
of the
the nonuniform
included
-
the body - typically
The basic
layer,
layer ....
flow
as the boundary
ii con-
:
equation.
also
of the
discusses
Being program
field
cooling
and exhaust
to augment
various
of
of the boundary
in the preparation
lations,
to better
include
(b) a nonuniform
by a rotating sites
to
and/or
or change
a simple, to modify
expenditious
- is the
input
reliable,
tool
potential largely
the body shape
and inexpensive,
a valuable shape
data to
to the
of a complete
flow
automated
information
this researcher
calcu-
scheme
by - a
who wishes
body or of regions
1
!
on the
body of particular interest before beginning the potential flow calculations.
.
2
_
:i:i i if
CI:iLCULRTZON_OF POTENTZML FLOW ,MOLLT THREEDZHEN$ZONnL NON-.I.IFTINOBODIE$ BY SURFRCE
The
problem
i)i
incompressible,
"_i!!
If
Ii.
Navier-Stokes
the
underconstderatton invtscid
fluid
density
fluid
is
_
fluid
to
+ (_
,:, , k' , ?
where
velocity
il
and p is the fluid pressure.
that
the
the
potential
the
Eulerian
any
is
I grad
p is
point,
zero,
equations
=
The continuity
flow
of
three-dimensional
viscosity
• g rad)_
at
of
an arbitrary
and
reduce
_!
the
about
constant
equations
V is
is
body.
the of
an
':
general
motion
:
p
the
(1)
constant
equation
fluid
density,
.,,
becomes
3 i
i '_
div(_)
(2)
= 0
i
_
_
All
body
forces
are
in the pressure.
assumed
Therefore
the flow field exterior
the
denote
the exterior
boundary
sented
of
the
conservative
equations
of
the
x,
y,
assumption
and
z are that
the
the
their
potentials
(I) and (2) are valid
R). the
The body
absorbed
expressions
for
surfaces.
the flow about a Chree-dimenslonal
is
body surface,
the surface of the body
assumed
to
have
a surface
let
(also repre-
form
s(x,y,z) where
and
flow field and S denote
region
by an equation
be
to the boundary
In order to discuss R'
to
Cartesian location
= o
coordinates of
all
boundary
(3) as
depicted
surfaces
in are
Figure known
1. and
Under that
I t
3
i
.
•
• ,
•
. _i:_1._,/
•
r
J
, ....
_
,4,, • -, ,.,_
, .....
_
,/ I
R' •
Z_
t
X
i!
![
Figure
?
1
Body of
_
surface represented the form S(x,y,z)
by = 0
an equation
!
,
i Li
the
normal
o.omponent
the
boundary
of
fluid
conditions
velocity
may be
is
given
n is
function
of
at
infinity
is
assumed
is
not It
the
unit
position must to
be
essential
flow.
Since
ality,
the
be
for
a uniform the
potential
the
stream
general that flow
approach
at To be
exterior
of
unit
(4) a point
on S and
complete, flow
a known
a regularity
problem.•
magnitude;
F is
condition
The onset
however,
this
flow
W
restriction
derivation. the
is to
boundaries,
s- F
vector
or both.
imposed
be noted
usual
normal
or time
to
should
outward
on these
as
• where
prescribed
above
equations
a consequence
determine
the
of
do not the
equations
define
condition of
potential
a potential of
irrotationflow
is
to
__i•
"_"
, '/__"w_rr'_' _
_--_' ........ .......... ..... "_;_'_'_'r"n•,
.....
......... "" t'f _-. ,_.L- _,. _', , ._,_ _-r_--. '__
" _ :, _ r_' __"_._
__,r_ I ¸_._:_tr_J'-_g"7"_ ---o:_-_....v. _'"m'w'_Wt'_Y='_'"'_U_"_. i ¸•
•
.•
_"_'_," _.... "_'_'_.,,r---,_. "'_:"w._w_._,t_.';• °_
_'____.,
!
OFpOOrQU_Li'I'Vi'
. !
assume.Chat the velocity
["i.
field
j_ r:.-
can be expressed
field 8s
_ Is trroCtt_onal
the ne$attve
and therefore
sradtent
of a scalar
the velocity
potential
function
14: i;
'
Lettins
!,
onset
_..
boundaries,
c:._
where
"'
flow
the velocity _
and the
field
_ be the sum of
perturbation
velocity
field
::
ttnuity
incompressible
_ due to the surface
1] ,,
v " - srad
Since
uniform,,
then
i!: i:j:
,.-
the
the
onset
flow
equation
(2)
and the is
::_!'
perturbation
qb
flow
(6)
are incompressible,
the con-
satisfied:
dtv(_®)
i 0
dtv(_)
o
I.
ii_ _
As expected,
the potential
I satisfies
Laplace's
i!
equation
!,ii
v2, - o in the re8ton tions
It* exterior
to surface
S.
(7)
By equation
(4)
the boundary
condt-
:il 1
]
:..I
on _ become
srad and the
resulartty
condition
_ "
for
"
_nIs
hie the
exterior
{grad O{ * 0
" _
(8)
p_oblem.becomes
at infinity
{9)
i.t 1
l,
t
Therefore
equations
I
equations
to
ill
be
(7),
velocity
field
If
of
i l !
be determined
!ii
(7)
iii
number
i 'i
ficulty
f!_
solution
L
body
above,
is
!.
the of
(6).
useful
exact
be
surfaces
distribution
*
theorem.
Ii i!!
and
_
are
II•.
the potential ....
now
problem
an integral
a unit
point
yq,
give
and
necessary
Zq in
derived
is
not
pressure. all
used,
Even partial
potential
is
the
flow
the
and
the
velocity
because
equation
of
indirect* the
r(P,q)
the the
various
i
dif-o
methods
i
Of
prescribed
conditions.
is
to
2.
equation
can be accomplished reduce For
located
Figure
to an integral
at
the
a point
At a point
by the use of Green's
potential
a single
for a sovrce-denslty
flow
equations
three-dimensional q whose
P with
Cartesian
coordinates
(7), body,
(8), con-
coordinates
x,
y,
and
z,
due to this source is
_
I ¢ = r(P,q) where
_
may
equations,
small
from
_he
condition
Laplace's
Therefore results
that
and
thoush
quite
fact
(2)
differential
conditions.
satisfactory
from
equation
solutions
equation. source
is
(1)
known of
of the problem
to
Xq,
the
on the body surface
The
the
continuity
boundary
and boundary
!I
the
analytical
to
flow
equation
of
the
used
The reduction
sider
Thus
and best
satisfying
must
(9)
by
independently simplest
in
represent
potential
determined
irrotationality
is
(9)
and
solved.
As demonstrated
Ii
(8),
is
the
distance
between
points
(10)
P and
q.
The solution
is
, Indirect or exact numerical methods contain the exact analytical fo_ulation to the problem and have the property that the errors in the calculated results can be made as small as desired by refining the numerical procedures. Approximate methods containanalytical approximations in the formulation itself and thus places an accuracy limit on the results regardless of the numerical procedures used.
6
i i
Figure
2.
Notation
used
in
describing
source-dlstrlbutlon
the
surface ,]
potential
]
constructed
of elementary
sources.
The resulting
tion
(7)
such
a potential
equation
S.
at
all
is
except
that
is
satisfies
of considerable
uous source
distribution
Let a(q) now represents tribution
potential
points
(9) and
It
potentials
be the
a general
q.
internal
above
of
the
or upon the (7) in
importance
source
the
linearity
resion
the
and satisfies ef
the
surface R'
of
that
potential
equa-
problem,
S satisfies is
external
to
of a contin-
S.
distribution
on the
(9)
boundary
todetermine
surface
form of an ensemble
equation
Because
equation
point
the
satisfies
on the local
of
intensity,
surface
S.
where the
The potential
point
of this
q dis-
is
¢
"_r(P,q) S
dS
(11)
7
-N.!
'i
By the
procedure
_.
equation
(11)
_..
by permlttln8
BSv_n.byKellos8 Is
[3],
dlfferent$sted,
the point
the
and the
P to
approach
pertutbaclon
boundary
a_polnt,
potential
condition
(8)
q on the surface
is
aSven
applltd S,
by
to
it
The result
"
! '
,
is
the
following
integral
equation
for
the source-density
distribution
o(p):
t
[.
2_o(p)
I: !:i _i:
I l: L
;_i I
li
-
o(q)dS
= - _(p)
• _. + F
(12)
,.
a where_denotes surface S at
differentiation in the direction of the outward normal to the point p, and _(p) is the unit outward normal vector (written
the
on
expllcitly to
show its
dependence
location).
Equation
(12)
is
a Fredholm
integral equation of the second kind over the boundary surface S. The method of solution of Equation (12) is demanded to be numerical
rather
than
arbi-
analytical
trary.
by the
The solution
fact
that
the
domain of integration
can be accomplished
by first
is
completely
representing
the body
surface by a large number of small quadrilateral elements or "panels" (Figure 3).
On each
quadrilateral
a control
are calculated. whereeventually the boundary condition
point
is
selected
(usually
the
centroid)
A is"matrix influence consisting to be of satisfied and coefficients", where surface velocities
of the complete set of velocities induced by the panels at each other's control points, is then determined. mated by a set strengths value
o_ linear
algebraic
on the panels.
of constant
source
The integral equation (12) is now approxi-
Since
equations each
strength,
panel
for is
the values
assumed
of
the source
to have an independent
the number of unknown parameters
(source i
strengths) linear
equations.
parameters numerlcally
8
equals
the number of panels Once the source
may be calculated. "exact"
This
and applicable
or,
strengths
more specifically, are
implementation to any arbitrary
the number of
determined, renders
the desired the
non-liftlng
method
flow
I i
as
body.
!_
9
IlOUNDIYLira[It8ON i
ZNM INVISCIDtTI[NTL
Because numerical this i _I
the considerations
solution
time.
layer real
of
of the
Yet the problem
flowing viscous
over flow
effects
numbers, layer
adjacent
body. where
the effects
the
is
flow
sufficiently
times,
equations
is
an "exact" not
the characteristics body is
feasible
at
|
of a boundary
of great
interest
i
if
are to be approximated.
unseparated
flow
of viscosity
are
surface
discussion
will
incompressible
small
Havier-Stokes
three-dimensional
to the body's
The following
FLOHFZELD
computation
of determining
a general,
For essentially
of large
complete
i
FORBODIES
about
a body at practical
important
in a very
thin
and in a thin
wake downstream
be restricted
to the
or where the
to be handled
only
Reynolds
by simple
correction
of the
low-speed
compressibility
boundary
regime
effects
are
to an incompressible
flow method. _
Smetana e_.tta__l. [4] and Hess [5] utilized a method of a two-dlmenslonal boundary that
I
layer
simulation
of surface
ducin8
displacement
a thicker
the original
_echnique
expounded
or flew
body by adding
reduction,
the boundary
body in the direction
by Lighthill
along
essentially layer
[6].
This
consists
displacement
the local
normal
method, of pro-
thickness
to
to the body surface.
I
i
The potential
flow
about
this
modified
body is
thus
the desired
potential
reasonably
accurate
flow
1
to approximate the body's
viscous
cross-sectional
flow
effects. area
This
method
is
and volume
do not
change
rapidly
if
in the streem-
r
wise
direction,
direction, 125-132). 10
if
and if
no significant the wake is
pressure adequately
gradients modeled
(see
exist
in the cross
Smetana
e_t.ta_l. [4],
flow pp.
,
!! iil
Since
ii'!
e ca__l.
_._
Invlscld,
the preach= work is eieontially
[_
of approximaclng incompressible
real
an extension
flows
flowmathod,
about their
light
of the work of 8moCana
aircraft
procedure
fuselages
for
the
with
calculation
!
an
'
of the
I .f_
_
I..!_
displacement
!i!i,
fuselage
!t_
is
generally
_
x-z
plane)
: _
simplifies
iI!
i! i il
thickness,
will
be discussed considered
rather the
boundary i
written
equations
on each points
_r
its
x-z
plane,
panel
major axis the
direction
condition
proportional
to the
may be used
by assuming constant
flow
is
and that
for the
are
the
a given quantity
panel
which
local
the
of flow
lines
flow is
the
generality.
equations the
fuselage
o£ a prelate and its
velocity
equations these
center
at
one point
(6).
At the
vectors
and whose lengths
determined.
streamlines; these
Its
describe
flow
velocity
directions
however,
dependent
across on the
(the are
The method for
of
computational
in a more analytical
direction
'
consideration
streamline*
of the
can be easily
(normally
two-dimensional
to be satisfied,
flow
these
to describe
is
a fuselage
three-dimensional
by a section
the
that
this
the
system
induced
(8)
magnitudes
Co sketch
desirable
that
by the
out
restricts
"simpler"
and nuagnitude
may be determined
also
above,
locally with
and drag on a
• or symmetry
but
coordinate
aligned
llft
Effectively,
to
fuselage
the
be pointed
apish
as mentioned
the
whose directions
it
should
of the method
streamlines)
purposes
ultimately,
of eyunetry.
curvilinear
where the boundary
isoclines
It
can be reduced
By representing
spheroidwith in the
an axis
conditions,
in a general
and,
briefly.
implementation
layer
surface.
shear,
to be a body with
than
Under certain
il
wall
this distance
fashion
panel
is
and average
*To adjacent streamlines form the boundaries of the flow of a given quantity of fluid. From the magnitude and direction of the flow over the surface, the position of these streamlines on the body may be determined. !
11 !
J
i
velocity
between
quantity
of fluid
is
increased
lines.
adjacent
for
Also,
streamlines.
Therefore
between
two streamlines
conversing
streamlines
this
assumption
is
seen
it
Is always
is
noted
that
constant,
and is
decreased
to be true
only
for for
since
the
thLflow
velocity
diverging
stream-
infinitesimal
_
panel
sizes. After iage,
fittins
as described
in general tion
a section
curvilinear
shear
the effects
using
means to
ere
of body curvature
describe
f
the body in terms of
the local
the reference
the boundary
layer
to a section
the boundary
used with
a momentum integral
necessary
spheriod
[4],
coordinates
i
as to write
the prolate
by SmetanaeCal.
to determine
and wall
of
the local
equations values
streamwtse
coordinate
Atthts
system
are
in a general
1
sec-
thickness
point,
and crossflow
fuse-
written
of the
on the displacement
formulation.
equations
layer
of the
the
coordinates
available(as
on
well
curvilinear
coordinate
system). To preserve displacement
the
thickness
metrics
of the general
curvilinear
must be added normal
coordinate
system,
to the body surface.
the
In essence,
J ] ;i
a surface
panel
to the value boundary t
of the
condition
the addition This
of
difficulty
1 and 2 co yield line* ficulty
i i i
is
dividing i8
translated displacement
the displacement is
quickly
two stripe
remedied
calculated
thicknesses
It is
of element8
by averaging
normal vector
ales
averaging
observed
now becomes
corresponding
of "line" space.
4, adjacent
may not have
by simply
by an amount equal
at the point
As shown in Figure
eliminated
a new point.
to its
thickness
was satisfied.
The connotation used above curves in three-dimen_ional simplicity in viewing.
12
parallel
panels
coincident
the
1
after
t
edges.
the new edge points
in Figure two lines.
points
where
on these
5 that Again lines
or "lines" actually represent The sole purpose of this usage
a single this
dif-
to yield
a curve is the
or
:_
Fisure
a sinsle
line.
recosnized Ii
in Ftsures
the panels.
system
are no longer
the surface Since
surface
of
this
pressures
The pressures !_
relatively
thickness
should
4 and 5 that Therefore
curvature
varies
method for
deteraintn8
end of the closed at the aft in this
low pressure
body.
introduced
from panel
it
always
As a result,
end of the body tnwhat
wake reston on the aft
is
8enerally
portion
this
8eneral
the pressures
one,
at
procedure
of the
The error rapidly
to a body
be mentioned
the metrics
preserved.
addition
the averastn8
the body is an tnvtscid
the downstream nation
Displacement
A word of caution
rotate
if
i
4.
less
point.
It
can t_anslate curvilinear
to adjacent
an___d
coordinate
may be quite
stsniftcant
!
panels,
and velocities places
is
i! over
the
a atasnatior_point
at
the method predlctsstasis
physically
than
a wake resion.
atmospheric.
of the body as opposed
I
This
to the hlsh
13
¥isure
5.
Illustration
of separated
strips
of elements
! pressure cion for
reKton
which bodies
is
near
coumonly
producln8
co represent
the nose
resolves
into
a force
known as form or pressure
reslons
of flow
the wake effects
separation
must be used
if
acttns
dra8.
It
in the flow
direc-
Is apparent
that
1
accurate
model
1
a reasonably meantnsful
draj
results
are
5
to
be obtained.
!
Smetana et
al.
physlcal
body since
relatlve
to
[4]
replaced
the physical
wake by a solid
the wake may be considered
as a reslon
of
extension "dead"
of the alr
!
14
the
resmlnln8
flow
fleld.
They also
assumed,
rather
arbltrarlly,
] ] i
:
6.
¥tsure
.i
Definition
of wake body
I
The pressures, the wake-body
as determined which
body are applied physical resulting a drag. generally inviscid on the
The pressures
forces
acting the
be less flow body.
drag and the
i_ediately
to the panels
body.
Since
lie
by the
on the
friction
the equivalent
integrated
on the rear
of
the integration drag
on the.body
onthose panels
body along over
portion
to find
of the
the physical will
of course,
of
on the physical
the body surface,
of forces is,
panels
the normale
body can be sunmed
on the upstream
those
The total
flow method,
physical
on the physical
colputetion,
skin
above
ere
pressures than
inviscid
to the and the
a Iift
wake-body
will
body according indicate the stua of
and
a net
to the drag
the pressure
i
drag.
q
L
15
_r ii ,'
The method discussed (1)
The surface large
(2)
All
st
number four
A source
of the
determines
normal
(4)
The resulting
(5)
The velocity
or
panel
of undetermined
over
are the
by the followLn8
represented panels,
moved into
the
condition are
body surface
is
solved
i a
through
'_ _.i
normal.
on each
Is required
'
.
same plane
of the
placed
steps:
by a sutf_ciently
four-sided
is
of equations
the
is
dtrecc£on
strength
boundary
system
characterised
fuselage
of quadrilaterals
which
prescribed
thel_by
the .isolated
corners
a procedure (3)
above *|
panel,
and the
Co be saClsfied.
for
the
calculated,
source
and the
strengths. streamlines i
and surface (6)
pressures
Two-dimensional,
are
determined,
i
momentum-inCesral-_ype
boundary
layer
computations
.:
i
are
(7)
performed
along
streamlines
ment thickness
and wall
The wall
is
shear
to find
the
local
values
o£ displace-
shear.
integrated
1 q
over
che surface
to
find
the
skin
fric-
I J
tion (8) _! !i
drag
of the
The body shape ins
fuselage.
is modified
by attaching
edge and by accounting
(9) A new set
of source
to the wake-body (10)
isolated
Th_eur_ace
for
the
strengths
shape
pressures
a wake-body
displacement
and surface
is
calculated.
are
Integrated
toward the trail. thickness effects.
pressures
to find
the
corresponding
lift
•
and pressure
drag, (11)
I.
The total and the
This i
in [4]. to
16
iterate
drag
is, determined
pressure
method does It should only
I _
from the
sum of the
skin
friction
drag
drag..
have
imposed
be observed
once because
1
that of the
restrictions the great
and limitations
boundary-layer
as discussed
computations
amount of work involved
were in
allo_ed
successively
i i
modifying
the _ody
displacement
thickness
the use made of methodts
dra8
adequately sradtents
shape
thls
over
such
tion
of the body,
well
to experimental
with
caution
and,
the
information
Co the that
flow
displacement
forward.part over
is rather
calculations
presented are
_o account,for
tnvtscid
the aft
flow
separation results
results.
Otherwise,
on experiments
portion
field
the
the
fuselase
computetion
quite user
only
small
and
8eometry
or if over
acceptable
the
is
pressure
_
_]
pot-
i
and compare
very
i
Judgement,
far
......
aft
must examine
and engtneertns
The
of the body in the present
If
tshmtnent are
effects,
the body Is usually
approximate.
the calculated
based
of
thickness
the results decide
their
reliability. i:!
i,
17
/
PROPELLER t#K[ $ZHULflTZON
'\
_ _
l
Flow visualizations aircraft
propeller
mathematically
of a typical
verifyChaC
exCrmely
wake (or
s_ipscremn)
prope=modelin$
difficult,
if
Sen•raced
by an is
of such • phenomenon
noC impossible.
For decades
i
_nvestii
sators
have been
mathematical the
scudy£n8
models
vake'-s
the
pzoblem
to ptedicc
Influence
made throush
this
on its
research
their It
devised simulate
nacelle.
differences
Is noC the
Chroush the decades the effects
In the the observed
its
rotors,
of this
report
of physical
Classical
*A prescribed wake is one chat is to form freely, A rtstd wake is
:i
!
havu been
by Stepnlewskt
propellers, the hovertns
Co expound
or co present
Co be utilized
concepts.
i
the wake and
advancements
summarized
ofrotors aircraft (in
adequate
[71.
assumtns of becourse mode) may con-
i
!
I
i
t
!
and understood.
of wake structures,
behavior
fundamental
. Stsn£ficant
on helicopter
of a chree-d_anensional study
within
to
th•c
body,
It the
methods
iS of concern
tnviscId
Co
potential
flow
commonly known as a prescribed, namely,
vortex wakes
on the various
a new one. wake upon
of • propeller-like
The method
calculations ristd wake.*
characteristics
surroundtnss,
are noted intent
co develop
the flow
sidered synon_nous chat Effectively, Co be the wake of with helicopter that
in the accmnpc
an aircraft
theory
is
espectally
can be mathematically
expressions
of the
fuselase
defined empirically rather one that remains invariable
or
useful
explained
Btot-Savart*
i
since Chrou&h
law can be
than •llowins with time.
!
l_!
1
it
z8
ii .i
'
I ORIGINAL OFpOORQUALITY applied of
yhen
the
vortices.,
The basic later
and
the the
definitions
relationships
ytloc£ties
and
laws
induced of
vortex
the
stranith
by Chem..in
motion
will
the be
and 8aometry
surroundin8
presently
fl
,,
stated
for
its
'_ _-
thoush
one
of
irrotationality,
few points, possible
It
to analyze
principal is
viscous
where
The vortlclty vector
the
necessary
of locally
fluid motio_
the rotatlo_
t_e
is a "vortex
is a vOrtex
following I.
2.
the vorticity
of vortex
alons the axis.
A vortex
filament
or_glnally &_ the
dlmens_o.al
tool
for
the
at every
It Is often
_i_
except
at
is always
point on that llne.
tansentlal.
cross-sectional
surface
(known
A _or_em
_i_a-
area, whose
.....
]
axis
18 soverned
the Blot-Savart
of
at all cross
that is, it mu_t
or form a closed
to conservative
will
determination
by the
and Kelvin:
of the motion
it
18 a llne in
area on whose
in an ideal fluid
fluid, _ubJect
vortex system,
A vor_ez
or tube cannot end in the fluid;
Irrotational,
a
to be twice the fluld rotation
filament or tube Is invariant
sections
_f an _nvlscld
which
of circulation.
filaments
extend to the boundaries 3.
motion in
irrotational,
vector.
vector
theorems or laws of Helmholtz The strenKth
flows
as beinK
tube'! with an infinitesimal
of vortex
consider
flo_ exit,
cross-sectlonal
line, and a finite value
The behavior
ideal-fluid
rotational
of the vorticlty
is a tube of finite
as a vorte_ e_faoe)
of
is concentrated.
or to be the curl of the velocity
A vortez
to
vector is slmply defined
the fluid 8Ivin 8 the direction
_ent
characteristics
often
lines, or resions
the locations
i
between
convenience. Even
is
sstabl£sh£n8
external
loop. forces,
i_
remain irrotatlonal. the
induced
flow
field
law can be developed
_f
a three-
by using
the-,
!
1 , k
1.9
i
F
_ +I- , ........
_........
a,_ _....
_:.¥,+.
,
-
, ..,-
,
,r, .....
,
.....
- ....
r
'l
Of _OR QUP.U'rf
!
d$ d
L
I
!
z
..
,
_xl
,,,__, ¥
i
Figure
by an element
7. Velocity induction by element Chree-dimensio_tal ring vortex
d_ of the filament
L of circulation
etrength
of
I" is
'rim. t+t+'t.t inducedvelocity a_ polnt P is
+
v - CPI+_)
71+
[(d_ x _)td 3]
(t_}
!
i
•
_: :;.
OFpOORQUALITY._ where the line line_of
the filament
i
around
'_
indicated
in
k
increunt
(13)
li, I;'
integral
L,
and _ is the
due
theg the inl'eil_.ation
the
distance
between
figure
to
the
and by
element
is
[8] suggested
the
is performed
of d_ wlth._aclockwise
L in the direction
above
e.._tel.
Basktn
_ndicates
the the
point
cross
P and
product
perpendicular
following
the
dL
element
plane
the
procedure'
the
circulation
d_ x _,
to
alone
the
as
velocity
of _ and d_.
The induced
velocity
l/
_.
vector
(14)
is
_
y,
z axes,
_
parametric
resolved
into
the
Cartesian
components
u,
v_
and
w alone
the
x,
'.,
_
and
respectively.
Let
the
equation
of
the
line
L be
given
in
the
form
_: i.
_ •- _(e)
,
n = n(e) ,
r, = _(e)
(zs)
]
!'
:
where
8_1s
-:_'
As the parameter point
the
Q(_,_,_)
_parameter
(being
e varies
describes
suggestive
as
from its initial the
curve
L.
an
value
angle
for
eI to
its final value
The vectors
_ and
the
curved
d_ can
be
filament) ef
expressed
as
i!
i: !,
_-
(_-x)_+
(n-y)_+
(_-z)_ (z_)
i'
f':
^t, J:^
where
and
Substituting of
the
induced
i
are
unit.vectors
the
above
velocity
are
u = _
of
the
x,
expression
into
dete_!ned
to be
y, (14),
z coordinate the
e
x,
_
system. y,
d3
and
z components
(17)
_f !_
V " _-'_I_ O!
' [dd-_B(x" _)
- _(Z
.
_)]d 3d__88
(18,
21
oI_IGIXP, I- pAQEI| ii
OFpoORQUAt.I_Y w-_
de . _(x . _, ]d3
i _ [_(y-n,
81
(_9, _.
where d = _x
Emanating These of
free
- _)2 + (y .
from the blades
vortices
leaving the
of the
can be subdivided
blade, are parallel to
n)2 +(z
propeller, into its
- r,) 2 .
free
(20)
vortices
shed vortices
form the wake.
which,
at the moment
axis, and trailing vortices outflow-
inS along the blade span in the direction either perpendicular or approximately perpendicular to the blade axis as depicted by Figure 8.
Among the trailing
vortices, the tip vortices (those leaving the blade tips) usually dominate the
TRRILING VORTICES
BOUNDVORTEX
_
F
;_
SHEDVORTICES
,
,_
,.
.:_ ,_
!
! i
ROOTVORTEX
!
1
! Figure
8.
Formation
of the wake by free
vortices i
i
22
I
t_
It is
I Tm (heaC
added),
EO_E w < EOA •
Cousequently, order
to The
atlons
the
flow
velocities
balance
the
mass
typical
behaviors
must
to variations
in
a constant
of
the
interior
orifice
pressure
englne power
DE_RE_SlNO _---_---_
area are shown
due
the freestream
in Figure 21a, while the specific
On a percent
21.
are shown in Figure
INCRER$IN9
fuel
consumption
dues
Figure
to
vari ....
temperathosedue
21b.
DECREMINO _---4--_
INCRER$INO
(b)
Typical
basis,
in
fuel consumption,
(a) Fisure
analysis
coefficients
the inlet velocity,
in the fuel's heat of combustion,
or the developed
density
flows.
in the freestreamdensity,
ture, or the effective
vary
__.
behaviors of the interior wlth parameter variation
a variation had
21 indicate
the
most the
in
the
effective
pronounced slopes
of
effect the
"lines"
pressure
orifice
coefficients
area
on Cpx and representin8
!
or
CPxx.
the
specific
Not Cp x and
only CPxx,
.,
+.
! k
' ! l_d fi
can be observed. This "drtvins potentisl" or pressure difference of ¥18ure _C should be noticed that amasure of the "driving potential" of the a_r masa 21a is seen to become smaller with increasing values of the pertinent parem-
_
!':,
stets,
while
:+
values
of Its
_,,
the
quantity
_:i_+:: _+,
It
is
that
of Figure
pertinent of air
parameters.
flow
Is possible
now possible
inlet
and exhaust
tions
for
21b Is seen
to calculate
panels
and apply
the potential
flow
to become
greater
with
Consequently,
a measure
by a strategic
selection
the normal them as the
velocities
calculations.
,
increasing
of control of
over
the parameters.
on the specified
complementary
The normal
1
boundary
velocities
condi-
on the
inlet
_..
_:
and exhaust
i_
coefficients
panels
are
surmised
and the pressure
to be functions coefficients
of
the
Interior
Chat existed
the body was closed (with no internal mass flow).
pressure
ou those
panels
when
Thusly,
I
i
l,
VI - V® ICpl F ill I
(43)
CPx
for the inlet panels and
!1
,,
Vt - V® lCPx x - Cpt
for the
exhaust
and V®(single
1) is
inlet
:
cient
i
and
i
eliminated
panels, the
CPout in the (44)
where Cpi is panel
freestream
pressure
velocity.
coefficient
determination
ta occasionally by proposing
that
Attributable
(43)
This
difficulty
and (44)
t t
t
pressure
to the
Cpt n and a sin_._exhaust of CPx and CPxx,
negative.
(44)
i's closed-body
coefficient
proposition pressure
the dtscriminants of imaginary
'.
of a
coefftof
numbers
(43)
i
is
are essentially
vI - v® ¢Icp I - CPxl ,2
++i
(4s)
for
the inlet
panels
and |
,,
v, - v®¢]¢Pxx"cPil for
the
exhaust
panels.
to be the
complementary
discussed
earlier.
In summary,
....
panels
l ::
baffles,
,
ill
(a)
of the
mass flow
the
were closed,
the effective
normal
velocities
of
(45)
and
conditions
for
the
velocities
are
inserted
(46)
potential
are
aaa_ed
flow
into
solution
(8) as the
F. the
upon
(c)
boundary
These
tlow-known+ functio_;
treatment
The normal
of air
pressures
which
(b) any internal
the
internal
orifice,
heat and the
through
a body is
existed
when the
pressure
drops
addition,
and (d)
exhaust
The present
dependent inlet
in this
and exhaust
due to engine
the
area
fins
ratios
method
and
of the
consists
inlet,
basically
fullowing steps: (I)
Panels
are
(2)
The total
inlet
individual
_" (3)
and exhaust
pressure
and the _xhaust
Internal the
to represent
heat
effective
(5) The interior velocities
the areas
inlet
and exhaust
are determined
sites.
by su_nning the
areas.
An area-averaged site
(4)
chosen
is
calculated
for
_he inlet
site.
addition orifice
I
is invoked
through
appropriate
changes
in
ares.
pressure on each
coef__eleut
i
coefficients
individual
inlet
are
determined,
and exhaust
and the panels
are
normal
!
calcu-
lated,
i i
J i
1 ,,
fl ORZDREFINEMENT $CHEHE FORHODIFICRTION
i'
!,
OF R BODY°$GEOHETRIC DRTR
_i _ :,,
Since
'
dimensional
l '_'_i "
the
preparation
body
for
consuming, a scheme Cartesian-coordinate _
• i
correct
body
network
(or
body,
i
the
and
grid) top
lot
as
that
this
procedure
the
8iven
from
this
is
time
along are
those
ular
to
geome_ric program
chang e the
body
data is
this this
or.quadrilaterals
to
form and
and
time-
Given a set may be used
geometry,
perspective,
a three-
tedious
task. scheme
that
of
refine
the
of to
•
Z
the
surface
stereoscoplc
of
the
views
of
body. for
specifying
Reference
4 for
(or the
inputting)
body
points
NCSU BODY program.
For
is
the
clarity,
now reviewed: is
points
on,
M-lines
a direction
constructed
forming
corresponding
in
the
to simplify of the body,
orthographic,
surface
corner
connecting
panels
modified
in
of
a potentlal-flow
to
procedure
The body ts their
the
various
and
same
with
into
has been developed data descriptive
of
The general
!-
input
misrepresentations,
original
,_
or modification
and
a network N-lines
points near
surrounding
the
to
by an arrangement
on the that
of
perimeter
intersecting
(Figure
22).
N-lines
snd
the of
of
major the
of
body
quadrilaterals lines
to
The M-lines are
are
generally
body
axis,
in
parallel
be
called,
those
those
while
the
planes
running
N-lines perpendtc-
!,
,
the
of
"defining"
no
N-line
although Since
!
!
the
major
body
points crosses
they the
axis.
Every
N-line
or M-line
must
have
as every
other
N-line
or M-line
with
the
another
N-line
may converge primary
NCSU BODY program
to
purpose and
the
and no M-line a common of the present
crosses
another
the
same
number
stipulation
that
M-line,
point. scheme report*s
is
to
generate
potentlal-flow
data
compatible
program
to
which
51
Of p@oP,
!.
Figure
5Z
22.
Schematic of indexing scheme used for a 3-1 ellipsoid with 40 panels describing the half-body
assumes • :.
the
necesssry front
for
of
N-lines i!.
body is input.
the body numbered
are ordered
symmetrical
about
X-Z _lane,
For compatibility,
(first
that
the
to encounter
consecutively
such
the
the
first
point
air
in the
of the bodySs
must be that
flow)
to back.
lies
half
N-line
freestream
from front
first
only
with
the remaining
The points lower
at the
on each
port,on
N-line
of the
X-Z
1
the "bottom"
i
plane
at
!:
points
ii
portion
L
corresponding
[
consecutively of
the
of the body increasing
X-Z plane
at
22,
(Figure
Section
counter-clockwise
the
"top"
points on successive
of
_he
N-lines,
A) with
(looking body.
generate
the remaining
aft)
to
These
points,
the
M-llnes.
the upper _._.,
the
The workhorse of this scheme is a cubic-spline curve-fittlng method [ii] coupled to a coordinate-system rotation-translationtechnlque.
Although cubic-
spline flcs are generally considered to be the smoothest of all curve flts [12_, they often have difficulty
i
Oscillations
In regions
become magnified.
of extremely
Spliningpolnts
against
high
curvature,
where
arc length alleviates
i
i
the
oscillations;
i
oscillations
the
present
by rotating
coordinate
system
to
investigators,
and translating
points
in
As an illustration of the consider •
body
(Figure
given
with
factory
one
the upper M-llne* 23).
respect
between
the
however,
the body points
new coordinate
the
points
1,
of the X-Zplane
*A three-dimensional and a lower one.
Since
reference 2,
to
in the
remove
the
reference
1
system.
rotation and translation of the body points, for some typical
A curve fit of the points to
chose
and
body contains M-lines are
three-dlmensional
!
I throush. 23 - with their values
coordinate possibly
I
3 due
system to
two M-lines increasingly
XYZ - may not
the
presence
of
be the
satishigh
in the X-Z plane - an numbered consecutively
upper from
the body's bottom to its top, the upper M-line corresponds to the maximumnumber M-llne whereas the lower M-llne corresponds to the mlnlmum-number M-llne.
i I J
I 53
!'
OF POORQUALf'_'_
OF POOR QUALIV_ slope •
becween.potnCs
body
points,
to
I and
those
2.
The alternative
appropriate
for
the
transformation
o5
the
followln S equations
to
points
the
_
procedure
new
1 through
coordinate 12 to
is
to
transform
systems.
those
in
the
For X'Y'Z'
the
!
!
!
instance, system,
may be used:.
X_ = (X i
- X12)cos
=1 + (Zi
" Z12)sin
al
(47) +
Z_ " (Zi - Zl2)cos
_I - (Xi " Zl2)sin
_I
(48)
where
! "
,
_I
tan-1
i = 1,2,...,12
i
i] ,T
X121 }
For the transformation
the following
of points
equations
12 through
23 to those
in the X"Y"Z"
•
system,
may be used:
!
X_ m (Xi . Xl2)co s _2 + (Zi - Zl2)sin
_2
(49)
Z_ - (ZI - Zl2)COS
_2
(50)
a2,-
(XI - X12)sln
where
L
. )
The ,
(X i' ,Z_)
generated.
system,
and Since
equations
(X i'',Z_) these
(47)
x.j, curve-fitted
points
are
points
must
and
(48)
are
be
and additional
transformed
solved
for
Xj
back
to
points the
are
reference
and Zj_ yielding
I
l
xj - x_ cos_1 " z_ sin _1 + x12 Zj
-
X_ sin
_1 + Z_ cos a 1 + Z12 -,t
ORIQINAt PAfii_ _ OF POOR QUALi'fY
while equations(49) and (5.0)....!re.,so!ved'for Xk and Zk yieldlnE t
-
oo."2-
" sin Zk " Zk
where
the
subscripts
Often
during
process
of
mental
J and the
tial-flow
k denote
preparation
keypunching
conception
Ot2 +
the
of
the
or
bodyts
calculations.
These
" cos a2 + Z12 Zk
appropriate, of
data
.i. "a+x.
data,
errors
through
shape,
the
which
errors
but
in
different,
are lack
made
of
point either
a clear
may be disastro.s
the
input
are
counters.
during
the
visual
or
to
poten-
difficult
the to
recognize
until the data is plotted. The present correct
method
these mistakes
data by explicitly body points
points
interpolation(s).
!i
panel geome_rles
i
J
of
orlglnally-inputted
information.
either by the average
intersecting
By the of the two
point P, the average intersecting
point
I
P, or
1, 2, 3, and 4 (Figure 24c) of the P-intersect-
as that of the second option,
refinement
of individual
the
|
The thlr.____doption uses the same polnt-ldentificatlon
to
The present method the
to effectually
The first option modifies
coordinate
of the M-line
of the four points
25 for a body assumed
in
(options)
i and 2 (Figure 24b) of the N-line
ing M- and N-llnes.
linear
the coordinates
a body point P is replaced
of the two points
arrangement
techniques
addltlonally-supplled
i and 2 (Figure24a)
the average
three
in a simple fashion.
changing
through
second option,
contains
the
Utilizations
grid
network.
a body point P by
of these options
be significantly incorporates
but replaces
in error
are shown
of the inlet and exhaust
options
in Figure
at one point.
two more geometry-related These
1
are
! I
options to
important
sites must be relatively
since
aid the
small
I
56
i
!I
ORIG|NA
:
..........'
M- I I me
i_
,,I
p,,
2,,.
M-..Ii _e.___
M-I Ine
;
P'"
M-I Ins
,:.
N-I Ins
• ,I
N-I lne
N-I Ins M-I Ine
N-I Ine
N- Ins
[_,
,,
;
N-IIns
(a)
,.
M-I Ins
(b)
i:I
,,
_': if"
Id • -,
!;i. I, _.
N-I Ins
I
M-I Ine
• P •_
..,2 'I, M-llne
a""
M-line
N-IIns
Ine
(c)
L E
i
Figure 24.
Coordinate information for averaging techniques
compared to the overall body geometry to allow for the assumption that the opened-body pressure coefficients (see previous section) to remain essentially equal
I
L
to those
of
the
closed
body.
The
first
of
these
options
augments
the
i
1
number of M-llnes and/or N-lines by equally distributing the user-specifled
I
number of additional M- and/or N-11nes along the arc length (assumed to be the linear distance) of every two successive M-llnes for addltlonal M-llnes and
I
along the perpendicular distance of every two successive N-llnes for additional N-lines.
The points on the addltlonal M- and N-llnes (equal in number and
order to those on the original M- and N-lines) are calculated by cubicpolynomlal spllne-flt interpolatlons. line
augmentation",
should
number of quadrilaterals the
individual
panel
be recognized (panels)
areas
(Figure
become more and more accurate
"
This scheme, to be called the "equal-
manyfold 26),
to have with Although
the
ability
to increase
a corresponding potential-flow
as more and more panels
are
used
decrease
the in
calculations to describe
a
57. ........................ JL
"',
'
t.J1
OF POORQUALIrf,
_;i I'i;
i!
ii'
ORigiNRLlily
_,.
body, ities,
care
i
must
be taken
For the above
(_ :
neighborhoods
noC to exceed
reason
of the
and that
inlet
option
has been included.
bution
techniques
and point
the available
only
a grid
network
and exhaust
sites
is
Although
uses
the
it
calculations
computer
sto_ase
refinement
in the
desired,
a second
usually
same M- and N-line
of the
first
capabil-
option,
distri-
the second
option au_nents the total number of M-llnes and/or N-11nes only by generating additional lines between any two specific M-llnes and/or N-llnes chosen by the user.
Without a drastic increase in the total number of body panels, this
scheme, to be called the "user-speclfled llne augmentation", has the ability to generate additional lines on specific regions of the body while increasing _
the number of panels in these regions with individual areas smaller than the
!
original panels (Figure 27).
If the user prefers, this option may be used to
'_
duplicate the results_of__the.firstoption.
For a given body, aspects of both llne augmentations may be used slmul-
-.
i
i 'i"
taneously if the one do not scheme override of thefor other. That is sometimes thepreferences equal-line of augmentation may those be desired M-1ines
1
i !.
(or •N-lines),while the user-supplied line-augmentatlon scheme may be desired
.i
i !
for N-lines (or M-llnes) • aecomplishgd
through
The implementation of these preferences are easily
the present
method's
computational
logic.
Containing the coordinates of the points describing the original body (with
the modifications final
modified-body,
invoked
first
three
first form is compatible as input to the NCSU BODY potentlal-flow program [4]
I
and that
i
the
second
form is
forms.
and/or
i
while
in two different
options)
the
report,
may be punched
geometry
i
of the present
cards
by the
1
Compatible
The
as input
!I
to the NCSU PLOT program [4] for plotting complete configurations.
I
60
Of pOORQ,j_.L.;T'"_' OR IOII_L BODY ,
.] %,,
F18ure
27.
Example
of
user-specified
ltne-ausmentatlon
scheme
1
Given
a set
of
body
data
(either
option
that
input
or_,final),
the
grid-refinement
r_ r I
program
contains
!
instructions
a plot
for
automatic
plotting
allows
for
of
body
the
the
generation
and
can
of
be
the
used
necessary
todraw
three-
f _
view _ _
_
and
oblique
scopic
projections.
errors
and
for
orthographic
projections,
This
option
displaying
i_..
plotting
routine
!_
have been presented
il_
Figures
the
(quadrilateral) components, since both
package
different
this report,
panels isolated
the
complete
by Craidon,
stereoinputted of
this
Reference
13)
explicit
examples
are presented
by Halsey
and Hess
[Reference
programs
but
program
is similar
curve fits for interpolations, on M- and N-llnes. method
derivative
Theyclaim cubic
Among
algorithms.
allow the input of sparse
The curve-fit second
by using
their
spline. are
and
in
!
logical
one of several
other options
intersections.
However,
thus
is gave
not
a true
significant
and perform
cubic-spline
consistently
point-distribution
This
configuratio_s
and
for repaneling
schemes
to
a fair
degree
feature the
study
should of
be extremely interference
................................................
i
for the
differences
fit
superior schemes
work
data, use independent many
in
results
are of
also
effects
1 I
do
I
continuity the
to
usual those
!1 3 of
significantly
accuracy.
useful
'
element
to that of the present coordinate
l4]
fuselages,
used by Halsey and Hess does not insure
method
Their
such as wings,
and provide
62
k
for
examples
tion, their geometry package contains a feature to calculate section among components and consequently repanel the regions at
and
checking
Although
components,
configurations
distribution
point distributions
a true
for
programmed
has been developed
the Halsey-Hess
cubic-spline
sense.
tool
perspective
28, 29, 30, and 31.
etc., of complete aircraft
the
as
modifications. and
throughout
which semi-automatically
of
body
a valuable
(orlglnallywritten
A geometry
exist.
is
as well
In
addi-
curves of interof the components for
design
among
the
of
.i ! I
1
w
NEWFRT NRCELLEFOR LESS DRRGWITH N-21 RNDM-21 YIELOINO qO0 PRNELS-X Z OUT 45,
10,
30.
6.0
i_
ORT
0
HIDDENLI'NE$IN
NEWFRT NRCELLEFORLESS DRROWITH N-21 RNDH'21 YIELDINO qO0 PRNELS-J
XZ
qS,
10,
30,
5,0
ORT
1
-
i )
Figure
29.
Example
of a oblique
orthographic
projection
i
OF POOR9:.U/I,,L['._;Y ...............................................................................
BESTCESSNR I82 WITHH'2I RNDN=29YIELDINg560 PRNELS -- FUSELRGE ONLY
-20, -50. Figure
50. 30.
12.
0.0
0.0
t4. I.O 8.0
Example of a perspective
PER
1
!
i
projection
t
65
i'
.. 1
t I
i i
I¸T
:! 1 t
t
i
I
j
t i
oL_gSGrNALPDx"_ _;, Ol'_ PO3_ QU_t2"_-
t
66
_.
components. this
Since
option
is
not
only
diate
but
accurate
program
expeditious
evaluation.
components
are
analyzed
by the
presen_
work,
ava$1able.
For a geometry accurate
isolated
While
algorithms,
the
to be efficient,
algorithms, both
programs
present
it
and present are
simple
program contains
must be simple results
logically
to use its
to use,
and have
own built-in
have
for
imme-
rapid
and
plotting
routines that allow the user to visually inspect the point modiflcations and line augmentations.
This feature eliminates the wasteful intermediate punch-
ing* of cards as input to separate plot programs, and therefore the overall time (program execution plus real tlm_) to analyze body data is signlflcantly reduced.
The specialization of the program to the specific analysis capability
described in previous sections also reduces the size of the geolnetryprogram and may provide more expeditious execution as well.
iI
i
card
*The recording of data to magnetic tape or disk is common practice to avoid punching,
i r
_
ha.
67
COMPUTER ZHPLEHENTFiTZON OFHETHOD$ F-
I. ;i.
The aforementioned
layer,
been
the
implemented
nonuniform
into
slipstream,
programs.
to
Ii.'
the cooling
interior-mass-flow
fill I_i
flow calculations has been named FLOWBODY,while a program performing the grid modifications has been named GRIDPLOT. The listings of both programs - along
I
with their user's instructions, sample input, and sample output - are provided
r
in Volume 2.
simulations,
propeller
computer
In addition
il
boundary
have
_i
I:
the
methods
a program performing
the
and potential
With logic easily adaptable to other computer facilities, both programs have been written in single-precision FORTRAN language. arithmetic was chosen for two reasons.
Single-precision
The first reason is that any smooth
ii
bodyrepresented byan
I!
inevitably crude, while the second is that the increase in computational times
L
(and therefore costs) for additional precision is undesirable.
I
arrangement of flnlte-sized plane quadrilateralsle
ORiGiNAL,PAGEISl OF POORQUALITY
DZSCU$$ZON OF RESULTS
An investigation craft for
fuselages the
air
and intake
contouring emerged
aid
in
that
of
theoretical
of
skin
surface the
nitude
and
forces).
of
skin
a means
to
to
or
turbulent)
hal
flow
and
large
changes less
to
to
integral
and of
form
it
is
pressure stream.
in
the the
*Three-dimensional the flow direction.)
pressures
bodies
all
shearing drag to
wall. wake
of
which
determine
on
with
the
lea
side
a X-Z plane
consists
taken
the
over
',
components
origin
an_d mast
theory
reversed the
this
also
provides offers
in-
separation
the
from body
sy_netry
flow
causing
formation
markedly
of
fluid
boundary-layer
by
of
certain
briefly.
of
and
As an
,
the total drag.
become
differs
of
(integral
fashion
body,
repattern
method,
stresses
a rational
the
with
reviewed
boundary-layer
Accompanied
locations
present
drag,
conditions,
air-
phenomena.
a stream
of a solid wall,
distribution The
in
important
light
A general
be
placed
take to minimize
certain
the
will
or pressure
of
investigated
physical
of
behavior
of
in
nelshborhood
losses
results
on a body
the
from
limitations. the
drag
and altering
were
as
flow
the
bodies*
well
quantities
under
separate
energy the
flow
may,
body
as
sight into what shape a body must
In the immediate
the
time
and pressure
these
reduce
of
physical
Since
to
because
forthcoming
drab
friction
explain
one
the
body)
means
Six
intuition
of
normal
of
sites.
on only
(equal
of the
the
exhaust
or ovez.-all
_rietion
made
by recontourins
satisfies
discussion
The _otaZ
the
and
the
aspects
been
nacelles
performed
ha_
of
has
that are
(plane
(laminar
the of
i
exter-
_f
eddies
J
phenomenon
:i
in those
J
a frictionof
!
the
parallel !
69
! _
!.i
OelOINAL. PAQZ 19 OFPOORQUALITY wake
and
substantially
ience
near-scasnaCion
shows
a large
below
those
on the
pressures.
drag.
Hence,
windward
Zncesracton
of
pressure
drag
a large
side such
of
the
body
a pressure
may be
which
exper-
dtmCributton
explained
by
the
exist-
r,
i
ence
of
: ,
a large
pressure
Schlichting tion
[15]
by considering
deviation. gives
the
_.
an excellent
flow
about
description
a blunt
body,
of e.g.,
boundary-layer about
separa-
a circular
i
cylinder.
!
ii
In
frictionless
(perfect
fluid)
flow,
the
fluid
particles
are
accelerated
on
f!'
if::
the
_i
to Bernoulli*s
_
increases
i
chin, the flow is frlctionless
i,
into kinetic
:
energy
!
rearmost
:_
fluid
1
pressure
L
upstream
half
theorem,
along
the
back
stagnation
particles
in
on the
the pressure
downstream
energy along
reverts
ideal
and decelerated
the
body
the upstream in
point exactly boundary
does
not
So long
such
under
externally,
experience
boundary
that
the
while
it
remains
transformed
the
half, kinetic
'
pressure
l
condltlons.
influence
the pressure
a pressure
accordance
half,
layer
being
that of ambient
remain
in
the upstream
On the downstream
amouots
equals
layer
the
Hence,
Is constantly
half.
proper
half.
along as
and pressure
field as that prevailing
and
decreases
half.
to pressure
the
downstream
of
at
the
Since the
the
same
distributions
are
1
drag.
W
When viscosity their
kinetic
(friction)
energy
during
is introduced,
their
travel
the particles
along
the
upstream
expend so much of
I I
half
i1
of
the
cylinder
i thaC the remaining the adverse condition, wall ing inder
is in
energy
pressure gradient
is sufficient
on the cylinder's
the fluid motion within
eventually separated
and
kinetic
their
constant-energy determination
stopped flow. fallure
and
the boundary
reversed
The wide
separation
to
smoothly
merge
type, and therefore of pressures
by
the
on the surface
to overcome
downstream
Under
half.
layer in the vicinity external
of indicate
Bernoulllts
for the particles
the
pressure
streamlines that
equation
In the wake.
the
flow
is
resultthe
not
is unsuitable Within
thls
of the
field, behind
1
the wake
cyl-
of
i
J
1 i
the
for the region
1
7O
.
ORIGINAl,,PAGE IS OF POOR QUAI,,,I'rY behind the cylinder, less-than-ambient drag
pressure.
Because
of
curve clearly this
pressure
depicts
suction
difference,
o_
a pressure
occurs. The shape
i.e.,
whether
drag,
it
of the
is
possible
1
a pressure-distribution
the
body
also
controls
flow
is
laminar
or
necessary
distance
or
of
logical
the
to
body.
the
nature
turbulent.
For
maintain
Although
of
the
minimum
a laminar
efforts
boundary-layer skin-friction
boundar
have
flow,
over
resulted
in
the
greatest
a reduction
/i
!:i
of
skin-friction
face
distance
sure
drag.
drag
and
capab]e
;
of
its flow
separation. r_duction
to
Even
to
the
layer
is
energy for
pressure
long
as
from
the
in skin-frictlon
too from
than
the
possible,
than
high
increases
the one
in
skin
and
gradient
freestream.
drag is usually
_.
pres-
skin-frlction
a laminar
and,
a sur-
a turbulent
pressure
distance
great
drag
layer
stable
a greater
is
because
Consequently,
_
turn,
1
much
delays
less than the
drag,
Since the danger of boundary-layer adverse
greater
a turbulent more
along
over-all
times as
though
remove
surface
The increase
in pressure
be many
the
flow
itself longer under an adverse
capacity
adheres
in
be delayed
boundary
of maintaining greater
can
should
desirable.
laminar
increases
drag
separation is
to maintain
large
pressure
a turbulent
i
i.
attempts
produce
Since
layer
friction,
the
can
flow
boundary ii _
drag,
gradients
with
its
separation
likelihood
of
always occurrence
exists
in regions
increasing
of
for
! i/.
bodies
with
sharp
_
ends),
attempts
experimental from
those
or should
pressure predicted
stream
direction
tion.
Consequently,
consists
steep
mainly
is
of
be
pressure made
to
distributions for
seek
pressure
skin-friction
(for
a more
for
frictionless
sufficiently the
curves
gradual
drag,
that so
is
bodies
streamlined
streamlined flow
drag
instance,
that
small
body
bodies the
pressure
there enough
is that
with shape.
differ rise
The
so
little
in
the
virtually the
blunt
no total
downsepara-
drag
1 !
4
ORIGINAl.PAGE IS !
OF POORQUALITY When the can
be
obtained,
mined. drag
I
L
ing
boundary-layer and
This,
in the
surface
of
shearing
stress
there
drag
because
the
tance
equal
to the
changed
even
pressure
is
displacement in
For _thls reason,
without
skin
of
external
allow
integrat-
in
affect
cases
flow
by a dis-
distributions
are
the
of
resultant
When applied
therethese
]
to actual
!
as blunt
of both
from the operational,
or bluff
due to pressure greater
effects
bodies.
deviations
I
(from
than that of stream-
surface
textures,
from appendages -Since
protuberances
to provide
I
!I _
the drag.
rivet heads,
_.
by pressure
the calculation
to rough
interference
gear, etc.) can be removed,
being impractical
zero.
of
Even
augmented
and
deter-
drag.
In addition
etc. can be modified
theory)
potential*
separation,
is generally
adversely
pipes, projecting
be
be
skin-friction
surface.
The pressure
method**
can
or
(in
the
the
distribution
separation
process
is no longer
velocity
viscous
may be categorized
experlence
that, normally,
the
must
flow
and, therefore, shape.
flow
onto
thickness.
absence
the
friction
displaces
and nacelles
and nacelles
and canopies,
of
fluid
and the present
of similar
exhaust
of
their drag is almost entirely
conditions)
(wings, landing engine
the
drag_ and thepressure
Most fuselages
tuberances
the
point
by a simple
in the flow direction
the skin-friction
fuselages
by
layer
intelrated,
calculation
the
boundary
the
body
imposed
this method
lined bodies
the
are
of
the
no__eparation,
forces
problems,
ambient
location allows
where
fore
the
turn,
around
tl_e
equations
actual
and pro-
few appendages
1
,I i
such as protruding
improperly-designed
cowl flaps
the cleanest possible maintenance,
design
and financial
points of view ....
*Flow external to the boundary therefore potential.
layer
is considered
**The reader should review the present simulation in an in_iscid.flow field.
72
report's
to be inviscid
section
and
on boundary-layer
'
i
.....
ii _
ORIGINALPAGE|_ OF POORQUALITY
i i The obvious il f,
makes
L
_nifoz_)
iI
Following
il
of
'i !i _
it
complexity
necessary flows
to
upon
the
fashion
the
of
vortex
over-all
drag
the
systems
of
that
bodies
fields
there
of
of
of
section
ring
vortices
diameters,
onto the body near
for a specified
power of 100..66 kilowatts.
power
The results
uniform
flows, whlle
39, 40, 41,_42, a nonuniform substantial
are given in Figures
increases
drags.
The_other
subdued
by a substantial
drag.
A closer examination
because Although
of the higher
local Reynold's
the skin-frictlon
the additional
velocity may be seen to frictlon-drag
reductions
of the higher velocities
bodies
locations
ten percent
in
reflected
airstream.
These
five percent
that,
possibly,
numbers
resulting
of the freenear
the tail
onset
flow
the friction
in Figures
38,
drag along with in larger
in pressure
drag but was
the skin friction
at or near the body expected
drag by
total
drag to yield a lower
of the flow upon the bodies,
reduce
about
skln-frlction
increase
drag was initially
"scrubbing"
in
in skln-frictlon
revealed
placed
_
five of the six bodies with
or form drag,
body also experlencedan reduction
were
to
approximation
flows are given
reductions
in the pressure
a crude
the
contrast method.
and nonuniform
As shown by the figures,
flow field experienced
(in
present
and
bodies
32, 33, 34, 35, 36, and 37 for the
those for the nonuniform
and 43.
aircraft
for
into
the nose to about
The six bodies were tested with both uniform fields.
the
strengths,
from approximately
stream velocity
real
nonuniform*
computations
and a specified
induced velocities
about
influence
a previous
systems
so
the
flow
the
slipstream,
a sy_tematic
actual
investigate
recommendations
a propeller
presence
of
because
a 30_ increase
were acceptable.
The pressure
over the surfaces
that significantly
decreased
surfaces.
to increase
7% or more.
total
Thus,
drag increased modified
of
in these because the
*A nonuniform flow is defined as that onset flow wlth velocities differing from a constant value, whereas, an uniform flow is that onset flow with a constant velocity.
73
pressure
distributions.
!
physical
phenonemon
!_
assumes
flow
may not
separate
The difference
between
the
analytical
method
and
!/
must
separation
a_so
be noted.
near
the
rear
The analytical of
the
body,
method
while
in
automatically
actuality
the
flow
r_
i, I: i
because
of the more of the
The drag calculations (Figure 42) were compared
energetic
flow.
ATLIT aircraft
with the experimental
fuselage
(Figure
drag findings
4) and nacelle
by Holmes
.
[16] of
7;
i:
a drag build-up
for the complete
aircraft.
Holmes estimated
the total aircraft
b__ '
J
i:
drag coefficient
_."
[16] arising
_:
angle of attack were accepted
i.
to be 0.044.
from the wing,
those arising
As a basis
for comparison,
the horizontal
tail, and the vertical
and used with the present
from the fuselage
tile drag contributions
and nacelles
method's
to produce
tall at zero prediction
of
a total drag coefficient
i
of 0.045.
This prediction
represents
_,
existing methods
_:
Fox [17]) as well as portraying
i:
estimations.
i '_
(including
a significant
the 0.0358 value the present
improvement
from earlier
work of Smetana
scheme as an useful
(Figure 37 or 38) was contrived
A "fat" nacelle
over previouslYand
tool for drag
for the purpose
of inves-
?
_
tLgating whether airplane.
such a conflguratlonmlght
Initial calculations
yield
a lower drag
for the fat nacelle
for the ATLIT
with an uniform
onset
flow
K
field (Figure 37) showed sure drag coefficient Initial calculations
a skin-friction
of 0.00317
coefficient
to yield
for the ATLIT
(/Sigure 36) showed a friction of 0.00414
drag coefficient
drag coefficient
to yield
an over-all
decrease of 23.4% in the pressure
bodies
A nonuniform
skin-frlctlon of 0.00323
drag decreased
and the pressure
of 0.00308
onset
of 0.00673.
flow fleld
and a pressure of 0.00722.
drag coefficient
was greater by 15.6%, a substantial
flow field was
results.
imposed onto
For the fat nacelle
by 9.2% to yield a skln-frlctlon drag increased
drag Where-
drag was seen to cause a 6.8% reduction
onset
to yield quite different
and pres-
drag coefficient
nacelle with an uniform
as, the friction drag for the fat nacelle
the total drag.
an over-all
of 0.00356
by 177Z
to yield
in
the same two
(Figure 43), the drag coefficient
a pressure
drag
! i"t
il
i
.........
.
.......
.
•
i
O_ POOR QUALITY
i'
coefficient
of
nacelle
i/ _
0.00879
(Figure
42),
for the
a
total
friction
drag
coefficient decreased
of by
0.01203.
7.5_
to
For
obtain
the
ATLIT
a skin-
friction drag coefficient of 0.00285 and the pressuredrag increased by 84_ to obtain a pressure drag coefficient of 0.00762 for a total drag coefficient of 0.01046.
Obviously,
the nonuniform
total drag for the fat nacelle i_
increased
by 44.9%.
i!!'
extremely
large increases
Although
were wider and flatter il
drag
of.the equivalent
flow had a slgniflcant
increased
by 78.7% and that-for
the smaller
frlctlon
in the pressure
than most bodies
circular
body
effect since
considered,
(discussed
the ATLIT
Since
the concept
in an earlier
!
the nacelle
drags were acceptable,
drags were not.
_-_
.....
the
these nacelles and utilization
section)
for the in-
_
duced velocities
by the propeller's
i
suitable.
For these nacelle
!< i_ _
more accurate
and realistic
an equivalent
eZZipgoid_l
cases and other
results would
circular body scheme,
diameter
less than the maximum
Consequently, _)
the propeller
the surfaces,
sure distributions Specification
realistic
causing
and,
of larger propeller
wlth
vortex
dimension
in a large
diameters
the use of
scheme produced
;
'
rings are te-
l .....
with a propeller
!
of the nacelles.
the air flow ont___._o (rather
resulting
flat bodies,
to the unsuitability.
tests were conducted
variation
not
than abou_
In the veloclty increase
should lessen
and.
and pres-
in pressure
the increase
drag.
_! i !
to more
values.
!
_umber of plane quadrilaterals
',i
In addition
an appreciable
in turn,
Since all of the bodies
modeling
the circular
cross-sectlonal
forced
surfaces were
cases of wlde
have been obtained
vortices. the present
onto the body
possible
body concept where
placed with elZipticalZy-s_ped of the
slipstream
were modeled (panels),
by an orderly
grouping
it was therefore
only approximate
representations
of a large
inevitable
that such
1 1
to the actual
bodies. For this reason, minor body recontourlng was performed to study the _everity of these crude models. The fuselage of a Cessna 182 airplane was
!
_-v__-::_'_:"
-
.-,: ,._,..-.: 4-..._.,,_..•
_•
_._ ..r_,_._-_,
,._.=.. _=_,.
•_TW_F_T_
'_4m_V_:_wr_=_
_
,
.,
_r:r_,
_
_
_
..
_,
ORiGiNALPAGE IS OF POORqUALITY
,' !
chosen
i _.
the
for
drag
•
this
test.
The
computations
The
study
were
revealed
.i.iI
typical
i
cent. sure
_.
•regions.
'i_
explicit example,
body
calculations
that
by
the
to
tothe larger total
total
by
the GRIDPLOT prosra_,
FLOWBODY program.
did
reductions
not
on
adverse drag actually pressure
change
the
increased gradients
Both
while
programs
cabin
recontoured_or
ficult to see these modifications
section
"sn_othed"
because
are
appreciatively
order
of
with
only
one
per-
because on the ofrecontoured greater
in friction drag was insignificant•
the upper rearward
slightly
the
drag
drag
In all cases the change
(Figure 38) was
recontoured
effected
leading
dragIn attributed some cases,
was
of a Cessna (Figure
_.
i
pres-
_
As an
182 fuselage
39).
Although
of the scale and orientation
dif-
of the
Q
drawings,
calculations
88_ of this change are encouraglng
yielded
arising
a 0.42_ total drag
from a decrease
since it is believed
reduction
in the pressure
that further
with approximately drag.
These
body modifications
results
may reduce d
tile i
drag
even more•
A different Tilenose
situation
occurred
of the representation
to better approximate results
!
of the Cessna
the actual
for the original
when more severe
fuselage
fuselage
changes
shape
fuselage was severed
(Figure
40).
When
were
imposed
or flattened
compared with
(Figure 38), this action produced
.1
the
an increase |
of
II.3X in the
friction
drag.
direction, :
the increase
tion
pressures pressure,
dragand
a slight
76
drag
in the pressure
flow field by the pressure
on the while
blunt-nose
panels
the pressures
were far less than the stagnation for_ changed,
reduction
Like the case of a flat. plate
of the external the
pressure
integration
of
on the value.
of the pressures
nearly
of 0.65X
perpendicular
was entirely
of the blunt the
fuselage
"same" panels With
' !
in the skinto the flow
due to the disruption
nose.
In other words,
approached
the
the pressure
distributions
over the entire surface
I
I
stagna-
of the original
!
1
fuselage
I
there,
I
produced
a
OF POOR QUALITY
net increase
I
because
of
in _he pressur.e
Although or
less,
the
intake
tion setting
main
and
size and
of the
these
the blunt-nose
body
of of
sites
work the
air
be
fuselage.
intake and exhaust
seen
flow
the
the
drag
area
influenced of
For the fuselagewith
the
loca-
the
power
engiue.
were
performed
on
the specification
sites and the same initial effective
of the
orifice
area
i I ,_
(Figures 44, 45, and 46), the total drag coefficient CD was found to vary linearly with power (Figure 47). The validity or pausibility of these drag
_
caefficients
may be seen by comparing
the present
results
_ _,
and
by
the
FLOWBOD¥ program
for
cooling
Intuitively,
on or
more
locations
effective
field.
orifice
affect
suitable
for
dependent
of
to
determine
flow
effective runs
to
mass
should the
priurlly B
may be
18
external
20 computer Cessna
shape
the
of
drag decreased
8tea,..
this
sites
magnitude
Approximately
identical
of
disruption
The skin-_f_iction
surface
to
purpose
exhaust
adverse
and
the
modifications
the
minimum
in
a decrease
drag.
with those
from windJ
tunnel tests of a llght single-engine
eugine alrcraft coe[flcients, with
[Reference
19].
aircraft
The power
and the drag coefficients
those from wind-tunnel
settings
tests corresponding
tunnel '
considered
coefflclent should
i
tests
be
extractions
only
_ingle-en$ine _i t
ferent
i_ I.
Such behavior
t'
i
the
30-40X aircraft's
as
full
pertained large.
aircraft
tests.
configurations,
The
from that of the twin-engine
curve
representing
tests
is
aircraft
to higher
shown
Whereas,
the to
to thrust
I
plotted
|
drag coefficients
the
behave
and the present local Reynold's
I
along
It can be obapprox-
the wind-
present
only to those of the fuselage
wind-tunnel
may be attributable
method were
to zero lift. yielded
60-70% below those from the wlnd-tunnel
18] and a llght twin-
were converted
of the present
served from Figure 48 that the present method
imately
[Reference
1
drag-
i 1
and, therefore,
results
of
remarkedly method's numbers
1
the dir-
t
findings. '
or to small
77 '
! i
or moderate
flow separation,
Further
oomparisons
for similarly-sh#ped
fuselaps
k
_
of References
9, 20, and 21 indicated
indeed we11 within
the range of typical
Upon the desisnaCion exhaust the
"opened"
:/t!
of
!,ii
ferenc
_i i
i I_ _,,
ports,
the
the
of specific
FLOWBODYprosram
panels
are
closed
body.
if
the
respective
of the body.
Careful
reasonable
results
equal
In actuality, panel attention
two interior perly.
that
the
coefficients
same
£mpermeable
on the
pressure
coefficients
are
large
in somparison
Since
thls analysls
the intake ports ports.
is necessary
fc,r the program
panels
quite
dif-
to
total
area
considers
if
the
an orifice
(engine),
and the engine and,
Therefore, to balance
consist
or
may be the
_
on
this assumption
a "black box" containing
occurs between
ports
pressure
must be paid to satisfying
coefficients
Since the models
.
existin_
the engine and the exhaust
pressure
drab coeffic._ants.wer_t.
on the body as air intake
assumes
are to be obtained.
drop normally
again, between
panels
the areas
the extracted
values,
Co those
interior of the body as essentially
a pressure
that
determination the mass
of an arrangement
1
of
flow pro-
4
of a large i
number of panels
