Dale L. Ashby, Michael R. Dudley, Steve K. Iguchi, Lindsey Browne, and Joseph Katz. Ames Research Center ...... using the Adler/Baron jet in crossflow code.
I!25 III1,_ lllll_
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NASA
Technical
Memorandum
102851
Potential Flow Theory and Operation Guide for the Panel Code PMARC Dale L. Ashby, Michael R. Dudley, Steve K. Iguchi, Lindsey Browne, and Joseph Katz (NASA1HE_,v,Y _P,rw_L
Ngz-32_22
r,_-i o?o51 ) PC'TF'=T [AL FL3W AN r_ CPF_,A/I3N GUIJf: F_R THc_ C"_Cr OMARC (NASA) d_, P
Uncl_s
G3/02
January
1991
National Aeronautics and Space Administration
.....
•
......
0111760
NASA Technical
Memorandum
102851
Potential Flow Theory and Operation
Guzde for the
Panel Code PMARC Dale L. Ashby, Michael R. Dudley, Steve K. Iguchi, Lindsey Ames Research Center, Moffett Field, California
January
1991
National Aeronautics and Space Administration Amc..sResesrch Center Moffett Field, California 94035-1000
Browne, and Joseph
Katz
NOMENCLATURE
BJK
velocity potential influence coefficienz distribution of unit source on panel
at control K
point of panel
J due to a uniform
CJK
velocity potential influence coefficient distribution of unit doublet on panel
at control K
point of panel
J due to a aniform
Cp
pressure
dS
differential
surface
element
fi
unit normal
vector
to surface
Ns
total number
of surface
Nw
total number
of wake
P
an arbitrary point
F
vector
S
surface
S**
imagina,-2,'
t
time
V
velocity
vector
V_tpK
velocity panel
influence K
coefficient
at point
P due to a uniform
distribution
of unit doublet
Vapz
velocity
influence
coefficient
at point
P due to a uniform
distribution
of unit source
coefficient
between
wake
panels panels
in space
an arbitrary
point
P and a surface
element
dS
of the configuration
panel W
on configuration
surface
at infinity
on
on
K
surface
total velocity perturbation free-stream
potential velocity velocity
potential potential
...
111
PRECEDING
PAGE
BLANK
NOT
FILMED
I.t
doublet
o
source
singulari.ty singularity
strength strength
per unit area per unit area
Subscripts i
interior
region
J
refers
to panel
J or its control
K
refers
to panel
K or its control
L
lower
surface
P
refers
to velocity
U
upper surface
-0
free-sn'eam
scan point
point point
P
conditions
iv
D _
i
-_
77
.
POTENTIAL
Dale
FLOW
L. Ashby,
THEORY
Michael
AND
R. Dudley,
OPERATION PMARC
GUIDE
Steve K. lguchi,* Lindsey Ames Research Center
FOR
THE
Browne,*
PANEL
CODE
and Joseph
Katz*
SUMMARY
The theoretical
basis for PMARC,
a low-order
potential-flow
panel
code
for modeling
complex
three-dimensional geometries, is outlined. Several of the advanced features currently included in the code, such as internal flow modeling, a simple jet model, and a time-stepping wake model, are discussed
in some
mensionexl
detail.
The code
is written
for the size problem
the program
input
being
is presented,with
using
solved
adjustable
size arrays
and the computer
a detailed
description
so that it can be easily
hardware
being
redi-
used. An overview
of the input available
of
in the appendices.
Finally, PMARC results for a generic wing/body configuration are compared with experimental data to demonstrate the accuracy of the code. The input file for this test case is given in the appendices.
INTRODUCTION
A potential being
flow panel
developed
at NASA
code, Ames
three-dimensional geometries for a well-documented code, tecture allow
which other
second allows
computers
allows as being routines,
(Panel
Center
making
Method
to numerically
agencies
modifications
and contractors
Ames
Researca
predict
Center),
flow fields
or adding to make
new
additional
features.
is currently
around
complex
by the need at Ames with an open archiAn open code
contributions
will
to the code.
A
in the development of PMARC was to create an adjustable-size panel code. This to be tailored so an optimum match can be achieved between the computer hardware
to the user and the size of the problem
the maximum
essential
PMARC
Research
(ref. 1). The creation of PMARC was prompted suitable for powered-lift aerodynamic predictions,
facilitate
government
objective PMARC
available
opment, include
would
called
number
ranging
of panels
being
can be changed)
from a Macintosh
solved.
in a matter
II workstation
Currently
PMARC
can be resized
of minutes.
PMARC
can be run on
Y-ME
At its present
to a Cray
(i.e.,
state of devel-
PMARC contains several features considered to be state-of-the-art for panel methods. These internal flow modeling for ducts and wind tunnel test sections, simple jet plume modeling for the analysis the study
and design
of both steady
of powered-lift
and unsteady
motions.
aircraft,
and a time-stepping
PMARC
is a research
wake
model
which
tool that is envisioned
in a continual state of development. Existing routines will be improved and new features and options added as they become available.
or replaced
by new
One of the decisions tbot had to be made in the development of PMARC was the type of panel method to be used. Panel n.,thods can be subdivided into two groups: low order and high order. In a
*San Diego State Unive,'si,y, San Diego, California.
low-orderpanelmethod,the singularitiesaredistributedwith higher-order panel.
method,
the singularity
Higher-order
panel
strengths
methods
claim
is at the expense of increased code ods such as PANAIR, MACAERO, mid/or
industry
internal
research
nearly
the same accuracy
tation
time for low-order
Additionally, methods
low-order
panel
method
was chosen
of a higher-order To avoid
unnecessary
method
and widely
Analytical VSAERO namic Center, tively
program
about
complex
3-5). The
were patterned
methods
but this
matching
between
is structured
can provide
however, panel
cost and compleaity,
The code
each
the compu-
methods
panels
(ref. 2).
as higher-order
the low-order
to accommodate
panel the addition
of previous
work, existing
.software
was utilized
whenever
dine of PMARC and cost to the government. Of the several lowthe 1000-panel version of VSAERO was felt to be the most robust, by the engineering
shapes.
one in 1982 and the other (refs.
through
that low-order
community.
During
its ten years
Methods Inc., which was supported largely by government has demonstrated that low-order panel methods are a viable
flows
of the flow field,
than for higher-order
do not require exact
over
time. Experience with panel methdeveloped under NASA contracts
a wide range of cases;
shorter
In a
at a later date, if warranted.
duplication
accepted
over
over each panel.
or quadratically
in the modeling
has shown
methods
for the basic methodology. solution
accuracy
is much
and to reduce
possible to reduce development order panel methods available, nmmre,
order
methods
strength
to vary linearly
and computation and QUADPAN,
and development,
methods
do. For these reasons,
a better
complexirj VSAERO,
as higher panel
are allowed
constant
Two
versions
in 1985 under
basic potential
after the most recent
flow
of VSAERO contracts
computational
1000-panel
were delivered
NAS2-11169 methods
version
of development
by
and industry contracts, means of predicting aerodyto Ames
and NAS2-11944,
and techniques
of VSAERO,
which
Rematch respec-
used in PMARC
is currently
available
to be inviscid,
irrota-
Cosmic.
THEORY
Potential In PMARC, tional, regions
the flow
and incompressible as shown
fictitious
q_,.e body
in figm'e
flow.
Figure
as the fictitious
flow.
field around
is modeled
This is the typical
potentials
in both regions
region
is assumed
surface
which
the flow field of interest as the flow
arrangement
satisfy
body
as a closed
contains
the external
uniform stream. This arrangement is reversed tains the flow field of interest and the external the velocity
Model
a three-dimensi,_nal
1. One region
1 shows
Flow
divides
and the other
field of interest
for external
flow
space
problems
into two contains
and the internal such as a wing
a
flow in a
for internal flow problems. The internal region conflow field is fictitious. In either case it is assumed that Laplace's
equation:
(I)
The potential both regions.
at any point
This results
P in either
region
in the following
may be evaluated
integr_
_ is the distance
normal
vector
represents
to the surface
with strength surface
-if-
wake
integral
P to the element
dS on the surface
into the flow field of interest. _om
a surface
represents
distribution
the contribution
from
to
a surface
distribution
may be simplified
(O - _i) of sources
by noting
that at the
due to the uniform onset flow. It is assumed thai the wake is thin and there so the source term for the wake disappears and the jump in normal velocity
is no across
the
equation
is essentially
per
only
the simplified
due to the configuration
the first integral
with strength
leaving
Hence
potential
_ is the unit
zero,
is zero.
the perturbation
and
In this equation
of doublets
(Vq) - Vq) i ) per unit area. This equation
at infinity,
the potential entrainment,
pointing potential
unit area and the second
Theorem
S+W+S_
from the point
the disturbance
Green's
equat!on:
S+W+S_
where
by applying
becomes:
_. (V_-Vq_ 8
i ) dS
S (3) W
The point become
P must be excluded
singular
the surface
in th:t case
centered
from
at point
the integration
if it lies on the surface,
P. This is done
at P. If the integral
is evaluated
by assuming
for this hemispherical
is allowed to go to zero and point P (and hence the hemispherical the surface, the contribution at point P is i/2(O-q)i)p. If point the contribution equation
at point
P is -1/2(q)-Oi)p.
Hence
for points
since
a hemispherical
the integrals
deformation
deformation
of
as its ladius
deformation) are on the outside of P lies on the inside of the surface, P lying
on the inside
of the surface,
(3) becomes:
a,p=
)
v
n (w,- va,i ) dS
dS -
S-P
+
S
4--_((1)U--g_)L
)fl"V(1)
dS
+
q)oop
-
(4)
2((l)-_)i)p
w
The boundary
condition
used to solve
equation
The total potential q) can be viewed as being made potential _ = q) - q_**.The potential of the fictitious this boundary fictitious
flow
condition,
the singularities
is set to zero
because
(4) is an internal
on the surface
the singularities
Dirichlet
boundary,
condition.
up of an onset potential 0oo and a perturbation flow is set equal to the onset potential, 0oo. With tend to be smaller
only have to provide
than
if the potential
the perturbation
of the
potential
histeadof the total potential.Usingthis boundaryconditionandlooking at points P face,equation(4) canbe rewrittenas: o=
(".
O_.v
rids
the sur-
) ,is
-
S-P
+
inside
S
4"_
(_U-OL)
fi.V
dS
(5)
2 Op
w
Refering doublet
to the definitions and source
Looking some
known
the surface
at equation value, are given
made
for equation
(2), the following
equations
may be written
for the
strengths: 4rtl_
=
_
4x¢1
=
-fi-(VO-VO**)
(7), if it is assumed
then the source by the following
=
(_-t_.,,)
that the normal
strengths
can be solved
(6)
(7)
velocity
at the surface
for immediately.
is either
The source
zero or
strengths
on
equation:
The normal velocity., Vnorm, on the surface is either zero (no flow through the surface) defined value (to simulate suction or blowing) and the onset velocity vector is known. equations (6) an,, (71 into equation (5) leaves the following doublet strengti_ c :; e the surface to solve for:
integral
equation
or a userSubstituting
with the unknown
(9)
The general
equation
for the potential
at any point
P can be written
as:
O.
point
to allow
frame
the motion
guide,
the instantaneous
to fix the rear stagnation
the wake at the separation line and all the preceding with the local velocity field (in the inertial reference prescribed
velocity
input
in a series
Wake
reference
in PMARC,
reference frame at each time step. The wake development on the other hand, must be done in the inertial reference
Time-Stepping
edges
of a constant
time step to develop
(eq. 8) must be updated
Currently
(see detailed
the prescribed
at each incremental
strengths
in the body-fixed ity computations,
could
through
axes
: > 0 in the inertial
frame.
in terms
coordinate
functions
at time
reference
can be described
the three
is marched
is computed
face source
frame
about
motion
The configuration
of the configuration
of the body-fixed
case,
is set
the second
summationin equation(11) canbecombinedwith the surfacepanelsummation,leavingonly the surfacedoublet strengthsas unknowns. On subsequenttime steps,a newrow of wakepanelsis addedto eachwakeatthe wakeseparation line andtheremainingrowsof wakepanelsareconvecteddownstream.The doubletstrengthson all the wakepanels,exceptfor the newfirst row of panels,areknown from the previoustime step andcanthereforebe transferedto theright handsideof equation(11). The doubletstrengthson the newfirst row of wakepanelsareagaindefinedin termsof the strengthsof the doubletson the surfacepanelsthat the wakeseparatesfrom. The termsfrom the secondsummationin equation(11) pertainingto the newfirst t_ow of wake panels a.-e then combined with the surface panel summation, yielding
a new matrix
equation
to be solved
at each time step.
Matrix The first step in the solution ence coefficient source
matrix
strengths.
For panels away,
PMARC
distributed
however,
point
source
over
radius.
field factor.
The characteristic
the centroid
of the panel
far-field
factor
PMARC most
cases.
coefficients
panel
value
The default
the influence
from
as the far-field for far-field
the midpoint radius
factor
have
surface.
For panels as though
starts
being
panel accurate
the unknown
size.
The In
results
if so desired.
savings
for
The main
in time with little
doublet
by
of one side to
side to the centroid.
by the user
a considerable
that are far it were a
is determined
from the midpoint
sufficiently
can be changed
methods.
size to give a far-
by the characteristic
produces
been evaluated,
used
panel
influ-
the singulari-
the panel
of an adjacent
divided
factor
in panel
by treating
b7 a characteristic
is that it provides
coefficients
the panel
potential
for the known
BJK
employed
by treating
this approximation
of 5.0 for the far-field
value
over
and
exactly
size is the sum of the distance
and the distance
is then defined
commonly
are calculated
at which
of the velocity
strengths
are calculated
is nondimensionalizcd
purpose in using this approximation in accuracy for most configurations. Once
coefficients
the panel and integratiJ_g
This distance
the default
doublet
use of an approximation
The distance
the far-field
(11 ) is the determination
for the unknown
the influence
the influence
or doublet.
CjK
makes
that are nearby,
ties as being
of equation
elements
Solver
strengths
loss
can be
solved for. Because the matrix equation that must be solved can become very large (the influence coefficient matrix contains 1,000,000 elements for a 1000-panel case), a fast iterative matrix solver that solves makes
line by line without
use of a matrix
solver
matrices
(ref. 9). The
of order
n x 20, where
handle, cess,
and some
allowing
the solution
solver
of fairly
complex
vector vector
vector
matrices
panels
without (1000
iterations
which
to be in memory
scheme
of size n are needed
problems
guess for the next iteration. guesses and the correction
matrix
for computing
of the order
of surface
to be solved
of solver
is computed
the whole
on an iterative
can handle
vectors
matrices
The limit on number correction
based
n is the number
scratch
large
requiring
in memory
to 4000
panels)
is set by the user
is applied
to the current
As the solution iterations vectors from each iteration
7
in PMARC during
large
matrices
solution
and mic"o-class
vector
of large
two small
of memory.
in the input deck. solution
PMARC
are dimensioned
the iterative
amounts
on mini-
is used.
the eigenvalues
of 106 x 106. Only
the arrays
requiring
at once
to pro-
This permits computers.
At each iteration,
guess
a
to get the solution
proceed, the solver stores in the two small matrices
all the solution of order
n x 20. The historyof solutionvector guessesandcorrectionvectorsfrom precedingiterationsis usedateachiteration to form thecorrectionvectorfor thecurrentiteration.After every,twenty iterations, rection
the current vector
set of small
and solution
from
becoming
too large
extra
iterations
to the solution
minimal
memory
matrices
guess
vector
is folded
to one (i.e., reset
from the previous
{ref. 9). The folding in return
iteration)
of the small matrices
for allowing
unlimited
so that it holds to prevent
usually
number
only the cor-
memory
adds
requirements
only one or two
of solution
iterations
with
requirements.
The doublet
influence
is read into memory has a parameter
coefficient
to perform
(MATBUF)
matrix
the matrix
remains
on a disk scratch
multiplication
that will allow
buffered
required
input
file and only one line at a time
at each solution
of the doublet
iteration.
influence
PMARC
coefficient
matrix
during each iteration of the solver. MATBUF can be set equal to one for no buffeting, or it can be set to NL, where NL is the number of lines of the doublet influence coefficient matrix to be transferred from
disk scratch
the number
file to memory
of physical
on each read.
IO requests
Setting
that are issued,
MATBUF
to a value
but it also increases
greater
than one reduces
the amount
of memory
required. The
solver
side vector
requires
the diagonal
to start the iterative
which
is the tight-hand-side
solver
uses
the doublet
ally reduces first one.
The convergence fied in PMARC iterations.
for certain
cases. cycle
The
required
as the. percent
in the solution
for most solver
4000
panels
on the CRAY
4000
panels
on a MicroVAX
change
to the solver.
indicate
converge
or 15 CPU
Once known;
the unknown thus,
to the panels
face are evaluated appropriate velocity
in the panel at each
between
tolerance
speci-
successive if the solu-
of 0.01 to
may
be necessary
in 50 to 150 iterations. and
after the
tolerance
to determine
and 0.695
the
This gener-
CPU
A single seconds
119 CPU
for
seconds
for
coordinate
the singularities can be evaluated.
by the user. The tangential
system
by differentiating
component
of velocity.
system,
the velocities
coordinate configuration
panel control
the following
Analysis
of the panels
specified
for each tangential of the entire
using
elements is used
tolerances
for 1000 panels
i_een determined,
at the cont, ol points
system velocity
have
zero or the value
calculated
be calculated
strengths
in a local panel
direction
coordinate resultant
doublet
the velocities are either
time steps, vector.
II.
On-Body
O
convergence
is created
on all the time steps
vector
for 1000 panels
seconds
guess
The convergence
change
to a solution
CPU seconds
vector
On subsequent
that a convergence
smaller
and the right-hand-
guess
solution
m the solution
although
of 0.0866
vector.
with the largest
run to date
will generally Y-MP,
matrix
time step as its starting
for a converged
vector
problems,
is of the order
coefficient
by the diagonal
the previous
must also be passed
or not. The cases
is adequate
iteration
of iterations
is defined
of the influence
For the first time step, a starting
divided
from
tolerance
The element
tion is converged 0.0005
vector
solution
the number
vector
process.
point,
and a resultant the pressure
equation:
8
With
on all the panels The
the doublet the three
velocities
velocities
coefficient
normal
on the sur-
strengths
in the
components
can be transformed
velocity
at each panel
of
into the
can be calculated.
are
Using
control
x, y, z the
point can
. The last termin equation(14) is the :'r_steady With
the p_-:,st_re distribution
body
can Ix evaluated.
nent,
assembly,
panels
Forces
and the whole
on user-specified
put in coefficient are written moment
model.
on which
file in wind, they were
are written
data for all the patches area,
is also written
component, stability,
written.
patch
and assembly
The total coefficients
has the capability
at points
the coordinates
force and moment
include
the contribution
of computing
off the body
of point
The
P. Thus
equation
a plane
on the compo-
_ach column and moments section
of are
coefficients
of aerodynamic
data
and total force axes, after
and
,.he panel
area, nondimensionalizcd of symmetry
coefficients
of the reflected
about
by y -- 0.0
are for the paneled image.
Analysis
the velocfty
are evaluated
The
assembly, and body
wetted
.... zh patch,
up,
after each column
The patch,
and moments
for
forces
and body axes.
axes,
file in wind,
Off-Bt_ly PMARC
The summed
stability,
and body
has been
(14)
forces
by panel,
are also summed
at this time. For the case where
was use.A, the patch, component,
velocities
the resultant up, panel
coefficients.
to wind,
stability, computed.
the reference
determined,
and moments
to the output
aerodynamic
only.
Forces
to give section
")
dO/dt.
are summed
form and are transformed
coefficients
geometry
the body
and moments
patches
to the output
for the patches
over
term,
_i
by taking
at arbitrary the gradient
points
in the flow field. The
of eqaation
(10) with respect
to
(10) becomes:
(15) S
Equation point
S
(15) can also be written
P. The resulting
discretized NS
w
in discretized equation
form similar
to the equation
for the potential
at
is: NW
NS
(16) K=I
L=I
K=I
where
dS
(17)
K
and
9
I
VI_pK "-
_
_-V
(18)
dS
K
The coefficients strength cients tions
Vow,,
for panel depend
and V,.
el,,
represent
_PK
K (surface
or wake
only on the geometry
(17) and (18) can be found
the far-field tions
approximation
(16), (17),
streamlines,
the velocity
panel)
acting
in reference
eling
PMARC
currently
supports
the ".-.ternal flow geometry
rior of the box (ref. normal
velocities
nuity equation other
objects
on groups is satisfied.
such
For internal
as wings
flows,
constant,
the potential must
or vanes
the doublet
(ref. 11). This is because an arbitrary
of panels.
whereas
at infinity
be specified
somewhere are known
of internal
coefficient
is substituted
an unknown. rewritten
into equatior
Assuming
must
Equa-
flow geometries
to circumvent
off-body
'oublet
value
-
"(_1"
pointing
into the inteas
so that the conti-
empty
duct,
tunnel
test section.
or it may contain
in its conventional
the arbitrary
as a boundary
by moa-
may be prescribed
be prescribed
is singular
this problem,
surface
vectors
flow geometries
is known
constant
the pc.,mtial
condition.
form
only to within
is determined (or a doublet
Normally,
(eq. (8)) and the doublet
values
by value)
the source
values
are solved
for as
can be eliminated by arbitrary specificaIn the matrix equation, this known doublet
(11) and the corresponding
the knot.,:
coefficients,
computing
a duct)
in a wind
matrix
for internal
on the geometry
normal
can be a simple
in equation (11). For internal flows, the matrix singularity tion of a known doublet value, usually zero, on one panel. value
influence coefficients.
This is accomplished
through
a test article
function
on a geometry
flows.
and outflow
geometry
to simulate
for external
(_**). In order
for all the panels
flow
coeffi-
to equa-
Model
to the box (flow
influence
the potential
Flow
The inflow
The internal
potcntial points,
influence
solution
influence
at scan
box with the panel
and outflow
The
wake.
modeling
as a closed
10). Inflow
the velocity
velocities
the ume-stepping
.
I. Tile velocity
6. As with the ve!ocit)
and (18) are used for computing
per unit singularity .
and its wakes.
in computing
Internal The code
coefficients ._
on the point
of the configuration
is empioyed
and for convecting
influence
source
is specified
value
on the panel
on the first panel,
is treated
equation
as
(11) can be
to yield "Bll
C12
Cl3
B21
C22
C23
...
g2
B3!
C32
C33
...
I.t3
C11
B12
B13
C21
B22
B23
...
-t_ 2
C31
B32
B33
...
-t_ 3
:
:
".
-l.tl
(19)
:
The ;olution panel
on which
that was obtained equation
•
:
of equation the doublet from
(19) results
m a new, and possibly
(I.tl) is prescriL_.
the matrix
(8). This procedure
".
allows
solution
Once is replaced
the soluuon
the matrix
solution
by the original
of an otherwise
iO
incorrect,
source
value
is obtained, source
indeterminate
value
(Ol)
for the
the source computed
matrix.
value using
The panelusedfor the specifieddoublethasanimpact on ally the best convergence
is obtained
panel).
The doublet
used also affects
scribed
doublet
value
set to zero. After
scribed
doublet
value
is set equal
panels.
This minimizes
prescribed.
In internal only at panel
control
by a combination Second, as close density
as possible vector
for all the doublet
distortions
is a certain
at the panel
with the pre-
is obtained,
values
on which
the prescribed
the pre-
on the neighboring
the doublet
doublet
Usu-
(i.e., the last
be made
sla-engths
of the doublet
amount
means.
First, panel
can be increased
sources.
Finally
to the average factor
strength
was
value can be set to a non-
is set to zero.
in or out of the internal
condition
from an internal density
so that more panels
being
flow geometry
can be minimized
vector
in the tunnel or duct.
increasing
the panel density
imposed or duct
as having
and/or
so that it is
to inctv.ase
leaking
even
walls.
distributed
can be adjusted
It is possible
to keep the tunnel or duct from
However,
on the tunnel
are treated
velocity
flow
for each panel
can be increased
the free-stream
velocity
enough
of leakage
boundary
(ref. 10). The leakage
factor
of point
and the far-field
velocity
there
points
near the end of the matrix The first run should
average
is a problem,
is due to the Neumann
of several
the far-field instead
the solution
of the solution.
rerun.
flow problems,
This leakage
is placed
convergence.
to the weighted
convergence
and the computation
geometry.
if this panel
any local velocity
If poor solver
zero value
sources
value
the convergence
the panel
if the free-stream
the far-field
factor
both
will increase the execution time of PMARC for a given problem. Varying the free-stream velocity vector will not change the execution time of PMARC significantly. Changing the free-stream velocity vector changes the source strengths leakage appears to be minimized when flow
geometry.
The free-stream
maximum
velocities
achieved.
Conservation
fications
velocity
in the internal of mass
and the velocities
(eq. 8) and therefore the doublet strengths vector
flow
is normally
geometry cross
by looking
sections
(ref.
12). This
surface
patgh
els. There
information
restrictions
The first restriction
normal
vector
velocity
ratio
ratios
free-stream
velocity
Adler/Baron
code does
back
is modeled imposed
outside tends
a reasonable
to PMARC
should
to break
where
by the Adler/Baron
down.
velocity
vector.
the restrictions
the global
11
specified
is
velocity
speci-
The code
effects
is modeled
with a
on the jet plume
pan-
on the type of jets that can be about
a plane
second gives
is that the angle
approximately
Within
job of modeling
code
be symmetric
The third restriction not exceed
of mass
and outflow
the jet plume
velocities
3.0 and 8.0. The Adler/Baron
this range.
vector
conservation
at inflow
and
a jet plume in a crossflow. The jet plume shape, using the Adler/Baron jet in crossflow code
is that the jet exit must
be between
the minimum
Model
with normal
to the jet exit and the free-stream should
jet velocity
PMARC
is then passed
and the entrainment
are several
modeled.
jet model for simulating velocities are computed
until
between
of the geometry.
Jet Plume PMARC has a simple trajectory, and entrainment
set to a value
and is adjusted
may be determined
at different
the doublet strengths }.t (eq. 11). The are minimized throughout the internal
restriction unpredictable
between
100 °. For angles described of a jet.
containing
above,
the
is that the jet results
for
the jet and the
greater
than
100 °, the
the jet model
in
tte
J
One of the keys to the success within the code. manipulated scheme
In a panel code
within
the code
disk scratch
space
use of variable between
required
as written the code,
scheme
to run the code.
Specific
aspects
within
of the parameter
the source code
disk space
available
statement
set in PMARC).
PMARC
the PMARC
of one particular
the dimensions
parameter
statements
values.
code
must
of arrays in PMARC,
modified
on a global basis
be recompiled
part of the code,
needs
for the changes
to run. The
The amount
PMARC only data
of scratch
run. The current
parameters,
of patches
will change
without
of memory
version
and
of PMARC
any problem.
A ver-
II with 2.5 Mb of memory
the user can increase
or wakes
allowed,
the user to customize
the amount
writes PMARC
of disk space
to disk scratch requires
space
without
and
the capacity having
to
the size of the code to fit
and memory
is the influence
to run can be calculated
equation: Disk space
(bytes)
= (NSPDIM)
12
.
can be changed
and 210 Mb of disk space.
panels
on a Macintosh
to
capacity.
PMARC
disk space
certain
code. This allows
and hardware
is being
is the amount
II with 3 Mb of memory
say the number
of the entire
Redimensioning
the code
can handle
with as many as 6000
changing
This eliminates
the number of surface panels PMARC can han= 1000 must be changed to NSPDIM = 4000.
source
run with 1000 panels
By selectively
the capacity
his particular
code
on which
on a MicroVAX
has even been
20 Mb of disk space.
of
process. The set of parameter in PMARC (there are 22 occur-
To change
of panels the code
has been run on the Clay Y-MP
sion of PMARC
increase
on the number panels
include balance
used, and elimination
in terms of the parameter
and the appropriate
on the machine
can be run with 3000
scheme
Sizing
the code are also defined
have been made,
limitation
and
of a reasonable
become effective. Thus the size of the code (i.e., the number of panels it can handle) from several hundred to 10 or 20 thousand or more in a matter of minutes. The main
to
adjustable size arrays throughout the code. A set of parameter stateof all the arrays in PMARC (see appendix A). Integer limits for
must be edited
the changes
seeks
of memory
of the data management space
and
the code and in the plot file.
throughout the source code. For e.,,.ample, to change dle from 1000 to 4000, all occurrences of NSPDIM Once
which
the amount
the code, provision
the possibility of forgetting an array or limit in the re.dimensioning statements is included at the beginninl_ of all the major subroutines fences
to be
too large, inefficient,
for PMARC
of disk scratch
is managed
that need
If a good data management
while minimizing
used and the amount
both within
of data
become
has been devised
for all major arrays within
PMARC was written using ments controls the dimensioning and loops
is how well data
to output and plot files.
Code
variables
method
the code can. quickly
the code can handle
of memory
of variables
of any numerical
management
of panels
dimensioning
the amount
redundan,'y
or failure
there are many large arrays and blocks
within
slow to be of any use. A data the number
MANAGEMENT
as well
is not implemented
maximize
DATA
-_.__
2 * 3 * RBYTES
required coefficient
using
by the matrices.
the following
where
NSPDIM
is the parameter
and RBYTES (typically
is the number
of disk space
but it is usually
required
small
required
computer
and scalar
of memory
output,
on the options
between
can handle
on the computer
for the input, disk space
the code
selected
required.
subroutines
being
used
and plot files. The in the input deck,
Minimizing
greatly
the disk
streamlines
the coding
required
to tun is not as easy
can be divided
The second ilx using
into two parts.
instructions).
Mactran
of disk
The first is the memory
allocated
allocation
for storing
part that is significantly
the DCM
as the amount
This memory
part is the memory
It is the second
to compute
Plus Fortran
is fixed
for a
the data (arrays
affected
by redimension-
77 compiler
with the opti-
and 4-byte integers and logicals, the storage required for the code is approximately With PMARC dimensioned according to the parameter statements listed in appendix
storage
compiler
of scratch
requires
and constants).
On a Macintosh
mize option 300 Kbytes.
a real number
files depends
itself (the execution
and compiler.
ing the code.
the data
PMARC
the code
variables
panels
code.
of memory
for storing
three
to pass information
a faster-running
is. The amount
for these
of surface
is required
blocks
common
allocated
to represent
disk space
to the amount
IO and using
The amount
the total number
compared
and produces
given
of bytes
RBY ,"ES -- 4). Additional
amount
space
controling
required
is approximately
uses static allocation
memory
for data
storage.
various
parameter
1.83 Mbytes.
for the data.
Compilers
The table in appendix
values
in PMARC
affect
It should
be noted
that use dynamic
that the DCM
allocation
will require
B will give the user a feel for how changing
the amount
of memory
required
A,
Fortran
for running
77
less the
the code.
Plot File The
PMARC
plot file is designed
and aerodynamic and have
a post-processor
be kept to a minimum data
within
The
geometry
the PMARC data
_he wake
block
following
the completion
The arrangement the PMARC rently
containing patch.
of the geometry
run and the number contains patch
After
each
number
record
identifying
after the patch
information
is written,
the first corner
stepping
(see fig. 4 for patch point
of each
at the panel centroid. contains
data
the coordinates
block
is as follows. have
of patches
and rows,
for each
to the file fh'st.
wake
from
time step.
and aerodynamic
of a patch,
patch,
nomenclature).
each
Each
the coordinates
At the end of each column
layer
The data
implemented
is a record of panels
column
record
of the panel of panels,
point of the last panel
The
by a set of records number
with the patch patch,
on each name. Next,
The panel
and each row on
of the (x, y, z) coordinates
centroid,
an extra
record
and the panel must
of
cur-
in PMARC).
in the geometry.
on each
consists
the length
iterations,
This is followed
and first and last panel
the total number
,,.hrough each
corner
not yet been
13
D
of the
will not change
to the wake
of boundary
in the geometry.
the parameters
set contains
of the second
is written
should
blocking
The fh-st record contains
(and the number
of columns
panel,
data is written
Computing general
data
geometry
do the computing
time step loop.
layer routines
number,
data
the geometry
data are appended
of time steps
the total number
next record each column
data
high. The
3. The geometry
and aerodynamic
streamline
regarding
the information.
to keep its speed
in figure
as possible
idea is to let PMARC
and display
package
of the wake
set to zero as the boundary
next record
process
information The
time step loop since
of wake
scan and off-body
as much
as possible.
package
the plotting
plot file is shown
is outside
velocity
a space
plotting within
time step to time step. A block off-body
to contain
data in as compact
normal
be included
in the column.
After
of vecter
which
the data for
thelast column of comer
point
column.
has been
of the panels
In this fashion
for each panel troid,
panels
and the side of that neighbor Following
centroids,
the geometry
within
data. Each
adjacent
to a given
data block
way as the geometry
is the wake
block is written using the same
The aerodynamic
quantities
nents
the velocity
of velocity,
each panel
comer
The
remainder velocity
that are written magnitude,
of the data
of lines,
velocity
components
the number
and the arclength
written of points
and the velocity at each point
nu,.mber of rectangular
within
streamline
has extensive
As with all panel
nience, the geometry patches. Each patch
volume.
fast
the same
cut through of a patch
to define
used
strength,
patch
wake
panel
the (x, y, z) compoMach
the geometry
the geometry
scan point
number
at
around becomes
the patch
for handling
side 3 of the patch.
consists
of the
of points
in
the velocity
are written.
14
For conve-
Figure
each patch A patch
4 shows
the PMARC
is four-sided;
however,
may also be folded
over
line. For instance,
wings
are normally
to form the trailing
edge
of the wing.
The direction
The direction
the outer
Columns
three-dimensional
by a set of panels.
is modeling.
side 1 of the patch. definition.
complex,
and modeled with sets of panels called A section is a set of points defining a
(i.e., a point).
a common
when viewing
scan data
and the number
number.,
INPUT
In general,
with sides 2 and 4 meeting
of the first section
the
the three
Math
number
include
includes
the local
the (x, y, z) location,
must be modeled
that the patch
becomes
These data
Modeling
used for a patch. form
blocks.
of each point,
and the local Mach
capabilities
may be of zero length
data
streamline
velocity
volumes,
OF PROGRAM
methods,
a patch
off-body
The off-body
coefficient,
modeling
patch
to define
as the direction a patch
to the plot replaces
data includes
coefficient,
of cylindrical
geometry
sides of the patch
with a folded
counterclockwise
cennumber
sides of that panel.
number
and the local
of optional
is usually subdivided into several pieces is constructed from two or more sections.
so that opposing section
coefficient,
data. The
For each
the pressure
and the conventions
one or two sides modelled
point, panel
data is written
the wake
the pressure
Geometry
itself
Thus
on each line, the (x, y, z) location magnitude,
OVERVIEW
nomenclature
The wake
are that wake
to the plot file consists
and the number
each
and magnitude,
cross-sectional
the corner
the neighbor
to the plot file are doublet the pressure
on each streamline.
volumes
•.he (i, j, k) directions
surfaces.
Following
in the last to the hint file
next. Aerodynamic data is written at the panel comer logic that is used to write the geometry and wake data.
scan data, and off-body
number
PMARC
are written
for each of the four
data block. panels.
of the last panel
vectors
contains
panel
to write the fourth
point and centroid.
off-body
components
a patch. record
data. The only exceptions
number and neighbor data is not written for wake comer points, centroids, and normal vectors. The aerodynamic data points and at the centroids
point
and normal
neighbor
panel
is included
and the third comer
points,
with no duplication
data is t:'_: panel
file in the same
an extra set of records
in the last column
all the corner
on each patch
and normal
written,
surface
of panels
of sides
The
of side I of _e patch
is
2, 3, and 4 proceed
of the patch. are established
on
The last section between
sides
used 1
and3 of the for panel
patch.
Rows
numbering
One important input
determines
input
factor to keep
in mind
and the thumb
the palm
out, it can be easily (see detailed
Because
PMARC
matches
Small should
reversed
input
using
guide,
gaps
The hierarchy dinate
for modeling
systems
mismatches
is pointing
from
reversal
a patch
is that the order of
whether
or not a patch
is inside
are pointing
in the direction
of sec-
the first section
on the outside
surface
option
panels
to the last section
of the patch.
on the PATCH1
do not have
can be tolerated will have
it is best to provide
system.
The
geometries
available
section
to match
in PMARC;
trouble
smooth
on
If a patch
namelist
exactly
however,
computing
is
in the
across
in panel
patch
the panel mis-
the surface
transitions
global
PMARC
coordinate
PMARC of a folded
transfers
system
velocities
near
size and density
Figure
6 illustrates
The
appendix
C. In order
the patch
to be closed
half of the corner comer
points
between
is used to form
in reverse matches
the two sections
guide,
appendix
order,
exactly
a tip patch
convected
to form
time steps appendix
is added
on the wing.
The wing
side
patch
into the
input
comer
to close
guide
points
is then divided
The number
off
section,
on the side of
in half. The
and the secona
of the tip patch.
1 or side 3 is folded
is then generated
is set by the user on the PATCH2
first
i_alf of the
In this way,
the panel-
of panels
to be generated
namelist
(see detailed
the wake from
model
the wake
to the wake
Modeling
in PMARC
separation
at the wake
is a time-stepping
line by the local
separation
also allows
an initial
wake
namelist
to be specified
15
wake
velocity
line with each
and the step size are sel. by the user on the BINP5 C). PMARC
systems
on either
in the detailed
of the tip patch
the last section
the paneling
The
coordinate
coordinate
tip patch
the panel points
up patches.
C).
earlier,
downstream
panels
corner
that make
c,tx)r-
and plot files.
wing patch.
is given
levels
of the hierarchy is the global below it to be translated, rotated,
The tip patch
identifies
of panel
Wake As mentioned
edge.
are several is the section
the component
the various
a closing
on a folded
the first section
of the tip patch
from
generate
PMARC
off. The total number
is used,
points
trailing
input for generating
Above
and for the output
a tip patch
a common
to form the tip patch,
points
ing on the tip patch
corner
5. There system
the sections
system.
at the top level all the elements
the code
to automatically
such that side 2 and side 4 form side 3 of the wing.
is used to define
system. Finally system allows
in figure
level coordinate
coordinate
all the panel
has the capability patch.
system
for use within
is shown
The bottom
is the component
system is the assembly _nate coordinate system. Each coordinate and scaled.
in PMARC
in PMARC.
coordinate
next level in the hierarchy
wake
The sequence
C).
or PMARC
In general,
to create
out. To determine
panel method,
and panel
not be too severe
sections
of the right hand
the patch
appendix
2 and 4 of the patch.
patches.
of coordinate
input
is inside
of the right hand
is a low-order
the pateL boundaries. between
defining
If the fingers
sides
4.
of the right hand will be resting
deck
boundaries.
between
in figure
when
or not the patch
rule can be used.
tion definition, inside
are established
is as shown
whether
out, a right-hand the patch,
of panels
on a patch
model.
flow field.
The
wake
A new row of
time step. The number (see detailed
if desired.
is
input
guide,
The time-stepping
of
functio_,sthe same_ith or without an initial wakespecified.The user to look at steady-state state condition. WAKE1
A third option
namelist
Figure
through
directly
the time
patch
modeling
into the global
a wake
the wake
modeled.
to tell PMARC in PMARC. sections.
system. directly
In this case a single
that there
If an initial
The wake
If no initial
in the global
a wake
from.
(whether
there
It also identifies
line can extend
is an initial
on the WAKE2
line and the row or column
within
over
the row or column.
will be one column
PMARC
treats
namelist.
the entire
wake
addition
within
wake
sec-
are then
and the wake
system
specified
is
as it goes
for each
from the trailing
line would
wake
sections
surface
or can be limited
edge
separates 8 shows
line)
wing
patch.
have
to a subset
from (see detailed input as the side KWSIDE.
that the wake
could
to
from.
a separate
of the wake. Figure
of a folded
The wake
the
which
is parallel
separates
more than one patch,
panel
line as the first section
identifies
which
that the wak_
of panels
from
--,r not) is to define
namelist
of the patch
the patch
separates
from side 2 of the patch.
been
and the only difference
from. the separa-
In this case, defined would
the wake
to separate
from
be that the direc-
be reversed.
is to be specified,
to the separation
surface
is specified,
definitions
is specified
The WAKE2
row or column
If the wake
side 2 and side 4 form a common
tion of the separation If an initial
wake
coordinate
the side (KWSIDE)
of panels
panels
separation
separating
to separate
side 4 (since
of wake
the wake
tion line for a wake was defined
are no wakes.
section
WAKE2 namelist must be included for each patch that the wake separates guide, appendix C). The wake separation line will be in the same direction There
allows the the steady-
steps.
separates
The separation of panels
coordinate
forms
line. This is done
the separation
no wakes
in the input deck
the wake
initial wake capability several time steps to reach
through
is to have
for wake
The first step in defining separation
going
are used to define
then PMARC
wake
in PMARC
the hierarchy
systems
time-stepped,
without
must be included
7 shows
tion coordinate transformed
prcblems
at least one more section
line. Additional
are (see detailed
input
wake guide,
sections
of the wake must be defined
can be specified
appendix
C). There
in the same
are two restrictions
manner
in as
on wake
section definitions. The first restriction is that the user-defined wake sections must all go in the same direction as the separation line, as shown in figure 8. The second restriction is that the total number of panels
defined
separates
from.
shape
on each Aside
from
and can be located
the wake
by fitting
wake
splines
must
equal
these restrictions,
anywhere through
the first section
(the wake
arbitrary
can be defined
shape
section
the wake
velocities umes
the doublet
coordinate
co"responding
panel
separation
can be computed
of uniformly
degenerated coefficient,
strengths spaced
into planes, and Mach
line) and going
in much
have
the same
lines,
The
are computed
patch
on all sections, Thus
velocity at every
by the user. components, scan
PMARC starting
an initial
wake
forms from of
is defined.
Scans
in the flow field.
16
W
points
tha: the wake
to have any arbitrary
the user chooses.
and the on-body
can be defined
or points.
comer
panels
can be defined
to the last section.
Velocity
points
of surface
system
way a surface
been determined
at user-defined scan points
number
sections
in the global
Off-Body Once
the total number
point.
analysis
Rectangular Either
has been
completed,
or cylindrical
type of scan volume
velocity
magnitude,
volcan be
pressure
The rectangular nating
scan volume
from a common
corresponding
point,
length
is specified
as shown
in terms
in figure
of three
direction
9. The length
of that side of the scan volume.
vectors
(i, j, and k'l all origi-
of each direction
The number
of points
vector
along each direction vector of the scan volume must be input. If zero is entered scan points along one direction vector, that side of the scan volume degenerates example,
if zero were
entered
for the number
of points
in the k direction,
by the i and j direction vectors. vectors is completely arbitrary.
vectors
set of vectors.
do not need
to form an orthogonal
The cylindrical used to define
the plane
der axis vector struct
scan volume
specified cylinder
in the input axis vector. must
while
of rotation
is measured,
as shown
system.
system. of scan
in the input
of scan points
axis vector
the length
The number
be specified
for the number
of a cylinder
along
PMARC
The cylindrical
The
beginning
deck.
scan
in figure
vector
10. The
can have
radii
along
angles
is determined
are
by the
radial,
scan volume,
that side of the scan volume
cylinto con-
any orienta-
and rotation
the axial,
As with the rectangular
one direction,
and a second
volume
scan volume
to be distributed
would
uses the two vectors
and ending
of the cylindrical
points
volume
of For
It is important to note that The i, j, and k direction
in terms
need not be orthogonal;
coordinate
coordinate
deck,
angle
vector
orthogonal
in the global
directions
which
and the second
a right-hand
tion desired
from
is specified
the
distributed
for the number to zero length.
the scan
degenerate into the plane of points defined the specification of the i, j, and k direction
defines
to be evenly
and angular
if zero is entered
degenerates
to zero
length.
Off-Body PMARC each
has the capability
streamline
must
of computing
be specified,
Streamlines
streamlines
in the flow field.
as well as the distance
upstream
A starting
and downstream
location
for
(measured
along
the streamline) the streamline calculation is to extend and the step size to be used. Care must be exercised in selecting the starting position for streamlines. If a streamline is started too close to a stagnation
line, the streamline
remedies:
increase
the far-field them, body
the panel
factor The
progressively
away.
are treated
to use if streamlines whose
The streamlines
A simple
symmetric
configuration
selected
tunnel tests (ref. fineness sting,
ratio yielding
wing/body
are needed
13) and which
of 12 (the wind an effective
configuration
was generic tunnel
fineness
model ratio
in close
locations
begin
are three
penetrates
distributed
sources
will increase
that penetrate
was one for which
there
the streamline
as having
starting
TEST
The
where
If this occurs,
step size. All of these
a set of streamlines
farther
the body.
in the region
panels
the streamline
best approach
is to specify
penetrate
density
so that more
or decreasing
PMARC.
could
possible
the body,
increase
and doublets
the execution proximity
on
time of
to the surface
at the stagnation
of the
line and move
the body can be ignored.
CASE
was one of the test cases extensive
in nature.
pressure The body
was truncated
of 10). The wing
17
data
used
has a circular
at the trailing is mounted
to validate
was available edge
from
cross-section for mounting
at the body
centerline
PMARC. wind and a on a near the
pointof maximumthickness.The wing hasa NACA 65A006airfoil, anaspectratio of 4.0,a taper ratio of 0.6, and is swept The PMARC
representation
the configuration reflecting
across
in PMARC.
the plane
in the chordwise
near the leading
chord.
of the wing/body
was modeled
the model
15 divisions spacing
back 45 ° at the quarter
configuration
direction
in figure
The other half of the configuration
of symmetry.
and trailing
is shown
The wing
on the upper edges,
arid lower
surface
half of
was generated
was represented
arid 10 divisions
11. Only
by
with 300 panels:
of the wing
in the spanwise
with denser
direction
with denser
spacing near the root and tip of the wing. The tip of the wing was closed off with a flat tip patch. The body was represented with 320 panels. The wing/body junction was modeled such that wing and body panels
matched
up exactly.
An initial
wake
was attached
to the trailing
edge
the aft fuselage and carried downstream 20 chord lengths. Three time steps were the wake start to roll up. The input file for this test case can be found in appendix A comparison spanwise ment
stations
between
of pressure mental
data. There
attributed
is shown
results
analysis.
is some
experimental
in figure
_'rom experimental
12. The
of 4 °. The PMARC
near the trailing
13 also illustrates
the body
to the body.
carries
edge
the importance
By attaching
a wake
Figure
data along
to allow
data at two
of attack
of 4 °. Agreea comparison
the centerline
of the body.
well with the experi-
but this can probably
The sting
of attaching
and to
13 shows
correlate
of the body,
results.
specified D.
13) and PMARC
is at an angle
results
no lift. The experimental
be
was not modeled
a wake
data shows
to the aft part of the
that there
to the aft part of the body,
in the
is carryover
the carryover
lift is
modeled.
CONCLUDING
The theoretical
basis for PMARC,
three-dimensional in the code, have been be easily
model
data and PMARC
of attack
difference
data (ref.
data is excellent.
of the sting in the experimental
Figure
a wake,
lift from the wing
from
and the experimental
is at an angle
to the presence
Without
properly
on the wing
coefficients
the model
body.
coefficients
PMARC
Again,
PMARC
of pressure
of the wing
geometries,
such as internal discussed
in some
redimensioned
An overview the appendices. experimental
modeling,
detail.
The code
for the size problem
of the program Finally,
a low-order
has been outlined. flow
input
PMARC
data to demonstrate
REMARKS
po:ential-flow Several
a simple being
solved
was presented,with results
for a generic
the accuracy
of the advanced
jet model,
was written
the appendices.
18
using
features
adjustable
size arrays
wing/body
description configuration
The input
complex
currently
and a time-stepping
and the computer
a detailed
of the code.
panel code for modeling
hardware
wake
included model,
so that it can being
of the input
were compared
file for this test case
used.
available
in with
is given
in
REFERENCES
Ashby, D. L.; Dudley, M. R.; and Iguchi, S. K.: Development Low-Order Panel Method. NA.qA TM-101024, Oct. 1988.
1.
and Validation
of an Advanced
Margason, R. J.; Kjelgaard, S. O.; Sellers, W. L.; Morris, C. E. K.; Walkey, K. B.; and Shi,:lds, E. W.: Subsonic Panel Methods--A Comparison of Several Production Codes. AIAA
.
Paper .
.
85-0280,
B.: Program of Arbitrary
VSAERO, A Computer Configurations, Users
Maskew,
B.: Program
VSAERO,
of Arbitrary
Maskew,
B.; Strash,
Techniques Feb, 1983.
°
1985.
Maskew, teristics
teristics
.
Jan.
Hess,
Configurations, D.; Nathman
J.L.; and Smith,
Configurations. Hess,
.
.
Davidson, sponding
Corp.
86-2180,
NASA
the Nonlinear
CR-4023,
F. A.: Investigation
of V/STOL
of Potential
Flow
Sept.
NASA
About
Charac-
1987.
to Advance
Aircraft.
Aerodynamic
Aug.
Prediction
CR-166479,
Arbitrary
Bodies.progress
Calculation
of Large
Model
for Complete
Aircraft
1986.
Flow About
Rep. No. MDC
lterative
Eigenvectors
Document.
Low-Speed
of Potential
Douglas E. R.: The
Calculation
for Calculating
Vol. 8, 1967, pp. I-138.
Paper
J. L.: Calculation
McDonnell
Theory
J.; and Dvorak,
B.: Unsteady
AIAA
Program
Aerodynamics
A.M.O.:
Sciences,
Katz, J.; and Maskew,
.
A Computer
of the Low-Speed
in Aeronautical
Program for Calculating the Nonlinear CharacManual. NASA CR-166476, Dec. 1982.
Arbitrary
J5679-01,
Three-Dimensional
Oct.
of a Few of the Lowest
Real-Symmetric
Lifting
Bodies.
1972.
Matrices.
Eigenvalues
J. Comp.
and Corre-
Phys.
17, 1975,
pp. 87-94. 10.
Ashby,
D. L.; and Sandlin,
Three-Dimensional 11. t
Hunt,
D. R.: Application
Internal
B.: The Panel Method
Formulations
and Numerical
Von Karman
Institute
Flow
for Subsonic Models
for Fluid
of a Low Order
Problems.
NASA
Aerodynamic
and an Outline
Dynamics,
Panel
CR-177424, Flows: Series
of Mathematical
British
1978-4,
to Complex
1986.
A Survey
of the New
Lecture
Method Sept.
Aerospace
vol. I, March
Scheme. 13-17,
1978.
P
12.
Adler,
D.; and Baron,
flow. 13.
Loving,
AIAA
Journal,
Vol.
65A006
Having Airfoil
of a Three-Dimensional
17, No. Sept.
D. L.; and Estabrooks,
Configuration NACA
A." Prediction
Section.
Aspect
RM L51F07,
19
!
of Pressure
of 45 ° Sweepback, NACA
Turbulent
Jet in Cross-
1978.
B. B.: Analysis
a Wing
Circular
Distribution Ratio
Sept.
of Wing-Fuselage
4, Taper
1951.
Ratio
0.6, and
APPENDIX PMARC C C C C C
CODE
DIMENSIONING
NUMBER
OF
PARAMETER C C C
NUMBER
NUMBER
NUMBER
SURFACE
PANELS
(NSPDIM
ALLOWED
PANELS
(NNPDIM
ALLOWED
= 500) ALLOWED
(NPDIM
OF BASIC
= 50) POINTS
ALLOWED
FOR
C (ALSO NUMBER OF SECTIONS ALLOWED C (ALSO NUMBER OF ROWS OR COLUMNS C CAUTION: DO NOT SET THIS PARAMETER C PARAMETER C C C
NUMBER
PARAMETER C C C
NUMBER
(NBPDIM
OF WAKE
SECTION
DEFINITION
PER PATCH) + 1 ALLOWED ON A PATCH) TO LESS THAN 50!
= 100)
PANELS
(NWPDIM
OF WAKE
SET
= 1000)
OF PATCHES
PARAMETER C C
STATEMENT
PARAMETERS
OF NEUMANN
PARAMETER C C C
PARAMETER
A
ALLOWED
= I000)
COLUMNS
ALLOWED
ON
EACH
WAKE
PARAMETER (NWCDIM = 50) C C NUMBER OF WAKES ALLOWED C PARAMETER
(NWDIM
= 10)
C C C
NUMBER
OF SCAN
PARAMETER. C C C
NUMBER
(NSVDIM
OF POINTS
PARAMETER
VOLUMES
OF EACH
TYPE
ALLOWED
= 10) PER
(NSLPDIM
OFF-BODY
STREAMLINE
ALLOWED
= 1000)
C C C C
NUMBER VELOCITY
OF GROUPS OF PANELS IS PRESCRIBED
PARAMETER
(NVELDIM
ON
= 200)
21
WHICH
NONZERO
NORMAL
C C NUMBER OF LINES AT A
TIME
TO BE READ
IN FOR
THE
INq::LUENCE
COEF. C MATRIX SCRATCH
IN THE
SOLVER
ROUTINE
(BUFFERED
INPUT
FROM
THE
C FILE) (CAUTION: DO NOT SET LARGER THAN ONE UNLESS YOU SURE C YOU HAVE ENOUGH MEMORY TO HANDLE BUFFERED INPUT!) C PARAMETER (MATBUF = 1) C C NUMBER OF WAKE CORNER POINTS ALLOWED C PARAMETER C C C
NUMBER
(NWCPDIM=(NWPDIM
OF SURFACE
PARAMETER
CORNER
(NSCPDIM=(NSPDIM
+ 1)'2) POINTS
ALLOWED
+ 1)'2)
C C C
NUMBER
OF EDGE
PARAMETER
PANELS
(NEPDIM
ALLOWED
= NBPDIM
_' 4)
22
ON A PATCH
ARE
L._t" |
APPENDIX MEMORY The
needed
_ted
storage
FOR
DATA
STORAGE
IN PMARC
can be divided into two types: colnmon block storage • - ..... for both wn'_s of storage is presented below and local storage. The memory• bles. requlremc-,_ _r" Storaee for local scalar variables and constants _s not in terms of the parameter vana ...... _ -r_ .... h,,_ n RBYTE below is the number of included in the mformauon presenteo oetow, l,,,_ ...... f bytes
data
REQUIREMENTS
B
for PMARC
to represent
a real
for common
NSPDIM NPDIM NSCPDIM
: ((NSPDIM
number.
RBYTE
is 4 for most
computers.
block_s * 38 * RBYTE * 16 * RBYTE * 4 * RBYTE * 3 * RBYTE
+ 1) * 2)
NNPDIM
* 15 * RBYTE
NWPDIM NWDIM NWCPD1M
* 13 * RBYTE * 3 * RBYTE * 4 * RBYTE
NWCDIM
= ((NWPDIM
+ 1) * 2)
* NWDIM
* 6 * RBYTE
NVELDIM 1
* 125 * RBYTE
in
r
in "
im nsi
n "
m n
Aerodat * 26 * RBYTE * 36 * RBY'IE * 24 * RBYTE
NPDIM 10 1
NSCPDIM
= ((NSPDIM
* 4 * RBYTE * 13 * RBYTE
+ 1) * 2)
4
B.alz9 NPDIM NEPDIM
* NPDIM
= (NBPDIM
* NPDIM
* 4)
NSPDIM
* * * *
1 * RBYTE 2 * RBYTE 2 * RBYTE 28 * RBYTE
1
* 3 * RBYTE NSPD1M
* 43 * RBYTE ":_BYT * 840
NSPDIM 1 23
B
E
NSPDIM NSPDIM
* 2 * RBYTE * 1 * RBYTE * MATBUF
* 10 * RBYTE NSI_PDIM
NBPDIM NBPDIM
* 35 * RBYTE * 3 * RBYTE * 22 * RBYTE * 9 * RBYTE
* NBPDIM
10 1
* 11 * RBYTE NSPDIM Vcalc * 6 * RBYTE * 6 * RBYTE * 28 * RBYTE
NSPDIM NWPDIM 1
* 31 * RBYTE * 9 * RBYTE
NSVDIM 1 Wakinfl NSPDIM NWPDIM NSPDIM
* * * *
* MATBUF
1 * RBYTE 1 *R.BYTE 1 * RBYTE 27 * RBYTE
1 Wakinit NWCDIM NWCDIM
* 35 * RBYTE * 3 * RBYTE * 1 * RBYTE * 3" RBYTE * 21 * RBYTE
* NWCDIM
NSPDIM NPDIM 1
NWCPDIM
: ((NWPDIM
* 3 * * 1 * * 1 * * 1*
+ 1) * 2)
NWPDIM NSPDIM NWDIM 24
RBYTE RBYTE RBYTE RBYTE
APPENDIX PMARC Basic
Input The
definitions. to handle
Section basic
to Run
data
section
C
DETAILED
INPUT
GUIDE
PMARC of the input
deck
for PMARC
consists
of a set of namelist
The required format for the basic data section is shown below. The best way the basic data section is to create a template file which can then be included into
any PMARC file and the values modified appropriately. All the namelists should always be included as shown below whether or not a particular namelist is needed for the job being run. It" a namelist is not needed for a particular job, PMARC merely skips over that namelist. Each namelist must begin with an & in the second column and the namelist name (i.e., BINP2, BINP3, etc.) and end with &END. ignored, so the items in each namelist can be spaced
Blank spaces in a namelist in whatever fashion the user
are desires.
A namelist can extend over as many lines as necessary. A description of each input variable and the valid input values follows. Under the Value column in the input description, the letter I means an integer value and the letter R means a real value. NOTE: Variables in the namelist definition which are arrays should have their elements listed out following the variable name. For example, if there were three values to be entered into the array NORPCH, the input would be as follows: NORPCH = N1,N2,N3. The rest of the elements in array NORPCH will automatically be left at zero.
TYPE
YOGR
TITLE
FOR
THIS
INPUT
FILE
HERE
&BINP2
LSTINP=2,
LSTOUT=0,
LSTFRQ=I,
LENRUN=0,
&BINP3
LSTGEO=0,
LSTNAB=0,
LSTWAK=0,
LSTCPV=0,
LSTJET=0, &BINP
4
&BINP5 &BINP
6
&BINP7
&END
MAX I T=75,
SOLRE$=0.0005,
Nq_TPS=I,
DTSTEP=0.1,
RSYM=0
. 0,
RGPR=0.0,
VINF=I
. 0,
VSOUND=!II6.0,
COMPOP= &BINP8
&END &END RFF=5.0,
RCORE=0.05,
0.0,
ALDEG=4.0,
&BINPI0 &BINPII
9
&END YAWDEG=0.0,
THEDOT=0.0,
CBAR=3.00,
SREF=I00.0,
SSPAN=I5.0,
RMPX=0.00,
RMPY=0.00,
RMPZ=0.00,
NORSET=0,
NBCHGE=0,
NCZGNE=0,
NCZPAN=0,
CZDUB=0.0,
VREF=00.0,
PSIDOT=0.0, &END
NOCF= &BINPI2
&END &END
NORPCH=0, NORF=0,
B
&END
UNIT=0,
PHIDOT=0.0, &BINP
&END
VNORM= KPAN=0,
NORL=0, 0,
NOCL=0,
0 .0,
&END KSIEE=0,
NEWNAB=0,
25
NEWSID=0,
&END
RECORD
1: Job Title
Variablg
Description
TEXT
Alphanumeric text identifying the job This record is not entered in namelist format, but merely typed in anywhere on the first line of the input deck.
BINP2: Variiibl_:
Job Control
Valu
LSTINP
Description_ Input
0
data
print
options
Prints all input data geometry input.
except
the
Prints all input data except coordinates of the geometry 2 LSTOUT
Prints Output
0 1
LSTFRQ
Basic
all input
the detailed input.
data.
print options print of output.
Allows
any or all of the additional
options
to be set manually
Controls frequency of printout time-stepping loop. 0
print
on BINP3. in the
Prints out detailed panel data only on last step. Force ar, d moment data and solution iteration history printed at ever)
step.
Prints
all data
at every
step.
Prints out detailed panel data at every Ith step, including the first and last step. Force and moment data and solution iteration history printed at every step.
26
i¢"
Variable
Value
LENRUN
0
Complete
run through
code.
2
Run thr_ agh geometry is written to plot file.
only.
Descriptio0
Run through initialization initial wake BINP3: Variable
Additional
Print
Options
LSTGEO
geometry and wake routines. Geometry and data are written to plot file.
(mu_;t be included
Value
Geometry
if LSTOUT=
I)
Description Panel
geometry
0
Print option
1
Panel corner panels.
printout
options.
off. points
printed
for all
Panel corner points and unit normal vectors printed for all panels. Panel corner points, unit normal vectors, and panel sets with prescribed normal velocities are printed out. LSTNAB
Panel neighbor options. 0
Print option
1
Prints neighbor panels.
LSTWAK
Wake
data
information
printout
information
for all
off
printout
0
Print option
1
Prints wake-shedding each w_ke column.
options.
off. information
lhints wake-shedding information each wake column and wake line
for
for
geometry. Prints wake-shedding information for each wake column, wake line geometry, and wake panel doublet values.
27
Value LSTCPV
Panel corner options.
LSTJET
BINP4:
S01vcr
printout
Print option
1
Prints out panel corner point analysis results. Will be printed according to the LSTFRQ value selected.
0
Print option
1
Print
off.
off
out jet
analysis
results
Parameters Valu_
MAXIT
I
SOLRES
R
Time-Step
Description Limit
on number
of solver
iterations
(150
is adequate
for most
cases)
Convergence criteria solver. Recommended
Descriotion
Value
NTSTPS
I
Number
DTSTEP
R
Size
Symmetry_
for the matrix setting is 0.0005.
Parameag_
V_lri_ble
BINP6:
analysis
0
Variable
BINPS:
point
and
t_omputation
Variable
Value
RSYM
0.0
of wake
time-steps.
of the time-step
(seconds).
ParamCt¢rs D¢l;cription Symmetrical case (about Y-0). Code computes the influence of the mirror image of the paneled geometry. The paneled geometry must lie in the +Y side of the global coordinate system and abut the Y=0 plane.
1.0
Asymmetrical case (about Y=0). The ent_.re geometry must be paneled. The paneled geometry may lie in +Y or -Y (or both) side of the global coordinate sy s :em.
RGPR
0.0
No ground
1.0
Ground
plane modeled
plane 28
modeled
at Z=0. at Z=0.
T ValUable
Value
RFF
5.0
Far-field-factor. (multiplies panel reference length to determine far-field radius for each panel).
RCORE
0.05
Core
radius.
Used
when
computing
velocities near a doublet panel edge. This is a dimensional quantity with units consistent with global geometry. Value can be made smaller or larger to make velocity calculations more or less sensitive to panel edges. BINPT:
Free
Stream
Conditions
Value VINF
1.0
Description Nondimensional
free stream
velocity.
(A velocity of 1.0 length unit/see is used for the time-stepping portion of the code, where length unit is the global units used for the paneled geometry). R
Dimensional free stream velocity (units should agree with option selected under UNIT below and with global units used for the geometry).
VSOUND
R
Speed of sound VINF).
UNIT
0
All velocities
1
Velocities
are
2
Velocities
are in (m/sec).
COMPOP
(units
should
agree
with
are nondimensionalized
Compressibility Incompressible
by VINF
in (ft/sec).
option. flow.
Prandtl-Glauert compressibility correction. This is essentially a twodimensional compressiblity correction that is applied The geometry compressibility
to the pressure coefficients. is not transformed into coordinates.
29
¢+,:,..7tmAl
BINPS:
Aneular
Position
and Rotation
Rates
Variable
Valu_
ALDEG
R
Angle
YAWDEG
R
Yaw
THEDOT
R
Rotation
rate
about
Y axis.
(deg/sec)
PSIDOT
R
Rotation
rate
about Z axis.
(deg/sec)
PHIDOT
R
Rotation
rate
about X axis.
(deg/sec)
BINtX):
Reference
DescriptiQn of attack angle
in degrees.
in degrees.
Dimensions
Varial_le
Val_e
CBAR
R
Description Reference chord used for normalizing pitching moment. (units must be consistent with units used to define geometry).
SREF
R
Reference
area for force
and moment
coefficients. If a plane of symmetry is used, the reference area for the paneled and reflected geometry should be used. (units must be consistent with units used to define SSPAN
R
geometry).
Semispan used for normalizing rolling and yawing moments. (units must be consistent with units used to define geometry).
RMPX RMPY RMPZ
R
Coordinates point
of the moment
in global
30
coordinate
reference system.
BINP10:
Special
Options
Variable
Value
NORSET
I
Descri__tion The number of groups which nonzero normal
of panels velocities
on are to
be prescribed. NBCHGE
The
number
of panel
neighbor
information changes that are to be made. Changing the r,eighbor information on one side of one panel constitutes one change. NCZONE
0
Regular
external
1
Internal
flow
NCZPAN
I
Panel number doublet value flow modeling.
CZDUB
R
The doublet value that is set on panel NCZPAN for internal flow modeling. A value of 0.0 is recommended unless
flow
problem of the panel on which the is specified for internal
convergence problems matrix solution. VREF
R
problem.
occur
in the
The reference velocity for computing Cp in internal flow problems. If left at 0.0, then VINF will be used to compute Cp.
31
BINP11:
Normal
Velocity
Specification
Variable
Value
NORPCH(N)
I
Patch number of patch containing the group of panels to receive a prescribed normal velocity.
NORF(N)
I
Number of first and last row of panels in defined panel set. Using 0 defaults
NOCF(N)
Description
I
all rows
on this patch.
Number
of first and last column
panels Using patch. VNORM(N)
NOTE:
R
N goes
BINP12:
Panel
from
in defined panel set. 0 defaults to all columns
of
NORL(N) to
NOCL(N)
on this
Specified normal velocity for the set of panels identified above. Positive direction is outwards from the surface.
1 to NORSET
Neighbor
Information
Chant, e
Variable
Value
KPAN(N) KSIDE(N)
I I
Panel number and the side of that panel requiring a modified neighbor.
NEWNAB(N)
I
NEWSID(N)
i
New neighbor and the side of that neighbor adjacent to KSIDE of KPAN. NEWNAB is set to 0 for a particular panel, then NEWSID should be set to
Descrip09n
-KS!DE. neighbor NOTE:
N goes from
1 to NBCHGE
32
If
This effectively cuts the relationship across side KSIDE.
Input Sectionfor SurfaceGeometryin PMARC The surfacegeometrysectionof the input deckfor PMARC consistsof a setof namelistdefinitions. The requiredformat for the surfacegeometryinput sectionis shown below. Each namelistmust begin with an & in the secondcolumn andthe namelistname (i.e. PATCHI, SECT1,etc.) andendwith &END. Blank spacesin a namelist are ignored, so the items in eachnamelistcan be spacedin whateverfashion the user desires. A namelistcan extendover as many lines as necessary.A descriptionof eachinput variable andthe valid input valuesfollows. Under the Value column in the input description,the letter I meansan integer value andthe letter R meansa real value. The only geometryinput datathat doesnot usethe namelist format is the basicpoinl coordinateinput. The basicpoint coordinateinput is handledusing a free format input. One setof three coordinatesseparatedby at least one spacemust appearon eachline. See the sample input below. &ASEMI &ASEM2
&COMP1
ASEMY=0"00' ATHET=0.00,
ASEMZ=0"00' NO DEA=5 ,
&END
APXX =0-00, AHXX=0.00,
APYY=0"00' AHYY,l.00,
APZZ=0"00' AHZZ=0.00,
&END
COMPX CSCAL
&COMP2
&PATCH1 PATCH &SECT1
ASE MX=0-00, ASCAL=I.00,
= =
CPXX CHXX
= =
IREV
=
0.0000, 1.0000, 0.0000, 0.0000,
0,
= =
CPYY CHYY
IDPAT
=
0.0000, 0.0000,
= =
COMPZ NODEC
0.0000, 1.0000,
I,
MAKE=
CPZZ CHZZ
0,
= = = =
KCOMP=
0.0000, 5,
&END 0.0000, 0.0000,
i,
&END
KASS =
I,
&E,':D
NAME STX =
0.0000,
STY =
ALF = INMODE
0 . 0, = i,
0.0
0.0
0.0
1.0
O.O
O.C
1.0 I.i
0.! 0.2
0.i 0.3
0.5
0.7
1.3 & BPNODE
COMPY CTHET
TNODE
=
3,
THETA TNODS
TNPC--
0.0000, = =
STZ =
0.0000,
SCALE
=
TINTS
=
1.00C_,
0.0, 3,
5,
TNPS=
TINTC
33
=
5,
0,
3,
&END
&END
Description ASEMI:
of Input Assembly
Variables Coor0inate
Syst.em
Information
V.a.r:.able
Value
Description
ASEMX ASEMY ASEMZ
R R R
Origin of assembly coordinate system in global coordinates.
ASCAL
R
Assembly namelist
scale. ASEM2
ASCAL
< 0 allows
If ASCAL < 0, then must be included. rotation
of assembly
about an arbitrarily defined axis (defined on ASEM2) instead of the default axis. ATHET
R
assembly
coordinate
system
Y
Rotation angle of the assembly coordinate system about the rotation axis. The default rotation axis is the assembly coordinate system Y axis. An arbitrary axis may be specified on ASEM2 if ASCAL < 0 above. Positive rotation angle Hand Rule.
NODEA
NOTE:
is determined
by Right
0
Another assembly coordinate be defined after this one.
5
This is the last assembly system to be defined.
Up to l0 assembly
coordinate
systems
system
coordinate
may
be
defined. One ASEMI land ASEM2 if required) must appear in the input deck for each assembly to be defined. Each ASEM2 that is required must follow immediately after its corresponding ASEM 1. The asseml_ly coordinate systems are numbered in the order in which they are defined. IP
34
to
ASEM2:
Assembly
Coordinate
System
Rotation
Axis
Input
Variable
Value
APXX APYY APZZ
R R R
Starting point for vector defining assembly coordinate system arbitrary rotation axis. (entered in assembly coordinates (i.e., prior to scaling by assembly scale factor)).
AHXX AHYY AHZZ
R R R
Ending point for vector defining assembly coordinate system arbitrary rotation axis. (entered in assembly coordinates (i.e., prior to scaling by assembly scale factor)).
COMPI:
Component
Coordinate
Description
Sy_.tem
Information_
V_riable
Value
Description
COMPX COMPY COMPZ
R R R
Origin of component system in assembly
CSCAL
R
Component scale. If CSCAL < 0, then namelist COMP2 must be included.
coordinate coordinates.
CSCAL < 0 allows rota:ion of component about an arbitrarily defined axis (defined on COMP2) instead of the default axis. CTHET
R
component
coordinate
system
Y
Rotation angle of the component coordinate system about the rotation axis. The default rotation axis is the component coordinate system Y axis. An arbitrary axis may be specified on COMP2 if CSCAL < 0 above. Positive rotation angle Hand Rule.
NODEC
NOTE:
is determined
0
Another component to be defined after
5
This is the last component system to be defined.
by Right
coordinate this one.
system
coordinate
Up to 10 component coordinate systems may be defined. One COMP1 (and COMP2 if required) must appear in the input deck for each component to be defined. Each COMP2 that is required must follow immediately coordinate systems defined.
after its corresponding COMP1.The are numbered in the order in _'hich 35
component they are
_OMP2:
Component
Coordinate
System
Rotation,,#xis
Input
Variable
_
CPXX
R
CPYY CPZZ
R R
CHXX CHYY
R R
Ending point for vector component coordinate
CHZZ
R
rotation axis. (entered in component coordinates (i.e., prior to scaling by component scale factor)).
PATCHI
Description Starting point for vector defining component coordinate system arbitrary rotation axis. (entered in component coordinates (i.e., prior to scaling by component scale factor)). defining system arbitrary
: Patchlnforr!3a!ion
Variable
Description
IREV
Patch reversal patches).
flag
0
Patch
not reversed.
-1
Patch
reversed.
Patch
type.
IDPAT
(for
inside
Wing type patch. Section moment data printed out. 2
4
force
Body type printed.
patch.
No section
Neumann
patch.
(Vortex
and
data
lattice
sheet).
Jet plume patch. (Computed by Adler/Baron code). This opuon requires JETI namclist to follow PATCHI. Then a single
B
out
SECT1
namelist
follows
(along
with necessary basic point coordinates and BPNODE namelists) to define the perimeter of the jet exit. Only half of the jet exit is modeled, with basic point input proceeding in a counterclockwise direction when looking towards the jet exit. The values of INMODE on SECT! are limited to between the jet plume patch.
36
! and a, inclusive,
for
V able
Value
MAKE
0
Normal patch must follow).
+I
Automatic tip patch of pat,.h I. (namelist follow).
generated PATCH2
for side 3 must
-I
Automatic tip patch of patch 1. (namelist follow).
generated PATCH2
for side must
KCOMP
I
Number of component coordinate system to which this patch belongs. Component coordinate systems are numbered sequentially as discussed in NOTE above on COMP1. If 0 is entered, KCOMP defaults to 1.
KASS
I
Number
input
of assembly
(namelist
coordinate
SECTI
1
system
to which this patch belongs. Assembly coordinate systems are numbered sequentially as discussed in NOTE above on ASEM 1. If 0 is entered, KASS defaults to 1. Neighbor relationships cut between patches on different assemblies.
RECORD
to be inserted
after
qa.riable
Value
PNAME
Text
PATCH1
namelist. Description
Patch
name
(A24)
37
are
PATCH2: Automatic PATCH 1 )
Tin Patch
Vaxiabl¢
Value
ITYP
Generation
Information
tneeded
only if MAKE
l)¢scription Tip patch
type
Flat tip patch TNODS
More
patches
Last patch input. TNPS
TINTS
I
Number "across"
to follow
in the surface
of panels the open
this one. geometry.
to be generated tip. See figure
6.
NOTE:
The tip patch paneling will match the edge paneling of the patch to which the tip patch is being fitted.
0
Full cosine spacing of panels "across" the open tip, with smaller panels near outer perimeter of the tip patch. Half cosine spacing of panels with smaller panels near the first section of the tip patch. See figure
2
NVITIP
Half cosine spacing of panels with smaller panels near the last of the tip patch. See figure 6.
3
Equal spacing open tip.
0
This
NOTE:
This namelist completes required for this patch.
variable
38
of panels
"across"
is not currently the
6.
section
the
in use. input
;_ 0 on
SECT1-
Section
Coordinate
Vari_hl_
Value
STX STY STZ
R R R
SCALE
R
System
lnformatior_ Descriptign Origin system
of section coordinate in component coordinates.
Section
scale.
If SCALE
= 0.0, the
defined section reduces to a single point at the origin of the section coordinate system. ALF
R
Rotation angle of the section coordinate system about its Y axis. A positive rotation angle is defined by the Right Hand Rule.
THETA
R
Rotation
angle
of the section
system about its Z axis. rotation angle is defined Right Hand Rule.
39
coordinate
A positive by the
Value INMODE
0
Description Copies section section.
definition
of previous
Inl_ut Y, Z, DX coordinates to define section. The X coordinate is defaulted 0.0, but local deviations can be entered in DX. (basic point BPNODE namelists
to
coordinates and follow this namelist
as needed). Input X, Z, DY coordinates section. The Y coordinate 0.G, but local deviations in DY. (basic point BPNODE namelists
to define is defaulted
to
can be entered
coordinates and follow this namelist
as needed). Input X, Y, DZ coordinates to define section. The Z coordinate is defaulted 0.0, but local deviations can be entered in DZ. (basic point BPNODE namelists
to
coordinates and follow this namelist
as needed). 4
Input X, Y, Z coordinates to define section. (basic point coordinates and BPNODE namelists follow this narnelist as
needed).
5
Generate a NACA 4 digit airfoil section. (SECT2 namelist must follow this namelist).
7
Input R, 0, X coordinates to define section. R is measured perpendicular the section X axis and 0 is measured from the section +Y axis with the positive angular direction defined by the Right Hand Rule. (basic point coordinates and BPNODE namelists follow
this namelist
40
as needed).
to
Value TNODS
O.r,.smmma
0
First
I
Break point on patch with continuous slope into the next region of patch.
2
Break point on patch with discontinuous slope into the next region of patch.
or intermediate
TINTS
of patch.
Last
section
definition
on this patch.
Last
section
definition
on last patch
surface TNPS
section
of
geometry.
Number of panels to be generated between this break point and the previous break point (or the fast section of this patch if this is the first or only break point). If TNPS = 0 at a break point, the input sections between this break point and the previous one will be used to define the panel edges. 0
Full-cosine spacing of panels between this break point and the previous one, with smaller panels near the two break
points.
Half-cosine spacing of panels between this break point and the previous one, with smaller panels near the previous break point. 2
Half-cosine spacing of panels between this break point and the previous one, with smaller point.
3
Equal break point.
panels
near
this break
spacing of panels between this point and the previous break
41
SECT2: NACA = 5 on SECT1)
4 digit
airfoil
section
generation
information
(needed
only if INMODE
Variable
Va!u____ee
Description
RTC
R
The thickness air*oil.
to chord
RMC
R
The
chamber
to chord
position
of the maximum
maximum
ratio
for the
ratio
for the airfoil. RPC
R
The chordwise chamber
IPLANE
(expressed
The plane in the section system used to generate coordinates. The 2
I
TINTC
to chord).
coordinate the airfoil
YZ plane.
The XZ plane. The XY
TNPC
as a ratio
plane.
The number of panels to be distributed between the trailing edge and the leading edge of the airfoil. The same number of panels are distributed on the upper and lower surfaces.
The type of panel spacing to be used the upper and lower svrfaces of the airfoil. 0
Full-cosine
spacing
with smaller
on
panels
near the !eading and trailing edges.(This is the recommended spacing). Half-cosine near 2
spacing
the trailing
with
spacing.
42
panels
smaller
panels
edge.
Half-cosine spacing with near the leading edge. Equal
smaller
[_ECORD point
: Section
defining
Basic
Point Coordinate
(This
record
is repeated
Value
B1 B2 B3
R R R
NOTE:
The free
Description Basic point coordinates for section definition The values that go in BI, B3 depend on the value of INMODE SECT1.
B2, on
values of BI, B2, B3 are entered as triplets in format, with at least one space separating each
value.
One
triplet
is entered
per line.
Break Point Input (inserted between basic voint coordinates on a section as needed. Must terminate basic _t_int input for a t/¢ction with a BPNODE
Variabl¢
Va!ue
TNODE
0
Description First
or intermediate
break point. and TINTC
point
Values entered are ignored).
(i.e.,
not a
for TNPC
Break point with continuous slope the next region on this section. 2
I
into
Break point with discontinuous slope into the next region on this section Final break definition.
TNPC
for each
this section)
Variable
BPNODE: definition namelist)
Inout
point.
End of this section
Number of panels to be generated between this break point and the previous one (or the first point of the section definition if this is the first or only break point). If TNPC = 0 at a break point, the input points will be used as the panel corner points this break point and the previous
NOTE:
The total number of panels to be generated on each section of a given patch must be the same.
43
!
between one.
basic
Vmable
Value
TINTC
0
Oescfiptign Full cosine spacing of panels between this break point and the previous one. with smaller panels near the two break points. Half cosine spacing of panels between this break point and the previous one, with smaller break point.
2
Jet Plume
Generation
near
the previous
Half cosine spacing of panels between this break point and the previous one, with smaller panels near this break point. Equal break point.
JETI:
panels
Information
spacing of panels between this point and the previous break
(needed
only
if IDPAT--4
on PATCH1
Variable
_
Description
V JET
R
The jet exit velocity. Units consistent with VINF.
NJDS
I
The number of jet diameters the jet plume is to be extended downstream.
DZO
R
The step size (in jet diameters or fraction of a jet diameter) for moving down the jet plume jet parameters.
JETIN
I
must
be
and computing
the
The number of the panel set with prescribed normal velocity (i.e. panel set #1, #2, #3, etc. under the NORSET option in the basic data input) which corresponds to the inlet for this jet. If there
NOTE:
is no inlet for this jet, just enter
The minimum panels plume
number
of columns
that will be computed patch can be estimateo
NJDS/DZ0
of
for the jet as:
+ 1
There is currently a limit of 50 columns of panels that can be computed for the jet plume patch. Thus NJDS and DZ0 must be set with this limit in mind. 44
0.
).
Input
Section
for Time-stepping
Wakes
in PMARC
The wake geometry section of the input deck for PMARC consists of a set of namelist definmons. The required format for the wake geometry input section is shown below. Each namelist must begin with an & in the second column and the namelist name (i.e., WAKE1, SECT1, etc.) and end with &END. Blank spaces in a namelist are ignored, so the items in each namelist can be spaced in whatever fashion the user desires. A namelist can extend over as many lines as necessary. A description of each input variable and the valid input values follows. Under the Value column in the input description, the letter I means an integer value and the letter R means a real value. The only coordinate input. One set of three
wake input data that does not use the namelist format is the basic point The basic point coordinate input is handled using a free format input. coordinates separated by at least one space must appear on each line.
the sample
below.
& WAKE
input
1
TYPE
I DWAK= WAKE
&WAKE2 &SECT1
NAME
1,
Description WAKEI:
& END
HERE
KWPACH=I, KWPAN2 = 0,
KWSIDE=2,
KWLINE=0,
NODEW=5,
INITIAL=I,
STX=
STY=
0 . 0000,
ALF=
&BPNODE
I FLXW=0,
0
9,
=
0.0
0.0
0.0
0.0
1.0
0.0
0.0
2.0
0.0
0.0
5.0
0.0
of input Wake
Variable
=
4,
=
TNPS
i0,
TINTC
=
=
I0,
TINTS
3,
=
3,
&END
&ENZ
type
0
No
wakes
1
Regular
0
Flexible
Rigid
wake wake. with wake.
stepped
WNAME
1.0000,
Description
stepped
Variable
SCALE=
identification
Wake
Wake
0.0000,
variables
IDWAK
RECORD:
&END
STZ =
3,
Value
IFLXW
KWPANI=0,
0.0,
TNODS=
TNPC
3,
0.0000,
THETA=
INMODE
TNODE
See
Name
(record
Value
local
Wake
with
to be inserted
Wake the
will be timevelocity.
will be time-
the free-stream
immediately
following
Description Text
identifying
(A24)
45
velocity
the wake
only.
WAKE1
namelist).
WAICE2:
Wake
Separation
V_...riable
Value
KWPACH
I
Lin¢
Information Description Surface geometry patch number that this wake separates from. If this wake separates from then additional
more than one patch. WAKE2 namelists must
be included for each separates from.
patch
this wake
KWSIDE
I
Side of the patch which is parallel to separation line. Separation line will be in same "direction" as the patch side specified (see fig. 8).
KWLINE
I
Row or column number within patch from which the wake separates. The side of the panels on row or column KWLINE from which the wake separates will be the same as KWSIDE. If KWLINE=0, separation is from edge (see fig. 4 for patch nomenclature).
KWPAN
1
I
Number of first panel on row or column from which wake separates (numbered locally on row or column, i.e., the first panel on the row or column is 1, the second is 2, etc.). KWPANI=0 defaults to the first panel
KWPAN2
I
patch
on the row
or column.
Number of last panel on row or column from which wake separates (numbered locally on row or column). KWPAN2=0 defaults column.
to the last panel
46
on the row
or
Value NODEW
12 mm.9.a Indicates that another will follow to continue
0
separation 3
WAKE2 the wake
line definition
namelist
for this wake.
Indicates this wake separation line definition is complete and there are more wakes to be defined after this wake. Indicates this wake separation line definition is complete and this is the last wake to be defined.
INITIAL
0
No initial specified.
wake
geometry
to be
Initial wake geometry to be specified. (SECT1 namelist must follow this namelist).
NOTE:
$E(7I'I;
Section
When specifying a wake which separates from more one patch, the order in which the separation patches (KWPACH) are input must be such that a single continuous separation line is defined. Coordinate
Variable
Valu_
STX STY
R R
STZ
R
SCALE
R
System
than
Information Description Origin of section system in global
Section
scale.
reduces system
to a point origin.
coordinate coordinates.
If SCALE---0.0, at the
section
the section coordinate
ALF
R
Rotation angle of the section coordinate system about its Y axis. A positive rotation angle is defined by the Right-Hand Rule.
THETA
R
Rotation angle of the section coordinate system about its Z axis. A positive rotation angle is defined by the Right-Hand Rule.
47
Variable
Description
INMODE
Copies the basic point coordinates of previous section and the values entered for STX, STY, and STZ on this section are displacement distances of the previous section. 0
Copies the basic previous section.
point
from
the origin
coordinates
of
Input Y, Z, DX coordinates to define section. The X coordinate is defaulted 0.0, but local deviations can be entered in DX. (basic point BPNODE namelists as 2
coordinates and follow this namelist
needed).
Input X, Z, DY coordinates to define section. The Y coordinate is defaulted 0.0, but local deviations can be entered in DY. (basic point BPNODE namelists as needed).
in DZ. (basic point BPNODE namelists
4
coordinates and follow this namelist
needed).
Inpu t X, Y, Z coordinates to define section. (basic point coordinates and BPNODE namelists follow this namelist as
needed).
48
to
coordinates and follow this namelist
Input X, Y, DZ coordinates to define section. The Z coordinate is defaulted 0.0, but local deviations can be entered
as
to
to
Variable
Value
TNODS
0
First
1
Break point on wake with continuous slope into the next region of wake.
-9
Break point on wake with discontinuous slope into the next region of wake. Last
TNPS
I
or intermediate
section
section
definition
of wake.
on this wake.
Number of panels to be generated between this break point and the previous break point (or the first section of this wake if this is the first only break point). If TNPS = 0 at a break point, the input sections between this break point and the previous one will be used to define the panel edges.
TLNTS
0
Full-cosine spacing of panels between this break point and the previous one, with smaller panel; near the two break points. Half-cosine spacing of panels between this break point and the previous one, with smaller panels near the previous break point. Half-cosine spacing of panels between this break point and the previous cnc, with smaller panels near this break point.
3
Equal
spacing
break point.
point
49
and
of panels
between
the previous
break
this
or
RECORD
: Section
l]gint; defining
Basic
Point
Input
(This
record
is repeated
Valu_
B1
R
B2 B3
R R
NOTE:
The
values
free
format,
basic
Description Basic point coordinates definition. The values B3 depend SECT1.
value.
One
of B 1, B2, with
on the value
B3 are entered
at least
triplet
one
is entered
Break Point Input (inserted between as needed. Must terminate basic point
Variable
Valu_
TNODE
0
space
for section that go in B 1, B2, of INMODE
as triplets separating
on
in each
per line. basic point coordinates on a section input for a section with a BPNODE
Description. First or intermediate point (ie., not a break point. Values entered for TNPC and TINTC are ignored). Break point with continuous slope the next region on this section.
2
I
:ato
Break point with discontinuous slope into the next region on this section. Final break definition.
TNPC
for each
this section)
Variable
I_PNODE: _l¢finition namelist)
Coordinate
Number between
p,;int.
End of this section
of panels to be generated this break point and the
previous one (or the first point of the section definition if this is the first or only
break
point).
If TNPC
= 0 at a
break point, the input points will be used as the panel comer points between this break point and the previous one. NOTE:
The total number of panels to be generated on each section of this wake must be the same as the total number of surface geometry this wake separates from.
50
panels
that
Variable TINTC
0
Full-cosine spacing of panels between tiais break point and the prev:ous one. with smaller panels near the two break points. Half-cosine spacing of panels between this break point and the previous one. with smaller panels near the previous break point. Half-cosine spacing of panels between this break point and the previous ooe, with smaller panels near this break ",oint. Equal
spacing
break point.
point
51
and
of panels
between
the previous
break
this
v_
Input Section Onbody because
Off-body Description
for Special
Options
in PMARC
su'eamlines and boundary layer analysis are not currently these routines are in the process of being replaced.
velocity
scan
of Input
functional
in PMARC
input section
Variables
The off-body velocity scan input data follows immediately after the end of the wake input section. The off-body velocity scan input section of PMARC consists of a set of namelist definitions. The required format for the velocity scan input section is shown below. The best way to handle the velocity scan input section is to create a template file which can then be included into any PMARC file and the values modified appropriately. All the namelists should always be included as shown below whether or not a particular namelist is needed for the job being run. If a namelist is not needed for a particular job, PMARC merely skips over that namelist. Each namelist must begin with an & in the second column and the namelist name (i.e., VS I, VS2, etc.) and end with &END. Blank spaces in a namelist are ignored, so items in each namelist can be spaced in whatever fashion the user desires. A namelist can extend over as many lines as necessary. A description of each input variable and the valid input values follows. Under the Value column in the input description, the letter I means an integer value and the letter R means a real value. NOTE: Variables in the namelist definition which are arrays shouM have their elements listed out following the variable name. For example, if there were three values to be entered into the array X0, the input would be as follows: X0 = R1,R2,R3. The rest of the elements in array X0 will automatically be left at zero. &VSI
NVOLR=
i,
NVOLC=
&V$2
X0 =
-2.0000,
Y0 =
0.0000,
Z0 =
-2.0000,
&VS3
Xl=
YI=
0.0000,
ZI=
-2.0000,
NPTI=
&VS4
X2 =
-2.0000,
Y2 =
0.0000,
Z2 =
-2.0000,
NPT2
&VS5
X3=
-2.0000,
Y3 =
0.0000,
Z3=
2.0000,
&VS6
XR0
=
0.0000,
YR0
=
0.0000,
ZR0=
0.0000,
&VS7
XRI
=
0.0000,
YRI
=
ZRI=
0.0000,
XR2
=
0.0000,
YR2=
0.O000,
ZR2
0.5000,
R2=
5.0000,
PHIl=
&VS8
RI=
&VS9
NRAD=
2.0000,
10,
NPHI=
I,
10.0000,
12,
52
&END
NLEN
=
&END
NPT3=
20, =
0, 40,
=
5,
&END &END
&END
1.0000, 0.0,
&END
&END PHI2=330.0,
&END &END
VSl.. Variable
Value
NVOLR
I
Number
of rectangular
NVOLC
I
Number
of cylindrical
Description scan scan
volumes volumes
VS2: Variilbl¢
Valu_
X0(N) Y0(N) ZO(N)
R R R
Description Coordinates scan volume
of origin N.
of rectangular
S,'-e figure
9.
vsB: Variable
Value
XI(N) YI(N)
Coordinates
ZltN)
R R R
NPT 1 (N)
I
Number of scan points to be distributed along side i of scan volume N.
Vafiabl_
Valu
X2_N) Y2(N) Z2(N)
R R R
NPT2(N)
Description
for rectangular See figure 9.
of comer scan
in i direction volume
N.
Descriptiqn Coordinates of corner in j direction for rectangular scan volume N. See figure 9. Number of scan points to be distributed along side j of scan volume N.
53
v_mak
Value
X3(N) Y3(N)
R R
Coordinazes
Z3(N)
R
See figure
NPT3(N)
I
Number
Description
along NOTE: NOTE: volume
N goes from 1 _o NVOLR If NPT1, NP f2, or NPT3 collapses
to a point.
of comer
for rectangular
Thus
is zero,
in k direction
scan volume
N.
9. of scan
points
side k of scan
the corresponding
a rectangular
to be distributed
volume
scan volume
N.
side of the rectangular can be reduced
line, or a point.
VS6". Val e XR0(N) YR0(N) ZR0(N)
R R R
Description Coordinates volume N.
of origin of cylindrical See figure 10.
scan
VST: Value XRI(N) YRI(N) ZRI(N)
R R R
Description Coordinates of point defining axis (from XR0, YR0, ZR0) of cylindrical scan volume N. (Cannot be XR0, YR0, ZR0).
XR2(N) YR2(N) ZR2(N)
R R R
See figure
Coordinates (from XR0, is measured figure
10.
54
10.
of point defining YR0, ZR0) from for scan volume
vector which PHI N. See
scan
to a plane,
a
VSS: Description RI(N)
R
Inner
radius
of cylindrical
R2(N)
R
Outer
radius
of cylindrical
PHI 1(N)
R
Starting angle (measured from the vector (XR2-XR0),(YR2-YR0), (ZR2-ZR0)) for cylindrical scan volume N. Positive angle is determined by the Right Hand Rule.
PHI2(N)
R
Ending vector
Value
NRAD(N)
I
Number
of points
the radial direction volume N.
volume
sczn
angle (measured from (XR2-XR0),(YR2-YR0),
for cylindrical scan angle is determined
Variable
scan
volume
to be distributed
in
for cylindrical
scan
Number of points to be distributed the f direction for cylindrical scan volume N.
NLEN(N)
I
Number of points the axial direction volume N.
NOTE: NLEN,
from
(ZR2-ZR0))
volume N. Positive by the Right Hand
I
N goes
N.
the
NPHI(N)
NOTE:
N.
Rule.
in
to be distributed in for cylindrical scan
1 to NVOLC
The cylindrical scan volume can be reduced NPHI, or NRAD equal to zero.
55
to a plane,
a line, or a point
by setting
Off-body Description
strcam!ine of Input
input
section
Variables
The off-body streamline input data must follow immediately after the off-body velocity scan data. The off-body streamline input section of PMARC consists of a namelist which defines the number of streamlines there _ ill be for the job and a namelist definition which is repeated for each separate streamline. The required format for the off-body streamline input section is shown below. The best way to handle the off-body streamline input section is to create a template file with a single streamline which can then be included into any PMARC file and the values modified appropriately. Both of the namelists shown below should always be included in the input deck, whether or not there will be any offbody streamlines. If a namelist is not needed for a particular job, PMARC merely skips over that namelist. Each namelist must begin with an & in the second column and the namelist name (i.e., SLIN1, SLIN2, etc.) and end with &END. Blank spaces in a namelist are ignored, so the items in each namelist can be spaced in whatever fashion the user desires. A name!ist can extend over as many lines as necessary. A description of each input variable and the valid input values follows. Under the Value column in the input description, the letter I means an integer value and the letter R means a real value.
&SLINI
NSTLIN=I,
&SLIN2
SX0= SU=
&END -3.0000,
SY0=
0.0000,
SZ0=
0.0500,
0.0000,
5D =
6.5000,
DS=
0.0250,
mmm
56
&END
iv
SLIN1." Variable
Description
NSTLIN
Number
of streamlines
to be defined.
_I_IN2: Variable
Value
SX0 SY0 SZ0
R R R
Global coordinates streamline.
SU
R
Distance
DescripJion for starting
streamline
to be traced
upstream direction (same length as geometry). SD
R
Distance
streamline
downstream length
DS
NOTE:
R
Record
SLIN2
be repeated
of
in
units of
to be traced (same
in
units of
as geometry).
Step size streamline must
direction
point
to be used in tracing (D distance)
NSTLIN
57
times
(one
for each
streamline).
APPENDIX SYMMETRIC
WING/BODY
WING BODY COMBINATION &BINP2 &BINP3
D TEST
CASE
INPUT
FILE
TEST CASE LSTOUT=0, LSTNAB_d),
&ASEMI
ASEMX= ASCAL=
0.0(X)O, ASEMY= I.{XX}O,ATHET=
0.0000, 0.0,
ASEMZ= NODEA=
&ASEM2
APXX= AHXX=
O.(XX)0, APYY= 0.0(X)0, AHYY=
0.0000, 1.0000,
APZZ=0.(X]00, AHZZ=0.0000,
&ASEMI
ASEMX= ASCAL=
0.0000, 1.0000,
0.0000, 0.0,
ASEMZ= NODEA=
&ASEM2
APXX= AHXX=
0.0000, APYY= 0.(X)00, AHYY--
0.0000, 1.0000,
APZZ_.O000, AHZZ=0.0000,
&COMPI
COMPX= CSCAL=
0.00(30, COMPY= i.0000, CTHET=
0.0000, 0.0,
COMPZ= NODE(:--
&COMP2
CPXX= CHXX=
0.0000, CPYY= 0.(X)00, CHYY=
0.0000, CPZZ= 0.0000, 1.0000, CI-IZZ,--0.0000,
&BINP4 &BINP5 &BINP6 &BINP7 &BINP8 &BINP9 &BINP10 &BINPI 1
&BINPI2
LSTFRQ=I, LSTWAK=3,
&END
LSTINP=-2, LSTGEO=0, LSTJET=O, MAXIT=200, NTSTPS=3, RSYM--O.0, VINF= 1.0, COMPOP--O.0, ALDEG_.0, PHIDOT=0.0, CBAR=6.125, RMPX--9.00, NORSET=0, NCZPAN=O, NORPCH=O, NORF-_, NOCF---O, VNORM=O.0, KPAN----O,
LENRUN=0, LSTCPV=0,
&END &END &END &END
SOLRES=0.0005, DTSTEP=3.0, RGPR---O.0, RFF=5.O, RCORE=0.10, VSOUND=I 116.0, UNIT=0,
&END YAWDEG=0.0,
THEDOT=0.0,
SREF=I47.0, RMPY=0.00, NBCHGE=0, CZDUB=0.0,
SSPAN= 12.0, RMPZ=O.00, NCZONE--O, VREF=00.O,
PSIDOT=0.0, &END &END &END
NO_, N_, NEWNAB--0,
KS_,
ASEMY= ATHET=
&END &END
NEWSID=0,
0.0000, 0, &END &END
0.0000, 5, &END &END
0.0000, 5, &END &END
59 PFECEDING
PAG£
6LANK
NOT
FILMED
I
&PATCH
I
IREV= 0, KCOMP=
IDPAT= I, KASS=
I, I,
MAKE=
0, &END
WING &SECTI
21.46,11 21.3866 21. ! 575 20.7868 20.2908 19.6855 18.9955 18.2571 17.5037 16.7691 16.0776 15.4628 14.9568 14.5818 14.3560 14.2985 14.3560 14.5818 14.9568 15.4628 16.0776 16.7691 17.5037 18.2571 18.9955 19.6855 20.2908 20.7868 21.1575 21.3866 21.4641
STX= 0.00130,STY-- O.0fXX3,STZ= ALF= 0.0, THETA= 0.0, INMODE= 4, TNODS= T_NTS= j, 1.6481 0.0000 1.6482 -0.0059 1.6484 -0.0228 1.6488 -0.0493 1.6495 -0.0847 1.6,140 -0.1260 1.6313 -0.1662 1,.6195 4). 1979 1.6103 -0.2125 1.6043 -02983 1.5933 -0.1902 1.5811 -0.1616 1.5731 -0.1252 1.5692 -0.0855 1.5698 -0.0434 1.5751 0.0000 1.5698 0.0434 1.5692 0.0855 1.5731 0.1252 1.5811 0.1616 1.5933 0.1902 1.6043 0.2083 1.6103 0.2125 1.6195 0.1979 1.6313 O. 1662 1.6440 O. 1260 1.6495 0.0847 1.6488 0.0493 1.6484 0.0228 1.6482 0.0059 1.648 i 0.0000
&BPNODE
TNODE=
3,
TNPC=
60
0,
0.0000, SCALE= O,
TNPS=
1.0000. 0, &END
TINTC=
0,
&END
&SECT1 SCALE= INMODE= 1.0000 0.9500 0.9000 0.8_KI 0.8000 0.7500 0.7000 0.6500 0.6000 0.5500 0.5000 0.4500 0.4000 0.3500 0.3000 0.2500 0.2000 0.1500 0.1000 0.0750 0.0500 0.0250 0.0125 0.0075 0.005 0.0 &BPNODE 0.0 0.005 0.0075 0.0125 0.0250 0.0500 0.0750 0. I000 0.1500 0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 0.5000 0.5500 0.6000 0.6500 0.7000 0.7500 0.8000 0.8500 0.9000 0.9500 1.0000 &BPNODE
STX= 4.5000, 2, 000000 -0.00370 -0.00727 43.01083 -0.01437 -0.01775 -0.02087 -0.02364 -0.02602 -0.02793 -0.02925 -0.02992 -0.02996 -0.02945 -0.02842 -0.02687 -0.02474 -0.02194 -0.01824 -0.01591 -0.01313 -0.00981 -0.00718 -0.00563 -0.00464 0.0 TNODE= 0.0 0.00464 0.00_3 0.00718 0.00981 0.01313 0.0i 591 0.01824 0.02194 0.02474 0.02687 0.02_2 0.02945 0.02996 0.02992 0.02925 0.02793 0.02602 0.02364 0.02087 0.01775 0.01437 0.01 083 0.00727 0.00370 0.03OO0 TNODE=
25.3750,
STY= 0.0, 3,
ALF= TNODS= 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2, 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3,
12.0000, THETA= TNPS= 10,
S'IZ= 0.0(_), 0.0, TINTS=
,
&END
TNPC=
TNPC=
61
15,
15,
TINTC=
TINTC=
0,
0,
&END
&END
,
&PATCH
I WING
&PATCH2
&PATCH
IREV= 0, KCOMP= TIP ITYP=
1,
IREV= 0, KCOMP= FORWARD FUSELAGE &SECT1 STX= 0.(X300, ALF= 0.0, INMODE= TINTS= 0, 0.0000 -1.0000 0.1735 -0.9845 0.3420 -0.9395 0.5000 -0.866O 0.6425 -0.7660 0.7660 -0.6425 0.8660 43_5000 0.9395 -03420 0.9845 -0.1735 1.0000 0.0000 0.9845 0.1735 0.9395 0.3420 0.8660 0.5000 0.7660 0.6425 0.6425 0.7660 0.5000 0.8660 0.3420 0.9395 0.1735 0.9845 0.0000 1.0000 &BPNODE &SECTI
&SECTI
&SECTI
&SECT1
&SECT1
&SECTI
1
TNODE= STX= 0.2000, ALF= 0.0, INMODE= TINTS= STX= 0.5000. ALF= 0.0, INMODE= TINTS= STX= 1.0000, ALF= 0.0, INMODE= TINTS= STX= 2.0000, ALF= 0.0, INMODE= TINTS= STX= 4.0000, ALF= 0.0, INMODE= TINTS= STX= 8.0000, ALF= 0.0, INMODE= TINTS=
[DPAT= I, KASS=
l, 2,
MAKE=
TNODS=
3,
TNPS=
IDPAT= 1, KASS=
2, 1,
MAKE=
STY= 0.0000, STZ= THETA= 0.0_ 1, TNODS=
&END 3,
TINTS=
3, &END
0, &END
0.0000,
SCALE=
0,
TNPS=
0.0090, 0, &END
0.0000 0.0000 0.0000 0.0000 0.0000 0.000(3 0.0000 0.000(3 0.0000 0.000(3 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3, STY= THETA= 0, 0, STY= THETA= 0, 0, STY= THETA= 0, 0, STY= THETA= 0, O, STY= THETA= 0, 0, STY= THETA= 0, 0,
TNPC= 0.0000,
10, STZ= 0.0,
TNODS= 0.0000,
STZ= 0.0,
TNODS= 0._,
STT_ 0.0,
]NODS= 0.0000,
STZ= 0.0,
TNODS= 0.0000,
STZ= 0.0,
TNODS= 0.000(3, TNODS=
62
STZ= 0.0,
TINTC= 3, 0.0000, SCALE=
o,
TNPS=
0.(]000,
SCALE=
0,
TNPS=
0.00130,
SCALE=
0,
TNPS=
0.0000,
SCALE=
o.
TNPS=
0.0000,
SCALE=
O.
TNPS=
0.0000,
SCALE=
0,
TNPS=
&END 0.0924,
0, &END 0.1712, 0, &END 0.2889, 0, &END 0.48oX),
0, &END 0.7884, 0, &END 1.2360, 0, &END
&SECTI
STX=
&SECTI
14.2983 14.2983 14.2983 14.2983 14.2983 14.2985 14.2983 14.2983 14.2983 14.2983 14.2983 &BPNODE
&PATCH
IREV= 0. KCOMP= LOWER MID FUSEE'.
&SECTI
14.2983 14.2983 14.2983 14.2983 14.2983 14.2985 &BPNODE &SECTI
14.3558 14.3558 14.3558 14.3558 14.3558 14.3560 &BPNODE &SECTI
14.5815 14.5815 14.5815 14.5815 14.5815 14.5818 &BPNODE
12.0000,
ALF= 0.0, INMODE= TINTS= STX= 0.(,_300, ALF= 0.0, INMODE= TINTS= 0.00)0 0.4893 0.9307 1.2808 1.5053 1.5751 1.5048 !.2800 0.9299 0.4888 0.OO00 TNODE=
!
S'IX= 0.0000, ALF= 0.0, INMODE= TINTS= 0.0000 0.4893 0.9307 1.2808 1.5053 1.5751
STY= THETA= 0, TNODS= 0, STY= 0.0000. THETA= 4, TNODS= 0, -! .5829 - 1.5050 - 1.2802 -0.9297 -0.4881 0.0000 0.4900 0 93(Z', 1.2807 1.5051 1.5829 3, TNPC=
IDPAT= 0, KASS= GE
0.0000, 0.0,
STZ= 0.0,
STZ=
0.00130,
SCALE=l.49t,.,,
0,
TNPS=
0,
0.0(X)0.
SCALE=
3,
"INPS=
&END 1.00(X), 7, &END
0,
2, 0,
STY= 0.0000, STZ,= THETA= 0.0, 4, TNODS= 0, -1.5829 - ! .5050 - 1.2802 -0.9297 -0.488 I 0.0000
TINTC=
0,
MAKE=
0,
0.0000,
SCALE=
0,
TNPS=
&END
0, &END
TNODE= 3. TNq:_C= 0, STX= 0.(_XX). STY= 0.00(O, SqT_,= ALF= 0.0, THETA= 0.0,
TINTC= C.S_).
SCALE=
0,
INMODE= TINTS= 0.0000 0.48 ! 1 0.9169 1.2664 !,4962 1.5698
4, 0, -i .5846 - i .5091 -1.2919 -0.9527 -0.5234 -0.0434
TNODS=
0,
TNPS=
TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 0.0000 0.4751 0.9070 1.2565 1.4913 1.5692 "I'NODE=
3, STY= THETA= 4. 0, -1.5912 -1.5176 - 1.3067 -0.9767 -0.5575 -0.0855 3,
TNPC= 0.000(3,
0, &END
0, S'I7_,= 0.0,
TNODS=
"rlNTC= 0.00130,
SCALE=
0,
0,
TNPS=
0, &END
TNPC=
63
0,
TINTC=
0.
&END
&SECT1
14.9565 14.9565 14.9565 14.9565 14.9565 14.9568 &BPNODE &SECT1
15.4626 15.4626 15.4626 15.4626 15.4626 15.4628 &BPNODE &SECT1
16.0776 16.0776 16.0776 16.0776 16.0776 ! 6.0776 &BPNODE &SECT1
16.7691 16.7691 16.7691 16.7691 16.7691 16.7691 &BPNODE &SECTI
17.5036 17.5036 17.5036 17.5036 17.5036 17.5037 &BPNODE
STX= 0.0C_, ALF= 0.0, INMODE=
STY= 0.01300, STZ= TflETA= 0.0, 4, TNODS=
TINTS=
o,
0.0009 0.4707 0.8999 1.25(K) I ,1896 1.5731 TNODE= STX= 0.0fg)0, ALF= 0.0, INMODE= TINTS= 0xO30 0.4676 0.8952 1.2463 i.4904 1.5811 TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 0.00130 0.4664 0.8935 1.246 1 1.4940 1.5933 TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 0.0000 0.4668 0.8948 1.2492 i.5000 1.6043 TNODE= STX= 0.00_, ALF= 0.0, INMODE= TINTS= 0.0003 0.4693 0.8997 1.2563 1.5089 1.6103 TNODE=
-1.6014 -1.5295 -1.3239 -1 _0016 -0.5908 -0.1252 3, STY= THETA= 4, 0, - 1.6139 -1.5432 - ! .3420 - ! .0260 -0.6219 -0.1616 3, STY= THETA= 4, 0, - 1.6271 - 1.5573 -1.3589 - 1.0470 -0.6472 43.1902 3, STY= THETA= 4, 0, - 1.6396 - 1.5701 - i .3730 - 1.0627 43.6645 -0.2083 3, STY= THETA= 4, 0, - 1.6507 - 1.5808 - ! .3830 -1.0715 -0.6716 -0.2125 3,
0.00013,
SCALE=
O,
TNPS=
1.0000.
O, &END
TNPC= 0.0000,
0, S'IZ= 0.0,
TNODS=
TINTC= 0, 0.0000, SCALE= 0,
TNPS=
&END 1.0003,
O, &END
TNPC= 0.0000,
0, STZ= 0.0,
TNODS=
TINTC= 0.0000,
SCALE=
0,
0,
TNPS=
&END 1.0000,
0, &END
TNPC= 0.0000,
0, S'17_,= 0.0,
TNODS=
TINTC= 0.fD00,
SCALE=
0,
O,
TNPS=
&END 1.0000,
O, &END
TNPC= 0.0003,
0, S'I7_,= 0.0,
TNODS=
TINTC= 0.00013,
SCALE=
0,
0,
TNPS=
&END 1.0000,
0, &END
TNPC=
64
0,
TINTC=
0,
&END
&SEC_I
18.2570 18.2570 18.2570 18.2570 18.2570 18.2571 &BPNODE &SECT1
18.9955 18.9955 18.9955 18.99,55 18.9955 18.9955 &BPNODE &SECT1
19.6855 19.6855 19.6855 19.6855 19.6855 19.6855 &BPNODE &SECT 1
20.2908 20.2908 20.2908 20.29C8 20.2908 20.2908 &BPNODE &SECTI
20.7869 20.7869 20.7869 20.7869 20.7869 20.7868 &BPNODE
STX= 0.1313130,STY= 0.0000, STZ= ALF= 0.0, THETA= 0.0, INMODE=. 4, TNODS= TINTS= 0, 0.0000 -1.6594 0.4747 -1.5884 0.9097 -1.3869 1.2691 - 1.0699 1.5221 -0.6635 1.6195 -0.1979
0.0000,
TNODE= 3, "INPC= 0, STX= 0.00(30, STY= 0.0000, STZ,= ALF= 0.0, THETA= 0.0, INMODE= 4, TNODS= TINTS= 0, 0.0000 -1.6650 0.4825 -1.5920 0.9236 -1.3844 1.2860 - 1.0582 1.5377 -0.6413 1.6313 -0.1662
TINTC= 0.0000,
SCALE=
0,
TNPS=
TNODE= STX= 0.01Xq0, ALF= 0.0, INMODE= TINTS= 0.0000 0.4910 0.9385 1.3032 1.5522 1.6440
3, I'Nqt_C= 0, STY= 0.0000, S'IZ= THETA= 0.0, 4, TNODS= 0, - 1.6670 -!.5918 - 1.3769 -I 0401 -0.6110 -0.1260
SCALE=
1.0(_'3,
TNPS=
O, &END
0,
0, &END
TINTC= 0, 0.0000, SCALE= 0,
TNPS=
&END
TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 0.0000 0.5944 0.9614 1.328 ! 1.5697 1.6488
3, TNPC= 0, STY--- 0.0000, S'I7_,= THETA= 0.0, 4, TNODS= 0, - 1.6635 -! .5844 -1.3570 - ! .0018 -0.5522 43.0493
TINTC= 0, 0.0000, SCALE=
TNODE=
3,
TINTC=
65
0,
&END 1.0003,
0,
TNODE= 3, TNPC= 0, TINTC= 0, STX= 0.01300, STY= 0.0000, S'17__,= 0.0000, SCALE= ALF= 0.0, THETA= 0.0, INMODE= 4, TNODS= 0, TNPS= 0, TINTS= 0, 0.00130 - 1.666O 0.4985 - !.5887 0.9515 -1.3669 1.3177 -1.0199 1.5630 -0.5794 1.6493 -0.0847
TNPC=
&END 1.0000,
0,
TNPS=
&END 1.O000,
&END
&END 1.0000,
0, &END
O,
&END
STX= 0.(K)00, STY= ALF= 0.0, THETA= INMODE= 4, TINTS= O. 0.0000 -1.660,5 0.5085 -1.5802 0.9682 - 1.3487 1.3349 -3.9875 1.5733 -0.5313 1.6484 t_ tr_',,_ TNODE= 3, STX= 0.00(Y0, STY= ALF= 0.0, THETA= INMODE= 4, TINTS= 0, 0.0000 - 1.6583 0.5110 -1.5771 0.9722 - 1.3431 1.3389 -0.9781 1.5751 -0.5179 1.6482 -0.0059 TNODE= 3, STX= 0.0000. STY= ALF= 0.0, THETA= INMODE= 4, TINTS= 0, 0.0000 - i .6574 0.5124 - 1.5759 0.9745 -I .3404 1.3412 -0.9734 1.5762 -0.5 ! 10 1.6481 0.0000 TNODE= 3,
&SECT1
21.1576 21.1576 21.1576 21.1576 21.1576 21.1575 &BPNODE &SECTI
21.3867 21.3867 21.3867 21.3867 21.3867 21.3866 &BPNODE &SECTI
21.4642 21.4642 21.4642 21.4642 21.4642 21.464 1 &BPNODE
&PATCH
1 UPPER
&SECTI
14.2985 14.2983 14.2983 14.2983 14.2983 14.2983 &BPNODE
IREV= 0. KCOMP= MID FUSELAGE STX= 0.(_,,_), ALF= 0.0, INMODE= TINTS= 1.5751 1.5048 1.2800 0.9299 0.4888 0.0000 TNODE=
0.0000,
ST'Z= 0.0,
_ODS=
0.00(D.
SCALE=
0.
TNPS=
1.0000,
0. &END
"I'NTJC= 0, 0.00(X), STZ.= 00, TNODS=
TINTC= 0.00013,
SCALE=
0,
0,
'."NPS=
&END 1.0000.
0, &END
TNPC= 0.0000,
0, S'IT_ 0.0,
TNODS=
TINTC= 0.00(D,
SCALE=
0,
3,
TNPS=
&END 1.0000,
0, &END
TNPC=
0,
TINTC=
0,
IDPAT= 0, KASS=
2. 0,
MAKE=
0.
STY= 0.00(D, S"IZ= THETA= 0.0, 4, TNODS= 0, 0.0000 0.4900 0.9309 1.2807 1.505 i 1.5829 3, TNPC= 0,
66
&END
&END 0._,
SCALE=
O,
TNPS=
1.0000, O, &END
TINTC=
0,
&END
&SECTI
14.3560 14.3558 14.3558 143558 14.3558 14.3558 &BPNODE &SECT1
14.5818 14.5815 14.5815 14.5815 14.5815 14.5815 &BPNODE &SECT1
14.9568 14.9565 14.9565 14.9565 14.9565 14.9565 &BPNODE &SECTI
15.4628 15.4626 15.4626 15.4626 15.4626 15.4626 &BPNODE &SECTI
16.0776 16.0776 16.0776 16.0776 16.0776 16.0776 &BPNODE
1
S'I'X= 0.00_, ALF= 0.0, INMODE= TINTS= 1.5698 1.4962 1.2664 0.9169 0.4811 0.0000
STY= 0.0000, STZ= THETA= 0.0, 4, TNODS= 0, 0.0434 0.5234 0.9527 1.2919 1.5091 1.58,,6
0.0000,
SCALE=
o,
TNPS=
TNODE= STX= 0.0030, ALF= 0.0, INMODE= TINTS= 1.5692 1.4913 1.2565 0.9070 0.4751 0.0000
3, "I NPC= 0, STY= 0.0000, STZ= THETA= 0.0, 4, TNODS= 0, 0.0855 0.5575 0.9767 1.3067 1.5176 1.5912
TINTC= 0, 0.0000, SCALE-:
TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 1.5731 1.4896 1.25_ 0.8999 0.4707 0.0000
3, TNPC= 0, STY-0.0000, ST7_ THETA= 0.0, 4, TNODS= 0, 0.1252 0.5908 1.0016 1.3239 1.5295 1.6014
TINTC= 0.0000,
SCALE=
o.
TN."S=
TNODE= STX= 0.0030, ALP= 0.0, INMODE= TINTS= 1.5811 1.4904 1.2463 0.8952 0.4676 0.0000
3, "I'NI:_= 0, STY= 0.0000, STZ= THETA= 0.0, 4, TNODS= 0, 0.1616 0.6219 1.0260 1.3420 1.5432 1.6139
TINTC= 0, 0.00_, SCALE=
TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 1.5933 1.4940 1.2461 0.8935 0.4664 0.0000
3, TNPC= 0, STY= 0.0030, STZ= THETA= 0.0, 4, TNODS= 0, 0.1902 0.6472 1.0470 1.3589 1.5573 !.6271
TINTC= 0, 0.0000, SCALE=
TNODE=
3,
TINTC=
"l]Xq:'C=
67
0,
1.0000,
0. &END
0,
TNPS=
&END I.(K)00,
0, &END
O,
&END 1.0000,
0, &END
0,
TNPS=
&END 1.0003.
0, &END
0,
TNPS=
&END 1.00130,
0, &END
0,
&END
I
&SECTI
STX=
16.7691 16.7691 16.7691 16.7691 16.7691 16.7691 &BPNODE &SECT1
ALF= 0.0, INMODE= TINTS= 1.6043 1.5000 1.2492 0.8948 0.4668 0.0000 TNODE= STX= 0.0000,
THETA= 0.0, 4, TNODS= 0, 0.2083 0.6645 1.0627 1.3730 1.5701 1.6396 3, TNPC= 0, STY= 0.00O3, STZ=
ALF= 0.0, INMODE= TINTS= 1.6103 1.5089 1.2563 0.8997 0.4693 0.0000 TNODE= STX= 0.0000, ALF-0.0, INMODE= TINTS= 1.6i95 1.5221 1.2691 0.9097 0.4747 0.0000 TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 1.6313 1.5377 1.2860 0.9236 0.,-'.825 0.0( 30 TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 1.6440 1.5522 1.3032 0.9385 0.4910 0.0000 TNODE=
THETA= 4, 0, 0.2125 0.6716 1.0715 !.3830 1.5808 1.6507 3, STY= THETA= 4, 0, 0.1979 0.6635 1.0699 1.3869 1.5884 1.6594 3, STY= THETA= 4, 0, 0.1662 0.6413 1.0582 1.3844 1.5920 1.6650 3, STY= THETA= 4, 0, 0.12.60 0.6110 1.0401 i.3769 1.5918 1.6670 3,
17.5037 17.5036 17.5036 17.5036 17.5036 17.5036 &BPNODE &SECT1
18.2571 18.2570 18.2570 18.2570 18.2570 18.2570 &BPNODE &SECTI
18.9955 18.9955 18.9955 18.9955 18.9955 18.9955 &BPNODE &SECTI
19.6855 19.6855 19.6855 19.6855 19.6855 19.6855 &BPNODE
0.0000,
STY=
0.0000,
STZ=
0.00130,
SCALE=
0,
TNPS= 0,
1.0000,
&END
TINTC= 0, 0.00013, SCALE=
0.0, TNODS=
0,
TNPS=
O, &END
TNPC= 0.0000,
0, STZ= 0.0,
TNODS=
TINTC= 0, 0.0000, SCALE=
o,
TNPS=
&END 1.0000,
0, &END
TNPC= 0.0000,
0, ST7__ 0.0,
,'INODS=
TINTC= 0.0000,
SCALE=
0,
O,
TNPS=
&END 1.0000,
0, &END
TNF'C= 0.13000,
0, STZ= 0.0,
TNODS=
TINTC= 0, 0.0000, SCALE=
o,
&END 1.0000,
TNPS= 0, &END
TNPC=
68
0,
TINTC=
0,
&END
&SECTI
20.2908 20.2908 20.2908 20.2908 20.2908 20.2.008 &BPNODE &SECTI
20.7868 20.7868 20.7868 20.7868 20.7868 20.7868 &BPNODE &SECT1
21.1575 21.1576 21.1576 21.1576 21.1576 21.1576 &BPNODE &SECTI
21.3866 21.3867 21.3867 21.3867 21.3867 21.3867 &BPNODE &SECTI
21.4641 21.4642 21.4642 21.4642 21.4642 21A642 &BPNODE
0.0000,
STZ= 0.0,
O.OOO0, SCALE=
STX= 6.0000, ALF= 0.0, INMODE= TINTS= 1.6495 1.5630 1.3177 0.9515 0.4985 0.0000 TNODE= STX= 0.0000. ALF= 0.0, INMODE= TINTS= 1.6488 1.5697 1.3281 0.9614 0.5044 0.0000 TNODE= STX= 0.0000, ALl:= 0.0, INMODE= TINTS= 1.6484 1.5733 1.3349 0.9682 0.5085 0.0000
STY= THETA= 4, 0, 0.0847 0.5794 ! .0199 1.3669 1.5887 1.6660 3, STY= THETA= 4, O, 0.0493 0.5522 1.0018 1.3570 1.5844 1.6635 3, STY= THETA= 4, 13, 0.0228 0.5313 0.9875 1.3487 1.5802 i .6605
TNODE= STX= 0.0000, ALF= 0.0. INMODE= TINTS= 1.6482 1.5751 1.3389 0.9722 0.5110 0.0000
3, TNPC= O, STY= 0.00120, S'I7_,= THETA= 0.0, 4, TNODS= 0, 0.0059 0.5179 0.9781 1.3431 1.5771 1.6583
TINTC= O, 0.0000, SCALE=
TNODE= STX= 0.0000, ALF= 0.0, INMODE= TINTS= 1.6481 1.5756 !.3402 0.9736 0.5118 0.0000 TNODE=
3, STY= THETA= 4, 0, 0.0000 0.5 i 32 0.9748 1.3411 1.5760 1.6574 3,
TINTC= 0.0000,
SCALE=
3,
TNPS=
TNODS=
0,
TNPS=
1.0000,
O, &END
TNPC= 0.0000,
0, S'I7_,= 0.0,
TNODS=
TINTC= 0.0000,
SCALE=
0,
O,
TNPS=
&END 1.0000.
O, &END
TNPC= 0.0000,
0, STZ= 0.0,
TNODS=
TINTC= 0.0000,
SCALE=
0,
0,
TNPS=
&END 1.0000,
0, &END
TNPC= 0.0(X)0,
0, STZ= 0.0,
TNODS=
O,
TNPS=
&END 1.0000,
0, ,&END
0,
&END 1.0000,
0, &END
T'NPC=
69
0,
TINTC=
0,
&END
I!Y
&PATCH
IREV= 0. KCOMP= AFT FUSELAGE
&SECT1
21.4642 21.4642 21.4642 21.4642 21.4642 21.464 1 21.4642 21.4642 21.4642 21.4642 21.4642 &BPNODE &SECT1
0.0000 0.1735 0.3420 0.50OO 0.6425 0.7660 0.8660 0.9395 0.9845 1.(3000 0.9845 0.9395 ,9.8660 0.7666 0.6425 0.5000 0.3420 0.1735 0.00130 &BPNODE &SECT1
&SECT1
&SECTI
1
STX= 0.01300, ALF= 0.0, INMODE= TINTS= 0.000(3 0.5124 0.9745 1.3412 1.5762 1.6481 1.5756 1.3402 0.9736 0.5118 0.00130 TNODE= STX= 24.0000, ALF= 0.0, INMODE= TINTS= - 1.(3000 43.9845 -0.9395 -0.8660 -0.7660 -0.6425 -0.5000 -0.3420 -0.1735 0.0000 0.1735 0.3420 0.5000 0.6425 0.7660 0.8660 0.9395 0.9845 1.0000 TNODE= S'IX= 28.0000, ALF= 0.0, INMODE= TINTS= STX= 32.0000, ALF= 0.0, INMODE= TINTS= STX= 33.3330, ALl::= 0.13. INMODE= TINTS=
IDPAT= 0,
KASS=
2, 0,
MAKE=
0, &END
STY= 0.(XI00, S'IZ= THETA= 0.0, 4, TNODS= 0, - ! .6574 -1.5759 - 1.3404 -0.9734 43.5110 0.0(K_ 0.5132 0.9748 13411 |.5760 1.6574
0.01300,
SCALE=
0,
TNPS=
3,
TINTC= STZ= 0.00(30,
0, &END SCALE= I .6096,
0,
0,
TNPC= STY=
THETA= 1, TNODS= 0, 0.01300 0.01300 0.0000 0.0000 0.0O(30 0.0000 0.0000 0.0O(3O 0.0(300 0.0000 0.0000 0.0(300 0.0000 0.0000 0.0330 0.0000 0.(3000 0.01300 0.01300 3,
TNPC= STY=
THETA= 0, TNODS= (3, STY= THETA= 0, TNODS= 0, STY= THETA= 0, TNODS= 0,
70
0, 0.00130, frO,
!.0000, 0, &END
I'NPS=
&END
10, 0.0000. frO,
0.13000, frO,
0.0000, frO,
TINTC= ST/_,=
0.00130,
3, &END SCALE=!.4248,
0,
TNPS=
0,
ST-Z=
0.0000,
SCALE=
0,
TNPS=
0,
STZ=
0.0(300,
&END SCALE=0.8332,
0,
TNPS=
0,
&END I .0104,
&END
W
&SECTI
&SECT1
&SECTI
&WAKEI
|DWAK=I, WING/BODY WAKE &WAKE2 KWPACH=6, KWPAN2=0, &WAKE2 KWPACH= 1, KWPAN2=0, &SECTI STX= 150.0000,
&SLIN2 &SLIN2 &SLIN2
TNODS= STY= TNODS=
0.0000,
&END SCALE=0.1756,
0,
TNPS=
0,
STZ=
0.0000,
&END SCALE=0.0000,
5,
TNPS=
10.
IFLXW=0,
&END
NVOLC= 2.0000, Z0= 2.0000, ZI= 16.00002.2= 2.0000, Z3=
0, -Z0000, -2.0(g10, -2.0000, 2.0000,
0.0000, ZR0= 10.0000ZRi= 0.0000, ZR2= 5.0000, PHIl= 12, NLEN=
0.0000, 0.00130, 1.0000, 0.0, 5,
YR0= YRI= YR2= R2= NPHI=
NSTLIN=0, SX0= 2.0000, SU= 0.0000, SX0= 2.0000, SU= 0.0(X_, SX0= 2.0000, SU= 0.0000, SX0= 2.0000, SU= 0.0000, SXO= 2.0000, SU= 0.0000, SX0= 2.0000, SU= 0.0000,
0,
&END
KWPAN
1 =0,
KWPAN
I=0,
&END
0.0000,
&END SCALE= I .0000,
20, &END
NPTI= NPT2= NPT3=
16, 3, 18,
&END &END &END &END &END &END
PHI2--330.0,
&END &END &END
&END SY0= SD= SY0= SD= SY0= SD= SY0= SD= SY0= SD=SY0= SI_-
5.0000, SZ0= 15.0000J)S= 5.0000, SZ0= 15.0000,DS= 5.0000, SZD= 15.0000,DS= 5.0000, SZO= ! 5.0000DS= 5.0000, SZ0= 15.0000,DS= 5.0000, SZ0= 15.0000,DS=
71
D
0.0000, 0.0,
SCALE=0.4500,
S'IZ=
0, 3.0000, Y0-18.0000,Y != 3.0000, Y2= 3.0000, Y3=
XR0= 0.0000, XRI= 0.0000, Xt'.2= 0.0000, RI= 0.5000. NRAD=I0,
&SLIN2
0.0000, 0.0,
ALF= 0.0, INMODE=- 1, TINTS=
&VS6 &VS7
&SLIN2
STY=
KWLINE=6, INITIAL=l, KWLINE--O, INIT! AL= 1, 0.0000, STZ= 0.0, 3, TNPS=
NVOLR= X0= Xi= X2= X3=
&SLINI &SLIN2
STY=
KWS IDF_,._, NODEW---0, KWS IDF__2, NODEW=5, STY= THETA= TNODS= l,
&VSI &VS2 &VS3 &VS4 &VS5
&VS8 &VS9
0.0000, ST'/,.= 0.0000, 0.0 TNODS= 0, TNPS=
STX= 36.0000, ALF-0.0, THETA= INMODE= 0, TINTS= O, ST'_' 38.0000, ALF= 0.0, THETA= INMODE= 0, TINTS= 0, STX= 40.0000, ALF= 0.0, THETA= INMODE= 0, TINTS= 0,
-0.5000,
0.1000, -0.4000, 0.1000, -0.3000, 0.1000,
&END &END &END
-0_2000, 0.1000, -0.1000, 0.1000, 0.0000, 0.1000.
&END &END &END
=\
s
l^ II
_u
W ,
.
L
Figure 1. Potential
flow model for PMARC.
73 FRECF..9tNG PAGE I_LA_'-_K,"-lOT FILMED
Constant
Vortex ring of same
strength doublet
sllenglh
m m
distribution
NOTE: reverses
as
doublet
Reversing the sign of the doublet strength the direction of the vortex lines on the panel.
Upper surfaee_ panel
Common
edge of two
rows or columns
of
panels forms separation line. (Single pair of panels shown for clarity). Strength of resu)_nt
vortex line is _ ¢ "_1. L Lower
s
panel
_.........._v
Upper surface panel
_
/
/ Lower
g L
/
Strength
" /
Wake panel
of doublet
panel must be
on wake
_I, U"
I_ L
surfac_
panel
in order to cancel vortex line along separation line. Figure
2. Determination
of doublet
74
strength
shed into wake.
Run control
information:
Length of run Number of time steps
Geometry data block: Patch info: number of rows arid columns, number, and patch name for each patch. Panel comer points, centroids, and normal Neighbor information for each panel.
Wake
first and last panel vectors.
data block:
Wake info: number of rows and columns, number, and wake name for each wake.
first and last panel
Panel
vectors.
comer
points,
centroids,
and normal
Next
me step Aerodyr, amic data block: Velocities, doublet strengths, pressure coefficients, number at panel centroids and corner points.
and Mach
Velocity scan data block: Number of rectangular scan volumes and cylindrical scan volumes, number of points in each direction within each scan volame, coordinates of point, velocities, pressure coefficients, and Mach number for each point.
Offtx_y Number
streamline data of streamlines
block:
coordinates, velocities, pressure coefficients. arc length for each point on each line.
Figure
3. Data
arrangement
within
75
PMARC
Mach
number,
plot file.
and
Side 4
2 4
(Panel
41
1
1
2
2
16
21
32
3
41
41
12
2
32 41
17
22
32
32
32
3!2
41
411
41
41
3
3
41
1
11
7
2
O a_
5
No.)
41
¢U
4
6 3
oN
4
8
13
3
23
18
r,.) o_
r./3 2
32
32
32
3
41
4 1
4
41
4
14
9 3
12
2
41
5
2
32
24
3
2
3]2
32
4
1
41
41
10
5
19
15
3
2
25
20 32
3:2
Side 2
NOTE: Sides of individual panels follow the same order and direction as the sides of the whole patch. Figure
4. PMARC
surface
76
"
,mMmlbL
patch nomenclature.
2
Global Coordinate System
5
j
1
I _'
Assembly Coordinate
5
Sysiem
I
_)
c
Systeml
Component Coordinate
Component Coordinate
System
System
I
,
Assembly Coordinate
!
i
5
5
Patch
5
I'
'1
Section Coordinate System
Figure
I
I
5
Patch
I
Section Coordinate System
,
5. PMARC
Section Coordinate System
surface
geometry
77
modeling
hierarchy.
I Section Coordinate System
The variableTNPSon namelistPATCH2 definesthe numberof panelsto be generated"across"the tip of the wing. (In this case,TNPS= 3).
Side3 of foldedwing patchwith 15panelson both upperandlower surfaces.
: -_Panel Panel
1
•
Comer points of tip patch. Comer define
of pane!s
1 - 15 define
first section
points of panels 30 - 16 (note reverse last section of tip patch.
Figure
6.
PMARC
automatic
78
tip patch
order)
option.
Panel
16 15
Global Coordinate System
I
J
f
b
b)
Wake
s-j
Wake
!
'!
Section Coordinate System
Section Coordinate System
a)
Initial
wake
i S
Section Coordinate System
Section Coordinate System
defined
Global Coordinate System
I
(
1
J
Wake
b)
No initial wake stepped wake)
Figure
7. PMARC
defined
wake
79
(completely
modeling
time-
hierarchy.
NOTE:
Usex can define sections of arbitrary shape to define complex initial wake shapes. single straight line section is shown here for simplicity.
A
NOTE: Direction of separation line is for a wake separating from side 2 of the folded wing patch. Direction of separation line would ae reversed if separation were from side 4. NOTE: "l'otal number of panels defined on each section of wake must be the same as the number of panels that the wake separates from.
Direction °_
separation
of line Wake
"__ __
as separation
defmiti.on direction
line
line
on namelist1 ofWAKE2) (Section wake, defined
"-_._.,
NOTE: Section must be in same
separation
Section defined
2 of wake, with SECTI
namelist, basic point coordinates, and BPNODE namelist
Figure
8. PMARC
wake
modeling
nomenclature.
80
6::
(XO,YOY.O) ._"'-._
_
i direcuon
:'\
./
(X2,Y2,Z2)
Y
v
NOTE:
i, j, and k directions orthogonal.
NOTE:
definition of the i, j, and k ,airec._,ons arbitrary and depends on the order the coordinates of the corners of the scan volume are entered in.
x
Global Coordinate
do not have
1"
System Figure
9. Rectangular
velocity
81
scan volume
nomenclature.
to be
t"
is
II
z ,y_ v
X
Global Coordinate System
NOTE: vector (X I-X0), (Y I-Y0), (ZI-Z0) (X2-X0), (Y2-YOL (Z2-Z0) do not have to orthogonal; PMARC will construct a right tvlinder with the vector (X I-X0), (YI-Y0), as the axis.
and vector be circular (ZI-Z0)
NOTE: The angles PHI1 and PHI2 (from namelist are measured from the plane containing points 0, 1, and 2, with positive angles being defined by the Right Hand Ruie about the cylinder axis. Figure
10. Cylindrical
velocity
82
.scan volume
nomenclature.
VS8)
Figure
11. PMARC
representation
83
of a symmetric
wing/body.
-1.2
I
Q exp. (gel _ PMARC
r_ exp.(tel. 13) *
PMARC
13)
-.8
-.4 Cp 0
.4 I I
.8
o
2o
40
60
Percent
80
100
0
20
Percent
chord
a) 2yPa = 0.2 Figure 12. Comparison wing of the wing/body
40
60
80
100
stations
on the
chord
b) 2yfo = 0.6
of experimental data and PMARC results for two spanwise configuration. Angle of attack is 4 ° .
-.2 o
o
exp. (ref. 13) upper surface
•
exp. (ref. 13) lower surface
Cp0
,
•
PMARC,
upper surface
PMARC,
lower surface
.2 0
l0
20
30
40
Percent Figure
13. Comparison
wing/body
configuration.
50 fuselage
of experimental Angle
60
70
80
90
100
length
data and PMARC
of attack is 4 ° .
84
results
along the fuselage
centerline
of the
Report Documentation
Page
fia_m
i. _oa No. NASA TM- 102851
2. Government
Accession
No.
3. Rec=pienl's
Subtitle
T_le and
Potential PMARC
5. Report
Row
Theory
and Operation
Guide
tor the Pm_el Code
January
1991
Lmdsey Browne, and Joseph San Diego, California)
Katz
and Steve
K. Iguchi,
(San Diego
State University,
Moffett
Research Field,
505-61-71 or Gta_
NO.
Center CA
94035-1000 13. Type of I_and
Technical National
Aeronautics
Washington,
Code
10. WOrk Urlit No.
11._
Ames
Orgar__a_on
81Perforrr.ngOrgar,zat_ ReportNo A-90244
7. Author(s)
R. Dudley,
No.
Date
6. Performing
Dale L. Ashby, Michael
Cataiog
DC
and
Space
Adrrdnistration
14.'_
Pe_od
_
Memorandum Agency Code
20546-0001
Point of Contact:
Dale L. Ashby, Ames Research Center, MS 247-2, Moffett (415) 604-5047 or FFS 464-5047
Field, CA
9403.5-1000
16. Abstract
The theoretical basis for PMARC,
a low-order potential-flow
panel code for rraxleling complex three-
dimensional geometries, is outlined. Several of the advanced features currently included in the code, such as internal flow modeling, a simple jet .model, and a time-stepping
wake model, are discussed in some
detail. The code is written using adjustable size arrays so that it ca:, be easily redimensioned for the size problem being solved and the computer hardware being used. An overview of the program input is presented, with a detailed description of the input available in the appendices. FLrmUy, PMARC results for a generic wing/body
configuration are compared with experimental
data to ;:lemonstrate the accuracy of
the code. The input file for this test case is given in the appendices.
17. Key Words
(Suggested
by Author(s))
18. D_'Utbulk:_
Panel method
Statement
Unclassified-Unlimited
Potential flow Unsteady 19. S_urity
Clas_.
aerodynamics (of this
report)
Subject 20.'Secur_
Unclassified
Gias,._.
(of I_is
Category
page)
- 02
21.No.
Unclassified
of Pages
90 I
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