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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.
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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

_FOI_

1626

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22161