3. Recipient't C,atalo_ No. I. NASA TM X73996. 4 Title Ind Subtitle. 5. Report .... X  X1 ,. Y = Y1  S(XI'Z!) ' Z = Z1. (5) to map the wing surface to a coordinate ... and to set. _IX _ m when. X > Xm ' with a corresponding form.ula when X ... a has the value ... form of the equations l:_ustbe used at points lying on tho singular. 6 ...
/
NASA
NASATMX73996
TECHNICAL MEMORANDUM
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(._iXSA_mX73_,C_6)
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N7715977
SHEPTgTNG Report CSCL 01A
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A BRIEF DESCRIPTION.OF
i
11.504
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COMPUTER
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Antony Jameson, David A. Caughey, Perry A..Newman, and Ruby M. Davis
Thll
Informal documentation
I :' i
197b
medium is usedto
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provide accelerated
or
ipeclal release of technical informationto selectedusers. The contents '
•
_,ay riot meet NASA formal editing and publication vised,
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or may be incorporated
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1
PROGRAM  FLO 22
December
t 
Llnclas
THE JAMESON.CAUGHEY
NyU ,TRANSONIC SWEPTWING
t
i
standards, may be re
in another publication.
_
NATIONAL AEIONAUTICS ANDSPACE ADMINIStrATION
1
LAN6LEY ESF.AICH CENTE,.HAMTON_ VIGIHIA23665
i
1. Report No.
I
I
NASA TM X73996 4
Government Accession No.
3. Recipient't C,atalo_ No.
Title Ind Subtitle
5. Report Date
A BT.ief Description SweptWing Computer
,.
2
of the ,l;Imea_mC;=ugh¢,y NYU Transonic Program  FI,_) 22
December
_,_j
1976
8
Performing Organ,zat,onCode
_
_'e,f¢,,'m=n00r,len_za,,,on Report ,%1o
i
:
I & i
;
7 ,._uthor_s)
_
} Antony James_n, I Ruby" M. Davis ,
:
I
David A. Caughe>,
Putty A. "_u_a]J, and "
I
J 1C ,_'crk Umt No
g" Performing Organiz,_tlon Name and Addre_
I
j_ 505061102
NASA Langley Research Center Hampton, Virginia 23665
[ I" ¢_,ntrac" orGrantNo I
i
i 13. Type of Report and Per,od Covered
! NASA Technical I
12. Sponsoring Agency Name and Address
National
Aeronautics
and Space Administration
Memorandum
J I:;_ SPonsoring Agency Code
i
Washington,
DC
20546
i t
15. _pplementary
'
Interim technical information formal publicat _.on 18
' ;
•
,,
,,
,
Notes
release,
subject
to possible
revision
and/or later
Abstract
Prof. Antony Jameson (N_U) and Prof. Dave Caughey (Cornell) have developed this computer program for analFzing inviscid, isentropic, transonic flow past 3D sweptwing configurations. This work was done at the Courant Institute of Mathematical Sciences, New York University, under NASA Grants NGR33016167 and NGRq3016201. Some basic aspects of the program are: The freestream Mach number is restricted only by the isentropic assumption. Weak shock waves are automatically located where ever they occur in the flow. The finitedifference form of the full equation for the velocity potential is solved by the method of relaxation, after the flow exterior to the airfoil is mapped to the upper half plane. The mapping procedure allows exact satisfaction of the boundary conditions and use of supersonic free stream velocities. The finite difference operator is "locally rotated" in supersonic flow regions so as
i .
to properly account for the domain of dependence. The relaxation algorithm has been stabilized using criteria from a timelike analogy. The brief description contained in this document should enable one to use the program until a formal user's manual is available.
i
17. Key W_,rdt (Suggested by Authorl$))
18
Aerodynamics Transonic Flow Compressible Flow Wings
Statement
UnclassifiedUnliml
Sor,, C,a.i,. (o,,hi,.eport, Un(,la,_stfied
Distribution
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j Unclasslfled • For sale by lhe Nal_or_;_r T=_._._
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Noo, 32
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I,,h_r_t,,,, 'r,'v, _, a;,,,,,r .. ,: , ','
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/
A BRIEF DESCRIPTION OF THE JAMESONCAUGHEY NYU TRANSONIC SWEPTWING COMPUTER PROGRAM  FLO 22
• _
"
i
Antony Jameson (NYU) David A Caughey (Cornel i) Perry A. Newman (NASA) Ruby M. Davis (NASA)
i i
_'
Langley
Research
Center
i
PREFACE
This :i
to
serve
document
was
prepared
as an interim
user
by
guide
the for
third the
and
fourth
authors
JamesonCaughey
NYU
i
i
Transonic
SweptWing
!
'
is pertinent
i _ :
I
of
1976.
program
to the
The
preparing
immediate
version
first
more FLO
Computer
and
This
demands
 FLO
provided
second
extensive
22.
Program
to NASA
authors
are
documentation
document
22
on
•
This
LaRC
in
information the
spring
in the
process
of
a later
version
of
is
intended
to meet
for useef this
computer
code
several
in NASAsponsored
programs. The Past
"
first
a Swept
two
Wing"
are
sections
The
last
section
reference
2 (an
program

FLO
5.7
17)
sections and
and
"Some
5.8
entitled input which
entitled
of
Results reference
"Input
description includes
"Calculation of
Swept
I with
Wing very
Description" for the
Jameson's sweptwing
of
the
Flow
Calculations" minor
editing.
is an update
of
yawed
wing
input
parameters.
_!
l
l
l
I
I
I
l
SUMMARY
Prof. Antony Jameson (NYU) and Prof. Dave Caughey (Cornell) have developed this computer program for analyzing inviscid, isertropic, transonic flow past 3D sweptwing configurations. This work was done at the Courant Institute of Mathematical Sciences, New York University, under NASA Grants NGR33016167 and NGR33016201. Some basic aspects of the progrmn are: The freestream Mach number is restricted only by the isentropic assumption. Weak shock waves are automatically located where ever they occur in the flow. The finitedifference form o_ the full equation for the velocity potential is solved by the method of relaxation, after the flow exterior to the airfoil is mapped to the upper half plane. The mapping procedure allows exact satisfaction o_ the boundary conditions and use of supersonic free stream velocities. The finite _ifference operator is "locally rotated" in supersonic flow regions so as to properly account for the domain of dependence. The relaxation algorithm has been stabilized using criteria from a timelike analogy. The brief description contained in this document should enable one to use the program until a formal user's manual is available.
i
_
I
i
CALCULATION It is desired equation
which
OF THE
to solve
can
the
be written
(a.2u2)_xx
u,
local
speed
potential
v
and
w
are
of sound.
a
is removed
is
the
A SWEPT
WING
threedimensional
in quasilinear
by
angle
 2VW_y z  2UWSxz
the
The
G = $  x cos
where
PAST
form
potential
flow
as
(a2v2)_byy+ (a2w2)ezz
 2UVSxy
where
FLOW
velocity
_  y sin
of attack.
a
'
components
singu_arlty
introducing
ffi0
at
infinity
and
a reduced
a
in the
(1)
is the velocity
potential
(2)
]
I
..... ....... I..... I In
the
J
case
of
is discontinuous the
wing.
the
conditions
the
vortex
the
up
of
to be
sheet
is
stream,
is continuous
the
through
the
except
where
will
vortex
to
the
be
the
surface
lie
are
be
along
that
normal
behind
ignored: in which
the
lines
jump
parallel
component
of
At
infinity
the
_
far
dimensional
I ..... i
potential
trailing
will
Trefftz
a two
velocity
sheet
sheet.
in the
I
sheet
at
is constant that
the
vortex
assumed
and
undisturbed there
the
I
flow
satisfied
potential
free
vortex
a lifting
across
Roll
rin the
J
flow
to
velocity __ow
....
is
do_mstrea_
induced
by
the
sheet. The
construction
coordinate
system
to
of suit
a satisfactory the
geometry
curvilinear of
the
configuration
Q
is one "
of
the
problem. by
i _.
Here
a sequence
the
are
square
difficult
aspects
of
the
nonorthogonal
coordinates
elementary
transformations.
of
coordinates by
most
introduced
root
in planes
three
will
dimensional
be
_enerated
First
containing
parabolic
the
wing
section
transformation
'
1/2 X 1 + iY 1
where
z
"
a singular
•
the
is
the
line
]eadlng
•
_uAJ_n_
[x  x0(z)
spanwise of
edge
transformation
=
is
the
(see
+
coordinate,
coordinate Figures
to unwrap
i(Yy0(z))]
1 and
and
system 2).
,
x 0 and
located The
the _ir1_ to form
Z1 = z ,
Y0 define
just
effect
of
a sha]]o_
inside this bump
(3)
"
1 mh_, 1
1 SINGULkR
. xOCz),
PLANE
OF
SYM_.mTRY
i
:
FIGURE
4
I.
CONFIGURATION
OF
SI£EPT
WING
LINE
Yo(Z)
b
y
!
Ii " _ _ ....
(a)
CARTESIAN COOR.DIt_ATES
B
=_
¥1
m,,,
_
X1
'
(b)
Y
•
PARABOLIC
_
COORDINATES
_

(C)
SIIEARED COORDII_ATES
Q
FIGURE ""
2.
CON"'_:,tC.IO_ '. 0}" C60RDII:A_T SYS"EY FOI: I:%'_'I;PT WING CALCULA'I'IO'.','
,)
I
YI  s(xl'zl) Tl_en s she_rin_
X 
to
map
the
in order
X1
,
wing
to
Y = Y1
surface
obtain
are
replaced
The
stretching
set
transformation
by
X = X
a
used in
an
(4)
is used
 S(XI'Z!)
'
to a coordinate
finite
s_etched the
inner
present
domain
X
> Xm
so that
X =
a has
the
Y and
Z.
the
Similar
vortex
sheet
singular
potential
two
sides
(Eq. between
of
the
by
the
continuation
Points
on
the
two
of
6
same the
and
Z
Z.
program '
and
is
to
to
set
_
m
T_p_cally stretchings
point
equations
in
sides the
which
when
X i.O.
BETAC.

Stabilization factor used a_ supersonic points in finite difference operator if BETAO > O. Mos_ needed when M_ _i., many ca_es operate sarisfactorily with 3ETAC= 0. Convergence is slowe_ bu_ s_abili_y enhanced when BETAO>0.
i• i
l'my
_
i
i !
STRL_C. 
Line relaxation control. Computational XY planes are relaxed by horizcntal lines (YSWEEP) in central strip, vertical lines (XSWEEP) in outer strips. STRIPO specifies the fraction of computation_l plane included in central strip: O. < STRIPO< 1., where STRIPO=I. gives all horizontal line relaxation.
FHALF.

Grid halving trigger. IFHALFI_> I. read another card (Read Order 5 format) containing computational parameters to be used on grid with mesh siz_ halved in _.Iidirections. IFHALFI< i._ must appear on finest grid card (last one read). Calculation procoeds automatically through the sequence cf computational grids.
DESC.

Description for Qard in Read Order 7
" .
•
6
i
i
ormat 7
l
FMACH, YA, AL, CD0
Format (Sale. 7)
FMACH.

Freestre_
Mach number.
YA.

Yaw _ngle (in degrees).
AL.

Angle of attacF_(in degrees) measured in plane containing fraestream direction.
CDO.

Drag coefficient due to skin friction (CD FRICTION on output). This input number is added tc the drag coefficient obtained by integrating the surface pressures (C_, FCP2,'. on out.put),
!I
L
i
i
i i
Rea_ Orde...Er
Number Cards .....
Description
and
Comments
._ead Orders 8 through 19 are used to specify the wing geometry (in physical space, of course). One cam define the wing a% up to ii span stations. A set of airfoil coord/na_es nus___t be read in at the first station. It need not be read i_ at other stations, if one is changingonly combinations of the
. ': _ i i
following three airfoil section parameters: chor&, thickness ratio or angle Of attack (_wist)_ The _ingshape at intermediate span positions (i.e., the computati_ual grid planes for example) is obtained by linear_interpolation in the spanwise direction in the physical space.
•i
._
Read CTders 8 and 9 are res_ only once: i0 and ii are read. FNC (see 9) time_; 12 through L7 (19 if nonsymmetric airfoil section) must be read at first section and may be required at other sections, _epending on the wing geometry. 
Description
for card
8
l
DESC.
9
1
ZSYM, FNC, SWEEP I, SWEEP DIHED 2, DIHED
in Read Order 9
2, SWEEP, DIHED
i,
ZSYM.
 Wing planform symmetry ZSYH = 0, yawed wing ZSYM _ l, swept wing
trigger:
FNC.
 Must be _ 3. The leading edge of the wing in physical space is fit with a cubic spline. Data at three span stations are requ%=ed (as minimum) as wall as the six angles which follow. If the wing leading edge has a slope discontinuity, three stations should be used fairly close to
I i
it. SWEEP i.
Sweep
angle of wing
section
leading
edge at root
(in degrees).
SWEEP 2.  Sweep angle of wing leading . section(i_ degrees).
! edge at tip 1 J
SWEEP.
DIHED l_JDihedral angle of wing leading section (in degrees).
edge at root
DIHED 2.
edge at tip
DIHED. ":'! i • I
.!
28
 Sweep angle of spanwise grid lines at = (off tip of wing) (in degrees).
Dihedral angle of wing leading section (in degrees).
 Dihedral angle of spanwise grid lines at (off tip of wing) (in degrees).
il
[
.

Read Orier
I0
Number Cards
I
Description
D_C.

Description
and Co_ne_t
for cards in _a_._
ii
Format _,8_0). 11
!
ZS(K),
XL,
• ZS(K).

YL, CHORD, THICK, Fozmmm (8EIO. 7)
AL,
i t i
: ,
_
i
FSEC
Spanwise_ coordinate of the wing section being specified. I% is in the same unitsas CHORD. These ste.t_ions are
!
orderel from tiptotip, in ascenling algebraic orde_ of ZS(E) for yawed wing and roottotip for swept wing.
XL ....
X
coordinate physical
Y_L.
.
CHORD.
of section
space
leadiag
edge in
(conr.rols sweep).
 Y coordinate of section leading edge in physical space (controls dihedral). 
Section chord length, The chord of the airfoil coordinates to be read in (or already read in at the prior station) will be scaled to this value.
•
THICK.

.,
Section thickness ratio relative to tha_ of the airfoil coordinates to be read in (or already read ir_a_ the
6
prior station). Note, this is a rati___.oo of thickness/chord ratios. The thickness of the airfoil coordinates will be scaled with this value..
• ,
AL.

Section angle of attack or twist (in degrees). Airfoil coordinates will be rotated through this angle about LE.
F_EC.

Section airfoil coordinate trigger. FSEC = O. Do not read airfoil coordinates. Last set of airfoil coordinates read will be used at this section. They m%y be scaled by a_y combination of CHORD, THICK, or AL read above. Skip Read Orders i'3 through 19 for I!
this section.
2c_
/
Re_,d Order
Number Car_$
Description and Comments
ESEC = i. Read a new s__ _._'_ airf¢il cocrdlnazes which will be used a: :his s_a_ion and perhaps a: c:her s_a_Icns.They may be scaled by arC"coSoina.icn cf CHORD, THICK; or i" rea_ above for this section_ At first station (K = l) FSEC is ignored; one must supply Read Orders 12 through 17' 12
1
DESC.

Description for cards in Rea_  Cr.er 13
Fcr t(8A10). 13
1
FSYM, FNU, F2_L For_t FSYM.

(8nO.T)
Airfoil symmetry trigger. FSYM > i. Symmetric airfoil. Read in only upper surface airfoil coordinates, ordered leading edge to_trailing edge.
!
I

FSYM