1 - NTRS - NASA

1 downloads 0 Views 1MB Size Report
3. Recipient't C,atalo_ No. I. NASA TM X-73996. 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. _I-X _ 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

NASATMX-73996

TECHNICAL MEMORANDUM

,,0 L,-

(._iXSA-_m-X-73_,C_6)

i

A _2_,¥

b_.SC,_IPT.IOJ 0F

Tii#_ JA_ESOL_-CLUGB_X _IU _IRA_SCI_£C C0aPU_ I_bOG_A_: _LC 22 Z_terlm (_ASA) 3_, p _C _03/_)" A01

N77-15977

SHEPT-gTNG Report CSCL 01A

>_

" .,_

2:

G3/(_ 2

A BRIEF DESCRIPTION.OF

i

11.504

_!

t

!

COMPUTER--

_, ....

Antony Jameson, David A. Caughey, Perry A..Newman, and Ruby M. Davis

Thll

Informal documentation

I :' i

197b

medium is used-to

i

provide accelerated

or

ipeclal release of technical informationto selectedusers. The contents '



_,ay riot meet NASA formal editing and publication vised,

_/.

or may be incorporated

""

1

PROGRAM - FLO 22

December

t |

Llnclas

THE JAMESON.--CAUGHEY

NyU ,TRANSONIC SWEPT-WING

t

i

standards, may be re-

in another publication.

_

NATIONAL AEIONAUTICS ANDSPACE ADMINIStrATION

1

LAN6LEY |ESF.AICH CENTE|,.HAMTON_ VI|GIHIA23665

i

1. Report No.

I

I

NASA TM X-73996 4

Government Accession No.

3. Recipient't C,atalo_ No.

Title Ind Subtitle

5. Report Date

A BT.ief Description Swept-Wing Computer

,.

2

of the ,l;Imea_m-C;=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_ 505-06-11-02

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 3-D sweptwing configurations. This work was done at the Courant Institute of Mathematical Sciences, New York University, under NASA Grants NGR-33-016-167 and NGR-q3-016-201. Some basic aspects of the program are: The free-stream Mach number is restricted only by the isentropic assumption. Weak shock waves are automatically located where ever they occur in the flow. The finite-difference 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 time-like 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

Unclassified-Unliml

Sor,, C,a.i,. (o,,hi,.eport, Un(,la,_stfied

Distribution

I

,., ,h,s

j Unclasslfled • For sale by lhe Nal_or_;_r T=_._._

] i

Noo, 32

_ed

i "

I,,h_r_t,,,, 'r,'v, _, a;,,,,,r .. ,: , ','

,t: _ i,'i0;

$4.00 !

/

A BRIEF DESCRIPTION OF THE JAMESON-CAUGHEY NYU TRANSONIC SWEPT-WING 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

Jameson-Caughey

NYU

i

i

Transonic

Swept-Wing

!

'

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 use-e-f this

computer

code

several

in NASA-sponsored

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 swept-wing

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 3-D swept-wing configurations. This work was done at the Courant Institute of Mathematical Sciences, New York University, under NASA Grants NGR-33-016-167 and NGR-33-016-201. Some basic aspects of the progrmn are: The free-stream Mach number is restricted only by the isentropic assumption. Weak shock waves are automatically located where ever they occur in the flow. The finite-difference 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 time-like 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.2-u2)_xx

u,

local

speed

potential

v

and

w

are

of sound.

a

is removed

is

the

A SWEPT

WING

three-dimensional

in quasilinear

by

angle

- 2VW_y z - 2UWSxz

the

The

G = $ - x cos

where

PAST

form

potential

flow

as

(a2-v2)_byy+ (a2-w2)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

r---in 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(Y-y0(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 X-Y 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 changing-only combinations of the

. ': _ i i

following three airfoil section parameters: chor&, thickness ratio or angle Of attack (_wist)_ The _-ing-shape 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 non-symmetric 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-_J-Dihedral 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 units-as CHORD. These s-te.t_ions are

!

orderel from tip-to-tip, in ascenling algebraic orde_ of ZS(E) for yawed wing and root-to-tip 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 i--n only upper surface airfoil coordinates, ordered leading edge to_trailing edge.

!

I

-

FSYM