The pockets of separation originating on the leading edges are surrounded by vortex sheets. Their configuration and intensity were determined by four conditions with the JONES approximation, which is itself corrected by a simple logic. Field pressures and stresses were computed for different cases and are compared with test results (pure deltas, swallow tails, truncations, strakes, ducks, fuselage)

Hirsch, P.

English

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3 1176 00148 8361 "' "
NASA TECHNICAL MP]MORA:_DUM , NASA TM-75863
<_ NASA-TM-75863 19810010500
STUDY OF THE VORTEX CONDITIONS OF WINGS WITH LARGE SWEEPBACK
BY EXTRAPOLATION OF THE JONES METHOD
P. Hirsch
LRBARY
qr-r, __ 1!)80
LANGLEY NdSE/\RC;--I CENTER
LIBRARY° NASA
_4AMPTON, VIRGil'"
Translation of "Essai d'4tude du rggime tourbillonnaire
des ailes de forte fl@che par extrapolation de la m4thode
de Jones," 16th Symposium of Applied Aerodynamics, Lille,
November 13, 14 and 15 1979
•7
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON D.C. NOVEMBER 1980
https://ntrs.nasa.gov/search.jsp?R=19810010500 2020-03-21T15:04:09+00:00Z
STANDARD TITLE PAGE
1. Report No. 2, Government Accession No, 3. Recipient's Catalog No.
TM- 7'5863
4. TitleandSubtitle. 5. ReportDote
STUDY OF THE VORTEX CONDITIONS OF December 1980
WINGS WITH LARGE SWEEPBACK BY EXTRA- 6. PerformlngOrganizotionCode
POLATION OF THE JONES METHOD
7. Author(s) 8. Performing Organization Report No.
P. Hirsch
10. Work Unit No.
.... 1. Contract or Grant No.
9. Performing Organization Name and Address NASw-3199
Leo Kanner Associates J13. Type of Report and Period Covered
Redwood City, Ca. 94063 I Translation
12. Sponsoring Agency Name and Address
National Aeronautics and Space Admini- 14. Sponsoring Agency Code
stration t Washington t D.C. 20546
15. Supplementary Notes
Translation of "Essai d'4tude du r4gime tourbillonnaire
des ailes de forte £1&che par extrapolation de la m4thode
de Jones," 16th Symposium of Applied Aerodynamics, Lille,
November 13, 14 and 15 1979.
16. Abstract
The pockets of separation originating on the leading
edges are surrounded by vortex eheets. Their configuration
and intensity are determined by four conditions with the
• JONES approximation, which is itself corrected by a simple
logic. Field pressures and stresses are computed for dif-
ferent cases and are compared with the test (pure deltas,
swallow tails, truncations, "strakes", _, fuselage).
o_4j
17. Key Words (Selected by Author(s)) 18. Distribution Statement
Unclassified-Unlimited
19. uncSeCuritYlaClasslf.sS i fi(°f edthisreport) 20. SecuritYuncClassif.l s i(°ffithiSedPage) I 21. No. of Pages 22. PriceI ,
I
NASA.HQ
STUDY OF THE VORTEX CONDITIONS OF WINGS WITH LARGE SWEEPBACK
BY EXTRAPOLATION OF THE JONES METHOD
P. Hirsch
SUMMARY
The pockets of separation originating on the leading edges are
surrounded by vortex sheets.
Their configuration and intensity are determined by four con-
ditions with the jONES approximation_ which is itself corrected by
a simple logic.
Field pressures and stresses are computed for different cases
and are compared with the test (pure deltas_ swallow tails_ trunca-
tions, "strakes", 4a_rks, fuselage).
I - INTRODUCTION /i
An increase in the angle of a strongly swept-back wing results
in the formation of a pocket of twisting separation upon the leading
edge.
The contact between sound fluid and the separated zone thus
produces vortex surfaces which wind around in horn pattern upon the
base of leading edges.
An attempt is made here to give an approximation of the phen-
omenon by using diagrams and simplified calculation assumptions
based on the traditional JONE_____Sapproximation.
Let us briefly review the principles:
Upon a strongly swept-back wing_ the variation of flows along
the longitudinal coordinate o0 is slow compared to their varia-
tion relative to the transverse coordinates _ and _ • In the
•Numbers in the margin indicate pagination in the foreign text.
1
condition of continuity, it follows that the derivative Mf is
smaller than derivatives j _ .
In a first approximation, the flows in v and _ , in each
transverse section, are almost independent from what occurs in the
other sections and are influenced very little by the presence of
longitudinal component _ .
Here, under the same assumptions_ the transverse diagram will
correspond to that shown on figures 1 and 1-a which define the an-
notations of the configuration.
The pockets of separation are assumed to be of circular sec-
tion. Inside the pocket, components v and w will be zero: the vor-
tex boundary is therefore the line of jet and the angular vortex density
Br_$ of radius _ which forms the boundary with the external
flow will be constant.
Between the two pockets of separation, the linear circulation
density of the vortex components connected to the wing will be
[@ and _(_ will be functions of _ which must be defined.
2 - CONDITIONS /2
The first condition to observe is that of the relative slip on
the wing assumed here to be flat.
Since _ is the component induced by the vortex system
matching the conditions of JONES, and [ the angle, we must have
9
To define the parameters of the problem, let us set:
/
The configuration of the system will therefore depend on parameter
wh ere
A-lt
The relationship above becomes:
This is a functional relationship defining U_. and _4j
for _L given. The solution is easier by using a small computer,
HP97, for example .
For O</_ _ O,_ , we thus find that _#) varies
little relative to '_ and is expressed by the relationship of
qcondensation :
Simultaneously, ___ _,_ _o,_ _o,,_)_ (2)
The slopes of 9c_of quantities k' _' _4' _/ define locally __the sweepback angles, such as:
3 I
The intensity of the vortex tube along its axis is _--
The twist velocity at the contact of the tube in a plane
perpendicular to the axis is _-_ _/_Z_ at the contact of
the wing.
Projected perpendicular to 07 it is _ _._D_
such that WZ __ (fig.2).
If we assume _ is the ratio between _ and the potential
O
incident component) here:
Therefore: _=_ _ _ COS_. , which will be expressed with
Let us now consider the distance 2_ between the leading
edge of the wing and outline on the wing of the vortex tube axis,
taken perpendicular to _ . Its slope will be:
A vortex component which follows the outline of this tube on
the wing surface is subjected to a drag velocity, perpendicular to
this outline is the half-resultant (*) between Vo_S_
coming from the external potential and:
In the axes related t° _ _ J_ __F
This gives us the relationship:
/'.,t
---. _ .---- : ..- . AJ(.o9
i.e. :
These are the conditions which define the configuration
_, _i , and _4. and the vortex intensities _ , _ when the
angle _ , sweepback _o and factor _ • are defined.
The problem is solved easily by using mini-computers, such as
the HP 97.
3 - CORRECTION FACTORS OF THE JONES APPROXIMATION
The approximation is in principle exactly applicable to the
boundary condition where sweepback _ reaches 9°o .
3o
It has two sources of error. The first results from the non-
zero slope on the symmetry plane of the vortex lines. The second
i ,, i ,, , ,
(*) The velocity of the vortex component is half the sum of the
external and internal velocities at the sheet, with the latter
being equal to zero.
one is because the vortex lines do not reach infinity with a
constant circulation intensity upstream and downstream the section
under consideration, which is implicitly assumed in the JONES approx-
imation.
For the first cause of error, we have seen that the circulation
r _ taken in a plane perpendicular to the plane of symmetry is de-
duced from the circulation around the vortex tube perpendicular to
its axis by the relationship F_ _ff('_ (fig.3)
A point _ of section _ is subjected to an induced velocity
with _ z451'_ " Expressed with _* and _ :
The correction factor _t_ thus appears in the condition of
/
relative slip which defines _.._1_d
It may be compared with the results of the comparison between
the calculation of lift performed at the ONERA with the rheoelectric
tank and calculations with the JONES approximation for different
sweepbacks:
_o 600 700 80 °
ONERA correction 0.70 0 79 0 89factor " '
Sin2 _ 0,75 0.88 0.97
Factor 1.2 is thus replaced in the expressions of _ and
.,_)j_. by 1.2 sin2 _o = _>"
J
In order to evaluate the effects of the second error of the
JONES approximation, the effects of each section of a vortex tube
with increasing linear radius and circulation from the apex to the
leading edge (beyond the latter _TD_ is reduced to zero and
has no more effect). The results will be compared with those of
the preceding formulas.
By carrying out this calculation, we have shown that the cor-
rection factor required is very close to one, except in the region
near the trailing edge of the wing (0.85 to 1 of the central chord)
where it drops to a limit value 0.5, as suddenly as the sweepback
is large.
4 - CHOICE of A! _/
If the leading edge is pointed, the separation must appear with
very small incidences: we must therefore find the value _ _o
for these incidences resulting in a lift at least equal to that of
the JONES theory corrected in _t'n_ .
r
We thus find: _ "_/_ o7" _,0o
In the case of a wing which has a leading edge of curve _/_
of slope _¢_ , the twisting velocity will be higher than for /6
the previous case, hence: _ <
It is possible to evaluate the variation /_-_/o by applying
relationships which define the tangential velocity of a profile at
the leading edge relative to the velocity of the perpendicular com-
ponent _ 6o_@ Therefore:
Here _= _,. _ and
6.---------_ e
5 - PRESSURE FIELDS AND LOCAL STRESSES
They will be determined by applying the KUTTA law:
d_F
_-.¢,V, r
V is the component of velocity perpendicular to the vortex
stream on this point.
By assuming q_ Vo_ , the calculation leads to:
-The average pressure under the horn:
a__ _. £rc)"_,
-The pressure between horns:
-and local pressures (fig. 4) under the horn.
The function is defined by:
may be calculated point by point from the formulae of BIOT SA-
VART and KUTTA as a function of coordinate _/_ centered on the pro-
jection of the vortex tube axis (Fig. 4). /7
Accordingly, the local stress is:
&. d"£____= _ x.,, _..!...___) . ,_., .
R
For a pure triangular Ll, we thus have with 5 = wing sur-
face:
The moment around the apex will be here:
where:
qteM(o)
(J,' -< ~ ~ O,G'?
--
for <f=central chord)
6 - RESULTS OF CALCULATIONS AND COMPARISON WITH THE TEST
6.1 - Pure Delta
Programs solved by using the small HP97 computer have resulted
in numerous applications.
Pl. 1 shows the results of comparisons between calculations
and tests found in various publications (ONERA - AGARD).
The calculated configurations of vortex tubes place the axes
of the latter inside the wing in the vicinity of the leading edges.
The pressure fields are satisfactorily shown; the test shows that
the peak decreases as we move closer to the leading edge.
For a sweepback of 75 0 , the calculation of c" (?() decreases
;!....
the slope after 15 0 of incidence, which is not shown by the tests.
6.2 - Special Wing Shapes
We were able to calculate the cases of small truncated and
swallow tail Wings.
Pl. II provides the results and the comparison with the tests
of BOBBIT and MONROE (wing of 71 0 2) on pressure fields, lift and
moment.
9
The diagrams of figure 5 show the principle of the calculations
and the regions where pressure integrations must be found.
In the region formed by the swallow tail, the distribution /8
of components "_ is the same as for the trailing edge of the
wing.
Let us point out that the calculation also applies to a "neg-
ative" swallow tail: _l< O •
6.3 - "Strake" and the Case of Multiple Sweepbacks
This is a difficult case because it must be shown that the
horn-shaped vortices originating on the "strakes" and those on the
downstream section of the wing are connected 4n position and inten-
sity, which results in displacing the latter relative to their na-
tural position. An additional intensity must be applied to them
without modifying the condition of relative slip (Fig. 6).
Comparisons were possible only in cases where a fuselage was
also present.
6.4 -_rk- __
------
It was necessary to take into account the effects of inductance
of the vortex tubes on the wake sheet of the duck downstream from
the latter: the result was a deflection to the bottom of this sheet
and a contraction of the tubes to the plane of symmetry. This
effects the main wing and modifies, as for the case of the "strakes",
the configuration of vortices of the main wing (Fig. 7).
By taking these precautions, it was possible to make satisfac-
.tory comparisons of the calculation - test (SAAB d_ek - PI. Ill).
¢. i0
6.5 - _uselage
The first comparisons with the test showed that a fuselage
with small diameter changed very little the results of a detached
wing by giving it the surface of the total wing surface. On the
other hand, in the case of a detached d_ck placed on a fuselage
(i.e. a wing with small external surface compared to the total sur- /9
face - 0NERA Test of EHRLICH) - the calculation based on only the
outside surface coincided more with the test result.
These observations have shown that there is an effect related to th_
ratio of the wing span divided by the diameter of the fuselage
squared (aspect ratios). This explains the introduction of an oper-
ator in (_/_ "_o)_. _ with _ the wing chord, _ the diameter
of the fuselage, taken in the form:
It moves to zero when _'_o -->
O
and assumes the value making it possible to verify the EHRLICH test,
for K Z _._/
Plates IV, Vp Vl, and VII result from the application of these
different calculation methods.
L f l-
.IfJ>i_,-J ~. • •.••/I ~/1'e
t·,~..--~---.-->- bJ I.-----~b
Jt
w
Figure 1
05
Figure J
.......
. ,
• v--... •• $'- '\ •
· r.....'• •-ZO]~o4;"
Figure 2
i
I
I
I
1
" .~.
. '(' ..
Figure 5
! l)~~=-= __.. ::>
°0 r.
4'-'--""
...... ,
. ,
• •
•,
•
oS
'-._--..--='.~'---
Figure 4
oS
I
-1f~ ----------
13
Figure 6 Figure 7 " _
II,
/_._S_...........................
0
Test _ [_
go"
J P_.5
0(=4/%o
Field Pressures
j £ t
0 +
'4 o -o_o(o
|
0[. _ _.,_ Test; -
"I .......I: .....I ......-_-- o
0 "...."----+--_--;---zt $_ -16'o(-° c_"o/! oQ4La6 ,%
! I 0
" . ~
SAAB~ (H. Behrbohrn)
- - - Test
<"'DL _.- x
r ,M
."'-- --_ "-'.'-' '."'-" "._.., -. "'-"'- .._ __._--.- _...•... .---
C
2
I ~
1
•. I
Index VI
for Win~~
wi thout f.- )
,. ;
- ........._ ..--==-~...
co
CD
CO
j
0 . r: 0 ~
1 iO .:..r C(.~ 00J
l Z( ~O;?:J o. Cf;
I G'
Ct"....
Test
~c':;' ?l,
e/1 Y/t; : cl-1~
) Co. A ~ Theory (.
IC1-
Ijft
I
i
___._..._.J~C'L.{-r _
I,
I
I
i
I
ij
!
-0[1 6
_____+- /.....,1 -4 .__-1__
o
. ~
•
fI'
- ... -
(Eh'tlich)
+ C<:) rC(,t[
~ S1 TEST
6
Airplane with ONERA
cluck- Cqlll.&o--r6
r<---"."" .1--..·-
I tt-l) ~
~o
C
7...
1--'-----------
o
.-10 .__.__... ._ ----.;...~1_ ..-'_'_.'__
/
r{
/
Q/ ./~V~ S1~ I
§ ~,~
~ I
~ 0+ /
Q)
~ +-----------..;J-..------ --- ----------~ t O~ '<>. !~ 0 .
'M (J' ,
~ l<.J~
~ ~0
'M Y
~
____________ 0
_......_._---- -•._----- ./
,.... .1_ _ ",.-...,r
Test _
"srrc.AL ..
ifSf0lCe" - -With
Without
Wing with
¥PORT OF ONEKA rr-026" Ay(oc\l1 rfe !.)
fuSrlage without and Wi~h "Strake" .~
_t- --+-,e._z L / i
~~ . A~~,
/
/ C,
~
\
..
--.
•
+
I
..- --
I
-l
I.
- ~- ..-
r
-- --
~
i
------ - i
i
Focuses
Focuses
TEST
-~~"""~
....;_ ...-:::-z-:~ ...:"'-_.-- ~--.~. --
--'---.-~~...~._- ._._~ .. _.__.- .
~o nco Y' c\ e... '\Of~£rz A"
( Flat Wing )
=-- /
=- / c.~~l
__------_----.....e::;=-----/---L-.-' - -++- ~-----''-- _
-<::"'--- < ..------- _-_.. ~--+t--_.- "I\~""--
- ........---------=:....::.~OO;;::_::_-.-.---........,-_ -_.--------------
.........
"111, ,. ... _ .........__-----:-~--~--
.~....~. -
._----_._-
,
Focuses with
~~~L
large/small
. ==1).....---
~..:..::r=._------ ---_--_.~.----•..-.:...-_._-,--....__._-~~
t...._-.J , j
,.
21
. I
.
.
~
Jones' Theory
(corr . )
(wi thout
wi thout <ktt5K~---.J.­
wi th~ c..-'--N. .
II large. fR·
Test
c..le,,[~ ~
lO
c
z
~ 1
I
, j
. \ 05 'j
,----'-,~-_., ..-~--
. j
i
1
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FFocus
I
.Lit ,,~
I 1°
I I
. I
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. I
t
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Study of the vortex conditions of wings with large sweepback by extrapolation of the Jones method

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