I i 0,1 1 1

I i 0,1 1 1
3 8006 100D8 1423
REPORT NO. 114
FEBRUARY, 1958
THE
COLLEGE
OF
AERONAUTICS
CR1NFIELD
An investigation into the flow aver delta
wimps at law speeds with
leading edge separation.
- by D.J. Marsden B.Sc., D.C.Ae., R,V:„SimpsonB.A.Sc., D.C.Ae.,
and W.J.Rainbird"B.E., A,F R.Ae.S.
June, 1957.
SiRgaRY
A low speed investigation of the flow over a 40° apex angle delta
wing with sharp leading edges has been made in order to ascertain
details of the flow in the viscous region near the leading edge of the
suction. surface of the wing. A physical picture of the flaw was
obtained from the surface flow and a smoke technique of flaw visualization,
combined with detailed measurements of total head, dynamic pressure, flow
directions and vortex core positions in the flaw above the wing.
Surface pressure distributions were also measured and integrated
to give normal force coefficients.
The results of this investigation were compared with those of other
experimental investigations and also with various theoretical results.
In particular, the normal force coefficients, vortex core positions and
attachment line positions were compared with the theoretical results of
Mangler and Smith, reference 19. It was found that:
( i)
Secondary vortices of opposite signs to the main vortices
exist on the upper surface of the wing outboard of and belay
the main vortices. These secondary vortices are formed as a
result of separation of the boundary layers developing outboard
of the top surface attachment lines.
- 2 -
SM.TIARY Continued.
(ii)
(iii)
The real flow vas found to differ somewhat from the model of
Mangler and Smith due to these secondary separations.
The "trailing edge" effect present at subsonic speeds was
found to be considerable even at small angles of incidence.
The normal force developed by spanwisc strips exceeded that
predicted by bungler and Smith near the apex, but fell
progressively as the trailing edge was approached, The centre
of pressure is however approximately independent of incidence
up to angles of incidence in excess of the semi apex angle.
1.
2.
3.
4.
5.
6.
33
TP.BL, OF CO7ri-21TS
C0711--21TS
Suranary
Summary
1.
1.
List of
of Symbols
List
Symbols
2.
2.
Introduction
Introduction
3.
3.
Description of
Description
of Apparatus
Apparatus
3.1 .. Wind
Wind Tunnel
3.1
Tunnel
Models
3.2.
Models
3.2.
Gearand
andPitch-Yavim
Pitch-Yameter
The Traverse
3.3, The
Traverse Gear
eter tube
tube
3.1.x. The Light Source and Smoke 'Bombs'
3.4.
Li-.
5.
Description of Tests
Description
Visualization
4.1 , Surface Flow Visualization
4.1
2. Surface
SurfacePressure
PressureMeasureme
Measurements
nts
4. 2.
4.3. Flow Survey
Visualization Technique
4, 4, Smoke Flow Visualization
Discussion
Description of the Flow
5.1, Description
The Viscous
5. 2. The
5.2.
Viscous Region
5. 3, Compariso
Comparison
theory
n of results with the theory
Smith
of Mangler and Smith
6.
Page
Page
11
77
7
77
77
88
88
88
88
99
9
9
10
10
10
10
11
11
12
12
cConclusions
one lusions
11}
14-
References
15
15
Appendix 1. Attachmen
Attachmentt lines on
on aa family
family of
of
elliptic cones
17
17
14-
SISMOLS
A
aspect ratio = 4. cot A = K = (1.4.6 for A = 70°)
b
span (trailing edge)
C
local chord.
root chord
mean aerod.ynamic... chord = 3 or for delta wing. Its loading
o
edge is is or friar' the wing apex.
P ~Pe,
pu :
A0
p
=C
PL
0N
=
711
..
+s
pressure coefficient
rU
AC
p dy local non-rra force coefficient per unit length
f-s 2 s
c
r
N.
2
C 2 s clx
=
N
0
2
WC:rail normal force
i
1- P U .S
coefficient
b
i
Fi
Total head
h
height of vortex core above wing
K
= cot A = tan 0
static pressure
P
a 03
s(x)
=
2
1
-2- ,P U„
local semi span
-
freestream velocity
x,Y,o
cartesian co-ordinates ( x measured chordwise)
( y measured spanwise)
-- 55 -incidence
incidence
aa
secondary
secondary separation
separation line
line angle
angle to
to wing
line
wing centre
centre line
nn
y
y
tertiary
tertiary
A
leading edge sweepback
density; attachment line angle to wing centre line
a
semi apex angle of delta
pitch angle
Appendix
major and minor axes of ellipse
a,b
h
= b/a
s
s
=
(freictien of semi span)
cross flow velocity component
C,n
co-ordinates of ellipse
-6-
2.
Introduction
The inviscid flow over slender flat wings, with the delta wing as
a particular case, was treated by Tt.T.Jones (ref.9) in 1946. The real
flaw over slender wings with 'sharp' leading edges at incidence was found
to d:iffer from the Jones model in that separation of the boundary layers
(developed outboard of the flow attachment lines on the pressure surface)
occurred at the wing leading edges. The vortex sheets shed_ off these
edges are blown back over the upper surface of the wing and roll up
to form two stable vortex cores. These leading edge vortices, which are
the man part of the trailing vortex system of the wing, considerably
modify the flow field and result in non-linear lifting effects.
To account for this difference in the flow field, theories have been
presented by Iegendre (1953), Brown and liichael (1954), and Mangler and
Smith (1957). All these theories represent the actual flow by theoretical
models of increasing complexity. Legcndre, reference 20, places isolated
vortices above the wing such.tbat the vortices are streamlines, and
determines their strength by making the outflow talrential to the surface
at the wing leading edges. Brown and/Aichael (ref. 10) have included
feeding vortex sheets along branch cuts from the leading edges . to the
vortices, and determined the position of the vortices from the condition
that the overall force on the vortex and vortex sheet be zero This model
does not satisfy the boundary condition of zero pressure difference
across the feeding vortex sheets, rangier and Smith (ref.19) have assumed
a curved shape for the vortex sheets feeding the vortex 'cores'. They
have translated the exact three dimensional boundary conditions back into
the cross flow plane, and solved the resulting problem by satisfying the
condition that the pressure difference across the vortex sheets is zero
at selected points on each sheet.
In all three of the above slender delta wing theories the flow has
been assumed to be non-viscous and conical. The presence of a subsonic
trailing edge, giving zero loading leads to the flow field being nonconical and this is not allowed for in the theories. The primary effect
of viscosity, namely the leading edge separation, has been taken into
account by allowing for the presence of the vortex sheets and rolled
up vortex cores.
nmberg (ref.2) and later Fink and Taylor (ref.1) showed by experiment
that there are also 'secondary' viscous effects associated with the suction
surface boundary layers. These boundary layers developing outboard of
the top surface flaw attachment lines eparate not al the sharp leading
edges but somewhat inboard of thesi6 edges at spanwise positions slightly
outboard of points under the main vortex cores where an adverse pressure
gradient wolad be encountered. These 'second v-ry' spoarations (so called
by ilaskell in ref.3) give rise to small triangular-shaped viscous regions
on the suction surface near the leading edges.
This present report dicusses the results of a low speed flow
investigation of this viscous region and its effect on the overall flow field.
3.
3.
Description of
Description
of Apparatus.
Apparatus.
3.1. Wind
Wind Tunnel,
Tunnel,
3.1.
The tests
tests were
The
performed in
wereperformed
in the
the College
College of
of Aeronautics
Aeronautics 1B
1B low
low speed
speed
wind tunnel
tunnel at
wind
at aa velocity
velocity of
of 130
130 ft/sec.;
ft/sec.; lower
lower speeds,
speeds, about
about 80
80 ft/sec.
ft/sec,
wereused
and
used
were
for the
surface
for
flow
the flow
and smoke
surface
smoke visualization
visualization tests.
tests. The
The wind
wind
tunnel has
the jetthe
size
being
elliptical,
has an
an open
tunnel
open working
working section,
section,
size jet
being
elliptical,
40" wide
wide xx 27"
27" high.
40"
high.
3.2. Models.
Model I was a sharp-edged (0.008" leading edge radius) delta wing
wing
leading edge sweepback. This model was only used for preliminary
with 60 loading
surface flow visualization tests.
Model II
II (see
(see figure
figure 1)
1) was
was aa sharp-edged
sharp-edged (0.008")
(0.008") delta
delta wing with
0Model
chord of 18 in. The model was made
70 leading edge sweepback and a root
root
sting. Pressure
from n 3/32" thick flat steel plate supported by a
plotting holes (0.018" dia) were
weredrilled through the plate, on forty
ecuiangula
ecuiangular
rays,
into plastic tubing
plate under surface.
r rays,
cemented
to the to
tubing
cemented
Near the leading edge the section tins too thin to accomodate the plastic
tubing so slots were cut in the plate
and araldite passages moulded into
plate
the edge. The under surface of the
was filled with a metallic filler
thewing
wing
and painted black to provide good contrast for surface flow visualization
tests.
tests.
Thettwing
flat surface and a blunt trailing edge
Thethus has
hasone
one
see figure 1. The wing support sting was held in an incidence changing
frame which pitched the model about a lateral axis through the centraid
of area.
3.3. Traversing Gear and Pitch-Yaw Meter Tube.
Tube.
The traversing gear was mounted on a base which could be tilted to
the incidence of the model, It allowed translation along the full length
of the 'model and across one half of the span. The traverse gear itself
itself 0
gave translation)
movement of 360
perpendicularto
to the
the surface
surface and
and angular
angular movement
perpendicular
in yaw and It 15 in pitch,
pitch. These angular movements were arranged so
that the nose of the pitch yaw probe remained in the same position.
Details of the yawmeter may be seen in Fig. 2. There are five tubes;
a central tube for reading total head and four chamfered lateral tubes
working in pairs to record pitch and yaw similar to a Conrad yawmeter.
By obtaining equal pressures from the yaw tubes and pitch tubes local
flow
head was
was then
then read
read from
from the
the central
central
flow direction
direction could
could be
be found
found and
and total
total
;;head
tube,
tube, By
By rotating
rotating the
the head
head through
through 10
10 (in
(in pitch,
pitch, say),
say), the
the dynamic
dynamic
head
head was
was also
also evaluated
evaluated from
from the
the instrument
instrument calibration.
calibration. The
The relatively
relatively
large
large diameter
diameter (0.2")
(0.2") of
of the
the pitch-yaw
pitch-yaw meter
meter prevented
prevented measurements
measurements
being
being made
made very
very close
close to
to the
the wing
wing surface.
surface. Also
Also the
the length
length of
of the
the tube
tube
prevented pitch
pitch angles
prevented
angles teeerds
tewerds the
the wing
wing (say
(say near
near the
the top
top surface
surface
attachment
attachment
lines)lines)
from being
measured
closemeasured
to the wing close
surface. to the wing surfac
from
being
The
relatively
illustrated
Figure
15
The relatively large size
of the tube
is well
large
size
illustrated
of the
in is
tubein
Figure
15
well
where
its length
half
length
where its
is about
half the
is about
the local
local semi-span
semi-span of
of the
the wing.
wing.
The Light
Light Source
Source and
and Smoke
Smoke 'Bombs'.
3.4„ The
'Bombs'.
and
The light source used was the
same
as the
the
same
asone used by
Peckham (Ref. 17). The cylindrical lenses were made up by turning
thick perspex sheet on a lathe. It was necessary to supply cooling
air to the lamp housing to prevent damage to the nearest porspex lens
due to heating, The lamp used was an Osram type MA/V mercury vapour lamp
of 400 watts giving 13600 lumens. It was overloaded 40C for six second
taken.
periods to give a brighter light while photographs were
werebeing
being
taken.
The smoke bombs were supplied by Brock's
Crystal Palace Fireworks
Brock's
Ltd., Hemel Hempstead (Type W36E) and give a dense plume of white smoke
for about 30 seconds. The smoke used was rather corrosive to unprotected
steel
ellrfaces.
steel
i7erfaces.
4.
4.
Description of Tests.
4.1. Surface Flow Visualization.
Surface flow patterns at zero yaw for models I and II through an
incidence range up to 30 are shown in figures 3,
3, 4,
4, 5,
5, 6.
6. These patterns
were obtained using a mixture of 100 parts water, 40 parts alabastine
powder and about 6 parts teepol
teepol by volume,
by
The settled mixture is
applied evenly to the model surface with a fine bristle paint brush.
Small air bubbles on the surface leave fine traces in the surface powder
as the air stream is turned on and the pattern
pattern dries. Low airspeeds
(about 80 ft/sec.) were used since the pattern formed and dried quite
rapidly under these conditions.
conditions, Regions of intense surface shear stress,
for example in the top surface boundary layer under the main vortex
cores,
cores, dry dry
very rapidly whereas near the secondary separation
separation line where
line
the excess surface liquid accumulates the pattern is probably distorted
and dries slowly.
4.2. Surface Pressure meansurements.
Sponwise pressure distributions were obtained at four lengthwise
stations
stations for model II (see figure 1) using a conventional tilting multitUbe
manometer. These are shown in Figs. 7,
7, 8,8,
9 and
9 10 in non-dimensional
form.
An
An incidence
incidence range
range up
up to
to 30
30°
steps at
at aa speed
speed
wascovered
covered in
in 2.50
2.5°steps
0was
of
of 130
130 ft/sec.
ft/sec. Both
Both pressure
pressure and
and suction
suction surfaces
surfaces readings
readings were
were obtained
obtained
by
inverting
by inverting
the
the model,
model, Corrections
Corrections to
to incidence
incidence for
for rig
rig deflection
deflection under
under
load
load and
and wind
wind tunnel
tunnel interference
interference have
have been
been applied;
applied; the
the latter
latter are
are based
based
on
on the
the formulae
formulae for
for small
small elliptically
elliptically loaded
loaded wings
wings with
with attached
attached flow.
flow.
_9
_9
4.3, Flow
Flaw Survey.
Survey.
4.3,
For model
model II
TI aa flow
For
arclamic pressure,
flow survey recording total head, dynamic
pressure,
and velocity
velocity direction
direction was
and
was carried
carried out
out at
at 3,9,
3,9, 8.8,
8.8, 14.0
14.00incidence.
incidence.
The viscous
viscous region
region in
in aa plane
The
plane normol
normna to
to the
the surface
surface above
above station
station 2,
2,
(66.7/0 root
rootchord)
chord)was
(66.T/0
wasinvestigated,
investigated,The
The positions
positions of
of vortex
vortex cores
cores were
were
traced for
for model
model II
II at
traced
at 3.9,
3.9, 8.8,
8.8, 14,0
incidence from
14.0°,, incidence
from the
the trailing
trailing
edge to
to near
near the
the tip,
edge
tip.
-
The survey
survey of
of the
the flow
The
flaw above
above station
station 22 was
was carried
carried out
out by
by taking
taking
readings at
at points
points on
readings
on aa grid
grid of
of spanwise
spanwise horizontal
horizontal lines
lines and
and lines
lines
perpendicular to
perpendicular
to the
the plane
plane of
of the
the-wing.
wing. Information
Information obtained
obtained along
along
these grid
grid lines
lines was
these
was plotted
plotted to
to give
give contours of constant total head
head
and dynamic
dynamic head,
head, Some
Some of
and
of these
these are seen in Fig.15.
✓ortex core
core positions
Vortex
positions were
were determined
determined by
by pointing
pointing the yawmeter
tov.nrds the apex and translating
toriards
translating vertica
vertically lly
and horizontall
horizontally
and
y to zero
zero the
the
and pitch
pitch readings
readings This
yaw and
This was
since
was thought to be fairly
fairly accurate
accurate
large :=)_17
:AW and
large
and pitch
pitch
indicationscorresponde
corresponded
to small
small translation
translational
indications
d to
al
movements
near
the
movumee.ts
near
the core.
The probe used was rather large and may influence the contours
Obtained but the readings were repeatable. The results are given
given in
in
figures 16 to 19.
4.4.
4.4.
Smoke Flory
Flow Visualizati
Visualization
Technique.
on Technique.
The flow over
over model
model II
investigated
using
aasmoke
II (70°
was was
(70
° Delta)
Delta)
using
investi
smoke
gated
technique
the
technique suggested
suggested by
by R.hrialtby
R,Maltby ofofthe
R
A
E.
Bedford.
The
flow
in the
the R A E. Bedford. The
in
cross flow plane is seen in figures 20
20 and 21 for station 2 along the
chord and in the wake behind the trailing edge.
the
With
Vdth the tunnel at a low speed, a smoke bomb was ignited
ignited in
in the
settling chamber such that the plume of smoke went onto the apex of
of the
the
model.
model. AA plane
plane of
of parallel
parallel light from a mercury arc lamp and lens
lens
system
system was
was then
then passed
passed across
across the
the model
model at
at the
the station
station under
under investigati
investigation
on
and
pictures
nose.
and pictures taken looking
looking down
down the
the model
model from
from the
the nose.
-10--
5.
Discussion.
5.1. General Description of Flow.
The three dimensional model of the flow studied by Mangler and
Smith is shown approximately in figure 22. The incident flow attaches
to the wing surface along the lower surface attachment lines AI.
(The reader is referred to Maskell, reference 3, for a discussion of
three dimensional flow separation and the definitions of flow separation
and attachment lines.) These lines divide the surface flow passing over
the trailing edge from that passing over the leading edge and are the
three dimensional equivalent of the more familiar front stagnation
strpnmline of two dimensional flow. The lower surface separation lines
S are along the sharp leading edges where a Kutta condition obtains.
Tio pseudo conical vortex sheets extend from the leading edges and roll
up above the suction surface of the wing to form the vortex 'cores/.
Due to the presence and strength of these vortices air is sucked down
onto the top surface of the wing and two top surface attachment lines A2
areformed. These attachment lines A are considerably inboard of the lower
2
surface attachment lines and with increase
of incidence they move towards
the centre line and coalesce. In Appendix I the predicted position of
the lower surface attachment line for attached flow past elliptic cones
is given; tore is of course no upper surface attachment line in this
case. Mangier and Smith have tabulated attachment line positions for
their model of the flaw - see Table III p.37 of reference 19, and have
clarified the physical nature of these attachment lines by drawing
radial projections of the three dimensional streamlines - see Figs, 15
and 16 of reference 19.
Air approaching the wing between the conical surface ab (see Fig. 22)
passes under the vortex core and flows out 'spanwisel whereas the air
outside this region and between the top and between the bottom surface
attachment lines flows in a more or less chordwise direction downstream
and off the trailing edge.
The extra lift force produced by a delta wing with edge separations
is then due to the extra entrainment of air by the vortices (see Weber
reference 4.). The non-linear nature of this extra lift is due to the
inboard and upward displacement of the vortex cores and their increase
of strength with increase of incidence, giving an ever increasing
entrainment offdot.
5.2. The
The Viscous
Viscous Regions.
5,2.
Regions,
Figure 23
Figure
23 is
is aa c.imposite
c.imposite figure
figure showing
showing the
the total
total head
head survey,
survey, the
the
upper surface
surface pressure
upper
pressure coefficient
coefficient distribution,
distribution, the
the surface
surface flaw
flaw and
and the
the
smoke visualization
visualization results.
smoke
results. These
These can
can be
be interpreted
interpreted as
as indicating
indicating the
the
type of
of viscous
viscous flow
type
flow pattern
pattern sham
sham in
in Fig.
Fig. 2424- Which
Which has
has been
been sketshed
sketshed for
for
on incidence
incidence of
on
of approximately
approximately 0.7
0.7 of
of the
the semi-apex
semi-apex angle (a = 14 ).
)•
The boundary
boundary layer
The
layer thicknesses
thicknesses shorn
shorn are
are thicker
thicker than
than those
those actually
actually
present.
present.
The thin
thin (probably
The
(probably laminar)
laminar) boundary
boundary layer
layer developing
developing outboard
outboard of
of
thelower surface attachment linesil separates at the edge and contributes
the
contributds
most of the vorticity in the leading1 edge vortex sheet and main vortex
care, The lioundary layer inboard of Aion
on the
the lower
lower surface
surface would
would
eventually
eventually
leave leave
the trailing
the edge. On the upper surface the boundary
layer growing outboard of .,12separates
separates at
at the
the secondary
secondary separation
separation line 52
and rolls up to form a secondary core of 'opposite sign' to the
themain
vor',Axs.. Figure 16 shows the pitch angles induced by this secondary core
near the leading ed7e on the top surface. The presence of this secondary
core was shorn in ti'e present experiments by a small (-',
1
," span) delta
shaped vol'%imeter which rotated in the opposite sense to the main vortex
placed at
when placed
at the
the core
core position
position of
of the
the secondary
secondary vortex.
vortex. The
The cuirponent
component
of the ciroalation at right angles to
crosscross
flow plane
was estimated
tothe
the
flow
for the circuits shown in figure 15, If the counterclockwise
counterclockwise circulation
around ABCEPC4
ABCEPaID,
-1D, embracing
embracing the
the main
main vortex
vortex core,
core, is called 100 units then
the circulation around HGFE embracing the secondary vortex core worked
out to be - 18 units. On some of the surface flow
flaw pictures, for example
figure 4 and 5, a third attachment lineA, is evident quite close to the
upper surface leading edge and inboard, qdite close to S2, is a third
separatio
separation line
n S3.
line
clearly evident in the
ThisSlatter detail is more clearly
3.
surface flow pictures given by Draugge and Larson in reference 7. In
In
the region
region 11,
R, sue
much ofofits total
sue figure
figure 24,
24, where
where the
the air has lost much
head there is probably some turbulent mixing It is evident then that
most of the upper surface boundary layer flow does not in fact enter the
main vortex core, but contributes to the wake from the upper surface
trailing edge and to the secondary vortex core. The existence of vorticity
in the wake of opposite sign has been noted by previous expetimenters
and figure 21 shows a sequence of smoke pictures illustrating the
rotation of the weak secondary core around the main vortex core after
the flaw has left the trailing edge.
The shape of the smoke pattern behind
behind the trailing edge is very
similar
reference 1.
1.
similar to
to the
the total
total head
head contours
contours taken
taken in
in aa wake
wake by
by Fink,
Fink, reference
The
The main
main effect
effect of
of the
the secondary
secondary separation
separation seems
seems to
to be
be to
to displace
displace the
the
main
main vortex
vortex core
core inboard
inboard and
and upwards
upwards which
which might
might be
be expected
expected to
to give
give more
more
lift
lift than
than the
the Mangler
Mangler and
and Smith
Smith theory
theory as
as suggested
suggested in
in reference
reference 4.
is
4-. It
It is
interesting
interesting to
to note
note that
that separation
separation at
at the
the leading
leading edge
edge only
only exists
exists at
at all
all
- 12 -
angles of incidence, other than zero, when the leading edge is sharp.
When the leading edge possesses curvature we can expect a very small
range cf incidence in which complete attachment of the flow occurs,
At a larger incidence, but still relatively small in magnitude, the
under surface boundary layer should separate close to the leading edge
and reattach on the upper surface forming a separation bubble. This type
cf flaw would be different from that discussed by Mangler and Smith
since no rolling up of the vortex sheet from the wing undersurface takes
place. However at still larger incidences we should expect the flow
to degenerate into that described by Mangler and Smith except that the
secondary separation would be present.
iris on of Results withthe theory of langler and Smith
refolences 1 1 and 19
5.3. C
The surface pressure coefficient distributions are shown in figures
7 to 10. The shape of the upper surface pressure peaks at the forward
station (station 4) is fairly flat with minor peaks corresponding te
the positions of the main and secondary vortices. The shape and
magnitude of the pi ensure distribution changes as the trailing edge is
approached (see figure 11) and the flow field for low speed flow is
clearly iar from conical due to the "trailing edge effect". Figure 12
shows a comarison of the pressure coefficient distributions at the forward
station with those predicted by Mangler and Smith. It is seen that the
theoretical pressure peaks are much greater and narrower than the
experimental results.
Spanwisc integration of the pressure coefficient distributions
gives the local normal force coefficient curves shown in figure 13 for
the four stations. When a comparison is made with the curve given by
Mangler and Smith for their A+ boundary conditions, it is seen that the
experimental results at the forward station lie above this curve. This
is the result anticipated in section 5.1 (and reference 4) and is due
to the presence of the secondary separation, The normal force coefficient
curves for the other stations fall progressively below the theoretical
curve due to the loss of loading as the subsonic trailing edge is approached.
One might anticipate on physical grounds that the presence of a
subsonic trailing edge would have a small effect at small incidence and
a precressively greater effect at larger incidence - this would give a
forward shift of the overall centre of pressure. Figure 14, which shows
the chDrdwise variation of C and Figure 14a which shows the normalised
N
a
distributions cf CNalong the root chord for various incidences (up to
—1.5)
indicated that the centre of pressure shift from 0.57 oris small and
the'trailing edge effect' is rather independent of incidence. (This has
been confirmed by independent balance measurements on delta wings with
sharp leading edges).
--1313 ••
from
apex
The centre
ofpressure
atC 0.57 Crrfrom
pressure is atis0.57
The
centre of
thethe
wingwing
apex or
0.36 0or 0.36 0
behind the
leading
edge ofedge
behind
the
leading
of aerodynamic
the mean aerodynamic
the mean
cherd. Figure 14-cherd.
shows Figure 14- shows
the overall
in
agreement
the measurenormal
coefficients
force
the
overall
normal force
coeffiare
in agreement
cients
withwith
the measureare
rents made
at R.A
R.AE.E.
a range
delta wings.
on aon
range
of delta of
rents
made-- at
wings.
The surface
flowflow
The
surface
pictures,
some
which
are shown in figures 3,
pictures,
some of which
areof
shown
in figures
3, 4,4,
look misleadingly
misleadingly
when it ishow
remembered
conicalconical
55 and
and6,6, look
when it is remembered
much the how much the
pressure coefficients
rays
through
the Measuremen
apex. Measurements
vary
pressure
coefficients
vary along
along
rays through
the apex.
ts
indicate however
the
attachment
or separation
that that none
indicate
however
noneof of
the attachment
or separation
lines are inlines are in
fact straight,
upper
surface
flow attachment
line
In
25 the
figure
fact
straight,
In figure
the
upper
25
surface
flow attachment
line
positions, measured
close toclose
positions,
measured
apex,
are shown
the apex,toarethe
shown
for Models
I and II for Models I and II
for various
seen
thesecorrespond
closely which
correspond
which is a
eic/ic
It
is seen
It is
for
various eic/K
thatthat
these closely
is a
'
'
little surprising
apex
angle
in view ofin
little
surprising
the
semi-,,
theview
ratherof
large
30 rather large 30°
apex angle
°semiof of
model
I.
Also
included
on the figure
model I. Also included
on the
figure for
is the predicted
for comparison
is thecomparison
predicted
position given
by Mangler
position
given
by Mangler
Thelyexperimentally
determined
and Smith.and
TheSmith.
experimental
determined
attachment
line
positions
attachment line positions
are
see to
lie aamount
roughly constant amount
are see to lie
a roughly
constant
inboard (for(for a/between
of
the
secondary
presence
inboard
between
0.21.0)
and
1.0)
due to the
0.2 and
due
to
the
presenc
of the
esecondary
a/ K
separation region.
separation
region.
In falt
this inward
In
falt
this inward
Casplacement
to width
the width
Casplacemen
t is very nearlyis very nearly equal
equal to the
of the
secondary
separation
The
upper
surface
of
the
secondary
separation
region (see region
figure (see figure 26).
26). The upper surface
secondary separation
together
line positions
secondary
separation
line are
positions
are shown in figure 26
shown in figure
26 together withwith
the
tertia
where
these
be
seen.
separations
ry (S (S3
the
tertiary
separations
3))where
these
could could
be seen. The positionsThe positions
of these
lineslines
are undoubtedly
of
these
arc undoubtedly
due to
the accumulation of excess
distorted duedistorted
to the accumulation
of excess
surface liquid
when the
results
surface
liquid
when
the patterns are
formed.
Here the
patterns
arebeing
being
formed.
the results
Here
for for
Models
II doII
notdo
coincide
ModelsI and
I and
not and
coincide
and the
secondary
the secondary
separation
region isseparation region is
rel%tively
widerwider
for thefor
rel%tively
the wing.
narrower wing.
narrower
The
of the of
The positions
positions
main
cores
measured
mainthe
vortex
coresvortex
measured
with the
five tube with the five tube
pitch-yaw
meter
are given
and18.
18.
Figure
19 compares
pitch-yaw
meter
areingiven
17 and
figures in figures 17
Figure
19 compares
these
withwith
the positions
these results
results
the positions
estimated
from
the flow field measureestimated from
the flow field
measurements
smoke
pictures
mentsand
and
smoke
pictures
= 0.667,
0.667, that
thatis at
isstation
at station
2.
taken at taken at 2V00 =
2.
Also
in thein
figure
Alsoincluded
included
thearefigure
are some
additional
some additional
exper;mental
points exper;mental points
from
Fink,
reference
=
0.417
onsemi-apex
a 10 semi-apex
angle
1, taken at
from.
Fink,
reference
1,x,taken at xi
= 0.417 on a 10
angle
0,
//0,
delta
wing,
and the
Mangler and
andSmith,
Smith,
Legendre,
theoretical
delta
wing,
and
the theoretical
estirnates of estirnates of Mangler
Legendre,
and
Michael.
andBrown
Brownandand
Michael.
The
path
corescase,
in with
the present case, with
The path
of the
coresofin the
the present
change
is similaristo Finks
changeof incidence
of incidence
similar
Finks
but
a given position occurs
but a to
given
position
occurs
at
a/
should
be remembered
that of
inthese
neither of these
ata different
a different
a/
ItItshould
be remembered
that
in neither
K.
K.
low
experiments
are
lowspeed
speed
experiments
are the
the flow
flowfields
fields
trulysoconical
truly conical
that the so that the
agreement
for for
the different
agreement
the different
lengthwise
stations ( xi_
0.667
lengthwise stations
(x
i _ = =0.667
and and
"r
"r
x/c
= 0.417)
is largely
x/c
= 0.417)
is fortuitous.
largely For
fortuitous.
For a given a/K
experimentally
/K
a given a
thethe
experimenta
lly
detErmined
corecore
positions
detErmined
positions
are
and above
are inboard
andinboard
above the position
given the
by position given by
the
of Mangler
and Smith
thetheory
theory
of Mangler
and
due toof the
presence of the secondary
dueSmith
to the presence
the secondary
separation.
The experimental
separation.
The experimental
as the total head minimum,
'core', taken'core',
as the totaltaken
head minimum,
is
however
not equivalent
is however
not exactly
exactly
equivalent
to the
ofinthe core region in
to the centre
of thecentre
core region
-
-
Mangler and
and Smith's
Smith's model.
model.
Mangler
6.
6.
Conclusions.
ons.
Conclusi
on regions
(i)Vortices
Vortices exist
exist in
in the
the so
so called
called secondar
secondary
separation
regions
y separati
(i)
Fluid
edges.
on
the
upper
surface
of
a
delta
wing
with
sharp
leading
edges.
Fluid
leading
sharp
wing with
on the upper surface of a delta
of
that
the
to
rotation
in
the
secondary
cores
is
in
the
opposite
sense
to
that
of the
sense
opposite
rotation in the secondary cores is in the
y of
to
te
vorticit
-the
main
leading
edge
vortices,
The
secondary
vortices
contribute
to
contribu
-the
vorticity
of
vortices
main leading edge vortices, The secondary
opposite
sign
found
in
the
wake
system
of
these
wings,
wings,
wake
these
the of
oppostte sign found insystem
e on
(ii)The
The secondar
secondary
separation
regions are
are fairly
fairly extensiv
extensive
on flat
flat
on regions
y separati
(ii)
the
of
ment
narrow
delta
wings
and
cause
an
inboard
and
upward
displacement
of
the
displace
narrow delta wings and cause an inboard and upward
in
Smith
and
vortex
cores
compared
to
the
positions
given
by
Dangler
and
Smith
in
vortex cores compared to the positions given by Dangler
reference
19.
e 19.
referenc
(iii)In
In low
low speed
speed flow
flow the
the forward
forward position
positions
of aa delta
delta wing
wing will
will give
give
s of
(iii)
ons.
separati
y
more lift
lift than
than predicte
predicted
in referenc
reference
19 due
due to
to the
the secondar
secondary separations.
e 19
d in
more
ntally has much
The shape
shape of
of local
local spanwise
spanwise loading determin
determined
experimentally
ed experime
The
tion.
flatter peaks
peaks under
under the
the vortices than the theoreti
theoretical
distribution.
cal distribu
flatter
(iv)':fith
':fith aa subsonic
subsonic trailing edge there is of course a marked
(iv)
ent
independ
loss
of
is
loading
towards
the effect
is not
independent
t highly
effec
this edge but the
towards
of
loading
loss
up
es
on incidenc
incidence
and the
the centre of pressure remains fixed for incidenc
incidences
e and
on
to
1.5
times
the
semi
angle,
apex
semi
the
to 1.5 times
— 15
15
—
• 0Di
4
Di
••Di
1.
1.
Fink,
Fink, P.r.. and and
Taylor,
Taylor, J. J.
2.
2.
lirnberg,
tIrnberg, T. T.
ES
ES
Some low
lowspeed
speed
experiments
°
experiments
with 20 with 20°
Delta
wings.
Delta wings.
A, R. A.R.C.17854.(1955).
0.17854.
(1955).
AA note
noteonon
flow around
delta wings.
the the
flow around
delta wings.
K.T.H. T.N.38
T.N.38 (1950.
1954).
(
3.
3.
Easkell,
E, 0.
Maskell, E.C.
Flaw
separation
indimensions.
three dimensions.
Flow separation
in three
R.
A.E.Acro
2565. (1955).
(1955).
R.A.E.Acro
2565.
4..
4..
Weber, J.J.
Weber,
Some
effects
flaw separation
Some effects
of flowofseparation
on slender on slender
delta
wings.
T.N.2425.(1955).
delta wings.
R.A.E.R.A.E.
T.N.2425.(1955).
5.
5.
Lee,G.G.H.
Lee,
H.
Note
delta wings
Note onon
thethe
flow flow
aroundaround
delta wings
with
sharp
leading
with sharp
leading
edges. edges.
Page
Interim
Handley
Handley-Page
Interim
ReportReport S.W.A.O.
Paper,
S.0149
Paper, No.No.
S.0149 (1955). (1955).
6.
6.
Fink,
P.T.
Fink, P.T.
Some
lowspeed
speed
aerodynamic pr
properties
Some law
aerodynamicoperties
of
cones L.
A R.C.17632
R.C.17632 (1955).
of cones
(1955).
7.
7.
Drougge,
Drougge, *C-. and and
Larson,
P.O.
Larson,
and
flow investigation
measurements
Pressure
Pressure measurements
and flow
investigation
speed.
on delta
delta
wings
at -supersonic
on
wings
at supersonic
speed.
57. (1956)
.
1%
A.Report 57.
F F.F.
A.Report
(1956)
.
8.
Pocock,P.J.P.J.
Pocock,
and and.
Laundry,W E. E.
Laundry,
aerodynamic
characteristics
of
Some aerodynamic
characteristics
of
Second
delta
wings
low speeds. Second
delta
wings
at lowatspeeds.
CanadianSymposium
Symposium
on Aerodynamics
Canadian
on Aerodynamics
Institute
of Aerophysics,
Univ. of Toronto,
Institute
of Aerophysics,
Univ. of Toronto,
(I 954).
(1
954).
Jones,
Jones,
R.T.R.T.
Properties
ofaspect
low ratio
aspect
ratio pointed
Properties
of low
pointed
wingsat at
speeds
above
and
wings
speeds above and below the below the
N.A.C.A.Report
speed
of
sound. N.A.C.A.Report
835,(1946).
speed of sound.
835,(1946).
10.
10.
Brown,C.E.
C.E.
Brown,
and and
Michael,
7,
Michael, W.H. H.
Effect
of leading
edge separation
on
Effect
of leading
edge separation
on
J.Ae.Sc.
the
lift
of
a
delta
wing.
J.Ae.Sc.
the lift of a delta wing.
Vol.21 (1954).
(1954).
Vol.21
11.
11.
Mangler,K.K.
Mangler,
W. VI.
and and
Smith,
J.H.B.
Smith,
J.H.B.
A theory
of slender
delta
wings
A
theory
of slender
delta
wings
with with
leading
edge
separation.
R
A.E.
leading edge separation. R A.E. T.N.Aero T.N.Aero
(1956).
24)12. (1956).
24)12.
9.
9.
- 16 -
12.
Brobner, G.G.
Boundary layer measurements on a 590
swept back wing at low soceds.
A.R.C. C.P.86 (1952).
13.
Stalker, R.J.
A study of the china film technique
for flow indication.
A,R.L. Report A.96.
14,
Bartlett, G.E. and
Vidal, R.J.
Experimental investigation of influence
of edge shape on the aerodynamic
characteristics of low aspect ratio wings
at low speeds. N.A.C.A. T.N.14.68 (1947).
15.
OrlikRilokemann, K.
Experimental determination of pressure
distributions and transition lines of
plane delta wings at low speeds and
zero yaw. Swedish K.T.H. hero Tech.
Note 3 (1948).
16.
Kilehemann, D.
Typos of flow on swept wings with special
reference to free boundaries and vortex
sheets. J.R.Ae.Soc„ Nov.1953,
17.
Maltby, R.L. and
Peckham, D.E.
Low speed flow studies of the vortex
patterns above inclined slender bodies
using a new smoke technique.
R.A E. T.N.Aero 2482 (1956).
18.
Prandtl, L.
The essentials of fluid dynamics.
Blackie and Sons (1952).
19.
Mangler, K.W. and
Smith, J.H.B.
Calculntion of the flow past slender
delta wings with leading edge separation.
R,A E. hero 2593 (1957).
20,
Legondre, R.
Ecoulement au voisinage de la pointe
avant [Pune aile sh forte flCche aux
incidences moyennes.
La Recherche Aeronautique (0.N.E.R.A.)
No. 31 1953.
7
LPPEINDIK
APPENDIX II
Attrdluent
Attae,
zwnt lines
lines on a^ farrdiy
of elliptic
elliptic cones.
family of
cones.
Consider aa family
Consider
family of slender
slender bodies
bodies of
of elliptical
elliptical cross-section.
cross-section.
Let us
us assume
assume the
Let
theflo=g
flat con
can be
be resolved
resolved into an
an axial
axial and
and aa cross
cross flaw.
flaw.
body
If Uc
the freestroam
frcestraw velocity
and the
U,
m isisthe
velocity
If
the
body is
and
is at
at aa small
small incidence
incidence aa
we can
can assume,
assume, since the body is slender that
we
that
the perturbation axial
axial
velocity component is small compared with U.,
cos a. The resultant of
Uoc, cos
the axial velocity component, Uco
cos aa and the cross-flow
Urocos
cross-flow velocity
velocity
gives the
the surface
surface flow
flow direction
direction (in
(in inviscid
inviscid flow). Under
uogives
component uo
extain conditions
c.rtain
conditions of
of body
body shape
shape and
and incidence
incidence the resultant velocity
vector
velocity
will lie
lieon
on aagenerator
generator passing
passing through
through the
the body
body apex.
apex. This
This line will
be called
c-lled either an
an attachment
attachment line or aa separation
separation line
line depending
depending on
whether the flow near the generator is respectively away from or towards
towards
the generator.
If the ellipse has major and minor axes of lengths a and b respectively
the circumferential
circumferential cross-flow velocity on the surface of the ellipse at
(F.
(g ,n ) aao to the cross-flaw component of the freestream
freestreem velocity,
U w sin
sin a
is
sin cc
a '/°2 Li
2
Uca sin
/a
11
(1
(i)
)
(1
a-b)2
a-b)
2
(::1
1!) Iljk2
al)
+g
a13
.
1.
a+bi
b
If /a
/a ==h (a
h (aheight
heightfactor
factordescribing
describingthe
the thickness
thickness of
of the
the ellipses)
ellipses)
for a.
a flat
= 00 for
flat plate
= 1 for a circle.
,
tan 0G K =
= a/0
where 0 is the semi-apex angle (spanwise) and
/cr
o r is the root chord
r
then
then u6
b
=
U sin
s (1
Um
sina a
s h)
(1 + h)
(2)
( 2)
j
s2(1
(1 -- h2)
h2)
1 - s2
7here s
s = ',/a
/a (fraction
(fraction of
of semi
semi span)
span)
—-181— 8 -
It can
can be
be shon
shownthat
thatthe
theresultant
resultantflow
It
if
flowis
isalong
alongaa generator
generator
if
'a
c
uc
I.J
c
,
)
cos aa
UCo cos
1(15 (1
(1 -•-• 32)(1
S2)(1 -— h2)
Ks
h2)
((33) )
(1- h2)
S2(1
11 - S2
h2)
-
-
Thus
equat
ing
(3) the
the
andflow
flow is
Thus
equating
(2)
and(2)
(3)
a generator
is along
along
generat
a
or if
if
S
when
when
±
4-1 )2
(77:7
- (ITTE)
=
(
'
(fla
plate
t)s s= = ± 1
hh0 0
(flat
plate)
1
(-f( Ka ))22
4)
(5)
(5)
(circle) ss is
is imaginary
imaginary unless
hh == 11 (circle)
unless Y
—
pc == 0
0
a
Inallall
s for
In
casescase
for real
sa
a
<
-h)
real
< (1
-h)
narrow delta
Fora narrow
a
delta wing
wing with
with attached
attached flow at
For
leading edge the underatthe
the
undersurface
attacline
hment
describ
lineed by (sce
surface
attachment
la described
(see (5))
= +
11
11
-(a)
( 7K)2
-
c
4-
2
For
a less
there are
are tw,r
two,attachm
attachment
lines on
on the
the
For values
values of
of a/K
less than one there
ent lines
undersu
rface which
which reduce
redune to one when a/K = 1.
flow is
is
1. When
When the
the flaw
undersurface
separat
ed at the leading edge the undersu
changed
undersurface
separated
rface flow
flow is not
not changed
appreci
ably. Hence
Hence the
the undersu
undersurfacc
attachment
lines
are
still
given
rface attachm
appreciably.
ent lines are still given
approxi
mately- by
(5).
approximatelyby (5).
STATION 4 (33 - 0 Cr)
STATION 3 (0-50 Cr)
— LEADING EDGE
RADIUS 0.008"
STATION 2 (0.67 Cr)
STATION I (0 83 Cr)
-- —HOLE SPACING 0 I0'
HOLE SPACING
SPACING ,,.155°
HOLE
—HOLE SPACING
SPACING 0
0 •20"
20"
--HOLE SPACING 0.25 '
srING
I
o
0- 57 n
PITCH -YAWMETER
-YAWMETER
-PITCH
-
PITCH QUADRANT
QUADRANT
PITCH
YAW ST E M
VERTICAL TRAVERSING
GEAR
2'1
4
2'14
-0r111111111•11.
/Al,/
- ------
55 TUBES
TUBES
STATIC
PRESSURE
STATICPRESSURE
HOLES
HOLES
70.
70.
II M
TUBES
M TUBES
MM
STATIC
PRESSURE
STATICPRESSURE
SUPPORT
STEM
SUPPORT STEM
(#)
- (#)
FRONT
VIEW
FRONT VIEW
YAWMETER
DETAILS
HEAD DETAILS
YAWMETER HEAD
SCALE
SCALE 22
FIG.
2.
FIG. 2.
FIG. 3. SURFACE FLOW VISUALISATIqN ON UPPER
SURFACE - MODEL I (A= 60 ) r)g = 14
FIG.
UPPEdi
ONITPPE.1
VISUALISATIONON
FLOWVISUALISATION
SURFACEFLOW
4. SURFACE
FIG. 4.
= 23.
9
23. 9`.
SURFACE
(A 7
pt =
60 )) Ot
= 60
MODELII (A
SURFACE --MODEL
FIG.
SURF
5.SURF
FIG.5.
UPPER
ONUPPER
FLAW,
VISUALISATIONON
FLAW,VISUALISATION
=70°)
SURFACi
A=70°)
MODELIIII((A
SURFACi--MODEL
aa
3°
G.G.3°
FIG. 6. SURFACE FLOW VISUALISATION ON UPPER
SURFACE - MODEL II (A =70°)
14. 0°
Cp
24
N
N
I
- 2. 2
N
I
0
- 2.0
I
03
- 18
1
.0
- I- 6
- I 4
1
+
+VORTEX
VO RTEX CORE POSITION
POSITIO N
_i.2
29.0°
•0° INCIDENCE
INCIDENCE
0
- I 0
a
- 6
- 4
0
2
'
•4
816
534
- 450
• 257
084 0 -064
2 57
I
T
FIG.
7 SPA
SPANWISE
FIG. 7
NWI SE VARIATION
VA RIATION OF Cp
STATION I MODEL A
450
634
• 916
4
0 ).
p
- 24
- 2 -2
4 VORTEX CORE POSITION_
-2 0
-I 8
4-
- 1•6
-1 4
- 12
FIG.8 SPANWISE VARIATION OF
Cp
STATION 2. MODEL
IL
N
fY
+ VORTEX CORE POSITION
1
fV
29 0° INCIDENCE
16
- 1.4
IN
12
- 1 .0
c
-•6
4
ry
-•2
2
o0
,
.6
-8
L
171
0
2
IL
0
LT
FIG. 9 SPANWISE
VARIATION OF Cp STATION
STATIO N 3 3 MODEL IL
SPA NWISEVARIATION
816
8
Io y
0
•084 0 •084
-634
OD
450
•267
rp
kr;
0
N
267
qo
•450
0
634
c0
816
m
%.0
1C
cc;
Y
0
Cp
-2 4
-2'4
29 0° INCIDENCE
- 22
- 22
+ VORTEX CORE POSITION
- 20
- 2'0
- I-B
-I 6
- I 6
-14
-I 2
-12
-I 0
- 10
-- a
-•4
A
.o"
-X
1.4
A A X
X
lfj
•
- 0
•
Y
X
IA
4 A
0
0
0
X—X
xX
Y A X
q
a
0
-a
10
816
634
450
267
X
• • • * •
450
FIG. 10 SPANWISE VARIATION OF Cp. STATION 4 MODEL II
•634
•8I6
•8
I 0 s
Cp
0
0
NO1111911±151❑
n
0.t71
3DN3OID NI 0
C)
-14
-
II
FIG. II PRESSURE DISTRIBUTION AT 14.0° INCIDENCE (A = 70°)
(-111 S ONV d31ONVIAI dO S1lf1531rf HIIM NOSIdVdINCYD)
SNO111191t1ISI ❑
0 I
91:111SS3ticl 3SIMNVcIS ZI 'Old
6
9 I-
II -13CION
NOIIVIS IV SI-111531:1
0
e-
aq
I
9
1-1111Ns (INV \
1:13 -1DNVIN
oB
E-
oe=
dp
AT STATIONS I, 2, 3, 4, MODEL U .
13001A1
E'z I SNOIIVIS IV
'
N
EN
FIG.13 VARIATION OFC AND — — e` FROM PRESSURE DISTRIBUTIONS
K2 K2 K
SNO1111911:11310 3101SS3):Id WO 1d
1.0
- ZA
5-0 ND
•8
0.1
9
•6
1.2
ZI
NV Z>I JO NOIIVII:1VA El DIJ
ND
9.
4
1.4
1
2
/
V
/ /
■
o■
/
/ ( /
o
/
9
STAT f ON
N01.1.VJLS
a
z
—
4
0/
10
01
R.A.E. (UNPUBLISHED)
(031-1S1-1911dN11) . 3Ar):1
•
C N/K 2
•
ZNiND
X
2
0
0
3
X
12
A
4
/
/
EN,K2
Z1
O STATION
I NOILVIS 0
CIN3D3 -1
0
LEGEND
14
-
7
P1
MANGLER & SMITH
(A+)
(+ V)
b310N VW
16
91
X
IB
SI
20
OZ
2
ZX
Na
C ts4
CN
ND
zr
K2
91
18
1
ig=30.5°
'
oS OE a's
16
91
Ith
14
41
23 9 °
12
ZI
k
Al
,c ,
tr
.,1
0!
10
nejl
l
a
.
n
.,
6
9
441.•
b1 ll
1161111
iri
le
09
4
9
2
■■■
9-0
I
S AO
40
0.6
0:8
1 0.7
0,9
2
SNO1IVIS
c6 C
E0
3
L.0
05
Z 0
I r)
4
9-0
04
0 3
3903
9NI1IV 2S1
X-.
x
a 2
01
0
NOSE
TRAILING
EDGE
3SON
STATIONS
0110HO 1008 9NO1V 3DNVISIO
JO NOIIVIdVA 3SIM0b0HD V VI 'DIA
FIG. 14 A CHORDWISE VARIATION OF -JA
C
K2
x/C,
11 13001 . 3DN3CIONI HIIM
DISTANCE ALONG ROOT CHORD
WITH INCIDENCE. MODEL U
P NOIIVIS IV S.1.111S3b1 . NOS111VdiNOD 1:10J - 310N
NOTE - FOR COMPARISON RESULTS AT STATION 4
3013NIOD 01 30VW 31JV
ARE MADE TO COINCIDE
CN
ND/ ZN
ND
K 2 /CN
6 0 ® rM
0 9
et =3 9° —
ec = 8 8°
0,14 0'
9 0
0 6
_ cd=19 .1
A4=- 23 9
9 0
S 0
t? o
0 6
07
2
08
0 9
1 0
TRAILING EDGE
atiOHD 100b9N0 -1V
EC
Z 0
SNO1 -viS
! 0
3SON
DISTANCE
035
L0
0 4
9 0
0 2
03
4
STATIONS
60
"405E
0I
E 0
0 3
3903 9N111Vb11
K 2 s
ALONG ROOT CHORD
3DN3OIDNI HIIM N011f1911:11SI4 No JO 3cIVHS AO NOIIVItIVA 9 VI DIA
FIG 14 B VARIATION OF SHAPE OF CN DISTRIBUTION WITH INCIDENCE
II 13GOIN
MODEL Il
HO
40
%SENA
SPA71
PAH
S
[35°
53°
30
30
a
TUBE V6611NE
VAANTIETER
TE R
TUBE
1:04 As..44■TO
-70 SCALE
SCALE 0016
0071
066•....
0
40
51ZE
C
Z ECOr1PYJl1
SI
0
1
10
cL 33•• 9
cL
9°
°
ff. 014
-9
SO
50
10
80
.55
100
540
90
/o StritSPRNi
41,
4
h
h
0/0
/0
0
SEM
SEM
SPA
SPA
3
3
irtil
1
NIIIIIIIIIIIIrIMIE a
.pg
CL
c I-- __
Sp
50
30
oC .=
aa--8°
oc
a°
•
-.NTI
a
a
a
q
_111"111111
GO
50
-
-
10
70
vo
'0
-1
irr
,/,',
/
—
- 80
80
A014
‘
.11
-1
7\.,
.
SA.
lik\
s 11 —
tkab9
*9
• ° 511.-:C1
D
90
/00
/00
SEMI
SPAN
W 471111111
*Cs
14 °
*CI= 14°
10
11
0
60
/ / / / / /
/ )19
70
0
.10
100
%Mr:
1100
SE11
SPAN
SPAN
FIG
15. TOTAL
TOTAL HEAD
HEAD SURVEY
SURVEY AT STATION 2 (0 • 67cr)
FIG.. 15.
AT
c6=33•• 9°
8.8 ° AND
AND 14°
9° 8.8
14°
AT c6
(LINES OF
11=22-'1' = CONSTANT)
cc>
•
300
oC = 8 8 °
200
0
I
3 -10NV
HDIld
I
-
E
h
Is
0
— 10
022
033 —15
043—W---
0 087
—20
130
-0
MAIN VORTEX
CORE
SECONDARY
VORTEX CORE
3 0
1.0
❑
0
0
0
0
0
Yls
TIP
a_
U
7
z
0_
tP
0 90
0 BO
0 70
0 60
SPANWISE DISTANCE FROM
WING
CENTRE
LINE
GCEN
TRELINE
FROM WIN
0
0 50
0 in
0
0 40
0
0 30
cc
0
el
0
FIG. 16 SPANWISE
A NGLE TOWARDS WING
WINGSURFACE
PITCHANGLE.
SURFACE
VA RIATION OF PITCH
SPANWISE VARIATION
2y
b
075
0 5
POSITION
O FVORTEXCORE
I 0
C
1 0r
NOSE
DISTANCE FROM APEX
TRAILING EDGE
FIG. 17 SPANWISE POSITION OF VORTEX COPE MEASURED WITH YAWMETER
(0 0L)E -13GOV4
MODEL IVA=70°)
0. = I 4. 0 0
2h
b
0.15
= 8 8o
O
0 10
I-
0' 05
„z= 3 90
0 5
025
NOSE
DISTANCE FROM APEX
0 75
TRAILING EDGE
0L =V)la 73001^1
AO N011Y11:1VA
( 0
35IMCIdOH O91 '01A
FIG. 18 CHORDWISE VARIATION OF VORTEX HEIGHT MODEL IL(A= 70°)
-
b3191^1MVA
C13811S V31^4
MEASURED WITH YAWMETER.
01 33d 13VHDIW ONV NM02:143 0
O BROWN AND MICHAEL REF 10
3A`c1110 H7Y3 NO N3AID 31:1V SNOLLISOd ){40
POSITIONS ARE GIVEN ON EACH CURVE
OZ d38 32:1ON3031
A LEGENDRE REF 20
61 J3ti HlIWS ON'd t131ONVIN
X MANGLER AND SMITH REF t9
71N13
I33)1 ZV•0
FINK Cr = 0.42 REF. 1
s/z
A3A1:111S M013
3130t1d
+ PROBE
O FLOW SURVEY
AND SMOKE
PRESENT TESTS
x
JX
s.
3NOVIS ONV
Cr ° 7
2 0
I
tr
•
A113
16
x2 °
rn
91
16
U
16
\
C.
m
I. 2
ED 67
\
1
-
2
AO 71
08
rn
e 42
08
004
1
0
4
0I9 04
10
cl
8
9
33NVISI0 3SIANNVdS
SNOWS0d 3d0) X31):JOA 61 'DU
HG. 19 VORTEX CORE POSITIONS
Yes
,
6
SPANWISE DISTANCE
0
5
L9 0 =
9
O
IN3S3t1d
("4/K
TI P
0( = 14
D6
29°
Z NOLLVIS
=
3-2101\IS 'OZ
'om
FIG. 20. SNIOKE PHOTOGRAPHS AT STATION 2
VLIACIE 0 0L NO
ON 700 DELTA
"a aNniasi
CMOHD i0011 SVC)
FIG. 21. ROTATION OF SECOXIARN VORTEX FLOW
AROUND MAIN VORTEX CORE AT-A = 29
011V
6Z = Y-IV :3110D X:41110A NIVIV (0111
,LOM •TE "01,4
MOld X:41.140,1 121V(1 \ODHS dO NOILV
•
0.55 ROOT CHORD
BEHIND T. E.
0.2 ROOT CHORD
BEHIND T. E.
'a
UNIHaU
0a
.1.0013.
0.1 ROOT CHORD
BEHIND T. E.
ammag
0
aHOHD sLOOH 1.
JO 1300W SH1INS ONV t1319NV1N JO 1-0137IS ZZ
FIG. 22 SKETCH OF MANGLER AND SMITHS MODEL OF
.ONIM V113❑
V inoqv
❑13I3 MO13
FLOW FIELD ABOUT A DELTA WING.
100
lieIn
-
W AN
FIG. 23. COMPARISON BETWEEN FLOW VISUALISATION, TOTAL
HEAD SURVEY 8 PRESSURE DISTRIBUTION AT STATION 2 (0.
oG
=
14 °MODEL 12 (A = 70°)
VORTEX
MAIN
VORTEX
MAIN
CORE
CORE
RY'
'SECONDA
SECONDARY'
CORE
CORE
S3
A2
--••••
3
enr.2.117fri
•
S
''"
•
FIG.24
24THE
THEVISCO
VISCOUS
REGIONS:
?Z ==00.7.7
NS: ?Z
US REGIO
FIG.
ERATED )
(BOUNDARY
LAYER
THICKNESSES
EXAGGERATED.)
EXAGG
ESSES
THICKN
LAYER
(BOUNDARY
o
0
r.
o
0
a
a
e
K.=
K.
= TAN 0
X
(RADIANS)
INCIDENCE (RADIANS)
co. == INCIDENCE
cA
ANGLE
LINE ANGLE
HMENT LINE
p==ATTAC
p
ATTACHMENT
,.,
8 SMITH
SMITH
MANGLER .5
0
. MANGLER
0.
II
MODEL II
EXPERIMENTAL MODEL
XX == EXPERIMENTAL
a
DX
0
0
D
•
ee
--
I
MODEL I
EXPERIMENTAL MODEL
== EXPERIMENTAL
APEX)
NEAR APEX)
MEASURED NEAR
(RESULTS MEASURED
(RESULTS
aa
II
•5
.5
1.0
1. 0
I5
I.5
FIG. 25 SUCTION SURFACE
POSITIONS.
LINEPOSITIONS.
ATTACHMENTLINE
SURFACEATTACHMENT
FIG. 25 SUCTION
--
•-• 1
.-.1
■
2.0
2.0
()1/9
TERTIARY SEPARATION
I0
0
s-+
_J
0
0
"••••-•
2
•-•
e =30° (MODEL I)
C
411%.
.
6=20° (MODEL
0 =30°
(
3Q0 (MODEL
MODEL I;
sry
II)
= 20° (MODEL
(
MODEL II)
B =20°
SECONDARY
SEPARATION
0
z
/ 1
SECONDARY
5ECONDA RY SEPARATION
5EPARA
1:!
5--1°‘4
05
K= TAN G
•
a
NEAR APEX)
0
0
Li)
Ui
(RESULTS MEAS
0
0
0 5
10
15
z
0
z
-71
z
FIG. 26 SUCTION SURFACE
SURFACE SECONDARY
T ERTIARY SEPARATION
S ECONDARY AND TERTIARY
SEPARATION LINE POSITIONS.
POSITIONS.