M I N I S T R Y OF A V I A T I O N

R. & M. No. 3424

AERONAUTICAL RESEARCH COUNC~L,~.,.., . . . : .

REPORTS AND MEMORANDA , ' , ~ , ~ . ! - . '2 j '

Low-Speed Wind-Tunnel Series of Sharp-Edged

Experiments on Delta Wings

By P. B. EARNSHAW and J. A. LAWFORD

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LONDON: HER MAJESTY'S STATIONERY OFFICE

1966

PRICE 18S, od. NET

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Low-Speed Wind-Tunnel Experiments on Series of Sharp-Edged Delta Wings

By P. B. EARNSHAW and J. A. LAWFORD

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COMMUNICATED BY THE DEPUTY CONTROLLER AIRCRAFT (RESEARCH AND DEVELOPMENT),

IV[INISTRY OF AVIATION

Reports and Memoranda No. 3424 *

March, z964

Summary. A series of six delta wings of varying angles of sweepback has been tested. A three-component strain-gauge

balance was used to investigate the forces and moments, and normal-force fluctuations for incidences between +_ 60 °. Positions of vortex breakdown on these wings were noted. Surface flow pattern and boundary-layer transition observations were made.

The three most highly swept wings (i.e. having sweepback angles of 65 ° , 70 ° and 76 ° ) appeared to have the most favourable characteristics of growth of normal-force fluctuations and had a smooth variation of forces and moments throughout the incidence range between positive and negative stalls.

The change from a vortex type of flow to one with complete flow reversal on the upper surface occurred at increased incidence with increase of sweepback angle. At moderate incidence c~ the main features of the flow pattern correspond to conical flow development, and correlate well with the single parameter c~/cot ~, where ~ is the sweepback angle of the leading edge.

Section

1. In t roduct ion

2. Apparatus and Tests

3. Discussion of Results

L I S T OF C O N T E N T S

3.1

3.2

3.3

3.4

3.5

3.6

Forces and moments

Normal- force fluctuations

Vortex breakdown

Surface flow patterns

Boundary-layer transition patterns

Some features of the surface flow and transition patterns

* Replaces R.A.E. Tech. Notes Nos. Aero 2780 and 2954--A.R.C. 23 111 and 26 032.

L I S T OF CONTENTS--continued Section

4. Conclusions

References

Il lustrations--Figs. 1 to 39

Detachable Abstract Cards

Figure

1.

2.

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4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

2O.

21.

22.

23.

L I S T OF I L L U S T R A T I O N S

Variatlon

Variation

Variation

Variation

Variation

Variation

Variation

General arrangement of model, balance, and supporting strut in the 4 ft × 3 ft Tunnel

General arrangement of strain-gauge balance for measurement of normal-force

fluctuations

of normal force with incidence

of lift with incidence

of pitching moment with incidence

of drag with lift

o f ( C L - CLo)/x/(S/C0) with (~x-%) for several gothic and delta wings

of low-frequency component of normal-force fluctuation with incidence

of low-frequency component of normal-force fluctuation with normal force

Low-frequency component of normal-force fluctuations on delta wings with 70 °

leading-edge sweepback

Chordwise position of vortex breakdown point in terms of the centre-line chord

Relation between incidence for vortex breakdown in plane of trailing edge and angle of

leading-edge sweepback

Typical flow over a delta wing at moderate incidence

55 ° delta wing, flat upper surface. Oil-flow pattern at a = 10 °

76 ° delta wing, convex upper surface. Oil-flow pattern at ~ = 20 °

Spanwise position of leading-edge vortex attachment line

Suggested secondary vortex system associated with 'whorl ' surface pattern

55 ° delta wmg,

76 ° delta wmg,

45 ° delta wmg,

60 ° delta wmg,

76 ° delta wing,

55 ° delta wing,

convex upper surface. Oil-flow pattern at ~ = 10 °

flat upper surface. Oil-flow pattern at ~ = 35 °

convex upper surface. Oil-flow pattern at ~ = 10 °

flat upper surface. Oil-flow pattern at o~ = 35 °

flat upper surface. Oil-flow pattern at ~ = 55 °

flat upper surface. Oil-flow pattern at c~ = 30 °

2

Figure

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

L I S T O F ILLUSTRATIONS--con t inued

45 ° delta wing, flat uppe r surface. Oil-flow pattern at ~ = 35 °

76 ° delta wing, flat upper surface. Oil-flow pat tern at c~ = 60 °

Variation of surface flow pattern type with incidence

55 ° delta wing, flat lower surface. Oil-flow pattern at ~ = 10 °

55 ° delta wing, flat lower surface. Oil-flow pattern at ~ = 40 °

Transi t ion patterns on 55 ° delta wing

Transi t ion patterns on 60 ° delta wing

Transi t ion patterns on 65 ° delta wing

Transi t ion patterns on 70 ° delta wing

Transi t ion patterns on 76 ° delta wing

65 ° delta wing, flat upper surface. Oil-flow and transition patterns at c~ = 20 °

70 ° delta wing, flat upper surface. Oil-flow and transition patterns at c~ = 25 °

70 ° delta wing, flat upper surface. Transi t ion pat tern at ~ = 10 °

Chordwise positions of vortex breakdown point and of secondary separation kink

55 ° delta wing, flat upper surface. Oil-flow pattern at ~ = 15 °

65 ° delta wing, flat upper surface. Oil-flow pattern on lower surface at ~ = 10 °

1. Introduction.

This report describes an investigation of some features of the separated flow around sharp-edged

delta wings of various leading-edge sweepback angles. I t was early established that the separated

flow f rom wings of zero or small sweepback takes the form of a closed 'bubble ' , whereas the highly

swept wing sheds tightly rolled vortices. Tests were therefore planned to investigate the behaviour

of the flow for a range of intermediate sweepback angles using a family of delta wings having

leading-edge sweepback angles f rom 45 ° to 76 °. A piano-convex section was used for ease of manu-

facture; it was thought that the effects of camber thus introduced would be comparat ively small.

Results of th ree-component force measurements , normal-force fluctuation measurements , and

surface flow visualisation are given, together with an assessment of the position of the breakdown

of the vortex core within the incidence range during which it occurs forward of the trailing edge.

2. Apparatus and Tests.

A family of six cambered delta wings, having sharp leading edges with different angles of

sweepback, were tested in the R.A.E. 4 ft x 3 ft Low Turbulence Wind Tunnel . Each wing had

a 6% thick piano-convex chordwise section, the convex surface being generated by straight lines,

drawn f rom the tips to the circular-arc centre-line section, giving geometrically similar chordwise

3

(92361) A 2

sections at all spanwise positions on all wings. The leading-edge sweepback angles were 76 °, 70 °,

65 °, 60 °, 55 '~ and 45 °. All the wings had a "planform area of 0. 347 sq.ft, with centre-line chords

ranging from 0-589 ft to 1.178 ft. The models were of polished metal, and boundary- layer

transition was not fixed.

1,ift, d r a g and p i tching-moment components were measured between incidences of + 60 ° on

two strain-gauge balances, one having a straight sting and the other having a sting cranked at 30 °

to the centre line of the balance. The former balance was used for wing incidences up to 30 ° and

the latter for incidences between 25 ° and 60 ° . The balances were clamped and pivoted between

two vertical, sliding struts (Fig. 1), which made it possible to position the models centrally in the

tunnel at each incidence. The technique used was to clamp the model at a given incidence and to

take balance readings with wind off before and after each reading with wind on. In order to explore

the magni tude of the sting interference, forces were measured between _+ 30 ° incidence by mount ing

tim models on the straight sting with the flat and convex surfaces uppermos t in turn, covering a

full incidence range in both cases.

Normal-force fluctuations were measured using the strain-gauge balance system shown in

Fig. 2. For this purpose the axial force balance of the three-component tests, turned through a

right angle, was used as a normal-force balance because of its greater stiffness. The fluctuating

signal f rom the balance was recorded on magnetic tape on an Ampex recorder, and the recordings

were replayed and analysed using a Muirhead Pametrada Wave Analyser. The tests were made on

the delta wing series at incidences f rom 0 to about 50 °, again both with the convex surface and the

fiat surface uppermost . Normal-force fluctuations at positive incidence only were measured also

on a 70" swept fiat-plate delta wing, s imply chamfered on one surface only to give sharp leading

edges (Fig. ll)), and on a rectangular wing of the same section as the piano-convex deltas; the

unchamfered and convex surfaces respectively were defined as the upper surface. These two wings

had the same planform area as those of the main series.

The position at which the tightly rolled leading-edge vortex breaks down to form a much more

diffuse vortex was found by using a fine tuft, at the end of a rod inserted through the tunnel wall.

At leading-edge sweep angles of 65 ° , 70 ° and 76 ° , the vortex core could be easily identified and the

breakdown point clearly established. At the lower sweepback angles, the vortex core was less steady

and the breakdown point could not be so clearly identified by this technique. At 45 ° sweepback,

it could not be found at all, and it seems likely that the point of breakdown was very close to the

apex of the wing. These vortex breakdown measurements were made using a wind speed of 80 ft/sec,

but a few tests on the 65 ° delta with the wind speed increased to 160 ft/sec showed no change in

breakdown point.

Surface flow tests were made using a support system similar to that used for the force measure-

ments, but omitt ing the balance. Patterns were obtained using a mixture of paraffin oil and

lampblack with a few drops of oleic acid as an anti-coagulant. The mixture was approximately

three parts of oil to one of lampblack by volume, but thicker or thinner mixtures were frequently

used, depending on the nature of the flow pattern; thicker mixtures were necessary for conditions

giving high surface velocities, and vice versa.

Photographs were taken of the patterns formed on each model at incidences f rom 0 to 60 ° both

with the convex and the flat surfaces uppermost . On the upper, or suction, surface observations

were made at intervals of 5 ° in incidence, but on the lower surface larger intervals were used at the

higher incidences.

In some cases an excessive amount of oil collected on a small area of the wing, giving a very dense

and ill-defined pattern. This was cleaned off locally, a thin coat of the mixture was applied, and the

tunnel was run again. The 'patch' effect in Figs. 15, 19, 21, 22, 23, 25 and 35 is due to this.

Tests were also made to determine the state of the boundary layer on the models over the same

incidence range using the china-clay technique ~, The models were sprayed first with blacl~ cellulose

and then with china clay in a solution of nitro-cellulose ('dope'), so that when dry the surface

appeared white, but when wetted with oil the china clay became transparent and the black

underlayer showed through. Diesel oil of a suitable distillation fraction was used to moisten the

surface, and Plasticene protuberances were used on the surface as required to help in the interpretation of the resulting patterns.

The wind speeds and corresponding Reynolds numbers (based on aerodynamic mean chord ~) for the tests were as follows:

Three-component balance tests

Normal-force fluctuation tests

Vortex breakdown tests

Surface flow visualisation

100 fl/sec (0.25 x 106 to 0-50 x 106 )

80 ft/sec (0.20 x 106 to 0.40 × 106 )

80 ft/sec (0.20 x 106 to 0.40 x 106)

180 ft/sec (0.45 x 106 to 0.90 x 106 )

3. Discussion of Results.

3.1. Forces and Moments.

The normal force, lift, drag and pitching-moment characteristics of the six cambered delta wings

are plotted in Figs. 3, 4, 5, 6 where positive incidences are defined as those incidences which have

the plane surface on the pressure side. Experimental points for the two methods of mounting the

models are not distinguished but are plotted generally in pairs at a particular incidence in these

figures and illustrate the large sting interference effects which must exist, particularly in the case

of pitching moments. However, irregularities on the curves could be reproduced by both methods,

suggesting that the slopes of the curves can be drawn to a better accuracy than the scatter of the points implies.

Figs. 3, 4 show that the highest three sweepbacks provide smooth normal-force and lift curves between positive and negative stalls, whereas those for the lowest three sweepbacks are irregular

at positive incidences, the 60 ° wing having a smooth curve up to 14 ° incidence where a 'kink'

begins. All the wings have zero lift at the same incidence and, after the stall, all the families of curves shown in Figs. 3, 4. 5, 6 appear to approach common curves.

The normal-force curve for the 76 ° wing has a curious 'bucket' at the positive incidence stall, which was repeated at a wind speed of 140 ft/sec. In order to see whether this might indicate hysteresis, the method of test was altered and the incidence change made while the tunnel was running. The incidence was increased slowly to a point above and reduced to a point below the stall, producing the broken-line curve, shown in Fig. 3, for both increasing and decreasing incidence. The accuracy of these results was much reduced owing to zero wander during the run but a sufficiently large number of readings were taken to be sure that the stall did develop as shown. The possibility of the two distinct curves being produced by hysteresis with respect to change of incidence is therefore excluded. As no changes were discovered within the range of speed permitted by the equipment, this problem remains unresolved.

An attempt was made to fit the low incidence points on the Cz, - c~ curves to a common curve, as demonstrated by Peckham. It was found possible with the 76 °, 70 ° and 65 ° wings to determine,

for each, a point about which the curve was antisymmetrical over a range of approximately _+ 20 °,

presumably the point of zero leading-edge vortex strength. Using this point as the new origin, ( C I . - Ci.o) / v (C o /S ) was calculated for several incidences on each wing and plotted in Fig. 7 along with Peckham's three symmetrical thick wings (12% thickness/chord ratio) and two symmetrical

thin wings (1",, thickness/chord ratio). It was found that an insufficient negative incidence range

had l;een covered, on Peckham's asymmetrical thin wings, to apply the technique used for the

present series; however, a rough value was taken for the centre of symmetry for one of these wings

and the points plotted in the figure. It can be seen that a mean curve, drawn through the points

from the thin wings, would be below Peckham's curve which, presumably, is affected by the finite

leading-edge vortex strength existing at zero incidence. The thick wing B of Ref. 1 lies well below

the other points. This wing, however, has a much greater volume, relative to the plan-form area,

than the other thick wings which lie quite close to the revised curve although consistently below it.

The heavily cambered thick wings of the present series lie on a curve which is above the revised

curve at low incidence and below it at high incidence.

3.2. Normal-Force Fluctuations.

The results of the normal-force fluctuation measurements are presented in terms of the following

quantities: ~ _ o vb '~ _ "~_~{D c

n :: Frequency parameter = f~v ' r ( "'

('x ~ The root-mean-square intensity of fluctuation of the normal-force coefficient C x.

F(n) - The spectrum fimction, such that F(n)dn is the contribution to (Cx) z of frequencies from

n t o Jz + dn,

i.e.

( Cx) z = F(n)dn. 0

The results are relevant to the problem of buffeting, which usually takes the form of excitation

of a particular mode of structural vibration corresponding to a discrete frequency. The mode can

bc excited by load fluctuations at or close to this frequency, so that the structure has a sharply

tuned resonance curve, or a narrow acceptance band. Thus, following the argument of Ref. 2, i f f is

the structural frequency and Af the acceptance bandwidth in such a case, Afl f being small, the

relevant root-mean-square intensity of the excitation ~/(ACx ~) is given approximately by

An AQ~ 2 = nF(n) - ,

n

i.e. An ~/ (ACx ~) = ~/{nF(n)} Af , since ~- = ~ .

The ratio Af / f is determined by the aircraft structural characteristics and is independent of wind speed. Hence ~/(,~Cx ~) is directly proportional to ~/{nF(n)}, which is therefore a suitable quantity fl)r the presentation of the results. The quantity \/~nF(n)] has been obtained at a fixed value of tile

frequency parameter, n.

6

In these tests the aerodynamic excitation is inferred from the response of the complete model, so it is obviously necessary to confine all measurements to frequencies well below the lowest natural frequency of the rig. Although care was taken to make this natural frequency as high as possible, and a relatively low tunnel speed of 80 ft/sec was used, the highest value of n at which reliable measurements could be made was 0' 05. This is lower than the value of 0.2 which has been used in measurements of pressure fluctuations 2, and is probably rather low for the representation of likely

aircraft critical conditions. However, it is of the correct order of magnitude and since the excitation spectrum has been found to be very flat in the low-frequency range, the value of v/{nF(n)} at n = 0.05 would be expected to give a good indication of the level of excitation at pr0.bable buffeting

frequencies. All the measurements of normal-force .fluctuation in this report are of th~is ' low-frequency com-

ponent ' , and the term 'normal-force fluctuation' is to be taken as referrin~ to this component only:

The results of the normal-force fluctuation measurements are plotted agaiflst'-irmffden-e~-ifi Fig. 8,

and against normal-force coefficient in Fig. 9, where positive incidences and coefficients are defined

with the curved surface considered as the upper surface. In Fig. 10 the normal-force fluctuations

on the 70 ° swept delta wing of this series are compared with those on the 70 ° swept flat-plate delta

wing, all incidences in this case being treated as positive, with the appropriate definition of upper

and lower surfaces. At low incidence the normal-force fluctuations are small and almost constant. This is followed

by an increase in the level of fluctuation to a value between ten and twenty times that at low incidence. This rise suggests a change in the nature of the aerodynamic excitation, and tends to

imply the onset of a form of unsteadiness which could not be tolerated in practice. There is a

marked change in the form of the curves at a sweepback angle of about 65 °, the lower sweepbacks giving a sharp rise in normal-force fluctuation when the normal force is approximately half its maximum value, i.e. at comparatively low incidence, whereas the more highly swept wings show

a more gradual increase in fluctuations until the normal force approaches its maximum. It appears therefore that there is tess likely to be a buffet problem with wings of high leading-edge sweepback. The sharp kinks in the curves for the 55 ° and 60 ° swept wings at incidences of about 12 ° and 15 ° respectively coincide with kinks in the curves of lift coefficient against incidence (Fig. 4). There is a similar but smaller kink in the curve for the 65 ° swept wing, in this case without a noticeable

kink in the lift curve. The normal-force fluctuation measured at zero lift is very small, being of the same order of

magnitude as that which would be caused by the component at this frequency of the known tunnel

incidence fluctuation. The normal-force fluctuation measurements on the 70 ° swept piano-convex and flat-plate delta

wings (Fig. 10) show that, in this case, the primary factor is the shape of the upper surface,

convexity or flatness of the lower surface having little effect.

I

t9 ( I .4 7

3.3. Vortex Breakdown. The chordwise position of the vortex breakdown point, expressed in terms of the centre-line

chord (Figs. 11 and 12), moves forward with increase of incidence and with decrease of sweepback

angle as expected. The following table lists the approximate position of the breakdown point

when the normal-force fluctuations reach a level of [\/{nF(n)]],_ 0.0.~ = 0. 0025, that is, close to the

start of the rapid rise in normal-force fluctuation.

While there is some variation from wing to wing, it is clear that the trend is for the rapid rise of

normal-force fluctuation to occur when the vortex breakdown is close to the trailing-edge. When

vortex breakdown is near the mid-point of the centre-line chord, normal-force fluctuations are

high on all the wings.

Sweepback

45 ° 12 55 ° 13 60 ° 15 65 ° 29 70 ° 6 76 ° 35

Positive incidence

Breakdown position

0.85 0.7 0.95 1.0

1.1 approx.

13 18 21 26~- 34 37

Negative incidence

Breakdown position

0.85 0.8

1.1 approx. 1-1 approx.

0.85

The vortex breakdown point is farther aft at positive incidence than at the corresponding

negative incidence (except in the region of 20 ° incidence at 65 ° sweepback). Since the lift coefficient

is numerically greater at positive incidence than at the equivalent negative incidence, this applies

to a greater extent at corresponding lift rather than incidence.

3.4. Surface-Flow Patterns.

The nature of the flow over sharp-edged delta wings at moderate incidence is now well known.

Vortex sheets are shed off the leading edges, and blow back over the upper surface, rolling up to

form a pair of stable vortices. This causes a strong outflow on the upper surface below the vortices,

which separates from the surface before reaching the leading edge, at a secondary separation line.

Between this line and the leading edge there is at least one smaller and weaker vortex, as sketched

in Fig. 13. There can be more than one vortex in this secondary region, but the surface shear is

very small and the associated surface flow pattern cannot easily be defined experimentally.

Patterns of this type were obtained on the suction surface of all the delta planforms tested.

Examples on the 55 ° and 76 ° swept wings are shown in Figs. 14 and 15. The positions of the main

w~rtex attachment line and of the secondary separation line varied with incidence and with planform.

But, for moderate incidences with the flat surface uppermost, the positions of both lines were found

to correlate well with the single parameter ~/cot q~, where q~ is the angle of sweepback of the leading

edge and ,~ is incidence relative to the no-lift angle, which, in all cases, corresponded to a geometric

incidence of the plane surface of 2 °. This supports earlier observations by Marsden, Simpson and

Rainbird 5. It implies, as does the straightness of the observed attachment and secondary separation

lines, that the flow is roughly conical in these conditions. The ratio of flat-upper-surface attachment

position to local semispan for all the wings is plotted against ~/cotq~ in Fig. 16. Except for the

45 ° swept delta wing, on which the flow was probably never approximately conical, and above

which a tightly rolled vortex may not be formed 1, the observations are fairly well represented by

a single curve. The theoretical curve derived by Mangler and Smith ~ is also shown in Fig. 16; agreement with measured values is poor.

On all ptanforms there formed at some incidences a 'whorl' near the outboard tips (see Fig. 20)

where the secondary separation line bent outwards and the main vortex outflow passed round it

and forwards close to the leading edge. The flow which it is suggested gives rise to this surface

flow pattern is sketched in Fig. 17, and further examples are shown in Figs. 18 and 19. The whorl

pattern appeared at quite low incidence on all the wings. Except in the case of the 45 ° swept leading

edge, increasing incidence at first led to its disappearance, but it subsequently reappeared and was

always a feature of the transition from the 'vortex' type of surface flow pattern to the complete flow reversal associated with the bluff-body wake which occurred at very high incidence. On the

45 ° swept wing with curved surface uppermost the whorl pattern was present at all incidences

from 5 ° up to the stall, and was the dominant feature of the pattern from 10 ° incidence upwards (Fig. 20). Following its second appearance on the other wings, increase of incidence caused the whorl to move forward near the leading edge, the region of forward curvature of the main vortex

outflow becoming larger and a forward flow developing over the trailing edge (Figs. 21 and 22). This flow is obviously very complex. Fig. 23 shows a surface pattern on the 55 ° swept wing at

30 ° incidence, with the fiat surface uppermost, on which there is an outflow from the centre line

and a forward flow from the trailing edge, with apparently a separation line where the two flows

meet. The surface shear near the apex is very weak. At still higher incidence the flow was

predominantly forward from the trailing edge (Figs. 24 and 25), the apex flow remaining weak.

Some patterns in this condition showed what appeared to be a secondary separation near the apex

but, at high incidence with a weak forward flow, gravity effects might be significant and this

apparent separation could have been spurious.

Fig. 26 shows how the type of surface flow pattern varied with incidence on each wing. All the

wings behaved in a similar way with increase of incidence, change of pattern from one form to

another taking place at higher incidence for higher sweepback angle. Incidences for maximum

lift and maximum normal force are approximately equal on these wings (see Figs. 3 and 4) arid this

incidence, and that at which vortex breakdown occurred at the mid-chord point, are included on Fig. 26. At the lower sweepback angles, maximum lift occurred just before forward flow developed

near the trailing edge, but at the higher sweepback angles leading-edge vortex flow continued

over the whole surface beyond the maximum lift point, for approximately 12 ° of incidence in the

case of the 76 ° swept wing. Vortex breakdown took place at the mid-chord position at an incidence approximately 10 ° to 15 ° lower than the lowest incidence for flow reversal on all the wings.

The surface flow on the lower surface was of the type shown in Figs. 27 and 28 at all incidences on all the wings, an attachment line moving inwards from near the leading edge with increase of

incidence with separation at the leading and trailing edges.

3.5. Boundary-Layer Transition Patterns.

Diagrams showing the distribution of laminar and turbulent boundary layers as shown by the china-clay technique are given in Figs. 29 to 33, and a specimen transition pattern is shown in Fig. 34 for the 70 ° swept wing at 10 ° incidence with the flat surface uppermost. The wedge of

turbulent flow behind the Plasticene protuberance inboard of the secondary separation line can be clearly seen, while there was no wedge from the one near the leading edge where the surface

shear was evidently very weak. In this case there was a small region of turbulent flow near the centre at the trailing edge.

9

At zero incidence, the boundary layer on the flat surface was predominantly turbulent for all

the wings tested, but there was a small laminar region near the apex (except in the case of 60 °

sweepback), and a region of laminar flow near the tips (except on the 76 ° swept wing). Fig. 26 indicates the probable cause of this pattern. At zero incidence, vortex separation occurred only

over part of the span near the apex, and was followed by attached flow near the tips. This was

evidently due to the inherent type of camber which caused some leading-edge separation at all

incidences and precluded the smooth development of the leading-edge vortices at very low

incidence. It seems clear, and has subsequently been confirmed in other experiments, that if the

wings had been uncambered, or the camber designed to the leading-edge restrictions proposed by

Maskell and Weber 7, the boundary layer would have been laminar everywhere when attachment

occurred at the leading edge. In the present case, transition was caused by the very weak part-span

vortices. Increase of incidence, with the flat surface uppermost, and the consequent strengthening

of the leading-edge vortices along the entire span, established regions of laminar flow under the

vortices and inboard of the secondary separation lines. At the lower sweepback angles there

remained, however, a central region of turbulent flow which spread out over the entire span near the trailing edge. With further increase of incidence the laminar regions extended right back to the trailing edge and, except on the wings with 55 ° and 60 ° sweepback, the central turbulent region was reduced in size. Before the incidence for reversal of the surface flow was reached, the boundary layer again became turbulent everywhere, and remained so up to the highest incidence

of the experiments. On the curved surface, the flow was attached at zero incidence for all the wings, and the

boundary layer was mainly laminar apart frmn local turbulence near the sting. As incidence was increased with the convex surface uppermost, the flow first became turbulent from the tips, behind

that part of the leading edge where the vortex first developed (Fig. 26). At 10 ° incidence, the bmmdary layer was entirely turbulent on all the wings and for 55 ° and 60 ° leading-edge sweepback

it remained so as incidence was further increased, apart from local laminar regions near the apex.

But with the higher sweepback angles laminar flow again developed under the vortices, in some

cases with transition to turbulence near the trailing edge. At still higher incidence the flow again

became entirely turbulent. The boundary layer on the lower surface, both flat and convex, was laminar at all incidences

from 5 ° upwards. Close comparison of corresponding transition and oil-flow patterns on the upper surface shows

a dark region on the transition pattern just inboard of the secondary separation line, indicating

small, laminar surface shear and, where it extends up to the separation line, laminar separation.

But in some cases a distinctly whiter region was observed just outboard of this dark line, suggesting

transition followed by turbulent separation. Two such patterns, and the corresponding oil-flow patterns, are given in Figs. 34 and 35. In some cases this transition before secondary separalion was accompanied by striations in the laminar region inboard of the separation line (Fig. 34) suggesting the cause of transition to be instability of the kind discussed theoretically by Owen and Randall 8, and Stuart 9 and studied experimentally by among others, Gray 1° and Gregory and Walker 9.

3.6. Some Features of the Surface Flow and Transitional Patterns.

A feature of the oil-flow pattern on all the wings except the 45 ° swept wing was the appearance

of a kink in the secondary separation line, so that the separation was closer to the leading edge

10

(in terms of local span) at the rear of the wing. The kink first appeared near the trailing edge as incidence was increased, and steadily moved towards the apex. This trend is similar to that of the breakdown position of the vortex core; the positions of vortex breakdown and of kinking in the secondary separation line are compared in Fig. 37. For moderate leading-edge sweepback angles, the kink and the vortex breakdown were at approximately the same chordwise position, the breakdown point being in general a little farther aft. At higher sweepback angles the kink occurred at incidences at which the vortex breakdown was well downstream, and under such conditions appeared to be associated with the transition from laminar to turbulent separation (Figs. 34, 35). It seems possible fhat a kink in the secondary separation line may be caused by either of these

distinct features of the flow. Kinks due to these two causes appear to differ slightly in form, that due to turbulent separation (Fig. 35) being an outward displacement of the separation line, while

that due to vortex breakdown is rather a decrease of sweepback of the separation line (Fig. 38). An unexpected feature of the surface oil-flow patterns was the appearance of an apparent separa-

tion line near the trailing edge on the convex lower surface at small incidences with the flat surface uppermost. This appeared on all the wings at incidences from 0 ° to 10 °, as illustrated in Fig. 39 for the 65 ° swept wing at 10 ° incidence, and is not fully understood. Although it may well have been a genuine laminar separation, it also seems possible that the oil was moving more under the influence of the pressure gradients than of the obviously weak laminar shear, and that the pattern is therefore spurious. When transition was forced by Plasticene protuberances farther forward this feature of the pattern was eliminated.

4. Conclusions.

The flow around the three most highly swept wings of this series leads to a smooth variation of forces and moments with incidence, between the positive and negative stalls. For the lower sweep angles, however, this variation is irregular at positive incidence when the curved surface is

uppermost. The low-frequency normal-force fluctuations rise sharply at comparatively low incidence

(between 10 ° and 20 °) for leading-edge sweepback angles of less than 65 °. With greater sweepback, these fluctuations rise more slowly with increase of incidence; if the leading-edge sweepback is between 65 ° and 76 °, there is no substantial rise until maximum normal force is approached.

At both constant incidence and constant lift, the vortex breakdown point is farther forward when the flat surface is uppermost than when the curved surface is uppermost. In most cases, the low- frequency normal-force fluctuations begin to increase rapidly with incidence when the vortex

breakdown point moves forward of the trailing-edge. The surface flow pattern on the upper surface changes with increase of incidence from that

associated with vortex flow to one with complete flow reversal, the change occurring at higher incidence with increase of sweepback angle.

At moderate incidences, the main features of the flow pattern indicate roughly conical flow development and correlate well with the single parameter c~lcot6, where q~ is theleading-edge sweepback angle.

A sufficiently strong primary vortex tends to favour the maintenance of laminar flow in the boundary layer from some way inboard of its associated attachment line to the secondary separation line. At the rather low Reynolds numbers of the present experiments, the region of laminar flow

11 P

under such a vortex tends to increase in extent with increase of incidence and therefore of vortex strength. But very small vortices, probably partially or wholly immersed in the boundary layer, behave as boundary-layer trips, effectively promoting transition at the leading edge; at high incidence, though before flow reversal occurs, the boundary layer always becomes fully turbulent.

Evidence was found of transition from laminar to turbulent secondary separation due to boundary-layer instability of the Owen-Stuart type.

12

No. Author(s)

1 P . H . Peckham . . . .

2 T . B . Owen . . . . . .

3 E.J . Richards and F. H. Burstall

4 E .C. Maskell . . . . . .

D. J. Marsden, R. W. Simpson and W. J. Rainbird

6 K. W. Mangler and J. H. B. Smith

7 E.C. Maskell and J. Weber ..

8 P .R . Owen amd P. G. Randall

9 Gregory, Stuart and Walker ..

10 W.E. Gray . . . . . .

LIST OF R E F E R E N C E S

Title, etc.

Low-speed wind-tunnel tests on a series of uncambered slender pointed wings with sharp edges.

A.R.C.R. & M. 3186. December, 1958.

Techniques of pressure-fluctuation measurements employed in the R.A.E. low-speed wind-tunnels.

AGARD Report 172. March, 1958.

The 'China clay' method of indicating transition. A.R.C.R. & M. 2126. August, 1945.

Flo,x separation in three dimensions.

R.A.E. Report Aero. 2565. A.R.C. 18 063. November, 1955.

An investigation into the flow over delta wings at low speeds with leading-edge separation.

C.o.A. Report 114. A.R.C. 20 409. September, 1958.

A theory of slender delta wings with leading-edge separation. Proc. Roy. Soc. A, Vol. 251, p. 200. May, 1959.

On the aerodynamic design of slender wings. J.R.Ae.S., Vol. 63, No. 588, pp. 709 to 721. December, 1959.

Boundary layer transition on a sweptback wing. A.R.C. 15 022. May, 1952.

Boundary layer effects in aerodynamics. N.P.L. Symposium. H.M.S.O. 1955. Part 3. On the stability of three-dimensional boundary layers, with

application to the flow due to a rotating disk.

The nature of the boundary layer flow at the nose of a swept wing.

A.R.C. 15 021. June, 1952.

13

FIG. 1. General arrangement of model, balance, and supporting strut in the 4 ft x 3 ft Tunnel.

FIG. 2.

~ $'IRAIN GAUG£~

~]~ . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . .

i , i J ~ . - ~ "!.i i . l J ~ . ~ - - :

_ lr, ............................... General arrangement of strain-gauge balance for measurement of

normal-force fluctuations.

14

f ,

X 76 ° DELTA Q 70 ° DELTA + {;5 ° DELTA & 600 DELTA

SS ° DELTA 4 5 ° DELTA

1"6

~.4

/

1 / i , ¢ - / ~--

-60 -50 -40 -30 -ZO -iO

1 I O ZO 3 0 4 0

0¢ DEGREES

J i i

i

I , i i I , !

I i

I

FIG. 3. Variation of normal force with incidence.

15

50 60

t X 7G ° DELTA __ _ _ e 70 Q DELTA + 65' DELTA • % 60" DELTA

I ~ 55 ° DELTA 45 ° DELTA

0'8

-60 -50 -40 -30 -20 -I0 ,~" IO I0 20 30 40 50 60

: -0'8 ~ - ~

---I 'O

- 2- . . . . . . i.Z

FIG. 4. Variation of lift with incidence.

I I

16

'---3

i I I ~-° X 7G ° DELTA

70" DELTA 65" DELTA ~ _ _ 60* DELTA - - _ 0,2 55" DELTA i 45" DELTA C~

O . I - -

- 6 0 -50 -40 -30 -~,0 -10 0

x

0 - 3

0 ' 2

C ~ x

x

Z 0 3 0 4 0 5 0 6 0

. . . . .

FIG. 5. Variation of pitching m o m e n t wi th incidence.

CO

- 1 ' 2 - I 0 - O - 8

1 X 7 6 ° OE LT~, ® 9 0 ° DELT~.

+ 6 5 : D E L T A

&. 6 0 ° DELT/~

'~ 5 5 ° b F. L T A

'~ 4 5 ° DELT.~

I cc

1"4

1"2

I 'O

0 " 8

0 - 4

I i !

I J L [ [

I

- 0 - 6 - 0 . 4 - 0 " 2 0 O 'Z 0 , 4 -

! i

0 - ~ 0 . 8 1 . 0 I - 2 io4 I ' ~

C L

FIG. 6. Variation of drag with lift.

12"--

I'0

O-B

C L - CL o

'W,:':, ." ,, ~I~- W o,6 --'o /

r %

0 ' 4

02'

FIG. 7.

112 s ' I / AL/'P/~' .../.'.'I

I

! i

/ .4 z J

,S, ! i

/ /,el ~, / / i

/ .v , " I :( I

I

t Io [=- %] 15 ao

Vm-iation of (C L - CLo)/~'S//C o with (c~-'%) for several gothic and delta'wings.

-/6 ° DELTA 70 ° D~'LTA ~- pRiF~IFN~ ~ERtES 65o DIELTA ) j WING P, WING B "WING C REE3

WING I J WING 2A WING ~,A

p£EXHAM CURVE REVISED CURVE

/- ,

q

76 °

" ~ . . j

, ~ 70a

¢ 1 ,, i , 6 5 "

\ 60 °

0 -Or!

O'OIC

' . \

,j°

\ 0 . 0 0 5

OI

. ,J!i

,o. ,, ,/li /

- 6 0 - 4 0 - 2 0 , . j 0 20 ~ 0 i

FIG. 8. Variation of low-frequency component of normal-force fluctuation with incidence.

6 0

19 ( 9 2 3 6 1 ) C

hJ

- - 0"02 l

f

t (~ 015 -16 °

,,'~. / ~ o o / ' - / / ~° ' \. / / ' / /~ °

",~ ",, ~! '~,~ '. !~ ", " , /%'x. ! "": ;

/" , , "-L " ~ " ',

\ ~___ -~. - . . . . . ~ .,... -. ~ . ~ . . ~ : ~ ~ _ ~ = ~

- - I - 5

I I

! i

' ~ < . / \ , 70° ~ - L ,"-'1 \ , ,

--:.',+--L, \

i . i - i I I ,

- - h - ... . . . . . ! . . ~ F j . . . ' " / " >

i~ ........ >J../ / -- I'0

FIG. 9.

1 o - o-5 o o,5 I-o 1.5

C.

Variation of low-frequency component of normal-force fluctuation with normal force.

20

b o

0"O2C

c<:Lo. O.O~ = .

O-0E

o LANO*CO!V

FL "I-4::'LA g W NG..., ..~ ~ /

I ,~: 0 I0 ~O 3 0 40

I B

~o 50 60

7 0 ° SWEPT ELAT--PLATE DELTA WING ~'UNCHAMFERED ¢~URFAC£ UPPERM05]" )

FIG. 10. Low-frequency component of normal-force fluctuations on delta wings with 70 ° leading-edge

sweepback.

io]

~XCo. B'

O o

, I

i " I

I O 20 30 ~ o 40 50

.55 a 5W E EP BACK

( ° i - '

°'I- | 60 ~ SWEEPBACk-

c / / l , ' ~ J ~ ,

o~-- i- , - ~ v ~ - --

0 I0 20 30 ¢:~ 4 0 50

5 ° SWE E PBACY,

;oj %1 05 ~

o ! 7 2 2 O IO 20 30 d. ° ,40 50

70 ~ e~W EE pl~=p.CK

°f r i r ~ U 7

o i I , O I0 ?0 ~0 c : ° 4 0 5(9

- - ) ~ - - C O N V E X UPPER 5[II:IFAC~ <'OR POSITIVE INCIO[NCE) - - - -~ - - - -FLAT UPPER SURFACE ( . NEGATIVE " )

Fro. 11. Chordwise position of vortex breakdown point in terms of the centre-line

chord.

FO FO

TE 4°I" i i x

UPPtR SU,R (AC E ~/, 3 so CONVqK l / . -. / ' l

~ FLAT UPPER SURFACE

2C /-/

IQ

5 5 6 0 6 5 q O 3 5 8 0 ¢o

O~Tk

¢

= INCIDENCE FOR VORTFJ ~, BREAKDOWN IN THE PLANE OF THE TRAILING EDGE

: LEADING-EDGE SWEEPBACK ANGLE

FIC. 12. Relat ion between incidence for vortex b reakdown in plane of t ra i l ing edge,

and angle of leading-edge sweepback.

((1) V O R T E X S H E E T S F O R M E D A B O V E THE WING

.'/ ~ , [ , . j / '~S~',,\

p;'~ , , i~, x

Jh) i l ,., / , ~ ,, ,~ '~,\,

i / , / i , f I "" ' \ \ \ I ," " . p , ' i T ' IX "" ~I '%.\ / / ' I .... -" I " - . t ~ ,,~.

4 / , ' u ..,. i ",,. " ',"\ . / . . . ~ ~ " _ ~ . J _ _ _ ~ J _ . . 7 _ ~ X _ x . . . . \ ~ . , , \

AT T &G'H I'YtEN T SEC ON C)NP~Y LINE. SEPA~ATION

LINE

(b ) S U R F A C E F L o w P A T T E R N

FIG. 13. T y p i c a l flow over a delta wing at mode ra t e incidence.

)

FIG. 14. 55 ° de l ta wing, flat u p p e r surface. Oi l - f low p a t t e r n at ~ = 10 °.

23

(92361) D

IX,

FIG. 15. 76 ° delta wing, convex upper surface. Oi l - f low pat tern at ~ = 20 °.

24

__%

-O'P- O O 2.

\

x x

\ \,~ ~ .THE OP,¥

" - . / " (b4~,,NGLF,.~, AND SMITh'

\ o d" -.."

n

4 5 ° X ',~ =

5 5 °

-~ 60 ~

~5 °

y 7 0 °

0 7G °

~ MEAN LINE EIKCLUDIN I,

O'G 0 ' 8 10 12.

o¢ ' Co~, ~p

y~ = DISTANCE. FP-.OM C~.NTP-.F-. L iNE TO A T T A G H h ~ - N T

b = L O C A L fipP,.N E:9~ z = INC.IOENC~F. (T,I~KEN F'P,.OIM Z E R O L IFT A N G L E ; IN F~,e',DIANSy

= LF-F'.DING-F_DGE 5 W ~ . P S A C K ANGLE.

FIG. 16. Spanwise position of leading-edge vortex attachment line.

FIe. 17. Suggested secondary vortex system associated with 'whorl' surface

pattern.

25

( 9 2 3 6 1 ) D 2

FIG. 18. 55 ° del ta wing, convex u p p e r surface. Oi l - f low p a t t e r n at ~ = 10 °.

26

FIG. 19. 76 ° delta wing, flat uppe r surface. Oi l - f low pat tern at ~ = 35 °.

27

ATTACHMENT LINE

Fie.. 20. 45 ° de l ta wing, convex u p p e r surface. Oi l - f low p a t t e r n at ~ = 10 °.

28

/ l\\ CENTRE-'INE ~/ ~ATTACHMENT

SECONDARY / ~ ~ ~ $ E P A R A T I O N LINE

TRAILING-EDGE ATTACHMENT

FIG. 21. 60 ° de l ta wing, flat u p p e r surface. Oi l - f low p a t t e r n at o~ = 35 °.

29

CENTR E-L INE

SEPARATION

MALL 'WHORI '

/ TRAI LING -EDGE

ATTACHMENT

FIG. 22. 76 ° delta w ing , flat u p p e r surface. O i l - f l o w pattern at c~ = 55 °.

30

NO IDENTIF IABLE PATTERN

RY WEAK CWHORL 'J

SEPARATION

FIG. 23. 55 ° delta wing , flat upper surface. Oi l - f low pattern at ~ = 30 °.

31

Fic . 24. 45 ° de l ta wing, flat u p p e r surface. Oi l - f low p a t t e r n at c~ = 35 °.

32

Fro. 25. 76 ° del ta wing, flat u p p e r surface. Oi l - f low p a t t e r n at o~ = 60 °.

33

~TRANGITIONAL 1 REVE~,SA~, NEAP- T. E ~ / / / / J LEADING-EDGE VORTEX. I ~ VORTEX. NEAR APEX,

COMPLETE FLOW RF..VER, GAL I~1 PARTIA I- L,E. VORTF..~ AT FORWARD E.ND ONL.•.

I-'7 ATTACHED FL.OW WI'[14 NO VOR.TE'/,. ~ PARTIAL L.E VORTEX NEAR THE WING TtP ONLY'. X INCIDENCE. FOR MAXIMUM CL ANOC N

O INCIDENCE FOR VORTEX. BREAKDOWN AT 0 5C O 10 ?,.O 30 4-0 ~ ~ n

Fie, 26. Variation of surface flow pattern type with incidence.

34

FiG. 27. 55 ° delta wing, flat lower surface. Oil-flow pat te rn at o~ = 10 °.

35

Fic . 28. 55 ° de l ta wing, flat lower surface. Oi l - f low p a t t e r n at c~ = 40 °.

36

A ~ = O° LI

?_0 °

A 5 •

~ UPPER SURFAC~~,

io °

A Z.S ° U 35 °

A 15 ° LI

UNSHADED AREAS- LAMtNAR 5OUNDA~Y LAYER. SHADED A~EAS-TU~E, ULENT OUNDA~Y LAYEr,

ok=O ° s ° U

&O° U

Fm. 29.

C O N V E X U P P E R S U R F A C E

J 15"

9 0 ° J

4 . 0 °

Transit ion patterns on 55 ° delta wing.

J ~Z.= 0 ° S ° 10 °

FLAT UPPER SURFACE

15 ° ° ° U as°,~o°U

CONVEX UPPER SURFACE

AAA ~ : o ° U s" U Io°LI ,s ° U

FIc. 30.

g_O ° 5 0 °

Transit ion patterns on 60 ° delta wing.

37

°('= °° U

FLAT UPPER SURFACE

30 °

IS °

UNSHADED .... AREAS LAMINAR BOUNDARY LAYER. kSHADED AREAS

C AYEB,.

q-O" CONVEX UPPER SURFACE

Transi t ion patterns on 65 ° delta wing. Fro. 31.

~ j . ~ ~ ~ ~ F L A T UPPER SURFACE ;o%%

u R.BULENT BOUNDARy

YEB" A

=5 = LI

~'o° LI A CONVEX UPPER ,~ A A

~o ° ~-o°U '~°U ~-s°ll

FIG. 32. Trans i t ion patterns on 70 ° delta wing.

38

J , :9.=0 ° 5 °

t 10 °

FLAT UPPER SURFACE

~o°11 i

50 ° 4C 45 °

UNSHADED A ~ E A B - L A M I N A R BOUNDARy L A Y E ~ SHADED AREAS - - T U R B U L E N T BOUNDA~Y LAYER

0 °

1 S °

1 CONVEX UPPER SURFACE

A N D 3 0 °

Transition patterns on 76 ° delta wing. FIC. 33.

39 ( 9 2 3 6 1 ) E

FIG. 34a. 65 ° de l ta wing, flat u p p e r surface. Oi l - f low p a t t e r n at ~ = 20 °.

40

FIG. 34b. 65 ° delta wing, flat upper surface. Trans i t ion pat tern at c~ = 20 °.

41

(92361) F

Fro. 35a. 70 ° delta wing, flat upper surface. Oil-f low pat tern at c~ = 25 °.

42

FIG. 35b. 70 ° delta wing, flat uppe r surface. T rans i t ion pat tern at ~ = 25 °.

43

FIG. 36. 70 ° del ta wing, flat u p p e r surface. T r a n s i t i o n p a t t e r n at c~ = 10 °.

4 4

SECONDARY RINK VORTEX BREAKDOWN - - ~ FLAT UPPEP~ SURF~.CF- / . . . . . ~. . . . . . CONVEX. UPPER SUP~FACE . . . . . . ~ . . . . . .

I'O

0 0

I ' 0

0 '5

0 0

I ' 0

O'5

O 0

I.O

O'g

0 0

1.0

0 ' 5

O O

I'O

0"5

0

I0 ~'0 3 0 4 0 d. ° 50

I0 Z.O ~ 0 ~ '0 Ok° 5 0

k

i 0 Z O 5 0 4t-0 oco 5 0

io ~ o 3 0 4 o ~ o s o

I 0 ~ '0 3 0 ~ '0 o(, ° SO

O IO E O 3 0 q-O o~, ° 5 0

FIo. 37. Chordwise positions of vortex breakdown point and of secondary separation kink.

4S ° DELTA WING

55 ° DELTA WING

6 0 ° DELTA WING

G5 ° D,E.LTA WING

70 ° DELTA ~ N ~

7G ° DELTA WING

45

Fro. 38. 55 ° de l ta wing, flat u p p e r surface. Oi l - f low p a t t e r n at ~ = 15 °.

4 6

FIG. 39. 65 ° de l t a wing, flat u p p e r surface. Oi l - f low p a t t e r n o n lower sur face at ~ = 10 °.

(92361) Wt. 67t7689 I(.5 866 Hw.

47

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