SUPERVENTILATED FLOW PAST DELTA WINGS by Taras …

Department of the Navy Naval Ordnance Tes t Station Contract N123(60530)34767A

SUPERVENTILATED FLOW PAST DELTA WINGS

by

T a r a s Kiceniuk

Reproduction in whole o r in p a r t i s permi t ted for any purpose of the United States Government

Hydrodynamics Laboratory Karman Laboratory of Fluid Mechanics and J e t Propulsion

California Institute of Technology Pasadena, California

Report No. E-101. 5 July 1964

NOMENCLATURE

Symbols

z max

Definition Units

Length of model F t

Plan form a rea of model Ft2 in ~ t 2

Longitudinaldistance along F t model, upstream from trailing edge

Transverse distance on F t model, from model centerline

Half-breadth of model a t F t 1 ongitudinal position x

Submergence measured F t vertically from undisturbed f ree surface

Submergence measured to model centroid

Longitudinal distance to center of pressure

Half-breadth of model a t widest point

Model total apex angle

Model angle of attack

F ree stream static pressure

Cavity pressure

Free stream static head measured relative to atmosphere

Cavity pressure measured relative to atmosphere

Mass density of water

Degrees

Degrees

L ~ S / ~ t '

~ b s / ~ t '

F t of water

F t of water

Symbols

- Lift C~ - 2 t p V o A

- Drag C~ - 2 t~ V o A

- - Moment ( t . e . ) C~ z p I V:AL

NOMENCLATURE (continued)

Definition Units

Acceleration of gravity F t / ~ e c 2

F r e e s t r e a m velocity F t / ~ e c

Cavitation o r ventilation Dimensionless number

Lift coefficient Dimensionless

Drag coefficient Dimensionless

Moment coefficient about Dimensionless trail ing edge

Introduction

Although delta wings have been known for some t ime in aeronautics (1)(2);k

their introduction into a hydrodynamic context has been quite recent. As

in the flow of a i r , the delta wing provides a simple but useful configuration

for investigating three-dimensional problems in cavity flows. At the s t a r t

of the present work (1 960), only one theoretical study on this subject was

known(3). No information on flow pat terns , fo rce charac ter i s t ics o r

other propert ies were available for these shapes. It was accordingly

decided to embark on an experimental program with the a i m of providing the

basic charac ter i s t ics of the cavitating flow past delta wings, to observe and

outline any interesting features of these flows and, finally, to provide a

physical basis for any mathematical analysis of the flow that might be

undertaken. .Measurements of lift, drag and pitching moment and p res su re

distributions were made on a family of simple flat plate delta shapes of

varying apex angle; severa l configurations outside this family were a l so

tested. These included a diamond plan fo rm, r e v e r s e delta, and a delta

with a 90 degree bottom. All were without camber and were tested with

no yaw angle.

After completion of this work, the exhaustive t rea tment of Reichardt

and ~ a t t l e r ' ~ ) appeared which a lso deals with cavitating delta wings. It i s

believed, however, that the cur rent r epor t and that of Reichardt a r e

sufficiently different in scope and method to justify the presentation of the

present resul ts . =

Instruments and Apparatus

The experimental program described in this repor t was performed in

the Free-Surface Water Tunnel a t the California Institute of Technology. (5)

The working section of this tunnel, shown diagrammatically in F igure 1 ,

permi ts force and p r e s s u r e measurements to be made a t velocities up to

27 fps in the presence of a f r e e water surface. The boundary layer sk immer

located a t the upstream end of the working section, removes the slow-moving

top layer of water in the nozzle. The resulting velocity profile, labeled B

in Figure 1, shows no perceptible variation except a t the lower boundary

and s ide walls of the 20 inch by 20 inch working section.

.*, ' F

Numbers in parenthesis re fer to re ferences a t end of text.

The fo rces and moment acting on the model were measured on the

three-component force balance. This balance, descr ibed in grea ter detail

in Reference 6, i s an electrical-mechanical type to which the model i s

attached by means of a shielded adjustable s t ru t assembly. Simultaneous

readings of forward lift, r e a r l if t , and drag a r e combined by a simple

computational procedure into lift, d rag , and pitching moment coefficients,

the la t ter being taken about the trail ing edge of the model. The elevating

mechanism to which this balance i s attached can be r a i sed o r lowered s o

that the model can be completely submerged, o r i t can be r a i sed through

the f r e e surface and out of the moving water .

The support-s t rut assembly consis ts of an inner support s t ru t and an

outer s t reamlined fairing. Within the fairing a r e contained the tubes which

supply a i r to the cavity and which permi t the cavity p r e s s u r e to be

measured. No mechanical sea l i s provided between the cavity bubble and

the outside a i r above the water surface, a condition which might have

resul ted in the maximum cavity p res su re being l imited by the leakage of

a i r f r o m within the cavity. To obviate this possibility, prel iminary

experiments were made using a water sea l , in which a generous external

supply of water a t low p ressu re was permitted to fill the space between

the fairing and the support s t rut . Although this sea l worked very well, i t

was found to be unnecessary since the r a t e of a i r l o s s past the s t ru t was - found to be small compared to the a i r entrainment a t the downstream end

of the cavity.

The angle of attack of the model could be changed during the course of

the run by means of the adjusting knob located a t the upper end of the s t ru t ,

but was l imited to an excursion of plus o r minus 10 degrees f r o m the p re - se t

midpoint. The dial indicator, reading in thousandths of a n inch, had

previously been calibrated to indicate angle of attack. This dial indicator

can be seen in F igure 2 which shows a s lender delta wing and the lower end

of the force balance during a typical run at moderate submergence. The

lower end of the support s t ru t fairing and the point of attachment a t the

model were not fa i red since they did not contact moving water inside the

a i r supported cavity.

The supplementary a i r supply probe can be seen in these same photographs,

extending upstream f r o m i t s surface-piercing support s t ru t to i t s terminating

point within the cavity. This supplementary supply was used only to check

whether o r not the upper value of cavity p res su re was being limited by the

a i r supply ra te obtainable through the piping within the s t ru t fairing. When

it was conclusively proved that this was not the case , the auxiliary a i r supply

was removed and the a i r supply l ines within the model support s t rut fairing

were used alone.

The p res su re in the cavity was measured on a water manometer since

the range of cavity p res su res usually encountered in a i r supported cavities

of this type a r e within a foot o r two of atmospheric p res su re for velocities

l e s s than 25 fps. In order to make su re that the p res su re tap line was f ree

of water a t all t imes , some a i r was continually bled into the cavity space

through the p res su re measuring tap. The p res su re drop associated with

this small a i r flow ra te through the p res su re line causes the cavity p res su re

manometer to read about . 01 feet too high. This e r r o r was easi ly compen-

sated for by adjusting the scale a t the s t a r t of the run by f i r s t raising the

model out of the water and using the ambient a i r p res su re a s the known zero

p res su re reference.

Description of Models --- The design requirement of each model was that i t be hydrodynamically -

equivalent to a flat plate, wetted only on the p res su re side and not contacting

the cavity wall on i t s upper surface. This goal could be met easi ly and

inexpensively by machining the model f r o m flat aluminum stock beveled

45 degrees along the sides of the hydrofoil. If handled carefully the edges

remain reasonably sharp, and prel iminary tes t s proved that the model did

not deform under the influence of the hydrodynamic loads. The plates were

made in thicknesses that var ied f rom 1 / 8 inch to 1 / 4 inch, depending upon

the strength and deflection requirements imposed by the part icular geometry

and point of support. The models tested, a s well a s cr i t ical dimensions, a r e

shown in Figure 3. Provisions for making p res su re distribution surveys of

the 15 degree model consisted of 1/16 inch diameter piezometer openings

distributed a t key points along the bottom of the model, communicating to

flexible polyethylene 'tubing by means of the short lengths of bent b r a s s

tubing which can be seen in Figure 3(a). The piezometer openings were made

la rge in the interest of increasing the response t ime of the p res su re measuring

system. Smaller openings would have been used had the p res su re not been

measured on the la rge-bore mult i -manometers . The same p res su re tap

openings were a l so used for flow visualization purposes by connecting the

thin polyethylene tubing to a low p ressu re source of water which had

previously been colored by dissolving potassium permanganate in it.

Figure 3 (a) a lso shows the b r a s s tubing f r o m which a jet of colored water

was discharged into the bubble wall near the tip of the model. Cotton tufts a l so

were employed for flow visualization. The model was prepared by drilling

small holes in the bottom, then counter-boring these holes with a l a rge r

diameter dr i l l f rom the upper or "suction" side. In this way a short length

of string knotted a t the end, could be inser ted through the model and held in

place by a plug of wax p res sed against the knot a t the base of the l a rge r

diameter hole in the upper surface. This method was deemed preferable to

gluing the tufts to the model surface itself since the thread protrudes normal

to the model surface and i s , therefore, f r e e to a s sume any flow direction

without initial bias.

At the extreme forward tip of the model close examination during

prel iminary runs showed that the water flowed around the sha rp edge of the w

model, clinging to the upper surface of the model for a distance of a s much

a s 1 /2 inch before springing f r ee at the sha rp edge! Since the models had

been made of aluminum, and since no part icular ca re had been taken to

achieve an extremely sha rp edge on the model, i t was felt that fabrication

defects, combined with the low Reynolds number which existed near the

extreme tip, produced this disparity f r o m the ideal flow. It was believed

that this wetting of the model tip might a l so account for the clinging of the

septum which could be observed along the ent i re upper surface of the model

a t angles of attack l e s s than 21 degrees for a l l of the deeply submerged

models. Similar to the "teapot" effect, the septum would cling o r spring

f r e e under the influence of small flow fluctuations near this minimum angle.

The wetting of the upper surface of the model by the septum did not

noticeably affect the forces acting on the model because the septum was

extremely thin, but i t had been hoped to achieve the lowest possible angles

of attack and sti l l maintain the bubble geometry a s presented in Figure 4.

F o r this reason a model was made f r o m stainless s teel with edges accurately

lapped to a razor edge to the extreme tip, a refinement which could not be

achieved on the more fragile aluminum models; Both for convenience of

fabrication and for the purpose of exploring another model geometry, the

upper surface of this model (Model 3A, Figure 3 ) was made V-shaped with

a dihedral angle of 90 degrees.

These attempts resul ted in no noticeable reduction in minimum angles

of attack and the upper surface of the t ip of this model was wetted to the

same extent a s were those made f r o m aluminum. The water viscosity and

surface tension appear to control the flow in this region, where the Reynolds

number (based on f r ee s t r e a m velocity and distance f r o m the tip) i s

approximately 15, 000.

Another attempt to reduce the angle of attack a t which superventilated

flow could be achieved was made by blunting the model tip. As expected,

this change in model shape had the effect of causing a local cavity to spring

f r o m the tip much the same a s i t would behind a flat disc, in the immediate

vicinity of the model tip. The effects of this smal l cavity disappeared within

an inch o r so and the remainder of the cavity bubble appeared the same a s

did those with sha rp t ips. A smal l reduction in the minimum angle of attack - was achieved before giving r i s e to the before-mentioned "teapot" effect, but

the gain was l imited to one o r two degrees and this scheme was abandoned.

A possible defect of the model support sys tem was that the deflection

of the model and support s t ru t could resu l t in a change in angle of attack of

the model. To check this possibility the models and support sys tems were

fastened to a heavy surface plate and loads were applied equal to those

measured during the run. The resulting deflections were measured and

recorded. All data presented in this repor t have been cor rec ted for model

deflection, even though that model deflection was, in nearly al l ca ses , l e s s

than 1 /10 of a degree.

Selection of Model Size - - The choice of model s ize was dictated by the following considerations:

1. The model must be smal l enough s o that tunnel blockage will not

noticeably affect the fo rces o r the shape of the cavity.

2. The model s ize must be compatible with the force range of the

available balance system. The upper l imit of these forces i s

10 pounds for the electr ical- mechanical balance, whe r e a s the

lower l imit i s se t , not by the accuracy of the balance, but by the

dimensions of the model support system. If the model i s made too

smal l , the cavity bubble produced by i t i s not l a rge enough to

envelop the existing s t ru t support fairing, with the resul t that

spray s t r ikes the model.

3 . The model must be la rge enough to show no velocity scaling

effects. If the model i s made too smal l i t can be expected that

viscosity and surface tension effects will play a l a rge role in

determining the flow configuration, whereas models which a r e too

la rge will be operating a t a sufficiently low Froude Number, for

gravity effects to be important.

The final verification of co r rec t model s ize was based on the prel iminary

experiments using delta wings with an apex angle of 15 degrees. Models 11. 2

inches long and 8.28 inches long were tested and found to exhibit identical

flow geometr ies and lift and drag coefficients. The sma l l e r one was chosen

for the reasons enumerated above. The a r e a of this model was 0. 063ft2:

The models with apex angle other than 15 degrees were made approximately

equal in plan f o r m a rea .

Observations and Flow Visualization - - Before placing the superventilated delta wing in the water tunnel i t was

not known what the resulting flow and bubble configuration would be. Resul ts

of tes t s performed in air"), and therefore corresponding to the fully-wetted

flow, indicated that a pair of vort ices would f o r m along the edges of the

delta wing and t r a i l downstream. Exactly what would become of these

vort ices a t cavitation numbers low enough to resul t in supercavitation o r

superventilation was a mat te r for conjecture. A plausible guess was that

a l a rge simple bubble such a s the one a s sumed by Cumberbatch and Wu (7 )

would envelop the upper surface of the hydrofoil and extend severa l chords

downstream. The actual bubble geometry observed was strikingly different

f rom the expected one. F i r s t , i t became apparent that moderate angles of

attack were necessary to achieve completely superventilated flow, in which

the upper surface of the model was not touched by the water. At angles of

attack grea ter than 21 degrees, with moderate quantities of a i r supplied in

the wake of the model, a c lear single bubble was obtained. The appearance

of this bubble i s best shown by the sketch in F igure 4, although cr i t ical

examination of Figure 2 and other photographs appearing in this report

reveals the same distinguishing features .

The drawing in Figure 4 i s a composite made f rom many photographs

and sketches and i s intended only to demonstrate the general features of the

flow ra ther than specific details associated with par t icular operating con-

ditions. Accurate survey techniques were not used to determine the shape

of the bubble c ross-sec t ion and so i t must be regarded a s an a r t i s t ' s sketch

only. The lines in the drawing represent the flow direction a s determined

by dye s t reak photographs and by photographs of the tufts on the model. The

angles depicted in the side view show how the flow begins to deviate f rom

being purely conical a s the base of the model i s approached.

Starting with the fully-wetted hydrofoil, and gradually increasing the

quantity of a i r which i s bled into the wake region aft of the hydrofoil, thin

frothy tip vort ices became visually apparent a s a i r was drawn into vortex - cores . Force measurements could not be accurately made with the existing

s t ru t and shield assembly for this flow condition since the model support

s t ruc ture was directly exposed to the s t r e a m of water between the vort ices .

As the a i r flow ra te was increased the p r e s s u r e within the pair of cavities

increased and the aera ted vortex co res grew l a rge r in s ize.

With fur ther reduction in the value of cavitation parameter , the vortex

co res were seen to coalesce and the wall of water between the vort ices

degenerated into a thin septum growing in thickness a s i t was convected

downstream, finally striking the fairing which surrounded the model support

s t ru t . This septum i s difficult to observe visually in the Free-Surface

Tunnel because i t must be seen through the cavity walls. Because of back-

ground tunnel turbulence, the cavity wall i s not perfectly smooth but shows,

instead, smal l waves and ripples. The resulting optical distortion makes

i t relatively difficult to see details within the cavity. To help increase the

contrast between the septum and the ambient s t r e a m and, incidently, to

obtain qualitative information about the flow in the vicinity of the cavity

walls, a jet of dye was directed against the bubble wall about 314 of an inch

behind the model t ip and about 1 18 of an inch above the point where the

bubble springs f r ee f rom the wetted lower surface. (Model 1C in Figure 3).

This dye s t reak can be seen in the sketch of Figure 4 and in the photograph

of Figure 5. After striking the cavity wall, the dye i s c a r r i e d along a

s t r e a m line over the "top" of one of the cavity lobes into the septum.

Observation of the dye s t reak in the septum i s difficult because it must be

viewed through the curved and "wrinkled" cavity wall and because the dye

has begun to diffuse.

That the septum i s not peculiar to this par t icular model o r to any

part icular model orientation can best be seen by inspection of F igures 6

and 7. Figure 6 shows the 15 degree delta wing mounted in an inverted

position within the tunnel working section, while Figure 7 presents models

of var ious apex angles within the range of 10 degrees t o 90 degrees a s well

a s V-bottom and the 15 degree diamond plan f o r m models. The appearance

of the septum at moderate angles of attack i s substantially the same for all

of these models.

The side views of the cavity, a s well a s the sketch of Figure 4 show an .- interesting feature of the flow. Tufts which were attached to the bottom of

the model and which were too long, slipped over the sha rp edge and s t reamed

along the cavity wall, thereby indicating the direction of flow in this region.

Although careful angle measurements were not ~ ~ d e r t a k e n , inspection of

the photographs shows that the flow angle i s not sensitive to the cavitation

number nor to the presence of the f r e e surface (F igure 8) . For the

15 degree apex angle delta wing, these tufts make an angle with the

undisturbed s t r e a m direction approximately a s shown in Figure 4, and a r e

independent of the model angle of attack for angles f r o m 21 degrees to

30 degrees.

When seen f r o m below, the tuft studies (F igure 9) show the relative

insensitivity of the flow direction, along the model surface, to cavitation

number and to model submergence. Since i t was not possible to obtain

high cavitation numbers a t low submergences o r low cavitation numbers a t

deep submergences, the spaces where the corresponding photographs belong

have been left blank. It should be noted that the photographs in F igure 9

were taken vertically, f r o m below the water tunnel. To eliminate the

apparent foreshortening due to the 30 degree angle of attack of the model,

the pictures were rectified during enlargement to produce a t rue view of the

plane of the model.

Effect of Model Submergence and Specification of Cavitation Number

Since the ear ly experiments of ~ e i c h a r d t ' ~ ) i t has been recognized that

the hydrodynamic forces and moments acting on a body which produces la rge

open cavities in i t s wake a r e the same whether that cavity i s filled with water

vapor o r with a i r , so long a s the cavitation parameter i s given in t e r m s of

the measured cavity pressure . The cavitation parameter i s usually expressed

in the f o r m

When the cavity p r e s s u r e and tunnel velocity a r e measured by means of

water-fi l led manometers it i s convenient to express the cavitation number a s

where h i s the reading of a water-fi l led manometer (in feet) measuring k

the cavity p res su re , and h i s the p r e s s u r e head (in feet) f a r ahead of the 0

model in the undisturbed flow. Since only the difference ho - h i s important, k both p r e s s u r e s may conveniently be measured with respect to the atmosphere,

and ho = Y i s mere ly the model submergence i n f e e t . The denominator 0

equals the reading of a water-fi l led manometer , r e f e r r e d to the moving

water surface in the working section, and connected to a tap located a t any

convenient point ups t ream of the tunnel nozzle.

F o r air-supported cavities a t velocities l e s s than 25 fps, the value of

hk i s usually within a few tenths of a foot of a tmospheric p res su re . Under

these conditions the specification of the cavitation number becomes

ambiguous since the value of ho will necessar i ly vary over a wide range

fo r relatively long models inclined to the flow. If the notion of a "local"

cavitation number

i s adopted to examine the importance of the difference in s ta t ic p res su re

at the ex t reme ends of the model, and i f Reichardt ' s well known formula

C D = C D (1 + K) for drag applies to elementary s t r ip s a t varying depths, 0

then it follows that the normal forces acting on the cavity-producing body

can be regarded a s being made up of three t e r m s

where only the l a s t t e r m depends on submergence and i s equal to C A Y;:. Do

F o r the conditions of velocity and p res su re examined during these tes t s

"local" cavitation numbers a r e actually negative a t the tip of the model. w

Using s imi lar procedures , i t can be shown that the moment coefficient

o r the center of p res su re location should a l so be cor rec ted for the effect

of difference in depth along the model, but these can be neglected since in

the worst case (in which the model tip just breaks' through the water sur face)

the e r r o r introduced by assuming that the "hydrostatic" fo rces act at the

centroid i s l e s s than the experimental sca t te r .

Lift and drag measurements taken a t an angle of attack of 21 degrees,

show no significant variation even when the model broaches the f r ee surface,

and a s much a s one quar te r a r e a of the model l i e s above the undisturbed

water surface. Under these conditions the septum no longer ex is t s ;

instead the cavity bubble exhibits a longitudinal gap which s t a r t s a t the

model t ip and inc reases in width downstream, creating a V-shapld opening

which connects the bubble with the outside a i r . If the force coefficients a r e

based on the plan f o r m a r e a of the model below the undisturbed water

surface, these constant force values mean that the lift and drag coefficients

increase slightly when the model p ierces the f r e e surface.

Force and P r e s s u r e Measurements

The resu l t s of the force measurements made on the superventilated

delta wing models a r e presented in F igures 10 through 15 for models with

increasing apex angle. In these f igures lift and drag coefficients a r e plotted

a s a function of model cavitation number, K, a s i s the position of the center - of p res su re x . The force coefficients and cavitation (or ventilation) number

have been defined in the usual way ( see l i s t of symbols on pages i and ii).

F igure 11, which presents the r e su l t s of the measurements performed

on the 15 degree delta wing, presents data taken over a grea ter range of

operation pa ramete r s than has been done for the other models since this

model had been singled out for exploration of the effect of variations in sub-

mergence, model scale , etc. The resu l t s for angles of attack l e s s than

21 degrees and those for cavitation numbers l e s s than 0.05 were obtained by

running the model nea re r the f r e e surface than the 0.65 ft. value used f o r

the main tes t sequence. As pointed out previously, in some cases the model

t ip was permit ted to broach the water surface.

The effect of apex angle on the force and moment coefficients a t a

constant value of cavitation number and angle of attack i s presented in the - c r o s s plot shown in F igure 16.

Some indication of the effect of model dead r i s e and plan fo rm, a s well

a s of deviations f r o m standard orientation and configuration, a r e shown in

F igure 17 for models with a nominal apex angle of 15 degrees and a t a

30 degree angle of attack.

A comparison of F igure 1 7 with F igure 1 1 shows that inverting the model

in the tunnel had no significant effect on the measured force coefficients o r

on the position of the center of p res su re . Likewise, the effect of blunting

the model, which had been done in a n attempt to secure better cavity bubble

formation a t the lower angles of attack had no significant effect on the

measured coefficients.

Running the model backwards so that the 15 degree apex t rai led

downstream resul ted in lift and drag coefficients ve ry close to those

obtained for the orthodox configuration. The center of p res su re , measured

in a l l ca ses f r o m the trail ing edge of the model shows a more pronounced

shift upstream f r o m the centroid of the plan f o r m and the re-entrant jet o r

septum i s not formed when the model i s in this attitude. Instead, the upper

surface of the cavity bubble soon i s flat in t r ansve r se section where i t

leaves the leading edge of the model and soon becomes more concave

(downward) a s the section i s taken f a r the r downstream.

The diamond-shaped model Number 8 and the 90 degree V-bottom

Model 3A, were tested only to explore, in a prel iminary way, the effect of

the change in model plan f o r m and dead r i s e on the measured force

coefficients and on the observed flow geometry.

The p res su re distributions of F igures 18 and 19 supplement the infor-

mation provided by the force measurements and provides bet ter insight

into the effect of change of angle of attack and cavitation number on the

15 degree model. The p res su re coefficient a s used he re i s r e fe r red to

the cavity p res su re p instead of the f r e e s t r e a m stat ic p res su re p a s i s k 0 '

customarily employed for fully-wetted flows. Using this notation the

stagnation p res su re i s equal to 1 t K and the p res su re coefficient anywhere

within the cavity bubble i s taken a s zero. The plan f o r m of the model i s

included in these f igures to show the approximate location of the p res su re *

taps and to define the distance coordinates used in the p res su re distribution

plots. F r o m this drawing i t can be seen that the p res su re taps a r e located

along selected r ays drawn through the t ip of the model. In the left hand

curves both the longitudinal center line p res su re distribution and the

individual t r ansve r se section p res su re distributions (shown rotated into the

plane of the paper) give a graphical representation of the p res su re forces

which ac t normal to the model. F o r clar i ty of presentation, p res su re

readings f r o m only the left hand side of the model have been included in

these t r ansve r se views, and the t r ansve r se tap position, although drawn to

the same scale a s the longitudinal position, has not been identified for each

of the sections. The representation on the right hand side of the f igures

shows the p res su re coefficient a t each of the t r ansve r se stations drawn

superimposed and normalized to the value of p res su re coefficient a t the

center line . Within the accuracy of the p ressure measure ments the

t ransverse pressure distributions a r e not affected by the longitudinal

position of the station along the model, nor i s the nature of the pressure

distribution significantly affected by changes in the cavitation number or

angle of attack of the model over the range of values of these variables

shown in the figures.

When the angle of attack of the model was reduced to 1 5 degrees, and

the model was permitted to approach the water surface in order to secure

low cavitation numbers, an interesting change in the pressure distribution

was observed:

(1) Because of an apparent tunnel flow asymmetry near the surface,

the pressure distribution was not symmetrical with respect to the model

centerline. (Compare tufts in Figure 9. )

(2) A pressure distribution, more nearly in agreement with those

in Reference 2 were obtained, that i s , the pressure coefficient increased,

rather than decreased, for rays outboard of the model centerline.

These latter distributions have not been included since the effect of the

flow asymmetry may be producing non-representative values.

ACKNOWLEDGMENTS

This report represents the combined efforts of many individuals:

Mr. Murphy Lum, who carr ied out most of the force and pressure

measurements; Mrs. Laura Gaard, who performed the calculations

and prepared the curves; Mr. Carl Eastvedt, who took the photographs;

and Mr. George Lundgren, who fabricated the models and model

attachments. The helpful suggestions of Professors Acosta and Wu were

instrumental in determining the scope and direction of the experiments.

REFERENCES

1. Jones, R. T. , "Propert ies of Low-Aspect Ratio Pointed Wings at Speeds Below and Above the Speed of Sound", Technical Note No. 1032, Langley Memorial Aeronautical Laboratory, March 1946.

2. Lee, G. H. , "Note on the Flow Around Delta Wings With Sharp Leading Edges", Aeronautical Research Council R and M No. 3070, 1958.

3. Tulin, M. P. , "Supercavitating Flow P a s t Slender Wingstt, Journal of Ship Research, Vol. 3, No. 3, p. 17, 1959.

4. Reichardt, H. and Sat t ler , W., "Three-Component Measurements on Delta Wings With Cavitationu, Max- Planck Institut fuer Stroemungsforschung , Goettingen, July 1962.

5. Knapp, R. T . , Levy, J . , O'Neill, J. P., and Brown, F. B. , "The Hydrodynamics Laboratory of the California Institute of Technology", Trans . ASME, July 1948.

6. Kic e niuk, T a r a s , "An Experimental Study of the Hydrodynamic F o r c e s Acting on a Family of Cavity- Producing Conical Bodies of Revolution Inclined to the Flow", California Institute of Technology, Report No. E 12.17, June 1954.

7. Wu, T. Y. and Cumberbatch, E. , "Cavity Flow P a s t a Slender Pointed Hydrofoilu, Vol. I1 Journal of Fluid Mechanics, pp. 187- 208, 1961.

m

8. Reichardt, H. , "The Laws of Cavitation Bubbles at Axially Symmetr ical Bodies in a Flow1f, R and T No. 766, Ministry of Aircraf t Production, August 15, 1946.

(a) 0 a = 30 K = ,120 V = 14 fps

(b) 0

a = 30 K = ,121 V = 14 fps

0 Fig. 2 - 15 Delta Wing Supported f r o m the Three -

Component F o r c e Balance in the Working Section of the F ree -Sur face Water Tunnel. Electronic F l a s h was Used in (a) Above; T ime Exposure in (b) .

( a ) Model I C

Apex Angle - 15'

Length - . 6 9 3 ft

Area - . 064 ft2

(b) Model 2 C

Apex Angle - 15O

Length - . 6 5 3 ft

Area - . 058 ft 2

( c ) Model 3A

Apex Angle - 15O

Length - . 6 0 0 ft

Area - . 048 ft2

Fig. 3 - Delta W i n g Models

(d) Model 4

Apex Angle - 45'

Length - . 375 f t

Area - . 058 ft 2

( e ) Model 5

Apex Angle - 90' Length - . 250 f t

Area - . 063 ft2

( f ) Model 6

Apex Angle - 60°

Length - . 333 ft ,

A r e a -.064 ft 2

Fig. 3 -(Continued) Delta W i n g Models

(g) Model 7

Apex Angle - 30°

Length - .458 f t

Area - . 056 ft 2

(h) Model 8

ex Angle - 15' ngth - . 9 06 ft ea - . 054 ft2

(i) Model 9

Apex Angle - l o 0

Length - . 828 ft

Area - . 060 ft 2

r i g . 3 -(continued) Delta Wing Models

Fig . 4 - Diagrammatic Sketch of Superventi lated Flow P a s t a 15O Delta Wing a t a Low Cavitation Number and a n Angle of Attack of 30°.

0 Fig. 5 - 15 Delta Wing Showing Injscted Dye

S t r eak and Septum. a = 30 , V = 14.7 fps , K = .13.

0 Fig. 6 - 15O Delta Wing Inver ted in Tunnel. a = - 30 ,

V = 16 fps.

(b) y = 15O a = 30 o

Fig. 7 - Superventilating Delta Wings of Various Apex Angles a t Moderate Angle of Attack.

(e) y = 60' 0

a = 30

(g) Y = 15O (90' V-Bottom) 0

a = 25

(h) Diamond plan f o r m y = 15' 0 a = 30

Fig. 7 - (Continued) Superventilating Delta Wings of Various Apex Angles a t Moderate Angle of Attack.

Fig . 8 - Compar i son of Flow Direct ion i n Cavity Wall Near Edge of Del ta Wing with Apex Angle = 15O and Angle of At tack of 25O. Upper Model is Near Sur face ( submergence t o cen t ro id - .087 ft). Lower Model is at Modera te Depth ( submergence t o centroid- . 57 f t ) . Model Length is . 69 ft.

.v,

Submergence, Y"' = . 250 f t . -7,

Submergence , Y". = = 650 ft .

Cavitat ion Number not Attainable

Cavitat ion Number Not Attainable

Ful ly- Wetted Ful ly- W-etted

F i g . 9 - Bottom View of Superventi lat ing Delta Wing a t Varying Cavitat ion Numbers and a t Two Submergences ( . 250 fee t , lef t hand c o l u y n and . 650 fee t , r igh t hand column) . Angle of At tack = 30 , Velocity = 15 fps .

.05 . I 0 . I 5 C A V I T A T I O N NUMBER, K

Fig. 10 -Lift, Drag and Center of P r e s s u r e Location for a Super- ventilated lo0 Delta W i n g a s a Function of Cavitation Number.

.05 .I 0 . I 5 C A V I T A T I O N N U M B E R , K

F i g . 11 -Lif t , Drag and Cente r of P r e s s u r e Location f o r a Super- venti lated 15 O Delta Wing a s a Function of Cavitation Number.

0 0 . 0 5 .I 0 . I 5 .2 0 .2 5

C A V I T A T I O N N U M B E R , K

Fig . 12 -Lif t , Drag a%d Cente r of P r e s s u r e Location f o r a Super - venti lated 30 Delta Wing a s a Function of Cavitation Number .

.O 5 .I 0 1 5 .20 . 2 5

C A V I T A T I O N NUMBER, K

Fig. 13 -Lif t , Drag and Cente r of P r e s s u r e Location for a Super- venti lated 4 5 O Delta Wing a s a Function of Cavitation Number .

Fig. 14 -Lift, Drag a@ Center of P r e s s u r e Location for a Super- ventilated 60 Delta Wing as a Function of Cavitation Number.

.05 .I 0 .I 5

C A V I T A T I O N NUMBER, K

Fig. 15 -Lift, Drag an$ Center of P r e s s u r e Location for a Super- ventilated 90 Delta Wing a s a Function of Cavitation Number.

MODEL APEX ANGLE, y , I N D E G R E E S

Fig . 16 -Effect of Apex Angle f o r a Supercavi ta t ing Del ta Wing a t an Angle of At tack of 30' and Cavitat ion Number of . l .

M O D E L 2 C

M O D E L 3 A

- - - -

I I I I I I I I I

0 5 .I 0 1 5

C A V I T A T I O N N U M B E R , K

.@a-

n .,

V

- -

- I I I I I I I I I

Fig. 17 -Lift , Drag and Cente r of P r e s s u r e Location fo r Various Superventi lated Delta Wings a t an Angle of Attack of 30°. Model descr ipt ions a r e given in F ig . 3. Flow i s f r o m le f t to r igh t fo r models a s shown.

* v - n V

MODEL NO.

a

2 C -

a ' 2 8 -

1°C -

e

3 A -

-7 I

- -

- - l I I 0 I l l l

h "

+

0 Fig. 18 - P r e s s u r e Distribution of a 15 Superventilated Delta Wing a t

21° Angle of Attack.

0 F ig . 19 - P r e s s u r e Distr ibution of a 15 Supervent i la ted Delta Wing a t 30° Angle of Attack.

APPENDIX I

SUMMARY OF FORCE DATA

2 Model vo -

X

K 2 g - Iesignation y A f t 2 a. y ::

C~ CD L

APPENDIX I

(continued)

Model Designation Y A f t2

APPENDIX I

(continued)

APPENDIX I

(continued)

Model Designation

APPENDIX I

(continued)

Model Designation Y A f t 2 a y ::: K

APPENDIX 11 Summary of P ressure Data

--t- z I - :--

-0- Z x 2

z 3 - 2 - - Z x 4

Apex Angle, y = 15O Velocity =18. 5 fps P r e s s u r e Tap No.

Angle of Attack, a = 30°

Angle of Attack, a = 30°

0 Angle of Attack, a = 2 1

Angle of Attack, a = 21°

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