Choking of strut ventilated foil cavities

CHOKING OF STRUT-VENTILATED FOIL CAVITIES

By

C. Elata May 1967

DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED

Prepared Under

Naval Ships Research and Development Center Department of the Navy

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-1-TABLE OF CONTENTS Page ABSTRACT 1 INTRODUCTION 2 AIR ENTRAINMENT 3

THE STRUT CAVITY 9

CHOKING 12 EXPERIMENTAL INVESTIGATION 1k R1SULTS 16 CONCLUSIONS 19 APPENDIX 21 REFERENCES 2k

LIST OF FIGURES

Figure 1 - Schematic Description of the Effect of Submergence

Depth and Velocity on Air Entrainment Coefficient Figure 2 - Differences in Cavity Shape Behind Strut with and

withoU.t Free Ventiiatd Foil

Figure 3 Progressive Choking of.a Ventilated Hydrofoil Figure 11 - Drag Coefficient as Function of Angle of Attack

Figure 5 - Lift Drag patio as a Function of Angle of Attack

Figure

6 -

Typical: ReCults of Choking-She'gence Depth versus Freestream Velocity

Figure 7 - Typical Results of Choking-Submergence Depth verSUS

Freesti'eam Velocity

Figure

8 -

Typical Results of. Choking-Submergence Depth versus Freetreeth Velocity

Fgure

9 - Froude Number at Choking as a Function of Force

Cdeff1ien.t

Figure 1O.- roudeNunber at Choking for Three.Fbil.s

Figure 11 - Froude Number at Choking. as a Function of Choking. Coefficient

Figure 12 Submergence Depths for Choking Cond,tiois of Cavity Behind 5-10 Foil

Figure 13 - Dimensions of Strut Models

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Figure 15 - The Effect of Depth of Submergence on the Spray Profile

Figure

i6

-

The Effect of.RakeAngie onSpray:Profile

Figure17 - The Effect of Freestream.Velocity bnSpray Profile Figure 18 Maximum Spray Height as aFunction Of FroudeNumber

NOTATION Area of foil

VOid Ootcentratiori Chord length of foil Drag coefficient Lift coefficient Entrainment coefficient Choking coefficient Diameter Drag Force Gravitational acceleration

Depth of submergence of leading edge of foil Froude number

Cavity length Pressure

Rate of au' flow Thickness of strut Velocity

;Thickness of spray sheet Work Spray height A C C CD CL CQ CCH d D g h Fr 2 p Q t V w W y

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-v-a Angle of attack

H constant

Entrainment coefficient

e Strut rake angle

Density V. Viscosity =

oc

_{cavitation number} Subscripts o free stream c :cavity foil at strut air watex,. of the order of proportional to

ABSTRACT

Presented in this report are the results of an investigation of the "choking" phenomenon in base vented strut cavities. In

practice such base vented struts support a ventilated foil and pro-vide the ventilation air for the foil through the strut cavity. An

expression for .the rate of air entrainment in ventilated cavities is derived. This expression fits previously reported experimental data except at low cavitation numbers, when free surface- solid boundary- and gravitational effects may become important.

The shape of the cavity behind a strut, supporting a strut-ventilated foil, is analyzed. It is. shown that the shortest sec-tion of the strut cavity is at the free surface,. and that its length is controlled by. the air flowthroughit.

The choking phenomenon is analyzed by. relating the air flow through the strut cavity to the air demand.of the foil cavity. From this analysis a choking coefficient CCH is defined

A series of experiments is described in which, for three strut-supported foils,. the depth at choking was determinedas a function of free stream velocity,.angle of attack, and air pressure. It was. found.from these experiments that choking would occur for

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-2-INTRODUCTI ON

It may be desirable for many practical applications to utilie hydrofoils which are purposely ventilated; Especially in flow re-gimes in which vapor cavities are unstable, the supply of air to the cavity may stabiize the force characteristics Of the foil.

Natural or surface ventilation may be achieved when atmo-spheric a.ir is supplied through a cavity formed behind a foil sup-porting strut. In this case air will be driven through tIe strut

cavity, from the free surface by the difference between cavity- and atmospheric pressures. The cavity pressure and the rate of air flow are also interrelated by the air entrainment characteristics of the foil cavity.

It has been observed that under certain conditions natural ventilation may be difficult to maintain because of Ttchoking". This choking apparently occurs when the strut cavity closes off at the free surfäce, thus preventing air to flow to the foil cav-ity, causing a decrease in cavity pressure and a collapsing, and finally vanishing of the cavity

The understanding of this phenomenon is of the utmost itnpor-tance for the desigh of strut-ventilated fOils, Experiments hav

shown that ItchokingT conditions do not solely depend on cavitation

number and foil and strut geometry, but also to a large degree on depth of submergence and atmospheric pressure. Before relevant model tests of this phenomenon can be performed a good physical understanding is nedessary.

The problem is treated in this report by analyzing the en-trainment characteristics of the foil cavity and the shape of the

strut cavity before combining the two to describe the choking phenomenon.

AIR ENTRAINT4ENT

A ventilated cavity is maintained only when air is constantly

supplied to it. This supply is needed to compensate for the air entrained at the downstream end of the cavity.

Several attempts have been made to derive suitable semi-em-piricál relationships for the rate of air entrainment. Cuthbert (i) assumed the entrainment to depend on the amount of air transported in the laminar air boundary layers along the cavity wa1l. ie de-duced the relation

V2f. V, [1]

where

Q is the rate of air entrainment, v the viscosity,

the length of the foIl cavity, and the free stream velocity.

Sciiièb.eatad Wetzel (2) assumed the air supplied to the cavity to be entrained by the reentrant jet and derived

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where

coorát ed

CA

C P

1-c

,-where D is the drag fOrOe.

=DV

0 131

CD

is the drag cOeffiient,

A

the aa ofthe foil,

a

the ca\r1tatipnnumber based on the cavity preLire

and

_H

c

is the void cocent'àtion in the r

ntrant jet,

th1.ch,

as determind eperimentally.

ExeMmehtai results are usually presented as a'e1atior

be-tween a dimensionless air entrã±ntrieht coefficient CQ

Q/CDAV

and the

aVitatior

tiirPber..

In generai. two regions of different

behavio±' have beei pbserved.

In short cavities the entrainment

coefficient is rlaively small and dcreases p'oporoai to a

In long cavities the air entrainment grows rapidly when a

ap-proaches a small firLite value and

seems to dëend oti veloc1t

ai

depth as well as ona.

Anothe

relat±dh for the rate. of entrainment may he derived

The air inside the cavity at pressure p reaches, after it is entrained, a pressure p equal to the static pressure at the level of the cavity. Thus, in order for air to be entrained work has to be done against this adverse pressure gradient. This work

(neglecting compressibility, effects) is

'o

[k]

Defining a work efficiency ii by

TI w2 [5] vv1 we maywrite Since D _{cDA ipV02}

[fl

CAV

D 0

a

Q = , or CDAV - =

The validity of Equation

[8]

is supported by the general trend of the data replotted by Cuthbert (i) giving

".' 0.05 - 0.1.

Q

_(p0

= DV.

_[6]

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it follows that

1

o'f

which gives a similar relationship between Q and as deduced by Cuthbert (Equation 1), though not between Q and V.

As mentioned previously, air entrainment does not follow the prediction of Equation

Ei8J

at very low cavitation numbers.

Several investigatos have measured entrainment rates in cavitie behind force-ventilated disks. Swanson and OtNeill

₍₃₎

found thSt the entrainment depended on free stream velocity as well as on

a.

They were able to correlate their air entrainment coefficients with V 0 a gd where

d is the maximum cavity diameter.

rn

Schiebe and Wetzel (2) also showed a similar velocity effecFt to exist for the eitrainment in cavities behind lifting foils at

low aTs.

-6-Since the length of the foil cavity may be expressed by

E i.oJ

9 2

Campbell and Hilborn (k) obtained similar results for disks of different rises. They also observed that the flowbondaries had an effect on the entrainment rate. This effect could. be

ex-'pressed n terms of a shift in cavitation number a = a - a',

where a' is the cavitation number in an unbounded flow. a was

found tobe negative asa result of the presence of the free sur-face and positive as a result of the presence of so4d.boundaries, i.e., the entrainPient rate would decrease when the cavity

ap-proached the free surface and increase when it apap-proached the chan-nel bottOm.

Similar free surface effects have also been reported for lifting foils by Schiebe and Wetzel (2) and Dawson and Bate (5). The effect of velocity on the entrainment rate was explained by

Cox and Clayden

(6)

as being due to the gravity effect. The grav-ity effect causes circulation and trailing vortices which were

supposed to entrain air. Campbell and Hilborn (k)derived f or such 'vortex entrainment an' entrainment coefficient.

gd a4 V 2

0

The effects of flow boundaries on the cavity characteristics have beenstudied theoretically by Birkhoff et al (7), Cohen and Gilbert (8), Cohen and DiPrima (9), Yim (10) and many others, Yim's calculations, whibh fit the experimental results of Dawson and Bate quite well, indicate the cavity length to decrease when

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the cavity approaches the free surface. In fact experimental

re-su1t indicate a similarity between, the dependence of cavity leng1h and rate of entrainment on a for low values of

d.

It was shown in the 'previbus discussion that air ehtrainment rates may in general be expressed by Equation [8]. At low cavi-tation nuthbers ril'l no longer be a constant however, but will depend on velocity and depth of submergence, i.e. will decrease1 when the velocity' increases and the depth of submergence decreases. We might thus assume a relationship of the form

Valid fr small valdesof a. In fact such a form ha been

sug-gested by recent work Of Schiebe and Wete'l [11] who foun. that

with i

h3/'Va

ubstituted into quatiOn[8].,. it would

pre-dict their air enträinthent data for low aspect ratio f,oil and

small ats.

A' schematic diagram showing the effect of depth and velocity on C. is presented in Figure 1.

gh

= 1 - ,

THE STRUT CAVITY

Behind a strut piercing afree surface,.a cavity may form when the flow velocities are sufficiently high. According to two-dimensional theory. - neglecting the effects of the free surface., the end of the strut and interference between flow conditions at different horizontal planes - we may'write for the cavity length

£ st 2 C st D t n a were 1 <n < 2.

In the ventilated cavity, the pressure is essentiaily

atmo-spheric,, so that V2 Fr2 and [13] 2 st. 2n CDFr [15]

It follows that 2st varies with,

hn,

approaching infinity at the free surface, Of course, Equation [15] does not actually describe the strut cavity profile. _{The fact that the caVity length}

de-creases with depth beneath the free surface is an observed experi-mental fact, as can be seen from the data of May (l2),.Thomsen _(13),

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Meyer (lii-), and many others, IJhen a submerged foil i,s attached

to the st±'ut a diffè'ent strut cavity length profile is obtained as ahoWn n Figure 2. The reason for this differenôe may be ex-plained as follows.

The ventilated foil cavity consumes air which i

uppied

through the stut cavity. Neglecting frictional lOses, the caviy

pressure. will be of the order of pV2 lower than attnospheric,

ie.,

PC PSY a is the air density and V

the velocity in the throat o the strut avity at the free surf5ce). The cavity presi-sures will also be approximately constanbalog the base f the strut and inthefoil cavity as was shown by Wadlin (15).

Wen

the strut supports a lare foil and subthegetice depths ar al.l

the static pressure in the fluid around the sttut:ceases to in-crease with depth. Tin that cage the fluid hitting the strut will bernore like a free jet with atmospheric pressurs at the upper free surfaCe Snd With S preSsure equal to that: in the foil-cavity St the lower free.surface. From such a sChematiC model it can bS been (Figure 2) that for a foil supporting strut, decreases from the upper' free si'face downwards, which may explain the .differen

strut cavity shape. The faCt that the shortest strut cavity length was at the free surface has been observed by Wadlin (15) and als

ih this study.

It may thus be conc1ided thata cavity of a foil supporting. ventiLlati,ng strut has a controlling section St the free surface. For the cavty length at thefree surface we may Write

£ st

In fact, the presence of the free surface must have a large ef-fect on the cavity length. The dynamic pressure at the'leading edge of the strut will be released through the creation of spray sheets which because of theirlower momentum,, will tend to shorten the cavity, i.e. the effective cavitation number will become larger.

Pn investigation of spray. heets on to geometrically similar struts, oI1e:pr Which was used in the"choking " experiments, is pre-sented in the appendix. Wadlin has indicated that the cavity length between the spray sheets may be expressed by

£ pV02 t a PaVa2 st

-

.'J I t

Vat

where

is the spray sheet thickness.

The experiments reported in the appendix indicate: that w is

neither affected by the free stream velocity nor by depth of sub-mergence.

In the following section Equation [16] will be assumed to express the variation of £ with a V 2/p V 2 In fact either

st

aa

wo

one of Equations [16] or [17] will lead to a similar result.

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V2t

Q will decrease when V increases, tNhich follows from either

equation.

CHOKING

In the previous sections, the characteristics of the air entrainment in the fcil cavity, and the shape of the strut cavity have been descr1bed.

In the following the choking phenomenon will be analyzed on the basis of this reyiew. We assume the lëngth.of the strut cavity at the free surface to be expressed by Equation

[16]

and the air

entrainment of the foil cavity by Equations

[8]

and [12]. It was seen in the previous section that the cavity pressure is _Pa\Ta2 The cavitation number relevant to the foil cavity is therefore

a a a

pV2

_wo

V2

o

By equating the rate of air flow through the strut cavity (from

Equations

_[16]

and [18]) withthe air entrainment in the foil cavity (from Equations

[8]

and [19]) we obtain

-12-In both cases 2 will become smaller when V increases. Further-a

V V

2gh

2

st V

0

It may be. seen that the solution of Equation [20], with from Equation [12], will give a smallest value for 2/t .of the form

which is obtained for

f3

paVa2

st

pv2

.v2

ww

0

Other solutions of Equation [20] are possible, giving larger values

for 2/t.

We will try to show in the following that Equation [21] represents the only stable solution.

Let us assume a state of equilibrium with a fully ventilated foil at a fixed depth of submergence. Small temporary changes in air demand may occur, however. An increase of Q for instance will cause a decrease in p and an increase -in V which will lead to a

decrease in2 (Equation [i6]). If the air demand is not signifi-cantly reduced in the meantime, the decrease in

2st will cause a

PDV

0

[20]

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-1k-further increase in V etc. As pointed out, only when the air demand is significantly reduced will the situation stabilize

it-self. Such a reduction in the air demand may be effected when

g .

(-p ) > . It is assumed here that in the opposite case,i.e.

c

0

for longer strut cavities, the equilibrium is .unstable and that such cavities willshrink to the values expressed by Equation 1121]. In

that case it may also be assumed that choking of the cavity, caused by a complete closure at the free surface may be represented by

CCH

( gh\

const

0/

[22]

Such closures have been previously investigated by Wadlin, who also showed that by attaching spray strips to the strut, partially submerged below the free water surface, a considerably improved ventilation could be obtained with a simultaneous reduction in

cavity pressure.

EXPERIMENTAL INVESTIGATION

The experiments were conducted in the HYDRONAUTICS, Incorpo-rated High Speed Channel. This facility is described in detail in Reference 16. Three sharp-edged flat-plate foils were used having chord-width dimensions of 6" x 12"; _5" x 10' and

3" x 9".

The foils were supported by a slender parabolic strut with a 2.5" chord and a maximum base thickness of

3/8".

With the foils submerged at a small depth and at afixed angle of attack, the flow velocity in the tunne,l was set to a particular .value,.sufficiently'high for the foil to be fully.ventilated.

There-after the water. depth was increased in small increments. At a cer-tain depth.the foil cavity would suddenly. and rapidly deorease in length and, finally, completely, disappear. PL1 this depth, and just

when:the cavity. started.to shorten,measurements were made:to.de-termine the depth of submergence, velocity, lift and drag and, in. a few cases, 'cavity pressure.

This procedure was repeatedwith different flow velocities. Thereafter the angle of attack of the foil was changed anda.nother

series of measurements made..: Finally this procedure was repeated with differerit'air pressures inthe tunnel.

For each of the threefoils, measurements of air pressure, angleof attack, lift, drag, depth of submergence and velocity..were made for a total of k50 'Tchoking" conditions. At high angles of attack and/or higher air pressures the collapse of the foil cavity was abrupt. 'At a submergence depth close to choking the cavity was found to be unstable, slowly decreasing in length and then

suddenly. to grow again. At choking the cavity would slowly

de-crease in length and.than suddenly. collapse (Figure 3).. The cavity pressures would slowly decrease while the water level. wasraised. Cavity collapse would be preceded by. a sudden reduction in cavity pressure, which was found to.be as good an indication of a choked

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-16--At small angles Of attack and/or lower air pressures the

cavity would not choice over -the range of depths and velocities at-tainable in the tunnel. In those cases- the cavity would shorten when the water -depth was increased, without any abrupt change in I

length. Even, for th largest foil at the highest angles of attack

and atmospheric air ressures the precise depth of submergence for the choking condition was difficult to determine and depended on the patience andjudgement of the observer This was even more' true for the smaller foils, at lower angles of attack and at low -, air pressures in th tunnel.

When the cavity had started to choke, it could not be made. fully. ventilating again, neither by slightly decreasing the depth nor by increasing the velocity. Only by decreasing the water

depth to much smallr values than those at which the cavity choked, would ventilation inception occur again.

RESULTS

The data resulting from the measurements were .punched on cards and processedby the.IBM 1130 computer. Corrections were applied for bottom ff'ects, the drag force on the strut and fric-tion drag on the foils, but not for blockage. These co'rections

caused an increase ftn both drag coefficient and effective angle of attack, from the measured values.

The drag coefficients versus angle of attack for all the mea-surements are preseted in Figure k. The applied corrections ha,. the effect. of shifting the points along the average line through,

the data.points. On the same diagram the theoretical curve is drawn for the drag coefficient as a function of angle of attack

for a two dimensional foil in aninfinite fluid. The.discrep-anciesbetween.the presented and the theoretical curvemay be due in part toboundary and three dimensional effects,

In Figure _{5 the lift-drag ratio is presented as a function of}

the angle of attack, together with the theoretical lift-drag

curve. Certainly, the scatter of the data in this diagram can

only be due to experimental error.

or each foil, and each air pressure, the depth at choking was plotted against the square of the free stream velocity for 'each angle of attack (force coefficient). Examples of such plots are preented in Figures

6,' 7

and

8.

Although there w'as'.found tbé a considerable scatter of 'data, it was possible to define an average choking Froude 'number for each angle of attack,

repre-sented by straight lines in the h-V2 diagrams.

These Froude numbers were plotted against the corresponding average force coefficient, as presented in Figure 9 for the 511_la?? foil. It can be seen from this figure that the choking Froude number depends on the density (relative pressure) of the air in the tunnel as well as onthe drag coefficient.

As suggested by the analysis the choking Froude numbers were plotted against _{CE\/ Pa"Pw} as shown in Figure 10. Three aver-age curves were drawn through these data, dne for each foil.

Finally Figure 11 presents the data plotted against the "choking11 coefficient _{CCH = CD} giving a relationship

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FrCH

Correspondingly all he neasured depths at choking for the 5"-lO" foil were plotted aginst

[23]

where

_a'a

is the relative density of the tunnel atmospheie

(Figure 12). The average curve through the data points again sugL

gest the relationship given by Equation [23]. The divergerce of some of the data at helargest. depths (VT) is probably caused by the cavity hittin the sipport of the strut, resulting in a premature choking.

CONCLUSIONS

The air entrainment in ventilated cavities behind foils can be expressed by

CDAVo a

This expression follows .from the assumption:that the work which has to be done to entrainthe air is proportional to the power required to move the foil.

At very low, cavitation numbers, the rate of entrainment will be affected ..by the free surface, solid boundaries and gravity.

These.effects will change the value of

T.

For larger a, T was

found to have a value of 0.05 - 0.1.

The cavity behind a strut supporting a (natural)

strut-ventilated foil has a length which increases with depth, the nar-rowest controlling section being at the free surface.

2k. By relating the airflow through the controlling section of

the. strut cavity, with the rate of air entrainment of the foil cavity it is found that the length of the strut cavity at the free surface depends on CCHfl where CCH is called the choking coeffi-cieñt defined by CCH = CD a A . gh

and fl=11

-wt2

V2

0

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-20-From a.series ofexperiments, the depth at which the cavity would collapse (choke) was determined as a function of foil size, angle of attack, free stream velocity and air pressure. It was found that the cavitr would be choked for

The drag and lift coefficients were foUnd to be in approximate agreement with the alues predicted for foils in a fluid of in-finite extent.

APPENDIX

Two geometrically similar, base-vented, parabolic strut models of 15 percent maximum thickness were used in the studies described

herein. The strut dimensions are shown in Figure 13. -Strut A and

Strut B are used to denote the 5-inch chord and 25-inchchord strut respectively.

The experiments were carried out in the HYDRONAUTICS High Speed Channel which are described in detail in Reference 16.

Observations of spray profile and thickness along the strut surface were carried outfor both: StrutsA and B without hydro-foils attached to the struts. Measurements of spray profile were obtained by drawing an x-y coordinate system on one side of the

strut and reading spray height "y" at each given "x" value of

chordwise position. Quantitative measurements of the spray thick-ness were not obtained; only qualitative observations can be given. A general description of observed spray over a vertical, base-vented strut is presented in the following paragraphs.

As shown in Figure 11 _{it is possible to distinguish three}

different regimes of spray. For a. relatively high speed, (or a

high Froude number based on the strut chord), the water surface is usually considered to be horizontal. . However, the water.

sur-face adjacent to the strut is almost linearly elevated from the strut leading edge to its trailing edge. . For the struts tested the height of this region is about 0.2 of the chord at the trail-ing edge of the strut. . Over the range of speeds tested, the

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-22-Above the root of the spray (that is, the deformed water su'face in the egibn of the strut-water intersection) there s a rg1on

of very thin, high vëloáity spray whic.h shoots ut behind the stri4t.

This portion of the pray is the most noticeable t.o the observer. The height of this sray-fi1m, region is velocity.dependent..

Above this thinspray layer, a third region exists. Here the spray energy has decreased and water "piles u to fOrm a stream of relativeiy low speed flowing over the strut and a1ling back t the water surface. The width of this stream is also velocity de-I

pendent.

By inserting thin wires perpendicular to the stru surface,

the thicknesses of the two latter spray regions were estimated. I

Over the thin, high speed spray layer this thickness was about 0.02 inches for both Struts A and B. The thickness of the streamF of water above the thin layer was estimated to be Q)4 to .08 ihchL Althoughno est.imatioi of the actUal thicknesses can be made for this region a typica.l variation of the thickness. of the root is

sketched in Figure 1k. No significant changes in thicknesa were I found over the range of speeds tested. HoweVer, this Play have been. due to the relatively rough estimates obtaThed by this methd

of measuring. . .

General featurs of. the spray over the strut si.rface do not change significantly with varying depths of submergence and str.

Pake angles.. I.f a supercayltating hydrofoil is attached to the

strut, the Whole spray pattern will be tilted upward due o the slope of the free surface produced by the hydrofoil cavity.

Spry profiles along the strut were measured over a range of speeds from 20 to 35 fps for depths of submergence from 0.5 to 2 0 strut chords, and strut rake angles from -15 to +15 degrees The results of these tests for Strut A. are shown

in FIgi'es 15,

16 and 17. It should be noted, that. the

spray

profijes shown In these figures do not include th

height

pf the.

lo

speed, thick, stream decribed in previOus pat'agraphs (seeFigure li-I-). It was fourd that the Influence of depth of submergence was veryslght over th ranges

tested

and

the

1nf1uence of

strut rake

angle

was

significant bnly..at negative or forward rake angles.

Negative

ang-e ...rye to reduce the height of the spray.

Te magnitude of

the free steam velocity has by far the principal affect on spray

profiles.. . .

Of particular interest is the maximuin height of spray y.,

1ocated.t the trailing edge of the scrUt.

Figure 18.shOws a.plot

of y

as a function of Froude number based on the strut

chord,

max .

V

Fr. =

9

It may be hOted in Figure 18 that the data fothee

two truts Ooliapse for givèhdeth-chordrätios

inthe

range of

.ighei' Fröude nurnbers

_(Fr

10).

It

appears that

the

sräjthIck-ness

i

essentially a linear function

of

Froudenumberfor a given

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REFERENCES

Cuthhert, J.W., 'tAn:Anaiysis of Air Entrainment in Cavity

Flows," HYDRONATjTICS, Incorporated Technical Report 003-1,'

October1960.

.

Schiebe, F. R. and Wetzel, J. M.

"Vèht!1ate

Cavities on

Submerged ThieeDimënsional HydrOfoils," St. .Anthony Falls

Hydraulic Laboratory, Technical Paper No

36, Series B,

December 1961.

SWanson, W. M

nd O'Neill, J. P., 'The.Sail1y of an Air

Maintained cavity Behind .a Stationary Object in Flowing

Water," IydrodynamicsLabortory, Cal. :Enst. of Tech.,.Mem.

Report.No.. M-2U.3, September ],95l.

.

Campbell, I. J.Hand.Hilbornè, D. V., "Air Entinrhent.Behind.'

inflated Cavities," Second Symposium on Naval Hydrodynan4cs,

ONR, August 1958.

5.

Dawson, T

E. and

ate

E. H;, "An Experimental Investi'gation

of a Fully Caviitating TwoDimensional Flat Plate Hydrofoil.

Near a.Free Suiface," HydrodynamicsLabortory,. Cal. Inst.

of Tech.. Report No

E-118.12, October '1962.

6.

Cox,R. N..andClaydeti,. W.-A., "Air..Entrainment at .theRear

of a

teady.CaVity," Proc. of the NPL Symposium on Cavitatin

in Hydrodynamics, London,.HJ4;S.O., 1956.

7

Birkhoff, G., Plesset, IVLS. and SimthônsM.,."Wall Effects

in Cavity Flow," Quart

Appl

Nath

Vol

8, No

2, 1950

8

Cohen, H. and Gilbert, H., Two-Dimensional, .Steady,Cavity

FlowAboUt S1eiider Bodies in Channels of Finite Breadth,"

Jour, of Appl.Mech., 1956.

9

Cohen, H. and. DiPrima,R. C., "Wall Efrects in Cavitating

Foils," Second Symposium on Naval Hydrodynamics, ONR,

10. Yim, B., "On a Fully Cavitating Two-Dimensional Flat Plate HydrOfoil with Non-Zero Cavitation Number Near a Free Sur-face," HYDRONATJTICS, Incorporated Technical Report k63-k, June

196k.

11.' Schiebe, F. H., and Wetzel, J. M., "Further Studiesof Ventilated Cavities on Submerged Bodies," St. Anthony Falls Hydraulic Laboratory, Project Report No. 72, October

196k.

May, A. D., "Flow About Semi-Submerged Cylinders of Finite Length," Princeton University, October

l9k7.

ThOmsen, P., "Cavity.Shape and Drag in Ventilated Flow; Theory and Experiment," TRGReport

_l56-SR-2,

February

_1963.

1k. Meyer, M.C., "An Experiment CQncerning Partly Closed

Cavities Behind a Surface Piercing Rod," Hydrodynamics

Laboratory, Cal. Inst. of Tech. Report No E-llO.I, January

1967.. .

15. Wadlin,. K. L., "Ventilated Flow with Flydrofoils," Tw1fth General Meeting of the ATTC, University of California, September

_1959.

16. Johnon, V. E., Jr.,. and Goodman, A., "The HYDRONAUTICS, Variable-Pressure, Free-Surface, High-Speed Channel,"

Cavitation Research Facilities and Techniues, Am. Soc.

a

U I-z Ui U U-Ui

0

U

I-z

U-i

z

z

u-i CAVITATION NUMBER - a

FIGURE 1 - SCHEMATIC DESCRIPTiON Of THE EFFECT OF SUBMERGENCE DEPTH AND VELOCITY ON AIR ENTRAINMENT COE;FFICIENT

(-)

/

/ /

/

/

/

/

FIGURE 2 - DIFFERENCES IN CAVITY SHAPE BEHIND STRUT WITH AND WITHOUT

FREE VENTILATED FOIL

P a

C

P

0 PC

.HYDRONAUTICS, INCORPORATED

IRLPHP CD =2P1 aSIN ALPHII4I P1 aSIN RLPHR) 3O_ 15 lU LEGEND FOIL12

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0. 3D I I I I I I I I I I I I I I I I l_ I I I I I I 0..05 0.10 0.15 0.20 0.25 DRPC COEFFICIENT CD

RLPHP 30 (n Li Li ID Li

g 25

15 CL/CD = COT ALPI-IP LEGEND ,< 1DI I I I I I 1.0 2.0 3.0 ILO 5.0 6.0

?0

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LIFT DRP

HYOPONPUTICS, INCORPORATED H 1 FR 5.08 _{5.92 6.31} COl 0.16'.!? COl + COl 0.1133

cm

o.oso FOIL 12. - 6. DENSITY

FIGURE 6 TYPICAL RESULTS OF CHOKING -submERGENcE DEPTH VEPSUS FREESTREAIT1 VELOCITY

6

=

L) 0 LJ D 3 2 1 I I 11 5 6 9 10 VELOCITY 1100 LFT/SEC) £

ci Li D FR 3.60 Q15 4.78 5.79 o

cm - 0.2363

CD1 - 0.207L + cm - (3.1821 COl 0.1565 I I I I I I I I I _I 3 '4 5 6 7 S 10 VELOCITY C_{/100 (FT/SEC]} c FOIL

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DENSITY 0.608

FIGURE 7 TYPICRL RESULTS OF CHOKING - SUBfl1ER&ENCE DEPTH

HYORONAUTICS, INCORPORATED LJ 6 H FR 5.13 5.60 3 4 5 6 ? VELOCITY 1100 6.33 + , I I I I I I _I 9 10 CFTJSEC) FOIL 10. - 5. DENSITY 0.?511

FIGURE 8 TYPICAL RESULTS OF CHOKING - SU6ERGENCE DEPTH

VERSUS FREESTRERIT1 VELOCITY

=4

0 LU 3 2 1

Cm

cm

0.2063

cm

0.1541

cm

0.1292

cat

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x

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FIGURE 10- FROIJDE NUMBER ATCHOKING FOR THREE FOILS

o

6-12

0

5-10,

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FIGURE 11 - FROUDE NUMBER AT CHOKING AS A FUNC11ON OF CHOKING

HYDRONRUTICS) INCORPORRTEO

a 1

FULLY VENTILATED

0.2 0.3 0.L4 _{0.5 0..6 0.7 0. 0.9}

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FIGURE 12 SU1I1ERGENCE DEPTHS FOR CHOIcING CONDITIONS OF CAVITY BEHIND S - 10 FOIL LEG [ND PRESSUPE 33.1 PRESSURE 250 + PRESSUPE 20.0 PRESSURE 16.0 PPESSURE - 12.0

MATERIAL -STAINLESS STEEL STRUT A

I-*---

5" 5" MATERIAL -ALUMI NUM STRUT B SECTION A-A SECTiON A-A

FIGURE 13 - DIMENSIONS OF STRUT MODELS

NOT TO SCALE

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FIGURE 14 - SKETCH OF SPRAY OVER STRUT SURFACE

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1.0 0.8 0.6 0.4 0.2 0. 0. 0. 0.25 0.50 0.75 x/C (a)V0=2OfpS, 0=00

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HYDRONAUTICS, INCORPORATED 1.2 hO 0.8 O.6 0.4 0.2 0 1.2 1.0 0.8 0.4 0.2 0 x/C (c) V030Fps,9=O° x/C (d) V 35 fps, 9 =cO FIGURE 15 (CONCLUDED)

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HYDRONA1JTICS, INCORPORATED 1.2 1.0 0.8 %0.6 0.4 0.2 h2 1.0 0.8 0.6 0.4 0.2 0.25

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0.50 0.75 x/C (c) V 3Ofps.h/C=1.O FIGURE 16 (CONCLUDED) 1.00 L25 0.25 0.50 0.75 1.00 1.25 x/C (d) Vr-35fp,h/C=1.O 0. -20. -25.3 +10. +15.

0

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.

A

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FIGURE 17 - THE EFFECT OF FREESTREAM VELOCITY ON SPRAY PROFILE

0.25 0.50 075. 1.00 1.25 x/C (c) =i.5,9O0 0 25 0.50 _x/C 0.75 (a) -D.5,8=O0 1.00 V 0= 1.25

2.0, 1.8 1.6 1.4 1.2 0.6 0.4 _0.2 2 4 6 8 Fr C. 10 12

FIGURE 18 -. MAXIMUM SPRAY HEIGHT

AS A FUNCTION OF FROUDE NUMBER

14 16 h/C I Stt A

0

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1.5 0.5

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ii. SUPPLEMENTARY NOTES - - 12. SPONSORING MILITARY ACTIViTY

Naval Ship Research and Development Center Department of the Navy

13 ASTRACT

t'resented in this report are the results of an base vented strut cavities. In practice such base

vide the ventilation air for the foil through the entrainment in ventilated cavities is derived

mental data except at low cavitation numbers, tational effects may become important.

The shape of the cavity behind a strut, supporting is shown that the shortest section of the strut cavity

controlled by the air flow through it.

The choking phenomenon is analyzed by relating

air demand of the foil cavity. From this analysis

A series of-experiments is described i.n which, choking was determined as a function of free stream

sure. It was found from these experiments that

Frh

Investigation of

vented struts support

strut cavity.. An

This expression

when free

surface-a strut-ventilsurface-ated

is at the free

the air flow a choking coefficient

for three strut-supported

velocity, angle

choking would occur

the 'choking" phenomenon in

a ventilated foil and

pro-expression for the rate of air fits previously reported

experi-solid boundary- and

gravi-foil, is analyzed. It surface, and that its length is

through the strut cavity to the CCH is defined.

foils, the depth at of attack, and air

pres-fpr

Ventilated cavities

Air entrainment

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DD

1JAN64

1473 (BACK)

D23551 UNCLASSI FlED