AYE0 USATRECOMA TECHNICAL REPORT 64-70

THE COANDA EFIECT AT DEFLECTION SURFACES

WIDEY SEPARATED FROod THE JET NOZZLE

yr

S. I. RENNILR

DECEMBER11 1114DO-R

1. S. Alit IIAISSIRAJIISU PESEARCI CSMMAND

FIRT EUSTIS. VIRGINIA

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U S ARMY TRANSPORTATION RESEARCH COMMANDPORT £uST5 V)RG4tN 23S04

In this report, the University of Toronto, Institutc for

Aerospace Studies, investigated the Coanda effect in"he deflection of two-dimensional jet sheets with turningiurfaces located at large horizontal and vertical dis-,ar.ýes from the nozzle.

I ht results are used to define permissible gap sizes forpractical appiications of detached deflection surfaces.

This command considers the conclusions made by the

contractor to be valid.

t

TasK ID121401AI4203Contr,".ct DA 44-177-AMC-11(T)

USATRFCOM Technical Report 64-70December 1964

THE COANDA EFFECT AT DEFLECTION SURFACES I

WIDELY SEPARATED FROM THE JET NOZZLE

UTIAS Tech. Note No. 78

Frepared by

INS'TTUTE FOR AEROSPACE STUDIESUNIVERSITY OF TORONTO

TORONTO. CANADA

for

U. S. ARMY TRANSPORTATION RESEARCH COMMANDFORT EUSTIS, VIRGINIA

ABSTRACT

The flow phenomenon in both liquids and gases of the adhe•emAof a jet or jet sheet to a solid surface has been named the Cownda Effect.This report discusses an experimental investigation, which has aainshown that the Coanda Effect is nvt limited to attached deflecLiin ,Jur-faces or to inclined single or multiple flat-plate surfaces. The horixon-tally ejected subsonic -And overchoked jet sheets successfully bridgedhorizontal and ve tical gaps of 32 and 10 times the nominal jet sheetthickness (t = 1/16 inclht. respectively; for t = 1/4 inch, the correspond-ing ratios were eight and two. The vertical gap was increased until theflow detached from the deflection surface. Vertical and horizontalforces acting on three different deflection surfaces were measured witha strain gauge balance. The configurations were tested at nominalpressure ratios of 1. 1, 1. 2, 1.7, and 2. 2, and the surface pressureswe.e recorded.

Uii

FOREWORD

The work described in this report was accomplished by theInstitute for Aerospace Studies, University of Toronto, Toronto,Canada, for the U. S. Army Transportation Research Command, FortEustis, Virginia. This report represents the work performed underContract DA 44- 177-AMC-If(T).

The project was conducted by the University cf Toronto'sInstitute for Aerospace Studies, with Dr. G. K. Korbacher, Associ-ate Professor of Aerospace Engineering Sciences, providing thetechnical direction. Mr. S. D. Benner, author and chief investigator,was assisted by Messrs. K. Sridhar and P. R. Stephens.

v

CONTENTS

ABSTRACT iii

FOREWORD.D v

LIST OP ILLUSTRATIONS. viii

LIST OF' SYMBOLS x

SUMMARY .

CONCLUSIONS . 2

INTRODUCTION

SIMPLE JET SHEET FLOW THEORY 4

TEST FACILITIES f,

TEST RIG 7

EXPERIMENTAL PROCEDURE . 9.

PRESENTATION OF RESULTS .Z

DTSCUSSION (01 RESULTS . . 14

BIBLIOGRAPHY .. 75

DISTRIBUTION . 76

APPENDIX I - EXACT PRESSURE RATIOS FOR PRESSUREDISTRIBUTIONS, PREUSUR COEFFICIENTS,AND MEASURED FORCES ACTING ON THEDEFLECTION SURFACES AS IN FIGURES 5TO 33 INCLUSIVE ... 77

APPENDIX II - COMPARISON OF MEASURED AND INTEGRATEDRESULTANT FORCES ACTING ON A DEFLEC-T[ON F'RFACE ..... 78

vii

Figure Page

26 to 27 Effect of Deflection Surface Radii on ,.he Non-DimensionalLift Force for Various Horizontal aiid Vtrtical Gap Sizesand Nozzle Pressure Ratios. 65 to 68

28 to 33 Contours of Ce.nst-nt Non-Dimensional Lift for VariousHorizontai anl( "ertical Gap Sizes atic Nozz.e PressureRatios. *,9 to 74

i1

j

ix

SY •\iPF LS

.rcr ,wal dist,,a, , bet'eci, to%. r nozzle h n aro' leading eo e

of tht defI,, i.,w .zurfa ,c ,i c r .(ni I(t - I in , positive in

.X~ fy '~J ' 1, 1 inn

AN M \ ,

Cp press1ur , _eflI ict ien-

P prt,.,sur,• ctr , licieil Inc co: pI -'ý. si, ow' , thin ,,t shect

c ( ~ -Ij rnf:1-,ctcrt t~',) ~ n ri~s, 'nconiiv t 1.tCp

1) .Irag2 or•b ', a,.tin., on defiecifcn •dt11vr, po',nt i:Z .,', arddir u.cti,,

F , "(','Cont iguratioii Notation" under P1dSF\ F "1ON OF RESU LTS

PC centrifugal force

F p pressure force

Fri resultant force acting on the deflection surface and = fAPwds

Frn resultant force acting on the deflection surface and =-2 +

horizontal distance between lower nozzle lip and leading edgeof the deflection surface at their center lines, positive inoutward direction

1. lift force acting an the deflection surface, positive in theupwards direction

Lf, I r vertical force restrained by the front and rear pair respectively

of the horizontally mounted steel flexures

dm mass of element of flow

) aatmospheric pressure

l's pressure at thL. bound surface of the jet sheet

V

P T iotal jet (ceservoir) pressur.p

AP, dP pressur,- diffhrence across ine jet sheet

qc com re ssio.¾e dynamin head

qi inccmpIreý7ilble dynamic Iead

P. radius of the jet sheet center line

Ro radius of the Coanda surface (quadrant)

s distance from leading edge, and measured along thedeflection surface

t nominal jet sheet thickness at nozile exit

TH thrust per unit jet sheet width

V jet sheet flow velocity

w width of deflection surface; width of jet sheet at nozzle e'yit

Y compressibility correction factor

ratio of specific heats

jet sheet flow turning angle

pO jtt sheet density

X, variable number

a/t non-dimensional vertical gap

2/t non-dimensional horizontal gap

L/(PTAN) non-c"mensional lift force

L. E. leading edge

PT/Pa pressure ratio (M P. R.)

s/t non-dimensional distance along deflection surface

T. E. trailing edge

xi

SUMMARY

This experimental investigation of the deflection of two-dimensionaljet sheets by means of the Co-inda Effect by surfaces widely separated fromthe nozzle in both the horizontal a.-d the vertical direction has again sbownthat the Coanda Effect is not limited to attached deflection surfaces or to in-clined single ,r multiple flat-plate surfaces. The horizontally ejected F 'b-sonic and overchoked jet sheets successfully bridged horizontal and vertical gaps of 32 and 10 times the nominal jet sheet thickness (t = 1/16-inch)respectively; for t = 1/4-inch, the corresponding ratios were eight and two.The vertical gap was increased until the flow detached from the deflectionsurface. Vertical and horizontal forces acting on three different deflectionsurfaces, formed by a combination of an initia" flat plate f1/4-inch thick)followed by a quadrant of a circular cylinder of 2-, 3-. and 4-inch radius,were measured with a strain gauge balance. The configurations were testedat nominal pressure ratios of 1. 1, 1. 2, 1. 7, and 2. 2, and the surfacepressures were recorded.

CONCLUSIONS

The conclusions which the presented experimental evidencesuggests on the turning of two-dimensional subsonic and overchoked jetsheets by means of detached Coanda surfaces are as follows•

(1) The Coanda Effect was fc, t,.nd to function even when the deflectionsurface was widely separated from the nozzle.

(2) The thicker the jet sheet at a given hoi izontal gap, the smallerthe possible vertical gaps which the jet sheet can bridge.

(3) The thicker the jet sheet at a given vertical gap, the larger thepossitble horizontal gaps which the jet sheet can bridge.

(4) The larger the radius of the deflection surface, the larger thepossible gaps.

(5) T-,. maintain a specific lift of a jet sheet on c. deflection surface.any changes in horizontal gap size must be accompanied byrelated changes in vertical gap size.

(6) For a given low-pressure ratio jet sheet, the maximum lift forceoccurs at rather smIll horizontal ( I i 1/4-inch) and vertical(a a l/8-inch)gaps. With increasing pressure ratio, the jetsheet can bridge largtr gap distances, and the size of the verticalgap increases faster than the horizontal gap for maximum iift.

The ultimate vertical gap sizes dtpend on the entrainmentproperties of the jet sheet underside in the wedge between the jet sh,•ctand the Coanda surface just before the jet sheet attaches itself to thesurface. If the suction pressure. A P. at this point becomes equal to-2(t/R)(,p/2)V2 , then the jet sheet will become attached and will followthe Coanda surface. Otherwise, it will not attach itself.

2

* , r

INTRODUCTION

The flow phenomenon in both liquids and gases of the adherenceof a jet or jet sheet to a solid surface has been named the Coanda Effect.N. H. Coanda, a Roumanian inventor, discovered that when air was ejectedfrom a rectangular nozzle, it would attach tc an inclined flat plate whichis connected to the nozzle exit with no gap. He deduced that the attachmentwas produced by a decrease in surface pressure in the separation bubblewhich he observed to form just downstream of the nozzle exit. Emphasiz-ing the requirement of a sharp angle between the nozzle and the flat plate,Coanda applied this principle to a series of deflecting surfaces, each at asharp angle with the preceding one, and succeeded in turning flows throughanrgles as large as 1800. In this investigation, the continuous curve of thequadrant of a circular cylinder was used as the "Coanda" or deflectionsurface.

For investigations prior to 1961, the deflection surfaces wereattached to the nozzle with no intervening gap. In References I and 5,the Coanda surfaces were detached for practical reasons only, and the gapbetween the deflection surface and nozzle was -pproximate!y 1/100-inch.IT was large enough to provide flex bility in the use and locaticn of differ-,L-nt deflection surfaces without detrimental effecth to the flow. Obviously,detached deflection surfaces are preferable for practical applicationsprovided that the permissible gap sizes are large enough not to createmechanical problems.

The present work is a continuation of the initial investigationsof detached surfaces by Dr. G. K. Kerbacher (Reference 3). The testequipment was basically similar, wxcept that the compressed air, pre -viously piped to one side of the seitling chamber, was supplied symmetri-cally to both sides (see Figure 4). The section of tin wali pipe downtzeamof the cooler was removed, and two flexible pieces of piping were locatedjust upstream of the settling chamber; the latter was completely freud ofthe weight and the reaction forces of the fixed piping.

The purpose of thim experimental lnvestigation was to d:,ermine

the effect of vertical and horizontal gap sizes on subsonic and overchokedjet sheets, which are produced by a rectangular convergent nozzle, as afunction of the nozzle pressure ratio, the jet sheet thickness, and theradius of a smoothly -curved deflection surface. Vertical and horizontalforces acting on the deflection surfaces were to be measured by means ofa strain gauge balance. Also, center-lt- surface pressure distributionswere to b- rccorded for comparison with iressure coefficients predictedby a simple theory.

3

SIMPLE JET SHEET FLOW THEORY

The fundamental theory of jet sheet bending, offered in Refer-ences 3 and 5, is summarized here for convenience. The bending of a jetsheet with one free and one bound surface (Coanda deflected jet sheet) isproduced by a pressure difference across it. The pressure at the boundsurface, Ps, is less than the pressure at the free surface, Pa, which isassumed to be atmospheric. This pressure difference, AP, is the resultof a suction pressure along the solid surface, and is due to viscous effectswhich entrain the air trapped between the surface and the jet sheet into thejet sheet.

Consider an element of flow, din, in a thin jet sheet of high aspecratio (defined as w/t) and assume that t < Ro, that the jet momentumalong the sheet is constant, and that the pressure gradient across the jetsheet is negligible (see Figure 2). In addition, the flow is considered tobe loss-free and two-dimensional.

The centrifugal force, Fc, and the pressure force, Fp, actingon the flow element are in radial equilibrium, and are given by

V2

pR dodR-T R do dP. (1)

The pressure differonce across the curved jet sheet followsthen as Ap = (P. - pa) = -pi- V2 It (2)

R I

Since the thrust per unit Jet sheet width is

TH = ,ptV 2 (*)

"AP" can also be expressed asTH (4)

R

Let us now define a pressure coefficient asAP

C = (5)p V2

2

which, after substitution of equation (2) into equation (5), becomes

2t (6)

R

"This pressure coefficient, for a given jet sheet thickness and Coanda sur-face radius, is a constant and independent of pressure ratio.

4

For incomp ressible flow, the pressure difference across thecurved jet sheet can be expressed, using Bernoulli's theorem -

V2 = _Pr-Pa (7,

as 2t(8)'&P = -(PT -Pa) 8

orAP 2t (9)

SR _Cpi4 PT-Pa)

For compressible flow, however,

.P 2t J__.V2 must be used.R 2

Therefore, A v2

AP 2t 2 = - 2t y (10)

(PT - Pa) R (PT - Pa) -

Since, for compressible flow, the dynamic head pressurc is given by

Nt LPT 1I P'a

"Y" follows as T ," T (12)

and, ther ifore, T

AP 1 - 2t (13)(PTp ") Y CpC T

Roderick (Reference 5) has developed an expression for thetheoretical pressure coefficient of a thick jet sheet (t 4 RO, but of thesam'ý order of magnitude) bending over a curved deflection surface. Fromhis assumptions that the flow is loss-free and two-dimensional, and thatthe pressure gradient across the jet sheet In not negligible, the followingincompressible pressure coefficient has been derived:

CO I ý_]a p~i I+nJ (14)•i R ~

These fimple expressions are very useful for a physical inter-Sretation and understanding of some of the characteristics of curved jetsheets with a free surface on one side.

5

TEST FACILITIES

Compressed air was produced by a small gas turbine airbleed engine. The compressor was able to deliver a maximum weightflow of 2. 7 pounids per second and to achieve a maximum pressureratio of 3.7. The engine was sutpported on a simple box frame andmounted in a small soundproof room. Intake and cooling air for theengine and engine room respectively was obtained through a windowopen to the outside of the laboratory, and the engine's exhaust gaseswere ducted outside to a vertically mounted muffler. Additional infor-mation about the compressed air system and turbine installation can befound in References 2 and 4. The air pressure and mass flow wereremotely controlled at an instrument panel outside of the engine room.

After leaving the engine, the hot compressed air was diffusedto an 8-inch diameter pipe, and then passed through a cooler whichutilized the main water supply. As the temperature of the bleed aircould be as high as 230 0 C, a large water cooler, which is able to re-duce it to approximately 15°C, was used.

Immediately downstream of the cooler, an immersed glassthermometer was located to record the temperature of the compressedair. Next, a gate valve was located, since two other test rigs weresupplied from the same compressed aii source. Farther downstreamwas a mass flow orifice measuring section with its two pressure tapsconnected to a water U-tube manometer. Beyoud L"is, ts-c -" --P-inag

was divided into two branches of 6-inch diameter piping. Two pieces ofcorrugated double-walled flerible piping, each followed by a 6-inch by8-inch diffuser, completed the air passage from the compre 3sor to thesymmetrical inlets of the settling chamber.

6

TEST RIG

The air entered a 24-inch diameter, horizontally mounted, settlingchamber. The chamber had two flat ends; one was solid, the other hadan opening into which a bell-mouth collector was fitted (see Figure 2).The purpose of the collector and settiing ,'hamber was to provide good nowcharacteristics to the hiterchangeable nozzle attached to the downstreamend of the collector.

The rectangular convergent nozzles which were used in thia.experiment were installed by bolting them to the flanged end of the bellmouth or contraction section mounted in the end of the settling chamber.The nominal exit heihts of these nozzes were 1/16-inch and 1/4-inch.Since each nozzle was made from four machined-steel sections which werewelded together, warping resulte'd and the exit heights were not uniformacross the span of the nozzle. The average exit heights were measured as0. 0674-inch and 0. 2560-inch respectively.

The settling chamber was supported by four aircraft cable flex-ures attached to a steel framework, which is bolted to the concrete floor.These flexures were to permit frictionless fore and aft movement of thesettling chamber, which was separated by means of the previously men-'ioned flexible piping from the rigid piping.

The leading edge of the deflection surface had to be adjusted insuch a way as to maintain its relative position with re.pect to the nozzlelip under all load conditions. A camera was used to record the multitubemanometer readings of the yu..isuires along the Cow Ja surface The totalhead pressure, total air temperature, qW MAss flow readipgs were also taken.

lnstrumentation

The basic Instrummentiin oste of a multitube mercury ma -nometer (fifty 45-indh tubels ilth.'tm ,WaIl'relservirs). a total headriercury manotneter with r quifp 'at.60 Umbs a -ti manometer formass flow measurement, and a two-conpoent srain gaug balance. Dueto the delayed delivery of a multitnbe water' manometer, mercury had to beused as a manometer fluid for all pressure ratios. At a nominal pressureratio of 1. 1 and a jet sheet thickness of li1-inch. the surface pressuremea-3urements tit inches of mercury were urreliable.

The multitube manometer was connected to the surface pressuretaps dril',3d along the center line of tUe deflection surface (see Figure ib).The tot i head manometer was connected to the parallel section of the bellmouth ,ust upstream of the nozzle attachment flange. The orifice platewas located iii the 8-inch piping, upstream of the settling chamber (seeFigure 4). The two pressure taps, located in the piping at spoeIfled distancesfrom the orifice plate. were connected to a U-tube manometer. The flowtemperature was measured just downstream of the water cooler.

7

An SR-4 strain indicator was used in combination with a multi-deck switch. Hence, it wae possible to read all the strain incre ients withone meter and without too much time delay.

The effects of pressure fluctuatiois on pressure readings wereminimized by photographing the multitube marometer which recorded thepressure distributions along the deflection surfaces. The camera produced4- by 5-inch plate negatives.

Due "o the high noise level of the jet sheet, normal voice comrnmu-nication between the operators was impossible. Carbon throat microphonesand soundproof earphones which were connected to an aircraft inter-Lommunication amplifier provided satisfactory voice contact.

Force Balance and Deflection Surfacas

It had been the practice in earlier Coanda Effect in, estigations,to attach the deflection surface rigidly to the nozzle. In this study thedeflection surface was not rigidly attached to the nozzle exit. The twomain advantages of detached deflection surfaces are as follows- 1) allow-ance for greater flexibility in the testing of different surfaces. 2) designof the force balance exclusively for the forces acting on the deflectionsurfaces and independent of the dead weight of the piping system.

The general layout of the force balance and deflection surfacemounting is, shown in Figure 3. The deflection surface being tested iaattached to the mounting plate by two bolts. Fig'ire 3 alao shows that thedeflection surface mounting column and its adjustment screws are attachedto a base plate. The base plate is connected to the hirrizontal andvertical force measuring beams by six rigid pin-jointed links.

In the ends of these links are small needle roller bearings whicnkeep friction forces at a minimum. With the assumption that the balanccsystem experiences small rotations only, the vertical links transmit thevertically applied force, and the horizontal links rotate without tranamittingany force; cooviesely for a horizontally applied force. Sidesway of thesystem is preventod by two wire braces, which do not introduce any con-straints in the vertical or horizontal directions.

The curved surfaces tested were circular arcs in shape (quadrants)machined from solid aluminum blocks. A series of static pressure holes,located on the center-line of these surfaces, were provided to measurethe surface pressure distribution. Each surface was fitted with Plexiglasside plates (see Figure lb) to eliminate flow separation and flow entrainmentfrom the side. These side plates were made at least as high as the maximumnozzle exit height used in this investigation. The quadrant could be movedvertically and hurizontally with respect to the nozzle to obtain any practicalgap size desired.

8

EXPERIMENTAL PROCEDUR'R

Test Objective

The purpose of this experimental investigatim was to explore theeffect of gap size - both vertical and horizontal, hetweer, deflection surfaceand nozzle - on the proficiency of flow turning. '1 he hasic teat rariableswere the nozzle pressure ratio, the deflection surface radius. and the jet slotthickness for two-dimensional converg.:nt nozzles.

Balance Calibration

The lift force e'ensing elements wvhich consisLed of four steel flexuresmoanted horizontally, and joined to the base plate by means of the vertical links,restrained vertical forces acting on the deflection PA. face (see Figure 3). Thefore and aft movement of the deflection surface wzs restrained by tNo verticallymounted steel flexures. The horizontal fle-ures, which hi. e a strain gaugebonded on both the top and bottom surfaces, are mounted In two pairs, andthir strain is read as "lift front" and "lift rear". The total lift force actingon the deflection surface is entual to he algebraic sum of the lo'-Is restrainedby the kront and rear pair of flexures. The "drag" strain is measured bymeans of the strain gauges on each side of the vertically mounted flexures.

This two-component balance was calibrated by applying loads in-crenentally to the deflection surface mounting plate atop of the supporungpsy Ion. First, a vertical load was applied, and the "lift front" -. "lift rear"and "drag"-strain readings were recorded. This load was increased slowlyto aoproximately 62 pounhis, then removed in a similar manner. The strainreadings were recorded during the increasing ad decreasing of the applied

load to ascertain the amount, if ay, of Wistereeis in the balance system.The resultIng calibrations indicated a negligible amount of stored energy forthe range of applied loads. Secor4 the .ading roess was repeated fora horizontally appl;ed load. ]frou tmem me•ws ments, the flexure spring

constants were obtazied. By applyg a pure lIft or drag load separately,it was determined that there was ne~gl4gble interaotion between the verticalaid horizontal sensing units, at least for small rotations of the base plate.

During the course of the experiment, two strain gauges began toseparate from the flexures due to thu deterioration of the bonding agentcaused by high frequency, vibratory loads on the steel flexures. Thesefaulty gauges w-tre removed, and replaced with new ones. Calibration of thebalance was repeated after each gauge installation to verify that n.he cali-bration factors were not affected by the re,.oval of the steel flexures fromthe balance.

At the time of the initial test runs at high pressure ratios, it wasdiscovered that a small portion of the deflected jet sheet was impinging onthe plate which supports the deflection surface pylon, and produced an errorin the strain reading, especial%, for the "lift front". For this impingement to

9

occur, a part of the jet sheet must have experienced a turning angle in ex-cess of 900. The piece of dexion cross-support which is parallel to thedeflection surface (see Figure lb) is actually well under and behind thetrailing edge of the deflection surface so a.; to avoid interference with thejet sheet. It was used to support a thin sheet of steel which was installedto make sure that under no circumstances could the deflected jet sheet hit thebalance platform.

The lower end of this curved piece of steel rested on a thick sheetof plywood which was attached by hinges at its top 'o the feamework support-ing the settling chamber; the floor supported the other end of the plywood sheet.

Te sting

The tests were conuucted in two parts. The first part employed arectangular convergent nozzle of t = 1, 16-inch (8 inches wide), which wasoperated at nominal nozzle pressure ratios of 1. 1, 1. 2, 1.7, and 2.2. Thehorizontal gap, . , between the nozzle and the leading edge of the deflectionsurface was varied from 1/t m- 0 to .l/t = 32. The vertical displace-ment, a. of the deflection surface normal to the jet was varied froma!t = 0, - equivalent to proper alignment of the surface leadirg edge withthe lower 1i) of the nozzle - to flow separation at approximately a/t = 8.The deflection surfaces were combinations of a 1/4-inch-thick flat plate, atzero-degree angle of attack, followed by quadrants of R.-- 2-, 3-, an-4-inch radius. Side-plates were instafled on' the 8-Inch-wide deflectionsurfaces to simulate two-dimensional flow. Horizontal and vertical forces dueto the jet acting on the deflection surface wre recorded by means of a straingauge balance. Static pressure distributions on the deflection surface werealso recorded, except for a presiure zatlo of 1. 1, because a multitubewater manometer could not be made a, ailable in time for the tfets.

The second part, similar to the first, wai conducted with a convergentnozzle of t v 1/4-inch. The variation 6f ",t /t" was from zero to eight,and that of "a/t" from zero to flow separation, at approximately two. Nominalpressure ratiop for these tests were confined to 1. 1, 1. 2, and 1. 7. Anattempt to operate at a pressure ratio of 2. 2 had to be discontinued due toextremely high noise levels generated by the high velocity air blowing overthe sharp edge of the flat surfane,- which precedes the quadrants. No effortwas made to OetcrininL the magnitude of this aerodynamic noise, as it was ccn-sidered to be beyond tie range of the available measuring equipment. Thenoise level was estimated in excess of 150 decibels.

Surface pressure distributions and forces acting on the deflectionsurface were also recorded. The j,-. sheet temperature was kept at approxi -

mately 15 OC.

Using one particular nozzle-deflection surface combination andkeeping both the nominal pressure ratio and horizontal gap constant, thevertical gap was varied from the zero position to flow separation in incre-

10

ments of 1/ 16-inch. This procedure was repeated for the other threepressure ratios. The horizontal gap was then changed, and the tests wererepeated as outlined above. After five horizontal gaps (0 inch to 2 inchesin 1/2 -inch increments) had been tested, the second nozzle was installed,and the complete test program was periormed again. Two other deflectionEurfaces were used in similar series of tests.

Although the forces - lift (vertical) and drag (horizontal) - actingonthe deflection surfaces were measured by the strain gauge balance, theycould also be obtained by integrating the surface pressure distributionover the deflection surface. The Ames dial (see Figure lb) rigidly mountedto the settling chamber at the nozzle attachment flange, was located so thatit could measure the vertica] travel of the leading edge of the deflectinnsurface from the zero position. The spindle was always raised and lockedto prevent its interference with the jet sheet as well as the force measurementduring a run.

Accuracy

The pressure distributions on the deflection surface were obtainedfrom the photographs of the multitube manornete;. The photo negatives wereprojected, and could be read with reasonable accuracy to the nearest 1/ 100inch of mercury. Since the pressure values at the lower pressure ratiosin combination with the nozzle exit height of t a 1/16 inch averaged 1/4 inchof mercury, an error of 4 percent in ti •rfac*e pre•suro. is possible atthe lower pressure ratios. However, tlbm error decreases with increasingpressure ratio to less than 1 percent. Ti t•t•1 bead pressure (measuredin the parallel section of the bell =*vth4qst ,qstrlaa of the noszle attachmentflange) was reel. in all cases with an aowracy of I percent or los. Mence,the measured pressure coefflftilt un ect•e teor flow compressibility,have an accuracy of approximatey S IpeWOcO The accuracy of the lift anddrag for :e measurements dcreased wfth Inreasiag pressure ratio, becauseat large horizontal gap (1 Inch to 2 inches) the deflection surface experienceda vibratory motion, the amplitude of whch increased Ir proportion to the totalhead pressure. This load flucteation made the strain readings rather difficultto obtain. However, a 5 percent error in the force measurements is con-sidered to be somewhat conservative.

Another cause for variation in the results was found to be theirsensitivity to the relative position of the leating edge o the deflection surfaceto the lip of the nozzle. Proper level alignn' ent was difficult since the nozzleslots were not perfectly uniform in height, s. A alignment was subject tocorrection with changing forces on the deflei don surface. The effect ofimproper alignment is examined in more det ll in the DISCUSSION OF RESULTS,

11

PRESENTATION OF RESULTS

The majority of the experimental results which ar-e presented inthis report consist of the surface pressure distributions and pressurecoefficients. The pressure distributions are plotted in two ways. For aparticular nozzle and deflection surface combination, the variation of thepressure distribution along the Coanda surface with pressure ratio forvarious gap sizes is demonstrated. Using the sane data but replotting fora constant pressure ratio, the variation in surface pressure distributionwith deflection surface radius is shown. This method of data presentationwas repeated for the pressure coe'ficients which, c,-rected for flowcompressibility.

Since this experiment involved the use of five aifferent parameterswhich were also varied (4-P. 16. 's, 2-t's, 3-Ro's. 5- Z's, and approximately8-a's) nearly 1000 separate tests were performed. Hence only a small,but significant, portion of the test results heve been presented. All measure -

ments taken forJ=L5 inches have been omitted except those of the lift forcesin Figures 28 to 33 inclusive. In selecting the cases to demonstrate theeffects of the vertical gaps, four values were chosen. These consisted ofzero vertical gap, two values between 1/16" and 1/4 inch inclusive(depending on the jet sheet tnicLness), and a vertical gap just before theflow detached from the deflection surface.

The vertical (lift) and horizontal (drag) forces acting on the deflectionsurface were calculated from the strain gaup readings. Some of thesevalaes were plotted for R0 * 3 inches to show how the lift and drag forcesare affected by the iuse of the vertical gap. However, all of the values ofthe measured lift fo1res were snon-dimslionalized by the produ,:t of thetotal head pressure md aossle exit area. These values were then plottedto demonstra hew the lift •o•*o vriled with the radius of the deflectionsurface; the prss'@ rto was selected as the parameter. The compositeset of graphs were arrangsd 4o show conveniently the effects of both thevertical and boreopta) gap sizes. The non-dimensional lift forces werealso plotted against vertical M size for two horizontal gaps and threequadrants. Aga*n, the pressure ratio was chosen as the parameter. Furtherto assist in the understanding of the effect of gap size on the lift force,the non-dimensional lift forces were multiplied by 100. and the valueswere plotted at a point on a grid which relresented the size of the gap.Contours of isolift lines were drawn. The sign convention used with thesefo.'ces is shown in Figure 2.

In plotting the pressure coefficients, no attempt was riade to connectthe points of a constant pressure. The addition of such lines would complicatethe display and tc id to show that the compressible pressure --- fficientsare dependent on pressure ratio even when allowance is made for experi -

mental errors in the readings (see Figures 14b, a/t = 0, and l7d, a/c = 3/4).

12

In non-dimensionalizing "al, "J", and "e", the noAinal Ve"nof "t" was used. For ease of comparison, the numerical value of the

theoretical pressure coefficients ( -2t/R) shown in Figures 13 to I9 wdetermined from the nominal value of "t" and the radius of the deflectionsurface, Ro.

When the graphs were initially plotted, a point was used as thesymbol for P. R. m 1. 2. During the final preparation of the graphs, thepoints were made larger and appeai" as soiid circles - the same size as the

open circles used for P. R, w 1. 7. In the case where the plotted values torP. R. = 1. 2 and P. R. % 1. 7 are approximately equal, only the solid circleis visible. Appendix I gives the exact pressure ratios used during thepa-ticular tests. The figures state the nominal pressure ratio. It wasintended to show the theoretical pressure coefficient line ( -2t/R) on allgraphs on which the measured pressure coefficients are shown. But, dueto insufficient space, several graphs had to be . ropped so that the data forfour vertical gap sizes could be displayed on one page. Hence, thetheoretical curve is shown only where space permits.

Configuration Notation

The nozzle and deflection surface coa*inatlom are summarizedby a notation which is shown in the following example.

t 1/16 - F 1/4 - Ro 2.O0

This presentatiom is interpretm, left IWIo Iw , as * rder whicM thejet sheet travel6 from the bossl* to thIM Ut1fIg sp oat the deflectionsurface; that is, the jet sheet ouip#ftbf

t /6ntert -gtils e fteW -Which

then, with or without a sr go .t U-tt. inO-sMi de'lectifs mWface.

it crosses 1s e

width f tI lN*W Od by te /4 -

Ro 2.0 U of 2•--h radius.

13

DISCU.;SION OF RESUVTS

(a) Pressure Distribution

(i) Figures 5 to 10

Figures 5 to 10 inclusive present the change in pressure, AP,along the curved jet sheet and are plotted against the non-dimensionaldistance, s/t, from the leading edge of the deflection surface. PT/Pa, thenozzle pressure ratio, is the parameter. Four combinations of verticaland hoA-izontal gap sizes were selected for each figure to show the effectof the gap size on the pressure distribution for a particular nozzle anddeflection surface combination. In plots of large vertical gap sizes(e. g. , Figure 5 (iii' various "a/t" values had to be shown since theultimate "a/t" changL•, with pressure ratio. In these cases, the gap closestto the one prior to flow detachment was then plotted.

From any of these graphs, it is evident that two regions of flowadjustment exist. In between these two regions, the flow follows theconstant curvature of the quadrant.

In general, the first region of flow adjustment was found to extendapproximately one inch downstream from the leading edge of the deflectionsarface, and to be independent of the configuration tested. The length ofthe subsequent attached flow region increased, of course, with increasingradius of the deflection surface, but decreased with increasing size of thevertical gap. The length of the second region of flow adjustment (the regioibetween the attached flow and the trailing edge of the deflection surfacewhere the flow has adjusted itself to the atmospheric pressure) indicateda similar variation with "Ro" and "a". Further, this variation due to "a"

was enhanced when ",A " was , creased. It is Lelieved that the reductionin the length of the attached flow region is caused by the growth in thi'kiiesýand decrease in momentum of the jet sheet, caused by entrainment on thelower side of the jet, and resulting in a reduction (i. e., less negative) in

"AP" across the jet sheet.

In Figure 5(i), for e..ample, the first static pressure tap in thecentre of the 1/4-inch-wide initial flat plate shows a AP g 0 for P. R.-1l..but for P. R.•1. 7 and 2.2, "A P" is positive. Tbhs indicates that highvelocity air from the jet she-et was entering the pressure tap. It is theresult of improper alignment of the nozzle lip with the leading edge of thedeflection surface, that is, a/i r0. In Figure 5(ii),this same pressuretap measured an extremely large negative " AP" for high-pressure ratiosas a result of th- underside entrained air ahead of the deflection surface beiforced around the sharp corner of the leading edge, thus lowering the staticprecsure further.

Figures 8 to 10 inclusive are pressure plots for the t = l/4-inch

nozzle. Due to the thicker jet, the pressure force required to bend the jet

14

sheet is greater, and the ultimate vertical gap sizes are smaller than fort 1/16 inch.

The scatter in the pressure readings, especially for configurationt 1/4 - Fl/4 - Ro 3.0. is caused by imperfect flushness of the pressuretaps in the quadrant.

(ii) Figures 11 and 12

Figures 11 and 12 show "AP" ;or 1. 1/2-inch and various "a/t",as a function of the deflection surface radius, Ro. The theoretical relation-ship given by equation (4) stating that "AP" at constant jet sheet thrust isinversely proportional to the jet sheet radius, R, is qualitatively verifiedin these two figures. Also, this relationship suggests that the integratedpressure force on the deflection surface is independent of "R"; and hence,both the lift and drag forces should be independent of "R," or "Ro". Thislatter hypothesis was also confirmed and is illustrated in Figures 26 and 27.

(iii) Figure 13

Korbacher in Figure 4a of Reference 3 demonstrated that when hisCP. = AP/(PT - Pa) values are plottei for four different pressure ratios,they do not collapse - at least in the attached flow region where the flowfollows the quadrant curvature - into the predicted single horizontal linefor incompressible or compressible flow, given by Cpi a -2t/R. (seeequation (9)). If, however, equation (13), which accounts for compressibility,is used, Korbacher in Figure 4b of the same Reference illustrated that thepressure coefficient for compressible and incompressible flows, Cp = -2t/R,is independent of pressure ratio.

In Figure 13 the values of "AP" along with the correspondingvalues of "Cpc" are plotted to demonstrate again that the pressure coefficientscorrected for compressibility effects are independent of pressure ratio.Even for a thick Jet (t a A/4 Inch), agreement between Korbacher's theoryand the experimental results is quite satisfactory in the attached flow regionwhere the jet sheet follows the curvature of the deflection surface. If thesimpie theory would also include the viscous losses in the fiow, agreementbetween the theoretical line and the experimental values in the attached regionwould be still better.

ib) Pressure Coefficients

(.) Figures 14 to 21

The !ssure coefficients plotted in these figures have all beencorrected for flow compressibility. The graphs of one figure, Figure 14afor example, are plotted to show the effect of the vertical gap, keeping thehorizontal gap constant. At a/t = 0, the static pressure tap in the centre ofthe 1/4-inch -wide initial flat plate measured near atmospheric pressure.

15

As "a/t" was increased, the "AP" measu,-ed at thk tap became negative, an(approached a constant value. Subsequent pressur, taps show increasingsuction pressures on the deflection surfaceý and, the•',fore, indicate a strongebending of the jet sheet with increasing vertical gap. This phenomenon isobserved more easily in these figures than in those- which show the "AP's',since two more vertical gap sizes are shown for a cons~ant " l/t".

In Figure 14a, for a/t = 2 and 4, the suct' n pre•ssure is smaller(less negative) at the end of the first region of flew adustment than it isfor a/t = 0. As the vertical gap increases, the suctiorn pressure in this re-gion increases, and the depression in the curves widi'ns and becomes moreshallow. Just before the flow detaches (a/tr6), nm evidence of this depressicis visible.

If ti suction pressure increases by increasing the size of verticalgaps, then this behaviour should result in an increase of the lift forceexerted on the quadrant by the curved jet sheet flow. This prediction isobserved in Figures 22 to 33 inclusive.

The effect of increasing ".1/t" is shown by comparing Figures 14b,c. and d with 14a for a constant "a/t". Since the radius of curvature ofthe flow between the nozzle exit and attachment to the deflection surface in-creases with increasing horizontal gap, the s.uction pressure, AP, becorneEless negative, and the point of flow attachment to the deflection surface movitoward the leading edge of the deflection surface.

The effect of the horizontal gap size on the pressure distribution,and hence, Cp, was small for values of "1,," equal to one inch or less; forlarger values, the effect was more pronounced and ",&P" became lessnegative. The measured lift and drag forces acting on the deflection surfaceexperienced this same effect of horizontal gap size, and are shown inFigures 22 to 25 inclusive.

The relationship between the theoretical and measured pressurecoefficients shows good agreement in the region of the attached flow forsmall vertical and horizontal gaps. As the size of the gap increases, themeasured values become less negative in comparison with the theoretcalvalues. This variation between the two values which is caused mostly withincreasing horizontal gap 1i3 primarily due to the assumption that the jet sheethas one fre ý and one bound surface. This is not the case, especially for

i ý Ro = 2. 0 inches, because the jet sheet actually starts with two free sur-faces and then, upon bending over the quadrant, the lower surface becomesbound. Also, the losses due to viscous effects are greater for a jet ,vithtwo free surfaces.

16

Op,

Probing the jet sheet would be most beneficial in explaining theeffect which the gap size has on the pressure distr'ibution and measuredforces ac.ing on the deflection surface. It would also be interesting tosee the behaviour of the mixing cone in the jet sheet as a function of gapsize. Since the length of the mixing cone is proportional to the nozzle exitheight, thicker jet sheets can bridge larger horizontal gaps. For the samereason, thin jet sheets can bridge larger vertical gaps.

The pressure coefficients for the other two quadrants and the1/16-inch nozzle are shown along with the same three quadrants ant. the1/4-inch nozzle. Figures 20 and 21 are plots of the pressure coefficientsdetermined from the "AP's" shown in Figures 11 and 12 respectively.

(c) Measured Lift and Drag Forces

(G) Figures 22 and 23

In Figure 22a, the vertical gap is varied, keeping "PT/Pa" and"I It/ constant, to show its effect on the measured lift and drag forcesacting on a deflection surface. P. is quite evident that the measured dragforces were influenced by the size of the vertical gap, the drag decreasingwith increasing "a/t". The drag force mreasured is the resultant horizontalforce acting on the quadrant. Flow which was entrained by the undersideof the jet sheet created a suction force that acted on the back of the quadrantand opposed the suction force on the deflection surface itself.

The lift force initially Increased and then decreased when "a/t"

was increased until the jet sheet detacwd from the quadrant; both liftand drag then fell off to zero. As the horizontal gap La increased from II /t 0 for a/t a 0 and constant, some of the jet sheet flow is peeled offby the leading edge of the quadrant, and results in a pressure force on theback of the quadrant. 71tis pressure force, when added to the integratedhorizontal pr essure force acting on the deflection surface, produced a dragforce larger than diue lift force (see Figures 22a and 22b). As the verticalgap was increased for a constant " A /t", this prexsure force became asuction force and the net drag force experienced a reduction.

In Figure 22b for L/t s 16, the peculiar shape of the lift and dragcurve for P.R.=I. 7 ant 2. 2 is unexplainable, especially since it occurredfor both Ro = 2 Fi.d 4 inc.hes. However; it did not occur at all for t = 1/4 inch(see Figures 23e cind 211-.

No attempt was made to show the ultimate value of "a/t" at which theflow broke away from the deflection surfaces. It may be mentioned, however,that the "alt" at which the flow separated increased with increasing valuesof '•,o". This is seen in Figures 26 and 27. The difference between the liftand arag forces for a constant "a/t", was proportional to the pressure ratio.

17

Since the measured drag force represented the net horizontal forceon the quadrant rather than the horizontal force acting on the deflectionsurface, no further analysis of the drag force was considered.

v'rom Figures 7 and 10, the areas under the pressure curves forP. R.-%I. 2 and 1. 7 were determined with a planimeter, and the resultantforces, Fri , acting on the deflection surfaces were calculated. From themeasured lift and drag forces, corresponding resultant forces, Frm, weredetermined. These resultant forces are compared for various gap sizes inAppendix 11.

For a/t = 0 and 1 1/2 inch, "Fr " is greater than "Fr." because

D" is composed of +c,, forces which are ad itive. If, then, the vertical gapis increased, "Fri" becomes greater than "Fr " since the "secondary" drag1 rmforce (acting on the back of the quadrant) now acts opposite to the positivedrag direction. For .L 2. 0 inches, the difference between the resultantforces is still larger.

(d) Non-Dimensional Lift

(i) Figures 24 and 25

The measured lift forces were non-dimensionalized by dividingthem by "PTAN", and then were plotted in these two Figures for two horizont:gaps. Nate t,:at the thicker the jet sheet, the smaller the vertical gapthe jet sheet can bridge before it detaches from the deflection surface.This behavior is due to the fact that a thicker jet sheet requires a stronger"AP" to bend it around a given curvature. However, "AP" can be mademore negative only as long as the suction pressure in the wedge betweenthe deflection surface and the curved jet sheet prior to its attachment canbe increased; this criterion is a function of the jet sheet entrainment andwedge angle. Therefore, the thick jet sheet detaches when its optimumpossible "AP" in the wedge is smaller than that required to bend the jetsheet enough to attach itself to the deflection surface. The thin jet sheetdetaches when the mixing has penetrated to the jet sheet's center, Lherebylimiting further entrainment and higher suction pressures.

Increasing the radius of the deflection surface reduces "AP" andhas the same effect as decreasing the jet sheet thickness. It enables,therefore, the jet sheet to bridge larger gaps before the "low detaches.

6ii) Figures 26 wid 27

It was noted in Figures 11 and 12 that the integrated pressure forceson the deflection surface in both the lift and drag direction should be inde-pendent of "Ro". To verify this observation, the non-dimensional lift forceswere plotted versus the three deflection surface radii for a constant " I/t"and "a/t". In general, the variation of "L/(PTAN)" with "Ro" is negligiole,buit the results show a considerable amount of scatter. However, if the values

18

are compared for a constant "PT/Pa" and either a constant "t, or "a", theyexhibit the expected trend. It is evident from these graphs that an Increasein the horizontal gap results in an appreciable decrease in the lift force.But, by increasing the vertical gap, the lift force approaches a constantvalue and then reduces to zero when the flow detaches.

In several of the graphs, the lift curves are shown partly by a brokenline to indicate that since no measured value was available, the line wassimply extrapolated. The results of the 1/4-inch nozzle are shown in Figure 27.

(e) Isolift Lines

(i) Figures 28 to 33

Th' non-dimensional lift forces were multiplied by 100, to convertall ratios into integers, and then plotted for a constant pressure ratio (seeFigure 28). The horizontal and verticpl axes are "A /t" and "a/t" respectively,and are positive in the direction shown.

The maximum lift force occurs for a horizontal gap ranging from zeroto 1/4 inch. As the pressure ratio is increased, this maximum lift forceshifts to larger values of "a/t". For PT/Pa * constant, corresponding iso-lift lines are displaced toward larger "L /t" values if the radius of thedeflection surface is increased.

It is apparent from these 11gures for contanl "PT'Pa" •-d "f I/t"*hat two values of ",R/t" provide the same lift force. Therefore, one particular"a/t" and ".1/t" conmaination willgive a maximum lft force. The locus ofthese points forms the gap sio* required for optimum lift. As "Lit" in-creases for a constant "P. R.': the ultimate lift force occurs for larger"a/t". For overchoked jet sheets (t a 116-inch), the shape of the optimumlift line was affected more by "ai/t" tba for subsonic jet sheets (see Figure32). A boundary line which separaes the region of attached and detachedflow can be considered to be located at the bottom of each set of graphs Inthese Figures. If "alt" is made larger than the vertical g•P which corre -

sponds to the limiting lift line, the flow will detach. Similarly, if "i/t" isincreased, a horizontal gap will be re•ached for which the jet sheet containsinsufficient momentum and will not attach itself to the deflection surface,because the "AP" required to deflect the jet sheet will not be possible toachieve. Hence, the limiting lift line must, then, turn back on itself, inthe same manner of the isolift lines.

Comparing the effect of jet sheet thickness for constant "Ro" and"P. R. ", it is seen that the optimum lift line occurs for larger "a/t" when "t"-E iecreased. Again, it is illustrated that thicker jet sheets have ! smallerrange of vertical gap sizes if the flow is to be deflected by the Coanda surface.

19

FLE AM

RMSEfRVlO

COANDA D3FLECTIMOBURFACE

/DRAG 4 IFFORCE BALANCE

GENERAL VIEW

CONVERGENT NOZZLE

AES DIAL (t - I/4 beb)

(b• CLOSE-UP VIEW OF THE TEST SECTION•

FIGURE L T• JUG FOR DETACHII) COANDA SURFACES.

20

-- L

CONVERGENT W(ZZLE

CURVED DEFLECTION

BE LL MO____ '- T

tI ooI

VERTICAL AND HORZZOS6TAL ADJWMT

j FIGUJIE P. SCHEMATIC DETAIL OF NOZZLU AND TEST? BECTIOI4.

S.....

•"" "'•-

I'-•. Eil

I

NOZZLE

\ DEFLECTION~ SURFACE

V

L O

DEJUO14

VERTZICAL MOTION CONTROLOL

NEEDLE ROLLER BEARINGS

ntUDOWAJ FMCZ BB*W ,VERTICAL FORCE

f AGURE 3. SCHEEMI tiC DETAIL OF THE STRAIN GAUGE BALANCE FOR MEASURINGFOPCE3 ACTING ON THE DEFLECTICON SURFACE.

22

TO JETASHEET RIG'T M Uww 23uALa G"nuu, mw

MM IA ICRTU PAC3

TO THE TMM3I

7.3

IP.R.- L3 .

"tl/16 - FI/4 - R,2.0 L7 o

2.2 x

(hi)-2.4 P/t - 8 2/t 0A 3 /•0//t 33 a,/twADJUSTING FLOW -2. ADJUST NGLOW

P - AUTEDUSTG FLOW

-1L6(in H ADJUST'ED FLOA)(in fig.) ,

-0..

0.0

.o / o.a__****~ .--

32 -- - -4 0 16 32 48s/t

- ' (iv)

-2A Pi u U/S. o - . - T 7 T IN G FLO WA, -- 00r ,

0.- 0 1- 32 0.

-L -. - 1 , -, -. -i •.i -

L.E. leL.. /t T, E. L.E. 5/t T. E.

FIGURE 5. EFFECT OF HORIZONTAL AND VERTICAL GAP SIZES ON THE PRESSUREDISTRIBUTIONS ALONG A DEFLECTION SURFACE AT VARIOUS NOZZLE.PRESSURE RATIOS.

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FIGRE 4b.EFFECT OF THE V1.RTIAL 6.P1 ZE ON THE PF.L~sURE COEFFYCIENTS Fý;ORRZCTED FOR FLOW C MRIMSIB1UI Y AT VARIOUS NOZ ZLE PRESSLREHAMMCJ.

34

P.R.sw LS 0ti/if -71/4 - ROL 0 LT70

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LE. T. L ilii. SFFECT OF TH't VERTC&L CAP SIZ ON TUX PRMUlZ COZYFICLINI

CCRRBCTED FOR FLOW CMRDTYAT VARIOU NOZZLE 133W13RATIOS.

35

P.Rmm L3.t/l16 - F!/4 - R 02.0 L7 I

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L. 24 I/t 32 40 48 56L. Z. T. E.

FIGURE l4d. EFFECT OF THE VERTICAL GAP SIZ). ON THE PRESSURE C-OFFICIENTsCORRECTED FOR FLOW COMPRkBSBILUTY AT VARIOUS NOZZLE PRESSURERATIOS.

36

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44

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FIGURE 17a. EFFECT OF THE VERTICAL GAP SIZE ON THE PRUSURE COEFFICIEIITCORRECTED FOR FLOW COMPRMIBITY AT VARIOW NOZZLE PRMEURERATIOS.

45

P.R.U, LI vtV4 - FV/4 -RC2. 0 L20

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FIGURE 17b. EFFECT OF THE VERTICAL GAP SIZE ON THE PRESSURE COEFFICIENTS FIGU

CORRECTED FOR FLOW COMPRESSIBILITY AT VARIOUS NOZZLE PRESSUIlERATIOS.

46

U_/4. -!4 - %LO P. IL-L 1. )P/t -4 L-0.le --- - .-;. a E. - - - *

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L E. 2 4 a/t o I 8 10 12K FIGURE 1lc. EFFECT OF THE VERTICAL G&P EU OW THi PRUVR CWMMCU

CORECTED FOR FLOW COkPRS=MtY AT VAUAM N• LE PR=tUI3RATIOS.

47

P.R.06 LI vWl4 - Fl/4 - ROL 0 L20L7O

-0 16-0.1 i i

Cpc~o -!'- !- -

0. OE I I I a -

0 2 4 s/t 6 8 10 12 14(ii)

-0.1 0,

-0.08 a/t- w0.L250.•o I ±,,1o. I

0 2 4 t 6 8 10 2 14

,-- -5-4-

-0.16 ! ""

v 0. 50

-o.oC - - A0.-0.I 20

11 0 (iv)I

-0. LA......

CPC

.,,•.- 0., 70 1R 2 4" 8A" 10 12 141.. L.I/ T. E.

FIGURE 17d. EFFECT OF THE VERTICAL GAP SIZE ON IHE PRESSURE COEFFICIENTSCORRECTED FOR FLOW COMPPESSIBILITY AT VARIOUSI NOZZLE PRESSURERATIOS.

48

L!/A -FI/4 -R0.

4tT o

- --- --

-0.~Vt 16--

u 46 1 1 0 15 - I s-

-0.08-- ----- -- -

0.0 4 6 -- I i t - I I I I -

01 s/tM

cpc I74k11

0 4 ' 1 1

-0.0 --- : : mml----I 1L. E. T. 2.i- -

FIGURE l8a. EFFE(C' OF THE VERTCAL T. I.I NTEPR UzCZnM

CORRECTED FOK F IlOW COMPR3UIDIUT AT VARIUS NOZZLZ pR=URRAMIOS.

49

P. P: .~ 1 vtt/4 - FI/4 - R03.0 1.2 0

l/t =2 1.7 0

41)

-2t/Ro -0. 16667 -0T -0

-K---, -t -I

-J---------o--o---- --------a/ -

0 4 5/ 14 16 18 20

00-0.16 Oi .... 7 7 -

0 (A I I)0 2 4 6 84w 10 12 14 l is 2

9 (ul)-0.o6 1 1 1 % a

Cp.

-0.06~ ±~ VlWoIt7 t~-Ikt-L OD t 0. 8 60 a/t -0. 75

O. T iý - I I I'll1 4/t 1 10 2 14 16 1

• {iv)

Cpc -"

0. l- t 2 - -0 2 6 a 0 2 14 1a isL. E. xlt T. E.

FIGU.E 18b. EFFECT OF THE VERTICAL GAP EIZE ON THE PrREs&URE COEFFICIENTSCORRECTED FOR FLOW COMPRESSIBILITY AT VARIOUS NOZZLE PRESSURERATIOS.

50

P.M. LI v,WV4 - I/4 C L2L L3

Pt 4

-I 0 I-7-0 .16 '" -

-0•tz 1-I,

_ _ t -

0.TJI f ?I .A I 16 I0 4 6 N/t 9 "A 14 16 11

(u)

-. 16 -a -a-J~tJL

c Tr ft I I I

0. 04 406 10 1 14 4 I)

-_ 1 1 -"l i' I...-o.1p Ie •T1 - - -i -,.i

-0 . 0 8 ! . ..

-' - 1. 0II ' -t. Los -

L 1 1i1

0.0 4 01 0 I 1

T. --,-- -~J'L - J

Lt. T.L

FIGURE 18c. EFFECT OF THE VERTICAL GAP 3Z1 ON TMIC PREUURE COX1VICIMCORRECTED FaR FLOW COMP I ILITY AT VAMW NMZLB PRURZRATIOS.

•5.

P.R.= Li vtV 4 - k1/4 - .R3. 0 L2i

Pt - L7 0

-0.16 0)-F-- -- T, TF_ FHi .

c 0.

0.I t I I I I t ,= I H ~

0 2 4 6 8 10 12 14 16 13 20,I t

-p 4 -- - - - -

0.08 a ~7f

o° 2 4 6 10 1 14 16 18 205/t

(Wil

cpc • ii -

-0.0 --- OIL-- ----

VT TV - ja/t - L----0 2 4 6 1 10 12 14 16 1

_1. 25 o o-~m -/ -L 3tt5s-0. EL ,/ I ,•....

0 2 4 6 8 10 12 14 16 Ilb

L.E. sit T.E.

FIGURE 18d. EFFECT OF THE VERTICAL GAP SIZE ON THE PRESSURE COEFFICIENTSCORRECTED FOR FLOW COMPRESSIBILITY AT VAROUS NOZZLE PRESSURERATIOS.

52

~*0

fU

w oa to

aw "r

*O.w go

00. 0 0A

bms _ _LI

53I

2w-,- - -

n- - -

-00- 4wM

0c P

0 C5

-~54

___1m

B;0 Ob-

mb b

-o W

F.

-40 M- MI-4D4

I II

000

a.0 1

C4 1 1 9

---ftii

CSRI

- sw

94 go e

co 0

C?.

C6 C6 06

56 ~

L4410 14

-fU Z

04 Hot

*Z 0* 03

64 JX

0 ~0- A?

00 0 o0.5 .- 4

A? D44 a

S4 0 cc

I5

ini

Nil..

1~ b4

71 v4

- - 0

CD 6

d

'.4 . 'I 7*18

tI/6-I/4R0 .OL2 9 0

LL0

D -7 -- --

4 1Vbt

4--

0E --7

0 2 3 45 6 7t

FI1UR 44.EFC FTEVRIA A SZ KTEMAUE MADDA

L OCSATN NTEDFETIKSRAEA AIWNZL

PRSUE AiS

Poe59

L Dtl/16 - FI/4 - N3 0 P.R.e 1.2 1 v

1.2 *1.7 o *2.2 x o

L

(00o 2 3 4 5 6 7

a/t

(i )

L

00 2 3 4 5 6 7 8

a/t

FIGURE 22b. EFFECT OF 'I HE VERTICAL GAP SIZE ON THE MEASURED LIFT AND DRAGFORCES ACTING ON THE DEFLECTION SURFACE AT VARIOUS NOZZ LEPRIESSURE RATIOS.

60

L D

ti/4 - FJ/4- Ro3.0 P.R. 1.1 v v

1.7 o o

(1) (ii)

2o - - --- 20 -I IL L I

D 1/ . .. . D 'ti.

12 12

(1b) ow - --

4

0.0 0.25 0.50 0.?5 00 & 0.0 0. 2 0.0 0.75 LOO

X/t

FIGURE 23a. EFFECT OF THE VERTICAL GAI SIZE ON THE MWASURED LIFT AND DRAGFORCES ACTING ON THE DEFLECTION SURFACE AT VARIOUS NOZZLEPRESSURE RATIOS.

61

L D

tl/4 - F/4 -R 0 3.0 P.R.=. L. v vL2 0 0L7 o 0

(z) _________(- )I i! +

28... 28 -4 :~1 r

24 24 ...... -f - -

20 20: --

D iD

12 12 -

- -- -

(lb) -(lb) 4

0.0 0.25 0.50 0.75 1.00 0.0 0.25 0.50 0.75 1.00

a/t a/t

FIGURE 23b. EFFECT OF THE VERTICAL GAP SIZE CON THE MEASURED LIFT AND DRAGFORCES ACTING ON THE DEFLECTION SUFFACE AT VARIOUS NOZZLEPRESSURE RATIOS.

62

j,4,

H r~J

C O :

ca0

----- 4 w

0 p. 'a

t9

0 - 0 -

0 0

t ilN

U'Pa

0 0Lo

t/16 - F1/4 -R 0 % P.R.= LI1L20L7 o

1/t o 1/t 16 t .32 2.2x

I ayt~0 a/ t-- -!to0.40 0.40 0 r.

2 3 4 2 3 4 2 3 4

Ro (Inches) (Inches) RGo (Inches)

(•v Wv (vi)

A,'t=

0. 40-- - -- ,0- .L _ _L L

PTA NýTAN =:4= PTAN

o2 - 0.20 20.20

o-0 - - -

0. 0. c- --

2 3 4 2 3 4 2 3 4Ro (Inches) n e) Ro (Inches)

(vi) (vu) (4i)-- 2'- -- - -2

0.40 - 0.40 0.

L -- L

PTA1 v.I PTAN

0.20 -.. .. . 0.2

2 3 4 2 3 4 0.0 2 3 4Ro (Inches) Ro (Ic..he) Ro (Inches)

FtGUR E 28a, EFFECT OF DEFLECTION SURFACE RADII ON" ' HE NON-DIMENSIONAL 1UFTFORCE FOR VARIOUS HORIZONTAL AND VERT14"AL GAP SIZES AMD NOZZLEPRE.SSUR•E .RATIOS.

65

tVWI - F/4 -R1% P.R,- LI 1L 2 P1.7 0

1/t - o Z/t. 16 ,/t 312 2.2x

(I) (a) ___ (il)

/Lm3 a/t, a/t 30.40 0.40 0.40- -I. L0

FTAN PTAN )f- - _T_.2 L -T- 0.2 -- o I -

0.0 20.O0i0.

3 4 2 3 4 2 3 4R0 (Inches) Ra (Inches) Ro (Inches)

(iv) (v) (vi)

t4 a/t

L L _ L I

Tj PTAN ---N

0.20 ---- - 0.20 0.20,

0.0 2 T4 0.0 0.-2 2 3 4 2 3 4

R0 (Inh.,M) R% (Inches) R0 (Incheb)

010i (VIU) (ix)

A/t a1/tuG a/t 60. j- 0 0.40

L - -4- LN PTAN PTAN

0.20 0.20 -- 0.20 "• -

0.0 1 1 .-0 ± 0.0

2 3 4 2 3 4

Ro (Inches) R0 (Inclies) R0 (Inches)

FIGURE 26b. "FFECT OF DEFLECTION SURFACE RADII ON ',HE NON -DIMENSIONAL LU*-TFORCE FOR VARIOUS HORIZONTAL AND VERTICAL GAP SIZES AND NOZZLEPRESSURE RATIOS.

66

i7

ti/4 - FV4 - Ro% P.R. so L I

//1t0 t . 4 8it. Lo

,)(ui) (iii)W 40

a/It 0 tit " a/t 0

0.40 - 0.40

L1 L LPT.N -_-- - . PTAN

0 020 0.20 0-. 4-

.. 0 22 3 4 2 3 4 1H0 (Inches) R0 (Inches) R0 (Inch~es)

(iv) I) (vi) ,

't 0.25 a/tu 0.25 a/t 0. 251' FAN 1J PTAN.

o -_ '.4 0.4-0

%o (Inches) %o O ch..,) % uh.

PU) rA m , (NAN PTAN

/ 0.2-0 -,o|- 0.2 2 7 4 0. 2/_-0. -L -0. 0.

2 0. 4 3 3 4 23 4

Ro (Inches) R0 (inches) R0 (Inches)

W#

H"Gt.. 27a. EFFECT OF DEFLEC5ION SURFACE RADII ON atHE NON-DIMEIONAJ L.IFT0

FORCE FOR VARIOUE HIORIZONTAL AND VERTICAL GAP SIZES AND NOZZLe.

PRESSURE RATIOS.

0.40 0. 0

tl/4 - F!/4 - Ro-k P.R.-~. LI v

L.20

I/t - 0 f/t- 4 fit - a L7

Wi (ii) {i

a/t 0. 75 ,'t - 0. 775 a/t O.750. 40 0. 40 J__-. 0. 4u -L L i -

PTAN . PTAN --- PTANo.220- - 0.20 0.20

0.0c O.-i- 0.02 4 2 3 4 2 3 4

%o (Inches) Ro (Inches) Ro (Inches)

(iv) (v) (vi)a/t 1: h 0 a/t ,1. 00 a/t 1.l 00

L L~ _ L -

PTNPTA----------- ----PANo. -0 0. 200 20 .. • 1

(.nL , -0. -- 0.0

2~ 3 2 3 .• 4 2 3 4Ro (Incme) Ro (Inches)

(vWi (viii) (4

a/i .1.5 A/t L25 I.t 12q0.40 - - - 0.40 0.0

L L LTTAN -- . PTANO. 20! 1 0 __0.20----- 0.20----- .20 0. -

2 3 4 2 3 4 2 3 4

Ro (Inches) R, (Inchem) Ro (Inches)

FIGURE 27b. EFFECT OF DEFLECTION SURFACE RADII ON THE NON-DIMENSIONAL LIFTFORCE FOR VARIOUS HORIZONTAL AND VERTICAL GAP SIZES AND NOZZLEPRESSURE RATIOS.

68

4' 0 0

0Pp x LAO

0

Pk0

C -<

CA .i~ N!4'X

o I ZN

9 0

4'0 >

44 2 1 F

1004'0 a0n

0 14

I ~ciNo c4

C 4 V4' i0 CI tQ 4' cc2 '

69

tl/4 - F•/4 - R02. 0

.oit

0 2 4

:7 7~

a./t I

OPTIMUM LIFT LAi" [i - i tP.R. 1.12LR•h I I1 (1 1

I/tS2 4 6 8

"140 270%1 50 200

a/t 1I! . .. '

OPTIMUM LIFT L LNE

2 ~ P.- .• 1. 2

(at)

0 8

FIGRE29 CNTURSOFCOSTNTNON-DIMENSIONAL LIFT FO=V O--HRZOT

AND VERTICAL GAP SIZES AND NOZZLE PRESSURE RATIOS.

70

LMt-tN

NC

z

NN

*0

Z

r In

00 0

0 'In

N; C1 0

71u

CI

tI/4 - FI/4 - R0 3. 0

1/t00 2 4 6 8

(Ii

a//,

NOtI-D TIMUM LIFT -LINE 6

PTT

A P. R.P N .O

7/t

2 4 6 8

P.R.=, 1. 2

I %A I I

NON-DIMENSIONAL LIFT = -PTAN

FIGURE 31. CONTOURSS OF CONSTANT NON-DIMENSIONAL LIFT FOR VARIOUS HORIZONTALAND VERT'ICAL GAP SIZES AND NOZZLE PRESSURE RATIOS.

C4

CC4

040

4 P4

0. L..

z Cl U _eq.

0 Cl

o& C4z

?l N* 4* 4

0 0.70

tl/4 - F - R4. 0

'it0 2 4 6 b

(1)0

lit00 2 4 6 8

130 "llo-. 1006.12-1255

lit

J/t0 0

pCK- .MI• m4L7 tooL

LL

NON-4DDGI=IOAL LIF ----

PTAN

FIGURE 33. CONTOURB OF CONSTANT NON-DIMENSIONAL LIFT FOR VARIOUS HORIZONTALAMD VERTICAL GAP SIZIS AND NOZZLE PRESSURE RATIOS.

74

BIB LIOGRAPHY

1. Bailey, A. B., Use of the Coanda Effect for the 1 /i.f ection of JetSheets Over Smoothly Curved Surfaces, Part I, Universityof Toronto, Institute of Aerophysics, Technical Note No. 49,August 1961.

2. Bailey. A. B., and Gariand, D. B., "Development of a CompressedAir Facility", Bulletin and Annual Progress Report 195P.University of Toronto, Institute of Aerophysics, October 1959,pp. 42-43.

3. Korbacher, G. K., "The Coanda Effect at Deflection Surfaces Detachedfrom the Jet Nozzle", Canadian Aeronzutics and Space Journal,Volume 8, Number 1, January 1962, pp. 1-6.

4. Palouste 500 Series, Technical Data, Iesue 1, Publication No. E. 1003,Blackburn-Turbomeca, Blackburn & General Aircraft Ltd.,Engine Division, Brough, E. Yorks, England, November 1957.

5. Roderick, W. E. B., Use of the Coanda Effect for the Deflection ofJet Sheets t)ver Smoothly Curved Surfaces, Part II, Universityof Toronto, Institute of Aerophys~cs, Technical Note No. 51,September 1961.

75

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APPENDIX I

EXACT PRESSURE RATIOS FOR PRESSURE DISTRIBUTIONS,PRESSURE COEFFICIENTS, AND MEASURED FORCER ACTINGON THE DEFLECTION SURFACES AS IN FIGURES 5 to 33 INCLUSIVE

t no •** PT/ Pa PT / Pa- PT /Pa PT / Pa

(inch) (inch) (inch) (1. 1)* (1.2)* (1.7)* (2. 2)*

0.0 1.13 1.20 1.71 2.221/16 2 0.5 1.10 1.20 1.71 2.20

1.0 1.10 1.20 1.71 2.192.0 1.10 1.20 1.71 2.25

0.0 . 10 1.20 1.71 2.211/16 3 0.5 1..10 1,20 1.72 2.24

1.0 1.10 1.20 1.73 2.202.0 1.10 1.19 1.70 2.22

0.0 1.10 1.21 1.71 2.221/16 4 0.5 1.11 1.21 1.71 2.28

1.0 1.10 1.21 1.71 2.172.0 1.10 1.20 1.71 2.22

0.0 1.10 1.20 1.71 N1/4 2 0.5 1.10 1.20 1.71

1.0 1.10 1.20 1.71 02.0 1.10 1. 20 1.70

0.0 1.10 1.20 1.701/ 3 0.5 1.10 1.21 1.70 D

1.0 1.10 1.20 1.702.0 1.10 1.20 1.72 A

0.0 1.10 1.20 1.72 T1/4 4 0.5 1.10 1.20 1.69

1.0 1.10 1.19 1.72 A2.0 1.10 1.20 1.71

* Nominal pressure ratio.

'* Pressure ratios shown in the Figures are average values during a test

run; i. e., a = 0 to flow detachment from the deflection surface.

77

E APPENDIX IT

IV) NM___, __4 _ 0

C~ C) ctr-t-4 C.J 3)0 C6 t-i - ) C4

4.Q~M ob o o

z .

0

m o

0

z U') 0 00a 0 to 0 0L O0t

00 0

C) ~ ~ ~ ~ l In0c c0 00 6 10O.

eq &000 n t-0.

a4 -4 -

C144

Security ClauaificatjonDOCUMENT CONTROL DATA - R&D

ICi ostiruowmr Acwi~Iy (c..PinU "okwJ 120 NIP**? 99CUM11 C LASSIPICAYWN"

institute for Aerospace Studies UcasfeUniversity of Toron~to I $owToronto. Cnad o"_____

3 NEPO)"r TIYLA

THE COANDA EFFECT AT DEFLUCTION SURFACES WIDELY SEPARATED FROM THEt JET NOZZLE

4 DESCRIPTIVW H0'15 (TyPo dojts.)

None5 AUTYIRO(S) (LO.' ý.. hu' "OW.. j.'Wu.)

Bennier, S. D.

6 ME PONT 13ATE [.TTL NO OF plows 76 no or er0eebr1964 I78

So COýrRACT GM QXANT .0 9 0ft* ONGATIftRS REtPORT NUW89%(3)

t, Rja,. T No USATRCON ,64 -70 e~ee~sAe ~% S

fask 1D1214D1A14203 ______________________

10 A V A IL AftLITY L-M17 ATION NOTICEIS

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I I SUPPL fUIlS ARY MOMTI isP~S U A*TW £ TV

None FW htis, yir iml

I I ABSTRACTI

The f low phenomenon in bWt liqud so #"ase of Uhe AIhuee of a jet or jetsheet to a solid sfwAw Mee beoa mined the Caeemt 11106e t. hs repea Awmessean experimental invextigati$m, wkh** k"e ogma sh dot the 00806 ofne" is

flat-plate surfaces. The heriumtuii ojeete sfshmaU i weverhebe jet sheets

sucessuly bidgd terstedr a NAma per eemiem eia( .1 S.1 w 1.2 1.7, e

o 2 n d thr e suffrfac efotm pressu es were , arecorwthaded. pg bll*

D D 1473 UnclassifiedSoeuaty Cleaues"c~

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