Use the Coanda effect for the deflection of jet sheets over smoothly curved surfaces. Part I. Test rig and some tests with subsonic, choked and overchoked jet sheets

USE OF THE COANDA EFFECT FOR THE DEFLECTION OF JET SHEETS OVER SMOOTHLY CURVED SURFACES

Part 1. Test Rig and Some Tests with SubsonicJ ChokedJ and Overchoked Jet Sheets

by A. B. Bailey

USE OF THE COANDA EFFECT FOR THE DEFLECTION OF JET SHEETS OVER .SMOOTHLY CURVED SURF ACES

Part 1. Test Rig and Some Tests with Subsonic, Choked, and Overchoked Jet Sheets

by A. B. Bailey

r=

•

ACKNOWLEDGEMENT

This work was carried out at the Institute of Aerophysics. University of Toronto, and the author wishes to thank its Director,

Dr. G. N. Patterson for the opportunity to conduct this investigation.

The author is also indebted to Dr. G. Korbacher for suggest-ing and supervissuggest-ing this work.

This investigation was made possible by the financial and technical assistance of AVRO Aircraft Limited and the Defence Research Board.

Thanks are due to W. Roderick and R. Smith for their assistance with the experimental work and to D. B. Garland whose help in all stages of the work was much appreciated.

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TABLE OF CONTENTS

Page

NOTATION _ii

1. INTRODUCTION ₁

Il. TEST FACILITIES ₃

2. 1 The Air Supply ₃

2.2 Test Rig ₄

2.3 Force Balance and Deflection Surfaces ₄

2.4 Apparatus ₆

IIl.

FORCE AND MASS FLOW CALIBRATION 6

3. 1 Force Gauge Calibration 6

3.2 Mass Flow Calibration ₆

IV. TEST OBJECTIVE 7

V. TEST PROCEDURE 7

'

.

VI. DISCUSSION OF RESULTS 8

6. 1 Turning Efficiency - Defini tions 8 6.2 Preliminary Qualitative Testing 10

6.3 Turning Efficiency 11

6.4 Surface Pressure Distributions 13

VII. CONCLUSIONS 16

(ii) NOTATION

'f m mass flow

~

density

A nozzle exit area - 1. 17 sq. ins.

V velocity

F

force

W weight flow

~ ratio of specific heats g gravitational constant R gas constant T tem perature PA ambient pressure

,

P surface pressure

PJ jet pressure gauge (=PT-PA) P T jet total pressure

FV

measured vertical force

FR

measured horizontal force

'?

v

vertical turning efficiency )

) see para. 6. 1

'7",

horizontal turning efficiency)

M Mach number

0( initial deflection surface angle a speed of sound

'

.

..

SUMMARY

In this series of tests a rectangular convergent nozzle with an exit height of 1/8" (nominal) was used. The Coanda deflection surfaces were combinations of a series of flat plates of 1/4" to 3/4" in length

followed by quadrants of 2. 0", 2.5", 3. O",and 4. 0" radius. The nozzle was operated at pressure ratios of 1. 2 up to 2. 1 (nominal). The vertical

(

'?v

)

and horizontal ( t( ... ) turning efficiencies were evaluated from the measurem.ents of the vertical and horizontal forces, which the deflected jet sheet exerted on the Coanda surfaces. Together with these force measure-ments, detailed surface pressure distributions were recorded.

For each of the deflection surfaces tested, a systematic variation of the flat surface length and the initial angle of the surface indi-cated that the magnitude of t?V is primarily determined by the initial sur-face angle. It is further apparent from this study that the length of the flat surface tends to reduce the turning efficiency, whereas an increase in pressure ratio seems to increase it.

For each of the quadrants tested, an almost constant

optimum value of

Y7.v

was found which occurred at larger initial surface angles the larger the quadrant radius was. There was a consistent varia-tion of this angle with the radius of the quadrant. It was not positive to correlate this data with that of Von Glahn (Ref. 5) using the radius of his circular arc surfaces as the correlating parameter. However, good agree-ment was obtained when a comparison was made on the basis of surface

radius to nozzle height ratio. This parameter also seems to explain an apparent anomaly in Von Glahn's results concerning multiple-flat-plate and circular arc deflection s.urfaces. The present tests indicate th at with the

1/8" convergent nozzle)an optimum value of. 92% can be obtained for F{v The surface pressure distributions indicated two marked effects, 1) the existence of regions of supersonic flow and their attendent shock systems,and 2) the existence of a region of separated flow at the upstream edge of the deflection surface. One characteristic of under-expanded straight jets, the regions of expansion and compression at super-critical pressure ratios also occur in curved jet sheets and are observed as pressure fluctuations in the pressure distributions over the deflection surfaces. It is believed that this shock pattern,at pressure ratios higher than investigated here,will have a detrimental effect on the turning efficiency of the surface. Von Glahn's results at pressure ratios of up to 2. 9 indicate that turning efficiencies start to decrease .

•

MODEL NOMENCLATURE ,

N 1/16, N 1/8, and,N 1/4 - Convergent nozzle exit Height, - 1/16", 1/8", and 1/4"

F 0 - Initial m ounting pla te - 1 /411 thick

F 1/8, F 1/4, ... - Flat surface extension, - 1/8", 1/4ft, ... thick C 2.0, C 2.5, C 3.0, and C 4.0 - Curved surface radius - 2.0", 2.5",

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1. . INTRODUCTION

H. Coanda found that when air was ejected from a rectangular slot, it would attach to an inclined surface fixed to the nozzle exit. Further-more, he found that flow deflection by a single flat plate was limited to a particular maximum angle. However, by placing a series of flat plates, each at an angle to the preceeding one, he was able to deflect the flow through 1800 _.

Coanda deduced that for the flow to deflect in this manner, there was a reduction in surface pressure at the nozzle exit, which caused an increase in velocity at this station. Furthermore, ássociated with this velocity increase, there was an increase in .air mass flow through the nozzle. He then concluded that these two factors together must produce an increase in the available jet thrust. It was this claim of thrust augmentation which made the use of the "Coanda Effect" so desirabie for application to 'VTOL and STOL aircraft. Coanda further emphasized the need for a sharp inter-section between the nozzle and the attached deflection surface for optimum performance.

Metral (Ref. 1) performed a theoretical analysis of. the pro-blem, considering the flow of an inviscid fluid over a flat plate placed at an angle to the inittal direction of the flow. This analysis predicted that such a surface would cause an increase in the mass flow through the nozzle and also that the flow would attach to the surface. Coanda's claim that a sharp corner was.i.n.ecessary for the realization of flow deflection was given some weight by this analysis.

A further theoretical treatment of the problem by Yen, (Ref. 2), in which he replaced the angled flat plate by a smoothly curved surface, yielded the following conclusions: 1) viscous effects are predominant and an inviscid analysis is not very meaningful, 2) replacing the sharp corner by a smooth transition caused a reduction in the increase of mass flow through the nozzle over the sharp corner case.

In considering a solution of the problem including viscous effect, Yen concluded that the difficulties presented by such 1::i.n analysis are such as to preclude the possibility of a practical solution.

/ '

As far as is known to the present author, these two analyses represent the only theoretical approaches to this problem.

Voedisch (Ref. 3) carried out an experimental investigation in which he studied the effects of nozzle exit geom etry and initial plate angle on the flat surface pressure distributions. These experiments were limited to low pressure ratios across the nozzle and no forces on the deflection surfaces were measured. In order to ensure attachment of the flow to the surface, it was necessary to have side plates extending over the whole length of the deflection surface. Voedisch conc1uded that placing

such a surface at the nozzle exit produced features similar to that of diffusers in that it produced an increase 'in mass flow and velocity at the nozzle exit. He considered that by using a series of flat plates, each at an angle to the

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preceding one, it should be possible to deflect the flow through a greater angle than would be possible with a single plate. He reasoned that a sharp corner strongly accelerates the flow around it and the slight flow separation which re su lts causes turbulence which in turn promotes mixing. and a

consequent renewal of the energy of the boundary layer. The efficiency of such a flow deflection device was therefore strongly dependent upon viscosity. To reduce the viscous losses to a minimuIIl"he suggested that a smoothly curved surface be used right up to the point of separation; at this point" the introduction of a sharp corner should renew the boundary layer energy and hence prevent flow separation.

Von Glahn (Refs. 4 and 5) has carried out detailed investiga-tions into the performance of a series of single-flat-plate, multiple-flat-plate, and some curved deflection surfaces over a wide range of operating pressures in conjunction with rectangular convergent nozzles. Measurements of

vertical and horizontal forces and pressure distributions along the deflection surfaces were made. In evaluating the suitability of shlgle and multiple-plate or curved deflection surfaces for STOL and VTOL applications, Von Glahn concluded tl1at it would be better to design an aircraft around the device rather than attempt to incorporate it in an existing aircraft.

With regard to the multiple -flat-plate and curved deflection surfaces, he found it possible to achieve turning efficiencies

('lv )

of 88% and 81. 5% respeciively. He concluded that neither of these values repre--sented the maximum that could be obtained and that more sophisticated surfaces should produce higher values of

'Iv

.

In light of Voedisch's remarks concerning the energy loss at a corner, Von Glahn's findings of superior efficiency for the multiple-flat-plate surface over the cu;rved surface seems inconsistent. However, it must be noted that the tests were cafried out with different nozzle heights, a fact which should explain the apparent anomaly.

Von Glahn's pressure distributions over the curved surfaces were characterised by large fluctuations in the suction pressure. He con-cluded that these fluctuations were caused by local discontinuities in the surface contour, and could be smoothed by making modifications to the surface contour.

In order to maintain attached flow over the deflection sur-faces he found it necessary to have side plates extending over the whole length of the deflection surface. Although an investigation was made into the effect of side pl:tte height on deflection surface perforrpance. it waS. not .suffi~ , ..

ciently detailed to enable any conclusions to be drawn concerning the

optimum height of the side plates. However, it did transpire that to ensure flow attachment at all times the height of the side plates should be at least as great as the nozzle exit height.

HUler Aircraft (Ref. 6) in their study of the "Coanda Effect" approached the problem with the hope that they would be able to achieve

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thrust augmentation with such a device; thrust augmentation being defined as the ratio of the measured vertical force to the measured. undeflected thrust of the basic nozzle. They believed that th is would be possible since some tests carried out at the Cornell Aeronautical Laboratory had shown augmentation ratios up to 1. 7: 1 for a deflection surface defined by a cubic equation. It was in an attempt to confirm these favourable augmentation ratios that Hiller aircraft repeated the Cornell work exactly. The results of their investigation showed no thrust augmentation. A further analysis of the Cornell results showed that the apparent thrust augmentation arose from a misunderstanding concerning the measured undeflected thrust of the basic nozzle.

Hiller did show, however, that the Cornell designed deflection surface, when used in conjunction with a rectangular nozzle and anannular nozzle, did produce a high value of turning efficiency, e. g.

t'l~

=

88%. Though these tests were limited to a maximum supply pressure of 13 inches of mercury, Hiller concluded that the reduction in pressure over the hump of the profile was sufficient to cause supersonic velocities to be present there. In contrast to the pressure distributions over the curved surfaces in Ref. 5, the surface pressure distributions in this case are smooth and regular. Hiller's report also gives a good review of most of the readily available experimental and theoretical analyses and also details of conversations with current researchers in this field.

The foregoing survey of the available literature on the

Coanda Effect indicated that there was a continuing need for further experi-mental investigations.

Af ter studying Refs. 3, 4, and 5, it was decided that further investigations into the turning efficiency and surface pressure distributions of curved deflection surfaces would be useful. However, it is not the

intention of this investigation to establish the configuration with the maxi-mum turning efficiency, but rather to evaluate the importance of several nozzle and deflection surface parameters . . For each of the configurations tested, the basic nozzle thrust, the forces on the deflection surface and the surface pressure distributions will be measured. The following vafiables are to be studied: jet height, deflection surface radius, initial angle of the surface, length of its flat plate portion

J and the nozzle pressure ratio. As in Refs. 3, 4, 5,and 6, attention at present will be con-fined to rectangular convergent nozzles ónly, which. will be tested at sub-critical, sub-critical,and supercritical pressure ratios.

Il. TEST F ACILITIES 2. 1 The Air Supply

Compressed air was supplied by a small gas turbine engine (Blackburn and General Aircraft Turbomeca Palouste 504)~ the air being

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bIed off the compressor at temperatures of up to 2300C and pressures of up·to 55 p. s~' L-a.·-~e .engine was mounted on a simple frame: and housed in a small.sound-proofed room. Intake and cooling air for the engine and room was brought in from outside the building and the engine exhaust gases were ducted out to an externally mounted muffler. The engine performance and air delivery were remotely controlled.

The hot compressed air was diffused to an 8" diameter pipe and then passed through a cooler which utilised the main water supply. Downstream of the cooler was a length of thin-wall stainless steel pipe of low stiffness, followed by the mass flow measuring section. This con-sisted of a traversible pitot-static tube, connected tQ an inclined ma,no

-meter,and a thermometer. Figure 1 shows the lay-out of the laboratory. 2. 2 Test Rig

Af ter passing through the cooler the air enters a 24" dia-méter horizontally mounted settling chamQer. This chamber has two flat

. ends, one of which is solid, the other has an opening into which is fitted . a .bell-mouth collector (Fig. ~). The purpose of the collector and settling chamber is to provide good flow characteristics to the nozzles attached to the downstream end of the collector.

. Figure,. 3 shows that the settling chamber is supported by four thin spring steel straps, which allow for frictionless fore and aft-movemenf of the chamber. Such movements are prevented by~ 1) the stiffness of the air supply pipe, 2) the stiffness 'of a strain-gauged beam mounted on a rigid support at the upstream end of the chamber (see Fig. 4). The purpose of this strain-gauged beam is to, measure the basic nozzle thr~st. In ord~r to ''make thls force measuring system sensitive, it is necessary to have the proportion of the nozzle thrust reacted by the beam as large as possible. On considering the tnanner in wbich the duct systern deflects under load., it will ... be noted that the centre of rotation of the

•

settling chamber is located at the downstream cooler flange (see Fig. 1) . . Resisting this rot~tion is the stiffness of the air supply line and the strain gauged beam. In order t? route as much of the nozzle thrust as possible through the beam, a secti~n of thin-wall stainless steel pipe' was placed just downstream of the cooler. In this way, the pipe stiffness was kept low withoût compromising. the overall strength of the system.

2.3 Force. Balance ~d Deflection Surfaces

In earlier Coanda Effect inve~tigations, it has been the prac-tice to attack the d«rllection surfaces rigidly to the nozzle. In, this study, a departure from this approach is made in th at the deflection surface is not rigidly attached to the nozzle exit. Some justification for this approach is contained in Ref. 4 where it was found experimentally that small gaps between the nozzle ·and deflection surface dil1 not apparently affect the· per-formance characteristics of the deflection surface tested. The advantages

•

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of detached deflection surfaces are; I} to allow for changes in the deflection surface angle without the use of hinges. Such hinges will usually give rise to variable-sized gaps between the nozzle and surface. When-the surface is mounted independently ofthe nozzlt; thesize of this gap can be controlled. 2} It allows for the design of a force balance exclusively for the forces

acting on the deflection surfaces and independent of the dead weight of the pipe system. 3) It allows for greater flexibility in the testing of different surfaces.

The general lay-out of the force balance and deflection sur-face mounting arrangement is shown in Fig. 5.

\

The deflection surface under test is attached to the mounting plate by two bolts. When the angle of this surface is changed, the upstream edge of the surface moves with respect to the nozzle exit plane. The two adjusting screws bring the surface back to its correct position with respect to the nozzle . . For normal operating conditions, the horizontal gap between the surface and the nozzle can be readily adjusted to 0.010".

Figure 5 shows that the deflection surface mounting column and its adjustment screws are attached to a base plate. This base plate is connected to the horizontal and vertical force measuring beams by six rigid pin-jointed links. In the ends of these links are small needIe roller bearings which' keep friction forces at a minimum. When a vertical load is applied to the system, with this arrangement of links, the vertical links transm it the whole forc e while the horizontal links rotate without trans-mitting any force. The converse is true for a horizontally applied force. These statements, however, are only true for' small rotations of the system. Sidesway of the system is prevented by two wire braces (Fig. 3) which do not introduce any constraints in the vertical or horizontal directions.

The curved surfaces tested were circular arcs in form (quadrants) made from aluminium. On the centre line of these surfaces, a series of static pressure holes were provided to measure the surface

pressur'e distribution (see Fig. 9). Reference 6 has shown that for a nozzle aspect ratio of the order that was tested here (i. e. 64: I), side plates on the deflection surfaces would not be necessary for flow attachrnent to the sur-face. However, each surface was fitted with sideplates in order to eliminate any effects due to sideways entrainment of air and flow separation on the measured forces and surface pressure distributions. In keeping with the results of Refs. 4, 5, and 6, these sideplates have been made at least as high as the nozzle height.

Three convergent nozzles are to be used in this series of tests, their heights being 1/16",

1/8"

.

and 1/4". The 1./4" height repre-sents the maximum nozzle height possible if sonic co.nditions at the nozzle exit are mandatory. This report deals with the test results of the 1/8" noz zIe only.

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2. 4 Apparatus

Because of budgetary limitations it was necessary to design and build two multi-tube manometers for the measurement ofthe surface pressures and nozzle jet pressures. As these manometers were also re-quired for the ground cushion test work, mercury had to be used as the mano-meter fluid, a condition which reduced the accuracy of these pressure mea-surements. One of the manometers has forty tubes each 60" long, split up into four banks of ten, each with a separately adjustable reservoir. The other was 84" taU, with five tubes and a fixed reservoir.

A commercial pitot-static tube was used to sense the dynamic pressure in the 8" pipe. This dynamic press,ure was measured with an inclined manometer. Air temperature was measured with a stand-ard glass thermometer.

A Tatnall Strain Indicator was used to measure the outputs . of the strain gauges.

lIl. FORCE AND MASS FLOW CALIBRA TION

To calibrate the strain-gauged beams,the deflection surface base plate and the links were removed. The strain-gauged beams were connected together in pairs by passing a rod through the holes in the mount-ing lugs on the beams. Weights were hung at the centre of these rods and the outputs of the strain gauges were measured on the TatnaU Strain Indi-cator. For both the vertical force beams, the calibration curve is linear over the full range of applied forc e (Fig. 6). Figure 7 is a calibration curve for the horizontal force measuring beams.

On calibrating the nozzle thrust gauge, two undesirable

fea-tures came to light (see Fig. 6). 1) It was very insensitive, indicating an error in the choice of the beam stiffness. 2) There was not a linear rela-tionship between the applied loads and the Tatnall Strain Indicator readings. Furthermore, when this gauge was used under normal nozzle flow

condi-tions, it became apparent that the flat end of the settling chamber became distorted and an additional input was given to the force beam. These fail~

ings could not be corrected in the time available so no direct nozzle thrust measurements could be made in this series of tests.

3.2 Mass Flow Calibration

It was quickly apparent that the system chosen for mass flow measurements could not give ,results of the required accuracy. The initial transverse surveys indicated that the flow in the measuring section was still strongly influenced by the turn in t,he pipe coming out of the cooler. The resulting flow asymmetry precluded reliable mass flow measurements.

,

.

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IV. TEST OBJECTIVE

The test objective was to investigate the dependence of the vertical and horizpntal forces an,d surface pressure distributions on the nozzle pressure ratio, the initial angle of the deflection surface, the radius of the deflection surface,and the nozzle aspect ratio for convergent nozzles. V. TEST PROCEDURE

The configuration - flat surface. curved deflection surface·and side plates - was attached to the mounting plate (see Fig. 5) and set at the required angle. With the model in position the engine was started and at the same time, the. water to the air cooler was turned on. For all the tests, the water flow rate throughthe cooler was a maximum since attempts to adjust this flow rate to get a constant air temperature for all pressure ratios

proved impractical. It was found that th is ope'rating technique kept the air temperature sensibly constant (ave rage value

=

SOC).

Before any measurements of force or pre.ssure were made, the whole system was allowed to attain equilibrium. The engine and air-bleed controls were then adjusted to give the operating conditions to be

investigated. Adjustm ents were then made to the deflection surface in order to bring it to its correct position relative to the nozzleexit. Care was

taken throughout th is series of tests to ensure that the horizontal gap was always close f:o Q 010" and that there was no vertical displacemenf of the

deflection surface .

At each test condition, the following measurem ents were made:-1) The Tatnall Strain Indicator readings were recorded.

2) The surface pressure distributions indicated on the multi-tube manometer were photographed for reduction and evaluation at a later date.

3) The air temperature was recorded.

4) The nozzle tota.l pressure as indicated by a pitot tube mounted just upstrearn of the nozzle,e.xilt was measured.

Àt eaèh initial plate angle s.etting, test readings were repeated for the rang'e'of nozzle pressures under consideration. At the conclusion of the pressure variation, the initial angle of the surface was changed and the above procedure waS r.epeated. This procedure was ~hen repeated for the. range of initial surface angles under consideration for each of the de-flection surfaces under test, using in all tl?-ese tests the l/S" convergent

(8) VI. DISCUSSION OF RESULTS

6. 1 Turning Efficiency - Definitions

, Three methods of defining the vertical turning èfficiency'

wiU be discussed here: '

(i) Von Glahn has used the definition:

'1v •

Fv measured

F 'measured

This method relies soley on measured quantities, i. e. the measured vertical force acting on the deflection surface and the measured thrust of the undeflected jet.

(ii) Another definition of turning efficiency is:

f1v

=

(F

Y

4ffr )

M"".ured

(F/wJT,-

)Idea.1

" In this definition the terms in the numerator F v' Wand TT are measured quantities . The denominator

(F)

éan be sh,own to be a functionof noz7.le pressure ratio only.

wrr,:-

Ideal

, We can write for the nozzle thrust

force:-Since Mach number M and the temperature ratio

To./

be expressed in terms of pressure ratio we can write

~

•

or

l

~ ~

(Po-)--ti-fr(~)_1;'_IJ

:fz

'N

ff,.

.9

f.,..

lL

P

T )

ij

F

w~

- f..

,

(

,

Pa.\

p-;J

for

can

" When a convergarit nozzle is operating at supercritical pressure ratios,there is a pressure t~rm in the nozzle thrust., i. e.

'I'

..

.

or So for (9)

.6.

F = (. 5283 PT - Pa) A P Á F

= (.

5283 - ~) A PT

P T

F

=

total

+(Q,5'~~3- ~)

'

'

AT?

P,-In order to express th is thrust force in the form

F

it is necessary to express the term A PT in a different form.

WK

_T )

Consider the nozzle mass flow:

-W

3

m

=-

f

A

\I

~

Pct

A

~

'i>

"

R{r

.

M

RTo.-F!. .

P

T

~

A

I r

M

P-r

fT:

/11-

J'R

.

or

WfÇ

.

=

Pa.

r-ç

IT

g

.

M.

~

Pr

p.,.

~~.JR

As before, bothC-r

I

~"'2. and M can be expressed in terms of the pressure ratio Pa/PT, so a.

7;,

(

W

_{A P}

ff,: \

::

F (

Po..;fJ

ï ' )

T

)Id.,al

. , WhenJP a/PT ~ .5283 then this mass flow parameter is a constant and equal

fa .

397 (TT is in OK)

SC,

AP,.

=

w

~

D'~~7

We can now express nozzle thrust for a convergent nozzle as:

~

~

0-5283

(:ff.)

.

=

CC

~p-a.

) •

rT IT ldeal j T

0'5283

CL)

=

L(Ii.)

+

(O-5"~83

-

P~R-)

W/TT Idet>.1

J

ft

S{RtO'~3

O'3'!!fl

. T

The mass flow and thrust functions are shown in Fig. 8.

(Hi)

(10)

Finally, turning efficiency'can be defined as:

~

= (

F

UPr)

Meo.sured

(KpT)rdeal

Where the values F v' A,and P T in the numerator are mea-sured quantities.

Then

For

The nozzle thrust force can be expressed as:

F

=

F

.

AP'-AV

L

~

tor

~" ~ O.5~83

,

r

L

-

~

'6'

Po.

~

R.

-~

l!'

J

.

+

~

Q,5283 -

Pa.

~

(A

P

T

lrde<L' -

lS'-t •

Pr

(p.;)

-1

~'O'52S5

P,:"

Pr

The variation of this thrust force parameter with pressure ratio is also shown in Fig. 8.

It was the intention of this investigation to compare vertical and horizontal turning efficiencies as defined by the above three methods. However, due to the difficulties encountered in the measurement of the basic nozzle thrust and the mass flow, it has only been possible to 'use the third definition of turning effic iency .

The horizontal turning efficiency ~H is defined in the same manner as the. vertical turning efficiency.

re

H

== (

t='

ti

~

P, ) Meo.::.ure.d

~~I

6.2 Preliminary Qua1.itative Testing

Prior to the arrival of the multi-tube manometers, some

. qualitative testing was carried out.

One of the first tests was to determine the suitability of a lampblack and oil flow visualization technique. With no side plates on the

,

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on the deflection surfaces. the regions of sideways entrainment and flow separation were readily apparent. Wh en small side plates were fixed to the deflection surfaces. these regions 'of sideways entrainment and flow separation were practically eliminated. Figure 9 gives a good indication of the quality of flow visualization obtainable with this m ethod. (The sm udge on the surface occurred af ter the surface was removed from the flow). In obtaining these pictures. another advantage of the use of non-rigidly attached deflection surfaces becomes apparent. The surface is coated with lamp-black and oil at such a distance below the jet thért the 'flow does not attach to it. When the flow is at its desired condition,the surface is rapidly brought iuto position. Af ter a suitable time interval,the surface is quickly retracted for photographing at a later time.

6.3 Turning Efficiency

In this series of tests. attention has been 'confined to the 1/8" convergent nozzle. On inspection,this nozzle showed that due to manufactur-ing difficulties. the nozzle height was not constant across its width. Since a knowledge of the jet exit area is necessary for the estimation of turning efficiency. the nozzle height was measured at a series of .. ,stations and the exit area was calculated from these values. In this series of tests. the deflection surfaces were fitted with sideplates having a height at least as

great as the nozzle height.

Because the deflection surfaces are mounted indep~ndently of the nozzle. these surfaces experience the full actual nozzle thrust. This means that when a comparison between the present results and those of Von Glahn. where the surface is rigidly attached to the nozzle. is to be made. we have to realize that:

ltl4

(Von Glahn)

=(1-

t?

~) (Present results )

Therefore for the convenience of such a comparison and the added convenience of comparing the vertical and horizontal turning efficiencies for a surface on the same graph. horizontal turning efficiency is plotted as

(1 - ~

H ).

An evaluation of some of the first vertical force data indicated that unexpectedly low

Y)y

values existed at large initia! surface angles. This was found to be caused by the deflected jet impinging on the base plate of the mounting rig (Fig. 5) for the deflection surface. This was causing a downward force on the strain-gauged beams and in this way accounting for the reduction in the measured vertical force on the surface. To prevent

the jet sheet from impinging on the base plat~,a large deflector was placed close to the downstream edge of the surface under test. In Figs. 10 and 13. the effects of shielding the base plate on the measured vertical and horizontal forc_es respectively are shown for zero initial angle. It will be seen that the deflector does not produce any effect at all on the measured forces for this configuration. In Figs. 10 to 15,the results of a series of tests at various

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initial surface angles are shown. They indicate that a't an initial angle of 200_{, the vertical force is reduced by 30%, whereas the horizontal forc,e} is reduced by only 4%. These test results also show that the jet sheet remains attached to the surfaces up to total deflection angles of 1100.

A limited investigation into the effect of the length of the flat surface was also made. The results of these tests are shown in Figs.

16 to 30. Testing was confined to the 2.5" and 3. 0" radius quadrants in combination with flat surfaces ranging in length from 1/4" to 3/4','.

Figures 16 and 17 present the force data on the 2. 5" radius quadrant with flat surface lengths of 1/4", 1 /2"., and 3/4". For the 1/4" and 1/2" flat surface lengths, the vertical and horizontal forces are prac-tically the same, but both decrease as the length increases to 3/4". In

Fig. 26, these results are plotted in terms of

n"

and (1 -

'?t-4 ).

Tests on the 3. 0" radius deflection surface indicate the same trend, that is, a

decrease of Fv (Fig. 18) or

t}v

(Fig. 27) with increase of plate length at 00 initial surface angle. Rowever, at initial surface angles of 300"the flat plate appears to exercise a beneficial effect upon F v (Fig. 21) and

t(V

(Fig. 30). Since the optimum angle for this surface occurs at an angle less than 300 , the beneficial effect of surface length at 300 _{does not} repre-sent the optimum

trv

value for this surface.

These results (see Figs. 26 to 29) show that flat surface length at small initial angles has a detrimental effect on the turning efficiency and that a long flat surface is not helpful in producing an

optimum value of

7v .

These findings seem to be at variance with Von Glahn's results, however, for thicker jet sheets. He considered that a length of flat surface at a particular initial angle was essential in order to eliminate any regions of positive pressure over the initial portions of the surface, thereby increasing ~. The present tests indicate that for a particular deflection surface 'radius,it is the initial surface angle which determines the magnitude of f)"l . They also indicate that the effect of increase of pressure ratio across the nozzle on

'1v

is small and that t')v

approaches a constailt value at the highest pressure ratios in this test series. (1 -

7

ti ) is shown to vary slightly with pressure ratio (see Figs. 26 and 27).

The results of the investigation into the effect of initial sur-face angle, nozzle pressure ratio,and radius of the deflection sursur-face on F v and FR are shown in Figs. 31 to 40. As with the preceding data, smooth curves can be drawn through the experimental points. Figures 41 to 45 show the values of

"tv

and (1-

'1 .. )

that can be derived from the experimental results of Figs. 31 to 40.

It will be noted that testing has been limited to maximum initial surface angles of 300 . This does not represent the maximum angle through which the flow could be turned,but rather an upper limit imposed by design specifications. '

'f

•

(13)

For the five configurations tested. covering surface radii of 2. 0", 2: 5", 3. 0", and 4. 0" and flat surface lengths of 1/4" and 3/4", the variation of the maximum value of '>'tv with surface radius is small. Fig -ure 46 shows that at a press,ure ratio of 2.1, ~v varies from 89% to ~ 91% for the radii tested. Intuitively, it would seem that, due to viscous effects, there should be a decrease in turning efficiency as the surface radius

in-creases.

Figures 41 to 45 also show that for each of the surface radii tested. the angle at which the optimum value of 'iJv occurs is dependent upon the surface radius. The variation of the inÜial angle of the surface

with surface radius for ,<?ptimum

1v

is shown in Fig. 47 at a nozzle pressure ratio of 2.1. This curve indicates that the flat surface angle increases with surface radius.

A comparison of the present results with those of Von Glahn on the basis of surface radius does not yield very good agreement. However, quite good agreement is obtained if the results are compared on the basis of the ratio, surface radius to nozzle height (see Fig. 48). Quite apart

from the agreementbetween the two sets of data, it does explain the apparent anomaly in Von Glahn's results concerning the greater efficiency of ·the

multiple-plate surface over the curved surface. It can be seen that when a

comparison is made on the basis of the above ratio, the multiple-plate con -figuration is operating at a somewhat lower value of this ratio than that for his curved surfaces .

In Fig. 49, a comparison was made of the present results with those of Ref. 5 for the variation of initial surface angle (optimum)

with the surface radius/nozzle height ratio. It was hoped that this co.rn-parison would indicate a reason for the slight inconsistency that occurs between the two sets of data for the 7. 10" and 7. 15" radius surfaces .

Finally, in Fig. 50 (at a pressure ratio of 2. 1) the present results and those of Ref. 5 are compared with the theoretical cosine relationship. It win be noted that the present results are presented in two forms, one on the basis of optimum

'Iv

'

the other on the basis of minimum (1- ~ ... ) . This pre-sentat.ion was chosen since either value of

1'1

or (1- ~ ... ) may be of interest depending on the requirements of the application. For example, a hovering vehicle of circular planform would require a maximum

7"

value.

regard-less of ( 1-

7 ... ),

for maximum economy. On the other hand, a conventional aircraft would need a combination of

1v

and (I

-11+

)values such that the total thrust required is a minimum. (assumed for a hovering condition also). 6.4 Surface Pressure Distributions

In presenting the surface pressure distributions (Figs. 51 to 68), several methods of presentaÜon have been used iD: order to emphasize particular features of these distributions .

Before any attem pt is made to discuss the form of these dis-tributions,it is considered pertinent to discuss some of the known facts.

(14)

concerning flow out of convergent nozzles and the interpretation of surface pressure measurements at near sonic velocities.

Reference 7 presents the results of a study of pressurè distributions over a circular arc airfoil at high subsonic speeds. It indiea-tea. that":at these flow conditions.,the boundary layer adjacent to the surface

affeds the measured pressure in such a manner that Mach numbers ca1cu-lated, using these measured pressures, are lower than the true Mach numbers. For exarnple, true local Mach numbers of 1. 04 were found to be only 0.87 when they were calculated from surface pressures. In the present tests, the flow over the surfaces is to a large extent in the sonic Mach number range so th at any Mach numbers calculated from the measured surface pressures would"be lower than the true Mach numbers.

In Ref. 8, a study is made of the structure of highly under-expanded" jets. The jets under discus sion in Ref 8 were circular,but there seems to be no reason why the general observations of that report should"

not be applicable to rectangular jets. Figure 69 shows the structure of such a highly underexpanded jet. In the present tests, the jets are only moderately underexpanded. This has the effect of modifying the form of the intercepting shocks (Fig. 69) such that they intercept on the jet axis giving rise to the familiar diamond structure in the jet wake. Associated with the expansions and compressions in the jet wake are expansions and contractions in the jet boundary. There is reason to believe that these fluctuations in the jet boundary persist for some distance downstream of the nozzle exit. However, as the jet becomes more and more diffused due to mixing with the quiescent air,these fluctuations should die out completely. It is a characteristic of both the present results and those in Ref. 5 that there are alternate troughs and peaks in the surface pressure distributions. At the low surface radius/nozzle height ratios of Ref. 5, these variations do not have sufficient length in which to mix fully with the quiescent air and the variations are quite marked. In the present tests at higher values of

this ratio where the mixing lerigth is much greater, the flucttiations are of lesser magnitude.

Reference 8 shows th at the position of the first normal shock is a function of the ratio of the nozzle pressure and the ambient pressure. With an increase of nozzle pressure ratio,the norm al shock moves further dównstream. This fact is qualitatively apparent from a study of Figs. 51 and 52 for pressure ratios greater than 1. 65. It is assumed that the shock systern is evidenced by the sudden rise in surface pressure .

Up to the station at which this sudden rise in pressure occurs, it is fair to assume that the jet total pressure is the same as that measured just upstream of the jet exit. Using this value of total pressure and the

:;:::;'~d surfac;:res{su~e~he;:e~n:Jmf~

ean be ealculated from the

p

:;t, - •

'

.

(15)

An analysis of the pressure distributions shown in Figs. 51 and 52 suggests:thal supersonic speeds are present at the jet exit. The varia-tion of the Mach number at the nozzle exit is given in Fig. 70. Bearing in mind the results of Ref. 7, it will be realized that these calculated Mach numbers will be less than the true Mach numbers. One would expect th at a shock system at the Mach numbers indicated in Fig. 71 would cause boundary-Iayer separation. However, Ref. 9 shows that such a separation will not occur for Mach numbers less than 1. 4.

Referring again to Figs. 51 and 52, it is apparent that at the lower nozzle pressure ratios,a region of separated flow exists just downstream of the nozzle exit. Reference 10 provides a graphic example of a related phenomenon. In this case,a schlieren photograph of the flow '

through a nozzle, designed to operate 'at supersonic speeds,at-.a below-design pressure ratio, shows the flow leaving the nozzle throat and attaching to one wall of the nozzle diffuser only. The region of detached flow upstream of the final flow attachment point is clearly defined. Also clearly shown in this photograph is the above-mentioned diamond shock structure in the deflected jet.

A further example of th is separation phenomenon is given in Ref. 11. Here a study was made of the flow through a sonic nozzle and a sudden expansion of flow area. It is shown that provided the pressure ratio across the nozzle was high, the flow would attach to both sides of the expanded section. However, as the pressure is lowered, a limiting pressure is reaehed where on leaving the nozzle, the flow attaches to one side of the expanded region onJy. A tentative conclusion th at can be drawn from these observations and applied to the present results is that as the pressure ratio across the nozzle is increased,the limiting pressure will be reached when the flow will separate from thé surfaee. Another significant eonclusion drawn in Ref. 11 is that the behaviour of the sonie jet is determined to a large degree by the eondition of the nozzle bounda.ry layer at the nozzle exit, i. e. the jet flow can be affeeted by the nozzle length.

When such a region of separated flow exists just downstream of the nozzle,it is evident that at the junction of the nozzle and the deflection surfaee there will be an expansion fan through which there is an increase in the loeal Mach'number. On the reattachment of this flow to the deflection surfaee,the flow direction is changed by passing through a shock system. Figures 51 and 52 show that this shock extends over a finite distance, indi-cating in all probability the assistance of a lambda, shock where the'normal shock in the stream interacts with the surface boundary layer.

Intuitively, it would appear that as the pressure ratio is inereased) the total pressure loss in the jet would increase due to the increased strength of the shock system. ' The present results do not bear this out specifically, but some of the higher pressure ratiodata of Ref. 5 (PT/Pa ~ 3. 0) indieate that

?v

is tending' to deerease at these higher pressures.

(16)

Figures 53 to 67 show the effect of initial surface angle and nozzle pressure ratio on the surface pressure distribution. These

distributions illustrate why none of the configurations tested with zero in.itial angle give high values of

"tv

.

At zero initial angle, the suction pressures over the initial part of the surface are lower than those for angles of 100 and 200_{. The Fo - C 2.5 - N 1/8 configuration (Figs. 53 to 57) s.hows the} .steady increase in length of ~he separated region as the nozzle pressure ratio is increased at an initial surface angle of 200 _{. Though th~ magnitude} of the pressure coefficient decreases with increase of pressure ratio, the suction pressure in the separated region. increases. This increase in pressure is similar to that predicted in Ref. 11. Also, the periodic struc-ture of the jet flow over the curved surface is well illustrated in these graphs. The flow over the curved surface seem s to be com pletely independent of

flow conditions at the jet exit, i. e. of pressure ratio and flat surface length, provided the flow is attached to the surface. To emphasize this point, the surface pressure distributions have been replotted, takiI:1g the downstream edge of the surface as being the origin of the graphs (see Figs. 68).

VII. CONC LUSIONS

The fact that the deflection surface was not attached rigidly to the nozzle (as has been customary to date) does not seem to have had any adverse effects on the test results. Th~s method of mounting the deflection surface allows for a more sensitive force measuring balance and considerable flexibility in the testing of various deflection surface~.

Although it has only been possible to consider one turning efficiency definition, it is considered that the definition used gives a real-istic .appreciation of the effects of the parameters investigation.

Yen (Ref. 2) has shown theoretically that deflection of the jet flow by a smooth continuous deflection surface would be less efficient than the deflection by a sharp corner. The present test results confirm Yen's analysis in that it has been shown that the optimum value of always occurs at angles greater than zero degrees.

A useful parameter that has been used in the correlation of . the present results with those of Von Glahn has been shown to be the, ratio

of surface radius /nozzle height. Projected tests on 1/16" and 1/4" con-vergent nozzles should be invaluable in establishing the valiçlity of th is parameter. Of the factors affecting the turning efficiency of a particular surface, initiçtl surface angle was found to be of most significance. A length of flat surface prior to the curved surface seems to serve no useful purpose, except in the case of large initial surface angles ( ~ 300 ). In fact,if this length is excessive, it exercises a detrimental effect on the turning efficie.ncy. It is evident that there is a lower limit to the surffl.ce radius to nozzle height ratio, below which the turning efficiency decreases rapidly. The upper limit of this rati,o was not reached in the present tests.

(17)

A turning efficiency, of

1

_v

=

92% was the maximum value obtained with srnooth curved surfaces at a pressure ratio of 2. 1. Although up to this ratio there seerns to be only a srnall variation of r(""1, it is antici-pated that for substantially higher pressure ratios, there will be a decrease in the value of

'7.v .

The surface pressure distributions are characterized by a region of separated flow at particular conditions of nozzle pressure ratio and initial surface angle. The variation of the pressure in this region is sub-stantially the s arn e as tha t shown in Ref. 11., i. e. an inc reas e of suction pressure in the separated region with increase of nozzle pressure ratio. Another characteristic of these results is the existence of regions of de-creasing and inde-creasing pressure on the curved surface'. It should be noted that these pressure fluctuations are similar to those observed in the wake of underexpanded jets.

It has been shown that regions of supersonic flow exist at the jet exit, the speed of the flow increasing with increase of pressure ratio.

It i~ considered that further increases in the nozzle pressure ratio will lead to 1) shock induced flow separation 2) a decre~se in the turning efficiency due to the increased tot al pressure loss through the normal shocks occurring at the higher flow"speeds. Further testing of the existing configuration at higher nozzle pressure ratio would be valuable in establishing the validity of the above conc1usions.

1. Metral, A. R. 2. Yen, K. T. 3. Voedisch, A., Jr. 4. Von Glahn, V. H. 5. Von Glahn, V. H. 6. Gates, M. F . 7. Carroll, J. B. Anderson, G. F. 8. Adamson, T. C., Jr. Nicholls, J. A. 9. Mager, A. 10. Lukasiewcz, J. (18) REFERENCES

Method of lncreasing Fluid Stream by Diverting lt from lts Axis of Flow, Coanda Effect. Trans. Rept. No.

F-TS-823-RE, WADC-AMC Feb. 1948.

On the Laminar Mixing of a Two-Dimensional Compressible Jet. Department of

Aero-nautical Engineering, Rensselaer Poly-technic Institute, Troy, New York, TR AE 5501.

Analytical Investigation of the Coanda Effect, Air Materiel Command, Wright Field,

Dayton, Ohio, Report No. F-TR-2155-N. D (1947) AT. No. 9881.

Use of the Coanda Effect for Obtaining Jet Deflection and Lift with a Single Flat Plate Deflection Surface. NACA. TN 4272,

June, 1958.

Use of the Coanda Effect for Jet Deflection and Vertical Lift with Multiple-Fla!-Plate and Curved-Plate Deflection Surfaces. N. A. C. A. TN 4377, Sept., 1958.

Static Lift Characteristics of Jet Slots -A Clarifying Study of the External Ejector, Hiller Helicopters A. R. D. 213.

Boundary-Layer Effect on Local Mach Number Measurements on a Circular Arc Profile. J ournal of the Aeronautical Sciences, Readers Forum, June, 1956. On the Structure of Jets From Highly

Underexpanded Jets into Still Air. Journalof the Aero-Space Sciences, Jan. 1959.

Prediction of Shock Induced Turbulent Boundary-Layer Separation. Journalof the Aeronautical Sciences, Readers Forum, March, 1955.

Diffusers for Supersonic Wind Tunnels, Journalof the Aeronautical Sciences, Sept. 1953.

11. Wiek, R. S.

(19)

The Effect of Boundary Layer on Sonic Flow Through an Abrupt Cross -Sectional Area

Change. Journalof the Aeronautical Sciences, October, 1953.

..

.

--10

11

FIGU RE I

DUMP CHAMBER FOR EXHAUST GAS

2 ENGINE EX HAUST PIPE EXTENSION

3 AIR INTAKE SHJTTER

4 PALOUSTE ENG'ME

5 ELE.CTRIC LEADS

6 CONCRETE BLOC K WALLS

7 REFRI G ERATOR TYPE DOORS

8 FLEXIBLE CO U PLING

9 DIFFUSER

10 OUT EP WALL

11 FLEX I BLE CO IJPLI N G

12 WATER ~OOL·ER PIT

---'I~ 13 WATER COOLER

I,.

SCHE I'tfATlC LAY OUT Of' LA80RA-mRY

l4 STAINLESS STEE'L SECTION 15 FLOW MEASURING SECTIO,.

16 SETTLING CHAMBER

17 N OZZLE

- - 1 - _. -- - -

-RESERV61R

BELLM OUTH COLLECTOR

XCHANGEA8LE NOZZLE

T SURFACE EXTENSION

CURVEO SURFACE

IN ITI AL ANGt.E VARIATION

VERTICAL AND HORIZONTAL

1

/AOJUSTMENTS

~

..

SETTLING CHAMBER

\JNDER PRESSURE THIS END PLATE DISTORTS

AlN GAUGED BEAM

OX BEAW SUPPORT FOR HRUST BEAM

"GURE 4 SCHIMATI C LAY- OUT OF THI 9ETTLING CHANBER THRUST

.

'

...

ANGLE SETTING

HORll.ONTAL MOTION CONT ROL

'"

~/

"

VERTICAL NOTION CONTROL

HORIZONTAL FORCE BEAMS

FIGURE 5 . SCHEMATIC LAY- OUT OF BALANCE BEAMS

SU RFACE

t

~

ERTICAL FORCE BEAM FVI~ FV

a:

o

t-.:t ~80~---4---~---+---~----~r---r--~--1 Q ~

z

ë

a: t-U)

:f

ct Z t-I---+---t----LI F T REA R ~ 60 ~---4---~---+---~~----~---~---1

~

Q ct &&J a: lAl .J .:t U (I) LIFT FRONT .J 40 ~----~---+--~~-r~u----r---,---~----~ .:t t-Z &&J 2 lAl a:

~

20 ~---+~-.~4---~---_r---T_----_!---1 NOZZLE THRUST

o

' 0 20 40 60 LOAD- LB.

~

o

...

_c U lilt Cl Z Z

~

...

Cl) ~ -' 200'----~~---~----~----~---~----~

!'50

r---~---+---~T-~---~----4

ti

...

C!) z Cl

.,

lil a:: lil -' C

'"

Cl) -' ~

100

~---+--~---~---+---4 Z lil 2 lil a:: U

z

50r---+---r---~---~----~

o

o

20 40 60 LOAD - LB.

O'3~---~~~---+---~

0'2~--+---4---+---~~--~ 1·0

o·e

1'0

D

o

o

1'0 0'8 0'6

PRESSURE RATIO 'kIPT

<

0,8 0-6 0'4 0'2

o

, -,

I

-',0 FO- C21/2- NI/8 INITIAL ANGLE

=

0 0

v

V

V

BALANCE SH IELDEO 0 BALANCE UNSHIELOEO 0

.

1'4 l'S 2'2

PRESSUR E RATIO PT/PA FI GU RE 10 EFFEC T OF SHIELDI NG THE BALANCE ON THE

FO - C21/2 - N 1/8 INITIAL ANGLE

=

10° O,8---~---~----~---_r----~ O,6~----~---+---4_~~--~~--~---~----__; BALANCE SHIELDED 0 8ALANCE UN SHIELDED 0 0'4 ~----_4----~~~----~---~----~---~----~ 0,2

o

1'0 FIGURE 11 2'2 1'4 ,>

.pRESSURE RATIO PT/PA

EFFECT OF SHIELOING THE e'ALANCE ON THE MEASURED

FO· -C21/2 - N

1/

8 F1j/AP. T I N ITI A L A N G LE

=

20° 0'8 ---~----~---~---.---~----_r----_, 0'6~----~--~~~----~--~~---T---I----_; 0'4 ~---+----~+---+-=~~r---~~---~---, 8ALANCE SHIELDED 0 8ALANCE UNSHIELDED 0 0'2 1---h~----1~----~---_+---T'_--__r--_;

o

1'0 1'4 _2'2

PR ESSURE RATIO PT/PA FIGlJRE 12 EFFECT OF SHI ELDING THE 8ALANCE ON THE MEASURED

()8

o's

0'4 0'2

o

1'0 F IGURE 13 FO-C21/2- NI/8 INITIAL. ANGLE: 00

BAL.ANCE SHI EL.DED 0

BALANCE UNSHIEL.DED 0

-~

~ ₀

V

. /

V

, 1'8 2'2 PRESSURE RATIO

Pr/

_PA EFFECT OF SH IELDI NG T HE BALANCE ON THE MEASURED

FO - C21/2- N 1/8 INITIAL ANGLE • 100 0·8 .~ ».

.

_{BALANCE SH'ELDE 0} 0 8AL.ANCE UNSHIELOED 0 0'6 I"\. ~

w---

~

r

1/

VU

,

0·2

o

,'0 1·8 _2'2

PRESSURE RATIO PT/PA

FIGURE 14 EFFECT OF SHI ELDI NG THE BA LANEO ON THE MEASURED

I ; •

FO- C2V2-NI/8 ~N ITIAL ANGLE : 20° 0·8 ---~---T---~---~----~ BALANCE SHIELDED 0 BALANCE UNSHIELDED 0 0·6 0'4 ~---+---~~----~---+---+---~~----~ 0'2 ~---+---~----~~----~---+---4---,

o

1·0 1'4 1'8 2'2 PRESSURE RATIO PT/P A

FIGURE IS EFFECT OF SHIELDI NG THE BALA NCE ON THE MEASURE 0

0·8 0'6 0'4 0'2

o

1'0 FIGURE 16 INITIAL ANGLE

=

0°

o

Cl FO-C21/2- N 1A3 FO -FV4-C2V2 -N

V8

FO - FI/2 -C21!2 - N 1A3 1·8 2'2 PRESSU RE RA T 10 PT

IR

Ä

EFFECT OF FLAT SU'RFACE LENGTH ON MEASURED

F~R T INITIAL ANGLE: 0° 0·8 ---~---~---~---~----~ FO -C21/2-NI/8 0 FO- F 1/4-C21!2- NI/8 0 FO- F

1/2 -

C21/2-N

V8

6. 0'6~----~-+---~---~----~---4---~----~ 0'4~---4---~--~~~~~-4---~---+---~ 0·2 ~---~~--~~---+---+---~---r---,

o

1'0 FIGURE 17 1'4 /'8 2'2 PRESSURE RATIO PT/P A EFFECT 0 F FL.AT SURFACELENGTH ON M EASURED HORIZONTAL FORCE

INrrlAL ANGLE • ~

0·8 __ ----__

---~----~---~----_r---~----_, 0·6~---+---+---+---~~~~---+---~ 0'4 ~----~----_+~~--~---~----_+---+_----_1 0·2

o

FIGURE 18 FO-C3'0-NI/8 0 FO - F 1/2-C2

V2 -

N

VI

6 1'4 Ie 2'2 PRESSURE RATIO PT/p. A

EFFECT OF FLAT SURFACE LENGTH ON NEA SURED

I N I T I A L A N GLE. I 00

0·8

v

~

/

V

~

0·6 0'4

/

FO-C3'0- N 1/8 0 j FO-A/2 -C30-NV8 6 0·2

o

"0 1·8 2'2

PRESSU RE RATIO PT/PA

F 'GURE 19 EFFECT OF FLAT SURFACE LENGTH ON M EASURED VERTrCAL FORCE

.NITIAL ANGLE

=

20° . . ; 0.8 P---~---~---~----~~----~---~----~ 0'6 ~---+---r---~~~~r---+---r----~ 0·4 FO- C3·0- NI/8 0 FO-FI/2-C3'0-NI/8 A 0'2 ~---+---+---;---,---+---+---1

o

1·0 1·4 1'8 2'2

PRESSURE RATIO PT/PA FIGURE 20EFFECT OF FLAT SURFACE LENGTH ON MEASURED

INIT/AL ANGLE = 30° Fy/A'T 0·8 ~----~---~---~---~----~---~----~ 0'6 0-4 0·2

o

1·0 FIGURE 21 FO- C 3'0- N 1/8 0 FO- F1/2- C3'0- NI/8 6 1'8 2·2

PRESSURE RATIO Pr/PA EFFECT OF F"LAT SURFACE LENGTH ON MEASURED

INITrAL ANGLE -: 00 0-8 .. .. 0-6 0-4

~

~

V

~

V

FO~C3-0-NI/8 0 FO- FI!2-C3-0- N 1/8 6 0-2

a

-

.

.

o

1-0 1"4 1-8 2-2

PRESSURE RATIO PT/PA

FIGURE 22 EFFECT OF FLAT SURFACE LENGTH ON MEASURED

I NITI AL A N C,LE: 100 -. -0-8 0·6

~

~

~

~~

V

0-4 FO- C3-0 - NI/8 0 FO- FI/2-C3-0 -NVS ~ 0'2

o

1-0 ·1·8 2-2 PRESSURE RAT 10 PT/P A

FIGURE 2'3 EFFECT OF FLAT SURFACE LEN GTH ON M EASURED

0'8 ~----~----~---~---r---r---~---,

0'6 ~---+---+---~~----~----~~~---+---~

0'4

o

FO- Cl' 0 - NI/8 0

FO- FI/2-C3 0 NI/8 Ij.

1·0 1·4 1'8 2'2

PRESSURE RATIO PT/PA

FIGURE 24 EFFECT OF FLAT SURFACE LEN6TH ON MEASURED HORIZON TAL "FORCE

INITIAL ANaLE 11 30° fM lAPT

o·a

~----~----~---~----'---~---r---~

o·a

0'2

o

FO- C3'0 -Nl/a 0 FO - FI/2 -C3·0- Nva 6 I· 0 1'4

PRESSURE RATIO PT/PA FIGURE 2S. EFFECT OF FLAT SURFACE LENGTH ON MEASURED

·NITIAL ANGLE = 0°

Qv

O'S

-R

~--

~~-C21/2-NI/a , , ~ 0- f V4-C21/2 - NI/S . . rlfO- FV2 - C21/2 - NI/S

-

/

_t::.

1- tb-l IJ /I 0·6 0-4 0·2 0 1·0 1-4 I·S 2-2 PRE·SSURE RATIO

PT/.

PA

FIGURE 26 VARIATION OF VERTICAL AND HORIZONTAL TURNING

EFFICIENCY WITH FLAT StJRFACE LENGTH

... .

_{. .}

_'

1-0 0-6 0-2

o

INITlAL ANGLE : 00

-

/

f/v

.,.,.. ~

/

~~

I

~

,.

..

1-0 FIGURE 27

/

IJ

FO -C3'O - N 1/8 :-1-1)1-/ 2·2 PRESSURE RATIO FlrjR A

VARIATION OF VERTICAL AND HORIZONTAL TURNING EFFICIENCY WITH FLAT SURFACE LE NGTH

INITIAL ANGLE: 10° 0'8

c("

I

/

V

V

/

/ I'

If

o

-

C3'O- N l / i

.1

ro -

FI/2- C3'0 ... 1/8

~

_1-

?H

. ~

~

0'4 ~

o

1'0 1·4 2'2 PRESSURE RATI 0 P-v. PA

FIGURE 28 _{VARIATION OF VERTICAL AND ttORIZONTAL TURNI NG}

1-0 0'8 0'6 0-4 0'2

o

::: 1'0 INITJAL ANGLE

=

20 0

L

L

Qv

VI

/

l/O- C3'O -

NI/al

.1

/

VO -

FI/2-C3-0- N 1/8

Il

_'-L..

I-?

_H -'-

--~

~

~::;;;.-' 1-4 1-8 _2'2 PRESSURE RATIO

Pr/p,

A

FIGURE 29 . VARIATION OF VERTICAL ANO HORllONTAL· TURNING

1-0 0-8

6-6

0-4 0-2

o

INITIAL ANGLE

=

30° I

1"2'1

-

-~

v

V

~

---

-1-0 FIGURE 30

/

i/O-C3'O-

NI/I

, /

FO-FI/2- C3'O- NI/8

J /

.

/;"

-

~ I-~

--

....

_-

_ ti

//

---., 14 PRESSUR E RATIO PT/P A

VARIATION OF VERTIC 4LAND HORIZONTAL TURNING EFFICIENCY WITH FLAT SURF4CE LENGTH

0'8 0'6 0'4 0·2

o

FIGURE 31 FO- C2'0- N 1/8 0 00 I:::. 100 JNITIAL ANGLE [J _2eP 0 3eP 1·4 -1·8 2·2

PRESSURE RATIO PT/PA

EFFECT OF I NITJAL ANGLE VARIATION ON THE MEASURED VERTICAL FORCE

0'8 0-6 0·2

o

FO- C2' 5 - NI/8 IN ITIAL ANGLE

o

300 1-8 2'2 \ ,.

PRESSURE R ATI 0 PT/PA

FIGURE 32 EFFECT OF IN ITIAL ANGLE VARI A TlON ON THE MEASURED VERTICAL FORC E

FO-C3'O- NI/8 Fv/AFT Q'8 0'6 O'45~----~---~~~~~---~---1---r---; 0'3 0 00 6 .00 INITlAL ANGLE CJ ₂₀0 0 300 CH5

o

',0 1'8

PRESSURE RATIO PT/PA

FIGURE 33 EFFECT OF I NIT lAL ANGLE VA RIATION ON THE MEASURE 0 V ERTICAL FORCE

0'8 06 0'4 0'2

o

FV/AP'-1·0 FO- FI/2-C3'O-NI/8 1',4

o

0° 6 10°

o

20°

o

30° INITlAL ANGU: 1'8 2-2

PRESSURE RATIO

FT/PA

FIGURE 34 EFFECT OF INITlAL ANGLE VARIATION ON THE MEASUREO VERTICAL FORCE

FO-C4'0- NV& 0-& 0'6 0-4 ~---4--~~~---~---L ______ J -_ _ _ _ ~~ _ _ _ _ ~ 0·2

o

1·0 1·4

o

0° 6 100

o

2.00

0300

INITIAL ANGLE 1-& 2'2 PRESSURE RAT 10 P,.IPA

FI GURE 35 EFFECT OF I NITIALANGLE VA RIATION ON THE MEASURED VERTIGAL FORCE

0'6 0'4

o

1·0 FO- C2'O- N

118

o

00

t::.

100 [J 200 INITIAL ANGLE <0 300 1'8 2-2

PRESSURE RATIO PT/PA FIGURE 36 EFF'ECT OF INITIAL ANGLE VARIATION ONTHE

0-6 0'4 0·2

o

"0 FI GURE 37 FO - (,2V2 - N 1/8

o

00 6 100

P

200 INITIAl ANGlE

<>

300

PRESSURE RATIO PT/PA EFFECT 0 F INITIAl ANGLE VARIATION ON THE

o's

0-6

o

F~~ . T 1-0 FO- C3-0- NI/S

o

00 6 100

o

200 INITIAl ANGlE I-S 2-2

PRESSURE RATIO ~/PA

FIGURE 38 EFFECT OF I NITIAl ANGL.E VARIATION ON THE MEASURED HORIZO .. TAl FORCE