Measurement of the derivative zw for oscillating wings in cascade

DELFT'^°°°°^^""°^' 10 - DELFT

't

THE COLLEGE OF AERONAUTICS

CRANFIELD

MEASUREMENT OF THE DERIVATIVE z FOR

w

OSCILLATING WINGS IN CASCADE

by

REPORT MD, 93

T H E C O L L E & E O F A E R O N A U T I C S ' C R A N F I E L D

Ifeasurement of the Derivative z for o s c i l l a t i n g w

Wings i n Cascade b y

-Ronald D, l i i l n e , B . S c , D.C.Ae,,

and

Frank G, v/illox, B . S c . , D,C,Ae,

SÜIIIAEÏÏ

Experimental results are reported of the damping derivative a. for rigid rectangular v/ings of various aspect ratios in cascades having gap-chord ratios of 2, 1, •§-, 1/3, l/4« The Insults show fair agreement with tvïo-dinensional theory,

The ranges of Reynolds numbers and frequency paraneters were 0,8 to 2,5 X 105 and 0,1 to 0,45 respectively,

The results show a strong dependence on Reynolds

number which increases with decrease in gap-chord ratio. This effect was eliminated by transition fixation by -vTires placed at suitable positions downstream of the vóng leading edge,

This report was submitted in 1954 as a part requirement for the award of the Diploma of the College of Aeronautics,

CONTENTS Page l i s t of symbols 3 1 , I n t r o d u c t i o n 3 2 , Apparatus 4 2.1 G e n e r a l 4 2 . 2 Ivleasurenent of ïïind Speed 5

2 . 3 tieasuremont of z . 5 2 . 4 Reynolds number and frequency p a r a m e t e r 5

3 , D e t a i l s of T e s t s 6 3.1 P r e l i m i n a r y i n v e s t i g a t i o n 6 3.2 i i a i n t e s t p r o c e d u r e 6 4 , R e s u l t s 7 4.1 V e l o c i t y c a l i b r a t i o n s 7 4«2 P r e l i m i n a r y t e s t s 8 4 . 3 Iiain t e s t s 8 5, Discussion of results 9 5.1 Preliminary tests 9 5.2 Hain tests 10 5.3 Air-resonance condition 13 6, Acknov/ledgements 13 7, Conclusions "14 8, References 14 Figures 1 - 29

IZST OF SE.ffiOI5

f-^ Natural frequency of oscillation f„ Resonant frequency of oscillation T Exciting amplitude p Static presstire S I'/ing area V Vfindspeed Z Aerodynamic f o r c e n o m a l t o planforr.i ZT, A n p l i t u d c of r e s o n a n t o s c i l l a t i o n of iTing Z_ = "v;:: Aerodynamic dai^ping d e r i v a t i v e Z 2 . = -rrs- Non-dimensional daraping d e r i v a t i v e \i pVS Spring stiffness 2'jtf c

a; = —r :— Non-dimensional frequency parameter

1, Introduction

The p\irpose of this experiment vreis to measure the damping derivative z _ for rectangular wings in cascade oscillating with sinaple harmonic motion,

T.'ork has already been done to determine the derivative z for isolated rectangular and sweptback wings (refs, 1,3 and 4)

and for rectangular \-nx\Qa in ca.scade (ref, 2 ) ,

The results of ref, 2 are inconclusive for gap-chord ratios of 1 and. less owing to a Reynolds number effect which gives rise to very erratic results,

It v/as found in ref, 6 that adjc-ccnt aerofoils in

cascade oscillated approximately 180° out of phase w^hen fluttering, They i;iay therefore be regarded as images of each other in a rigid plane boundary between them. These conditions nay be represented

experimental 1y by an aerofoil oscillating between t\70 parallel plates. In theory these plates should be of infinite length but on approximation to the true conditions can be obtained with plates of finite length,

Experiments along the same lines as those of ref, 2 were niade at gap-chord ratios of •§• and l/3> but on the basis of

some preliminary investigations, transition wires were added to aerofoils and image plates in an attempt to fix transition and thus eliminate Reynolds number effects,

2, Apparatus 2,1, General

The tunnel and oscillating rig vrare basically those used far tlie experiments of reference 1 v/ith the addition of t\70 parallel plates in the vrorking section as shown in figure 1,

Three rectangular wing models T/ere used all of 3in» constant chord and having aspect ratios of 5> 4 and 3» The

aerofoil section xras NACA 0010,

Transition wires v/ere fitted to the aerofoils and to the plates as described in para, 5»'l»

The frequency of oscillation of the rig lyas measured by means of an electrical tachometer wiiich had been calibrated against a Kasler revolution counter connected directly to the

eccentric shaft (figs, 2 and y),

The forcing araplitude v/as measured by means of a dial gauge reading directly tiie stroke of the eccentric. The ampli-tude at resonance \7as measured by observing the deflection of a bean of light sliining on a small mirror attached to the rig, The reflected iiage could be measured to within 0,01 in, dis-placement,

Ti/o sets of springs v/ere used and they irere adjusted so that the spring tension was the same iTith each set of springs in position on the rig,

The stiffnesses of the springs \7ere measured by hanging vraights from the springs and measta^ing the deflections with a pair of Vernier Calipers, The t\ro sets are referred to a^ (A) and (B) and have the follov/ing

stiffnesses,-(A^ - 210 lb,/ft,| A springs | ^ . 23O Ib,/ft,|

fB^ - 85.5 Ib,/ft,] B springs j^^^ _ Q^^^ it./f.t.[

2,2 lleasurement of vfind speed

The vrind speed v/as, measured by a Prandtl I.Ianometer

connected to a static hole in tlie roof of the tunnel. During the tests ir./o such static lioles •vTcre used owing to the blocl:age of the normal hole for gap-chord ratios less than •§•, (See fig, 4 ) .

The normal static hole is situated 1.3/8in. off the tunnel axis (see fig, 4)« Since this static hole could not be used for the tests at •§• and l/3 gap-chord ratio another static hole v/as chosen on the tiinnel axis (hole No, 4> fig« 4 ) .

Typical calibz-^ation curves for these two static holes are shown in fi^js, 5 and 6, Tiiese curves were obtained by coircparing the nancraotei- reading v.dth the true velocity as read by a pitot tube, in tlie v.=t)rking section between the plates at

the model position,

The static pressure distribution along the tunnel axis is sham in fig, 7 fcr the l/3 and rf gap-chord ratio configurations ,

The pitot tube used fctr the calibrations was also traversed bet\7een tlie plates at the model position. It was foimd that the velocity'' was constant between the plates,

2.3 The measurement of z

The method used for the r.Teasui'ement of z.^ is described in detail in reference 1,

For a 2iven vrdue of the exciting aiirplitude (T)

readings \7ere taken of the resonant frequency (f^,) and resonant

ariplitude (z,^) at a v/ind speed (v),

2.4 Reynolds nur.iber and frequency parameter

The range of Reynolds number (Vc/v) used in these tests V7as 0,8 x 105 to 2,5 x 10^,

2r.fj^c

The range of frequency parameter o) = — r : — v/as 0,1 to 0,45 v/herc f_ is tlie resonant frequency

c is the aerofoil chord V is the wind speed,

3» Details of Tests

3,1 Preliminary Investigations

The data of ref, 2 for a gap-chord ratio of ^,

indicated that considerable scatter of the results was obtained v/hich \7as found to be due to a Reynolds number effect due

presumably to transition movements on botli plates and aerofoils,

It was therefore decided to make e. preliminary

quali-tative investigation designed to shov7 the mean transition pos-ition under oscillatory condpos-itions, A sublirmtion technique

was erïployed. The aerofoil \ra.s sprayed Vidth a

Napthalene-Betroleum Ether - Toluene mixture. For these tests a tunnel speed of l60 f,T3,s, was lised,

The results obtained were not conclusive but on an average it appeared thiit transition occurred at about 60 per cent chord but no tvro tosts gave identical results,

On the basis of this information it v/as decided to fit transition vares at 25 per cent chord on the aerofoil, The size of wire used was determined from the accepted relation

for steady flo\7 Vd/v .•> 600, Since the i-esuits of reference 2

becai^ie irregular in the speed range 70-100 f,xJ,s,, a vnxe diameter of 18 thousandths of an inch v;as used,

It was subsequently found (see para, 5 » O that this

diameter "v7as insufficient and rather than increase xrrce

dia-meter, the \7ires on the aerofoils were brought forv/ard to 10 per cent chord and \7ires of the same diameter (18 thou,in,) were fixed on the plates at 10 tjer cent of the plate chord,

3,2 I'.Iain Test Procedure

It v/as noted in ref, 2 that variation of resonant

amplitude did not appreciably affect the value of z^, This

was substaiitiated by a preliminiry test at a gap-chord ratio of 1 in v/hich curves v/ere obtained of Z T / T against 1/V (fig, 8) both keeping resonant amplitude constant and forcing amplitude constant,

It was therefore decided to keep tlie exciting amplitude constant and alio';/ the resonant amplitude to vary, Furtheiraore three exciting a^^litudes v/ere used v/here possible;

the largest being limited by the aerofoil banging against the plates and the smallest limited by the amplitude viiich could be measured reasonably accin^ately by the technique used,

After experience gained in initial tests the follor,ang values of exciting amplitude v/ere decided

upon,-,0300in., ,0150in., ,0075in,

All the main tests v/ere performed v/ith transition

wires of 18 thou,in, diameter on aerofoils and plates at 10 per cent chord. Tests v/ere perfoiraed for each v/ing v/ith each

set of springs at gap-chord ratios of •§-, l/3 and l/4 using sel-ected values of the chosen exciting amplitudes,

Before cammencing tests it was checked the.t the aerofoil incidence v/as zero by running up the tunnel with the forcing rig stationary, and noting v/hether the model v/as dis-placed frcm the central position. If this was the case the incidence v/as corrected by 'trial and error',

To avoid 'banging', the aerofoil v/as pulled against the plates ajid the amplitude set on the scale. The tunnel was tlien run at a reasonably high speed, say 80 f,p,s,, and the frequency brouglit to resonance when it could be seen from tlie aniplitude trace v/hether the aerofoil v/a^ 'bringing' or not. If it v/as not 'banging' tlic tunnel speed v/as decreased until either the a.erofoil \/as 'banging' or mininura tunnel speed v/as reached,

For any particular tunnel speed tha resonant amplitude v/as most accurately and easily measured by going slov/ly througli

tlie resonant condition in both directions several tiraes, Graphs of z^/T against l/V v/ere plotted

con-c\rrrent3y v/ith the test to ensure that enough readings xrere

being taken to give sxifficient accuracy. To allov/ for hysteresis effects several check readinf^s v/ere taken wliile decreasing tunnel speed, the main set of readings having been obtained v/hile

increasing tunnel speed,

4» Results

4.1 Velocity Calibrations

Velocity calibration curves for ^ and l/3 gap-chord ratios are shovm in figs, 5 and 6,

The distribution of static pressure along the tunnel axis for ^ and l/3 gap-chord ratios is sha.n in fig, 7« These curves are the averages of distributions corresponding to a

series of tunnel speeds throughout the speed range used in ths tests,

* It was found in reference 1 that z^VI v/as arjproxiiiately linear vath 1/V,

4,2 Preliminary Tests

4.2.1 Gap-chord r a t i o of 1

Fig, 8 shows curves of ZrVT against l/v for V^ing III \,dth transition v/ires of 18 thou,in, diameter on aerofoil and plates both for fixed resonant and fixed exciting amplitudes,

4.2.2 Gap-chord ratio of j

-Figs, 9 and 10 sho\7 curves of z^VT against l/V for Y/'ings II and III v/ith no transition v/ires ""on plates or aerofoils,

and fig, 11 corresponding results for Yfing III xrxth transition

v/ires on aerofoil only at 25 per cent cliord,

4 . 2 . 3 Gap-chord r a t i o of l / 3

F i g s , 12 and 13 show curves of z_/T against l/V

for 17ings I and I I v/ith no t r a n s i t i o n v/ires" and f i g , 14 sliov/s

TI±ng I I \"/ith t r a n s i t i o n vdres of 34 t h o u , i n , diai:icter on a e r o f o i l

and p l a t e s a t 10 per cent chord,

4 . 2 . 4 Gap-chord r a t i o of l / 4

A fev/ r e s u l t s v/ere obtained f o r a gap-chord r a t i o of

0,25 for \Jings I , I I and I I I vri.th 0,018in, diaiueter t r a n s i t i o n

v/ires fixed a t 10 per cent chord. The r e s u l t s did not give a

l i n e a r r e l a t i o n bet\/een 2_/T and 1/V and i t was suspected

t h a t the diameter of the t r a n s i t i o n \/ires v/as i n s u f f i c i e n t to

f i x t r a n s i t i o n i n t h i s c a s e ,

4,3 I'.Iain Tests

4,3«1 ^ T / ^ against l/V ciirves

In f i g s , 15-20 are drawn curves of z - - ^ against

l/V for •§• and I / 3 gap-chord r a t i o s , for T/ings T, I I and I I I

;7ith t r a n s i t i o n wires of 18 t h o u , i n , diameter a t 10 per cent

chord on the a e r o f o i l s and p l a t e s ,

4,3»2 z against a curves

T./

From the curves of figs, 15-20, z^ is calculated according to the foniïula

-1

^7 ~ pVS ^"^ ' (ref. 1)

This assumes that frictional danïping in the oscillating rig has been neglected, Tliis is justified since it is shown in

ref, 3, Appendix I, that \x is only significant v;hen the resonant

angplitude is large (zTj>0,3in.) Tliroughout these tests the resonant amplitude v/as alv/ays smaller than 0,3in,

It is shown in ref, 2, para, 3,4, that the natural frequency of the system, f,T, may be taken equal to the resonont

(forced) frequency, f„, within the liviits of experiraental error. HoT/evcr, in all cases xhe results i/ere evaluated using the measured resonant frequency,

Curves of (z ) against w are shov/n in figs, 21 - 26,

4*3«3 Summary of Results for &) = 0,2

In fig, 27 arc shown curves, of (-z. ) against inverse

of aspect ratio for constant gap-chord ratio and these are extra-polated to give values of (-z J for infinite aspect ratio for gap-chord ratios of '^ , 2, -g- and I/3,

The curve for gap-chord ratio of 2 is obtained from ref, 2 and the cvirve for infinite gap-chord ratio from ref, 5»

In fig, 28 a curve for each v/ing is given showing the variation of (-z.) v/ith gap-chord ratio,

In fig, 29 the values of (-z ) for infinite aspect ratio as obtained from fig, 26 are compared v/ith the theoretical,

tv70-diaensional values obtained from ref, 6 for low gap-cliord ratios and from ref, 5 for infinite gap-chord ratio,

5, Discussion of Results 5,1 Preli:iinary Tests

Before eliminating any Reynolds number effect by fitting transition v/ires it v/as felt desirable to try and reproduce tlie results obtjïined in ref, 2, figs, 11 end 12 far a gap-chord ratio of •§-, Tests v/ere therefore done v/ith no transition wires and the Zp/I against l/V curves are shov/n in figs. 9» "10* "12 and 13

for gap-chord ratios of ^ and I/3,

It v/as found impossible to reproduce exactly the results of figs 11 and 12, ref, 2,

Figs, 12 and I3 far gap-chord ratio of I/3 show curves of the same form as fig, 9 "but the trend is more sharply defined,

Kanaalstraat 10 - DELFT

1 0

-This suggests that the irregular cuzves of Zp/T against l/V which are associated with a Reynolds number effect are also a function of gap-chord ratio,

It v/as felt that if the Reynolds nur.iber effect could be completely eliminated the curves of Zp/T "-^ l/V obtained r/ould resenible those of figs, 2 - 6 , ref, 1 v/hiSi are almost linear,

Fig, 11 shows that -when 18 thou,in, diameter v/ires w-ere fitted at 25 per cent chord on YV'ing III a partial imi^rovenent of the results -v/as obtained but it v/as not until the vdres v/ere moved foiT/ard to 10 per cent chord on the aerofoil and similar vdres were fitted at 10 per cent chord on the plates that the desired result ^-/as obtained (see figs, 15, 16, and 17).

The fact that it v/as found impossible to reproduce the results of figs, 11 and 12, ref, 2, suggests that the inconsistencies

shov/n in thsse results can not be v/holly explained by Reynolds nunibcr effect. From experience gained usJLng the apparatus the

authors suggest that lack of rigidity in the model supports could have caused the othervdse unexplained irregularities in the previous results,

Conditions v.ithout transition v/ires v/ere -very unsteady

and it v/as difficult to obtain acciu:'ate readings of resonant

aiuplitude ov/ing to irregulai- movements of the centre of oscillation

of the aerofoil. In contrast, tests performed xrxta transition

v/ires on aerofoils and plates could be carried tlirough in a straiglit-fon/ard manner and the results reproduced at idll,

It v/as found that, for any one set of springs, the curves of z.jyT A- 1/V for different forcing amplitudes were distinctHy separated v/hen no transition wires i/erc present, while the corresponding curves far transition v/ires in position v/ere practically coincident (cf, figs, 10 and 17), In addition test conditions v/ere found to be much steadier v/hen the stronger set of springs (A) v/ere used,

5,2 Llain Tests

5,2,1 Curves of Zp/T against l/V

Comparing figs, 15 - "17 vdth figs, 2 - 6 of ref, 1 it v/ill be seen that using different sets of springs has the sam.e general effect on the value of Zp/I,

The curves for a gap-chord ratio of l/3, figs, 18 - 20,

are similar to those at a gap-chord ratio of ^ (figs, 15 - 17)

but at lev/ tunnel sx^eeds the curves change slope. It v/as thought that this effect was again due to Reynolds nui-iber,

In order to verify this tests v/ere performed using wires of

34 thou,in, diameter at 10 per cent chord on the aerofoil (V/ing II) and plates, and the results obtained are shov/n in fig, 14. Tliese

curves are nav/ very regular and conditions during the test v/ere

found to be even steadier than those associated vdth the 18 thou,in, diameter wires on aerofbóL and plates. This indicates that the Reynolds number effect increases ;dth decrease in gai>-chord ratio,

5*2,2 Variation of z. vdth >(o

The curves of (-z.)<--v to at a gap-chord ratio of -j

(figs, 21 - 23) are similar to those obtained for a gap-chord ratio of 2 in ref, 2 (figs, I5, 16 and 17) and in ref, 1 far

isolated rectang-ular v/inf^s (figs, 7 and 8 ) ,

According to theory there should be a unique curve for any one vdng but this is not borne out by the present results or the results of refs, 1 and 2, It has been suggested in ref, 1, para, 8 that this discrepancy between theory and practice is due entirely to experiraental error, Tliis is bozne out, to scxie extent in the present tests, since the curves at a gap-chord ratio of •§•

(figs, 21 - 23) for different springs and different forcing amp-litudes are not displaced far from each other and there does not appear to be any definite trend in the relative displaceiiients of the curves for any particular vdng,

The experimental curves for (-z..) '-^- w at a gap-chord

ratio of I/3 (figs, 24 - 26) appear to be vadid only over a limited range of frequency parameter tmd tliis, as rejaarked in para. 5«'t» is due to the Reynolds number effect reasserting itself at lov/ tunnel speeds, (it can be seen from fig, 14 that mare consistent results v/ould have been obtained, if 34 thou,in,

diameter transition xrlres had been used),

Although the effect of changing exciting amplitude is still small the relative displaccxnents of curves for dii'ferent springs appear to be much larger than for a gap-chord ratio of •^,

In order to demonstrate that the sudden increase in z

for the A and B springs occurs at the scawe ve2ue of the Reynolds

nuinbei-", let us assume tliat a Reynolds raxmber effect talces place

at a speed V., such tlia.t for V > V. the variation of z _, xrLth

<io is siaall, but for V <' V. there is a sudden increase in the value of z , The resonani; frequency using springs B is in

the region of 7«6 c,p.^. and vdth springs A is in the region of "53 c,p,a. Thus the values of 0 corresjponding to the sixdden

* All the tests at I/3 gap-chord ratio had been completed, using a transition v/ire 0,018in, diameter at 10 per cent chord on both the aerofoils and plates, before the tests using a wire 0,034in, diameter v/ere perf omied,

increase i n z (.for a fixed sj

('^^B springs ._ 7.6

'^'^A springs "' ""^

Reference to figs. 24 - 26 shews that this is the case and that there does exist a criticsuL speed V. at v/hich the flow changes character. A similar effect was observed in ref. 2

where, by plotting z against l/V, curves for different springs were made to coincide approximately (fig. 17» ref. 2 ) .

It is the different relative positions of the rapid increase in z for the two sets of springs which makes the curves appear to be displaced. Results obtained using larger v/ires v/ould probably eliminate the rapid rise and v/ould give

results similar to those for a gap-chord ratio of •§• (figs, 21-23),

5,2,3 Final Results

It is necessary to fix on a value of a before the

variation of z vdth aspect ratio and gap-chord ratio can be presented, A value of <Ü= 0,2 was taken since it lies in the middle of the range considered and in the ca^e of gap-chord ratio

of 1/3 the curves at (0= 0,2 are above the 'critical speed', V., for both sets of springs, and therefore not in the range affected by Reynolds number,

Results for a = 0,2 sliould be tj^icEtl of those far

w general (over the range considered), since, v/hen Reynolds number effect is eliminated, the dependence of z. on o is smpJJ-,

In order to conrpare the results of the present tests \d.th those derived on the basis of t\70-dimensional theory in

ref, 6 it v/as necessary to estimate the value of z corresponding to infinite aspect ratio at each gap-chord ratio. As a basis

for the extrapolation the results of ref, 5 for infinite

gap-chord ratio and rectangular aerofoils v/ere plotted and it v/as

fomid (fig, 27) that the extrapolation v/as linear. Accordingly, mean straight lines v/ere dravwi through the groups of points talcen from the curves of figs, 21 - 26, for each spring and exciting amplitudes and produced to meet the (-z_) axis (fig, 27),

v/

The set of results seems to be consistent; the rate of increase of z with aspect ratio being more rapid at smaller gap-chord ratios. This is brought out more clearly in fig, 28,

The results of ref, 2 for a gap-chord ratio of 1 v/ere inconsistent vdth the curves of fig, 27 and so v/ere omitted,

Pig, 28 shows that the variation of z_ vdth gap-chord ratio is similar for all the aspect ratios considered. As gap-chord ratio decreases, z. increases and for gap-gap-chord ratios less than 0,5 the rate of increase is very rapid,

It is iniprobable that (-z ) v/ill continue to increase as indicated in fig, 28 and this v/as confirmed in the preliminary tests made at a gap-chord ratio of l/4,*

It is shov/n in fig. 29 that for gap-chord ratios in the range l/3 to l/2 very good agreement is obtained boti7cen theory and experiment. The theoretical curve v/as derived from approximate formulae given in ref, 6 which only apply for small gap-chord ratios

5,3» Air-resonance condition

It is pointed out in ref, 7 that for aerofoils oscillating betv/cen v/alls in a compressible floi/ a transverse resonance phenom-enon can exist v/hich can greatly change the nature of the flov/, This is due to the fact that in a compressible fluid there is a

definite time lag betv/eon a disturbance initiated at one point and

its effect at another. Under certain conditions this phase lag can give rise to a resonant condition (of the air) v/hich involves large corrections,

¥oolston and Runyan (ref, 7) give a ctirve relating the critical frequency at i/hich the above resonant condition occurs to tunnel height and loach number. For the ilach number range used throughout the present tests this critical frequency is practically constant and furthemora this frequency is much higher than either of the resonant frequencies associated \d.th springs A and B (13 and 7,6 c,p,s, respectively),

6, Acknov/ledgements

The authors id.th to acknov/ledge the assistance given by

lie, G,II, lillcy and Ivtr, K,D, Harris throughout this investigation,

lir. S.H, lAlley v/as responsible for improving the accuracy of the apparatus, iir, S, Clarke made the plates and i.ir, C D . Bruce the T/ooden aerofoils,

Acknowledgements arc also due to lüessrs, B.S. Cacipion and E.G. Seacy for use of unpublished infoixiation.

« As noted above the results at a gap-chord ratio of l/4 probably suffer from lack of transition fixation. It is for this reason that these results are not reported,

7, Conclusions

1, z has been measijred, using a forced oscillation

technique, on rigid rectangular v/ings oscillating between parallel plates. The results rxe applicable to aerofoils in cascade when adjacent blades are oscillating in antiphase.

2, Attention is drawn to the large Reynolds number effect on the values of z , This effect, which increases vdth decrease

Y/

in the gap-chord ratio, is associated vdth the movement of the transition region on the aerofoils and side plates. Tests show that the Reynolds number effect can be eliminated by fixing a large enough transition wire to the aerofoil near the leading edge of both the aerofoils and side plates,

3, 1'flien the Reynolds nuraber effect is eliminated the

dependence of z on the frequency parameter is small. The range of frequency parameters used in the tests was 0.1 to 0,45 and the range of Reynolds number v/as 0.8 x 10^ to 2,5 x 105,

4» The variation of z. vdth gap-chord ratio was found for aerofoils of aspect ratios 5» 4 ^^nd 3 at gap-chord ratios of 2, 1,

2f 1/3 end 1/4, The results, when extrapolated to infinite aspect

ratio, shov/ed fair agreement v/ith the approximate theoretical values obtained in reference 6, The large increase in the value of z vdth decrease in gap-chord ratio, as predicted by theory, is shov/n

to be true far values of gap-chord ratio above I/3» At smaller values of gap-chord ratio the values of z. decrease, but the experimental results v/ere not conclusive in this range,

8, References

1, A,L, Buchan, Measiirement of the derivative z for K,D, Harris, an oscillating aerofoil,

P,M, Somervail, College of Aeronautics Rep, No, 40 (1950), 2, B,S, Canipion, ileasurement of the derivative z. far

E,G, Seacy oscillating v/ings in cascade.

Report on experimental v/ork done at C. of A, (1953). Unpublished,

3, G,E, T/hitmarsh Ivleastirement of the derivative z for oscillating sv/eptback wings,

College of Aeronautics Rep, No, 92, 1955» 4, H,A, Simon, Ileasurement of the damping derivative z^

F,E, Bartholcmev/ for s;7ept-back v/ings, ^'^ Report on experimental v/ork done at C,of A,

R,eference3 (Contd,)

5, Yf, P, Jones

6, G, M, lilley

7, D,S, Yfoolston, H,L, Runyan

Theoretical Air-load and Derivatives

Coefficients far Rectangular Mings,

A,R,C, R, and M, No. 2142.

An investigation of the Flexure-Torsion flutter characteristics of aerofoils in cascade,

College of Aeronautics Rep, No, 60, 1952,

Some considerations on the air forces on a vdng oscillating betv/een two walls for

subsonic compressible flov/,

HUB aRECTlOW • - 2 - H CTtre HOLE I ' -_{ICHORO RATIO Of 'i^l} PLATE fOR C A P

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FOfl FURTHER DETAILS OF RIG SEE REF L

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POSITION OF STATIC HOLES IN ROOF OF TUNNEL. FIG. 4. BOO

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5 0 0 lOOO liOO J/DOO 2.500 3 0 0 0 3,SOO ELECTRIC TACHOMETER READING —R.PM.

CALIBRATION OF ELECTRIC TACHOMETER AGAINST HASLER COUNTER. FIG. 2. 4P00 •0I« ^ • 0 . . •013

V

r 1 r

20 4 0 ÖO eo 100 I20 I40 lAO 100 2 0 0 3 2 0 240 CORRECTED PHANDTL READING (M.M. METHS.)

PLATE SWCING — ^2 C

FREESTREAM WKDSPEEO BETWEEN PLATES AT MODEL POSITION.

RG. 5 •020 ' -0(« ("'.«r •OIO \ \\ \\ "^ ^

bi

WTHOUT TRANSITION WIRES.

1 1 1 K j s ? ^ 4UIIIVWI. „ l « l l < - MULJ-^

1

i

» 4 0 «O BO lOO I 3 0 I40 I » IBO 3 0 0 330 240 CODRECTtO PRANDTL READING (M.U. METHS)

FREQUENCY OF OSCILLATION AGAINST ELECTRIC TACHOMETER READING.

FIG. 3.

PLATE SPAQNG — %C

FRCESTRCAM WINDSPEED BETT«EN PLATES AT MODEL POSITIOH

-a- V j - C SWQNC WITH I WITHOUT WRES

2 E S . 3

STATIC HOLE NUMBER

DISTANCE ALONG TUNNEL AXIS 2CM E 3 *

RATIO OF STATIC PRESSURES AT HOLES ALONG TUNNEL AXIS TO THAT AT HOLE No. I. FIG 7 T TRANSITION Wnes AT ) 0 % : 0 N AEROFOIL AND PLATES.

-t"

ê

T

WING H I ( « = 3) PLATE SPACING — I C FIG. a

f

r

WING H { A I - 4 ) PLATE SPACING — 'I2 C RG. 9^ 2 T 0 4 2 0 ^ •^ ^ , * • ' p . * ^ *

^ 4

WING H L ( « = 3 ) PLATE SPACING— \i C. FIG. 10. \ ("/•«J WNG m { « - 3 ) PLATE SPACING — \ ^ RG I I 16 4 12

t

4 2 • 2 T R A N S I OF 34 ? riON WIRE TMOU, 0 / ï ON A£R< AMETER. y / 3FOIL AND / / ^ L E G E N D ; -PLATES / ^

^y

y

y

y^

„^

WING I ( A ( = S ) PLATE SPACING — ' / 2

C-FIG. IS.

WlNGm (A(-3) PLATE SWCING—'/j C. FIG 17 IS 14 12 8 6 a • 1 ? — ^ [ 1 ^ [ -- -- ^ - ^

y

J^

A

WING I ( A « - 5 ) PLATE SPACING—ïa C.

12

't

y

W I N G n (Al-4) PLATE SPOCWG—V3 C

RG. igi •OIO _ | • O B w i N G n r { A > - 3 ) PLATE S B V C N G —1(3 C FIG. 2 Q ( - 0 s-s •v _{- « ^} -- : ^ LEGEND:-" * = ? ? • " " - ?-OBo'"l I - 0 3 0 0 " ! E-MOcfl J-ooo'. — — J • — A s p f m b s B SMtt4GS •OS • « • « '20 JS -SO •» •«> rVtCUEHCI PARAMETER—Ö' WING I ( A < - S ) P L A T E SWMCING—II2 C HG. 2L M 4.S 3-5 S-O

^ï;~

•ik

(-rj

WING I (Al-S) PLATE SRVCING-'/a C FIG.24

LEGEND:LEGEND: -E= oiso""] _ . ^ A SPRINGS £ = 0 0 7 5 ' J f | - 0 1 5 0 ' 1 B SPRINGS 'E -oaoo'J

Ï

WNG H (/«=4) PLATE SPACING—'/3 C. FIG. 25. 7-5 (-Z.„) S5 4-5 4 0 ^ 1 LEGEND:— '~*i C ! .

-1

•05 10 •IS 'SO •as •so •as 4 0 FREQUENCY WRAMETER — 0 ^

WINGUr ( « - 3 ) PLATE SPAaNG—'/3 C. FIG. 26. ö ' - o . j CHORD GAP '^CHORO GAP 2 CHORD GAP FINITE CHORD SAP REF S ASPECT RATIO (-Z.u)

1

i

tx

EXPERIMENTAL VALUES OF Z(j FOR VftRYING

G A P - C H O R D RATIO

FIG. 2a

A>—M"

O

. S ' - 0 - 2

.EXPEBtiCNTAL \HLUES FOB INFINITE « OaTAINED BY EXTRAPOLATION FROM FINITE « RESULTS

-EXPERIMENTAL

rHEORETlCAL

J '

-0.5 |.0 IS 2 0 2.5 3-0 GAP - CHORD PATIO

COMPARISON O F THEORETICAL AND EXPERIMENTAL VALUES OF 2 „ FOR INFINITE ASPECT RATIO.

FIG. 29 EXPERIMENTAL RESULTS FOR Z „ EXTRAPOLATED TO GIVE

VALUES OF Zu- AT INFINTTE ASPBCT RATIO.