C.P. Nd.’ 323 (19,031)

A.R.C. Technlcal Report

C.P. ,I$, 323 A.R.C. Technical Report

/* ’ d

-\

MINISTRY OF SUPPLY

AERONAUTICAL RESEARCH COUNCIL

CURRENT PAPERS ’

Low Speed Wind Tunnel Tests on Perforated Square flat plates

normal to the airstream: Drag and Velocity Fluctuation Measurements

5Y

B. G. de Bray, M.Sc.

LONDON: HER MAJESTY’S STATIONERY OFFICE

1957

PRICE 2s. 6d. NET

C.P. No.323

U.D.C. No. 621.45-59

Teahniad. Note No. Aero 2473

Ootober, 19%

ROYAL AIRU?Al?C ESTK6LISHldENT

Law Speed Wind Tunnel Tests on Perforated Square Flat Plates Normalto the Airstream:

Drag and Veloaity l?luatuation Measurements

B. G. de Bray, &SC.

The effects of perforations upon the drag, and veloaity fluatuations downstream, of square plater normal to the airstream are desaribed.

It is shown that perforations csn havs a powerful effect upon the level of velocity fluctuations, ps2ticularly the low-frequency co~nents, With only a aoupszatively small reduotion in drag coeffiaient.

It is also shown th2t perforating the central region only of a square plate is as effeotivs in reduaing velocity fluctuations as perforating the whole plate while giving a slightly higher tiag coefficient than the latter. On the other hand, perforations near the periphery only are less effective.

-I-

LIST OF CBNTEiiS

1 Intro&.&ion

2 Description of Tests

3 Results

3.1 Drag measurements 3.2 Measurements of velocity fluctuations

4 Disoussion of Results

5 Conclusions

List of symbols

References

Table I - Partioulers of Perforated Plates

M

3

3

4

4 4

5

6

7

7

8

LCST OF ILLUSTRATIONS Figure

Details of Perforated Plates 4

Drag of Uniformly Perforated Plates 2

Drag of Plate No.4 partly Perforated 3

R&S. Velocity Fluctuations 18" behind Plates 4(a)

Velocity Fluctuation Spectra 18" beh5nd Plates. Y/B = 0.8 5(e)

Low-Wequency Band of Velocity Fluatuation 18" behind Plates 6

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1 Intro&x&ion

The work desorlbed in the present note ia a wntinuation of the investi- gations into the behaviour of flat plates at high inoidences, with psrtioular referenoe to their use as aFr brakes.

Previous -k1n2 dealt with the effeot of iraidence and the shape and aspect ratio of solid (i.e. unperforated) plates.

At inaidenoes of the order of 50° and above, the flow round a solid plate separates at the whole of the peri@ery of the plate and a bubble is formed behind the plate. This type offlowis usuallyassooiatedwithwlo- city fluctuations having large low-frequanoy components, which may cause vibration troubles in any installation of such a plate as sn air brake.

The present work is an investigati.on Fnto the effect of perforations on the drag and velocity fluotuations with this type of flow. Perforations admit air into the bubble and tend to r&x8 the general level of velooity fluctuations,

The work is limited to isolated square plates normal to the airstream. The presence of a body adjacent to ens edge of the plate, as in an air brake installation, is not wnsidered likely to have a major effeot upon the f inaings3.

2 DesoriDtion of Tests

The expsrimsnts were made in the l+ ft x 3 ft tunnel at a speed of 140 ft/sec. The amatus and technique used have been fully described in reference 2.

Details of the 5" x 5" square plates tested are given in Table I a?d Fig.1. The main series of plates (Nos.1 to 5) have 80 holes based on a square mesh of 0.5" pitch. In order to obtain the large psrforation area of plate 6 it was necessary to use a roughly hexagonal mesh with 92 holes. Plate 4a ms made in order to test the effect of Mividual hole area as against total hole area.

The numbering of the plates corresponds approximately to the& free area ratio, e.g. plate No.1 has approximately IGfi, plate No.2 2C$, etc.

The perforationa were shsrp-edged in all cases.

Tests were made with plate No.4 to find the effeot of perforating only Part of the surface. For this purpose, successive rows of holes wsre blocked Up, working fN!I the centre outwards and then from th8 edge inwadS.

The expcperiments consisted of:-

(i) Drag measuremsnts, using a capacity-type drag balance.

(ii) Measurements of longituainal velooity fluctuations in a plane 18" behind the plats, using ahot-wire plaoednormaltothe airstream and radial to the axis of the plate. The distance of 18" was chosen to be clear of the bubble.

R.&S. velodty fluctuations were measured at points along a radial Line PUYiLlel to one pair of edges of the plates and to the 4 ft dimension of the tunnel.

In alcdition, frequency spectra were obt&d at 4" radius, this position beingapproximatelythatatiwhiohthe maximum total Phatuation8 owLum?&

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3 Presentation of Results

3.1 Drw measurements

Drag coefficients for the uniformly perforated plates are plotted in Pig.2 against free area ratio sF/S. Fig.3 shows the drag coeffioients for plate No.4 pertly perforated. Stsrtingwiththe solidplate, qxming sue- cessive rows from the centre outward gave the upper -e, and opening the outer row (i.e. nearest the edges) first and working inward towsrds the aentre gave the lower curve.

The drag coefficients are expressed in tsrms of the gross area of the plates, and at-e o~rrsatt?dforblockageby the semi-smpiricalmethodof Maskelllcr

3.2 Measurements of velocity fluctuations

The r.m.s. velocity fluctuations are presented as the ratios + , 0

plotted against radial distances from the centre of the plates.

The spectra are presented in ths form d?(n) plotted against log n. ec n is the non-dimensional frequency u

0 and F(n) the spectrum fmd.on,

definea SO that F(n) dn is the oontrikon to of frequenoies

between n and (n + dn).

It follows that:-

* I

nF(n) d(log n).

0

In the case of spectra, the mean square of the analyser output Au2 is

measured over a bandwidth &I (e being mall), so that:-

F(n) w 'i2 oJo Ann)

and @b) f Au2 approximately,

where sA = $ , the analyser bandwidth ratio.

Figs. 4(a&b) give the r.m.s. velooity fluctuations + in a plane 18" 0

downstreamof the plate. The ~~~~G~~fluhtions occur atabout4" radius

(% = 0.8) in all oases, so this radius was seleoted for the speotra, which

are plotted ti Figs. 5(a&b). in addition, spectra (not shown) were obtained at 8" radius to deterzine the main sheading frequency, which can be done more accurately where the general turbulence level is low.

In order to assess the relative merits of the plates tested from the point of view cf the low-frequency component of the velocity fluctuations, which is the most imp4rtant nent are used as air brakes, the a n) curves were integrated between limits T

in causing buffeting when such plates

n = 0.0-l and n = 0.05, the results converted to units of $ , and plotted

in Fig.6 0

[*II::: = lo lo5 nF(n) log n ,

.

The range of frequencies oovered by the ohosen limits of n, taldng representative values of U. and 15 are as follows:-

f

u. vs n= 0.04 n = 0.05

20.0 13.3

I

4 Discussion of Results

Considering fFrst the uniformly perforated plates, increase in the free

sF area ratio F gives progressive reductions in CD (Fig.2), r.m,s. velooity sF fluctuations (Fig.,.lla), and z-S(n) (Fig.5a). Up to r = 0.35, the main

shedding frequency (shown by the position of the peaks of the spectra) remains constant at n = 0.115, but the peak amplitudes deorease progressively.

Beyond $ T E 0.35 the shedding peak does not appear. The curves of Fig.5a

can therefore be divided into two distinct groups.

The reduction in nF(n) with increase in free area ratio is more marked in the frequency range below n = 0,115 than at higher frequencies. This reduction is shown in Fig.6, which also shows a break in the ourve at the pdntatwhich shedding is sup~ssed.

Of the two arrangements of partially perforated plates tested, that with

SF central perforations, - = 0.25,

c

gave as low +- valuesas aunifordyper-

forated plate with T = O.&O, and a drag ooeffi&nt @higher. On the

other hand, perforations near the -es only gave higher e values than a

% 0

uniformly perforated plate of equal F l~lowe%

value (0.29), and. a drag coeffioient

-5-

These results fcr partial perforations are associated with the values of the main shedding frequencies (Fig.%), which are largely determined by the siee and shape of the unperfcrated portions. of a hollow square rim about 1"

These consist, respectively, wide and 20" peripheral length, and a solid

square with about gl sides. The latter, as expected, gave a shedding fre- quency somewhat higher than for the solid 5” square plate. The shedding frequency for a square rim is tudaumn, but if it be considered as a strip of high aspect ratio, closed end to end, previous experiments2 indicate a value of n much higher than for a square, together with a higher %.

A shedding frequency assoaiated with the spacing between individual holes (0.5” for the 80 hole plates) was not detected, prcbably due to the relatively large distanae dcwnstresmto the measuringplane.

The single test with very small holes (plate 4.a) did not show sny scale effeat for the sise of individual holes, either upon or velocity fluctuations. (Compare plates 4 ti &x in Figs. 2, l+a and This result will not necessarily apply to a case where shedding occurs.

5 Conolusions

For the isolated square plates tested, unifcrm perforations give sub- stantial reductions in the level of velocity fluctuations, at the expense of comparatively small reduaticns in drag cceffioient.

The reck&ions in fluctuaticns are more marked at the lcw-frequency end of the spectrum, this being the more important range of frequencies from the point of view of buffeting in the wake when using these plates as air brakes.

A free srea ratio of 0.40 (with uniform perforations) gives a reduotion in the low-frequency component of velooiQ fluatuaticnz to about one-third of that for an unperfcrated plate, with a loss in drag coefficient of less than 2qi. It is suggested that this value of 0.40 should be a midmum for design purposes.

With free area ratios larger than 0.40, the gain in fluctuaticn level becomes less but the loss in drag greater.

A somewhat better arrangement is to perforate cnly the oentral portion, leaving an unperforated rim. In the arrangement tested, such a plate with a free area ratio of 0.25 gave as low velocity fluctuations as a uniformly perforated ptite with a ratio 0.40, with w higher drag coeffioient.

Perforating near the edges only is less effective thsn uniform perfara- king from the point of view of both drag and velocity fluctuations.

A single test to determine the effect of size of individual holes gave negligible scale effeot.

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CD

s

SF

UO

f

List of Symbols

= Drag ooeffioient, corrected for blockage

= Gross area of plate (sq ft)

= Free area of plate (total area of perforations) (sq ft)

= Tunnel speed, oorreoted for blockage

= frequency (cyoles/sea)

U = root mean square value of longitudinal velooity fluctuations

Y = transverse distanoe from axis of plate

F(n) = Spectrum function (see psrs.52)

Au2 = mean sq- value of velocity fluctuations passed by analyser

An = analyserbtiath

=A An =:-= n analyser bandwidth ratio

n-0.05 v

[I UO

= mean value of + between n values of 0.01 and 0.05 0

na 0.01

3. Author Title, eta

1 B. Fail, Preliminary low speed wind tunnel tests on flat plates T.B. Owen, and air brakes: flow, vibration and balance measurements. B.C.W. Eyre c.p.251. JanuarJ 1955.

2 R. Fail, Low speed experiments on the wake characteristics of J.A. Lawford, flat plates non&. to an airstream. R.C.W. Eyre To be published

3 T.B. Owen Lrw speed statio and fluokating pressure distributions on a oylkdrioal body with a square flat plate air brake. C.F.288. January 1956.

4 E.C. Maskell A theory of wind tunnelblo~kaga effects on stalled flOWS.

To be published.

-7”

Partiaulsrs of Perforated Plntes

Elate No. of Hole Dia. Wee Area Ref.No. Holes (-1 Ratio(z)

1 80 0.214 0.114

2 11 0.280 0.197 3 ” 0.341 0.292

3.5 w 0.372 0.347

4 I, 0.406 0.414

4a 2600 0.069 0.395

5 80 0.4% 0,517

6 92 0.472 0.643

-8- b'~.2OT3.C.P.323.K3 - Prtnted tn Great B7rtam.

CENTRE HOLE

OMITTED. (&EQUAL SPACING.

T-- L

0.5” EQUAL SPACING

5.00” 1

, 1

-

-

-

r - 5o01’ I _-

1 5 T

+

;oo” ---

HOLES 0 472” DIA. \

FT”” EQUAL SPACING.

JMITTED

0.080 ” -

PLATES NOS l-5

- (80 HOLES, FOR HOLE

SIZES SEE TABLE I.)

/c\ 60’

1

1.044’ 7

PLATE N94a

- (2,600 HOLES.)

0 425” EQUAL SPACING.

500” PLATE N9 6

_ (92 HOLES.)

FIGI. DETAILS OF PERFORATED PLATES. -.’ F “‘\I 0 n.

12

co

IO

06

04

0.2

0

. 2600 HOLES

PLATES.

06-

o+

0*2-

20 40 60 80 NO OF HOLES 0

0 01 02 0.3 04 05 06 07 SF/S

FIG. 3. DRAG OF PLATE No.4. PARTLY

(SIZE 8, SP:&?!?Rk;E?iOLES AS FIGI.)

u/y 0 2c

0 I5

0 IO

00s

0

-Q- SOLID PLATE PLATE NO I.

4 PLATE N9 2 PLATE No 3

-y- PLATE N? 3.5 + PLATE N”4. --o-- PLATE N*4a

--P- PLATE No 5.

+- PLATE NO 6.

80 HOLES

92 HOLES.

0.20

vu0

F a

T NO HOLES,

0 IS --P- INNER 3 ROWS

-A- OUTER 2 ROWS

* ALL HOLES 01

0.10

OPEN.

OPEN.

‘EN.

0 05 I,0 I5 2.0 %(I%

0 PLATE No. 4. PARTLY PERFORATED.

FlG.4. (as b) R.M.S. VELOCITY FLUCTUATIONS. 18” BEHIND PLATES.

Q I I

-o- SOLID PLATE -x- PLATE N? I.

0 -B- PLATE NO 2

80 -+- PLATE N“3. HOLES.

, -+- PLATE No3 5 -a- PLATE No 4 1 --.-- PLATE N04a 2600 HOLf I

003 + PLATE N“5. 80 HOLES.

+ PLATE N“6. 32 HOLES.

0 Ci UNIFORMLY PERFORATED PLATES.

o-05

nF6-4

004

+ NO HOLES

* INNER 3 ROWS OPEN

-k- OUTER 2 ROWS OPEN.

0 0 005 0.01 005 01 05 I 7-L 5

PLATE No. 4. PARTLY PERFORATED.

FIG.5 (ale b) VELOCITY FLUCTUATION SPECTRA. 18” BEHIND PLATES y/&=0.8.

0 06

n:b05

n*O01 UNIFORM PERFORATIONS.

n PLATE N9 4, INNER 3 ROWS DRILLED.

PLATE N“4, OUTER

2 ROWS DRILLED.

PLATE N“4, OUTER

2 ROWS DRILLED.

06 08 ‘F s /

IO

FIG. 6. LOW- FREQUENCY BAND OF VELOCITY FLUCTUATIONS 18” BEHIND PLATES.

C.P. ($I!;, 323

A.R.C. TechnIcal Report

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C.P. No. 323